Electrical Power and Energy Systems 53 (2013) 714–718

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Transmission lines fault location using transient signal spectrum

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.05.045

⇑ Corresponding author. Tel.: +90 422 3774816; fax: +90 422 3410046.E-mail addresses: mehmet.mamis@inonu.edu.tr (M.S. Mamis�), muslum.arkan@

inonu.edu.tr (M. Arkan), cemal.keles@inonu.edu.tr (C. Keles�).

Mehmet Salih Mamis� ⇑, Müslüm Arkan, Cemal Keles�Inonu University, Engineering Faculty, Electrical & Electronics Eng. Dept., Malatya, Turkey

a r t i c l e i n f o a b s t r a c t

Article history:Received 22 June 2012Received in revised form 26 May 2013Accepted 29 May 2013

Keywords:Transmission linesFault locationTravelling wavesFFT

This paper proposes a method for fault location on transmission lines, which is based on time to fre-quency domain transformation of transient signals of the fault instant measured at one end. Fast FourierTransform (FFT) is used for time to frequency domain transformation and frequency of the first fault gen-erated harmonic is utilised for determination of the fault location using the travelling wave theory of thetransmission line. The accuracy of the method has been tested using the simulations carried out in Alter-native Transients Program (ATP/EMTP) with frequency-dependent distributed parameter transmissionline model by considering several cases and various types of faults, different values of fault resistanceand phase angle at fault instant. The method has good accuracy and the simulation results show thatthe accuracy of the method is insensitive to the fault resistance and phase angle of the fault instant. Reac-tive elements may affect the resolution but, it can be removed by applying the correction procedureproposed.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Power outages lead to loss of manpower and resources in indus-trial plants; on the other hand reliability and continuity of electri-cal energy has gained more importance in last decades due toenhanced competition and limited resources. The most importantcause of disturbances in the power systems is unexpected failures,and within them, short circuit faults are more common, which arearisen due to lightning surges, usage of defective materials, impro-per system operation, human error, overloading and aging. Besidesthe economical losses in industry, a fault may cause loss of systemstability, failure of transformers, generators and transmission linesand therefore, fast clearing of faults is greatly significant. First con-dition for clearing a fault in a short time is to estimate the faultlocation quickly and precisely. This subject gained more impor-tance in last decades and advance in the computer technology al-lows development of new algorithms for determination of faultlocation. In recent years several methods have been proposed forfault location in power systems, which may be classified into twocategories; the methods which employ electric quantities and themethods based on the travelling wave theory. In some of the firstcategory methods, fault distance is estimated from the informationreceived from one end of the transmission line [1–4], usually byusing fundamental frequency voltages and currents measured atone terminal [1,2] or by measuring impedance from measuring

terminal to the fault point [3,4]. However, some of these methodsrequire accurate modelling of both the faulted transmission lineand the power system in which the line is embedded and someothers cannot be used to locate symmetrical faults. In addition,for short lines, the equivalent impedance variation can have a high-er influence in method precision. Also unknown fault impedanceaffects the accuracy and some methods are sensitive to errors inthe value of the local bus impedance. Due to these restrictions,two- or multi-ended fault location techniques have been proposed[5–8]. However, measurement from two ends is expensive andsynchronised sampling of the voltage and current data from twoends of the line are usually required.

In the travelling wave based methods [9,10] on the other hand,time-space analysis have been used for fault location. Short andopen circuit faults on transmission lines cause sudden changes inthe distribution of electric and magnetic energy which result trav-elling waves. In order to determine the fault distance, the analysisof wave time-position graphs are employed. In recent years, manystudies have been devoted to develop different methods based onwavelet transform to determine the fault type and location [10,11].Wavelet transform (WT) is a recently developed mathematicaltool, which is used to capture the dynamic characteristics of unsta-ble signals using short data windows. Depending on the directionin the protection of transmission lines, fault classification and faultdistance identification using wavelet transform was carried out byseparating the necessary information from the short circuit tran-sient behaviour. The most important limitation of the existingmethods based on the wavelet transformation is the low degreeof accuracy in the prediction fault points near the busbar in gen-eral. In addition, there are other techniques, which use elements

Fig. 1. Two-terminal power network.

M.S. Mamis� et al. / Electrical Power and Energy Systems 53 (2013) 714–718 715

of artificial intelligence in the form of artificial neural networks(ANN’s) [12,13] and support vector machine approach [14].

Using the theory of travelling waves, transient signal spectrumcan also be used for determination of fault distance. This methodhas been applied for fault location estimation in single-phasetransmission lines and satisfactory results have been obtained[15]. In this study, using modal transformations, the method is ex-tended for three-phase transmission lines. Frequency spectrumwhich is obtained by Fast Fourier Transform (FFT) of the transientsignals measured on one terminal of the transmission line is usedto detect the travel time of the fault generated wave, which makesavailable the fault distance. The proposed method is applied to thesimulations carried out in Alternative Transients Program (ATP). Atwo-terminal three phase system with distributed and frequencydependent parameters is considered. The effects of phase angle,fault resistance and source parameters are also investigated.

