Research ArticleLocating High-Impedance Fault Section in ElectricPower Systems Using Wavelet Transform 119896-MeansGenetic Algorithms and Support Vector Machine
Ying-Yi Hong and Wei-Shun Huang
Department of Electrical Engineering Chung Yuan Christian University 200 Chung Pei Road Chung Li 320 Taiwan
Correspondence should be addressed to Ying-Yi Hong yyh10632yahoocomtw
Received 22 July 2014 Accepted 14 November 2014
Academic Editor Vishal Bhatnaga
Copyright copy 2015 Y-Y Hong and W-S HuangThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
High-impedance faults (HIFs) caused by downed conductors in electric power systems are in general difficult to be detected usingtraditional protection relays due to small fault currents The energized downed conductor can pose a safety risk to the public andcause a fire hazard This paper presents a new method for locating the line (feeder) section of the HIF with the help of limitedmeasurements in electric power systemsThe discrete wavelet transform is used to extract the features of transients caused by HIFsA modified 119896-means algorithm associated with genetic algorithms is then utilized to determine the placement of measurementfacilitiesThe signal energies attained by wavelet coefficients serve as inputs to the support vector machine for locating the HIF linesection The simulation results obtained from an 18-busbar distribution system show the applicability of the proposed method
1 Introduction
High-impedance faults (HIFs) in general occur in electricdistribution systems HIFs occur when a conductor contactsa tree with a high-impedance or when a broken conductortouches the ground These faults may impose fire risks andcause electric shock that endangers lives of personnel There-fore HIF detection is essential to ensure safety Howeverdetection of HIFs using traditional protection devices (egovercurrent and distance relay) is difficult because the result-ing level of fault current is usually smaller than the nominalcurrent
Lien et al proposed a method for detecting HIFs usingthree-phase energy variance for the second fourth andsixth harmonics of unbalanced current Then counters aredesigned to detect HIF arcing through statistical confidence[1] Emanuel et al proposed that 120Hz and 180Hz com-ponents may be employed to detect HIFs The field testwas supported by a simple theoretical model and laboratorymeasurement [2] Kim et al usedwavelet transform to extractHIF features for developing anHIF indicator [3] Sedighi et alpresented a statistical pattern recognition namely principal
component analysis and Bayes classifier for detecting HIFand discriminating it from other disturbances [4] Lai et alused the nearest neighbor rule approach to classify HIF andlow-impedance fault (LIF) with the help of wavelet transformand voltagecurrent rms values [5] Michalik et al employeda phase displacement relation between wavelet coefficients ofzero sequence voltages and currents to detect HIFs [6] Shengand Rovnyak used rms current harmonic magnitudes andphases in a decision tree for detecting HIFs [7]
On the other hand the wavelet transform (WT) has beenwidely used for analyzing transient signals because of itsvaried window function for the time domain The featuresof signalsfunctions can be easily extracteddecomposed viamultiresolution analysis (MRA) [8] There are many papersusing discretewavelet transform (DWT) to detect and classifyPQ events [9ndash12] Furthermore artificial neural networks(ANNs) can be employed to map the input and outputnonlinear relationship The support vector machine (SVM)which is one of the ANNs has recently been proposed fornonlinear regression and classification Dash et al used threeSVMs for training to achieve fault classification grounddetection and section identification respectively for the line
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 823720 9 pageshttpdxdoiorg1011552015823720
2 Mathematical Problems in Engineering
using thyristor-controlled compensated compensators [13]Srinivasan et al employed SVMs with linear and polynomialkernels developed for signature extraction and device identi-fication [14] Janik and Lobos used space phasor for featureextraction from three-phase signals to build distinguishedpatterns for SVM classifiers [15] Other applications usingSVM are for example load forecasting [16] and transientstability analysis [17]
In previous methods ldquodetectionrdquo means identification ofan HIF in a feeder (or transmission line) [1ndash4] or in oneof the multiple feeders (or transmission lines) [5ndash7] fromthe secondary side of a transformer at a substation Locatinga line (feeder) section where an HIF occurs has not beenaddressed in these papers Moreover different features forexample even harmonics [1] low harmonics [2 7] waveletcoefficients [3ndash5] voltagecurrent rms values [5] and phasedisplacement [6] were considered for detection There wasno salient result showing which features were better
In this paper locating the HIF line (feeder) sectioninstead of detecting HIFs is addressed in a distributionsystem Placement ofmultiplemeasurement facilities is deter-mined first by a modified 119896-means algorithm associated withgenetic algorithms The discrete wavelet transform (DWT)is then used to extract features from these measurementlocations for classification Finally the SVM is utilized tolocate an exact HIF line section
In Section 2 the problem description and assumptionsare provided The proposed method for locating the HIFsection is given in Section 3 Simulation results obtained froman 18-busbar distribution system with HIFs are discussed inSection 4 Concluding remarks are given in Section 5
2 Problem Description and Assumptions
Power engineers in general deal with the power eventaccording to the following steps (i) localization (ii) classi-fication (iii) locating and (iv) remedial action These canbe achieved with the help of the power supply monitoringsystem When the monitored signals (voltage and current)are measured the important features can be extracted usingdigital signal processing techniques The monitoring systemwill assimilate the information including the features intouseful knowledgeinformation through soft computing andmachine learning for engineers to develop control strategyand to achieve decision-making
In the last paragraph ldquolocalizationrdquo means to identifythe time for HIFs to occur ldquoClassificationrdquo indicates thatHIFs should be discriminated from other disturbances forexample load switching and low-impedance (short circuit)fault ldquoLocatingrdquo implies that an exact HIF line section shouldbe identified The second and third tasks will be emphasizedin this paper After locating the HIF proper remedial actionswill be activated by power engineers
This paper deals with locating the HIF line section ina distribution system with multiple feeders using a powersupply monitoring system including multiple measurementfacilities at different lines Locating a line (feeder) section
where an HIF occurs has not been addressed in the previouspapersThere are several assumptions in this paper as follows
(i) The number of measurement facilities is given Inthis paper it is assumed that the supplier (utility) hasa monitoring system including some measurementfacilities that can be placed at different locations forrecording
(ii) Locating single HIF is considered The data-windowsize of the signal for processing in this paper is fivecycles Simultaneous HIFs at different lines hardlyoccur
(iii) Configuration of the studied distribution system isfixed If the system topology is changed the proposedneural network requires retrainingHowever possiblesystem configurations are generally known to engi-neers and the corresponding neural networks shouldbe trained in advance
(iv) The HIF generally occurs at a single phase of a linesection The proposed method employed MATLABSIMULINK SimPowerSystems and all the three-phasetransient voltagescurrents at each busbarline in thesystem are obtained
3 The Proposed Method
The presented method includes three stages (i) determin-ing measurement sites (ii) discriminating HIFs from otherdisturbances and (iii) locating the HIF The measurementsites are first determined by modified 119896-means algorithmassociated with genetic algorithms The proposed methodthen uses the wavelet coefficients of the currents (obtainedby the measurements) as the features for classification ofdisturbances and the inputs of the SVM for locating the HIF
31 Determination of Measurement Sites In general thenumber of power supplymonitoring facilities ismuch smallerthan the regular power voltage and current meters that areinstalled at all busbars and lines Hence a modified 119896-meansalgorithm is used to partition the system into 119862 clusters(119862 is the number of power supply measurement facilities)119862 measurement facilities are placed at the lines near thepseudocenters of the 119862 clusters This subsection describesthe modified 119896-means algorithm for partitioning the systemfor placement of the power supply measurement facilitiesMoreover the proposed modified 119896-means algorithm isenhanced from 119896-means [18 19] and fuzzy-119888-means (FCM)[20 21] as follows
Let 119869(119880 119881) be an objective
119869 (119880 119881) =
119873
sum
119894=1
119862
sum
119888=1
(119880119888119894) times1003817100381710038171003817119883119894 minus 119881119888
10038171003817100381710038172 (1)
where 119862 is the number of clusters119873 represents the numberof data (line section) 119881
119888signifies the vector of the center in
the 119888th clustering 119883119894is the 119894th (known) data vector for clus-
tering119880119888119894denotes the characteristic value (0 or 1) as a weight-
ing factor between 119881119888and 119883
119894 If the minimum of 119869(119880 119881) is
Mathematical Problems in Engineering 3
gained the 119873 sets of vectors are partitioned into 119862 clustersand 119881
119888is formulated by
119881119888=sum119873
119894=1119880119888119894times 119883119894
sum119873
119894=1119880119888119894
1 le 119888 le 119862 1 le 119894 le 119873 (2)
Matrix of the characteristic values can be defined as follows
For the 119894th column in the matrix 119880 the sum of all elementsequals one and only one element in this column is unity Thetraditional 119896-means algorithm did not consider (1) which isimplemented in this proposed enhanced 119896-means algorithm
The unknown variables in the problem of placement ofmeasurement facilities are 119880
119888119894 119888 = 1 119862 and 119894 = 1 119873
Traditional optimization methods involving the gradientsof objective function cannot minimize (1) because of dis-continuity of the objective function The genetic algorithmwas adopted to minimize (1) herein because the geneticalgorithm can deal with binary variable 119880
119888119894efficiently [22]
The population size crossover rate and mutation rate inthe genetic algorithm were assigned with 100 09 and 001respectively
In this paper 119883119894represents one of the current vectors
(signal energies calculated by DWT) caused by an HIF at aline ℓ The dimension (1 times 3660 herein) of 119883
119894varies with
the number of studied cases Symbols 119862 and119873 (3660 in thispaper) are the numbers of measurement facilities and thescenarios with HIFs respectively Let 119871 be the number ofthe line sections Then 119871 119883
119894rsquos need to be partitioned into 119862
clusters The vector 119881119888(1 times 3660) consisting of the virtual
HIF currents serves as the center in the 119888th cluster All vec-tors of the HIF currents 119883
119894rsquos in the 119888th cluster geometrically
center at119881119888Therefore the criterion for placingmeasurement
facilities in the electric distribution system is as followsplace a measurement facility at line ℓ at which the totalEuclidean distance between119883
119894rsquos (HIFs occurring at line ℓ) and
119881119888is minimal in the 119888th cluster
32 Discrete Wavelet Transform (DWT) Fourier transform(FT) is a suitable approach for studying problems withsteady state responses Short-time Fourier transform (STFT)divides the full-time interval into a number of smallequal-time intervals which can be individually analyzed using FTAlthough the result obtained from STFT contains time andfrequency information the equal-time intervals are fixedThus STFT cannot be used to detect the transient signals Onthe other hand the discrete wavelet transform (DWT) hasbeen widely used for analyzing the transient signals due toits varied scale and wavelet functions [23ndash25]The features ofsignals can be easily extracted via themultiresolution analysis(MRA) DWT avoids the disadvantages of both FT and STFT
A signal can be represented as a sum of wavelet functions120593(119905) and scale functions 120601(119905) with coefficients at differenttime shifts and scales (frequencies) using DWT DWT canextract the features of transient signals by decomposing signalcomponents overlapping in both time and frequency [8]
According to DWT a time-varying function (signal) 119891(119905) isin1198712(119877) can be expressed as follows
119891 (119905) = sum
119896
1198880 (119896) 120601 (119905 minus 119896) +sum
119896
sum
119895=1
119889119895 (119896) 2
minus1198952120593 (2minus119895119905 minus 119896)
= sum
119896
1198881198950(119896) 2minus11989502120601 (2
minus1198950119905 minus 119896)
+sum
119896
sum
119895=1198950
119889119895 (119896) 2
minus1198952120593 (2minus119895119905 minus 119896)
(4)
where 1198880and 119889
119895represent the scaling (coarse) coefficient at
scale 0 and wavelet (detailed) coefficient at scale 119895 respec-tivelyThe symbol 119896 represents the translation coefficientThescales 119895 = 1 2 denote the different (high to low) frequencybands The variable 119895
119900is an integer The translated and scaled
(dilated) version of the wavelet 120593(2minus119895119905 minus 119896) used in themultiresolution analysis (MRA) constructs a time-frequencypicture of the signal
There are some other wavelets in the wavelet theory [8]Haar wavelets have compact support (a finite bounded set)but are discontinuous Shannonwavelets are very smooth butare not compactly supported and they decay at infinity veryslowly Compared with these wavelets Daubechies-4 belongsto a class of orthonormal basis-generating continuous andcompactly supported wavelets Daubechies-4 is adopted inthis paper to extract the features of the line currents at scales1 2 and 3 with a sampling rate of 128 pointscycle
33 Multiresolution Analysis (MRA) As shown in (4) 119891(119905)is constructed by 120601(119905) and decomposed by 120593(119905) at differentscales (resolution levels) 120593(119905) generates the detailed versionof 119891(119905) and 120601(119905) generates the coarse version of 119891(119905) It can beshown that [8]
119888119895+1 (119896) = sum
119898
ℎ (119898 minus 2119896) 119888119895 (119898) (5)
119889119895+1 (119896) = sum
119898
ℎ1 (119898 minus 2119896) 119888119895 (119898) (6)
where ℎ(119898 minus 2119896) and ℎ1(119898 minus 2119896) are the low-pass and high-
pass filters respectively [8] These two equations show thatthe scaling and wavelet coefficients at different scale levelscan be obtained by convolving the expansion coefficientsat scale 119895 by the time-reversed recursion coefficients ℎ(sdot)and ℎ
1(sdot) and then downsampling or decimating to give the
expansion coefficients at the next level of 119895 + 1 The termldquodownsamplingrdquo indicates that the number at lower scale 119895is double compared with that at higher scale 119895 + 1 due to thefilters ℎ(119898 minus 2119896) and ℎ
1(119898 minus 2119896) This process is called the
ldquoanalysis (decomposition)rdquo from the fine scale to the coarsescale The reverse process called synthesis (construction)from the coarse scale to the fine scale is omitted here Figure 1illustrates a three-scale MRA decomposition for a signalThesymbols ℎ ℎ
1 and ldquodarr2rdquo denote the low-pass filter high-pass
filter and ldquodownsamplingrdquo respectivelyThe small scales represent high-frequency ranges Only
the wavelet coefficient (119889119895) is regarded as a feature due to
4 Mathematical Problems in Engineering
Signalh1 darr2
h1 darr2
h1 darr2h darr2
h darr2
h darr2
d1
d2
d3
c3
Figure 1 A three-scale MRA decomposition for a signal
the high-frequency phenomena fromHIFsMore specificallyif the sampling rate from the measurement facility is 128pointscycle then scales 1 2 and 3 cover 384sim192 kHz 192sim096 kHz and 096sim048 kHz respectively Lower harmonicswere not considered for the SVM because they (with largevalues) do not provide significant discrimination amonglines
34 Parseval Theorem When the MRA is applied to a tran-sient signal a large amount of wavelet coefficients will beattained Although the wavelet coefficients are useful it isdifficult for SVM to trainvalidate that much informationMore specifically if sampling rate is 128 pointscycle andfive cycles are utilized the numbers of wavelet coefficients atscales 1 2 and 3 are 320 160 and 80 due to ldquodownsamplingrdquorespectively Implementing 560times119862 input neurons in an SVMbecomes impractical where119862 is the number of measurementfacilities defined in Section 31 A trade-off treatment usingParsevalrsquos theorem is presented in this paper
In this paper only sum119896sum119895=1|119889119895(119896)|2 in (7) is calculated
because the HIF belongs to transients This term is calledldquocurrent energyrdquo or simply ldquoenergyrdquo in this paper Applicationsof sum119896sum119895=1|119889119895(119896)|2 are as follows
