enhancing the performance of transmission line directional relaying, fault classification and fault...
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Published in IET Generation, Transmission & DistributionReceived on 26th May 2014Revised on 18th September 2014Accepted on 14th October 2014doi: 10.1049/iet-gtd.2014.0498
T Gener. Transm. Distrib., pp. 1–12oi: 10.1049/iet-gtd.2014.0498
ISSN 1751-8687
Enhancing the performance of transmission linedirectional relaying, fault classification and faultlocation schemes using fuzzy inference systemAnamika Yadav, Aleena Swetapadma
Department of Electrical Engineering, National Institute of Technology, Raipur, CG, India
E-mail: [email protected]
Abstract: This study aims to improve the performance of transmission line directional relaying, fault classification and faultlocation schemes using fuzzy system. Three separate fuzzy inference system are designed for complete protection scheme fortransmission line. The proposed technique is able to accurately detect the fault (both forward and reverse), locate and alsoidentify the faulty phase(s) involved in all ten types of shunt faults that may occur in a transmission line under different faultinception angle, fault resistances and fault location. The proposed method needs current and voltage measurements availableat the relay location and can perform the fault detection and classification in about a half-cycle time. The proposed fuzzylogic based relay has less computation complexity and is better than other AI based methods such as artificial neural network,support vector machine, and decision tree (DT) etc. which require training. The percentage error in fault location is within 1km for most of the cases. Fault location scheme has been validated using χ2 test with 5% level of significance. Proposedscheme is a setting free method and is suitable for wide range of parameters, fault detection time is less than half cycle andrelay does not show any reaching mal-operation so it is reliable, accurate and secure.
1 Introduction
The detection, classification, identification of faulty phase andlocation of faults on power transmission lines are the mainobjectives of any protective relaying scheme. The modernpower system networks are highly interconnected, thusdirectional relaying scheme which is set to respond to faultsin forward direction only and within the protection zonewithout intentional time delay is needed to ensure the highspeed fault clearing and maintain the system stability. Faultclassification, faulty phase identification and determining itslocation are essential to carry out the maintenance of powertransmission line and allow single pole tripping of linecircuit breakers in the event of single phase to earth faults.A variety of methods exist for detecting, classifying andlocating the faults on power transmission lines [1–24].Artificial neural network (ANN) based fault locationscheme is reported which uses fundamental components ofboth currents and voltage in [1]. ANN based faulty phaseselection scheme [2] has been developed using faultgenerated high frequency noise, captured using stack tunersand coupling capacitor combination. Some faultclassification schemes have been developed utilisingcombined un-supervised/supervised neural network [3],PSO trained ANN [4], fuzzy [5, 6], fuzzy-neuro [7],combined fuzzy–wavelet schemes [8, 9] and decision-treebased method [10] for protection of transmission lines. Thetechnique reported in [3] uses combined self-organising
feature map and backpropagation network for faultclassification in double circuit line. PSO has been used tofind optimum number of neurons in hidden layer of ANNin [4] which classifies the fault using detailed waveletcoefficients of current signals. Further fuzzy logic has beenused for fault classification only in [5, 6], and inconjunction with ANN in [7] and wavelet technique in [8,9]. All these schemes only classify the fault but do notestimate the fault location, also they do not deal withdirectional relaying. Combined ANFIS with wavelet [11]has been developed for both fault classification andlocation, but it is also non-directional. It is worthwhile tomention here that ANN based schemes [1–4, 7, 11] havesome limitations in classification accuracy, such as multipleoptimum solutions, dependability on large input space, thetedious training process and it follows heuristic path. Forbetter classification, support vector machine (SVM) is usedin series-compensated transmission line for faultclassification [12] by utilising three line currents and zerosequence current and for both classification and location[13] utilising voltage and current transient signals. Themajor demerit of all the above mentioned soft computingtechniques (ANN, fuzzy-neuro, ANFIS, DT and SVM) isthat they are time consuming algorithms as they need a lotof training data. Recently, symmetrical components ofreactive power have been used for fault classification andfaulty phase selection in transmission line [14]. It is alsoworth pointing out that all these techniques only detect/