The organisation of the paper is as follows: After this introduc-tory section, the theory of fault distance calculation using travel-ling wave theory of the distributed parameter transmission lineis introduced in Section 2. In Section 3 the simulation model is gi-ven. In Section 4 application results are introduced; the effect offault resistance, the affect of phase angle and the effect of sourceinductance is investigated.

2. Fault distance calculation using travelling waves

Voltage and current phasors V and I at any point on the linewith per unit length series impedance z = r + jxl and shunt admit-tance y = g + jxc are determined as [16]

V ¼ C1ecx þ C2e�cx ð1Þ

I ¼ 1z0

C1ecx � 1z0

C2e�kx ð2Þ

where r, l, g and c are resistance, inductance, conductance andcapacitance of transmission line per unit length, respectively; andc ¼ ffiffiffiffiffi

zyp

is the propagation constant, z0 ¼ffiffiffiffiffiffiffiffiz=y

pis the characteristic

impedance of the line. The constants C1 and C2 can be evaluated byusing the boundary conditions at terminals of transmission line.Propagation constant of a transmission line can be written asc = a + jb, where attenuation constant a measured nepers per unitlength and phase constant b radians per unit length. A wavelengthk is the distance along a line between two points of a wave whichdiffer in phase by 360�, or 2p rad. If b is the phase shift in radiansper km, the wavelength in km is

k ¼ 2pb

ð3Þ

The velocity of propagation of a wave in km per second is

v ¼ fk ð4Þ

where f is frequency in Hz and k is wavelength in km. The velocity ofpropagation in terms of line parameters can be simply obtained as

v � 1ffiffiffiffilcp ð5Þ

Let sf is travel time from fault point to measuring point which hastheoretical value calculated as

sf ¼xv ð6Þ

where x is the distance between the fault point to the measuringpoint. Each 2s generates a period and it has been observed fromthe simulation results that the frequencies of the voltage and cur-rent harmonics generated after the fault are proportional to the tra-vel time as

f1 ¼1

2sf; f2 ¼

1sf; � � � fi ¼

i2sf

ð7Þ

Hence, if the wave speed and frequency of ith harmonic fi is known,the fault distance can be found from the following equation:

x ¼ vsf ¼iv2f i

ð8Þ

The frequency of the fault related harmonics of the voltage and cur-rent signals can be obtained by transforming transient signals intofrequency domain. FFT is used for this purpose.

3. Simulation model

In this study a 240 km 400 kV fully transposed three phase lineshown in Fig. 1 is considered in the computer simulations to verifythe accuracy of the proposed algorithm. Tower configuration of thesystem is illustrated in Fig. 2 and physical parameters of the trans-mission line are given in Table 1.

Marti frequency dependent transmission line model [17,18] isused in ATP simulations. ATPDraw file of the test system is illus-trated in Fig. 3. Sequence current and voltage waveforms obtainedby ATP simulation are transformed into frequency domain usingFFT. As the positive sequence inductance of overhead lines is prac-tically constant, wave speed is not affected from the frequencydependence of the line; hence the positive sequence voltage andcurrent data are used. The voltage and current waveforms in timedomain are transformed to modal quantities by using the followingtransformation:

Im ¼ T�1Ip

Vm ¼ T�1Vp

ð9Þ

where subscript p and m denotes the phase and modal quantities,respectively. Modal transformation is not unique and for a trans-posed three-phase transmission line the following transformationmatrix may be used:

T ¼1 1 01 0 11 �1 �1

264

375 and T�1 ¼ 1

3

1 1 12 �1 �1�1 2 �1

264

375 ð10Þ

Positive sequence transmission line parameters at power frequencyare used to calculate the wave speed from the following equations[19]:

lpos ¼ 10�7 ln2dmhm

GMReqDmH=m ð11Þ

cpos ¼2pe0

ln 2dmhmreqDm

F=m ð12Þ

where hm is geometric mean height, dm is geometric mean distance,Dm is geometric mean distance to images, req is equivalent radius ofsub-conductor and GMReq equivalent geometric mean radius ofconductor.

Fig. 2. Tower configuration of 400-kV test systems.

Table 1Data for 400 kV, 50 Hz, 240 km three-phase line.

