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Electric Power Systems Research 77 (2007) 501–507

A fuzzy logic based fault classificationapproach using current samples only

R.N. Mahanty a,∗, P.B. Dutta Gupta b

a Department of Electrical Engineering, National Institute of Technology, Jamshedpur 831014, Indiab Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India

Received 29 October 2005; received in revised form 14 February 2006; accepted 29 April 2006Available online 9 June 2006

bstract

An approach for classification of transmission line faults is presented. The approach is based on fuzzy logic and requires the consideration ofhe samples of three phase currents at one end of transmission line. To illustrate the effectiveness of the proposed approach extensive simulationtudies, using EMTP and MATLAB, have been carried out for different types of fault considering wide variations in the operating conditions.

2006 Elsevier B.V. All rights reserved.

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eywords: Fuzzy logic; Fault classification; Transmission line

. Introduction

The identification of the type of fault and the faultyhase/phases is known as fault classification, which is an impor-ant aspect of transmission line protection. Fault classificationas been a topic of interest for several years and as a result of thisnumber of fault classification techniques have been developedy different researchers from time to time. Some of the impor-ant fault classification techniques are: (i) wavelet transformased techniques [1–6], (ii) neural network based techniques7–14] and (iii) fuzzy and fuzzy-neural network based tech-iques [15–18]. These techniques are effective over wide varia-ions in the operating conditions and hence are widely acceptedor fault classification. The techniques based on wavelet trans-orm are computationally complicated and the techniques basedn neural network involve a tedious training process. The fuzzyogic based fault classification approaches involve some linguis-ic rules only [19] and as such are simpler than the waveletransform based techniques or the neural network based tech-iques.

Ferrero et al. [15] proposed a fuzzy logic based approach fordentifying the type of fault (whether l-g or l-l-g). Wang et al.16] proposed an improved method based on fuzzy-neural net-

∗ Corresponding author.E-mail address: rnmahanty2002@yahoo.co.in (R.N. Mahanty).

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378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2006.04.009

ork approach to determine whether the fault is of l-g, l-l or-l-g type. As a further improvement, Dash et al. [17] proposedfuzzy-neural network based method and Das et al. [18] pro-

osed a fuzzy logic based method for fault classification. Bothf these approaches can identify all ten types of short circuitaults.

In this paper, an alternative fuzzy logic based fault clas-ification approach for transmission line protection has beenroposed. Samples of three phase currents at one end of trans-ission line are required to be considered for fault classification

y the proposed approach.To validate the proposed approach, extensive simulation stud-

es have been carried out using EMTP and MATLAB for differ-nt types of fault considering wide variations in fault location,ault inception angle, load angle and fault resistance. Fault dataenerated by EMTP [20] have been used for fault classificationy a MATLAB program, which makes use of the “fuzzy logicoolbox” [21].

. The fault classification methodology

The fault classification technique has been developed on the

asis of extensive simulation studies carried out on the powerystem model shown in Fig. 1 using EMTP and MATLAB. Thearameters of the power system model of Fig. 1 are as follows18]:

502 R.N. Mahanty, P.B.D. Gupta / Electric Power Systems Research 77 (2007) 501–507

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Table 1Values of Δ1, Δ2 and Δ3 in case of a-g fault under variable operating conditions

Fault condition: d, RF, FIA, δ Δ1 Δ2 Δ3

0.15, 0 �, 0◦, 10◦ 0.944 0.053 −0.9980.15, 0 �, 0◦, 30◦ 0.899 0.084 −0.9830.15, 200 �, 0◦, 10◦ 0.684 0.208 −0.8920.15, 200 �, 0◦, 30◦ 0.441 0.219 −0.6600.15, 0 �, 90◦, 10◦ 0.909 0.082 −0.9920.15, 0 �, 90◦, 30◦ 0.871 0.094 −0.9660.15, 200 �, 90◦, 10◦ 0.682 0.206 −0.8870.15, 200 �, 90◦, 30◦ 0.438 0.229 −0.6670.85, 0 �, 0◦, 10◦ 0.924 0.054 −0.9780.85, 0 �, 0◦, 30◦ 0.791 0.123 −0.9140.85, 200 �, 0◦, 10◦ 0.599 0.190 −0.7900.85, 200 �, 0◦, 30◦ 0.327 0.242 −0.5700.85, 0 �, 90◦, 10◦ 0.814 0.127 −0.9420.85, 0 �, 90◦, 30◦ 0.661 0.174 −0.8350.85, 200 �, 90◦, 10◦ 0.615 0.181 −0.7970.85, 200 �, 90◦, 30◦ 0.315 0.241 −0.555