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classify the fault [1–10, 12, 14] and some classify and locatethe fault [11, 13]; but all these techniques do not deal withdirectional relaying.Directional relays are set to respond to faults in forwarddirection and within the protection zone without intentionaltime delay and are, therefore, used where high speed faultclearing is needed. Some directional relaying schemes havebeen developed in past for fault direction detection onlyemploying ANN [15, 16], wavelet [17], mathematicalmorphology [18], travelling wave based scheme [19–21],fuzzy [22] and positive sequence components [23].However, all these directional relaying schemes [15–23]only detect the fault and its direction but they do notclassify the fault or identify the faulty phase, nor do theylocate the faults. Further ANN routine for fault directiondetection, classification and fault section estimation hasbeen proposed in [24], but it requires one cycle time, also itdoes not estimate the exact location. Another schemeutilising synchronised measurements of the two terminalsusing PMU has been presented in [25], but it requirescommunication link, thus its reliability is dependent onavailability of communication link. Recently the authorshave proposed ANN based directional relay for faultdetection and classification [26], but it does not estimatethe location of fault. In order to reduce the down time andto carry out the maintenance work, it becomes imperative todetermine the exact location of fault and the fault type sothat the repair crew can restore the power flow as fast aspossible. In all the authors’ previous works [27–31] on faultdirection identification, fault classification and locationestimation are based on training based method, namelyANN, which uses fundamental components of voltage andcurrent signals as input. On the other hand, the proposedwork is based on fuzzy inference system which uses phaseangle of positive sequence current for fault directionestimation, magnitude of positive sequence current andvoltage for fault location estimation and magnitude offundamental component of voltage and current as well aszero sequence current for fault classification.The methods based on training either ANN, SVM, DT,
combined neuro-fuzzy and ANN-wavelet are timeconsuming and increase the computation complexity. Theselection of the transfer functions, number of hidden layers,number of neurons, mean square error goal, trainingalgorithms and epochs to achieve a good performance intraining is not an easy task. Hence, these schemes cannotbe considered as very efficient techniques, instead anymethod that can detect, classify and locate the fault withoutany training will be better, like fuzzy logic. To the best ofthe knowledge of the authors, no study has been reportedyet employing fuzzy system to provide all function ofprotective relaying: directional fault detection, faultclassification, faulty phase identification and fault location.This paper presents fuzzy logic approach to detect (both
forward and reverse), classify and locate all the shunt faults(symmetrical and unsymmetrical) in a transmission line.Further, an advanced fuzzy based relay is suggested withimproved first zone protection of the line by consideringwide range variation in fault parameters such as fault type,fault location, fault resistance and fault inception angle. Theproposed technique is able to accurately detect the fault(both forward and reverse) in about a half-cycle time andalso identify the faulty phase(s) involved in all ten types ofshunt faults that may occur in a transmission line underdifferent fault inception angle, fault resistances and locationof fault. The paper is organised as follows. The Section 2
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presents the proposed fault direction detection, classificationand location scheme using fuzzy inference system. InSection 3, the performance of the proposed scheme isevaluated under various fault situations. Further, thevalidation of the fault location scheme using χ2 test isdiscussed in Section 4. Comparison with other schemes isgiven in Section 5 and advantages of the proposed methodare stated in Section 6. Concluding remarks are given inSection 7.
2 Proposed fuzzy inference system basedfault direction detection, classification andlocation
The flow chart of the proposed fuzzy inference system basedprotection scheme is shown in Fig. 1. Three separate fuzzyinference system (FIS) are designed for complete protectionscheme for transmission line. FIS-1 is designed fordirectional fault detection which discriminates between nofault, forward fault and reverse fault, FIS-2 is designed forfault classification which classifies the fault type andidentifies the faulty phase and FIS-3 finds the location offault. The voltage and current signals are recorded at oneend of the line. The presence and direction of fault on atransmission line is determined from the phase angle (Φ) ofpositive sequence current. The output of directional faultdetection FIS-1 with respect to time should be ‘0’ if there isno fault, ‘1’ if there is a forward fault and ‘−1’ if there is areverse fault.If there is forward fault then the fuzzy based fault
classification network FIS-2 is activated, which determinesthe type of fault along with the faulty phase. Inputs forFIS-2 are magnitude of fundamental components of eachphase voltage and currents. In case of phase to phase fault,no zero sequence current flows, while in case of phase(s) toground fault, large zero sequence current flows. In order todetect whether ground is involved in fault loop or not, zerosequence current is taken as another input for ground faultdetection. Four outputs corresponding to the three phasesand ground were considered as outputs provided by thenetwork to determine which of the three phases: A, B, Cand/or ground are present in the fault loop. After classifyingthe fault; location of faults is estimated using FIS-3.Designing of each FIS is described in the subsections.Various fault parameter variation e.g. fault type, faultlocation, fault inception angle and fault resistance arestudied. Most important part of the fuzzy logic is designingthe rules for different modules. Current and voltage signalsare studied extensively to design the three FIS so that it canachieve maximum accuracy.