Phase arrangement Horizontal tower configuration

Phase conductorsHeight at tower 24 mHeight at midspan 12 mPhase spacing 12 mNumber of bundle 2Radius of sub-conductor 1.521 cmSpacing between sub-conductors 40 cmGeometrical mean radius (GMR) 1.2253 cmDC resistance 0.0596 O/km

Ground wiresHeight at tower 33 mHeight at midspan 20 mSpacing 15.2 mRadius 0.8 cmDC resistance 0.3527 O/km

U U

Fig. 3. ATPDraw model of power system.

Fig. 4. Transient voltage and current waveforms for a balanced three-phase fault at120 km from the sending-end.

716 M.S. Mamis� et al. / Electrical Power and Energy Systems 53 (2013) 714–718

4. Applications and results

Four types of faults; single line-to-ground fault (SLG), line-to-line fault (LL), double line-to-ground fault (LLG) and symmetricalthree-phase fault (LLL) are simulated in ATP by using frequencydependent overhead line model to obtain fault transients. Positivesequence parameters at 50 Hz calculated from Eqs. (11) and (12)

are: l = 1.075 mH/km and c = 10.805 nF/km and positive sequencesurge velocity calculated from these values is v � 1=

ffiffiffiffilcp¼

293:42� 103 km/s. Source resistance is assumed to be 0.1 O andsource inductance is 1.0 mH. Transient current waveforms forone period in time domain (20 ms) are used for frequency spec-trum. Time domain signals are sampled at 25.6 kHz with 512 num-bers of samples. To reduce FFT leakage, prior to FFT, sampledvoltage and current signals are windowed by using Hanning win-dow. For 20 ms sampling time the FFT spectrum resolution is50 Hz. This resolution may affect the accuracy of fault distanceestimation especially at low frequencies. To increase FFT frequencyresolution to 12.5 Hz, after windowing, 1536 zeros are appended tothe windowed sampled signal. It has been observed from the sim-ulation results that a resolution of 12.5 Hz is adequate for the pro-posed fault distance location technique. Other possible cause oferror is truncation error in numerical calculations.

In the voltage and current signals, source frequency is domi-nated. This makes it difficult to visualise the fault related frequen-cies. For the overhead transmission line considered, the lowestfrequency of the first fault related harmonic from (8), which is in-versely proportional to the total line length, is approximately611 Hz for a fault point at 240 km. This means that the frequencycomponents between 0-to-611 Hz are not related to fault. Becauseof unavoidable of leakage effect in the spectrum instead of 0-to-611 Hz after FFT, masking is applied to the spectrum for removing0–400 Hz components and after extracting the fundamental fre-quency, transient frequency associated with fault can easily bespecified.

Fig. 4 shows the sending end voltages and currents signalswhen three phase symmetrical fault occurs at 120 km at t = 0. Tomake the voltage transients more noticeable, the source induc-tance is taken to be 10 mH. Fig. 5 shows the power spectrum den-sity of the positive sequence voltage and current signals for thesame fault. As it can be seen from the figure, transient frequenciesare clearly apparent and more than one transient frequency asso-ciated with the fault exist in both spectrums. The measured firstfault generated frequency in both spectrums is 1137.5 Hz, whichcorresponds to x = v/(2f1) = 293.42 � 103/(2 � 1137.5) = 128.97 kmand the fault distance is calculated with 3.74 percentage error. This

Fig. 5. Spectrum of positive sequence transient voltage and current.

Table 3Estimated fault distance and accuracy for LL, LLG and LLL for several fault locations.

Actual faultdistance (km)

Measured 1st harmonicfrequency (Hz)

Estimated faultdistance (km)

Percentageerror

40 3612.5 40.61 0.2580 1825.0 80.39 0.16

120 1225.0 119.76 0.10160 912.5 160.78 0.32200 737.5 198.93 0.45

Table 4Estimated fault distance and accuracy for LLL at 120 km for different values of faultresistance.

Fault resistance (O) Estimated fault distance (km) Percentage error

0.1 119.76 0.101 119.76 0.105 119.76 0.1010 119.76 0.1020 119.76 0.1050 119.76 0.10

Table 5Estimated fault distance and accuracy for LLL fault at 120 km for different phaseangles.

Phase angle in degree Estimated fault distance (km) Percentage error

0 119.76 0.1030 119.76 0.1060 119.76 0.1090 119.76 0.10

120 119.76 0.10150 119.76 0.10

M.S. Mamis� et al. / Electrical Power and Energy Systems 53 (2013) 714–718 717

error is reduced to 0.12% by the correction algorithm describednext. It can also be observed from the frequency spectrum thatthe other transient frequencies are multiple of the first fault gener-ated transient frequency, which can also be used to calculate thefault distance.