(i) Determination of measurement facility placementsum119896sum119895=1|119889119895(119896)|2 is computed for each line section to
be an element of 119883119894for a given scenario described
in Section 31 The number of given scenarios is 3660which will be discussed in Section 41
(ii) Feature extraction of transient signals sum119896sum119895=1|119889119895(119896)|2
is separated into the first to third scales (1198891sim 1198893 119895 =
1 2 and 3) for an HIF current at each line sectionThese features will serve as inputs for SVM
35 Support Vector Machine (SVM) Traditional multilayerneural networks have some limitations (i) many inputs dueto need of diversity for inputs (ii) requirement of crucialfeatures for inputs (iii) trial and error for number of neuronsin the hidden layer and (iv)multimodalwithmany localmin-imums Avoiding the above demerits SVM is a supervisedartificial neural network designed for solving classificationproblems [26 27] In essence SVM maximizes the margin
between the training data and the decision boundary whichcan be formulated as a quadratic optimization problem Thesubset of patterns that are closest to the decision boundary iscalled the support vector
SVM maximizes the separating margin between twoclasses given by a set of 119875 data pairs (119909
119901 119888119901) where 119909
119901
and 119888119901denote the input vector and class 119901 = 1 2 119875
respectively For linear separable training pairs of two classesthe separating hyperplane ℎ(119909) is given by
ℎ (119909) = 119908119905119909 + 119887 = 0 (8)
where119908 and 119887 are the vectors of weighting factors and biasesrespectively If a nonlinear hyperplane120595(sdot) is considered then
The maximal separating margin can be attained by mini-mizing the following primal problem if two classes are notlinearly distributed [28]
min 1
2119908119905119908 + 119870
119875
sum
119901=1
120585119901 (10)
subject to 119888119901(119908119905120595 (119909119901) + 119887) ge 1 minus 120585
119901 119901 = 1 2 119875
(11)
where 120585119901is the so-called fulfilling variable The symbol 119870 is
a regularization parameter In order to search a proper 119870performance of the trained SVMneeds assessment as followsThe training data are divided into two sets One is used totrain the SVM while the other called the validation set isused for evaluating the SVM According to the performanceon the validation set a proper value of 119870 can be attained
Equations (10) and (11) can be transformed into theunconstrained Lagrangian
119871 (119908 119887 120585 120583) =1
2119908119905119908 + 119870
119875
sum
119901=1
120585119901
+
119875
sum
119901=1
120583119901[119888119901(119908119905120595 (119909119901) + 119887) minus 1 + 120585
119901]
(12)
where 120583119901
is the dual variable (Lagrange multiplier) forinequality constraint (11) Obviously the form of (11) is thesame as the output of a neuron if 120593(sdot) and 120585
119901are considered
the activating function of a neuron and nonnegative slackvariable respectively
4 Simulation Results
41 Simulation Data The applicability of the proposedmethodology is verified by simulation results in this sectionAn 18-busbar radial system with 17 line sections illustrated inFigure 2 serves as a sample system in this paper Its busbar andline data are provided in [29] To train the SVM the originalload level was varied within plusmn10 (61 conditions) and theHIFs occur at different angles within 0∘sim359∘ (4 conditions)
Mathematical Problems in Engineering 5
Line 4 Line 2Line 3Line 5Line 6 Line 1Line 7Line 8Line 9
Line 10 Line 11
Line 12
Line 13
Line 14
Line 15Line 16Line 17
Figure 2 One-line diagram for studied distribution system
and at 15 different line sections for obtaining a total of 3660(= 61 times 4 times 15) data 70 10 and 20 of these 3660 datawere used stochastically for training validating and testingthe proposed SVM respectivelyThe arc of HIF was modeledwith two antiparallel DC sources and diodes which wereconnected to a random resistor [2] The proposed methodswere implemented by MATLAB 70 (SimPowerSystems) ona C2D (Core 2 Due) 213 GHz computer (RAM 35G) Thedata-window size of the signal for processing in this paper isfive cycles
Because the power supply measurement facilities aremore expensive than general meters the number of measure-ment facilities is limited Discussion of purchasing the mea-surement facilities and determination of a proper number forthemeasurement facilities are beyond the scope of this paperHence 14 11 8 4 and 2 measurement facilities (ie 119862) areassumed to be available in this paper Table 1 illustrates theSVM information associated with measurements BecauseHIF energies of the first to third scales (119889
1sim 1198893) were consid-
ered the number of input neurons equals measurements (119862)multiplied by 3 These are cases 1sim5 Moreover the current atthe neural line of the main transformer is generally availableand can be utilized These are cases 6sim10 Finally four binarybits are sufficient for discriminating 15 line sections excludingprimary sides (line 1) and the main transformer (denoted byline 2) in this system
42 Feature Extraction by DWT As described in Sections 33and 34 the ldquoenergiesrdquo for HIF currents of the first to thirdscales at each line section are used as features for SVM inputsAssume that an HIF occurs (90∘) at line section 12 Figure 3shows the energy distribution of the neighborhood of linesection 12 (ie line sections 11 and 13) The energies for the
Table 1 SVM information associated with measurements
Facility number (119862) Input neurons Output neuronsCase 1 2 2 times 3 4Case 2 4 4 times 3 4Case 3 8 8 times 3 4Case 4 11 11 times 3 4Case 5 14 14 times 3 4Case 6 2 + 1 3 times 3 4Case 7 4 + 1 5 times 3 4Case 8 8 + 1 9 times 3 4Case 9 11 + 1 12 times 3 4Case 10 14 + 1 15 times 3 4
first to sixth scales at these three line sections are shown It isapparent that the normal energy and HIF energy are almostthe same for the current of the fourth (also for fifth and sixth)scale Hence current energies for the fourth to sixth scalescannot serve as features and only current energies for thefirst to third scales are considered further Please note thatthe energies are normalized to be per unit and are in termsof log
10because the energies of the fifth and sixth scales are
much larger than those of other scales
43 Scaled Energies at Line Sections AnHIF occurring at linesection 12 is discussed in this section Figure 4 illustrates theHIF currents in terms of the DWT-scaled energy distribu-tions at each line sectionThe vertical axis denotes the energymagnitude while the horizontal axis means the 119889
1sim 1198893at
each line section Please note that the energies are normalizedto be per unit
6 Mathematical Problems in Engineering
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(a) 1stndash6th normal and HIF energies at line section 11
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(b) 1stndash6th normal and HIF energies at line section 12
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(c) 1stndash6th normal and HIF energies at line section 13
Figure 3 Energy distributions near faulted line
0010203040506070809
1
Line 1 Line 2 Line 3 Line 4 Line 5 Line 6
1st scale2nd scale
3rd scale
Ener
gy (p
er u
nit)
0010203040506070809
1
Line 7 Line 8 Line 9 Line 10 Line 11 Line 12
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
0010203040506070809
1
Line 13 Line 14 Line 15 Line 16 Line 17
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
Figure 4 HIF energy distributions at all line sections
Mathematical Problems in Engineering 7
Table 2 Different 119862s and corresponding clusters (119896-means)
When the busbar load varies and the HIF occurs atdistinct angles the above phenomena will be discriminatedHence the ldquoenergiesrdquo of the HIF currents of the first to thirdscales are important features for locating theHIF line section
44 Measurement Facility Placement Because 14 11 8 4 and2 power supply measurement facilities are assumed to beavailable in the test sample 119862 may be 14 11 8 4 or 2 and119873 = 3660 respectively (119862 and119873were defined in Section 31)For a given 119862 the same 3660 sets of data were employed toperform the HIF current energy clustering by the modified119896-means algorithm Table 2 illustrates the different 119862rsquos andcorresponding clusters Each cluster is quoted by parenthesesThe line section with an italic font in Table 2 denotes the oneinstalled with ameasurement facility Traditional FCM is alsoemployed to study the line section clustering as shown inTable 3 As can be seen some clusters obtained by the FCMare infeasible because lines in a cluster may not be adjacentto each other For example in the last row of Table 3 linesections 7 8 and 9 in a cluster are not adjacent to line sections10sim17
More specifically the condition for 119862 = 2 and 119888 = 2 inthe last row of Table 2 is described here Table 4 illustratesthe distances (norm) between 119883
119894 119894 = 3 4 17 and its
clustering center 1198812(119888 = 2) for 119862 = 2 As can be seen the
distance between 11988312
and 1198812is the smallest Therefore the
measurement facility is placed at line section 12In this paper the dimension of119883
119894is 1 times 3660 where 3660
is the number of scenarios from the test system Each elementof 119883119894is the total energy at line section 119894 for one of the 3660
cases Moreover there are 17 119883119894rsquos (number of lines) for the
18-busbar system where 17 is the line number
0
10
20
30
40
50
60
()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Energy ranges
HIFLIF
CS
Figure 5 Total energy disturbances for 3 different disturbances
45 Classification among HIF Short Circuit and SwitchingThere are 930 cases with short circuits (low-impedance faultsLIFs) and 620 cases with capacitor switching (CS) for furtherinvestigation of energy distributions Figure 5 shows the totalenergy of the first to third scales for different HIFs LIFs andCS The vertical axis denotes the percentage of occurrencefor the three individual disturbances The horizontal axisincludes 15 energy ranges (log
10) More specifically ranges 1
2 and 15 represent 348ndash356 357ndash365 and 1009ndash1079 purespectively It can be found that HIFs include smaller totalenergies from range 1 to range 5 Hence the total energy canbe employed to discriminate HIFs from other disturbancesfor example LIF and CS
46 Accuracy of Locating HIFs by SVM As described inSection 41 70 10 and 20 of the 3660 data are usedstochastically for training validating and testing respec-tively Table 5 illustrates the number of iterations CPU timefor training the SVM and the accuracy rate for the 10 casesdefined in Table 1 The following comments can be drawnfrom Table 5
(i) The numbers of iterations for all cases are almost thesame for the SVM despite the different number ofinput neurons
(ii) The CPU time required varies with the number ofinput neurons
(iii) Accuracy rates are greater than 99 except for cases 1and 6
(iv) Cases 1 and 6 with only two measurement facilitiesstill gain accuracy rate of 974 and 9836 respec-tively This result ensures the advantage of the pro-posed method using the SVM
(v) The neutral current at the substation improves accu-racy rates only for cases 1 and 2 (corresponding tocases 6 and 7) with fewer measurements
8 Mathematical Problems in Engineering
Table 4 Distances (times105) between 119883119894and its clustering center
This paper proposed a new method for locating the linesection with an HIF using DWT modified 119896-means andSVM Compared with the existing methods involving iden-tification of an HIF in a feeder (or transmission line) or inone of the multiple feeders from the secondary side of asubstation the proposed approach is able to locate anHIF linesection in a distribution system with multiple feeders usinga power supply monitoring system including multiple powersupply measurement facilities at different lines Classificationof disturbances and locating the HIF are addressed
The features (current energies) at three distinct scales(frequency bands) were extracted by MRA in DWT Thesefeatures provide important information for the SVM to locatethe line sectionwith anHIFMoreover the energies ofHIF arediscriminated obviously from those of LIF and CS
The simulation results obtained from an 18-busbar distri-bution system show that good accuracy can still be attainedusing only a few measurements (eg two in this paper) dueto the SVM Hence SVM is very useful when only a fewmeasurements are available
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors gratefully acknowledge the financial supportfrom the National Science Council Taiwan under Grant no96-2221-E-033-069-MY2
References
[1] K Y Lien S L Chen C J Liao T Y Guo T M Lin and J SShen ldquoEnergy variance criterion and threshold tuning schemefor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 14 no 3 pp 810ndash817 1999
[2] A E Emanuel D Cyganski J A Orr S Shiller and E MGulachenski ldquoHigh impedance fault arcing on sandy soil in15kV distribution feeders contributions to the evaluation of thelow frequency spectrumrdquo IEEE Transactions on Power Deliveryvol 5 no 2 pp 676ndash686 1990
[3] C H Kim H Kim Y H Ko S H Byun R K Aggarwal and AT Johns ldquoA novel fault-detection technique of high-impedancearcing faults in transmission lines using the wavelet transformrdquoIEEE Transactions on Power Delivery vol 17 no 4 pp 921ndash9292002
[4] A-R Sedighi M-R Haghifam O P Malik and M-H Ghas-semian ldquoHigh impedance fault detection based on wavelettransform and statistical pattern recognitionrdquo IEEE Transac-tions on Power Delivery vol 20 no 4 pp 2414ndash2421 2005
[5] T M Lai L A Snider E Lo and D Sutanto ldquoHigh-impedancefault detection using discrete wavelet transform and frequencyrange and RMS conversionrdquo IEEE Transactions on PowerDelivery vol 20 no 1 pp 397ndash407 2005
[6] M Michalik W Rebizant M R Lukowicz S J Lee and SH Kang ldquoHigh-impedance fault detection in distribution net-works with use of wavelet-based algorithmrdquo IEEE Transactionson Power Delivery vol 21 no 4 pp 1793ndash1802 2006
[7] Y Sheng and SM Rovnyak ldquoDecision tree-basedmethodologyfor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 19 no 2 pp 533ndash536 2004
[8] C S Burrus R A Gopinath and H Guo Introduction toWavelets and Wavelet Transforms Prentice Hall Upper SaddleRiver NJ USA 1998
[9] A Elmitwally S Farghal S Abdelkader and M Elkateb ldquoPro-posed wavelet-neurofuzzy combined system for power qualityviolations detection and diagnosisrdquo IEE Proceedings Genera-tion Transmission and Distribution vol 148 no 1 pp 15ndash202001
[10] L Angrisani P Daponte M DrsquoApuzzo and A Testa ldquoA mea-surement method based on the wavelet transform for powerquality analysisrdquo IEEE Transactions on Power Delivery vol 13no 4 pp 990ndash998 1998
[11] S Santoso E J PowersWM Grady and A C Parsons ldquoPowerquality disturbance waveform recognition using wavelet-basedneural classifier Part 1 theoretical foundationrdquo IEEE Transac-tions on Power Delivery vol 15 no 1 pp 222ndash228 2000
[12] H Mokhtari M Karimi-Ghartemani and M R IravanildquoExperimental performance evaluation of a wavelet-based on-line voltage detection method for power quality applicationsrdquoIEEE Transactions on Power Delivery vol 17 no 1 pp 161ndash1722002
[13] P K Dash S R Samantaray and G Panda ldquoFault classificationand section identification of an advanced series-compensatedtransmission line using support vector machinerdquo IEEE Trans-actions on Power Delivery vol 22 no 1 pp 67ndash73 2007
[14] D SrinivasanW S Ng and A C Liew ldquoNeural-network-basedsignature recognition for harmonic source identificationrdquo IEEETransactions on Power Delivery vol 21 no 1 pp 398ndash405 2006
Mathematical Problems in Engineering 9
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
using thyristor-controlled compensated compensators [13]Srinivasan et al employed SVMs with linear and polynomialkernels developed for signature extraction and device identi-fication [14] Janik and Lobos used space phasor for featureextraction from three-phase signals to build distinguishedpatterns for SVM classifiers [15] Other applications usingSVM are for example load forecasting [16] and transientstability analysis [17]
In previous methods ldquodetectionrdquo means identification ofan HIF in a feeder (or transmission line) [1ndash4] or in oneof the multiple feeders (or transmission lines) [5ndash7] fromthe secondary side of a transformer at a substation Locatinga line (feeder) section where an HIF occurs has not beenaddressed in these papers Moreover different features forexample even harmonics [1] low harmonics [2 7] waveletcoefficients [3ndash5] voltagecurrent rms values [5] and phasedisplacement [6] were considered for detection There wasno salient result showing which features were better
In this paper locating the HIF line (feeder) sectioninstead of detecting HIFs is addressed in a distributionsystem Placement ofmultiplemeasurement facilities is deter-mined first by a modified 119896-means algorithm associated withgenetic algorithms The discrete wavelet transform (DWT)is then used to extract features from these measurementlocations for classification Finally the SVM is utilized tolocate an exact HIF line section
In Section 2 the problem description and assumptionsare provided The proposed method for locating the HIFsection is given in Section 3 Simulation results obtained froman 18-busbar distribution system with HIFs are discussed inSection 4 Concluding remarks are given in Section 5