2.1 Design of fuzzy based fault direction detector(FIS-1)
The input for FIS-1 for fault direction detector is phase angleof positive sequence current signal only. FIS used here is‘Mamdani’ type with triangular member function. Phaseangle (Φ) is set to certain range which corresponds toforward or reverse fault. Three ranges of Φ are selectedusing triangular member function, that is, ΦLOW, ΦMIDand ΦHIGH. The degree of membership functions of phaseangle for fault direction is shown in Fig. 2a. The output triplogic also contains three ranges of triangular memberfunction, that is, trip reverse TR (−1), trip not TN (0) and
IET Gener. Transm. Distrib., pp. 1–12doi: 10.1049/iet-gtd.2014.0498
Fig. 1 Flowchart of the proposed fuzzy based protection scheme
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trip forward TF (1). Three rules used for fault directiondetection are:-
1. If phase angle is ΦLOW then (trip is TF)2. If phase angle is ΦMED then (trip is TN)3. If phase angle is ΦHIGH then (trip is TR)
2.2 Design of fuzzy based faulty phaseidentification and classification (FIS-2)
Inputs to the faulty phase identification and classificationFIS-2 are fundamental components of three phase current,voltage and zero sequence current signal is identification ofground faults. Each input signal is distributed in threeranges with triangular member function, that is, low,medium and high as shown in Fig. 2. There are four
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outputs for faulty phase identification corresponding tothree phases A, B, C and G (ground) which becomes high(1) in case of fault otherwise low (0). The output trip logicalso contains two ranges of triangular member function, thatis, trip low TL (0) and trip high TH (1). The rules used infuzzy based faulty phase identification and classificationFIS-2 are shown in Table 1.
2.3 Design of fuzzy based fault location (FIS-3)
Inputs given to the fuzzy inference system (FIS-3) for faultlocation estimation are positive sequence current andvoltage signals. FIS-3 used here is Mamdani type withtriangular member function. From positive sequence currentand voltage signals, positive sequence impedance iscalculated using (1). From positive sequence impedance; 40post fault samples are taken after one cycle of occurrence of
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Fig. 2 Degree of fuzzy membership functions for input variables
a Phase angle for fault direction detectionb Voltage for fault classificationc Current for fault classification
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fault. Mean impedance value is calculated from these samplesas per (2), which varies from location to location for differenttypes of fault
Z = Vp/Ip (1)
where Z is positive sequence impedance, Vp is positivesequence voltage and Ip is positive sequence current
Zmean =∑N1
Z/N (2)
where Zmean is the mean impedance and N is the number ofsamples taken.Mean impedance obtained is set to certain range which
corresponds to location of fault. Range of mean impedanceis different for different fault type. Forty two ranges of Zare selected using triangular member function, that is,ZLOW, ZMID1, ZMID2, …, ZMID40 and ZHIGH. Theoutput trip logic of the protection scheme also contains 42ranges of triangular member function representing the faultlocation values. For each fault type LG, LLG, LL and LLLseparate FIS is designed to estimate the location of fault,that is, total four FIS modules for fault location are designed.
Table 1 Rules of Fuzzy based faulty phase identification andclassification (FIS-2)
Parameters V low V mid V high
ILOW TL TL TLIMID TH TH THIHIGH TH TH TH
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3 Performance evaluation and discussion
A typical 400 kV, 50 Hz, power transmission system is takenfrom our earlier reported work [26], wherein fault directiondetection and classification scheme has been developed, butfault location estimation has not been done. Finding theaccurate fault location is equally very important for apermanent fault in the line in order to make necessaryrepairs, and reduce the repair and down time so as torestore power as soon as possible. The time needed todetermine the fault point along the line will affect thequality of the power delivery. In this paper fuzzy logicbased fault direction detection, classification and faultlocation schemes are developed. Test system shown inFig. 3 is considered to test the suitability of the proposedprotective relaying algorithm. It consists of two sourcesconnected through a 200 km transmission line. Relay islocated at Section 2 at bus2, which is taken as primarysection. The fuzzy based protective relaying scheme givesprotection to both forward and reverse sections. Test resultsare shown below by varying fault type (LG, LL, LLG, LLLand LLLG), fault location (1–99 km) in a step of 2 km,fault inception angle (0–180°) in a step of 45° and faultresistance (0, 10 and 100 Ω).