The estimated fault distance by using the transient frequency ofthe current signal and total percentage error for LG is given in Ta-ble 2 and the estimated fault distance total percentage error for LL,LLG and LLL faults are given in Table 3, respectively. The percent-age error is calculated as:

Error% ¼ jActual fault distance� Estimated fault distancejLine length

� 100

ð13Þ

As it can be seen from Table 2, for single line-to-ground fault errorincreases as fault point is far from the measuring point. The maxi-mum error for LL, LLG and LLL is 0.45% which is reasonable. Forthe same fault distance, the error in the case of LG fault is greaterthan the error in other fault types, which is due to mutual effects.However, fault distance can be estimated more accurately by pro-cessing two end measurements, which is not required to besynchronised.

For all fault types the total error covers the error associatedwith FFT and truncation error in the numerical calculations. Similarresults are also obtained in the case when voltage signals are pro-cessed. However, when the source impedance is small, the tran-sient voltage signals may not be noticeable, which may affect theaccuracy.

When compared with other methods that employ transient sig-nals such as WT, estimations are more accurate especially for thefault very near to the substation ends. In [11], WT was used and

Table 2Estimated fault distance and accuracy for LG fault for several fault locations.

Actual faultdistance (km)

Measured 1st harmonicfrequency (Hz)

Estimated faultdistance (km)

Percentageerror

40 3675.0 39.92 0.0380 1750.0 83.83 1.60

120 1162.5 126.20 2.58160 862.5 170.10 4.21200 700.0 209.58 3.99

the error for LLG and LL is high as 6.16%, which is 0.45% in the pro-posed technique for the same type of faults.

Tables 4 and 5 show the effect of fault resistance and phase an-gle on the accuracy of fault distance for a fault at 120 km, respec-tively. As it can be seen from the tables, the fault resistance andphase angle do not affect the accuracy. Detailed analysis of currentspectrums carried out in this work have shown that different val-ues of the fault resistance and phase angles do not affect the faultgenerated harmonics frequency as well as the harmonics magni-tude for all fault types. Although fault generated harmonics areclearly present for different phase angles, their magnitude mayget smaller around zero crossing point, which makes difficult thedetection process.

One limitation of the method is that reactive elements such assource inductance may affect the accuracy. But this restrictioncan be overcome by distributing source inductance through theline. The effect of source inductance on the accuracy of fault loca-tion for a three phase fault is given in Table 6. As seen from the ta-ble error is very high. However, we have investigated that faultdistance can be estimated with a reasonable error by modifyingdistributed line inductance by including the delay effects of thesource inductance. The modification is as follows: First, the faultdistance x is taken to be the total of line length in distributingthe source inductance on the line and an approximate fault dis-tance is estimated. Then, this estimated distance is used as new va-lue of the fault distance and modified value of l is calculated. Ourpractical investigation shows that two step improvements are ade-quate for a reasonable error. The proposed improvement procedureis described by the following steps:

Table 6Estimated fault distance and accuracy for LLL fault at 120 km for different values ofsource inductance.

Source inductance (mH) Estimated fault distance (km) Percentage error

0.1 119.76 0.101.0 119.76 0.1010 128.97 3.7450 156.49 15.20

Table 7Estimated fault distance and accuracy for a fault at 120 km for different values ofsource inductance after improvement.

Source inductance (mH) Estimated fault distance (km) Percentage error

0.1 119.67 0.141.0 118.84 0.4810 120.28 0.1250 120.01 0.01

718 M.S. Mamis� et al. / Electrical Power and Energy Systems 53 (2013) 714–718

Step 1: Set i = 1 and xi = total line length.Step 2: Calculate line inductance li ¼ lþ 2Ls

xi.

Step 3: Calculate propagation velocity v ¼ 1=ffiffiffiffiffilic

p.

Step 4: Calculate corrected fault distance xi+1 = vsf.If i = N stop; otherwise xi = xi+1 and i = i + 1 goto step 2.

where N is the maximum correction step, Ls is the source induc-tance (H). The accuracy on the locating fault distance for differ-ent values of the source inductance after applying theimprovement algorithm is given in Table 7. Before improve-ment, the largest error is 15.20% which is reduced to 0.48% bythe correction procedure. Using the improvement procedure, asimilar enhancement is achieved for other types of faults.

5. Conclusion

A travelling wave based fault detection technique for transmis-sion lines is developed in this paper. Fault distance is estimated byconsidering the frequency of travelling wave with lower frequencywhich is obtained by processing transient current or voltage wave-forms transformed into frequency domain using Fast FourierTransform (FFT). Current data measured at one end are used. Themethod is applied to four types of faults in three-phase overheadline with frequency-dependent distributed parameter representa-tion. The results show that the accuracy of the method is

insensitive to fault resistance and phase angle at fault instant.When compared with other travelling wave based methods, faultlocation can be estimated more accurately especially for the faultvery near to the substation ends. It has been also shown that thenegative effect of source inductance on the accuracy of fault loca-tion estimation can be almost eliminated by using the proposedcorrection algorithm.

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