Research Article Accurate Fault Classifier and Locator for...

Research ArticleAccurate Fault Classifier and Locator for EHV TransmissionLines Based on Artificial Neural Networks

Moez Ben Hessine and Souad Ben Saber

Latice Laboratory at Higher National Engineering School of Tunis ENSIT University of Tunis 05 Avenue Taha HusseinMontfleury 1008 Tunis Tunisia

Correspondence should be addressed to Moez Ben Hessine benhessinemoezyahoofr

Received 6 March 2014 Revised 31 May 2014 Accepted 31 May 2014 Published 15 July 2014

Academic Editor Haipeng Peng

Copyright copy 2014 M Ben Hessine and S Ben Saber This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The ability to identify the fault type and to locate the fault in extra high voltage transmission lines is very important for the economicoperation of modern power systems Accurate algorithms for fault classification and location based on artificial neural network aresuggested in this paper Two fault classification algorithms are presented the first one uses the single ANN approach and the secondone uses the modular ANN approach A comparative study of two classifiers is done in order to choose which ANN fault classifierstructure leads to the best performance Design and implementation of modular ANN-based fault locator are presentedThree faultlocators are proposed and a comparative study of the three fault locators is carried out in order to determine which fault locatorarchitecture leads to the accurate fault location Instantaneous current andor voltage samples were used as inputs to ANNs Forfault classification only the pre-fault and post-fault samples of three-phase currents were used For fault location pre-fault andpost-fault samples of three-phase currents andor voltages were usedThe proposed algorithms were evaluated under different faultscenarios Studied simulation results which are presented confirm the effectiveness of the proposed algorithms

1 Introduction

The design of the high performance protection techniquesremains an important subject for the development within theuniversity community and the industry Indeed a transmis-sion line is an important element of the electrical power sys-temNevertheless transmission lines present the highest faultappearance rate considering the environmental conditionswhich are subjected Hence the protective relaying systemsare integrated in transmission lines to quickly detect faultsoccurrence and to isolate the faulted part from the rest ofpower system as soon as possible These protective relayingsystems serve to ensure the power system stability minimizedamage equipment and restore the service quality For trans-mission line protections various algorithms were proposedin the literature In the 70s travelling wave techniques wereintroduced into the transmission line protection algorithms[1] However most researchers [2ndash4] mentioned that themethod founded on the travelling wave does not functionwell for the faults near the relaying site and for faults havingsmall fault inception angles The synchronized measurement

technology seems to be a promising perspective to obtainreal time protection With the global positioning system(GPS) digital measurement of the three-phase current andvoltage signals for the two line ends can be carried outinto a synchronous manner [5ndash8] These techniques aremore precise than the distance relaying protection algorithmswhich are affected by the insufficient transmission linemodeling and the parameter uncertainty due to the aging oflines Moreover these techniques require the installation ofa GPS where the measurements are synchronized comparedto a GPS clock Nevertheless the synchronized measurementtechnology presents many drawbacks as the high cost andthe presence of a communication channel between the lineterminals which is not available in the majority of linesTherefore the fault diagnosis techniques using one-terminaldata could be more attractive for researchers In this contextit is necessary to develop algorithms having the ability toadapt dynamically with the system operating conditions suchas the system configuration changes and the fault conditions(fault resistance fault inception angle and fault position)Recently modern technologies of the protection relays are

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 240565 19 pageshttpdxdoiorg1011552014240565

2 Mathematical Problems in Engineering

based on artificial intelligence tools such as fuzzy logic (FL)artificial neural networks (ANNs) and the adaptive network-based fuzzy inference system (ANFIS) Fuzzy logic-basedtransmission line relaying techniques for fault classificationand fault location are proposed by many researchers [9ndash11] However these techniques cannot in any way guaranteeprecision results for wide variation of faultconditions (highfault resistance high fault inception angle and far distancelocation from relay site) A recent study [12] has proposed analgorithm having the synergy to calculate with high precisionthe fault locations at distances less than 80of the line lengthIn [13] a fault classification algorithm based on fuzzy logicsystem is presented Nevertheless this algorithm is valid onlyfor a less range variety of fault resistance

Other protection relaying researchers have used theadaptive network-based fuzzy inference system (ANFIS) [14ndash17] In [18] a fault detection and classification scheme isdeveloped This technique uses three-phase currents andzero sequence current but the fault location procedure isnot indicated In [19] a fault classification and locationalgorithms for combined overhead transmission line havebeen proposed The current and voltage samples are usedfor the proposed scheme These values were obtained withinone cycle after the fault inception that implies a responsetime superior than one operating cycle The protection faultapproaches based on fuzzy logic (FL) and adaptive networkfuzzy inference system (ANFIS) techniques are sensitive tothe system frequency variations and require large trainingsets

The artificial neural networks were integrated in the pro-tection relaying techniques These techniques used samplesof current andor voltage without calculating the symmet-rical components [1] Various neural network types suchas the multilayer perceptron (MLP) radial basis function(RBF) and probabilistic neural network are applied forfault diagnosis in transmission lines [20ndash24] The protectionapproaches based on ANNs were used for the developmentof reliable accurate and rapid algorithms in real time forfault detection classification and location In this context[25] developed an application of radial basic function (RBF)neural network applied to fault location in transmission linesThe maximum error of the proposed algorithm is equal to05 Besides [26 27] developed neural network approachesfor fault detection and fault location in transmission linesNevertheless these approaches detect only the faults whichappeared in the first zone of the line namely 80 of thetransmission line length In [28] a fault location algorithmfor transmission lines was developed The algorithm usesa single artificial neural network based on the Levenberg-Marquardt optimization technique However the fault typeis not indicated and the percentage error of the algorithmis maintained below 065 In [29] fault classification andlocation schemes are proposed These schemes use three-phase currents and voltages waveforms at one terminal lineThe response time of the proposed scheme is not indicatedand the percentage error for fault location is equal to 3 In[30] a new scheme for fault classification and fault locationis presented The maximum error of the proposed scheme is305 and the response time is not indicated Reference [31]

proposed a fault location module for fault diagnosis whichincorporates two stages adaptive structures neural networkThe fault detection classification and location algorithmsare presented with average fault location error of 04 and05411 The results show clearly that this approach leads toa reliable location for all types of faults The operating timeof this method is equal to 128 cycles after inception fault In[32] fault distance and direction estimation based on ANNfor protection of doubly fed transmission lines are proposedbut the fault type is not indicated The operating time of thisapproach is about 15 cycles and the percentage error rate offault location lies between 0052 and 157

In order to develop fault classification and locationalgorithms leading to desired results with a good precisionand fast response time compared to former work we haveproposed in the present paper a new fault classification andlocation algorithms based on ANNs Thus optimal neuralnetworks architecture used in the fault classification andlocation algorithms (number of hidden layers number ofneurons in hidden layers reduced training sets fast conver-gence to the desired results and reliability and precision ofprotection algorithms) were proposed These algorithms arebased on artificial neural networks (ANNs) (feed-forward)trained by a supervised learning algorithm called back-propagation In this context two fault classifiers are proposedthe first one uses a single ANN approach and the secondone uses a modular ANN approach A comparative study ofthe proposed two fault classifiers is carried out in order todetermine which reliable and effective ANN fault classifierleads to the best performance For fault location three faultlocators based on modular ANN approach are proposed inorder to choose an optimal architecture strategy with a highprecision and fast convergence to the exact fault locationThefault neural classifiers and locators were trained and testedunder different fault conditions (fault types fault locationsfault resistances and fault inception angles) The simulationresults show clearly the high accuracy of the proposed faultclassification and location algorithms

2 Power System under Study

To evaluate the performance of the proposed neural network-based fault detector and locator a 400 kV 100 km transmis-sion line extending between two sources is considered in thisstudy The power system model simulated using MATLABsoftware is shown in Figure 1 It contains a synchronousgenerator (driven by hydraulic turbine) connected to aninfinite bus The transmission line has been represented bydistributed parameter of one line model using Power Systemtoolbox of MATLAB software and the frequency dependenceof the line parameters is taken into account The proposedfault classification and location algorithms require only thethree-phase voltages andor currents samples at the sendingend of the transmission lines A large number of fault samplesdata have been generated using MATLAB considering widevariations on fault conditions such as fault locations faultresistances fault inception angle and fault types Using thesedata fault classification and location have been carried out

Mathematical Problems in Engineering 3

Vang0S V

ang120575119871R

CT

VT

Bus i

CBTransformer

Relay

Synchr Gen615 MVA

Transmission lineInfinite bus

400 Kv

Bus j

Transmission line model

Fault

FLf middot Zline (1 minus Lf) middot Zline

Lf middot Ycc

2

Lf middot Ycc

2

(1 minus Lf) middot Ycc

2


2

CT current transformerVT voltage transformer

CB circuit breaker

120575L load angleLf fault location

Figure 1 System under study

by means of MATLAB that make use of its ldquoneural networktoolboxrdquo

The transmission line parameters are as follows

(i) line length = 100 km(ii) voltage = 400Kv(iii) transmission line impedance

(a) positive sequence impedance = 00275 +1198950422Ωkm

(b) zero sequence impedance = 0275 +1198951169Ωkm

(c) positive sequence capacitance = 9483 nFkm(d) zero sequence capacitance = 6711 nFkm

We adopted for the synchronous generator a fourth stateorder model as follows [33ndash37]

1198891198641015840119902

119889119905=

1

1198791015840119889119900

sdot [119864119891119889minus 1198641015840

119902+ (119883119889minus 1198831015840

119889) sdot 119868119889]

1198891198641015840119889

119889119905=1

1198791015840119902119900

sdot [minus1198641015840

119889+ (119883119902minus 1198831015840

119902) sdot 119868119902]

119889120596

119889119905=1

119872sdot [119875119898minus 119875119890minus 119863 sdot (120596 minus 1)]

119889120575

119889119905= 120596 minus 1

(1)

where

1198641015840119889 1198641015840119902 and 119864

119891119889are respectively the (119889 119902) axe transient

emf and the emf excitation 119883119889 119883119902 1198831015840119889 and 1198831015840

119902are

respectively the (119889 119902) axe reactances and the (119889 119902)axe transient reactances119863 is the damping coefficient119872 is the inertia constant119875119890 119875119898 120596 and 120575 are respectively the electrical power

mechanical power speed and the rotor angle

In order to identify the fault type and to reach a highdegree of accuracy in the location of a fault in transmissionlines a series of contributions have been introduced toestimate the fault distance for transmission lines Currentlythe most widely used method of transmission lines faultlocation is to determine the apparent reactance of the lineduring the time that the fault current is flowing and to convertthe ohmic result into a distance based on the parameters ofthe line It is widely recognized that this method is subject toerrors when the fault resistance is high and the line is fed fromboth ends [38]

There is a need for the measuring algorithms that havethe ability to adapt dynamically to the system operatingconditions such as changes in the system configurationsource impedances and fault resistances Many successfulapplications based on artificial neural networks to power sys-tems have been demonstrated including security assessment[39] and load forecasting control [40] Recent applicationsin protection have covered fault diagnosis for electric powersystems [41] Hence in order to improve the former work


sum sum sum

sum sum sum

sum sum sum

y[0]1

y[0]2

y[0]3

y[0]n0

1 S L

f1 f2 f3

f1 f2 f3

f1 f2 f3

u[1]1 y[1]

1u[S]

1 y[S]1 u[L]

1 y[L]1

u[1]2 y[1]

2u[S]

2 y[S]2 u[L]

2 y[L]2

b1(1) bS(1) bL(1)

b1(2) bS(2) bL(2)

b1(n1) bS(ns) bL(nL)W[S]W[1] W[L]

u[1]n1

y[1]n1

u[S]nS

y[S]n119878

u[L]n119871

y[L]nL

Figure 2 Multilayer network model

results for fault classification and location in transmissionlines we have resorted towards the artificial neural networkstools

3 Artificial Neural Networks

The ANN represents a parallel multilayer information pro-cessing structure The characteristic feature of this networkis that it considers the accumulated knowledge acquiredduring training and responds to new events in the mostappropriate manner given the experiences gained during thetraining process ANNs imitate the learning process of thehuman brain and can process problems involving nonlinearand complex data even if the data are imprecise and noisyThe model of the ANN is determined according to networkarchitecture transfer function and the learning algorithmsGiven their diversification all the types of neural networksavailable nowadays cannot be listed easily The researchersare constantly endeavored to invent new types better suitedto resolve specific problems Among neural networks typesmultilayer perceptron (MLP) recurrent neural networkHopfield neural networks Kohonen neural networks and soforth can be cited