2 Problem Description and Assumptions
Power engineers in general deal with the power eventaccording to the following steps (i) localization (ii) classi-fication (iii) locating and (iv) remedial action These canbe achieved with the help of the power supply monitoringsystem When the monitored signals (voltage and current)are measured the important features can be extracted usingdigital signal processing techniques The monitoring systemwill assimilate the information including the features intouseful knowledgeinformation through soft computing andmachine learning for engineers to develop control strategyand to achieve decision-making
In the last paragraph ldquolocalizationrdquo means to identifythe time for HIFs to occur ldquoClassificationrdquo indicates thatHIFs should be discriminated from other disturbances forexample load switching and low-impedance (short circuit)fault ldquoLocatingrdquo implies that an exact HIF line section shouldbe identified The second and third tasks will be emphasizedin this paper After locating the HIF proper remedial actionswill be activated by power engineers
This paper deals with locating the HIF line section ina distribution system with multiple feeders using a powersupply monitoring system including multiple measurementfacilities at different lines Locating a line (feeder) section
where an HIF occurs has not been addressed in the previouspapersThere are several assumptions in this paper as follows
(i) The number of measurement facilities is given Inthis paper it is assumed that the supplier (utility) hasa monitoring system including some measurementfacilities that can be placed at different locations forrecording
(ii) Locating single HIF is considered The data-windowsize of the signal for processing in this paper is fivecycles Simultaneous HIFs at different lines hardlyoccur
(iii) Configuration of the studied distribution system isfixed If the system topology is changed the proposedneural network requires retrainingHowever possiblesystem configurations are generally known to engi-neers and the corresponding neural networks shouldbe trained in advance
(iv) The HIF generally occurs at a single phase of a linesection The proposed method employed MATLABSIMULINK SimPowerSystems and all the three-phasetransient voltagescurrents at each busbarline in thesystem are obtained
3 The Proposed Method
The presented method includes three stages (i) determin-ing measurement sites (ii) discriminating HIFs from otherdisturbances and (iii) locating the HIF The measurementsites are first determined by modified 119896-means algorithmassociated with genetic algorithms The proposed methodthen uses the wavelet coefficients of the currents (obtainedby the measurements) as the features for classification ofdisturbances and the inputs of the SVM for locating the HIF
31 Determination of Measurement Sites In general thenumber of power supplymonitoring facilities ismuch smallerthan the regular power voltage and current meters that areinstalled at all busbars and lines Hence a modified 119896-meansalgorithm is used to partition the system into 119862 clusters(119862 is the number of power supply measurement facilities)119862 measurement facilities are placed at the lines near thepseudocenters of the 119862 clusters This subsection describesthe modified 119896-means algorithm for partitioning the systemfor placement of the power supply measurement facilitiesMoreover the proposed modified 119896-means algorithm isenhanced from 119896-means [18 19] and fuzzy-119888-means (FCM)[20 21] as follows
Let 119869(119880 119881) be an objective
119869 (119880 119881) =
119873
sum
119894=1
119862
sum
119888=1
(119880119888119894) times1003817100381710038171003817119883119894 minus 119881119888
10038171003817100381710038172 (1)
where 119862 is the number of clusters119873 represents the numberof data (line section) 119881
119888signifies the vector of the center in
the 119888th clustering 119883119894is the 119894th (known) data vector for clus-
tering119880119888119894denotes the characteristic value (0 or 1) as a weight-
ing factor between 119881119888and 119883
119894 If the minimum of 119869(119880 119881) is
Mathematical Problems in Engineering 3
gained the 119873 sets of vectors are partitioned into 119862 clustersand 119881
119888is formulated by
119881119888=sum119873
119894=1119880119888119894times 119883119894
sum119873
119894=1119880119888119894
1 le 119888 le 119862 1 le 119894 le 119873 (2)
Matrix of the characteristic values can be defined as follows
For the 119894th column in the matrix 119880 the sum of all elementsequals one and only one element in this column is unity Thetraditional 119896-means algorithm did not consider (1) which isimplemented in this proposed enhanced 119896-means algorithm
The unknown variables in the problem of placement ofmeasurement facilities are 119880
119888119894 119888 = 1 119862 and 119894 = 1 119873
Traditional optimization methods involving the gradientsof objective function cannot minimize (1) because of dis-continuity of the objective function The genetic algorithmwas adopted to minimize (1) herein because the geneticalgorithm can deal with binary variable 119880
119888119894efficiently [22]
The population size crossover rate and mutation rate inthe genetic algorithm were assigned with 100 09 and 001respectively
In this paper 119883119894represents one of the current vectors
(signal energies calculated by DWT) caused by an HIF at aline ℓ The dimension (1 times 3660 herein) of 119883
119894varies with
the number of studied cases Symbols 119862 and119873 (3660 in thispaper) are the numbers of measurement facilities and thescenarios with HIFs respectively Let 119871 be the number ofthe line sections Then 119871 119883
119894rsquos need to be partitioned into 119862
clusters The vector 119881119888(1 times 3660) consisting of the virtual
HIF currents serves as the center in the 119888th cluster All vec-tors of the HIF currents 119883
119894rsquos in the 119888th cluster geometrically
center at119881119888Therefore the criterion for placingmeasurement
facilities in the electric distribution system is as followsplace a measurement facility at line ℓ at which the totalEuclidean distance between119883
119894rsquos (HIFs occurring at line ℓ) and
119881119888is minimal in the 119888th cluster
32 Discrete Wavelet Transform (DWT) Fourier transform(FT) is a suitable approach for studying problems withsteady state responses Short-time Fourier transform (STFT)divides the full-time interval into a number of smallequal-time intervals which can be individually analyzed using FTAlthough the result obtained from STFT contains time andfrequency information the equal-time intervals are fixedThus STFT cannot be used to detect the transient signals Onthe other hand the discrete wavelet transform (DWT) hasbeen widely used for analyzing the transient signals due toits varied scale and wavelet functions [23ndash25]The features ofsignals can be easily extracted via themultiresolution analysis(MRA) DWT avoids the disadvantages of both FT and STFT
A signal can be represented as a sum of wavelet functions120593(119905) and scale functions 120601(119905) with coefficients at differenttime shifts and scales (frequencies) using DWT DWT canextract the features of transient signals by decomposing signalcomponents overlapping in both time and frequency [8]
According to DWT a time-varying function (signal) 119891(119905) isin1198712(119877) can be expressed as follows
119891 (119905) = sum
119896
1198880 (119896) 120601 (119905 minus 119896) +sum
119896
sum
119895=1
119889119895 (119896) 2
minus1198952120593 (2minus119895119905 minus 119896)
= sum
119896
1198881198950(119896) 2minus11989502120601 (2
minus1198950119905 minus 119896)
+sum
119896
sum
119895=1198950
119889119895 (119896) 2
minus1198952120593 (2minus119895119905 minus 119896)
(4)
where 1198880and 119889
119895represent the scaling (coarse) coefficient at
scale 0 and wavelet (detailed) coefficient at scale 119895 respec-tivelyThe symbol 119896 represents the translation coefficientThescales 119895 = 1 2 denote the different (high to low) frequencybands The variable 119895
119900is an integer The translated and scaled
(dilated) version of the wavelet 120593(2minus119895119905 minus 119896) used in themultiresolution analysis (MRA) constructs a time-frequencypicture of the signal
There are some other wavelets in the wavelet theory [8]Haar wavelets have compact support (a finite bounded set)but are discontinuous Shannonwavelets are very smooth butare not compactly supported and they decay at infinity veryslowly Compared with these wavelets Daubechies-4 belongsto a class of orthonormal basis-generating continuous andcompactly supported wavelets Daubechies-4 is adopted inthis paper to extract the features of the line currents at scales1 2 and 3 with a sampling rate of 128 pointscycle
33 Multiresolution Analysis (MRA) As shown in (4) 119891(119905)is constructed by 120601(119905) and decomposed by 120593(119905) at differentscales (resolution levels) 120593(119905) generates the detailed versionof 119891(119905) and 120601(119905) generates the coarse version of 119891(119905) It can beshown that [8]
119888119895+1 (119896) = sum
119898
ℎ (119898 minus 2119896) 119888119895 (119898) (5)
119889119895+1 (119896) = sum
119898
ℎ1 (119898 minus 2119896) 119888119895 (119898) (6)
where ℎ(119898 minus 2119896) and ℎ1(119898 minus 2119896) are the low-pass and high-
pass filters respectively [8] These two equations show thatthe scaling and wavelet coefficients at different scale levelscan be obtained by convolving the expansion coefficientsat scale 119895 by the time-reversed recursion coefficients ℎ(sdot)and ℎ
1(sdot) and then downsampling or decimating to give the
expansion coefficients at the next level of 119895 + 1 The termldquodownsamplingrdquo indicates that the number at lower scale 119895is double compared with that at higher scale 119895 + 1 due to thefilters ℎ(119898 minus 2119896) and ℎ
1(119898 minus 2119896) This process is called the
ldquoanalysis (decomposition)rdquo from the fine scale to the coarsescale The reverse process called synthesis (construction)from the coarse scale to the fine scale is omitted here Figure 1illustrates a three-scale MRA decomposition for a signalThesymbols ℎ ℎ
1 and ldquodarr2rdquo denote the low-pass filter high-pass
filter and ldquodownsamplingrdquo respectivelyThe small scales represent high-frequency ranges Only
the wavelet coefficient (119889119895) is regarded as a feature due to
4 Mathematical Problems in Engineering
Signalh1 darr2
h1 darr2
h1 darr2h darr2
h darr2
h darr2
d1
d2
d3
c3
Figure 1 A three-scale MRA decomposition for a signal
the high-frequency phenomena fromHIFsMore specificallyif the sampling rate from the measurement facility is 128pointscycle then scales 1 2 and 3 cover 384sim192 kHz 192sim096 kHz and 096sim048 kHz respectively Lower harmonicswere not considered for the SVM because they (with largevalues) do not provide significant discrimination amonglines
34 Parseval Theorem When the MRA is applied to a tran-sient signal a large amount of wavelet coefficients will beattained Although the wavelet coefficients are useful it isdifficult for SVM to trainvalidate that much informationMore specifically if sampling rate is 128 pointscycle andfive cycles are utilized the numbers of wavelet coefficients atscales 1 2 and 3 are 320 160 and 80 due to ldquodownsamplingrdquorespectively Implementing 560times119862 input neurons in an SVMbecomes impractical where119862 is the number of measurementfacilities defined in Section 31 A trade-off treatment usingParsevalrsquos theorem is presented in this paper
In this paper only sum119896sum119895=1|119889119895(119896)|2 in (7) is calculated
because the HIF belongs to transients This term is calledldquocurrent energyrdquo or simply ldquoenergyrdquo in this paper Applicationsof sum119896sum119895=1|119889119895(119896)|2 are as follows
(i) Determination of measurement facility placementsum119896sum119895=1|119889119895(119896)|2 is computed for each line section to
be an element of 119883119894for a given scenario described
in Section 31 The number of given scenarios is 3660which will be discussed in Section 41
(ii) Feature extraction of transient signals sum119896sum119895=1|119889119895(119896)|2
is separated into the first to third scales (1198891sim 1198893 119895 =
1 2 and 3) for an HIF current at each line sectionThese features will serve as inputs for SVM
35 Support Vector Machine (SVM) Traditional multilayerneural networks have some limitations (i) many inputs dueto need of diversity for inputs (ii) requirement of crucialfeatures for inputs (iii) trial and error for number of neuronsin the hidden layer and (iv)multimodalwithmany localmin-imums Avoiding the above demerits SVM is a supervisedartificial neural network designed for solving classificationproblems [26 27] In essence SVM maximizes the margin
between the training data and the decision boundary whichcan be formulated as a quadratic optimization problem Thesubset of patterns that are closest to the decision boundary iscalled the support vector
SVM maximizes the separating margin between twoclasses given by a set of 119875 data pairs (119909
119901 119888119901) where 119909
119901
and 119888119901denote the input vector and class 119901 = 1 2 119875
respectively For linear separable training pairs of two classesthe separating hyperplane ℎ(119909) is given by
ℎ (119909) = 119908119905119909 + 119887 = 0 (8)
where119908 and 119887 are the vectors of weighting factors and biasesrespectively If a nonlinear hyperplane120595(sdot) is considered then
The maximal separating margin can be attained by mini-mizing the following primal problem if two classes are notlinearly distributed [28]
min 1
2119908119905119908 + 119870
119875
sum
119901=1
120585119901 (10)
subject to 119888119901(119908119905120595 (119909119901) + 119887) ge 1 minus 120585
119901 119901 = 1 2 119875
(11)
where 120585119901is the so-called fulfilling variable The symbol 119870 is
a regularization parameter In order to search a proper 119870performance of the trained SVMneeds assessment as followsThe training data are divided into two sets One is used totrain the SVM while the other called the validation set isused for evaluating the SVM According to the performanceon the validation set a proper value of 119870 can be attained
Equations (10) and (11) can be transformed into theunconstrained Lagrangian
119871 (119908 119887 120585 120583) =1
2119908119905119908 + 119870
119875
sum
119901=1
120585119901
+
119875
sum
119901=1
120583119901[119888119901(119908119905120595 (119909119901) + 119887) minus 1 + 120585
119901]
(12)
where 120583119901
is the dual variable (Lagrange multiplier) forinequality constraint (11) Obviously the form of (11) is thesame as the output of a neuron if 120593(sdot) and 120585
119901are considered
the activating function of a neuron and nonnegative slackvariable respectively
4 Simulation Results
41 Simulation Data The applicability of the proposedmethodology is verified by simulation results in this sectionAn 18-busbar radial system with 17 line sections illustrated inFigure 2 serves as a sample system in this paper Its busbar andline data are provided in [29] To train the SVM the originalload level was varied within plusmn10 (61 conditions) and theHIFs occur at different angles within 0∘sim359∘ (4 conditions)
Mathematical Problems in Engineering 5
Line 4 Line 2Line 3Line 5Line 6 Line 1Line 7Line 8Line 9
Line 10 Line 11
Line 12
Line 13
Line 14
Line 15Line 16Line 17
Figure 2 One-line diagram for studied distribution system
and at 15 different line sections for obtaining a total of 3660(= 61 times 4 times 15) data 70 10 and 20 of these 3660 datawere used stochastically for training validating and testingthe proposed SVM respectivelyThe arc of HIF was modeledwith two antiparallel DC sources and diodes which wereconnected to a random resistor [2] The proposed methodswere implemented by MATLAB 70 (SimPowerSystems) ona C2D (Core 2 Due) 213 GHz computer (RAM 35G) Thedata-window size of the signal for processing in this paper isfive cycles
Because the power supply measurement facilities aremore expensive than general meters the number of measure-ment facilities is limited Discussion of purchasing the mea-surement facilities and determination of a proper number forthemeasurement facilities are beyond the scope of this paperHence 14 11 8 4 and 2 measurement facilities (ie 119862) areassumed to be available in this paper Table 1 illustrates theSVM information associated with measurements BecauseHIF energies of the first to third scales (119889
1sim 1198893) were consid-
ered the number of input neurons equals measurements (119862)multiplied by 3 These are cases 1sim5 Moreover the current atthe neural line of the main transformer is generally availableand can be utilized These are cases 6sim10 Finally four binarybits are sufficient for discriminating 15 line sections excludingprimary sides (line 1) and the main transformer (denoted byline 2) in this system
42 Feature Extraction by DWT As described in Sections 33and 34 the ldquoenergiesrdquo for HIF currents of the first to thirdscales at each line section are used as features for SVM inputsAssume that an HIF occurs (90∘) at line section 12 Figure 3shows the energy distribution of the neighborhood of linesection 12 (ie line sections 11 and 13) The energies for the
Table 1 SVM information associated with measurements