3.1 Performance of fault direction detection FIS-1
The fault direction detection FIS-1 detects the presence offault and also finds the direction of fault. Input given to thefuzzy based fault detector is phase angle of positivesequence currents only. When there is no fault in thesystem the output will be always zero. Once any faultoccurs in the line, the output starts changing and reaches toeither +1 or −1 depending upon the forward or reverse
IET Gener. Transm. Distrib., pp. 1–12doi: 10.1049/iet-gtd.2014.0498
Fig. 3 400 kV Test system
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faults, respectively. Fig. 4a, top plot, shows the input given tothe fuzzy based direction detector during fault in the reversesection (LHS) at −0.1 km from bus-2 at 60 ms. The bottomplot shows the output of fuzzy based detector and directionestimator is ‘0’ up to 60 ms of time; indicating there is nofault in the system. After 60 ms of time it startsdecreasing, which shows that there is a fault in the reverse
Fig. 4 Input and output of fault direction detector during AG fault at 6
a in Section 1 at −0.1 kmb in Section 2 at 0.1 km
Table 2 Test results of fuzzy based fault direction detector FIS-2 duri
Faultsection
Fault location,km
Faulttype
Faultresistance, Ω
Fault incepangle (0
reverse −95 AG 0 0−90 BG 10 45−70 CG 100 90−50 ABG 0 135−30 BCG 10 180−10 CAG 100 0
forward 10 AG 0 030 BG 10 4550 CG 100 9070 ABG 0 13590 BCG 100 18095 AB 10 0
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line section and reaches to −1 in 65 ms time, thus theproposed relay take 5 ms time to detect the reverse fault.Similarly, Fig. 4b shows the input and output result forAG fault in the forward section (RHS) at 0.1 km frombus-2 at 60 ms. The output of fuzzy based directiondetector is ‘0’ up to 60 ms of time, showing that and thereis no fault in the system. After 60 ms of time, it started
0 ms
ng variation in fault parameters
tion)
Output of fuzzy baseddirection detector
Time required to detectthe fault in ms
−1(Reverse) 6−1 (Reverse) 5−1 (Reverse) 5−1 (Reverse) 7−1 (Reverse) 7−1 (Reverse) 31(Forward) 71(Forward) 71(Forward) 71(Forward) 71(Forward) 91(Forward) 10
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Fig. 5 Fault classifications during an AG fault 0.1 km at ti = 60 ms
a Inputs to fault classification FIS-2: fundamental three phase currents, zero sequence current and fundamental voltagesb Output of fault classification FIS-2
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increasing and reaches to +1 at 67 ms, thus it take 7 ms timeto detect the forward fault. Table 2 gives some of the testresults of fuzzy based fault direction detector depicting thefault detection time for different types of fault withvarying fault location, fault resistance, fault inception anglein forward or reverse direction from bus-2. From Table 2,it can be seen that fault direction detection time is within10 ms for all fault cases.
3.2 Performance of faulty phase identification andfault classification FIS-2
If the fault occurs in forward direction, the fuzzy based faultyphase identification and fault classification FIS-2 gives fouroutputs A, B, C and G which should be ‘0’ when there isno fault and ‘1’ if there is any fault. The appropriateness ofthe proposed scheme is checked graphically during an AGfault at 0.1 km from bus-2 at 60 ms and Fig. 5a shows theinputs given to the fault classification module: fundamentalthree phase currents, zero sequence current and fundamentalvoltages. Zero sequence current is required to determinewhether the fault loop involves ground or not. Fig. 5b
Table 3 Performance of faulty phase identification and fault classifica
Fault location (in km) Fault resistance (in Ω) Fault inceptio
10 100 920 0 1330 10 1840 10050 0 460 10 970 100 1380 0 1890 10095 0 4
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shows the outputs of fault classification FIS-2. Outputs ofFIS-2 shows that ‘A’ phase goes high (1) at 64 ms time andG goes high (1) at 67 ms time, with other outputs B and Cremaining low (0) and unaffected confirming that it is asingle line to ground fault (AG). The effects of variation ofdifferent fault parameters, namely fault type, fault location,fault resistance and fault inception angle, have been studied.The performance of faulty phase identification and faultclassification FIS-2 is shown in Table 3, which shows thetime taken to identify the faulty phase(s) and ground iswithin 10 ms for all fault cases.