In the recent years the memristor-based recurrent neu-ral networks represent the main advanced neural networktechnologies which have been proposed and implemented invarious applications fields Some works of synchronizationcontrol problem of this type of networks have been evokedstudied and discussed by [42]

Authors have employed the differential inclusions theoryand the Lyapunov functional method in order to ensure theconvergence of the system to the equilibrium point Fur-thermore other several new neural networks architectureshave been proposed namely the dynamic recurrent neural

networks For these kinds of neural networks the dynamicsanalysis study is generally imposed [43ndash45]

Once the type and the architecture of a neural networkare selected for a given application it is necessary to performlearning algorithms able to determine the weight valuesallowing the output of the neural network from being as nearas possible to the referred aim

Learning neural network techniques are based on opti-mization algorithms that seek to minimize the gap betweenthe actual responses of the network and the desired responsesand this by changing the settings successively for any step(called ldquoepochsrdquo) Many learning algorithms have been usedsuch as back-propagation algorithm conjugate gradient algo-rithms quasi-Newton algorithms and Levenberg-Marquardtalgorithm Recently new learning algorithm is used fortraining the ANN such as genetic algorithms GA [46ndash48]particle swarm optimization algorithm PSO [49ndash51] andchaotic ant swarm optimization algorithm CAS [52ndash56]

In this paper the multilayer perceptron (MLP) neuralnetwork was used and trained with a supervised learningalgorithm called back-propagation

31 Multilayer Perceptron Neural Network Multilayer per-ceptron (MLP) is one of the most frequently used neuralnetwork architectures in various applications and it belongsto the class of supervised neural networks A typical multi-layer (MLP) neural network consists of three layers an inputlayer an output layer and one or more hidden layers Eachlayer consists of a predefined number of neurons We recallthat the neural network is a collection of cells of neuronsinterconnected by synaptic weights and biases The inputsare connected to the first hidden layer Each hidden layer isconnected to the next hidden layer and the last hidden layeris connected to the output layer (Figure 2)


Summingjunction

Activationfunction

Output

Synapticweights

Inpu

ts

Threshold

y[sminus1]1

y[sminus1]2

y[sminus1]n119904minus1

W[s]j1

W[s]j2

W[s]jn119904minus1

b[s]j

u[s]j

y[s]j

sum f(middot)

Figure 3 A basic structure of a neuron

The neuron used is a standard type It consists in makingthe sum of all the weighted inputs through its synapticcoefficients which represents the linear output and thenapplying it to an activation function The output obtainedis then connected to all inputs of the next layer The basicstructure of a neuron is shown in Figure 3

Aneuronmathematicalmodel has a very simple structurecompared to a biological neuron [57ndash59] Hence a neuron jcan be describedmathematically with the following equation

119910[119904]

119895= 119891(119887

[119904]

119895+

119899119904minus1

sum119894=1

119908[119904]

119895119894119910[119904minus1]

119894) (2)

where

119891 represent the transfer function (activation func-tion) of neuron 119895

119910[119904minus1]

119894 119894 = 1 119899

119904minus1 represents the inputs signals

of neuron 119895

119908[119904]

119895119894 represents theweight coefficients of the connec-

tion between inputs and neuron 119895

119887[119904]

119895is the bias of neuron 119895

A feed-forward NN consists of input hidden and out-put layers which is considered with 119875 119876 and 119877 neuronsfor each layer respectively In this structure [119910[119875]] =

[119910[119875]

1 119910[119875]

2 119910

[119875]

119875] which represents the inputs is applied

to the first layer then the inputs vectors are transferredto the hidden layer using the connection weight betweenthe input and the hidden layer The output vector [119910[119876]] =[119910[119876]

1 119910[119876]

2 119910

[119876]

119895 119910

[119876]

119875] of the hidden layer is then

obtained The neuron output 119910[119876]119895

is determined as follows

119910[119876]

119895= 119891hidden(119887

[119876]

119895+119875

sum119894=1

119908[119876]

119894119895119910[119875]

119894) (3)

where

119908[119876]

119894119895represents the connection weight between the

neuron 119895 in the hidden layer and the 119894th neuron ofthe input layer

119887[119876]

119895represents the bias of neuron 119895

119891hidden represents the activation function of the hid-den layer

The values of the vector 119910[119876]119895

of the hidden layer aretransferred to the output layer using the connection weightbetween the hidden layers and the output layer However theoutput vector [119910[119877]] = [119910

[119877]

1 119910[119877]

2 119910

[119877]

119896 119910

[119877]

119877] of the

output layer is determined The output 119910[119877]119896

of the neuron 119896(on the output layer) is obtained as follows

119910[119877]

119896= 119891out(119887

[119877]

119896+

119876

sum119895=1

119908[119877]

119895119896119910[119876]

119895) (4)

119908[119877]


neuron 119896 in the output layer and the 119895th neuron ofthe hidden layer119891out is the activation function of the output layer

The error in the output layer between the output 119910119896and

its desired value 119910119896-desired (119910119896 minus 119910119896-desired) is minimized by the

mean square error at the output layer defined as follows

Error = 12

119877

sum119896=1

(119910119896-desired minus 119910119896)

2

(5)

32 Back-Propagation Algorithm Back-propagation trainingalgorithm (BP) is an iterative gradient descent algorithmwhich is a simple way to train multilayer feed-forwardneural networks The BP algorithm has become the standardalgorithm used for training multilayer perceptron It is a gen-eralized least mean squares (LMS) algorithm that minimizesthe sumof the squares of the errors between the actual and thedesired outputs During training the weights and biases ofthe network are iteratively adjusted to minimize the networkperformance function

The main steps of the back-propagation algorithm aresum raised as in Algorithm 1

The training data set of an ANN should contain thenecessary information to generalize the problem In this


CT

VT

Transmission line

Currents Voltages

Antialiasing filter

Discrete Fourier transform (DFT)

ANN1 L-G

ANN4L-L-L

ANN3L-L-G

ANN2L-L

Sampling by 1 kHz

Window of 4 samples (5 ms)

ANN-based fault classifier

Magnitude of fundamentalcomponents of three-phase voltages

and currents

ANN-based fault location

Figure 4 Process for generating inputs patterns to the ANNs faultclassifier and fault locator

work different combinations of various fault conditionswere considered and training patterns were generated bysimulating a different fault situation on the power systemstudy Fault conditions such as fault resistance fault locationand fault inception angle were changed to obtain trainingpatterns covering a wide range of different power systemconditions

4 Configuration of Fault Classification andLocation System Using ANN

The fault classifier and fault locator configuration is shownin Figure 4 The protection relay inputs are presented by thevoltage and current waveforms acquired at the line end (relaylocation) via current transformer CT and voltage transformerVT These signals are used as inputs to the ANN-based faultclassifier and fault locator The phase current and voltagesignals extracted from the simulation at the relay locationare processed with an anti-aliasing filter in order to filter the

Step BP1 InitializationInitialize random matrices synoptic weight119882[119904] 119904 = 1 119871StepBP2 PropagationCalculate for each layer 119904 = 1 119871

119906[119904]119895=

119899119904minus1

sum119894=0

119908[119904]

119895119894119910[119904minus1]

119894

119910[119904]119895= 119891 (119906[119904]

119895)

StepBP3 Errors calculationCalculate local errors for(i) Output layer120575[119871]119895119901= 119890[119871]1198951199011198911015840 (119906[119871]119895119901)

(ii) Layers 119904 = 119871 minus 1 1

120575[119904]

119895119901= 1198911015840 (119906

[119904]

119895119901)

119899119904+1

sum119903=1

(120575[119904+1]

119895119901119908[119904+1]

119903119895)

119882[119904+1] is deprived of its first lineStepBP4 AdaptationModify the following synaptic weightsΔ119908[119904]

119895119894(119896) = 120583119910

[119904minus1]

119894119901120575[119904]

119895119901 119904 = 1 119871

StepBP5 Stop testTest the total squared Error

Algorithm 1 Steps of the back-propagation algorithm

higher order harmonics A simple 2nd-order low-pass Butterworth filter with cut-off frequency of 400Hz has been usedThree-phase voltages and currents waveforms are sampledat a sampling frequency of 1 KHz This sampling rate iscompatiblewith sampling rates presently used in digital relays[38] Furthermore a discrete Fourier transform (DFT) is usedto extract the fundamental components of these signalswhichare used as inputs to the ANN-based fault classifier and faultlocator On one side the proposed fault classifier is designedto identify the fault type and on the other side the faultlocator is designed to estimate the exact fault location in thetransmission line

The design process of the fault classifier and the faultlocator based on ANN is given by the following algorithmdepicted in Figure 5

41 Fault Classification

411 Inputs and Outputs A feed-forward neural networkof three layers trained by the back-propagation algorithm isselected for the fault classification task In this section twoneural fault classifiers are developedThe first classifier (FC

1)

based on the integration of single artificial neural network isused to classify the fault type which can affect a transmissionline The block diagram of the proposed single ANN-basedfault classifier (FC

1) is illustrated in Figure 6 The single

neural network conceived for the proposed fault classifier(FC1) takes into consideration the fundamental signals of the

three-phase currents and the zero sequence currents Thesesignals are sampled at a frequency of 1 kHz (20 samples per50Hz cycle) The inputs data for the single ANN-based-fault


Start

Obtain input data and target data from the simulation

Step 1

Assemble and preprocess the training data for the ANN

Test and conduct regression analysis

Store the trained network

End

Offline process

Online process

Step 2

Step 3

Step 4

Step 5

Step 6

Create the network object and

train the network until condition

of network setting parameters is

reached

Preprocess the new inputs before

they are subjected to the trained

network to obtain required data

Figure 5 The implementation procedures in the training of theANN

classifier are four prefault and four postfault for each phasecurrent and for the zero sequence current

The (119868119894(119896)119868119894minusPF(119896) with 119894 = 119877 119878 119879) are the per-unit

values calculated by the division of the samples currents infault time 119868

119894(119896) (postfault) to the prefault samples current

119868119894minusPF(119896) in related phase Consequently the selected inputnumbers for the fault classification algorithm (FC

1) are equal

to 16 four current samples for each phase (119877 119878 and 119879) andfour samples for zero sequence current The input vector ispresented according to the following equation

119883FC1

= [119868119877(119896)

119868119877minusPF (119896)

119868119877(119896 + 3)

119868119877minusPF (119896 minus 3)

119868119878(119896)

119868119878minusPF (119896)

119868119878(119896 + 3)

119868119878minusPF (119896 minus 3)

1

1

22

1

2

3

44

x1

x2

x4

w12

wn2

w14

w11

w21

w22

w24

wn4

w99840042

w99840023

w99840022

w99840011

w99840021

w99840031

w99840041

w9984002n

w9984003n

w9984004n

w99840012

w998400n1

w9984001n

R

S

T

G

n

Figure 6 A feed-forward multilayer for the fault classifier (FC1)

119868119879(119896)

119868119879minusPF (119896)

119868119879(119896 + 3)

119868119879minusPF (119896 minus 3)

1198680(119896) 119868

0(119896 + 3)]

(6)

The ANN outputs related to FC1are called 119877 119878 119879 and 119866

which represent the three phases and the ground If eachof the outputs 119877 119878 and 119879 is near to 1 this indicates thatfault occurred in this phase When the output 119866 takes thevalue 1 in this case the fault is related to ground Taking thefollowing example if the fault classifier output is 0101 thisindicates that the appearing fault is a single-phase fault whichhas occurred in the phase 119861 and connected to ground (119861-119866)In the same context an output 0110 shows that the fault whichhas occurred is a two-phase fault (119861-119862)

The second proposed fault classifier (FC2) used the mod-

ular ANN approach The proposed approach based on faultclassification consists of four independent artificial neuralnetworks one for each phase (119877 119878 and 119879) and another forfaults involving ground (119866) which are called ANN-119877 ANN-119878 ANN-119879 and ANN-119866 respectively The ANNs inputs arethe samples of currents signals and the outputs are presentedby the logic values (0 or 1) All network outputs are integratedto determine the fault type via a logic circuit see Figure 7Each network designed (ANN-119894 with 119894 = 119877 119878 and 119879)treated four prefault and four postfault samples for eachphase current Thus the ANN-119866 treats four samples of zerosequence current Figure 6 shows the schematic diagram ofthe proposed fault classification algorithm Consequently theinput numbers selected for each ANN-j(j = R STG) isequal to four currents samplesThus the total inputs numbernecessary to carry out the fault classification task via themodular ANN technique is equal to 16 normalized samplesThe input vector of each ANN-119894 (119894 = 119877 119878 and 119879) is called119883119894FC2

and for ANN-119866 is called 119883119866FC2

shown by the followingequation system

119883119894

FC2

= [119868119894(119896)

