ANALYSIS OF SINGLE-ENDED TRAVELING-WAVE FAULT LOCATION BASED ON CONTINUOUS WAVELET TRANSFORM INFERRED FROM SIGNAL

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1 ANALYSIS OF SINGLE-ENDED TRAVELING-WAVE FAULT LOCATION BASED ON CONTINUOUS WAVELET TRANSFORM INFERRED FROM SIGNAL L. U. Iurinic*, A. S. Bretas*, E. S. Guiarães, D. P. Marzec* * Federal University o Rio Grande do Sul -UFRGS, Porto Alegre, RS, Brazil. (uririnic@ece.urgs.br abretas@ece.urgs.br, denisearzec@ece.urgs.br) Copanhia Estadual de Distribuição de Energia Elétrica (CEEE-D), Porto Alegre, Brazil. (edersong@ceee.co.br) Keywords: Fault location; Continuous-wavelet transor; Electroagnetic transients; Traveling waves. Abstract This paper presents an approach based on the wavelet transor or analysing transission line transients in order to locate aults. The basic theoretical aspects related to ault transients are irst presented. Then, a ethodology is proposed to estiate the ault location taking into account voltage signals only, easured ro one terinal. The other wavelets are inerred ro the analysed signals, having an optial way to identiy the wave-ronts. For the case study, ATP was used to siulate a transission line with requencydependent line odels. The obtained test results highlight that the proposed algorith perorance is not aected by the ault resistance and operating conditions. 1 Introduction When protections schee have operated due to a ault in a power line, aintenance crew will try to correct the proble as ast as possible, in order to restore the syste without seriously aecting its reliability. To achieve this objective, a precise ault location estiate ust be provided [1]. Methods o locating power syste aults introduced so ar can be broadly classiied under two categories: based on the power requency coponents [4],[9], and on higher requency contents o the transient ault signals. The latter is also reerred to as traveling wave or ultra-high speed ault location ethods, due to its use o traveling wave theory and shorter sapling windows [7]. The traveling-wave ault location techniques are recognized as soe o the ost accurate ethods currently in use, and can generally be categorized as synchronized or unsynchronized [6]. The synchronized algoriths are the ost accepted algoriths, but require two easuring points synchronized with a GPS clock [13] or eploying appropriate digital signal processing techniques [15],[10]. Fault location is calculated using the relative arrival tie o traveling-wave transients at each terinal. On the other hand, unsynchronized algoriths use signals ro only one terinal data, observing the tie delay between successive relections o the wave ront [7]. The last, are interesting due to their relatively inor cost and coplexity associated. However, there is a corresponding increase in the required signal processing as each relection ust be identiied and then related in tie to the signal wave ront. Reerence [] has proposed a procedure based on the Continuous Wavelet Transor (CWT) applied on voltage transients to estiate ault location on power distribution systes. Later, the sae authors iproved this ethodology by building a speciic other wavelet inerred ro the aultoriginated transient waveor [1],[3]. The CWT provides better overall accuracy than the Discrete Wavelet Transor (DWT) in presence o transducers [6],[13]. This paper introduces a theoretical analysis reerred to aulttransients, explaining the correlations between the ault localization and characteristics requencies. Then, CWT and its proprieties are presented, showing how this approach can be used. Finally, test results on a siulated transission line are presented and analysed. Theoretical Issues.1 Travelling Waves on Transission Lines The dierentials equations that represent a ulti-phase transission line are indicated in (1) and (). They are written in the requency doain, where Z (s) and Y (s) are the ipedance and adittance per-unit-length atrixes. These equations show that phase voltage and current are unction both distance and requency. ph V x, s Z, s Y s V x s x ph ph I xs, Y, s Z s I xs x ph In tie doain the last are wave-equations, eaning that a variation in one side o the line will be propagated up the other with certain velocity. (1) ()