3.3 Performance of fault location FIS-3
After fault phase identification and fault classification, faultlocation is estimated. Inputs given to the fuzzy based faultlocator are the positive sequence voltage and currentsignals. Four fault location modules are designed for LG,LLG, LL and LLL faults using fuzzy logic. Fault locationerror is calculated using the (3) [13] for faults involvingground (LG, LLG) and faults not involving ground (LL,LLL) and given in Tables 4 and 5, respectively. The %
tion FIS-2 during variation in fault parameters
n angle (in°) Time taken by fuzzy basedfault classifier FIS-2 to
identify the faulty phase (s)& Ground (in ms)
Fault type
A B C G
0 – – 5 2 CG5 6 4 – 2 ABG0 – 4 3 2 BCG0 10 – 10 9 CAG5 6 4 9 – ABC0 4 4 – – AB5 – 5 4 – BC0 8 – 8 – CA0 6 – – 2 AG5 4 5 – – AB
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Table 4 Performance in case of fault location for LG and LLG fault
Fault inception angle (°) Actual fault location, km LG LLG
Estimated fuzzy location, km % error Estimated fuzzy location, km % error
45 10 8.687 −1.312 8.902 1.09790 20 19.658 −0.341 21.600 1.645 30 31.241 1.241 28.616 1.383135 40 39.931 −0.068 39.75 0.2590 50 50.074 0.074 50.25 0.250 60 60.476 0.476 59.383 0.616135 70 68.863 −1.136 69.623 0.3760 80 79.460 −0.539 80.25 0.25135 90 90.331 0.331 91.622 1.622180 95 95.087 0.087 98.521 −3.521
Table 5 Performance in case of fault location for LL and LLL fault
Fault inception angle (°) Actual fault location, km LL LLL
Estimated fuzzy location, km % error Estimated fuzzy location, km % error
45 10 9.921 −0.078 9.750 0.2590 20 20.046 0.046 21.600 1.6135 30 30.455 0.455 31.546 1.546180 40 40.133 0.133 40.184 0.1840 50 49.971 −0.028 50.959 0.95945 60 59.728 −0.271 59.221 0.77890 70 72.198 2.198 67.910 −2.0890 80 80.004 0.004 81.794 1.79445 90 90.262 0.262 90.776 0.776180 95 94.347 −0.652 95 0
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error is within 1 km for most of the faults, showing that it canbe used efficiently unlike other training based methods.
% Error = Actual Location− Estimated Location
Line length
[ ]∗100
(3)
3.4 Analysis of faults near far end boundary todetermine the protection range
Proposed fuzzy based method correctly detects the forwardand reverses faults, identifying the faulty phase andclassifying the faults up to 95% of line length. This hasbeen verified by testing the proposed scheme for a numberof faults near far end boundary. Some of the results aregiven in Table 6 to show that the protection range of the
Table 6 Fault near boundaries to evaluate reach setting
Faulttype
Faultlocation,
km
Faultinceptionangle (°)
Faultresistance,
Ω
Faultdetectiontime, ms
AG 80 0 0 10BG 82 45 10 9CG 84 90 100 9ABG 86 135 0 8BCG 88 180 10 7CAG 90 0 100 8ABC 92 45 0 6AB 94 90 10 7BC 95 135 0 7
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proposed scheme is up to 95% of the line length. Figs. 6aand b show the graphical time domain results of faultdirection detection and faulty phase identification andclassification scheme for an AB fault at 95 km at 60 ms.Fig. 6a shows output of fault direction detector FIS-1,which is low up to 60 ms time and it goes high (1) after68 ms time, showing that there is a fault in forward section.Fig. 6b shows the output of faulty phase identification andclassification FIS-2 in which A and B phase goes highshowing there is AB fault. The fuzzy based fault locationFIS-3 is also tested for different types of faults simulatedbetween 80–95 km from relaying point in the step of 2 km,that is, near far end boundary and % error in fault locationestimation is calculated and given in Table 7. It can be seenthat most of the faults can be located with % error less than2%, however in some cases it is up to 4%. Hence, it can beconcluded that the protection range of the proposed fuzzybased scheme is 95% of line length.