119868119894minusPF (119896)

119868119894(119896 + 3)

119868119894minusPF (119896 minus 3)

] 119894 = 119877 119878 119879

119883119866

FC2

= [1198680(119896) 119868

0(119896 + 3)]

(7)

The suggested modular structure of the proposed faultclassifier (FC

2) based on four independent artificial neural


AN

N-R

AN

N-S

AN

N-T

AN

N-G

1 ground fault0 not ground fault

middot middot middot middot middot middot middot middot middot middot middot middot

middot middot middot








I0(k) I0

0 no fault 0 no fault 0 no fault

Logic circuit for fault classification

Fault type

1 fault in phase R 1 fault in phase S 1 fault in phase T

IR(k)

IRminusPF(k)

IR(k + 3)

IRminusPF(k minus 3)IS(k)

ISminusPF(k)

IS(k + 3)

ISminusPF(k minus 3)IT(k)

ITminusPF(k)

IT(k + 3)

ITminusPF(k minus 3) (k + 3)

Figure 7 Modular ANN-based fault classifier (FC2)

Table 1 Neural network desired outputs

Type of faults Desired network outputs119877 119878 119879 119866

119877-119866 fault 1 0 0 1119878-119866 fault 0 1 0 1119879-119866 fault 0 0 1 1119877-119878 fault 1 1 0 0119877-119879 fault 1 0 1 0119879-119878 fault 0 1 1 0119877-119878-119866 fault 1 1 0 1119877-119879-119866 fault 1 0 1 1119879-119878-119866 fault 0 1 1 1119877-119878-119879 fault 1 1 1 0

networks (ANN-119877 ANN-119878 ANN-119879 and ANN-119866) at fouroutputs is detailed in Figure 7 Each artificial neural network(ANN-119877 ANN-119878 and ANN-119879) is designed to indicate thepresence or not of a fault in related phases (119877 119878 and 119879) andthe ANN-119866 is designed to indicate the involvement or not ofthe ground throughout the faultThus the ANNs outputs takethe logic value (0 or 1) indicating the absence or the presenceof a fault on the corresponding phase (119877 119878 and 119879) and ifthe fault is related to ground or not (119866) We notice that theoutputs admitting a value higher than 09 will be consideredto be active (presence of fault) and the outputs having a valuesmaller than 01 (absence of fault) will be considered to beinactive The various possible combinations can design thefault type The proposed modular neural network should beable to distinguish with precision between the ten faults typesaffecting one transmission line The neural network desiredoutputs for all the ten fault types are shown in Table 1

412 Training Data To lead to optimal and effective ANNarchitectures conceived for the fault classification task forthe two suggested fault classifiers (FC

1and FC

2) a suitable

Table 2 Training and test generation data of FC1 and FC2

Parameter Training Testing

Fault type

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

Fault location119871119891(km)

1 10 20 30 80and 90 km 12 56 78 and 94

Fault inceptionangle FIA (∘) 0∘ and 180∘ 0∘ 75∘ 135∘ and

225∘

Fault resistance119877119891(Ω) 01 and 100Ω 2 33 99 and 199

number of representative examples of the phenomenon inquestion must be selected Moreover the neural networksANNs can learn the fundamental characteristics of theproblem and provide correct outputs in new situations whichare not considered during the training process In order totrain each ANN to obtain sufficient examples we consideredvarious fault scenarios at different fault conditions such asdifferent fault locations (between 0 and 100 of line length)with various fault resistances119877

119891(01 100Ω) and various fault

inception angles FIA (0 and 90∘) The number of these fullscenarios is 10 fault locations lowast 2 fault resistances lowast 2 faultinception angles lowast 10 fault types = 400 fault cases destinedfor the ANN training process The parameter values used togenerate the data training sets and the ANN tests models forthe two adopted fault classifier types are illustrated in Table 2

413 Structure of the Neural Fault Classifier The determina-tion of hidden layers number and the number of neurons perlayer is very important considering that it affects the trainingtime and the generalization property of the neural networkThe most used approach to find adequate architectures isbased mainly on the various tests and various networkconfigurations After a series of ANN structure tests and


Tan-sigmoidtransfer function

Linear transferfunction

Input

Output

Hidden layer Output layer

IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1

Figure 8 Architecture of ANN-based fault classifier (FC1and FC

2)

Table 3 Architecture of modular ANN-based fault classifier (FC2)

Modular ANN-based fault classifier Architecture Mean square error (MSE) Number of epochsANN-119877 4-6-1 591e minus 06 12ANN-119878 4-5-1 785e minus 06 14ANN-119879 4-8-1 488e minus 06 10ANN-119866 4-6-1 597e minus 06 13

modification the best architecture obtained of each ANNis that which provides satisfactory results In this work thebest performance of the two proposed fault classifiers (FC

1

and FC2) is obtained by the three-layer neural network For

all ANNs used for the two proposed fault classifiers (FC1

and FC2) a ldquotan-sigmoidrdquo function was used as activation

function of the input layer and ldquopurelinrdquo function in theoutput layer Figure 8 shows the architecture of each ANNbased on fault classifier (FC

1and FC

2)

The numbers of hidden layer neuron for single ANNapproach based fault classifier (FC

1) are chosen initially as 5

and then increased in step to 10 15 20 25 to 30 as describedabove The best performance is achieved by using a three-layer neural network with 16 inputs and 4 outputs and theoptimal number of neurons in the hidden layer was found tobe 30 neurons In this learning strategy themean square error(mse) decreases in 100 epochs to 667119890minus06 in around 8minand 35 sec learning time on a PC (P4 213 GHz 2GB RAM)The single ANN approach based fault classifier (FC

1) requires

large training sets and long training time Also the networkcomplexity is higher and it has slower learning capabilityAlthough the procedure for development of the architectureof modular ANN-based fault classifier is the same as that ofsingle ANN-based fault classifier the training time is veryless for modular networks approximately 1min and 49 sec forall four modules and the final architecture of modular ANN-based fault classifier is shown in Table 3

414 Testing of the Fault Classifier In order to evaluate theperformances of the proposed fault classification algorithms(FC1and FC

2) based respectively on the single neural

network approach and themodular artificial neural networksapproach we consider various fault scenarios more thanthose taken into account during the training process Thesescenarios are subjected under various fault conditions suchas different fault locations 119871

119891 different fault resistances 119877

119891

and different fault inception angles FIA The tests results ofthe two proposed fault classifiers (FC

1and FC

2) are presented

in Table 4

The simulation results prove well the precision of the twoproposed algorithms Indeed ANN outputs converge to thedesired values (either very near to zero or one) However itcan be seen that from the tests results presented in Table 4the modular artificial neural network based on fault classifier(FC2) is more precise than the single artificial neural network

based on fault classifier (FC1) since the first one converges

towards the desired results with a minimum error comparedto the second classifier

An output of 08 or 09 given by one of the two suggestedfault classification algorithms represents the same result infault classification task and indicates at the same time afaulty phase whereas for a fault location task an outputof 08 implies a fault produced at a distance of 80 fromthe line length and an output of 09 means that the fault isproduced at a distance of 90 from the line length The faultlocation requires more precision than the fault classificationSo the use of single ANN approach for the fault locationtask presents disadvantages such as complexity ANN longtraining time and less accuracy compared to the modularANN approach as already seen for the fault classificationtask Consequently in order to estimate the exact faultlocation it was decided to develop an accurate fault locationalgorithm based on modular artificial neural networks

42 Fault Location The proposed fault location algorithmsin this part are based on the modular ANN approach Inthis approach during the appearance of a fault in transmis-sion line the fault detection and fault classification unitsidentify the fault appearance and its type Then it activatesthe fault location unit The fault classification unit will becapable of determining the fault type if it is single line toground (119871-119866) double lines (119871-119871) double lines to ground(119871-119871-119866) or three-line fault (119871-119871-119871) The proposed faultclassification unit based on modular ANN approach detectsand identifies the fault type Thus the outputs generated bythe fault classification unit activate the particular moduleof fault locator see Figure 9 The proposed fault locationalgorithm consists of four independent ANNs when each


Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G

Modular ANN-based faultclassifier

1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit

Inputs from fault typeclassifier

ANN1 L-G

Modular ANN-based faultlocator

ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf

Figure 9 The proposed modular ANN-based fault locator

fault type is trained by a neural network ANN-119896 with119896 = 119871-119866 119871-119871 119871-119871-119866 and 119871-119871-119871 The block diagram of theproposed fault location is shown in Figure 9

421 Inputs and Outputs The determination of the inputsand outputs number presents the principal factor in deter-mining the adequate size and the best architecture forthe neural network Hence the sufficient inputs data tocharacterize the problem must be assured In this contextthree fault locators are presented The first (FL

1) uses only

the magnitudes of the fundamental components of three-phase currents the second (FL

2) uses only the magnitudes

of the fundamental components of three-phase voltages andthe third (FL

3) uses at the same time the magnitudes of

the fundamental components of three-phase currents andvoltages The purpose of the fault location task is to estimatethe exact fault location Consequently only obtained outputsby the fault location algorithm corresponding to the faultdistance will be provided by the proposed modular neuralnetwork based on fault locator

Thus we indicated by InputFL1

InputFL2

and InputFL3

theinputs vectors taken by each proposed fault locator based onmodular ANN approach

InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]


Table 5 Training and test generation data of FL1 FL2 and FL3


Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879

Fault location 119871119891(km) 1 10 20 30 80 and 90 km 05 06 07 09 12 13 14 23 90 94 96 km

Fault inception angle FIA (∘) 0∘ 180∘ and 270∘ 5∘ 10∘ 25∘ 40∘ 225∘ 315∘ 360∘

Fault resistance 119877119891(Ω) 01 50 100 and 150Ω 26 10 22 26 190 195Ω

InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)

The output for fault location task is given by

OutputFL = [119871119891] (9)

422 Training Data A large number of training data fordifferent ANNs based on fault location task were generatedusing MATLAB software taking into account various faultscenarios subjected under different fault conditions such asdifferent fault locations 119871

119891(1 10 20 30 90 of

line length) different fault inception angles FIA (0∘ 180∘and 270∘) and various fault resistances 119877

119891(01Ω 50Ω

100Ω and 150Ω) Thus the simulated fault numbers forthe ANNs training process are equal to 648 for the faultrelated to ground 6 (fault types) lowast 9 (fault location) lowast 4 (faultresistance) lowast 3 (fault inception angles) For faults which didnot involve ground the number of fault simulation is equalto 108 simulation cases 9 (fault locations) times 4 (fault types) times3 (fault inception angles) Consequently the full number ofsimulated faults is 756 Table 5 presents the parameter valuesused to generate the data training sets and test models for thethree proposed fault locators

423 Structure of the Neural Fault Locator Once the inputsand outputs numbers of each proposed fault locator basedon the modular ANN are determined it is necessary todetermine the number of hidden layers and the numberof neurons in each hidden layer The major problems inthe ANN architecture design are to make sure that thenumbers of hidden layers and the number of neurons in eachhidden layers converges to the adequate results (exact faultlocation with a minimum error) with a fast response timeANNs architectures including the input network numberthe hidden layers number and the neurons number in eachhidden layer are given due to an experimental study withvarious network configurationsThrough a series of tests andmodifications of ANNs architectures the final architecturefor the different ANNs leads to the best performance thatis obtained using a neural network with three layers The

number of neurons in the input layer corresponds to theinputs variable number in ANNs The number of neuronsin the hidden layers was given after a series of tests and forthe output layer only one neuron corresponds to the faultdistance

All computation time for the three adopted fault locators(FL1 FL2 and FL

3) is carried on a PC (P4 213 GHz and 2GB

RAM) The training time for the first fault locator (FL1) is

approximately 11min and 35 sec for all four modules For thesecond fault locator (FL

2) the training time is about 12min

and 31 sec for all four modules The third fault locator (FL3)

has a training time equal to 8min and 17 sec for all fourmodules Hence it can be seen that the third fault locator(FL3) which uses current and voltage phasor magnitudes

presents a fast training time compared to the other faultlocator algorithms

The final architectures of the proposed modular ANN-based fault locator for each algorithm are given by Table 6