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• for a-g fault Δ1 = highg, Δ2 = mediumg, Δ3 = lowg;• for b-g fault Δ1 = lowg, Δ2 = highg, Δ3 = mediumg;• for c-g fault Δ1 = mediumg, Δ2 = lowg, Δ3 = highg;• for a-b-g fault Δ1 = lowg, Δ2 = highg, Δ3 = lowg;

Table 2Values of Δ1, Δ2 and Δ3 in case of a-b-g fault under variable operatingconditions

Fault condition: d, RF, FIA, δ Δ1 Δ2 Δ3

0.15, 0 �, 0◦, 10◦ −0.953 0.999 −0.0460.15, 0 �, 0◦, 30◦ −0.875 0.993 −0.1170.15, 200 �, 0◦, 10◦ −0.650 0.966 −0.3160.15, 200 �, 0◦, 30◦ −0.343 0.841 −0.4980.15, 0 �, 90◦, 10◦ −0.964 0.998 −0.0350.15, 0 �, 90◦, 30◦ −0.899 0.991 −0.0910.15, 200 �, 90◦, 10◦ −0.661 0.968 −0.3070.15, 200 �, 90◦, 30◦ −0.339 0.838 −0.4990.85, 0 �, 0◦, 10◦ −0.831 0.988 −0.1570.85, 0 �, 0◦, 30◦ −0.520 0.924 −0.4040.85, 200 �, 0◦, 10◦ −0.229 0.808 −0.5790.85, 200 �, 0◦, 30◦ −0.131 0.713 −0.583

Fig. 1. The power system model.

line length = 300 km;source voltages:◦ source 1: v1 = 400 kV; source 2: v2 = 400∠δ kV, where δ is

the load angle;source impedance (both sources):◦ positive sequence impedance = 1.31 + j15.0 �;◦ zero sequence impedance = 2.33 + j26.6 �;frequency = 50 Hz;transmission line impedance:◦ positive sequence impedance = 8.25 + j94.5 �;◦ zero sequence impedance = 82.5 + j308 �;◦ positive sequence capacitance = 13 nF/km;◦ zero sequence capacitance = 8.5 nF/km.

Post-fault samples of three phase currents, generated throughMTP, are considered for fault classification. Using these faultata the task of fault classification is carried out using MAT-AB. The sampling interval is 1 ms and the number of sampleser phase is ten, starting from the 6th sample up to the 15thample. In order to reduce the effect of the dc offset in the faulturrent waveform the first five post-fault samples have not beenonsidered. This means that the data window is of half cycle,hich starts from the 6th and extends up to the 15th post-fault

ample. The total time taken for obtaining the ten post-fault sam-les for each phase is more than half cycle but less than one cyclefter fault inception. The prerequisite of the proposed fault clas-ification approach is that the fault should be detected. The faultlassification technique has been developed as follows:

The characteristic features of different types of fault are foundut in terms of Δ1, Δ2 and Δ3, which are calculated as describedelow. First of all, from the post-fault current samples, as men-ioned above, the ratios r1, r2 and r3 are calculated as follows:

1 = max{abs(Ia)}max{abs(Ib)} , r2 = max{abs(Ib)}

max{abs(Ic)} ,

3 = max{abs(Ic)}max{abs(Ia)}

here Ia, Ib and Ic are the post-fault samples of the three phaseurrents.

Next, the normalized values of r1, r2 and r3 are found out asollows:

1n = r1

max(r1, r2, r3), r2n = r2

max(r1, r2, r3),

3n = r3

max(r1, r2, r3)

inally, the differences of these normalised values are found outs follows.

1 = r1n − r2n, Δ2 = r2n − r3n, Δ3 = r3n − r1n

0000

= fault location in p.u. of line length from bus 1, FIA = fault inception angle,

F = fault point resistance and δ = load angle.

s already mentioned, the characteristic features of differentypes of fault are determined in terms Δ1, Δ2 and Δ3. The fuzzyule base for fault classification is developed on the basis of thealues of Δ1, Δ2 and Δ3.