Facility number (119862) Input neurons Output neuronsCase 1 2 2 times 3 4Case 2 4 4 times 3 4Case 3 8 8 times 3 4Case 4 11 11 times 3 4Case 5 14 14 times 3 4Case 6 2 + 1 3 times 3 4Case 7 4 + 1 5 times 3 4Case 8 8 + 1 9 times 3 4Case 9 11 + 1 12 times 3 4Case 10 14 + 1 15 times 3 4
first to sixth scales at these three line sections are shown It isapparent that the normal energy and HIF energy are almostthe same for the current of the fourth (also for fifth and sixth)scale Hence current energies for the fourth to sixth scalescannot serve as features and only current energies for thefirst to third scales are considered further Please note thatthe energies are normalized to be per unit and are in termsof log
10because the energies of the fifth and sixth scales are
much larger than those of other scales
43 Scaled Energies at Line Sections AnHIF occurring at linesection 12 is discussed in this section Figure 4 illustrates theHIF currents in terms of the DWT-scaled energy distribu-tions at each line sectionThe vertical axis denotes the energymagnitude while the horizontal axis means the 119889
1sim 1198893at
each line section Please note that the energies are normalizedto be per unit
6 Mathematical Problems in Engineering
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(a) 1stndash6th normal and HIF energies at line section 11
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(b) 1stndash6th normal and HIF energies at line section 12
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(c) 1stndash6th normal and HIF energies at line section 13
Figure 3 Energy distributions near faulted line
0010203040506070809
1
Line 1 Line 2 Line 3 Line 4 Line 5 Line 6
1st scale2nd scale
3rd scale
Ener
gy (p
er u
nit)
0010203040506070809
1
Line 7 Line 8 Line 9 Line 10 Line 11 Line 12
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
0010203040506070809
1
Line 13 Line 14 Line 15 Line 16 Line 17
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
Figure 4 HIF energy distributions at all line sections
Mathematical Problems in Engineering 7
Table 2 Different 119862s and corresponding clusters (119896-means)
When the busbar load varies and the HIF occurs atdistinct angles the above phenomena will be discriminatedHence the ldquoenergiesrdquo of the HIF currents of the first to thirdscales are important features for locating theHIF line section
44 Measurement Facility Placement Because 14 11 8 4 and2 power supply measurement facilities are assumed to beavailable in the test sample 119862 may be 14 11 8 4 or 2 and119873 = 3660 respectively (119862 and119873were defined in Section 31)For a given 119862 the same 3660 sets of data were employed toperform the HIF current energy clustering by the modified119896-means algorithm Table 2 illustrates the different 119862rsquos andcorresponding clusters Each cluster is quoted by parenthesesThe line section with an italic font in Table 2 denotes the oneinstalled with ameasurement facility Traditional FCM is alsoemployed to study the line section clustering as shown inTable 3 As can be seen some clusters obtained by the FCMare infeasible because lines in a cluster may not be adjacentto each other For example in the last row of Table 3 linesections 7 8 and 9 in a cluster are not adjacent to line sections10sim17
More specifically the condition for 119862 = 2 and 119888 = 2 inthe last row of Table 2 is described here Table 4 illustratesthe distances (norm) between 119883
119894 119894 = 3 4 17 and its
clustering center 1198812(119888 = 2) for 119862 = 2 As can be seen the
distance between 11988312
and 1198812is the smallest Therefore the
measurement facility is placed at line section 12In this paper the dimension of119883
119894is 1 times 3660 where 3660
is the number of scenarios from the test system Each elementof 119883119894is the total energy at line section 119894 for one of the 3660
cases Moreover there are 17 119883119894rsquos (number of lines) for the
18-busbar system where 17 is the line number
0
10
20
30
40
50
60
()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Energy ranges
HIFLIF
CS
Figure 5 Total energy disturbances for 3 different disturbances
45 Classification among HIF Short Circuit and SwitchingThere are 930 cases with short circuits (low-impedance faultsLIFs) and 620 cases with capacitor switching (CS) for furtherinvestigation of energy distributions Figure 5 shows the totalenergy of the first to third scales for different HIFs LIFs andCS The vertical axis denotes the percentage of occurrencefor the three individual disturbances The horizontal axisincludes 15 energy ranges (log
10) More specifically ranges 1
2 and 15 represent 348ndash356 357ndash365 and 1009ndash1079 purespectively It can be found that HIFs include smaller totalenergies from range 1 to range 5 Hence the total energy canbe employed to discriminate HIFs from other disturbancesfor example LIF and CS
46 Accuracy of Locating HIFs by SVM As described inSection 41 70 10 and 20 of the 3660 data are usedstochastically for training validating and testing respec-tively Table 5 illustrates the number of iterations CPU timefor training the SVM and the accuracy rate for the 10 casesdefined in Table 1 The following comments can be drawnfrom Table 5
(i) The numbers of iterations for all cases are almost thesame for the SVM despite the different number ofinput neurons
(ii) The CPU time required varies with the number ofinput neurons
(iii) Accuracy rates are greater than 99 except for cases 1and 6
(iv) Cases 1 and 6 with only two measurement facilitiesstill gain accuracy rate of 974 and 9836 respec-tively This result ensures the advantage of the pro-posed method using the SVM
(v) The neutral current at the substation improves accu-racy rates only for cases 1 and 2 (corresponding tocases 6 and 7) with fewer measurements
8 Mathematical Problems in Engineering
Table 4 Distances (times105) between 119883119894and its clustering center
This paper proposed a new method for locating the linesection with an HIF using DWT modified 119896-means andSVM Compared with the existing methods involving iden-tification of an HIF in a feeder (or transmission line) or inone of the multiple feeders from the secondary side of asubstation the proposed approach is able to locate anHIF linesection in a distribution system with multiple feeders usinga power supply monitoring system including multiple powersupply measurement facilities at different lines Classificationof disturbances and locating the HIF are addressed
The features (current energies) at three distinct scales(frequency bands) were extracted by MRA in DWT Thesefeatures provide important information for the SVM to locatethe line sectionwith anHIFMoreover the energies ofHIF arediscriminated obviously from those of LIF and CS
The simulation results obtained from an 18-busbar distri-bution system show that good accuracy can still be attainedusing only a few measurements (eg two in this paper) dueto the SVM Hence SVM is very useful when only a fewmeasurements are available
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors gratefully acknowledge the financial supportfrom the National Science Council Taiwan under Grant no96-2221-E-033-069-MY2
References
[1] K Y Lien S L Chen C J Liao T Y Guo T M Lin and J SShen ldquoEnergy variance criterion and threshold tuning schemefor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 14 no 3 pp 810ndash817 1999
[2] A E Emanuel D Cyganski J A Orr S Shiller and E MGulachenski ldquoHigh impedance fault arcing on sandy soil in15kV distribution feeders contributions to the evaluation of thelow frequency spectrumrdquo IEEE Transactions on Power Deliveryvol 5 no 2 pp 676ndash686 1990
[3] C H Kim H Kim Y H Ko S H Byun R K Aggarwal and AT Johns ldquoA novel fault-detection technique of high-impedancearcing faults in transmission lines using the wavelet transformrdquoIEEE Transactions on Power Delivery vol 17 no 4 pp 921ndash9292002
[4] A-R Sedighi M-R Haghifam O P Malik and M-H Ghas-semian ldquoHigh impedance fault detection based on wavelettransform and statistical pattern recognitionrdquo IEEE Transac-tions on Power Delivery vol 20 no 4 pp 2414ndash2421 2005
[5] T M Lai L A Snider E Lo and D Sutanto ldquoHigh-impedancefault detection using discrete wavelet transform and frequencyrange and RMS conversionrdquo IEEE Transactions on PowerDelivery vol 20 no 1 pp 397ndash407 2005
[6] M Michalik W Rebizant M R Lukowicz S J Lee and SH Kang ldquoHigh-impedance fault detection in distribution net-works with use of wavelet-based algorithmrdquo IEEE Transactionson Power Delivery vol 21 no 4 pp 1793ndash1802 2006
[7] Y Sheng and SM Rovnyak ldquoDecision tree-basedmethodologyfor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 19 no 2 pp 533ndash536 2004
[8] C S Burrus R A Gopinath and H Guo Introduction toWavelets and Wavelet Transforms Prentice Hall Upper SaddleRiver NJ USA 1998
[9] A Elmitwally S Farghal S Abdelkader and M Elkateb ldquoPro-posed wavelet-neurofuzzy combined system for power qualityviolations detection and diagnosisrdquo IEE Proceedings Genera-tion Transmission and Distribution vol 148 no 1 pp 15ndash202001
[10] L Angrisani P Daponte M DrsquoApuzzo and A Testa ldquoA mea-surement method based on the wavelet transform for powerquality analysisrdquo IEEE Transactions on Power Delivery vol 13no 4 pp 990ndash998 1998
[11] S Santoso E J PowersWM Grady and A C Parsons ldquoPowerquality disturbance waveform recognition using wavelet-basedneural classifier Part 1 theoretical foundationrdquo IEEE Transac-tions on Power Delivery vol 15 no 1 pp 222ndash228 2000
[12] H Mokhtari M Karimi-Ghartemani and M R IravanildquoExperimental performance evaluation of a wavelet-based on-line voltage detection method for power quality applicationsrdquoIEEE Transactions on Power Delivery vol 17 no 1 pp 161ndash1722002
[13] P K Dash S R Samantaray and G Panda ldquoFault classificationand section identification of an advanced series-compensatedtransmission line using support vector machinerdquo IEEE Trans-actions on Power Delivery vol 22 no 1 pp 67ndash73 2007
[14] D SrinivasanW S Ng and A C Liew ldquoNeural-network-basedsignature recognition for harmonic source identificationrdquo IEEETransactions on Power Delivery vol 21 no 1 pp 398ndash405 2006
Mathematical Problems in Engineering 9
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
For the 119894th column in the matrix 119880 the sum of all elementsequals one and only one element in this column is unity Thetraditional 119896-means algorithm did not consider (1) which isimplemented in this proposed enhanced 119896-means algorithm
The unknown variables in the problem of placement ofmeasurement facilities are 119880
119888119894 119888 = 1 119862 and 119894 = 1 119873
Traditional optimization methods involving the gradientsof objective function cannot minimize (1) because of dis-continuity of the objective function The genetic algorithmwas adopted to minimize (1) herein because the geneticalgorithm can deal with binary variable 119880
119888119894efficiently [22]
The population size crossover rate and mutation rate inthe genetic algorithm were assigned with 100 09 and 001respectively
In this paper 119883119894represents one of the current vectors
(signal energies calculated by DWT) caused by an HIF at aline ℓ The dimension (1 times 3660 herein) of 119883
119894varies with
the number of studied cases Symbols 119862 and119873 (3660 in thispaper) are the numbers of measurement facilities and thescenarios with HIFs respectively Let 119871 be the number ofthe line sections Then 119871 119883
119894rsquos need to be partitioned into 119862
clusters The vector 119881119888(1 times 3660) consisting of the virtual
HIF currents serves as the center in the 119888th cluster All vec-tors of the HIF currents 119883
119894rsquos in the 119888th cluster geometrically
center at119881119888Therefore the criterion for placingmeasurement
facilities in the electric distribution system is as followsplace a measurement facility at line ℓ at which the totalEuclidean distance between119883
119894rsquos (HIFs occurring at line ℓ) and
119881119888is minimal in the 119888th cluster
32 Discrete Wavelet Transform (DWT) Fourier transform(FT) is a suitable approach for studying problems withsteady state responses Short-time Fourier transform (STFT)divides the full-time interval into a number of smallequal-time intervals which can be individually analyzed using FTAlthough the result obtained from STFT contains time andfrequency information the equal-time intervals are fixedThus STFT cannot be used to detect the transient signals Onthe other hand the discrete wavelet transform (DWT) hasbeen widely used for analyzing the transient signals due toits varied scale and wavelet functions [23ndash25]The features ofsignals can be easily extracted via themultiresolution analysis(MRA) DWT avoids the disadvantages of both FT and STFT
A signal can be represented as a sum of wavelet functions120593(119905) and scale functions 120601(119905) with coefficients at differenttime shifts and scales (frequencies) using DWT DWT canextract the features of transient signals by decomposing signalcomponents overlapping in both time and frequency [8]
According to DWT a time-varying function (signal) 119891(119905) isin1198712(119877) can be expressed as follows
119891 (119905) = sum
119896
1198880 (119896) 120601 (119905 minus 119896) +sum
119896
sum
119895=1
119889119895 (119896) 2
minus1198952120593 (2minus119895119905 minus 119896)
= sum
119896
1198881198950(119896) 2minus11989502120601 (2
minus1198950119905 minus 119896)
+sum
119896
sum
119895=1198950
119889119895 (119896) 2
minus1198952120593 (2minus119895119905 minus 119896)
(4)
where 1198880and 119889
119895represent the scaling (coarse) coefficient at
scale 0 and wavelet (detailed) coefficient at scale 119895 respec-tivelyThe symbol 119896 represents the translation coefficientThescales 119895 = 1 2 denote the different (high to low) frequencybands The variable 119895
119900is an integer The translated and scaled
(dilated) version of the wavelet 120593(2minus119895119905 minus 119896) used in themultiresolution analysis (MRA) constructs a time-frequencypicture of the signal
There are some other wavelets in the wavelet theory [8]Haar wavelets have compact support (a finite bounded set)but are discontinuous Shannonwavelets are very smooth butare not compactly supported and they decay at infinity veryslowly Compared with these wavelets Daubechies-4 belongsto a class of orthonormal basis-generating continuous andcompactly supported wavelets Daubechies-4 is adopted inthis paper to extract the features of the line currents at scales1 2 and 3 with a sampling rate of 128 pointscycle
33 Multiresolution Analysis (MRA) As shown in (4) 119891(119905)is constructed by 120601(119905) and decomposed by 120593(119905) at differentscales (resolution levels) 120593(119905) generates the detailed versionof 119891(119905) and 120601(119905) generates the coarse version of 119891(119905) It can beshown that [8]
119888119895+1 (119896) = sum
119898
ℎ (119898 minus 2119896) 119888119895 (119898) (5)
119889119895+1 (119896) = sum
119898
ℎ1 (119898 minus 2119896) 119888119895 (119898) (6)
where ℎ(119898 minus 2119896) and ℎ1(119898 minus 2119896) are the low-pass and high-
pass filters respectively [8] These two equations show thatthe scaling and wavelet coefficients at different scale levelscan be obtained by convolving the expansion coefficientsat scale 119895 by the time-reversed recursion coefficients ℎ(sdot)and ℎ
1(sdot) and then downsampling or decimating to give the
expansion coefficients at the next level of 119895 + 1 The termldquodownsamplingrdquo indicates that the number at lower scale 119895is double compared with that at higher scale 119895 + 1 due to thefilters ℎ(119898 minus 2119896) and ℎ
1(119898 minus 2119896) This process is called the
ldquoanalysis (decomposition)rdquo from the fine scale to the coarsescale The reverse process called synthesis (construction)from the coarse scale to the fine scale is omitted here Figure 1illustrates a three-scale MRA decomposition for a signalThesymbols ℎ ℎ
1 and ldquodarr2rdquo denote the low-pass filter high-pass
filter and ldquodownsamplingrdquo respectivelyThe small scales represent high-frequency ranges Only
the wavelet coefficient (119889119895) is regarded as a feature due to
4 Mathematical Problems in Engineering
Signalh1 darr2
h1 darr2
h1 darr2h darr2
h darr2
h darr2
d1
d2
d3
c3
Figure 1 A three-scale MRA decomposition for a signal
the high-frequency phenomena fromHIFsMore specificallyif the sampling rate from the measurement facility is 128pointscycle then scales 1 2 and 3 cover 384sim192 kHz 192sim096 kHz and 096sim048 kHz respectively Lower harmonicswere not considered for the SVM because they (with largevalues) do not provide significant discrimination amonglines
34 Parseval Theorem When the MRA is applied to a tran-sient signal a large amount of wavelet coefficients will beattained Although the wavelet coefficients are useful it isdifficult for SVM to trainvalidate that much informationMore specifically if sampling rate is 128 pointscycle andfive cycles are utilized the numbers of wavelet coefficients atscales 1 2 and 3 are 320 160 and 80 due to ldquodownsamplingrdquorespectively Implementing 560times119862 input neurons in an SVMbecomes impractical where119862 is the number of measurementfacilities defined in Section 31 A trade-off treatment usingParsevalrsquos theorem is presented in this paper
In this paper only sum119896sum119895=1|119889119895(119896)|2 in (7) is calculated
because the HIF belongs to transients This term is calledldquocurrent energyrdquo or simply ldquoenergyrdquo in this paper Applicationsof sum119896sum119895=1|119889119895(119896)|2 are as follows