424 Testing of the Fault Locator Once the ANNs trainingprocedure is entirely carried out the fault locators FL

1 FL2

and FL3based on modular ANN approach are tested with

various fault scenarios which are not presented during thetraining process These lasts are tested under various faultconditions such as different fault location (119871

119891= 0ndash100 of

the line length) different values of the fault resistances (119877119891=

0ndash200Ω) and various fault inception angles (FIA = 0∘ndash360∘)Furthermore the influences of the fault condition variationwere tested

The percentage error relating to fault location task isbased on the following equation

Absolute Error

=|Estimated Distance minus Actual Distance|

Length of linelowast 100

(10)

(1) Influence of the Fault Type and the Fault LocationTable 7 presents the effect of the fault type on the proposedfault location algorithms (FL

1 FL2 and FL

3) Indeed the

examined fault types are phase-ground faults (119871-119866) phase-phase-ground faults (119871-119871-119866) phase-phase faults (119871-119871) andphase-phase-phase faults (119871-119871-119871) According to the testresults in Table 7 the percentage error for the fault locationalgorithm FL

1which uses only currents magnitudes of the

fundamental components (50Hz) of three phases (119877 119878 and119879) lies between 01007 and 14599 For the algorithm


Table 6 Architectures of ANN based fault locators (FL1 FL2 and FL3)

Modular ANN-based fault locator Proposed fault locator Architecture Mean square error (MSE) Training time (min)

1 phase to groundFL1 3-14-1 423e minus 04 280FL2 3-16-1 538e minus 03 332FL3 6-32-1 971e minus 06 243

Phase to phaseFL1 3-16-1 327e minus 04 219FL2 3-18-1 499e minus 04 292FL3 6-28-1 866e minus 05 288

2 phases to groundFL1 3-13-1 388e minus 03 314FL2 3-18-1 499e minus 04 328FL3 6-30-1 682e minus 05 212

3 phasesFL1 3-8-1 362e minus 04 282FL2 3-14-1 374e minus 04 279FL3 6-18-1 733e minus 05 234

FL2which uses only voltages magnitudes of the fundamental

components (50Hz) of three phases (119877 119878 and 119879) thepercentage error varies between 01086 and 12862 Forthe third proposed algorithm FL

3using the magnitudes of

the fundamental components of three-phase currents andvoltages the percentage error is within 00175 and 03041Thus it can be seen from the test results that the proposedfault locator algorithm (FL

3) is more accurate than FL

1and

FL2 Thus the percentages errors prove well the capacity

of the proposed modular ANN-based fault locator FL3to

determine the exact fault distance compared to FL1and FL

2

(2) Influence of the Fault Resistance The effect of the faultresistance on the precisions of the proposed fault locationalgorithms (FL

1 FL2 and FL

3) was tested on the power

system study The simulation results given by Table 8 showthe effects of 119877

119891on accuracy of the proposed algorithms

In addition these algorithms were tested for various faultresistances 119877

119891for a ldquophase-ground fault (119877-119866)rdquo among a

fault distance equal to 75Km and for an inception angle FIAequal to 10∘ During the test the percentage error estimated bythe proposed fault location algorithms lies between 01111and 12019 for FL

1 02218 and 19713 for FL

2 and

00912 and 03071 for FL3 Consequently the proposed

modular ANN-based fault locator uses the magnitudes ofthe fundamental components of three-phase currents andvoltages (FL

3) is highly accurate compared to FL

1and FL

2

and is practically independent of the fault resistanceThe criteria for evaluating the performance characteris-

tics of the proposed fault locator based on modular ANN aretranslated by the stability of ANNoutput values in the normalsituation and in the fault situation Thus minimal responsetime 119879

119903 which presents the difference between the fault

appearance time 119879119891and the time 119879

119890where the ANN output

indicates the exact fault location is expressed as follows119879119903= 119879119891minus 119879119890 (11)

The best ANN based on fault locator is obtained by thestability of ANN outputs under minimal response timeTherefore the ANN output is stable in the normal situation

50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

) Inception fault at sample number 69time = 69 ms

Located at sample number 92time = 92 ms

X = 69Y = 110

X = 92Y = 751297

Figure 10 Test result of FL3during 119877-119866 fault with 119871

119891= 75Km

119877119891= 200Ω and FIA = 10∘

and in the fault situation and capable of providing fast andexact fault location with a wide variety of fault conditionsIn our study case the ANN-based fault locator is trained toshow the output as 110 Km for no fault situation or for faultoutside the line segment For faults which appeared on theline segment the ANN is trained to show the output as theexact fault position

In a perspective to evaluate the response time of theproposed algorithm we simulated a single phase to groundfault (119877-119866) with119871

119891= 75 km119877

119891= 200Ω and a fault inception

angle FIA = 10∘ corresponding to the occurrence fault at time69ms see Figure 10The output of the proposed fault locationalgorithm FL

3converges to 751297 km at time equal to 92ms

as against the set value of 75 km The response time 119879119903of

the proposed algorithm is about 23ms This proves that themodular ANN-based fault locator responds quickly to thedesired outputs with minimum error

(3) Influence of the Fault Inception Angle In practice thefaults can occur at any line location that is the faultinception angle FIA cannot be defined in advance Thusit is important to check the performance of the proposedalgorithm with various fault inception angles FIA In thiscontext we simulated a double phase to ground fault with


Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053


Table 8 The effect of the fault resistance of modular ANN-based fault locators (FL1 FL2 and FL3)

Fault conditions Desired output (Km) Actual output (Km) Error ()Fault type FIA (∘) 119877

119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297

Table 9 The effect of the fault inception angle of modular ANN-based fault locators (FL1 FL2 and FL3)

Fault conditions Desired output (Km) Actual output (Km) Error ()Fault type 119877

119891(Ω) FIA (∘) FL1 FL2 FL3 FL1 FL2 FL3

119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608

Table 10 The effect of critical fault condition of modular ANN-based fault locators (FL1 FL2 and FL3)


119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110

Inception fault at sample number 70

Located at sample number 92

time = 70 ms

time = 92 ms

Figure 11 Test result of FL3during 119877-119878-119866 fault with 119871

119891= 11Km

119877119891= 33Ω and FIA = 60∘

fault resistance 119877119891= 33Ω fault location 119871

119891= 11Km and

various fault inception angles FIA (30∘ 60∘ 90∘ 180∘ and360∘) The simulation results are presented in Table 9 It canbe seen from these results that the percentage error for theestimation of the fault using FL

3is between 00009 and

01608 that of FL1is between 02009 and 04015 and

that of FL2lies between 00977 and 04197 Consequently

it is clearly obvious that algorithm FL3is more accurately

compared to other algorithms (FL1and FL

2) Consequently

the proposed algorithm (FL3) is practically independent of

the fault inception angle

In order to show the fast convergence of the proposedalgorithm FL

3under the influence of fault inception angle

FIA a double phase to ground fault (119877-119878-119866) with faultlocation 119871

119891= 11 km fault resistance 119877

119891= 33Ω and

fault inception angle FIA = 60∘ a fault occurrence at time70ms was simulated see Figure 11 We noticed that the faultlocator (FL

3) makes it possible to locate the fault with a good

precision and a fast convergence time The fault occurrenceat time 119879

119891= 70ms was located at time 119879

119890= 92ms at a

distance 119871119891= 110967 which implies a fast response time

about 119879119903= 22ms and a precision of 00967 Thus it is clear

that the proposed fault locator based on modular ANN (FL3)

can accurately locate the fault with high fault inception angleFIA

(4) Influence of Critical Fault Conditions In this context wesimulated various fault types under extreme fault conditionssuch as maximum fault resistance (119877

119891max) maximum faultinception angle (FIAmax) and a fault location created at96Km for the transmission line (119871

119891max) Hence the threeproposed algorithms were tested on the four fault types andthe simulation results are illustrated in Table 10 Thus it canbe seen that the proposed algorithm FL

3is more accurate

and presents high performances especially for critical faultconditions compared to other algorithms FL

1and FL

2 The

corresponding percentage error represents very satisfactoryresults


Table 11 Comparison of ANN-based fault classification and location schemes

Algorithms suggested Fault classifierinputs Fault locator inputs FIA range

(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime

Joorabian et al [22]

Five consecutivesamples ofthree-phasecurrents andvoltages


0ndash90∘ 0ndash94 0ndash100 00397 to04123

Notindicated

Mahanty and Gupta[10]

Five consecutivesamples ofthree-phasecurrents


0ndash90∘ 0ndash82 0ndash200 00007to 445

Notindicated

Jiang et al [31]

Negative-sequencecomponents ofthree-phasecurrents and

voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated

041 to054 128 cycles

Yadav andThoke [32] No method forfault classification

Three consecutivesamples ofthree-phasecurrents andvoltages

Notindicated 0ndash90 0ndash100 0052 to

15693 15 cycles

Proposed scheme

Four consecutivesamples ofthree-phasecurrents

Magnitudes offundamentalcomponents ofthree-phasecurrents andvoltages


1 cycletime frominceptionof fault

In the same way this algorithm is qualified effective sinceit presents a fast response time in convergence to the desiredresults Indeed we simulated two phases to ground faults(119878-119879-119866) at time 75ms with 119871

119891max = 96 km 119877119891max = 199Ω

and a fault inception angle FIA = 360∘ see Figure 12 Wenoticed that the proposed fault locator (FL

3) located the

fault at time 119879119890= 100ms at a distance 119871

119891= 962999

which implies a fast response time equal to 119879119903= 25ms and

a precision of 02999 see Figure 12 This shows that themodular ANN-based fault locator converges correctly withfast time when the transmission line is affected by severalfaults under extreme fault conditions

5 Comparison between Proposedand Existing Schemes

The suggested fault classification and location algorithmsbased on modular ANN are compared with some formerworks These proposed algorithms are developed for all theten fault types which can affect a transmission line undervarious fault conditions such as wider range of fault resistance119877119891 different fault inception angles FIA and different fault

location 119871119891 The main features of certain existing artificial

neural network-based fault classification and location algo-rithms are presented in Table 11

The accuracy of the proposed fault location algorithm(FL3) lies between 00175 and 03041 as indicated in

Table 11 This shows the high performance of the (FL3)

50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999


Inception fault at sample number 75 time = 75 ms


119891= 96Km

119877119891= 199Ω and FIA = 360∘

algorithm and proves that it ismore accurate than the existingalgorithms Thus in this present work we proved that theresponse time of the proposed fault classification and faultlocation algorithms is estimated to one cycle from the faultoccurrence This response time is comparable to the classicaldistance relay protection [32]

6 Conclusion

An efficient fault classification and location algorithms inextra high voltage (EHV) transmission lines based on arti-ficial neural networks were presented For fault classification


two algorithms were proposed the first one used a singleANN approach and the other used the modular ANNapproach Prefault and postfault samples of three-phase cur-rents were used as inputs for these algorithms A comparativestudy of the single and modular neural network shows thatthe modular approach gives more accuracy in order to iden-tify the fault type For fault location three algorithms weredeveloped The first treats only the fundamental magnitudesof the three-phase currents samples the second treats thefundamentalmagnitudes of the three-phase voltages samplesand the third uses the fundamental magnitudes of three-phase currents and voltages samples The modular approachof neural networks was applied to evaluate these algorithmsThe simulation results of these algorithms have been shownunder a variety of fault situations such as different faultlocations different fault inception angles and different faultresistances The obtained results prove that the proposedmodular ANN-based fault distance locator algorithm whichuses fundamental magnitudes of three-phase currents andvoltages is the most effective fault locator The obtainedresults indicate that the proposed fault protection algorithmbased on modular ANNs approach is capable of identifyingall fault types and of estimating the exact fault location inthe transmission lines with high accuracy Moreover theresponse of the proposed fault protection algorithm requiresone cycle from the inception fault Therefore the modularANN-based fault protection can be used for online faultclassification and location in transmission lines

Conflict of Interests

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

References

[1] K V Babu M Tripathy and A K Singh ldquoRecent techniquesused in transmission line protection a reviewrdquo InternationalJournal of Engineering Science and Technology vol 3 no 3 pp1ndash8 2011

[2] X Dong W Kong and T Cui ldquoFault classification and faulted-phase selection based on the initial current traveling waverdquoIEEE Transactions on Power Delivery vol 24 no 2 pp 552ndash5592009

[3] E Vazquez-Martınez ldquoA travelling wave distance protectionusing principal component analysisrdquo International Journal ofElectrical Power and Energy System vol 25 no 6 pp 471ndash4792003