3.5 Performance of the proposed scheme fordifferent voltage levels
The performance of the proposed fuzzy based schemedesigned for fault direction estimation, fault classificationand fault location is checked for different voltage levels like220, 400 and 500 kV. The phase angle of positive sequencecurrent which is used as input to FIS-1 is not affected muchby varying the voltage level as compared with thedeveloped scheme FIS-1 for fault direction estimation for400 kV system. Thus, the proposed fuzzy based directionestimation scheme is not affected by variation in voltagelevels.Further, the faulty phase identification and fault
classification FIS-2 uses fundamental components of current
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Fig. 6 Output of fault direction and faulty phase identification and classification during AB fault at 95 km at ti = 60 ms
a Output of fault direction detectionb Output of faulty phase identification and classification
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and voltage signals for faulty phase identification and zerosequence currents for ground detection. For differentvoltage levels; the magnitude of fundamental componentsof current, voltage and zero sequence current varysignificantly, which have been used as inputs to FIS-2.Thus, in order to make the proposed scheme suitable forother voltage levels, the range of membership functions ofthe input variables is required to be modified after studyingthe ranges of the input variables for no-fault situation andfault situation with varying fault parameters. For differentvoltage levels, the range of membership function for FIS-2for fault classification is shown in Table 8. By setting therange of input variables for 220, 400 or 500 kVtransmission voltages as per Table 8, the proposed schemecan be used for fault classification of different voltagelevels. For example, consider a single line to ground faultin phase ‘A’ occurring in transmission line of differentvoltage levels, say 220 and 500 kV, that is, AG fault at 90 km
Table 7 Location estimation in case of faults near far end boundary
Fault location,km
LG LLG
Estimatedlocation, km
%error
Estimatedlocation, km e
82 81 1 81.60 084 83.059 0.941 83.522 086 85 1 84.921 188 88.35 −0.35 86.263 190 90.717 −0.717 89.247 092 93.015 −1.015 92.068 194 92.225 1.775 93.727 195 92.367 −2.632 95.050 −0
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in Section 2 at 60 ms with Rf. 0.001 Ω. Figs. 7a–d showthe test results of fault direction estimator and faultclassifier for the two voltage levels 220 and 500 kV,respectively.FIS-3 for fault location estimation takes the mean of
positive sequence impedance (Z) as input, which dependson ratio of positive sequence voltage and current which willbe different for different voltage levels. The number ofranges of Z is determined by studying the changes in valueof Zmean for fault at different locations with varyingdifferent fault parameters, and also the number of ranges ofZ is dependent upon the total line length of thetransmission system to be protected. For example, in thepresent case, 42 ranges are made for 100 km line length bydividing the line length to a number of ranges (0–2.5 km,2.5–5 km, 5–7.5 km …… 97.5–100 km and no fault). For,the proposed method, in each 2.5 km fault distance oneinput and output member function is designed which makes
LL LLL
%rror
Estimatedlocation, km
%error
Estimatedlocation, km
%error
.4 81.5 0.5 79.921 2.079
.478 82.973 1.027 81.60 2.4
.079 83.400 2.6 85.883 0.117
.737 87.447 0.553 88.808 −0.808
.726 90.275 −0.275 90.776 −0.776
.015 90.176 1.824 90.997 1.003
.775 93.173 0.827 92.640 1.36
.050 95.250 −0.250 94.966 −0.033
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Table 8 Range of member functions of FIS-2 for faultclassification for different voltage levels
Voltagelevels
Memberfunctions
Triangularmember function
range offundamentalcurrent signal
Triangular memberfunction range of
fundamentalvoltage signal
220 kV MF1 [−600, 0, 600] [−1000, 0, 1000]MF2 [0, 600, 1000] [0, 1000, 10000]MF3 [600, 1000, 4000] [1000, 10000,
200000]400 kV MF1 [−400, 0, 400] [−3000, 0, 3000]
MF2 [0, 400, 1100] [0, 3000, 15000]MF3 [400, 1100, 4000] [3000, 15000,
400000]500 kV MF1 [−300, 0, 300] [−5000, 0, 5000]
MF2 [0, 300, 1300] [0, 5000, 20000]MF3 [300, 1300, 3000] [5000, 20000,
500000]
Table 9 Range of member function for fault locationestimation for different voltage levels
Output faultlocation, km
Triangular member function range of Zmean fordifferent voltage levels
220 kV 400 kV 500 kV
2.5 [180 185 189] [370 372 375] [546 548 551]5 [185 189 193] [371 375 379] [548 551 553]7.5 [189 191 193] [372 379 380] [551 553 555]10 [191 193 195] [375 380 383] [553 555 557]12.5 [193 195 198] [379 383 384] [555 557 559]15 [195 198 201] [380 384 388] [557 559 561]17.5 [198 201 204] [383 388 389] [559 561 563]20 [201 204 206] [384 389 393] [561 563 565]22.5 [204 206 208] [388 393 394] [563 565 567]25 [206 208 210] [393 395 396] [565 567 569]27.5 [208 210 212] [395 397 400] [567 569 571]30 [210 212 214] [396 399 402] [569 571 573]
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40 ranges (for fault situation), and two ranges are selected forno fault conditions. If the length of line to be protected isdifferent from 100 km, the number of ranges of Z will alsochange, that is, number of ranges of Z will increase if linelength increases and vice versa.For different voltage levels, the range of membership
function of input Zmean is determined by studying thechanges in value of Zmean by varying different faultparameters (fault location, fault type, fault inception angleand fault resistance. For different fault location, the value ofZmean will be different for different fault parameters (faultinception angle, fault type etc). The range of membershipfunction for input Zmean for different voltage levels say 220,400 and 500 kV for LG faults at different fault locations inkm (2.5, 5, 7.5, 10 etc.) is depicted in Table 9. Similarly,the ranges of Zmean for other fault locations are calculatedbut not shown here for brevity. From Table 9 it can beobserved that, for a particular fault location range, the range
Fig. 7 Test results of fault direction estimator and fault classifier duringlevels (a, b) 220 kV and (c, d) 500 kV, respectively
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of membership function also differ for different voltagelevels.