(i) Determination of measurement facility placementsum119896sum119895=1|119889119895(119896)|2 is computed for each line section to
be an element of 119883119894for a given scenario described
in Section 31 The number of given scenarios is 3660which will be discussed in Section 41
(ii) Feature extraction of transient signals sum119896sum119895=1|119889119895(119896)|2
is separated into the first to third scales (1198891sim 1198893 119895 =
1 2 and 3) for an HIF current at each line sectionThese features will serve as inputs for SVM
35 Support Vector Machine (SVM) Traditional multilayerneural networks have some limitations (i) many inputs dueto need of diversity for inputs (ii) requirement of crucialfeatures for inputs (iii) trial and error for number of neuronsin the hidden layer and (iv)multimodalwithmany localmin-imums Avoiding the above demerits SVM is a supervisedartificial neural network designed for solving classificationproblems [26 27] In essence SVM maximizes the margin
between the training data and the decision boundary whichcan be formulated as a quadratic optimization problem Thesubset of patterns that are closest to the decision boundary iscalled the support vector
SVM maximizes the separating margin between twoclasses given by a set of 119875 data pairs (119909
119901 119888119901) where 119909
119901
and 119888119901denote the input vector and class 119901 = 1 2 119875
respectively For linear separable training pairs of two classesthe separating hyperplane ℎ(119909) is given by
ℎ (119909) = 119908119905119909 + 119887 = 0 (8)
where119908 and 119887 are the vectors of weighting factors and biasesrespectively If a nonlinear hyperplane120595(sdot) is considered then
The maximal separating margin can be attained by mini-mizing the following primal problem if two classes are notlinearly distributed [28]
min 1
2119908119905119908 + 119870
119875
sum
119901=1
120585119901 (10)
subject to 119888119901(119908119905120595 (119909119901) + 119887) ge 1 minus 120585
119901 119901 = 1 2 119875
(11)
where 120585119901is the so-called fulfilling variable The symbol 119870 is
a regularization parameter In order to search a proper 119870performance of the trained SVMneeds assessment as followsThe training data are divided into two sets One is used totrain the SVM while the other called the validation set isused for evaluating the SVM According to the performanceon the validation set a proper value of 119870 can be attained
Equations (10) and (11) can be transformed into theunconstrained Lagrangian
119871 (119908 119887 120585 120583) =1
2119908119905119908 + 119870
119875
sum
119901=1
120585119901
+
119875
sum
119901=1
120583119901[119888119901(119908119905120595 (119909119901) + 119887) minus 1 + 120585
119901]
(12)
where 120583119901
is the dual variable (Lagrange multiplier) forinequality constraint (11) Obviously the form of (11) is thesame as the output of a neuron if 120593(sdot) and 120585
119901are considered
the activating function of a neuron and nonnegative slackvariable respectively
4 Simulation Results
41 Simulation Data The applicability of the proposedmethodology is verified by simulation results in this sectionAn 18-busbar radial system with 17 line sections illustrated inFigure 2 serves as a sample system in this paper Its busbar andline data are provided in [29] To train the SVM the originalload level was varied within plusmn10 (61 conditions) and theHIFs occur at different angles within 0∘sim359∘ (4 conditions)
Mathematical Problems in Engineering 5
Line 4 Line 2Line 3Line 5Line 6 Line 1Line 7Line 8Line 9
Line 10 Line 11
Line 12
Line 13
Line 14
Line 15Line 16Line 17
Figure 2 One-line diagram for studied distribution system
and at 15 different line sections for obtaining a total of 3660(= 61 times 4 times 15) data 70 10 and 20 of these 3660 datawere used stochastically for training validating and testingthe proposed SVM respectivelyThe arc of HIF was modeledwith two antiparallel DC sources and diodes which wereconnected to a random resistor [2] The proposed methodswere implemented by MATLAB 70 (SimPowerSystems) ona C2D (Core 2 Due) 213 GHz computer (RAM 35G) Thedata-window size of the signal for processing in this paper isfive cycles
Because the power supply measurement facilities aremore expensive than general meters the number of measure-ment facilities is limited Discussion of purchasing the mea-surement facilities and determination of a proper number forthemeasurement facilities are beyond the scope of this paperHence 14 11 8 4 and 2 measurement facilities (ie 119862) areassumed to be available in this paper Table 1 illustrates theSVM information associated with measurements BecauseHIF energies of the first to third scales (119889
1sim 1198893) were consid-
ered the number of input neurons equals measurements (119862)multiplied by 3 These are cases 1sim5 Moreover the current atthe neural line of the main transformer is generally availableand can be utilized These are cases 6sim10 Finally four binarybits are sufficient for discriminating 15 line sections excludingprimary sides (line 1) and the main transformer (denoted byline 2) in this system
42 Feature Extraction by DWT As described in Sections 33and 34 the ldquoenergiesrdquo for HIF currents of the first to thirdscales at each line section are used as features for SVM inputsAssume that an HIF occurs (90∘) at line section 12 Figure 3shows the energy distribution of the neighborhood of linesection 12 (ie line sections 11 and 13) The energies for the
Table 1 SVM information associated with measurements
Facility number (119862) Input neurons Output neuronsCase 1 2 2 times 3 4Case 2 4 4 times 3 4Case 3 8 8 times 3 4Case 4 11 11 times 3 4Case 5 14 14 times 3 4Case 6 2 + 1 3 times 3 4Case 7 4 + 1 5 times 3 4Case 8 8 + 1 9 times 3 4Case 9 11 + 1 12 times 3 4Case 10 14 + 1 15 times 3 4
first to sixth scales at these three line sections are shown It isapparent that the normal energy and HIF energy are almostthe same for the current of the fourth (also for fifth and sixth)scale Hence current energies for the fourth to sixth scalescannot serve as features and only current energies for thefirst to third scales are considered further Please note thatthe energies are normalized to be per unit and are in termsof log
10because the energies of the fifth and sixth scales are
much larger than those of other scales
43 Scaled Energies at Line Sections AnHIF occurring at linesection 12 is discussed in this section Figure 4 illustrates theHIF currents in terms of the DWT-scaled energy distribu-tions at each line sectionThe vertical axis denotes the energymagnitude while the horizontal axis means the 119889
1sim 1198893at
each line section Please note that the energies are normalizedto be per unit
6 Mathematical Problems in Engineering
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(a) 1stndash6th normal and HIF energies at line section 11
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(b) 1stndash6th normal and HIF energies at line section 12
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(c) 1stndash6th normal and HIF energies at line section 13
Figure 3 Energy distributions near faulted line
0010203040506070809
1
Line 1 Line 2 Line 3 Line 4 Line 5 Line 6
1st scale2nd scale
3rd scale
Ener
gy (p
er u
nit)
0010203040506070809
1
Line 7 Line 8 Line 9 Line 10 Line 11 Line 12
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
0010203040506070809
1
Line 13 Line 14 Line 15 Line 16 Line 17
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
Figure 4 HIF energy distributions at all line sections
Mathematical Problems in Engineering 7
Table 2 Different 119862s and corresponding clusters (119896-means)
When the busbar load varies and the HIF occurs atdistinct angles the above phenomena will be discriminatedHence the ldquoenergiesrdquo of the HIF currents of the first to thirdscales are important features for locating theHIF line section
44 Measurement Facility Placement Because 14 11 8 4 and2 power supply measurement facilities are assumed to beavailable in the test sample 119862 may be 14 11 8 4 or 2 and119873 = 3660 respectively (119862 and119873were defined in Section 31)For a given 119862 the same 3660 sets of data were employed toperform the HIF current energy clustering by the modified119896-means algorithm Table 2 illustrates the different 119862rsquos andcorresponding clusters Each cluster is quoted by parenthesesThe line section with an italic font in Table 2 denotes the oneinstalled with ameasurement facility Traditional FCM is alsoemployed to study the line section clustering as shown inTable 3 As can be seen some clusters obtained by the FCMare infeasible because lines in a cluster may not be adjacentto each other For example in the last row of Table 3 linesections 7 8 and 9 in a cluster are not adjacent to line sections10sim17
More specifically the condition for 119862 = 2 and 119888 = 2 inthe last row of Table 2 is described here Table 4 illustratesthe distances (norm) between 119883
119894 119894 = 3 4 17 and its
clustering center 1198812(119888 = 2) for 119862 = 2 As can be seen the
distance between 11988312
and 1198812is the smallest Therefore the
measurement facility is placed at line section 12In this paper the dimension of119883
119894is 1 times 3660 where 3660
is the number of scenarios from the test system Each elementof 119883119894is the total energy at line section 119894 for one of the 3660
cases Moreover there are 17 119883119894rsquos (number of lines) for the
18-busbar system where 17 is the line number
0
10
20
30
40
50
60
()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Energy ranges
HIFLIF
CS
Figure 5 Total energy disturbances for 3 different disturbances
45 Classification among HIF Short Circuit and SwitchingThere are 930 cases with short circuits (low-impedance faultsLIFs) and 620 cases with capacitor switching (CS) for furtherinvestigation of energy distributions Figure 5 shows the totalenergy of the first to third scales for different HIFs LIFs andCS The vertical axis denotes the percentage of occurrencefor the three individual disturbances The horizontal axisincludes 15 energy ranges (log
10) More specifically ranges 1
2 and 15 represent 348ndash356 357ndash365 and 1009ndash1079 purespectively It can be found that HIFs include smaller totalenergies from range 1 to range 5 Hence the total energy canbe employed to discriminate HIFs from other disturbancesfor example LIF and CS
46 Accuracy of Locating HIFs by SVM As described inSection 41 70 10 and 20 of the 3660 data are usedstochastically for training validating and testing respec-tively Table 5 illustrates the number of iterations CPU timefor training the SVM and the accuracy rate for the 10 casesdefined in Table 1 The following comments can be drawnfrom Table 5
(i) The numbers of iterations for all cases are almost thesame for the SVM despite the different number ofinput neurons
(ii) The CPU time required varies with the number ofinput neurons
(iii) Accuracy rates are greater than 99 except for cases 1and 6
(iv) Cases 1 and 6 with only two measurement facilitiesstill gain accuracy rate of 974 and 9836 respec-tively This result ensures the advantage of the pro-posed method using the SVM
(v) The neutral current at the substation improves accu-racy rates only for cases 1 and 2 (corresponding tocases 6 and 7) with fewer measurements
8 Mathematical Problems in Engineering
Table 4 Distances (times105) between 119883119894and its clustering center
This paper proposed a new method for locating the linesection with an HIF using DWT modified 119896-means andSVM Compared with the existing methods involving iden-tification of an HIF in a feeder (or transmission line) or inone of the multiple feeders from the secondary side of asubstation the proposed approach is able to locate anHIF linesection in a distribution system with multiple feeders usinga power supply monitoring system including multiple powersupply measurement facilities at different lines Classificationof disturbances and locating the HIF are addressed
The features (current energies) at three distinct scales(frequency bands) were extracted by MRA in DWT Thesefeatures provide important information for the SVM to locatethe line sectionwith anHIFMoreover the energies ofHIF arediscriminated obviously from those of LIF and CS
The simulation results obtained from an 18-busbar distri-bution system show that good accuracy can still be attainedusing only a few measurements (eg two in this paper) dueto the SVM Hence SVM is very useful when only a fewmeasurements are available
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors gratefully acknowledge the financial supportfrom the National Science Council Taiwan under Grant no96-2221-E-033-069-MY2
References
[1] K Y Lien S L Chen C J Liao T Y Guo T M Lin and J SShen ldquoEnergy variance criterion and threshold tuning schemefor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 14 no 3 pp 810ndash817 1999
[2] A E Emanuel D Cyganski J A Orr S Shiller and E MGulachenski ldquoHigh impedance fault arcing on sandy soil in15kV distribution feeders contributions to the evaluation of thelow frequency spectrumrdquo IEEE Transactions on Power Deliveryvol 5 no 2 pp 676ndash686 1990
[3] C H Kim H Kim Y H Ko S H Byun R K Aggarwal and AT Johns ldquoA novel fault-detection technique of high-impedancearcing faults in transmission lines using the wavelet transformrdquoIEEE Transactions on Power Delivery vol 17 no 4 pp 921ndash9292002
[4] A-R Sedighi M-R Haghifam O P Malik and M-H Ghas-semian ldquoHigh impedance fault detection based on wavelettransform and statistical pattern recognitionrdquo IEEE Transac-tions on Power Delivery vol 20 no 4 pp 2414ndash2421 2005
[5] T M Lai L A Snider E Lo and D Sutanto ldquoHigh-impedancefault detection using discrete wavelet transform and frequencyrange and RMS conversionrdquo IEEE Transactions on PowerDelivery vol 20 no 1 pp 397ndash407 2005
[6] M Michalik W Rebizant M R Lukowicz S J Lee and SH Kang ldquoHigh-impedance fault detection in distribution net-works with use of wavelet-based algorithmrdquo IEEE Transactionson Power Delivery vol 21 no 4 pp 1793ndash1802 2006
[7] Y Sheng and SM Rovnyak ldquoDecision tree-basedmethodologyfor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 19 no 2 pp 533ndash536 2004
[8] C S Burrus R A Gopinath and H Guo Introduction toWavelets and Wavelet Transforms Prentice Hall Upper SaddleRiver NJ USA 1998
[9] A Elmitwally S Farghal S Abdelkader and M Elkateb ldquoPro-posed wavelet-neurofuzzy combined system for power qualityviolations detection and diagnosisrdquo IEE Proceedings Genera-tion Transmission and Distribution vol 148 no 1 pp 15ndash202001
[10] L Angrisani P Daponte M DrsquoApuzzo and A Testa ldquoA mea-surement method based on the wavelet transform for powerquality analysisrdquo IEEE Transactions on Power Delivery vol 13no 4 pp 990ndash998 1998
[11] S Santoso E J PowersWM Grady and A C Parsons ldquoPowerquality disturbance waveform recognition using wavelet-basedneural classifier Part 1 theoretical foundationrdquo IEEE Transac-tions on Power Delivery vol 15 no 1 pp 222ndash228 2000
[12] H Mokhtari M Karimi-Ghartemani and M R IravanildquoExperimental performance evaluation of a wavelet-based on-line voltage detection method for power quality applicationsrdquoIEEE Transactions on Power Delivery vol 17 no 1 pp 161ndash1722002
[13] P K Dash S R Samantaray and G Panda ldquoFault classificationand section identification of an advanced series-compensatedtransmission line using support vector machinerdquo IEEE Trans-actions on Power Delivery vol 22 no 1 pp 67ndash73 2007
[14] D SrinivasanW S Ng and A C Liew ldquoNeural-network-basedsignature recognition for harmonic source identificationrdquo IEEETransactions on Power Delivery vol 21 no 1 pp 398ndash405 2006
Mathematical Problems in Engineering 9
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
Figure 1 A three-scale MRA decomposition for a signal
the high-frequency phenomena fromHIFsMore specificallyif the sampling rate from the measurement facility is 128pointscycle then scales 1 2 and 3 cover 384sim192 kHz 192sim096 kHz and 096sim048 kHz respectively Lower harmonicswere not considered for the SVM because they (with largevalues) do not provide significant discrimination amonglines
34 Parseval Theorem When the MRA is applied to a tran-sient signal a large amount of wavelet coefficients will beattained Although the wavelet coefficients are useful it isdifficult for SVM to trainvalidate that much informationMore specifically if sampling rate is 128 pointscycle andfive cycles are utilized the numbers of wavelet coefficients atscales 1 2 and 3 are 320 160 and 80 due to ldquodownsamplingrdquorespectively Implementing 560times119862 input neurons in an SVMbecomes impractical where119862 is the number of measurementfacilities defined in Section 31 A trade-off treatment usingParsevalrsquos theorem is presented in this paper
In this paper only sum119896sum119895=1|119889119895(119896)|2 in (7) is calculated
because the HIF belongs to transients This term is calledldquocurrent energyrdquo or simply ldquoenergyrdquo in this paper Applicationsof sum119896sum119895=1|119889119895(119896)|2 are as follows
(i) Determination of measurement facility placementsum119896sum119895=1|119889119895(119896)|2 is computed for each line section to
be an element of 119883119894for a given scenario described
in Section 31 The number of given scenarios is 3660which will be discussed in Section 41