[4] D Spoor and J G Zhu ldquoImproved single-ended traveling-wave faultlocation algorithm based on experience with con-ventional substation transducersrdquo IEEE Transactions on PowerDelivery vol 21 no 3 pp 1714ndash1720 2006

[5] Y Lin C Liu and C Chen ldquoA new PMU-based fault detec-tionlocation technique for transmission lines with consid-eration of arcing fault discriminationmdashpart I theory andalgorithmsrdquo IEEE Transactions on Power Delivery vol 19 no4 pp 1587ndash1593 2004

[6] W Xiu and Y Liao ldquoAccurate transmission line fault locationconsidering shunt capacitances without utilizing line parame-tersrdquo Electric Power Components and Systems vol 39 no 16 pp1783ndash1794 2011

[7] C-S Chen C-W Liu and J-A Jiang ldquoA new adaptive PMUbased protection scheme for transposeduntransposed paralleltransmission linesrdquo IEEE Transactions on Power Delivery vol17 no 2 pp 395ndash404 2002

[8] J Suonan G Song Q Xu and Q Chao ldquoTime-domainfault location algorithm for parallel transmission lines usingunsynchronized currentsrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 4 pp 253ndash260 2006

[9] A Ferrero S Sangiovanni and E Zappitelli ldquoFuzzy-setapproach to fault-type identification in digital relayingrdquo IEEETransactions on Power Delivery vol 10 no 1 pp 169ndash175 1995

[10] R N Mahanty and P B D Gupta ldquoA fuzzy logic based faultclassification approach using current samples onlyrdquo ElectricPower Systems Research vol 77 no 5-6 pp 501ndash507 2007

[11] O A S Youssef ldquoA novel fuzzy-logic-based phase selectiontechnique for power system relayingrdquo Electric Power SystemsResearch vol 68 no 3 pp 175ndash184 2004

[12] P K Dash A K Pradhan and G Panda ldquoA novel fuzzy neuralnetwork based distance relaying schemerdquo IEEE Transactions onPower Delivery vol 15 no 3 pp 902ndash907 2000

[13] B Das and J V Reddy ldquoFuzzy-logic-based fault classificationscheme for digital distance protectionrdquo IEEE Transactions onPower Delivery vol 20 no 2 I pp 609ndash616 2005

[14] J S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[15] S Vasilic and M Kezunovic ldquoFuzzy ART neural network algo-rithm for classifying the power system faultsrdquo IEEETransactionson Power Delivery vol 20 no 2 pp 1306ndash1314 2005

[16] N Zhang and M Kezunovic ldquoCoordinating fuzzy ART neuralnetworks to improve transmission line fault detection andclassificationrdquo in Proceedings of the IEEE Power EngineeringSociety General Meeting (PES rsquo05) pp 734ndash740 San FranciscoCalif USA June 2005

[17] J Sadeh and H Afradi ldquoFault location scheme for combinedtransmission lines using artificial neural networksrdquo in Proceed-ings of the 22nd International Power System Conference (PSCrsquo07) Tehran Iran November 2007 (Persian)

[18] S M Yeo C H Kim K S Hong et al ldquoA novel algorithmfor fault classification in transmission lines using a combinedadaptive network and fuzzy inference systemrdquo InternationalJournal of Electrical Power and Energy System vol 25 no 9 pp747ndash758 2003

[19] J Sadeh and H Afradi ldquoA new and accurate fault locationalgorithm for combined transmission lines using AdaptiveNetwork-Based Fuzzy Inference SystemrdquoElectric Power SystemsResearch vol 79 no 11 pp 1538ndash1545 2009

[20] P K Dash A K Pradhan and G Panda ldquoApplication ofminimal radial basis function neural network to distanceprotectionrdquo IEEE Transactions on Power Delivery vol 16 no 1pp 68ndash74 2001

[21] W Lin C Yang J Lin and M Tsay ldquoA fault classificationmethod by RBF neural network with OLS learning procedurerdquoIEEE Transactions on Power Delivery vol 16 no 4 pp 473ndash4772001


[22] M Joorabian S M A T Asl and R K Aggarwal ldquoAccuratefault locator for EHV transmission lines based on radial basisfunction neural networksrdquo Electric Power Systems Research vol71 no 3 pp 195ndash202 2004

[23] Z Chen and J Maun ldquoArtificial neural network approachto single-ended fault locator for transmission linesrdquo IEEETransactions on Power Systems vol 15 no 1 pp 370ndash375 2000

[24] M Al-Shaher A S Saleh andMM Sabry ldquoEstimation of faultlocation and fault resistance for single line-to-ground faults inmulti-ring distributionnetwork using artificial neural networkrdquoElectric Power Components and Systems vol 37 no 7 pp 697ndash713 2009

[25] J Gracia A J Mazon and I Zamora ldquoBest ANN structures forfault location in single- and double-circuit transmission linesrdquoIEEE Transactions on Power Delivery vol 20 no 4 pp 2389ndash2395 2005

[26] G Chawla M S Sachdev and G Ramakrishna ldquoArtificialneural network applications for power system protectionrdquoin Proceedings of the Canadian Conference on Electrical andComputer Engineering pp 1954ndash1957 Saskatoon Canada May2005

[27] K Z Hassan and L Zuyi ldquoAn ANN based approach to improvethe distance relaying algorithmrdquo Turkish Journal of ElectricalEngineering and Computer Sciences vol 14 no 2 pp 345ndash3542006

[28] G Banu and S Suja ldquoANN based fault location technique usingone end data for UHV linesrdquo European Journal of ScientificResearch vol 77 no 4 pp 549ndash559 2012

[29] Y Aslan ldquoAn alternative approach to fault location on powerdistribution feeders with embedded remote-end power genera-tion using artificial neural networksrdquo Electrical Engineering vol94 no 3 pp 125ndash134 2012

[30] A Dasgupta S Nath and A Das ldquoTransmission line faultclassification and location using wavelet entropy and neuralnetworkrdquo Electric Power Components and Systems vol 40 no15 pp 1676ndash1689 2012

[31] J Jiang C Chuang YWang et al ldquoA hybrid framework for faultdetection classification and locationmdashpart I concept struc-ture and methodologyrdquo IEEE Transactions on Power Deliveryvol 26 no 3 pp 1988ndash1998 2011

[32] A Yadav and A SThoke ldquoTransmission line fault distance anddirection estimation using artificial neural networkrdquo Interna-tional Journal of Engineering Science and Technology vol 3 no8 pp 110ndash121 2011

[33] M B Hessine H Jouini and S Chebbi ldquoFault detection andclassification approaches in transmission lines using artificialneural networksrdquo inProceedings of the IEEEMediterraneanElec-trotechnical Conference (MELECON 14) pp 520ndash524 BeirutLebanon April 2014

[34] M B Hessine H Jouini and S Chebbi ldquoA new and accuratefault classification algorithm for transmission lines using fuzzylogic systemrdquoWulfenia Journal vol 20 no 3 pp 336ndash349 2013

[35] M B Hessine H Jouini S Chebbi and S Marrouchi ldquoVoltageand frequency stabilization of electrical networks by using loadshedding strategy based on fuzzy logic controllersrdquo Interna-tional Review of Electrical Engineering vol 7 no 5 pp 5694ndash5704 2012

[36] R Abbassi and S Chebbi ldquoEnergy management strategy for agrid-connected wind-solar hybrid system with battery storage

policy for optimizing conventional energy generationrdquo Interna-tional Review of Electrical Engineering vol 7 no 2 pp 3979ndash3990 2012

[37] K Jemai H Jouini and S Chebbi ldquoVoltage stability control ofelectrical network using intelligent load shedding strategy basedon fuzzy logicrdquoMathematical Problems in Engineering vol 2010Article ID 341257 17 pages 2010

[38] T Bouthiba ldquoFault location in EHV transmission lines usingartificial neural networksrdquo International Journal of AppliedMathematics and Computer Science vol 14 no 1 pp 69ndash782004

[39] E A Mohamed and N D Rao ldquoArtificial neural network basedfault diagnostic system for electric power distribution feedersrdquoElectric Power Systems Research vol 35 no 1 pp 1ndash10 1995

[40] A I Megahed and O P Malik ldquoAn artificial neural networkbased digital differential protection scheme for synchronousgenerator stator winding protectionrdquo IEEE Transactions onPower Delivery vol 14 no 1 pp 86ndash93 1999

[41] M R Zaman and M A Rahman ldquoExperimental testingof the artificial neural network based protection of powertransformersrdquo IEEE Transactions on Power Delivery vol 13 no2 pp 510ndash515 1998

[42] W Wang L Li H Peng J Xiao and Y Yang ldquoSynchronizationcontrol of memristor-based recurrent neural networks withperturbationsrdquo Neural Networks vol 53 pp 8ndash14 2014

[43] Y Tang and W K Wong ldquoDistributed synchronization ofcoupled neural networks via randomly occurring controlrdquo IEEETransactions on Neural Networks and Learning Systems vol 24no 3 pp 435ndash447 2013

[44] W Zhang Y Tang J Fang and X Wu ldquoStability of delayedneural networks with time-varying impulsesrdquoNeural Networksvol 36 pp 59ndash63 2012

[45] W Zhang Y Tang Q Miao and W Du ldquoExponential syn-chronization of coupled switched neural networks with mode-dependent impulsive effectsrdquo IEEE Transactions on NeuralNetworks and Learning Systems vol 24 no 8 pp 1316ndash13262013

[46] K Hu A Song M Xia X Ye and Y Dou ldquoAn adaptive filteringalgorithm based on genetic algorithm-backpropagation net-workrdquoMathematical Problems in Engineering vol 2013 ArticleID 573941 8 pages 2013

[47] W Chang ldquoAn RBF neural network combined with OLSalgorithm and genetic algorithm for short-term wind powerforecastingrdquo Journal of Applied Mathematics vol 2013 ArticleID 971389 9 pages 2013

[48] Y Chang J Lin J Shieh and M F Abbod ldquoOptimization theinitial weights of artificial neural networks via genetic algorithmapplied to hip bone fracture predictionrdquo Advances in FuzzySystems vol 2012 Article ID 951247 9 pages 2012

[49] E Cuevas D Zaldıvar and P Cisneros ldquoA swarm optimizationalgorithm for multimodal functions and its application inmulticircle detectionrdquo Mathematical Problems in Engineeringvol 2013 Article ID 948303 22 pages 2013

[50] Y-K Lin ldquoParticle swarm optimization algorithm for unrelatedparallel machine scheduling with release datesrdquo MathematicalProblems in Engineering vol 2013 Article ID 409486 9 pages2013

[51] A Liu andM Yang ldquoA new hybrid nelder-mead particle swarmoptimization for coordination optimization of directional over-current relaysrdquoMathematical Problems in Engineering vol 2012Article ID 456047 18 pages 2012


[52] L Li Y Yang H Peng and XWang ldquoParameters identificationof chaotic systems via chaotic ant swarmrdquo Chaos Solitons ampFractals vol 28 no 5 pp 1204ndash1211 2006

[53] H Peng L Li Y Yang and F Liu ldquoParameter estimation ofdynamical systems via a chaotic ant swarmrdquo Physical Review Evol 81 no 1 Article ID 016207 2010

[54] L Li Y Yang H Peng and X Wang ldquoAn optimization methodinspired by ldquochaoticrdquo ant behaviorrdquo International Journal ofBifurcation and Chaos in Applied Sciences and Engineering vol16 no 8 pp 2351ndash2364 2006

[55] H Peng L Li J Kurths S Li and Y Yang ldquoTopology identifi-cation of complex network via chaotic ant swarm algorithmrdquoMathematical Problems in Engineering vol 2013 Article ID401983 5 pages 2013

[56] K N Yu H T Yau and JY Li ldquoChaotic extension neuralnetwork-based fault diagnosis method for solar photovoltaicsystemsrdquo Mathematical Problems in Engineering vol 2014Article ID 280520 9 pages 2014

[57] S Abid F Fnaiech andM Najim ldquoA fast feed-forward trainingalgorithm A modified form of the standard back-propagationalgorithmrdquo IEEE Transactions on Neural Network vol 12 no 2pp 424ndash430 2001

[58] S Abid F Fnaiech B W Jervis and M Cheriet ldquoFast trainingof multilayer perceptrons with a mixed norm algorithmrdquo inProceedings of the IEEE International Joint Conference on NeuralNetworks (IJCNN 05) vol 2 pp 1018ndash1022 August 2005