The values Δ1, Δ2 and Δ3 for a-g, a-b-g, a-b and a-b-c faultsnder variable operating conditions are shown in Tables 1–4. Thealues of Δ1, Δ2 and Δ3 have also been found out for other l-g,-l and l-l-g faults and it has been observed that the characteristiceatures of the different types of fault can be determined on theasis of the values of Δ1, Δ2 and Δ3, as illustrated below.

Ground faults (faults involving ground):

.85, 0 �, 90◦, 10◦ −0.892 0.988 −0.096

.85, 0 �, 90◦, 30◦ −0.600 0.875 −0.275

.85, 200 �, 90◦, 10◦ −0.221 0.816 −0.595

.85, 200 �, 90◦, 30◦ −0.580 0.720 −0.140

R.N. Mahanty, P.B.D. Gupta / Electric Power Systems Research 77 (2007) 501–507 503

Table 3Values of Δ1, Δ2 and Δ3 in case of a-b fault under variable operating conditions

Fault condition: d, RF, FIA, δ Δ1 Δ2 Δ3

0.15, 0 �, 0◦, 10◦ −0.971 0.999 −0.0290.15, 0 �, 0◦, 30◦ −0.913 0.994 −0.0810.15, 200 �, 0◦, 10◦ −0.737 0.949 −0.2110.15, 200 �, 0◦, 30◦ −0.577 0.723 −0.2860.15, 0 �, 90◦, 10◦ −0.964 0.999 −0.0350.15, 0 �, 90◦, 30◦ −0.884 0.989 −0.1060.15, 200 �, 90◦, 10◦ −0.738 0.949 −0.2110.15, 200 �, 90◦, 30◦ −0.569 0.733 −0.2840.85, 0 �, 0◦, 10◦ −0.888 0.990 −0.1020.85, 0 �, 0◦, 30◦ −0.612 0.931 −0.3190.85, 200 �, 0◦, 10◦ −0.551 0.883 −0.3310.85, 200 �, 0◦, 30◦ −0.313 0.730 −0.4170.85, 0 �, 90◦, 10◦ −0.856 0.985 −0.1290.85, 0 �, 90◦, 30◦ −0.313 0.847 −0.53400

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Table 5Values of max(Ia + Ib + Ic) in amps for different types of fault corresponding toδ = 15◦

Fault condition: d, RF, FIA Type of fault

a-g a-b a-b-g a-b-c

0.1, 0 �, 0◦ 2.37 × 104 0.057 1.35 × 104 0.1000.1, 200 �, 0◦ 1.42 × 103 0.010 1.45 × 103 0.0100.1, 0 �, 90◦ 1.61 × 104 0.080 1.36 × 104 0.0800.1, 200 �, 90◦ 1.53 × 103 0.006 1.52 × 103 0.0100.5, 0 �, 0◦ 5.50 × 103 0.040 2.96 × 103 0.0300.5, 200 �, 0◦ 7.91 × 102 0.008 8.24 × 102 0.0100.5, 0 �, 90◦ 3.60 × 103 0.010 3.24 × 103 0.0200.5, 200 �, 90◦ 8.29 × 102 0.006 8.05 × 102 0.0080.9, 0 �, 0◦ 2.42 × 103 0.005 1.53 × 103 0.0080.9, 200 �, 0◦ 2.06 × 102 0.004 2.09 × 102 0.00600

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σ

.85, 200 �, 90◦, 10◦ −0.537 0.887 −0.350

.85, 200 �, 90◦, 30◦ −0.312 0.720 −0.408

for b-c-g fault Δ1 = lowg, Δ2 = lowg, Δ3 = highg;for c-a-g fault Δ1 = highg, Δ2 = lowg, Δ3 = lowg.

here “highg” means a value between 0.2 and 1.0, “mediumg”eans a value between 0.02 and 0.3 and “lowg” means a value

etween −1.0 and −0.005. The suffix “g” has been used toepresent a ground fault.