4 Validation of fuzzy based locationtechniques using chi square (χ2) test
The proposed fuzzy based fault location FIS-3 has been testedfor different types of fault with varying fault location, faultinception angle and fault resistance and % error is calculated.The number of fault cases in which the % error in faultlocation is within the ranges 0 to ±2.0% and ±2.1 to ±5%are counted. Fig. 8 shows the percentage of fault cases inwhich the fault location error is within 0 to ±2.0% and ±2.1to ±5% ranges for each type of fault (LG, LLG, LL andLLL). In most of the cases the fault location is within 2%error and highest error obtained in this method is 5%.As different fault type has different values and some errors
are up to 5% of range it is necessary to confirm this method isefficient to use or not. Different tests are used for error
AG fault at 90 km in Section 2 at 60 ms with Rf = 0.001 Ω for voltage
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Fig. 8 % error distribution for different faults
a LG faultb LLG faultc LL faultd LLL fault
Table 11 χ2 test for fault location error for different types offault
Faulttype
Parameters Range of percentage error Σ
0% to ± 2% ± 3% to ± 5%
LG fo 209 77 Σ{( fo− fe)2/fe} =
4.027fe 211.184 67.815( fo− fe)
2/fe 1.737 2.290LLG fo 219 61 Σ{( fo− fe)
2/fe} =0.0287fe 216.543 63.456
( fo− fe)2/fe 0.0278 0.0009
LL fo 263 71 Σ{( fo− fe)2/fe} =
0.3761fe 258.305 75.694( fo− fe)
2/fe 0.0853 0.291LLL fo 128 31 Σ{( fo− fe)
2/fe} =0.9092fe 122.966 36.033
( fo− fe)2/fe 0.206 0.7032
χ2[all] = Σ{( fo− fe)2/fe} = 5.341
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analysis to conform the efficiency of the method. For thismethod chi square (χ2) test is chosen to do the validation[32]. The computed value must equal or exceed theappropriate critical value to justify rejection of the nullhypothesis or the assumption of independence at the 0.05 orthe 0.01 level of significance. Null hypothesis shows thatthe fuzzy based location method will be accepted. Itconcerns a judgment as to whether apparent differences orrelationships are true differences or relationships or whetherthey merely result from sampling error. The rejection oracceptance of a null hypothesis is based on some level ofsignificance as criterion. Generally, there are two levels ofsignificance 1 and 5%. 5% (0.05) level of significance isoften used as a standard for rejection. This suggests a 95%probability that the difference was because of theexperimental treatment rather than to sampling error. Thenumber of fault cases (known as observed frequency)within a range of % error for different types of fault isshown in the Table 10.Expected frequency of occurrence of error for each of the
cell for all types of fault is calculated from the observedfrequency of the error using (4). χ2 is calculated for alltypes of fault for all the ranges of error and shown inTable 11 by using (5). Different levels of significance fordifferent degrees of freedom are shown in Table 12. Degree
Table 10 Number of fault cases within a range of% error fordifferent types of fault
Fault type Range of percentageerror (no. of Fault cases)
Σ Rows = ΣfrNo. of Fault cases
0% to ±2% ±3% to ±5%
LG 209 77 286LLG 219 62 280LL 263 71 334LLL 128 31 159Σ Columns = Σfc 819 240 Total no.