[59] S Haykin Neural Networks A Comprehensive FoundationPrentice Hall Englewood Cliffs NJ USA 1994

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


based on artificial intelligence tools such as fuzzy logic (FL)artificial neural networks (ANNs) and the adaptive network-based fuzzy inference system (ANFIS) Fuzzy logic-basedtransmission line relaying techniques for fault classificationand fault location are proposed by many researchers [9ndash11] However these techniques cannot in any way guaranteeprecision results for wide variation of faultconditions (highfault resistance high fault inception angle and far distancelocation from relay site) A recent study [12] has proposed analgorithm having the synergy to calculate with high precisionthe fault locations at distances less than 80of the line lengthIn [13] a fault classification algorithm based on fuzzy logicsystem is presented Nevertheless this algorithm is valid onlyfor a less range variety of fault resistance

Other protection relaying researchers have used theadaptive network-based fuzzy inference system (ANFIS) [14ndash17] In [18] a fault detection and classification scheme isdeveloped This technique uses three-phase currents andzero sequence current but the fault location procedure isnot indicated In [19] a fault classification and locationalgorithms for combined overhead transmission line havebeen proposed The current and voltage samples are usedfor the proposed scheme These values were obtained withinone cycle after the fault inception that implies a responsetime superior than one operating cycle The protection faultapproaches based on fuzzy logic (FL) and adaptive networkfuzzy inference system (ANFIS) techniques are sensitive tothe system frequency variations and require large trainingsets

The artificial neural networks were integrated in the pro-tection relaying techniques These techniques used samplesof current andor voltage without calculating the symmet-rical components [1] Various neural network types suchas the multilayer perceptron (MLP) radial basis function(RBF) and probabilistic neural network are applied forfault diagnosis in transmission lines [20ndash24] The protectionapproaches based on ANNs were used for the developmentof reliable accurate and rapid algorithms in real time forfault detection classification and location In this context[25] developed an application of radial basic function (RBF)neural network applied to fault location in transmission linesThe maximum error of the proposed algorithm is equal to05 Besides [26 27] developed neural network approachesfor fault detection and fault location in transmission linesNevertheless these approaches detect only the faults whichappeared in the first zone of the line namely 80 of thetransmission line length In [28] a fault location algorithmfor transmission lines was developed The algorithm usesa single artificial neural network based on the Levenberg-Marquardt optimization technique However the fault typeis not indicated and the percentage error of the algorithmis maintained below 065 In [29] fault classification andlocation schemes are proposed These schemes use three-phase currents and voltages waveforms at one terminal lineThe response time of the proposed scheme is not indicatedand the percentage error for fault location is equal to 3 In[30] a new scheme for fault classification and fault locationis presented The maximum error of the proposed scheme is305 and the response time is not indicated Reference [31]

proposed a fault location module for fault diagnosis whichincorporates two stages adaptive structures neural networkThe fault detection classification and location algorithmsare presented with average fault location error of 04 and05411 The results show clearly that this approach leads toa reliable location for all types of faults The operating timeof this method is equal to 128 cycles after inception fault In[32] fault distance and direction estimation based on ANNfor protection of doubly fed transmission lines are proposedbut the fault type is not indicated The operating time of thisapproach is about 15 cycles and the percentage error rate offault location lies between 0052 and 157

In order to develop fault classification and locationalgorithms leading to desired results with a good precisionand fast response time compared to former work we haveproposed in the present paper a new fault classification andlocation algorithms based on ANNs Thus optimal neuralnetworks architecture used in the fault classification andlocation algorithms (number of hidden layers number ofneurons in hidden layers reduced training sets fast conver-gence to the desired results and reliability and precision ofprotection algorithms) were proposed These algorithms arebased on artificial neural networks (ANNs) (feed-forward)trained by a supervised learning algorithm called back-propagation In this context two fault classifiers are proposedthe first one uses a single ANN approach and the secondone uses a modular ANN approach A comparative study ofthe proposed two fault classifiers is carried out in order todetermine which reliable and effective ANN fault classifierleads to the best performance For fault location three faultlocators based on modular ANN approach are proposed inorder to choose an optimal architecture strategy with a highprecision and fast convergence to the exact fault locationThefault neural classifiers and locators were trained and testedunder different fault conditions (fault types fault locationsfault resistances and fault inception angles) The simulationresults show clearly the high accuracy of the proposed faultclassification and location algorithms

2 Power System under Study

To evaluate the performance of the proposed neural network-based fault detector and locator a 400 kV 100 km transmis-sion line extending between two sources is considered in thisstudy The power system model simulated using MATLABsoftware is shown in Figure 1 It contains a synchronousgenerator (driven by hydraulic turbine) connected to aninfinite bus The transmission line has been represented bydistributed parameter of one line model using Power Systemtoolbox of MATLAB software and the frequency dependenceof the line parameters is taken into account The proposedfault classification and location algorithms require only thethree-phase voltages andor currents samples at the sendingend of the transmission lines A large number of fault samplesdata have been generated using MATLAB considering widevariations on fault conditions such as fault locations faultresistances fault inception angle and fault types Using thesedata fault classification and location have been carried out


Vang0S V

ang120575119871R

CT

VT

Bus i

CBTransformer

Relay

Synchr Gen615 MVA


400 Kv

Bus j


Fault


Lf middot Ycc

2

Lf middot Ycc

2


2


2


CB circuit breaker










1198891198641015840119902

119889119905=

1

1198791015840119889119900

sdot [119864119891119889minus 1198641015840

119902+ (119883119889minus 1198831015840

119889) sdot 119868119889]

1198891198641015840119889

119889119905=1

1198791015840119902119900

sdot [minus1198641015840

119889+ (119883119902minus 1198831015840

119902) sdot 119868119902]

119889120596

119889119905=1


119889120575

119889119905= 120596 minus 1

(1)

where

1198641015840119889 1198641015840119902 and 119864



119902are






sum sum sum

sum sum sum

sum sum sum

y[0]1

y[0]2

y[0]3

y[0]n0

1 S L

f1 f2 f3

f1 f2 f3

f1 f2 f3

u[1]1 y[1]

1u[S]

1 y[S]1 u[L]

1 y[L]1

u[1]2 y[1]

2u[S]

2 y[S]2 u[L]

2 y[L]2

b1(1) bS(1) bL(1)

b1(2) bS(2) bL(2)


u[1]n1

y[1]n1

u[S]nS

y[S]n119878

u[L]n119871

y[L]nL













Summingjunction

Activationfunction

Output

Synapticweights

Inpu

ts

Threshold

y[sminus1]1

y[sminus1]2


W[s]j1

W[s]j2

W[s]jn119904minus1

b[s]j

u[s]j

y[s]j

sum f(middot)




119910[119904]

119895= 119891(119887

[119904]

119895+

119899119904minus1

sum119894=1

119908[119904]

119895119894119910[119904minus1]

119894) (2)

where


119910[119904minus1]

119894 119894 = 1 119899


of neuron 119895

119908[119904]



119887[119904]



[119910[119875]

1 119910[119875]

2 119910

[119875]



1 119910[119876]

2 119910

[119876]

119895 119910

[119876]




119910[119876]

119895= 119891hidden(119887

[119876]

119895+119875

sum119894=1

119908[119876]

119894119895119910[119875]

119894) (3)

where

119908[119876]



119887[119876]





[119877]

1 119910[119877]

2 119910

[119877]

119896 119910

[119877]

119877] of the



119910[119877]

119896= 119891out(119887

[119877]

119896+

119876

sum119895=1

119908[119877]

119895119896119910[119876]

119895) (4)

119908[119877]






Error = 12

119877

sum119896=1

(119910119896-desired minus 119910119896)

2

(5)





CT

VT

Transmission line

Currents Voltages

Antialiasing filter


ANN1 L-G

ANN4L-L-L

ANN3L-L-G

ANN2L-L

Sampling by 1 kHz




and currents







119906[119904]119895=

119899119904minus1

sum119894=0

119908[119904]

119895119894119910[119904minus1]

119894

119910[119904]119895= 119891 (119906[119904]

119895)


(ii) Layers 119904 = 119871 minus 1 1

120575[119904]

119895119901= 1198911015840 (119906

[119904]

119895119901)

119899119904+1

sum119903=1

(120575[119904+1]

119895119901119908[119904+1]

119903119895)


119895119894(119896) = 120583119910

[119904minus1]

119894119901120575[119904]

119895119901 119904 = 1 119871







1)






Start


Step 1




End

Offline process

Online process

Step 2

Step 3

Step 4

Step 5

Step 6




reached










1) are equal


119883FC1

= [119868119877(119896)

119868119877minusPF (119896)

119868119877(119896 + 3)

119868119877minusPF (119896 minus 3)

119868119878(119896)

119868119878minusPF (119896)

119868119878(119896 + 3)

119868119878minusPF (119896 minus 3)

1

1

22

1

2

3

44

x1

x2

x4

w12

wn2

w14

w11

w21

w22

w24

wn4

w99840042

w99840023

w99840022

w99840011

w99840021

w99840031

w99840041

w9984002n

w9984003n

w9984004n

w99840012

w998400n1

w9984001n

R

S

T

G

n


119868119879(119896)

119868119879minusPF (119896)

119868119879(119896 + 3)

119868119879minusPF (119896 minus 3)

1198680(119896) 119868

0(119896 + 3)]

(6)







119883119894

FC2

= [119868119894(119896)

119868119894minusPF (119896)

119868119894(119896 + 3)

119868119894minusPF (119896 minus 3)

] 119894 = 119877 119878 119879

119883119866

FC2

= [1198680(119896) 119868

0(119896 + 3)]

(7)




AN

N-R

AN

N-S

AN

N-T

AN

N-G











I0(k) I0



Fault type


IR(k)

IRminusPF(k)

IR(k + 3)


ISminusPF(k)

IS(k + 3)


ITminusPF(k)

IT(k + 3)








1and FC

2) a suitable



Fault type

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879


1 10 20 30 80and 90 km 12 56 78 and 94


225∘









Input

Output


IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1


2)




1





1and FC

2)




1) requires






119891


1and FC

2) are presented

in Table 4







Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Vang0S V

ang120575119871R

CT

VT

Bus i

CBTransformer

Relay

Synchr Gen615 MVA


400 Kv

Bus j


Fault


Lf middot Ycc

2

Lf middot Ycc

2


2


2


CB circuit breaker










1198891198641015840119902

119889119905=

1

1198791015840119889119900

sdot [119864119891119889minus 1198641015840

119902+ (119883119889minus 1198831015840

119889) sdot 119868119889]

1198891198641015840119889

119889119905=1

1198791015840119902119900

sdot [minus1198641015840

119889+ (119883119902minus 1198831015840

119902) sdot 119868119902]

119889120596

119889119905=1


119889120575

119889119905= 120596 minus 1

(1)

where

1198641015840119889 1198641015840119902 and 119864



119902are






sum sum sum

sum sum sum

sum sum sum

y[0]1

y[0]2

y[0]3

y[0]n0

1 S L

f1 f2 f3

f1 f2 f3

f1 f2 f3

u[1]1 y[1]

1u[S]

1 y[S]1 u[L]

1 y[L]1

u[1]2 y[1]

2u[S]

2 y[S]2 u[L]

2 y[L]2

b1(1) bS(1) bL(1)

b1(2) bS(2) bL(2)


u[1]n1

y[1]n1

u[S]nS

y[S]n119878

u[L]n119871

y[L]nL













Summingjunction

Activationfunction

Output

Synapticweights

Inpu

ts

Threshold

y[sminus1]1

y[sminus1]2


W[s]j1

W[s]j2

W[s]jn119904minus1

b[s]j

u[s]j

y[s]j

sum f(middot)




119910[119904]

119895= 119891(119887

[119904]

119895+

119899119904minus1

sum119894=1

119908[119904]

119895119894119910[119904minus1]

119894) (2)

where


119910[119904minus1]

119894 119894 = 1 119899


of neuron 119895

119908[119904]



119887[119904]



[119910[119875]

1 119910[119875]

2 119910

[119875]



1 119910[119876]

2 119910

[119876]

119895 119910

[119876]




119910[119876]

119895= 119891hidden(119887

[119876]

119895+119875

sum119894=1

119908[119876]

119894119895119910[119875]

119894) (3)

where

119908[119876]



119887[119876]





[119877]

1 119910[119877]

2 119910

[119877]

119896 119910

[119877]

119877] of the



119910[119877]

119896= 119891out(119887

[119877]