Phase faults (faults not involving ground):

for a-b fault Δ1 = lowph, Δ2 = highph, Δ3 = lowph;for b-c fault Δ1 = lowph, Δ2 = lowph, Δ3 = highph;for c-a fault Δ1 = highph, Δ2 = lowph, Δ3 = lowph;for a-b-c fault Δ1 = mediumph, Δ2 = mediumph, Δ3 = lowph;or Δ1 = lowph, Δ2 = mediumph, Δ3 = mediumph;or Δ1 = mediumph, Δ2 = lowph, Δ3 = mediumph;

or Δ1 = lowph, Δ2 = lowph, Δ3 = mediumph;or Δ1 = mediumph, Δ2 = lowph, Δ3 = lowph;or Δ1 = lowph, Δ2 = mediumph, Δ3 = lowph.

able 4alues of Δ1, Δ2 and Δ3 in case of a-b-c fault under variable operatingonditions

ault condition: d, RF, FIA, δ Δ1 Δ2 Δ3

.15, 0 �, 0◦, 10◦ 0.501 0.029 −0.530

.15, 0 �, 0◦, 30◦ 0.435 0.087 −0.523

.15, 200 �, 0◦, 10◦ −0.662 0.571 0.091

.15, 200 �, 0◦, 30◦ −0.518 0.428 0.090

.15, 0 �, 90◦, 10◦ −0.085 −0.322 0.408

.15, 0 �, 90◦, 30◦ −0.076 −0.350 0.426

.15, 200 �, 90◦, 10◦ −0.609 0.516 0.093

.15, 200 �, 90◦, 30◦ −0.523 0.421 0.102

.85, 0 �, 0◦, 10◦ 0.581 0.019 −0.600

.85, 0 �, 0◦, 30◦ 0.271 0.259 −0.530

.85, 200 �, 0◦, 10◦ −0.516 0.476 −0.040

.85, 200 �, 0◦, 30◦ −0.350 0.335 −0.016

.85, 0 �, 90◦, 10◦ −0.059 −0.344 0.403

.85, 0 �, 90◦, 30◦ −0.026 −0.433 0.459

.85, 200 �, 90◦, 10◦ −0.509 0.472 −0.038

.85, 200 �, 90◦, 30◦ −0.328 0.331 −0.002

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.9, 0 �, 90◦ 1.91 × 103 0.007 1.74 × 103 0.010

.9, 200 �, 90◦ 2.94 × 102 0.005 2.27 × 102 0.006

here “highph” means a value between 0.5 and 1.0, “mediumph”eans a value between 0.01 and 0.6 and “lowph” means a value

etween −1.0 and −0.005. The suffix “ph” has been used toepresent a phase fault.

From the above discussions it is evident that there should beeparate fuzzy rule bases for classification of ground faults andhase faults. It is also evident that there should be a separateechnique to distinguish between ground faults and phase faults.he technique which has been used in the proposed scheme toistinguish between ground faults and phase faults is discussedelow.

.1. Detection of ground fault

To determine the involvement of ground in fault the value of= max(Ia + Ib + Ic) has been considered. It has been observed

hat the values of σ are high (greater than 100) for faults involv-ng ground and low (less than 1) for faults not involving ground.able 5, which shows the values of σ for some representa-

ive cases of a-g, a-b, a-b-g and a-b-c faults, confirms that thenvolvement of ground in a fault can be easily detected on theasis of the value of σ.

. Development of the fuzzy logic scheme

As discussed in the previous section, the characteristic faulteatures for different types of fault have been determined in termsf Δ1, Δ2 and Δ3. Fuzzy variables have been used to representhe terms Δ1, Δ2 and Δ3 and with these fuzzy variables, theollowing fuzzy rule bases have been developed for classificationf ground faults and phase faults, respectively. After determininghether the fault involves ground or not, the appropriate fuzzy

ule base is used for fault classification.Fuzzy rule base for ground faults:

If Δ1 is highg and Δ2 is mediumg and Δ3 is lowg it is an a-gfault;If Δ1 is lowg and Δ2 is highg and Δ3 is mediumg it is a b-gfault;

504 R.N. Mahanty, P.B.D. Gupta / Electric Power Systems Research 77 (2007) 501–507

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Table 6Fuzzy variables in the antecedent parts of fuzzy rules corresponding to groundfaults