(ii) Feature extraction of transient signals sum119896sum119895=1|119889119895(119896)|2
is separated into the first to third scales (1198891sim 1198893 119895 =
1 2 and 3) for an HIF current at each line sectionThese features will serve as inputs for SVM
35 Support Vector Machine (SVM) Traditional multilayerneural networks have some limitations (i) many inputs dueto need of diversity for inputs (ii) requirement of crucialfeatures for inputs (iii) trial and error for number of neuronsin the hidden layer and (iv)multimodalwithmany localmin-imums Avoiding the above demerits SVM is a supervisedartificial neural network designed for solving classificationproblems [26 27] In essence SVM maximizes the margin
between the training data and the decision boundary whichcan be formulated as a quadratic optimization problem Thesubset of patterns that are closest to the decision boundary iscalled the support vector
SVM maximizes the separating margin between twoclasses given by a set of 119875 data pairs (119909
119901 119888119901) where 119909
119901
and 119888119901denote the input vector and class 119901 = 1 2 119875
respectively For linear separable training pairs of two classesthe separating hyperplane ℎ(119909) is given by
ℎ (119909) = 119908119905119909 + 119887 = 0 (8)
where119908 and 119887 are the vectors of weighting factors and biasesrespectively If a nonlinear hyperplane120595(sdot) is considered then
The maximal separating margin can be attained by mini-mizing the following primal problem if two classes are notlinearly distributed [28]
min 1
2119908119905119908 + 119870
119875
sum
119901=1
120585119901 (10)
subject to 119888119901(119908119905120595 (119909119901) + 119887) ge 1 minus 120585
119901 119901 = 1 2 119875
(11)
where 120585119901is the so-called fulfilling variable The symbol 119870 is
a regularization parameter In order to search a proper 119870performance of the trained SVMneeds assessment as followsThe training data are divided into two sets One is used totrain the SVM while the other called the validation set isused for evaluating the SVM According to the performanceon the validation set a proper value of 119870 can be attained
Equations (10) and (11) can be transformed into theunconstrained Lagrangian
119871 (119908 119887 120585 120583) =1
2119908119905119908 + 119870
119875
sum
119901=1
120585119901
+
119875
sum
119901=1
120583119901[119888119901(119908119905120595 (119909119901) + 119887) minus 1 + 120585
119901]
(12)
where 120583119901
is the dual variable (Lagrange multiplier) forinequality constraint (11) Obviously the form of (11) is thesame as the output of a neuron if 120593(sdot) and 120585
119901are considered
the activating function of a neuron and nonnegative slackvariable respectively
4 Simulation Results
41 Simulation Data The applicability of the proposedmethodology is verified by simulation results in this sectionAn 18-busbar radial system with 17 line sections illustrated inFigure 2 serves as a sample system in this paper Its busbar andline data are provided in [29] To train the SVM the originalload level was varied within plusmn10 (61 conditions) and theHIFs occur at different angles within 0∘sim359∘ (4 conditions)
Mathematical Problems in Engineering 5
Line 4 Line 2Line 3Line 5Line 6 Line 1Line 7Line 8Line 9
Line 10 Line 11
Line 12
Line 13
Line 14
Line 15Line 16Line 17
Figure 2 One-line diagram for studied distribution system
and at 15 different line sections for obtaining a total of 3660(= 61 times 4 times 15) data 70 10 and 20 of these 3660 datawere used stochastically for training validating and testingthe proposed SVM respectivelyThe arc of HIF was modeledwith two antiparallel DC sources and diodes which wereconnected to a random resistor [2] The proposed methodswere implemented by MATLAB 70 (SimPowerSystems) ona C2D (Core 2 Due) 213 GHz computer (RAM 35G) Thedata-window size of the signal for processing in this paper isfive cycles
Because the power supply measurement facilities aremore expensive than general meters the number of measure-ment facilities is limited Discussion of purchasing the mea-surement facilities and determination of a proper number forthemeasurement facilities are beyond the scope of this paperHence 14 11 8 4 and 2 measurement facilities (ie 119862) areassumed to be available in this paper Table 1 illustrates theSVM information associated with measurements BecauseHIF energies of the first to third scales (119889
1sim 1198893) were consid-
ered the number of input neurons equals measurements (119862)multiplied by 3 These are cases 1sim5 Moreover the current atthe neural line of the main transformer is generally availableand can be utilized These are cases 6sim10 Finally four binarybits are sufficient for discriminating 15 line sections excludingprimary sides (line 1) and the main transformer (denoted byline 2) in this system
42 Feature Extraction by DWT As described in Sections 33and 34 the ldquoenergiesrdquo for HIF currents of the first to thirdscales at each line section are used as features for SVM inputsAssume that an HIF occurs (90∘) at line section 12 Figure 3shows the energy distribution of the neighborhood of linesection 12 (ie line sections 11 and 13) The energies for the
Table 1 SVM information associated with measurements
Facility number (119862) Input neurons Output neuronsCase 1 2 2 times 3 4Case 2 4 4 times 3 4Case 3 8 8 times 3 4Case 4 11 11 times 3 4Case 5 14 14 times 3 4Case 6 2 + 1 3 times 3 4Case 7 4 + 1 5 times 3 4Case 8 8 + 1 9 times 3 4Case 9 11 + 1 12 times 3 4Case 10 14 + 1 15 times 3 4
first to sixth scales at these three line sections are shown It isapparent that the normal energy and HIF energy are almostthe same for the current of the fourth (also for fifth and sixth)scale Hence current energies for the fourth to sixth scalescannot serve as features and only current energies for thefirst to third scales are considered further Please note thatthe energies are normalized to be per unit and are in termsof log
10because the energies of the fifth and sixth scales are
much larger than those of other scales
43 Scaled Energies at Line Sections AnHIF occurring at linesection 12 is discussed in this section Figure 4 illustrates theHIF currents in terms of the DWT-scaled energy distribu-tions at each line sectionThe vertical axis denotes the energymagnitude while the horizontal axis means the 119889
1sim 1198893at
each line section Please note that the energies are normalizedto be per unit
6 Mathematical Problems in Engineering
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(a) 1stndash6th normal and HIF energies at line section 11
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(b) 1stndash6th normal and HIF energies at line section 12
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(c) 1stndash6th normal and HIF energies at line section 13
Figure 3 Energy distributions near faulted line
0010203040506070809
1
Line 1 Line 2 Line 3 Line 4 Line 5 Line 6
1st scale2nd scale
3rd scale
Ener
gy (p
er u
nit)
0010203040506070809
1
Line 7 Line 8 Line 9 Line 10 Line 11 Line 12
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
0010203040506070809
1
Line 13 Line 14 Line 15 Line 16 Line 17
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
Figure 4 HIF energy distributions at all line sections
Mathematical Problems in Engineering 7
Table 2 Different 119862s and corresponding clusters (119896-means)
When the busbar load varies and the HIF occurs atdistinct angles the above phenomena will be discriminatedHence the ldquoenergiesrdquo of the HIF currents of the first to thirdscales are important features for locating theHIF line section
44 Measurement Facility Placement Because 14 11 8 4 and2 power supply measurement facilities are assumed to beavailable in the test sample 119862 may be 14 11 8 4 or 2 and119873 = 3660 respectively (119862 and119873were defined in Section 31)For a given 119862 the same 3660 sets of data were employed toperform the HIF current energy clustering by the modified119896-means algorithm Table 2 illustrates the different 119862rsquos andcorresponding clusters Each cluster is quoted by parenthesesThe line section with an italic font in Table 2 denotes the oneinstalled with ameasurement facility Traditional FCM is alsoemployed to study the line section clustering as shown inTable 3 As can be seen some clusters obtained by the FCMare infeasible because lines in a cluster may not be adjacentto each other For example in the last row of Table 3 linesections 7 8 and 9 in a cluster are not adjacent to line sections10sim17
More specifically the condition for 119862 = 2 and 119888 = 2 inthe last row of Table 2 is described here Table 4 illustratesthe distances (norm) between 119883
119894 119894 = 3 4 17 and its
clustering center 1198812(119888 = 2) for 119862 = 2 As can be seen the
distance between 11988312
and 1198812is the smallest Therefore the
measurement facility is placed at line section 12In this paper the dimension of119883
119894is 1 times 3660 where 3660
is the number of scenarios from the test system Each elementof 119883119894is the total energy at line section 119894 for one of the 3660
cases Moreover there are 17 119883119894rsquos (number of lines) for the
18-busbar system where 17 is the line number
0
10
20
30
40
50
60
()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Energy ranges
HIFLIF
CS
Figure 5 Total energy disturbances for 3 different disturbances
45 Classification among HIF Short Circuit and SwitchingThere are 930 cases with short circuits (low-impedance faultsLIFs) and 620 cases with capacitor switching (CS) for furtherinvestigation of energy distributions Figure 5 shows the totalenergy of the first to third scales for different HIFs LIFs andCS The vertical axis denotes the percentage of occurrencefor the three individual disturbances The horizontal axisincludes 15 energy ranges (log
10) More specifically ranges 1
2 and 15 represent 348ndash356 357ndash365 and 1009ndash1079 purespectively It can be found that HIFs include smaller totalenergies from range 1 to range 5 Hence the total energy canbe employed to discriminate HIFs from other disturbancesfor example LIF and CS
46 Accuracy of Locating HIFs by SVM As described inSection 41 70 10 and 20 of the 3660 data are usedstochastically for training validating and testing respec-tively Table 5 illustrates the number of iterations CPU timefor training the SVM and the accuracy rate for the 10 casesdefined in Table 1 The following comments can be drawnfrom Table 5
(i) The numbers of iterations for all cases are almost thesame for the SVM despite the different number ofinput neurons
(ii) The CPU time required varies with the number ofinput neurons
(iii) Accuracy rates are greater than 99 except for cases 1and 6
(iv) Cases 1 and 6 with only two measurement facilitiesstill gain accuracy rate of 974 and 9836 respec-tively This result ensures the advantage of the pro-posed method using the SVM
(v) The neutral current at the substation improves accu-racy rates only for cases 1 and 2 (corresponding tocases 6 and 7) with fewer measurements
8 Mathematical Problems in Engineering
Table 4 Distances (times105) between 119883119894and its clustering center
This paper proposed a new method for locating the linesection with an HIF using DWT modified 119896-means andSVM Compared with the existing methods involving iden-tification of an HIF in a feeder (or transmission line) or inone of the multiple feeders from the secondary side of asubstation the proposed approach is able to locate anHIF linesection in a distribution system with multiple feeders usinga power supply monitoring system including multiple powersupply measurement facilities at different lines Classificationof disturbances and locating the HIF are addressed
The features (current energies) at three distinct scales(frequency bands) were extracted by MRA in DWT Thesefeatures provide important information for the SVM to locatethe line sectionwith anHIFMoreover the energies ofHIF arediscriminated obviously from those of LIF and CS
The simulation results obtained from an 18-busbar distri-bution system show that good accuracy can still be attainedusing only a few measurements (eg two in this paper) dueto the SVM Hence SVM is very useful when only a fewmeasurements are available
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors gratefully acknowledge the financial supportfrom the National Science Council Taiwan under Grant no96-2221-E-033-069-MY2
References
[1] K Y Lien S L Chen C J Liao T Y Guo T M Lin and J SShen ldquoEnergy variance criterion and threshold tuning schemefor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 14 no 3 pp 810ndash817 1999
[2] A E Emanuel D Cyganski J A Orr S Shiller and E MGulachenski ldquoHigh impedance fault arcing on sandy soil in15kV distribution feeders contributions to the evaluation of thelow frequency spectrumrdquo IEEE Transactions on Power Deliveryvol 5 no 2 pp 676ndash686 1990
[3] C H Kim H Kim Y H Ko S H Byun R K Aggarwal and AT Johns ldquoA novel fault-detection technique of high-impedancearcing faults in transmission lines using the wavelet transformrdquoIEEE Transactions on Power Delivery vol 17 no 4 pp 921ndash9292002
[4] A-R Sedighi M-R Haghifam O P Malik and M-H Ghas-semian ldquoHigh impedance fault detection based on wavelettransform and statistical pattern recognitionrdquo IEEE Transac-tions on Power Delivery vol 20 no 4 pp 2414ndash2421 2005
[5] T M Lai L A Snider E Lo and D Sutanto ldquoHigh-impedancefault detection using discrete wavelet transform and frequencyrange and RMS conversionrdquo IEEE Transactions on PowerDelivery vol 20 no 1 pp 397ndash407 2005
[6] M Michalik W Rebizant M R Lukowicz S J Lee and SH Kang ldquoHigh-impedance fault detection in distribution net-works with use of wavelet-based algorithmrdquo IEEE Transactionson Power Delivery vol 21 no 4 pp 1793ndash1802 2006
[7] Y Sheng and SM Rovnyak ldquoDecision tree-basedmethodologyfor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 19 no 2 pp 533ndash536 2004
[8] C S Burrus R A Gopinath and H Guo Introduction toWavelets and Wavelet Transforms Prentice Hall Upper SaddleRiver NJ USA 1998
[9] A Elmitwally S Farghal S Abdelkader and M Elkateb ldquoPro-posed wavelet-neurofuzzy combined system for power qualityviolations detection and diagnosisrdquo IEE Proceedings Genera-tion Transmission and Distribution vol 148 no 1 pp 15ndash202001
[10] L Angrisani P Daponte M DrsquoApuzzo and A Testa ldquoA mea-surement method based on the wavelet transform for powerquality analysisrdquo IEEE Transactions on Power Delivery vol 13no 4 pp 990ndash998 1998
[11] S Santoso E J PowersWM Grady and A C Parsons ldquoPowerquality disturbance waveform recognition using wavelet-basedneural classifier Part 1 theoretical foundationrdquo IEEE Transac-tions on Power Delivery vol 15 no 1 pp 222ndash228 2000
[12] H Mokhtari M Karimi-Ghartemani and M R IravanildquoExperimental performance evaluation of a wavelet-based on-line voltage detection method for power quality applicationsrdquoIEEE Transactions on Power Delivery vol 17 no 1 pp 161ndash1722002
[13] P K Dash S R Samantaray and G Panda ldquoFault classificationand section identification of an advanced series-compensatedtransmission line using support vector machinerdquo IEEE Trans-actions on Power Delivery vol 22 no 1 pp 67ndash73 2007
[14] D SrinivasanW S Ng and A C Liew ldquoNeural-network-basedsignature recognition for harmonic source identificationrdquo IEEETransactions on Power Delivery vol 21 no 1 pp 398ndash405 2006
Mathematical Problems in Engineering 9
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
Line 4 Line 2Line 3Line 5Line 6 Line 1Line 7Line 8Line 9
Line 10 Line 11
Line 12
Line 13
Line 14
Line 15Line 16Line 17
Figure 2 One-line diagram for studied distribution system
and at 15 different line sections for obtaining a total of 3660(= 61 times 4 times 15) data 70 10 and 20 of these 3660 datawere used stochastically for training validating and testingthe proposed SVM respectivelyThe arc of HIF was modeledwith two antiparallel DC sources and diodes which wereconnected to a random resistor [2] The proposed methodswere implemented by MATLAB 70 (SimPowerSystems) ona C2D (Core 2 Due) 213 GHz computer (RAM 35G) Thedata-window size of the signal for processing in this paper isfive cycles
Because the power supply measurement facilities aremore expensive than general meters the number of measure-ment facilities is limited Discussion of purchasing the mea-surement facilities and determination of a proper number forthemeasurement facilities are beyond the scope of this paperHence 14 11 8 4 and 2 measurement facilities (ie 119862) areassumed to be available in this paper Table 1 illustrates theSVM information associated with measurements BecauseHIF energies of the first to third scales (119889
1sim 1198893) were consid-
ered the number of input neurons equals measurements (119862)multiplied by 3 These are cases 1sim5 Moreover the current atthe neural line of the main transformer is generally availableand can be utilized These are cases 6sim10 Finally four binarybits are sufficient for discriminating 15 line sections excludingprimary sides (line 1) and the main transformer (denoted byline 2) in this system
42 Feature Extraction by DWT As described in Sections 33and 34 the ldquoenergiesrdquo for HIF currents of the first to thirdscales at each line section are used as features for SVM inputsAssume that an HIF occurs (90∘) at line section 12 Figure 3shows the energy distribution of the neighborhood of linesection 12 (ie line sections 11 and 13) The energies for the
Table 1 SVM information associated with measurements