119896+

119876

sum119895=1

119908[119877]

119895119896119910[119876]

119895) (4)

119908[119877]






Error = 12

119877

sum119896=1

(119910119896-desired minus 119910119896)

2

(5)





CT

VT

Transmission line

Currents Voltages

Antialiasing filter


ANN1 L-G

ANN4L-L-L

ANN3L-L-G

ANN2L-L

Sampling by 1 kHz




and currents







119906[119904]119895=

119899119904minus1

sum119894=0

119908[119904]

119895119894119910[119904minus1]

119894

119910[119904]119895= 119891 (119906[119904]

119895)


(ii) Layers 119904 = 119871 minus 1 1

120575[119904]

119895119901= 1198911015840 (119906

[119904]

119895119901)

119899119904+1

sum119903=1

(120575[119904+1]

119895119901119908[119904+1]

119903119895)


119895119894(119896) = 120583119910

[119904minus1]

119894119901120575[119904]

119895119901 119904 = 1 119871







1)






Start


Step 1




End

Offline process

Online process

Step 2

Step 3

Step 4

Step 5

Step 6




reached










1) are equal


119883FC1

= [119868119877(119896)

119868119877minusPF (119896)

119868119877(119896 + 3)

119868119877minusPF (119896 minus 3)

119868119878(119896)

119868119878minusPF (119896)

119868119878(119896 + 3)

119868119878minusPF (119896 minus 3)

1

1

22

1

2

3

44

x1

x2

x4

w12

wn2

w14

w11

w21

w22

w24

wn4

w99840042

w99840023

w99840022

w99840011

w99840021

w99840031

w99840041

w9984002n

w9984003n

w9984004n

w99840012

w998400n1

w9984001n

R

S

T

G

n


119868119879(119896)

119868119879minusPF (119896)

119868119879(119896 + 3)

119868119879minusPF (119896 minus 3)

1198680(119896) 119868

0(119896 + 3)]

(6)







119883119894

FC2

= [119868119894(119896)

119868119894minusPF (119896)

119868119894(119896 + 3)

119868119894minusPF (119896 minus 3)

] 119894 = 119877 119878 119879

119883119866

FC2

= [1198680(119896) 119868

0(119896 + 3)]

(7)




AN

N-R

AN

N-S

AN

N-T

AN

N-G











I0(k) I0



Fault type


IR(k)

IRminusPF(k)

IR(k + 3)


ISminusPF(k)

IS(k + 3)


ITminusPF(k)

IT(k + 3)








1and FC

2) a suitable



Fault type

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879


1 10 20 30 80and 90 km 12 56 78 and 94


225∘









Input

Output


IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1


2)




1





1and FC

2)




1) requires






119891


1and FC

2) are presented

in Table 4







Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










sum sum sum

sum sum sum

sum sum sum

y[0]1

y[0]2

y[0]3

y[0]n0

1 S L

f1 f2 f3

f1 f2 f3

f1 f2 f3

u[1]1 y[1]

1u[S]

1 y[S]1 u[L]

1 y[L]1

u[1]2 y[1]

2u[S]

2 y[S]2 u[L]

2 y[L]2

b1(1) bS(1) bL(1)

b1(2) bS(2) bL(2)


u[1]n1

y[1]n1

u[S]nS

y[S]n119878

u[L]n119871

y[L]nL













Summingjunction

Activationfunction

Output

Synapticweights

Inpu

ts

Threshold

y[sminus1]1

y[sminus1]2


W[s]j1

W[s]j2

W[s]jn119904minus1

b[s]j

u[s]j

y[s]j

sum f(middot)




119910[119904]

119895= 119891(119887

[119904]

119895+

119899119904minus1

sum119894=1

119908[119904]

119895119894119910[119904minus1]

119894) (2)

where


119910[119904minus1]

119894 119894 = 1 119899


of neuron 119895

119908[119904]



119887[119904]



[119910[119875]

1 119910[119875]

2 119910

[119875]



1 119910[119876]

2 119910

[119876]

119895 119910

[119876]




119910[119876]

119895= 119891hidden(119887

[119876]

119895+119875

sum119894=1

119908[119876]

119894119895119910[119875]

119894) (3)

where

119908[119876]



119887[119876]





[119877]

1 119910[119877]

2 119910

[119877]

119896 119910

[119877]

119877] of the



119910[119877]

119896= 119891out(119887

[119877]

119896+

119876

sum119895=1

119908[119877]

119895119896119910[119876]

119895) (4)

119908[119877]






Error = 12

119877

sum119896=1

(119910119896-desired minus 119910119896)

2

(5)





CT

VT

Transmission line

Currents Voltages

Antialiasing filter


ANN1 L-G

ANN4L-L-L

ANN3L-L-G

ANN2L-L

Sampling by 1 kHz




and currents







119906[119904]119895=

119899119904minus1

sum119894=0

119908[119904]

119895119894119910[119904minus1]

119894

119910[119904]119895= 119891 (119906[119904]

119895)


(ii) Layers 119904 = 119871 minus 1 1

120575[119904]

119895119901= 1198911015840 (119906

[119904]

119895119901)

119899119904+1

sum119903=1

(120575[119904+1]

119895119901119908[119904+1]

119903119895)


119895119894(119896) = 120583119910

[119904minus1]

119894119901120575[119904]

119895119901 119904 = 1 119871







1)






Start


Step 1




End

Offline process

Online process

Step 2

Step 3

Step 4

Step 5

Step 6




reached










1) are equal


119883FC1

= [119868119877(119896)

119868119877minusPF (119896)

119868119877(119896 + 3)

119868119877minusPF (119896 minus 3)

119868119878(119896)

119868119878minusPF (119896)

119868119878(119896 + 3)

119868119878minusPF (119896 minus 3)

1

1

22

1

2

3

44

x1

x2

x4

w12

wn2

w14

w11

w21

w22

w24

wn4

w99840042

w99840023

w99840022

w99840011

w99840021

w99840031

w99840041

w9984002n

w9984003n

w9984004n

w99840012

w998400n1

w9984001n

R

S

T

G

n


119868119879(119896)

119868119879minusPF (119896)

119868119879(119896 + 3)

119868119879minusPF (119896 minus 3)

1198680(119896) 119868

0(119896 + 3)]

(6)







119883119894

FC2

= [119868119894(119896)

119868119894minusPF (119896)

119868119894(119896 + 3)

119868119894minusPF (119896 minus 3)

] 119894 = 119877 119878 119879

119883119866

FC2

= [1198680(119896) 119868

0(119896 + 3)]

(7)




AN

N-R

AN

N-S

AN

N-T

AN

N-G











I0(k) I0



Fault type


IR(k)

IRminusPF(k)

IR(k + 3)


ISminusPF(k)

IS(k + 3)


ITminusPF(k)

IT(k + 3)








1and FC

2) a suitable



Fault type

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879


1 10 20 30 80and 90 km 12 56 78 and 94


225∘









Input

Output


IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1


2)




1





1and FC

2)




1) requires






119891


1and FC

2) are presented

in Table 4







Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Summingjunction

Activationfunction

Output

Synapticweights

Inpu

ts

Threshold

y[sminus1]1

y[sminus1]2


W[s]j1

W[s]j2

W[s]jn119904minus1

b[s]j

u[s]j

y[s]j

sum f(middot)




119910[119904]

119895= 119891(119887

[119904]

119895+

119899119904minus1

sum119894=1

119908[119904]

119895119894119910[119904minus1]

119894) (2)

where


119910[119904minus1]

119894 119894 = 1 119899


of neuron 119895

119908[119904]



119887[119904]



[119910[119875]

1 119910[119875]

2 119910

[119875]



1 119910[119876]

2 119910

[119876]

119895 119910

[119876]




119910[119876]

119895= 119891hidden(119887

[119876]

119895+119875

sum119894=1

119908[119876]

119894119895119910[119875]

119894) (3)

where

119908[119876]



119887[119876]





[119877]

1 119910[119877]

2 119910

[119877]

119896 119910

[119877]

119877] of the



119910[119877]

119896= 119891out(119887

[119877]

119896+

119876

sum119895=1

119908[119877]

119895119896119910[119876]

119895) (4)

119908[119877]






Error = 12

119877

sum119896=1

(119910119896-desired minus 119910119896)

2

(5)





CT

VT

Transmission line

Currents Voltages

Antialiasing filter


ANN1 L-G

ANN4L-L-L

ANN3L-L-G

ANN2L-L

Sampling by 1 kHz




and currents







119906[119904]119895=

119899119904minus1

sum119894=0

119908[119904]

119895119894119910[119904minus1]

119894

119910[119904]119895= 119891 (119906[119904]

119895)


(ii) Layers 119904 = 119871 minus 1 1

120575[119904]

119895119901= 1198911015840 (119906

[119904]

119895119901)

119899119904+1

sum119903=1

(120575[119904+1]

119895119901119908[119904+1]

119903119895)


119895119894(119896) = 120583119910

[119904minus1]

119894119901120575[119904]

119895119901 119904 = 1 119871







1)






Start


Step 1




End

Offline process

Online process

Step 2

Step 3

Step 4

Step 5

Step 6




reached










1) are equal


119883FC1

= [119868119877(119896)

119868119877minusPF (119896)

119868119877(119896 + 3)

119868119877minusPF (119896 minus 3)

119868119878(119896)

119868119878minusPF (119896)

119868119878(119896 + 3)

119868119878minusPF (119896 minus 3)

1

1

22

1

2

3

44

x1

x2

x4

w12

wn2

w14

w11

w21

w22

w24

wn4

w99840042

w99840023

w99840022

w99840011

w99840021

w99840031

w99840041

w9984002n

w9984003n

w9984004n

w99840012

w998400n1

w9984001n

R

S

T

G

n


119868119879(119896)

119868119879minusPF (119896)

119868119879(119896 + 3)

119868119879minusPF (119896 minus 3)

1198680(119896) 119868

0(119896 + 3)]

(6)







119883119894

FC2

= [119868119894(119896)

119868119894minusPF (119896)

119868119894(119896 + 3)

119868119894minusPF (119896 minus 3)

] 119894 = 119877 119878 119879

119883119866

FC2

= [1198680(119896) 119868

0(119896 + 3)]

(7)




AN

N-R

AN

N-S

AN

N-T

AN

N-G











I0(k) I0



Fault type


IR(k)

IRminusPF(k)

IR(k + 3)


ISminusPF(k)

IS(k + 3)


ITminusPF(k)

IT(k + 3)








1and FC

2) a suitable



Fault type

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879


1 10 20 30 80and 90 km 12 56 78 and 94


225∘









Input

Output


IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1


2)




1





1and FC

2)




1) requires






119891


1and FC

2) are presented

in Table 4







Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










CT

VT

Transmission line

Currents Voltages

Antialiasing filter


ANN1 L-G

ANN4L-L-L

ANN3L-L-G

ANN2L-L

Sampling by 1 kHz




and currents







119906[119904]119895=

119899119904minus1

sum119894=0

119908[119904]

119895119894119910[119904minus1]

119894

119910[119904]119895= 119891 (119906[119904]

119895)


(ii) Layers 119904 = 119871 minus 1 1

120575[119904]

119895119901= 1198911015840 (119906

[119904]

119895119901)

119899119904+1

sum119903=1

(120575[119904+1]

119895119901119908[119904+1]

119903119895)


119895119894(119896) = 120583119910

[119904minus1]

119894119901120575[119904]

119895119901 119904 = 1 119871







1)






Start


Step 1




End

Offline process

Online process

Step 2

Step 3

Step 4

Step 5

Step 6




reached










1) are equal


119883FC1

= [119868119877(119896)

119868119877minusPF (119896)

119868119877(119896 + 3)

119868119877minusPF (119896 minus 3)

119868119878(119896)

119868119878minusPF (119896)

119868119878(119896 + 3)

119868119878minusPF (119896 minus 3)

1

1

22

1

2

3

44

x1

x2

x4

w12

wn2

w14

w11

w21

w22

w24

wn4

w99840042

w99840023

w99840022

w99840011

w99840021

w99840031

w99840041

w9984002n

w9984003n

w9984004n

w99840012

w998400n1

w9984001n

R

S

T

G

n


119868119879(119896)

119868119879minusPF (119896)

119868119879(119896 + 3)

119868119879minusPF (119896 minus 3)

1198680(119896) 119868

0(119896 + 3)]

(6)







119883119894

FC2

= [119868119894(119896)

119868119894minusPF (119896)

119868119894(119896 + 3)