Fuzzy variable Triplets

A B C

Highg 0.2 0.6 1.0Mediumg 0.02 0.16 0.3Lowg −1.0 −0.5 −0.005

Table 7Fuzzy variables in the antecedent parts of fuzzy rules corresponding to phasefaults

Fuzzy variable Triplets

A B C

Highph 0.5 0.75 1.0Mediumph 0.01 0.3 0.6Lowph −1.0 −0.5 −0.005

Table 8Fuzzy variables in the consequent parts of fuzzy rules

Fuzzy variable Triplets

A B C

a-g 4.5 5 5.5b-g 9.5 10 10.5c-g 14.5 15 15.5a-b-g 19.5 20 20.5b-c-g 24.5 25 25.5c-a-g 29.5 30 30.5a-b 34.5 35 35.5b-c 39.5 40 40.5ca

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4. Results and discussions

To validate the proposed fault classification approach, simu-lation studies have been carried out on a 400 kV, 3 phase, 300 km

Fig. 2. The triangular fuzzy membership function.

If Δ1 is mediumg and Δ2 is lowg and Δ3 is highg it is a c-gfault;If Δ1 is lowg and Δ2 is highg and Δ3 is lowg it is an a-b-gfault;If Δ1 is lowg and Δ2 is lowg and Δ3 is highg it is a b-c-g fault;If Δ1 is highg and Δ2 is lowg and Δ3 is lowg it is a c-a-g fault.

Fuzzy rule base for phase faults:

If Δ1 is lowph and Δ2 is highph and Δ3 is lowph it is an a-bfault;If Δ1 is lowph and Δ2 is lowph and Δ3 is highph it is a b-cfault;If Δ1 is highph and Δ2 is lowph and Δ3 is lowph it is a c-afault;If Δ1 is mediumph and Δ2 is mediumph and Δ3 is lowph it isan a-b-c fault;If Δ1 is lowph and Δ2 is mediumph and Δ3 is mediumph it isan a-b-c fault;If Δ1 is mediumph and Δ2 is lowph and Δ3 is mediumph it isan a-b-c fault;If Δ1 is mediumph and Δ2 is lowph and Δ3 is lowph it is ana-b-c fault;If Δ1 is lowph and Δ2 is mediumph and Δ3 is lowph it is ana-b-c fault;If Δ1 is lowph and Δ2 is lowph and Δ3 is mediumph it is ana-b-c fault.

The variables in the antecedent parts as well as the consequentarts, in the above fuzzy rules, should be fuzzy variables. Theriangular membership function, shown in Fig. 2, has been usedo represent the various fuzzy variables in the antecedent andonsequent parts of the fuzzy rules. The triangular membershipunction can be defined with reference to the points A, B and, referred to as triplets [19]. As shown in Fig. 2, the points And C have membership value of 0.00 while the point B has a

embership value of 1.00.The selected values of triplets corresponding to fuzzy vari-

bles in the antecedent parts of the fuzzy rules for ground faultsnd phase faults are shown in Tables 6 and 7, respectively. Table 8

-a 44.5 45 45.5-b-c 49.5 50 50.5

hows the selected values of triplets corresponding to fuzzy vari-bles in the consequent parts of the fuzzy rules.

Fig. 3 shows the fuzzy logic scheme (FLS) for fault clas-ification. The input quantities are Δ1, Δ2 and Δ3. As can beeen from Fig. 3, the inputs are converted to their correspond-ng fuzzy variables. The fuzzified inputs are fed to the fuzzynference engine, which gives the output (type of fault) in theuzzy form in accordance with the fuzzy rule base. The appro-riate fuzzy rule base is selected on the basis of whether theault involves ground or not. The output of the fuzzy inferencengine is defuzzified to get the output in the crisp form. MAT-AB’s “fuzzy logic toolbox” has been used to implement theLS.

Fig. 3. The FLS for fault classification.