Facility number (119862) Input neurons Output neuronsCase 1 2 2 times 3 4Case 2 4 4 times 3 4Case 3 8 8 times 3 4Case 4 11 11 times 3 4Case 5 14 14 times 3 4Case 6 2 + 1 3 times 3 4Case 7 4 + 1 5 times 3 4Case 8 8 + 1 9 times 3 4Case 9 11 + 1 12 times 3 4Case 10 14 + 1 15 times 3 4
first to sixth scales at these three line sections are shown It isapparent that the normal energy and HIF energy are almostthe same for the current of the fourth (also for fifth and sixth)scale Hence current energies for the fourth to sixth scalescannot serve as features and only current energies for thefirst to third scales are considered further Please note thatthe energies are normalized to be per unit and are in termsof log
10because the energies of the fifth and sixth scales are
much larger than those of other scales
43 Scaled Energies at Line Sections AnHIF occurring at linesection 12 is discussed in this section Figure 4 illustrates theHIF currents in terms of the DWT-scaled energy distribu-tions at each line sectionThe vertical axis denotes the energymagnitude while the horizontal axis means the 119889
1sim 1198893at
each line section Please note that the energies are normalizedto be per unit
6 Mathematical Problems in Engineering
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(a) 1stndash6th normal and HIF energies at line section 11
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(b) 1stndash6th normal and HIF energies at line section 12
0
02
04
06
08
1
1 2 3 4 5 6Scales
Ener
gy (p
er u
nit)
NormalHIF
(c) 1stndash6th normal and HIF energies at line section 13
Figure 3 Energy distributions near faulted line
0010203040506070809
1
Line 1 Line 2 Line 3 Line 4 Line 5 Line 6
1st scale2nd scale
3rd scale
Ener
gy (p
er u
nit)
0010203040506070809
1
Line 7 Line 8 Line 9 Line 10 Line 11 Line 12
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
0010203040506070809
1
Line 13 Line 14 Line 15 Line 16 Line 17
Ener
gy (p
er u
nit)
1st scale2nd scale
3rd scale
Figure 4 HIF energy distributions at all line sections
Mathematical Problems in Engineering 7
Table 2 Different 119862s and corresponding clusters (119896-means)
When the busbar load varies and the HIF occurs atdistinct angles the above phenomena will be discriminatedHence the ldquoenergiesrdquo of the HIF currents of the first to thirdscales are important features for locating theHIF line section
44 Measurement Facility Placement Because 14 11 8 4 and2 power supply measurement facilities are assumed to beavailable in the test sample 119862 may be 14 11 8 4 or 2 and119873 = 3660 respectively (119862 and119873were defined in Section 31)For a given 119862 the same 3660 sets of data were employed toperform the HIF current energy clustering by the modified119896-means algorithm Table 2 illustrates the different 119862rsquos andcorresponding clusters Each cluster is quoted by parenthesesThe line section with an italic font in Table 2 denotes the oneinstalled with ameasurement facility Traditional FCM is alsoemployed to study the line section clustering as shown inTable 3 As can be seen some clusters obtained by the FCMare infeasible because lines in a cluster may not be adjacentto each other For example in the last row of Table 3 linesections 7 8 and 9 in a cluster are not adjacent to line sections10sim17
More specifically the condition for 119862 = 2 and 119888 = 2 inthe last row of Table 2 is described here Table 4 illustratesthe distances (norm) between 119883
119894 119894 = 3 4 17 and its
clustering center 1198812(119888 = 2) for 119862 = 2 As can be seen the
distance between 11988312
and 1198812is the smallest Therefore the
measurement facility is placed at line section 12In this paper the dimension of119883
119894is 1 times 3660 where 3660
is the number of scenarios from the test system Each elementof 119883119894is the total energy at line section 119894 for one of the 3660
cases Moreover there are 17 119883119894rsquos (number of lines) for the
18-busbar system where 17 is the line number
0
10
20
30
40
50
60
()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Energy ranges
HIFLIF
CS
Figure 5 Total energy disturbances for 3 different disturbances
45 Classification among HIF Short Circuit and SwitchingThere are 930 cases with short circuits (low-impedance faultsLIFs) and 620 cases with capacitor switching (CS) for furtherinvestigation of energy distributions Figure 5 shows the totalenergy of the first to third scales for different HIFs LIFs andCS The vertical axis denotes the percentage of occurrencefor the three individual disturbances The horizontal axisincludes 15 energy ranges (log
10) More specifically ranges 1
2 and 15 represent 348ndash356 357ndash365 and 1009ndash1079 purespectively It can be found that HIFs include smaller totalenergies from range 1 to range 5 Hence the total energy canbe employed to discriminate HIFs from other disturbancesfor example LIF and CS
46 Accuracy of Locating HIFs by SVM As described inSection 41 70 10 and 20 of the 3660 data are usedstochastically for training validating and testing respec-tively Table 5 illustrates the number of iterations CPU timefor training the SVM and the accuracy rate for the 10 casesdefined in Table 1 The following comments can be drawnfrom Table 5
(i) The numbers of iterations for all cases are almost thesame for the SVM despite the different number ofinput neurons
(ii) The CPU time required varies with the number ofinput neurons
(iii) Accuracy rates are greater than 99 except for cases 1and 6
(iv) Cases 1 and 6 with only two measurement facilitiesstill gain accuracy rate of 974 and 9836 respec-tively This result ensures the advantage of the pro-posed method using the SVM
(v) The neutral current at the substation improves accu-racy rates only for cases 1 and 2 (corresponding tocases 6 and 7) with fewer measurements
8 Mathematical Problems in Engineering
Table 4 Distances (times105) between 119883119894and its clustering center
This paper proposed a new method for locating the linesection with an HIF using DWT modified 119896-means andSVM Compared with the existing methods involving iden-tification of an HIF in a feeder (or transmission line) or inone of the multiple feeders from the secondary side of asubstation the proposed approach is able to locate anHIF linesection in a distribution system with multiple feeders usinga power supply monitoring system including multiple powersupply measurement facilities at different lines Classificationof disturbances and locating the HIF are addressed
The features (current energies) at three distinct scales(frequency bands) were extracted by MRA in DWT Thesefeatures provide important information for the SVM to locatethe line sectionwith anHIFMoreover the energies ofHIF arediscriminated obviously from those of LIF and CS
The simulation results obtained from an 18-busbar distri-bution system show that good accuracy can still be attainedusing only a few measurements (eg two in this paper) dueto the SVM Hence SVM is very useful when only a fewmeasurements are available
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors gratefully acknowledge the financial supportfrom the National Science Council Taiwan under Grant no96-2221-E-033-069-MY2
References
[1] K Y Lien S L Chen C J Liao T Y Guo T M Lin and J SShen ldquoEnergy variance criterion and threshold tuning schemefor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 14 no 3 pp 810ndash817 1999
[2] A E Emanuel D Cyganski J A Orr S Shiller and E MGulachenski ldquoHigh impedance fault arcing on sandy soil in15kV distribution feeders contributions to the evaluation of thelow frequency spectrumrdquo IEEE Transactions on Power Deliveryvol 5 no 2 pp 676ndash686 1990
[3] C H Kim H Kim Y H Ko S H Byun R K Aggarwal and AT Johns ldquoA novel fault-detection technique of high-impedancearcing faults in transmission lines using the wavelet transformrdquoIEEE Transactions on Power Delivery vol 17 no 4 pp 921ndash9292002
[4] A-R Sedighi M-R Haghifam O P Malik and M-H Ghas-semian ldquoHigh impedance fault detection based on wavelettransform and statistical pattern recognitionrdquo IEEE Transac-tions on Power Delivery vol 20 no 4 pp 2414ndash2421 2005
[5] T M Lai L A Snider E Lo and D Sutanto ldquoHigh-impedancefault detection using discrete wavelet transform and frequencyrange and RMS conversionrdquo IEEE Transactions on PowerDelivery vol 20 no 1 pp 397ndash407 2005
[6] M Michalik W Rebizant M R Lukowicz S J Lee and SH Kang ldquoHigh-impedance fault detection in distribution net-works with use of wavelet-based algorithmrdquo IEEE Transactionson Power Delivery vol 21 no 4 pp 1793ndash1802 2006
[7] Y Sheng and SM Rovnyak ldquoDecision tree-basedmethodologyfor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 19 no 2 pp 533ndash536 2004
[8] C S Burrus R A Gopinath and H Guo Introduction toWavelets and Wavelet Transforms Prentice Hall Upper SaddleRiver NJ USA 1998
[9] A Elmitwally S Farghal S Abdelkader and M Elkateb ldquoPro-posed wavelet-neurofuzzy combined system for power qualityviolations detection and diagnosisrdquo IEE Proceedings Genera-tion Transmission and Distribution vol 148 no 1 pp 15ndash202001
[10] L Angrisani P Daponte M DrsquoApuzzo and A Testa ldquoA mea-surement method based on the wavelet transform for powerquality analysisrdquo IEEE Transactions on Power Delivery vol 13no 4 pp 990ndash998 1998
[11] S Santoso E J PowersWM Grady and A C Parsons ldquoPowerquality disturbance waveform recognition using wavelet-basedneural classifier Part 1 theoretical foundationrdquo IEEE Transac-tions on Power Delivery vol 15 no 1 pp 222ndash228 2000
[12] H Mokhtari M Karimi-Ghartemani and M R IravanildquoExperimental performance evaluation of a wavelet-based on-line voltage detection method for power quality applicationsrdquoIEEE Transactions on Power Delivery vol 17 no 1 pp 161ndash1722002
[13] P K Dash S R Samantaray and G Panda ldquoFault classificationand section identification of an advanced series-compensatedtransmission line using support vector machinerdquo IEEE Trans-actions on Power Delivery vol 22 no 1 pp 67ndash73 2007
[14] D SrinivasanW S Ng and A C Liew ldquoNeural-network-basedsignature recognition for harmonic source identificationrdquo IEEETransactions on Power Delivery vol 21 no 1 pp 398ndash405 2006
Mathematical Problems in Engineering 9
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
When the busbar load varies and the HIF occurs atdistinct angles the above phenomena will be discriminatedHence the ldquoenergiesrdquo of the HIF currents of the first to thirdscales are important features for locating theHIF line section
44 Measurement Facility Placement Because 14 11 8 4 and2 power supply measurement facilities are assumed to beavailable in the test sample 119862 may be 14 11 8 4 or 2 and119873 = 3660 respectively (119862 and119873were defined in Section 31)For a given 119862 the same 3660 sets of data were employed toperform the HIF current energy clustering by the modified119896-means algorithm Table 2 illustrates the different 119862rsquos andcorresponding clusters Each cluster is quoted by parenthesesThe line section with an italic font in Table 2 denotes the oneinstalled with ameasurement facility Traditional FCM is alsoemployed to study the line section clustering as shown inTable 3 As can be seen some clusters obtained by the FCMare infeasible because lines in a cluster may not be adjacentto each other For example in the last row of Table 3 linesections 7 8 and 9 in a cluster are not adjacent to line sections10sim17
More specifically the condition for 119862 = 2 and 119888 = 2 inthe last row of Table 2 is described here Table 4 illustratesthe distances (norm) between 119883
119894 119894 = 3 4 17 and its
clustering center 1198812(119888 = 2) for 119862 = 2 As can be seen the
distance between 11988312
and 1198812is the smallest Therefore the
measurement facility is placed at line section 12In this paper the dimension of119883
119894is 1 times 3660 where 3660
is the number of scenarios from the test system Each elementof 119883119894is the total energy at line section 119894 for one of the 3660
cases Moreover there are 17 119883119894rsquos (number of lines) for the
18-busbar system where 17 is the line number
0
10
20
30
40
50
60
()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Energy ranges
HIFLIF
CS
Figure 5 Total energy disturbances for 3 different disturbances
45 Classification among HIF Short Circuit and SwitchingThere are 930 cases with short circuits (low-impedance faultsLIFs) and 620 cases with capacitor switching (CS) for furtherinvestigation of energy distributions Figure 5 shows the totalenergy of the first to third scales for different HIFs LIFs andCS The vertical axis denotes the percentage of occurrencefor the three individual disturbances The horizontal axisincludes 15 energy ranges (log
10) More specifically ranges 1
2 and 15 represent 348ndash356 357ndash365 and 1009ndash1079 purespectively It can be found that HIFs include smaller totalenergies from range 1 to range 5 Hence the total energy canbe employed to discriminate HIFs from other disturbancesfor example LIF and CS
46 Accuracy of Locating HIFs by SVM As described inSection 41 70 10 and 20 of the 3660 data are usedstochastically for training validating and testing respec-tively Table 5 illustrates the number of iterations CPU timefor training the SVM and the accuracy rate for the 10 casesdefined in Table 1 The following comments can be drawnfrom Table 5
(i) The numbers of iterations for all cases are almost thesame for the SVM despite the different number ofinput neurons
(ii) The CPU time required varies with the number ofinput neurons
(iii) Accuracy rates are greater than 99 except for cases 1and 6
(iv) Cases 1 and 6 with only two measurement facilitiesstill gain accuracy rate of 974 and 9836 respec-tively This result ensures the advantage of the pro-posed method using the SVM
(v) The neutral current at the substation improves accu-racy rates only for cases 1 and 2 (corresponding tocases 6 and 7) with fewer measurements
8 Mathematical Problems in Engineering
Table 4 Distances (times105) between 119883119894and its clustering center
This paper proposed a new method for locating the linesection with an HIF using DWT modified 119896-means andSVM Compared with the existing methods involving iden-tification of an HIF in a feeder (or transmission line) or inone of the multiple feeders from the secondary side of asubstation the proposed approach is able to locate anHIF linesection in a distribution system with multiple feeders usinga power supply monitoring system including multiple powersupply measurement facilities at different lines Classificationof disturbances and locating the HIF are addressed
The features (current energies) at three distinct scales(frequency bands) were extracted by MRA in DWT Thesefeatures provide important information for the SVM to locatethe line sectionwith anHIFMoreover the energies ofHIF arediscriminated obviously from those of LIF and CS
The simulation results obtained from an 18-busbar distri-bution system show that good accuracy can still be attainedusing only a few measurements (eg two in this paper) dueto the SVM Hence SVM is very useful when only a fewmeasurements are available
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors gratefully acknowledge the financial supportfrom the National Science Council Taiwan under Grant no96-2221-E-033-069-MY2
References
[1] K Y Lien S L Chen C J Liao T Y Guo T M Lin and J SShen ldquoEnergy variance criterion and threshold tuning schemefor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 14 no 3 pp 810ndash817 1999
[2] A E Emanuel D Cyganski J A Orr S Shiller and E MGulachenski ldquoHigh impedance fault arcing on sandy soil in15kV distribution feeders contributions to the evaluation of thelow frequency spectrumrdquo IEEE Transactions on Power Deliveryvol 5 no 2 pp 676ndash686 1990
[3] C H Kim H Kim Y H Ko S H Byun R K Aggarwal and AT Johns ldquoA novel fault-detection technique of high-impedancearcing faults in transmission lines using the wavelet transformrdquoIEEE Transactions on Power Delivery vol 17 no 4 pp 921ndash9292002
[4] A-R Sedighi M-R Haghifam O P Malik and M-H Ghas-semian ldquoHigh impedance fault detection based on wavelettransform and statistical pattern recognitionrdquo IEEE Transac-tions on Power Delivery vol 20 no 4 pp 2414ndash2421 2005
[5] T M Lai L A Snider E Lo and D Sutanto ldquoHigh-impedancefault detection using discrete wavelet transform and frequencyrange and RMS conversionrdquo IEEE Transactions on PowerDelivery vol 20 no 1 pp 397ndash407 2005
[6] M Michalik W Rebizant M R Lukowicz S J Lee and SH Kang ldquoHigh-impedance fault detection in distribution net-works with use of wavelet-based algorithmrdquo IEEE Transactionson Power Delivery vol 21 no 4 pp 1793ndash1802 2006
[7] Y Sheng and SM Rovnyak ldquoDecision tree-basedmethodologyfor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 19 no 2 pp 533ndash536 2004
[8] C S Burrus R A Gopinath and H Guo Introduction toWavelets and Wavelet Transforms Prentice Hall Upper SaddleRiver NJ USA 1998
[9] A Elmitwally S Farghal S Abdelkader and M Elkateb ldquoPro-posed wavelet-neurofuzzy combined system for power qualityviolations detection and diagnosisrdquo IEE Proceedings Genera-tion Transmission and Distribution vol 148 no 1 pp 15ndash202001
[10] L Angrisani P Daponte M DrsquoApuzzo and A Testa ldquoA mea-surement method based on the wavelet transform for powerquality analysisrdquo IEEE Transactions on Power Delivery vol 13no 4 pp 990ndash998 1998