of cases = 1059
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of freedom can be calculated as per (6)
fe =∑
fc
( )∗
∑fr
( ){ }/Total
[ ](4)
where fe is the expected frequency of error, fc is observed
Table 12 Levels of significance for different degree of freedom
Degree of freedom Level of significance
5% 1%
1 3.84 6.642 5.59 9.213 7.82 11.344 9.49 13.285 11.07 15.096 12.59 16.817 14.07 18.488 15.51 20.099 16.92 21.67
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Table 13 Comparisons with ANN based scheme
Methods Protective relaying functionsprovided
Computation complexity Fault detectiontime, ms
Accuracy,%
ANN based scheme[26]
fault direction detection andfault classification
more (because of large training datageneration, training parameter selection,
large training time)
half cycle inmost fault cases
99
fuzzy inferencesystem basedscheme
fault direction detection, faultclassification and fault location
less ( does not requires training) half cycle in allfault cases
99
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frequencies in columns, fr is observed frequencies in rows andtotal is the sum of all the frequencies.
x2 =∑
{(fo − fe)/fe} (5)
where fo is the observed frequency of error.
D = Rows− 1( )∗ Columns− 1( ) (6)
where D is the degree of freedom.In this method there are 4 rows and 2 columns, so degree of
freedom is 3. From Table 12 with degree of freedom 3,calculated χ2 value is less for both 5 and 1% significantlevels for all types of fault. This shows that null hypothesisis accepted. This shows that the error for fault location willnot be same for replication of experiment. Thus, the fuzzybased fault location FIS-3 scheme is accurate and can beused for transmission line protection application.
5 Comparison with ANN scheme
Earlier authors had proposed ANN based directional relayingscheme [26] in which the fault detection time was half cyclefor most of the cases. Fault classification [27, 29–31] and faultlocation [28, 29] schemes are also developed using ANN.However, the disadvantage of these ANN based methods isthat it requires tedious training process which requires largetraining data set to learn the relationship between no-faultand fault patterns with varying fault parameters. Also, theselection of the transfer functions, number of hidden layers,number of neurons, mean square error goal, trainingalgorithms and epochs to achieve a good performance intraining is not an easy task. Hence, a method withouttraining and without complex computation will be better,such as proposed fuzzy based scheme. The comparison ofthe proposed fuzzy based scheme with ANN based scheme[26] is shown in Table 13. Building a fuzzy inferencesystem for transmission line relaying application is mucheasier as compared to ANN and provides good results withless complexity. Moreover, the proposed method also findsthe location of fault with good accuracy along withdirection detection and fault classification.
6 Advantages of the proposed scheme
(a) Most important advantage of fuzzy based relayingscheme is that it does not need any training so computationburden is much less than any training based methods likeANN, ANFIS, SVM and DT etc.(b) Proposed fuzzy based scheme provides protection to 95%of the line length, compared to conventional distance relayingscheme which provides protection to 80–85% of line length.
IET Gener. Transm. Distrib., pp. 1–12doi: 10.1049/iet-gtd.2014.0498
(c) Fault detection time is within half cycle (10 ms) for allfault cases. The proposed fuzzy based method can detectthe close in fault and far end faults as only phase angle ofpositive sequence current is used for determining thedirection of fault. On the other hand methods utilisingsequence components of voltage signals as input are notable to detect the close-in faults because the magnitude ofvoltage becomes approximately zero during close-in faults.(d) High accuracy is achieved utilising single terminal dataonly, thus avoiding the need of communication link.(e) The proposed fuzzy based directional relaying scheme isunaffected by variation in parameters like fault location, faulttype, fault resistance and fault inception angle. Proposedscheme can work well with large number of fault casestudies considering wide variations in fault parameterswhere as performance of other training based methodsdegrades.(f) Error in case of fault location is within 1 km for most ofthe fault cases except some cases which is validated using χ2
test.
7 Conclusion
The proposed fuzzy inference system based fault directiondetection, classification and location scheme is found to bevery effective under various fault situations. The proposedscheme is very simple and does not require training ascompared with ANN, ANFIS, SVM and DT based scheme.The reliability of this scheme is not affected by differentfault conditions such as fault type, fault distance, faultinception angle, fault resistance etc. Results demonstratethat the proposed scheme effectively detects the faultdirection and the fault type within half cycle time. Faultlocation error in most of the fault cases is up to 2%excluding some cases. Fault location error is validated usingχ2 test. The proposed fuzzy logic based technique offersprimary protection to 95% of line length and backupprotection in case of reverse faults.
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