R.N. Mahanty, P.B.D. Gupta / Electric Power Systems Research 77 (2007) 501–507 505

Table 9Simulation results in case of ground faults

Fault type Fault condition: d, RF, FIA, δ FLS inputs: Δ1, Δ2, Δ3 FLS output

a-g 0.1, 5 �, 30◦, 15◦ 0.889, 0.106, −0.995 5.1200.5, 100 �, 75◦, 25◦ 0.488, 0.250, −0.739 5.0200.9, 50 �, 5◦, 10◦ 0.663, 0.151, −0.814 5.045

b-g 0.2, 200 �, 20◦, 30◦ −0.662, 0.405, 0.257 10.0070.4, 100 �, 90◦, 10◦ −0.921, 0.736, 0.185 10.0800.8, 10 �, 45◦, 20◦ −0.813, 0.657, 0.156 10.037

c-g 0.1, 50 �, 45◦, 15◦ 0.168, −0.967, 0.799 15.0400.5, 100 �, 0◦, 30◦ 0.262, −0.689, 0.427 15.0000.9, 0.1 �, 90◦, 10◦ 0.108, −0.918, 0.810 15.040

a-b-g 0.1, 20 �, 45◦, 20◦ −0.868, 0.996, −0.127 20.0000.4, 200 �, 90◦, 10◦ −0.574, 0.948, −0.374 20.0000.8, 100 �, 5◦, 30◦ −0.011, 0.653, −0.642 20.000

b-c-g 0.2, 75 �, 30◦, 15◦ −0.238, −0.746, 0.984 24.9600.5, 150 �, 75◦, 30◦ −0.541, −0.239, 0.781 25.0000.9, 15 �, 15◦, 10◦ −0.476, −0.449, 0.925 24.960

c-a-g 0.1, 0.1 �, 90◦, 30◦ 0.997, −0.056, −0.941 29.920◦ ◦

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ransmission line for variations in the values of fault resistanceRF), fault inception angle (θ), fault location (d) and load angleδ) using EMTP and MATLAB. As the transmission line modelith sources on both sides is a widely accepted model for devel-pment of line relaying algorithms, it has been considered forhe development of the proposed method. The FLS outputs forifferent types of fault under some representative fault situa-ions are shown in Tables 9 and 10. From the results presentedn these tables it can be observed that the proposed method hasigh accuracy.

The fault classification method proposed in this paper andhe method proposed by Das et al. [18] are similar in the sense

hat both are fuzzy logic based schemes which require the con-ideration of the post-fault samples of three phase currents athe relay location. Further, the same network configuration haseen considered for simulation study of both the methods.

fe

p

able 10imulation results in case of phase faults

ault type Fault condition: d, RF, FIA, δ

-b 0.1, 50 �, 45◦, 30◦0.5, 150 �, 0◦, 20◦0.9, 5 �, 90◦, 10◦

-c 0.2, 0.1 �, 30◦, 10◦0.4, 75 �, 15◦, 30◦0.8, 200 �, 80◦, 20◦

-a 0.15, 0.1 �, 90◦, 10◦0.6, 200 �, 45◦, 30◦0.9, 70 �, 0◦, 20◦

-b-c 0.1, 30 �, 10◦, 10◦0.5, 200 �, 45◦, 30◦0.9, 80 �, 75◦, 20◦

0.872, −0.565, −0.306 29.9560.951, −0.404, −0.547 29.920

The proposed method is applicable for a wider variation inhe operating conditions in comparison to the method proposedy Das et al. Whereas the latter is valid for variation in RF upo 50 � and variation in d up to 0.8 (in p.u. of line length), theormer is valid for variation in RF up to 200 � and variation inup to 1, the variation in δ being up to 30◦ for both the cases.Further, the proposed method is computationally simpler as it

equires the computation of some ratios and differences of ratiosrom the post-fault current samples for determining the fault fea-ures. On the other hand, a filtering algorithm (half cycle DFT)or extracting the fundamental frequency components of cur-ents and determination of the sequence components are required

or determining the fault features in case of the algorithm by Dast al.