119868119894minusPF (119896 minus 3)

] 119894 = 119877 119878 119879

119883119866

FC2

= [1198680(119896) 119868

0(119896 + 3)]

(7)




AN

N-R

AN

N-S

AN

N-T

AN

N-G











I0(k) I0



Fault type


IR(k)

IRminusPF(k)

IR(k + 3)


ISminusPF(k)

IS(k + 3)


ITminusPF(k)

IT(k + 3)








1and FC

2) a suitable



Fault type

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879


1 10 20 30 80and 90 km 12 56 78 and 94


225∘









Input

Output


IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1


2)




1





1and FC

2)




1) requires






119891


1and FC

2) are presented

in Table 4







Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Start


Step 1




End

Offline process

Online process

Step 2

Step 3

Step 4

Step 5

Step 6




reached










1) are equal


119883FC1

= [119868119877(119896)

119868119877minusPF (119896)

119868119877(119896 + 3)

119868119877minusPF (119896 minus 3)

119868119878(119896)

119868119878minusPF (119896)

119868119878(119896 + 3)

119868119878minusPF (119896 minus 3)

1

1

22

1

2

3

44

x1

x2

x4

w12

wn2

w14

w11

w21

w22

w24

wn4

w99840042

w99840023

w99840022

w99840011

w99840021

w99840031

w99840041

w9984002n

w9984003n

w9984004n

w99840012

w998400n1

w9984001n

R

S

T

G

n


119868119879(119896)

119868119879minusPF (119896)

119868119879(119896 + 3)

119868119879minusPF (119896 minus 3)

1198680(119896) 119868

0(119896 + 3)]

(6)







119883119894

FC2

= [119868119894(119896)

119868119894minusPF (119896)

119868119894(119896 + 3)

119868119894minusPF (119896 minus 3)

] 119894 = 119877 119878 119879

119883119866

FC2

= [1198680(119896) 119868

0(119896 + 3)]

(7)




AN

N-R

AN

N-S

AN

N-T

AN

N-G











I0(k) I0



Fault type


IR(k)

IRminusPF(k)

IR(k + 3)


ISminusPF(k)

IS(k + 3)


ITminusPF(k)

IT(k + 3)








1and FC

2) a suitable



Fault type

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879


1 10 20 30 80and 90 km 12 56 78 and 94


225∘









Input

Output


IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1


2)




1





1and FC

2)




1) requires






119891


1and FC

2) are presented

in Table 4







Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










AN

N-R

AN

N-S

AN

N-T

AN

N-G











I0(k) I0



Fault type


IR(k)

IRminusPF(k)

IR(k + 3)


ISminusPF(k)

IS(k + 3)


ITminusPF(k)

IT(k + 3)








1and FC

2) a suitable



Fault type

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878119871-119871-g 119877-119878-119866119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879


1 10 20 30 80and 90 km 12 56 78 and 94


225∘









Input

Output


IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1


2)




1





1and FC

2)




1) requires






119891


1and FC

2) are presented

in Table 4







Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Input

Output


IW11

b1

a

n

+1

minus1

sum sum

LW21

b2

a

n

+1

minus1


2)




1





1and FC

2)




1) requires






119891


1and FC

2) are presented

in Table 4







Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table4Re

sults

ofthefaulttype

classifier

usingsin

glea

ndmod

ular

ANN(FC 1

andFC

2)

Faulttype

Faultlocation(K

m)

Faultinceptio

nangle(∘)

Faultresistance

(Ω)

Network

Desire

dou

tput

Actualou

tput

AB

CD

AB

CD

119860-119866

1225

0Sing

leANN

11112

01281

01187

09287

Mod

ular

ANN

10

01

10013

minus00071

000

0410

005

94225

199

Sing

leANN

09051

01266

01108

11290

Mod

ular

ANN

10071

minus000

0300037

10085

119862-119866

1225

0Sing

leANN

minus00784

01420

11128

12940

Mod

ular

ANN

00

11

00021

minus000

4110

093

09941

94225

199

Sing

leANN

01328

minus01007

12871

11008

Mod

ular

ANN

minus00074

minus00032

10078

09814

119860-119861-119866

1225

0Sing

leANN

11850

09072

00088

09653

Mod

ular

ANN

11

01

10085

1006

6minus000

4211473

94225

199

Sing

leANN

10951

09552

0117

811008

Mod

ular

ANN

10082

10077

minus000

0409993

119861-119862

-11986612

250

Sing

leANN

01136

10951

09867

1100

0Mod

ular

ANN

01

11

minus00031

09972

10007

10081

94225

199

Sing

leANN

01807

1100

911150

1087

Mod

ular

ANN

minus000

0110

023

10744

10003

119860-119861-119862

1225

mdashSing

leANN

09962

11007

11105

minus01042

Mod

ular

ANN

11

10

10087

10025

09992

00035

94225

mdashSing

leANN

09198

09289

11008

minus01008

Mod

ular

ANN

10008

10036

10089

004

29


ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










ANN-R

ANN-S

ANN-T

ANN-G


1 faultR

0 no fault

1 faultS

0 no fault

1 faultT

G

0 no fault

1 fault

0 no fault

Logi

c circ

uit


ANN1 L-G


ANN2 L-L-G

ANN3 L-L

ANN4 L-L-L

Fault location

IR(k)

IRminusPF(k)

IS(k)

ISminusPF(k)

IT(k)

ITminusPF(k)

VR(k)

VRminusPF(k)

VS(k)

VSminusPF(k)

VT(k)

VTminusPF(k)

Lf




1) uses only







InputFL2

and InputFL3


InputFL1

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

]

InputFL2

= [119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]




Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Fault type119871-g 119877-119866 119878-119866 119879-119866119871-119871 119877-119878 119877-119879 119879-119878

119871-119871-g 119877-119878-119866 119877-119879-119866 119879-119878-119866119871-119871-119871 119877-119878-119879

L-g 119877-119866 119878-119866 119879-119866L-L 119877-119878 119877-119879 119879-119878

L-L-g 119877-119878-119866 119877-119879-119866 119879-119878-119866L-L-L 119877-119878-119879




InputFL3

= [119868119877(119896)

119868119877minusPF (119896)

119868119878(119896)

119868119878minusPF (119896)

119868119879(119896)

119868119879minusPF (119896)

119881119877(119896)

119881119877minusPF (119896)

119881119878(119896)

119881119878minusPF (119896)

119881119879(119896)

119881119879minusPF (119896)

]

(8)


OutputFL = [119871119891] (9)


119891(1 10 20 30 90 of


119891(01Ω 50Ω














1 FL2



119891= 0ndash100 of




Absolute Error



(10)


1 FL2 and FL

3) Indeed the
















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















1and




2


1 FL2 and FL







1 02218 and 19713 for FL

2 and




1and FL

2








50 60 70 80 90 100 110405060708090

100110120

Time (ms)

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km



X = 69Y = 110

X = 92Y = 751297


119891= 75Km

119877119891= 200Ω and FIA = 10∘



119891= 75 km119877








Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table7Th

eeffectof

thefaulttype

andthelocationof

mod

ular

ANN-based

faultlocators(FL

1FL

2andFL

3)

Faulttype

Fault

locatio

n(K

m)

Fault

inception

angle(∘)

Fault

resistance

(Ω)

Outpu

tof

ANN-based

FL1(K

m)

Outpu

tof

ANN-based

FL2

(Km)

Outpu

tof

ANN-based

FL3

(Km)

Percentage

error

ofANN-based

FL1(

)

Percentage

error

ofANN-based

FL2(

)

Percentage

error

ofANN-based

FL3(

)

Sing

lelin

etogrou

ndfaults(119871-g)

07325

26068971

071137

070196

01029

0113

700196

13125

130

134461

125841

1274

10044

6104159

02590

23145

26

226988

233415

228875

03012

03415

01125

34275

195

352511

3512

86342173

12511

11286

02173

475

120

4610

81474954

472511

08919

04954

02511

5825

95570910

583599

5812

7109090

03599

01271

66215

122

6712

41669714

662791

11241

09714

02791

7510

53756487

744259

748118

064

8705741

01882

8340

144

8214

75819471

828334

08525

10529

01666

96135

125

945401

970778

957126

14599

10778

02874

Dou

blelinetogrou

ndfaults(119871-119871-g)

0925

101017

120917

8390

708

01712

01783

00708

1455

26

138277

138054

139271

01723

01946

00729

26125

190

249810

247138

257297

10190

12862

02703

38225

70385714

384293

3818

6605714

04293

01866

44315

9544

9141

449785

442317

09141

09785

02317

52360

55527129

526129

5217

1107129

06129

01711

63120

170

6212

5964

0709

627199

08741

10709

02801

7890

99788012

770878

7815

3108012

09122

01531

88120

65881150

868019

878914

11150

11981

01086

9275

120

929908

9315

999217

0509908

11599

01705

Line

tolin

efaults

(119871-119871)

06325

mdash062371

058914

059825

02371

01086

00175

16125

mdash1610

99162514

160180

01099

02514

00180

22145

mdash224147

219471

223041

04147

00529

03041

31275

mdash3119

453412

86309197

01945

01286

00803

455

mdash4532

74452748

450923

03274

02748

00923

5425

mdash542998

550074

5413

5902998

10074

01359

67215

mdash6719

29672387

668147

01929

02387

01853

7710

mdash774128

767035

768041

04128

02965

01959

8240

mdash824511

826326

819033

04511

06326

00967

90135

mdash907080

928615

902734

07080

08615

02734

Three-

linefaults

(119871-119871-119871)

0525

mdash0512

880514

3104

9212

01288

01431

00788

1255

mdash1210

07122041

120704

01007

02041

00704

23125

mdash232051

227733

2310

9702051

02267

01097

36225

mdash358134

352010

360914

01866

07990

00914

42315

mdash4212

75417187

420868

01275

02813

00868

57360

mdash573488

57400

9568003

03488

040

0901977

66120

mdash66

2914

652799

6612

7702914

07201

01277

7490

mdash736811

750719

738384

03189

10719

01616

83120

mdash824087

836729

827337

05913

06729

02663

9475

mdash959971

949129

942053

09971

09129

02053




119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119877-119866 10∘ 0 75 748889 753175 750912 01111 03175 00912119877-119866 10∘ 10 75 747792 747782 751008 02208 02218 01008119877-119866 10∘ 100 75 758217 753390 737193 08217 13390 02807119877-119866 10∘ 150 75 758944 756008 753071 08944 06008 03071119877-119866 10∘ 200 75 762019 769713 751297 12019 19713 01297




119877-119878-119866 33 30∘ 11 113129 109023 110009 03129 00977 00009119877-119878-119866 33 60∘ 11 106189 107948 108984 03811 02052 00967119877-119878-119866 33 90∘ 11 112009 112078 111299 02009 02078 01299119877-119878-119866 33 180∘ 11 113914 115851 111007 03914 04149 01007119877-119878-119866 33 360∘ 11 114015 114197 108392 04015 04197 01608



119891(Ω) FL1 FL2 FL3 FL1 FL2 FL3

119878-119866 360∘ 199 96 937422 935863 958197 22578 24137 01803119878-119879 360∘ mdash 96 967001 968100 957881 07001 08100 02119119878-119879-119866 360∘ 199 96 938066 979806 963011 21934 19806 03011119877-119878-119879 360∘ mdash 96 950009 971732 962999 09991 11732 02999

0

20

40

60

80

100

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

50 60 70 80 90 100 110Time (ms)

X = 92Y = 110967

X = 70Y = 110



time = 70 ms

time = 92 ms


119891= 11Km

119877119891= 33Ω and FIA = 60∘


119891= 11Km and







2) Consequently







119891= 33Ω and





119890= 92ms at a








3is more accurate


1and FL

2 The





(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












(∘)119871119891range()

119877119891range(Ω)

Errorrange

Responsetime





Notindicated





Notindicated

Jiang et al [31]


voltages quantities


voltages quantities

Notindicated

Notindicated

Notindicated





15693 15 cycles

Proposed scheme






119891max = 96 km 119877119891max = 199Ω


3) located the


119891= 962999









50 60 70 80 90 100 11092949698

100102104106108110112

Time (ms)

X = 75Y = 110

AN

N-o

utpu

tes

timat

ed fa

ult l

ocat

ion

(km

)

X = 100Y = 962999




119891= 96Km

119877119891= 199Ω and FIA = 360∘


6 Conclusion






References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













References






































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Accurate Fault Classifier and Locator for...

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Transcript of Research Article Accurate Fault Classifier and Locator for...