[11] S Santoso E J PowersWM Grady and A C Parsons ldquoPowerquality disturbance waveform recognition using wavelet-basedneural classifier Part 1 theoretical foundationrdquo IEEE Transac-tions on Power Delivery vol 15 no 1 pp 222ndash228 2000
[12] H Mokhtari M Karimi-Ghartemani and M R IravanildquoExperimental performance evaluation of a wavelet-based on-line voltage detection method for power quality applicationsrdquoIEEE Transactions on Power Delivery vol 17 no 1 pp 161ndash1722002
[13] P K Dash S R Samantaray and G Panda ldquoFault classificationand section identification of an advanced series-compensatedtransmission line using support vector machinerdquo IEEE Trans-actions on Power Delivery vol 22 no 1 pp 67ndash73 2007
[14] D SrinivasanW S Ng and A C Liew ldquoNeural-network-basedsignature recognition for harmonic source identificationrdquo IEEETransactions on Power Delivery vol 21 no 1 pp 398ndash405 2006
Mathematical Problems in Engineering 9
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
When the busbar load varies and the HIF occurs atdistinct angles the above phenomena will be discriminatedHence the ldquoenergiesrdquo of the HIF currents of the first to thirdscales are important features for locating theHIF line section
44 Measurement Facility Placement Because 14 11 8 4 and2 power supply measurement facilities are assumed to beavailable in the test sample 119862 may be 14 11 8 4 or 2 and119873 = 3660 respectively (119862 and119873were defined in Section 31)For a given 119862 the same 3660 sets of data were employed toperform the HIF current energy clustering by the modified119896-means algorithm Table 2 illustrates the different 119862rsquos andcorresponding clusters Each cluster is quoted by parenthesesThe line section with an italic font in Table 2 denotes the oneinstalled with ameasurement facility Traditional FCM is alsoemployed to study the line section clustering as shown inTable 3 As can be seen some clusters obtained by the FCMare infeasible because lines in a cluster may not be adjacentto each other For example in the last row of Table 3 linesections 7 8 and 9 in a cluster are not adjacent to line sections10sim17
More specifically the condition for 119862 = 2 and 119888 = 2 inthe last row of Table 2 is described here Table 4 illustratesthe distances (norm) between 119883
119894 119894 = 3 4 17 and its
clustering center 1198812(119888 = 2) for 119862 = 2 As can be seen the
distance between 11988312
and 1198812is the smallest Therefore the
measurement facility is placed at line section 12In this paper the dimension of119883
119894is 1 times 3660 where 3660
is the number of scenarios from the test system Each elementof 119883119894is the total energy at line section 119894 for one of the 3660
cases Moreover there are 17 119883119894rsquos (number of lines) for the
18-busbar system where 17 is the line number
0
10
20
30
40
50
60
()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Energy ranges
HIFLIF
CS
Figure 5 Total energy disturbances for 3 different disturbances
45 Classification among HIF Short Circuit and SwitchingThere are 930 cases with short circuits (low-impedance faultsLIFs) and 620 cases with capacitor switching (CS) for furtherinvestigation of energy distributions Figure 5 shows the totalenergy of the first to third scales for different HIFs LIFs andCS The vertical axis denotes the percentage of occurrencefor the three individual disturbances The horizontal axisincludes 15 energy ranges (log
10) More specifically ranges 1
2 and 15 represent 348ndash356 357ndash365 and 1009ndash1079 purespectively It can be found that HIFs include smaller totalenergies from range 1 to range 5 Hence the total energy canbe employed to discriminate HIFs from other disturbancesfor example LIF and CS
46 Accuracy of Locating HIFs by SVM As described inSection 41 70 10 and 20 of the 3660 data are usedstochastically for training validating and testing respec-tively Table 5 illustrates the number of iterations CPU timefor training the SVM and the accuracy rate for the 10 casesdefined in Table 1 The following comments can be drawnfrom Table 5
(i) The numbers of iterations for all cases are almost thesame for the SVM despite the different number ofinput neurons
(ii) The CPU time required varies with the number ofinput neurons
(iii) Accuracy rates are greater than 99 except for cases 1and 6
(iv) Cases 1 and 6 with only two measurement facilitiesstill gain accuracy rate of 974 and 9836 respec-tively This result ensures the advantage of the pro-posed method using the SVM
(v) The neutral current at the substation improves accu-racy rates only for cases 1 and 2 (corresponding tocases 6 and 7) with fewer measurements
8 Mathematical Problems in Engineering
Table 4 Distances (times105) between 119883119894and its clustering center
This paper proposed a new method for locating the linesection with an HIF using DWT modified 119896-means andSVM Compared with the existing methods involving iden-tification of an HIF in a feeder (or transmission line) or inone of the multiple feeders from the secondary side of asubstation the proposed approach is able to locate anHIF linesection in a distribution system with multiple feeders usinga power supply monitoring system including multiple powersupply measurement facilities at different lines Classificationof disturbances and locating the HIF are addressed
The features (current energies) at three distinct scales(frequency bands) were extracted by MRA in DWT Thesefeatures provide important information for the SVM to locatethe line sectionwith anHIFMoreover the energies ofHIF arediscriminated obviously from those of LIF and CS
The simulation results obtained from an 18-busbar distri-bution system show that good accuracy can still be attainedusing only a few measurements (eg two in this paper) dueto the SVM Hence SVM is very useful when only a fewmeasurements are available
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors gratefully acknowledge the financial supportfrom the National Science Council Taiwan under Grant no96-2221-E-033-069-MY2
References
[1] K Y Lien S L Chen C J Liao T Y Guo T M Lin and J SShen ldquoEnergy variance criterion and threshold tuning schemefor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 14 no 3 pp 810ndash817 1999
[2] A E Emanuel D Cyganski J A Orr S Shiller and E MGulachenski ldquoHigh impedance fault arcing on sandy soil in15kV distribution feeders contributions to the evaluation of thelow frequency spectrumrdquo IEEE Transactions on Power Deliveryvol 5 no 2 pp 676ndash686 1990
[3] C H Kim H Kim Y H Ko S H Byun R K Aggarwal and AT Johns ldquoA novel fault-detection technique of high-impedancearcing faults in transmission lines using the wavelet transformrdquoIEEE Transactions on Power Delivery vol 17 no 4 pp 921ndash9292002
[4] A-R Sedighi M-R Haghifam O P Malik and M-H Ghas-semian ldquoHigh impedance fault detection based on wavelettransform and statistical pattern recognitionrdquo IEEE Transac-tions on Power Delivery vol 20 no 4 pp 2414ndash2421 2005
[5] T M Lai L A Snider E Lo and D Sutanto ldquoHigh-impedancefault detection using discrete wavelet transform and frequencyrange and RMS conversionrdquo IEEE Transactions on PowerDelivery vol 20 no 1 pp 397ndash407 2005
[6] M Michalik W Rebizant M R Lukowicz S J Lee and SH Kang ldquoHigh-impedance fault detection in distribution net-works with use of wavelet-based algorithmrdquo IEEE Transactionson Power Delivery vol 21 no 4 pp 1793ndash1802 2006
[7] Y Sheng and SM Rovnyak ldquoDecision tree-basedmethodologyfor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 19 no 2 pp 533ndash536 2004
[8] C S Burrus R A Gopinath and H Guo Introduction toWavelets and Wavelet Transforms Prentice Hall Upper SaddleRiver NJ USA 1998
[9] A Elmitwally S Farghal S Abdelkader and M Elkateb ldquoPro-posed wavelet-neurofuzzy combined system for power qualityviolations detection and diagnosisrdquo IEE Proceedings Genera-tion Transmission and Distribution vol 148 no 1 pp 15ndash202001
[10] L Angrisani P Daponte M DrsquoApuzzo and A Testa ldquoA mea-surement method based on the wavelet transform for powerquality analysisrdquo IEEE Transactions on Power Delivery vol 13no 4 pp 990ndash998 1998
[11] S Santoso E J PowersWM Grady and A C Parsons ldquoPowerquality disturbance waveform recognition using wavelet-basedneural classifier Part 1 theoretical foundationrdquo IEEE Transac-tions on Power Delivery vol 15 no 1 pp 222ndash228 2000
[12] H Mokhtari M Karimi-Ghartemani and M R IravanildquoExperimental performance evaluation of a wavelet-based on-line voltage detection method for power quality applicationsrdquoIEEE Transactions on Power Delivery vol 17 no 1 pp 161ndash1722002
[13] P K Dash S R Samantaray and G Panda ldquoFault classificationand section identification of an advanced series-compensatedtransmission line using support vector machinerdquo IEEE Trans-actions on Power Delivery vol 22 no 1 pp 67ndash73 2007
[14] D SrinivasanW S Ng and A C Liew ldquoNeural-network-basedsignature recognition for harmonic source identificationrdquo IEEETransactions on Power Delivery vol 21 no 1 pp 398ndash405 2006
Mathematical Problems in Engineering 9
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
This paper proposed a new method for locating the linesection with an HIF using DWT modified 119896-means andSVM Compared with the existing methods involving iden-tification of an HIF in a feeder (or transmission line) or inone of the multiple feeders from the secondary side of asubstation the proposed approach is able to locate anHIF linesection in a distribution system with multiple feeders usinga power supply monitoring system including multiple powersupply measurement facilities at different lines Classificationof disturbances and locating the HIF are addressed
The features (current energies) at three distinct scales(frequency bands) were extracted by MRA in DWT Thesefeatures provide important information for the SVM to locatethe line sectionwith anHIFMoreover the energies ofHIF arediscriminated obviously from those of LIF and CS
The simulation results obtained from an 18-busbar distri-bution system show that good accuracy can still be attainedusing only a few measurements (eg two in this paper) dueto the SVM Hence SVM is very useful when only a fewmeasurements are available
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors gratefully acknowledge the financial supportfrom the National Science Council Taiwan under Grant no96-2221-E-033-069-MY2
References
[1] K Y Lien S L Chen C J Liao T Y Guo T M Lin and J SShen ldquoEnergy variance criterion and threshold tuning schemefor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 14 no 3 pp 810ndash817 1999
[2] A E Emanuel D Cyganski J A Orr S Shiller and E MGulachenski ldquoHigh impedance fault arcing on sandy soil in15kV distribution feeders contributions to the evaluation of thelow frequency spectrumrdquo IEEE Transactions on Power Deliveryvol 5 no 2 pp 676ndash686 1990
[3] C H Kim H Kim Y H Ko S H Byun R K Aggarwal and AT Johns ldquoA novel fault-detection technique of high-impedancearcing faults in transmission lines using the wavelet transformrdquoIEEE Transactions on Power Delivery vol 17 no 4 pp 921ndash9292002
[4] A-R Sedighi M-R Haghifam O P Malik and M-H Ghas-semian ldquoHigh impedance fault detection based on wavelettransform and statistical pattern recognitionrdquo IEEE Transac-tions on Power Delivery vol 20 no 4 pp 2414ndash2421 2005
[5] T M Lai L A Snider E Lo and D Sutanto ldquoHigh-impedancefault detection using discrete wavelet transform and frequencyrange and RMS conversionrdquo IEEE Transactions on PowerDelivery vol 20 no 1 pp 397ndash407 2005
[6] M Michalik W Rebizant M R Lukowicz S J Lee and SH Kang ldquoHigh-impedance fault detection in distribution net-works with use of wavelet-based algorithmrdquo IEEE Transactionson Power Delivery vol 21 no 4 pp 1793ndash1802 2006
[7] Y Sheng and SM Rovnyak ldquoDecision tree-basedmethodologyfor high impedance fault detectionrdquo IEEETransactions onPowerDelivery vol 19 no 2 pp 533ndash536 2004
[8] C S Burrus R A Gopinath and H Guo Introduction toWavelets and Wavelet Transforms Prentice Hall Upper SaddleRiver NJ USA 1998
[9] A Elmitwally S Farghal S Abdelkader and M Elkateb ldquoPro-posed wavelet-neurofuzzy combined system for power qualityviolations detection and diagnosisrdquo IEE Proceedings Genera-tion Transmission and Distribution vol 148 no 1 pp 15ndash202001
[10] L Angrisani P Daponte M DrsquoApuzzo and A Testa ldquoA mea-surement method based on the wavelet transform for powerquality analysisrdquo IEEE Transactions on Power Delivery vol 13no 4 pp 990ndash998 1998
[11] S Santoso E J PowersWM Grady and A C Parsons ldquoPowerquality disturbance waveform recognition using wavelet-basedneural classifier Part 1 theoretical foundationrdquo IEEE Transac-tions on Power Delivery vol 15 no 1 pp 222ndash228 2000
[12] H Mokhtari M Karimi-Ghartemani and M R IravanildquoExperimental performance evaluation of a wavelet-based on-line voltage detection method for power quality applicationsrdquoIEEE Transactions on Power Delivery vol 17 no 1 pp 161ndash1722002
[13] P K Dash S R Samantaray and G Panda ldquoFault classificationand section identification of an advanced series-compensatedtransmission line using support vector machinerdquo IEEE Trans-actions on Power Delivery vol 22 no 1 pp 67ndash73 2007
[14] D SrinivasanW S Ng and A C Liew ldquoNeural-network-basedsignature recognition for harmonic source identificationrdquo IEEETransactions on Power Delivery vol 21 no 1 pp 398ndash405 2006
Mathematical Problems in Engineering 9
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
[15] P Janik and T Lobos ldquoAutomated classification of power-quality disturbances using SVM and RBF networksrdquo IEEETransactions on Power Delivery vol 21 no 3 pp 1663ndash16692006
[16] S Fan and L Chen ldquoShort-term load forecasting based on anadaptive hybrid methodrdquo IEEE Transactions on Power Systemsvol 21 no 1 pp 392ndash401 2006
[17] L S Moulin A P Alves Da Silva M A El-Sharkawi and R JMarks II ldquoSupport vector machines for transient stability anal-ysis of large-scale power systemsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 818ndash825 2004
[18] N K Bose and P Liang Neural Network Fundamentals withGraphs Algorithms and Applications McGraw-Hill New YorkNY USA 1996
[19] Y K Lam and P W M Tsang ldquoeXploratory K-Means a newsimple and efficient algorithm for gene clusteringrdquo Applied SoftComputing Journal vol 12 no 3 pp 1149ndash1157 2012
[20] T Velmurugan ldquoPerformance based analysis between k-Meansand Fuzzy C-Means clustering algorithms for connection ori-ented telecommunication datardquo Applied Soft Computing Jour-nal vol 19 pp 134ndash146 2014
[21] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquo Computers amp Geosciences vol 10 no 2-3pp 191ndash203 1984
[22] D Datta ldquoUnit commitment problemwith ramp rate constraintusing a binary-real-coded genetic algorithmrdquo Applied SoftComputing Journal vol 13 no 9 pp 3873ndash3883 2013
[23] M Jamil A Kalam A Q Ansari andM Rizwan ldquoGeneralizedneural network and wavelet transform based approach forfault location estimation of a transmission linerdquo Applied SoftComputing vol 19 pp 322ndash332 2014
[24] D Bayram and S Seker ldquoWavelet basedNeuro-Detector for lowfrequencies of vibration signals in electric motorsrdquo Applied SoftComputing Journal vol 13 no 5 pp 2683ndash2691 2013
[25] H Eristi ldquoFault diagnosis system for series compensated trans-mission line based on wavelet transform and adaptive neuro-fuzzy inference systemrdquo Measurement vol 46 no 1 pp 393ndash401 2013
[26] S Ekici ldquoSupport Vector Machines for classification and locat-ing faults on transmission linesrdquo Applied Soft Computing Jour-nal vol 12 no 6 pp 1650ndash1658 2012
[27] MMatsumoto and J Hori ldquoClassification of silent speech usingsupport vector machine and relevance vector machinerdquoAppliedSoft Computing Journal vol 20 pp 95ndash102 2014
[28] K S Chua ldquoEfficient computations for large least square sup-port vectormachine classifiersrdquo Pattern Recognition Letters vol24 no 1ndash3 pp 75ndash80 2003
[29] WMGradyM J Samotyj andAHNoyola ldquoMinimizing net-work harmonic voltage distortion with an active power lineconditionerrdquo IEEE Transactions on Power Delivery vol 6 no4 pp 1690ndash1697 1991
![Page 1: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/1.jpg)
![Page 2: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/2.jpg)
![Page 3: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/3.jpg)
![Page 4: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/4.jpg)
![Page 5: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/5.jpg)
![Page 6: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/6.jpg)
![Page 7: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/7.jpg)
![Page 8: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/8.jpg)
![Page 9: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/9.jpg)
![Page 10: Research Article Locating High-Impedance Fault Section in ...downloads.hindawi.com/journals/mpe/2015/823720.pdfdisplacement [ ], were considered for detection. ere was no salient result](https://reader033.documents.pub/reader033/viewer/2022060703/606fdedabb066d2f20482bce/html5/thumbnails/10.jpg)
![University of Exeter · (scra ps) 40 (scraps) 507 (indented) Civ 200 SJ 609 Civ 40 FRB Civ 5 40 FRB PRI) Civ 5 40 PRI) 200 S] 527 ... 225 ERE ERE ERE ERE ERE ERE ERE ERE 750 40 1000](https://static.documents.pub/doc/80x56/60837eaeb9acca7ec204cbf1/university-of-exeter-scra-ps-40-scraps-507-indented-civ-200-sj-609-civ-40.jpg)