The sampling interval for the proposed method is 1 ms. Tenost-fault samples of each phase current, starting from the 6th

FLS inputs: Δ1, Δ2, Δ3 FLS output

−0.816, 0.972, −0.156 35.029−0.496, 0.837, −0.341 35.005−0.821, 0.979, −0.158 35.043

−0.049, −0.949, 0.998 40.020−0.318, −0.567, 0.885 40.000−0.439, −0.221, 0.659 39.999

0.999, −0.025, −0.974 44.9800.681, −0.429, −0.252 44.9960.713, −0.444, −0.269 44.998

−0.407, 0.490, −0.083 49.885−0.567, 0.421, 0.147 50.000−0.502, 0.506, −0.004 49.890

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06 R.N. Mahanty, P.B.D. Gupta / Electric P

ample up to the 15th sample, are considered. To reduce theffect of dc offset the initial five samples are ignored. This meanshat the sampling is completed after elapse of half cycle butithin one cycle of the post-fault signal. However, in case of theethod proposed by Das et al. the task of fault classification is

ccomplished within half cycle of post-fault signal.The performance of the proposed approach has also been

tudied under variation of source impedance of both the sources.t has been observed that the accuracy of the proposed techniques not affected for variation of 10–40 in the X/R ratios of theource impedances.

The ranges of “highg”, “mediumg”, “lowg”, “highph”,mediumph” and “lowph” values of Δ1, Δ2 and Δ3 have beenound out on the basis of extensive simulation studies usingMTP and MATLAB considering wide variations in the oper-ting conditions. Although the ranges of “highg”, “mediumg”,lowg”, “highph”, “mediumph” and “lowph” will vary from sys-em to system, the proposed approach will be applicable forifferent systems. The advantage of using fuzzy logic is thatt allows for overlapping between the ranges of “high” andmedium” and between the ranges of “medium” and “low”. Thisroperty of fuzzy logic makes the proposed approach suitableot only for one particular system but for different systems.

Simulation results in case of the 400 kV, 3 phase, 300 kmorizontal formation of conductors transmission line have beenresented in Tables 9 and 10 for illustrating the validity of theroposed approach. The validity of the proposed approach haslso been checked on simulated results in case of a 230 kV, 3hase, 300 km transmission line. Simulation studies extendedo the second system shows identical conclusions as derivedn the first case. Also preliminary simulation studies carriedut for both the case examples with variations in transmissionine operations with simple FACTS devices in the steady stater for faults with unbalanced line parameters indicate the cor-ectness of conclusions that have been derived in the earliertudies.

. Conclusions

A fuzzy logic based technique for classification of trans-ission line faults has been presented. The proposed technique

equires the consideration of the three phase current sam-les at one end of line only. Separate fuzzy rule bases forlassifying faults involving ground and faults not involvinground have been developed. A separate technique is used toetermine the involvement of ground in fault. The appropriateule base is selected for fault classification, on the basis ofhether the fault involves ground or not. Simulation studies

arried out considering wide variations in fault location, faultnception angle, fault resistance and load angle for differ-nt types of fault have proved the validity of the proposedpproach.

The proposed fault classification method has been extensively

ested on the 400 kV, 3 phase, 300 km line. Similar results haveeen obtained for second system—230 kV, 3 phase, 300 km line.reliminary studies also indicate the validity of the proposedethod in the steady state when simple FACTS devices are

[

[

Systems Research 77 (2007) 501–507

ssociated with the transmission line or for unbalanced line con-ition. The method is therefore quite robust.

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R.N. Mahanty, P.B.D. Gupta / Electric P

.N. Mahanty received B.Sc. Engg. degree from University College of Engi-eering, Burla, Orissa, India in 1985, M.Tech. degree from Regional Institute ofechnology, Jamshedpur, India in 1988 and Ph.D. degree from Indian Institute

f Technology, Kharagpur, India in 2003. He is presently a Senior Lecturer inhe Department of Electrical Engineering at National Institute of Technologyformerly Regional Institute of Technology), Jamshedpur, India. His areas ofesearch interest include power system protection, digital relaying and applica-ion of ANN, wavelet transform and fuzzy logic to power system protection.

tIiPL

Systems Research 77 (2007) 501–507 507

.B. Dutta Gupta received B.Tech. degree from Indian Institute of Technology,haragpur, India in 1963, M.Engg. degree from Indian Institute of Science,angalore, India in 1965 and Ph.D. degree from University of Warwick, Coven-

ry, UK in 1980. He is a Professor in the Department of Electrical Engineering,ndian Institute of Technology, Kharagpur, India. His areas of research interestnclude power system protection, digital relaying and power system stability.rof. Dutta Gupta is a Fellow of the Institution of Electrical Engineers (IEE),ondon, UK.