2 The odal transoration is a way to ake diagonal the atrixes given by the products between Z (s) and Y (s), decoupling the line into i single-phase lines called odes. The results o products are not equal but have the sae eigenvalues, leading the dierential equations in requencyodal doain. Z TV Z Z 1 (9) V x V (3) I x V I I (4) ph Tv V (5) ph Ti I (6) Where is a diagonal atrix coposed by the eigenvalues i and T v, T i are the eigenvector atrixes o Z (s)y (s) and Y (s)z (s) respectively. Then, i is the propagation constant o ode i, constituted by a coplex nuber i = i +j i where i is the attenuation constant and i the phase constant o ode i. Finally, the wave-propagation velocity o ode i at requency given by. Wave Propagation vi (7) i The ault can be seen as a step-unction source triggered by the ault occurrence [1]. Fig. 1 shows the low o the travelling waves at constant speed v, along a transission line o length L due to a ault at distance x. The traveling waves are relected and transitted at line terinations, junctions and ault location. Fig. 1. Lattice diagra that represent the traveling wave low along the line. Fig. illustrates a voltage wave-ront arriving at a discontinuity, showing that a part is relected and another is transitted. The aount o relection ( RV ) and transission ( TV ) is given by the relative values between the surge ipedances Z 1 and Z, listed below to a single-phase circuit. RV Z Z Z 1 1 Z (8) Fig.. Illustration o the wave transission and relection through a line discontinuity. Then, each discontinuity is characterized by a relection coeicient RV. The point where the ault is occurring has a coeicient between 0 and -1, as the ault has an ipedance value lower than the line surge ipedance. This eans that the wave is relected with opposite sign, and is copletely relected without transissions when the ault is solid. The extreity where the load is connected can be considered as an open circuit, whose relection coeicient is close to +1. There, the voltage-wave is totally relected with the sae sign. Finally, the extreity where the Thevenin equivalent source o the syste is located is characterized by a negative relection coeicient. As the voltage-wave produced by a ault is relected any ties at discontinuities, it produces an oscillatory transient seen ro one end. Since the propagation speed is calculated by (7), a characteristic requency i or the I th ode can be associated with the ault location. v k x i i (10) In (10), k is a constant depending on the sign o the relection coeicients o the two extreities; it is equal to i the corresponding coeicients have the sae sign or 4 i they have opposite sign. By the considerations ade in this paper, k has a value o. I the i requency is identiied ro the voltage-waveor, the ault distance can be calculated using (10). Thus, the CWT is used or this purpose as will be explained later..3 The Wavelet Transor Reerence [14] shows that wavelet transor decoposes signals over dilated and translated other wavelets v L (R), called daughter-wavelets. 1 * t u W(u,s) t dt s s (11) The scale paraeter s takes values greater than zero, and the translation paraeter u can take any real values. This transor allows the adoption o arbitrary other wavelets as long as coply with the adissibility condition

3 C ˆ d. (1) 0 To guarantee that integral (1) is inite, two conditions ust be ensured: ˆ 0 0 (13) 1 t t dt (14) The irst eans that the wavelet ust have zero average, and the second that the Fourier transors o the wavelet is continuously dierentiable. In copliance with the adissibility condition, the signal can be reconstructed ro W(u,s) (wavelets coeicients) by applying the inverse wavelet transor. There exist a variety o standard other wavelets that can be used [14]. In practice analysed signals are discrete, resulting in the discretization o the CWT with a sapling tie t. 1 N 1 * nt (15) W(t,s) t nt s n0 s Where N is the nuber o recorded saples and t is the translation paraeter, with =0,1, N. The wavelet transor can be rewritten as a convolution product: W(u,s) * u, (16) With 1 * s t t s s s (17) The convolution (16) can be expressed in the requency doain: W(u,s) F s ˆ s 1 * ˆ (18) Where F -1 denote the inverse Fourier transor. Equation (18) shows that the Fourier transor o a wavelet acts as a transer unction o a band-pass ilter. The convolution (16) coputes the wavelet transor with dilated band-pass ilters and the sae operations can be done with the discrete version o the CWT. The axiization o convolution product is achieved in the scale-translation point where ajor siilarity between the analyzed signal and the daughter wavelet exists. This allows identiying the tie-scale localizations o dierent patterns that are siilar to the wavelet in the signal..4 Construction o a other Wavelet inerred ro the analysed signal Here will be suarized the procedure developed in [1]. The axiization o the wavelet transor is related to the siilarity between the signal and wavelet. Thereore, the proposed approach builds the other wavelet by applying the adissibility condition to the initial part o the ault transient waveor. As the reconstruction o signal is not necessary in this work, the so called orthogonality condition is not taken into account. Thus, the wavelet ust have only zero average and a ast decrease to zero or t±. Being (t) the relevant ault transient signal, w (t) is extracted as the initial part o (t). Function w (t) is taken ro the aultoccurrence up the tie corresponding to the iniu expected requency content o analysed signal Ts. w (t) is noralized with respect to its axiu value and then is shited in order to obtain a ean value equal to zero. wn t w t ean w t ax w t (19) Finally, the other wavelet is built as a series o several w (t) shited by qts and ultiplied by an exponential decay characterized by. t t wtqts wtqtse (0) qn With w t w 0 t 0 t Ts t 0; t Ts Identiication o Characteristic Frequencies (1) As was explained, the CWT is an integral o the product between a signal (t) and tie translated and scaled versions o the other wavelet (t), these versions are called daughters wavelets. The W(u,s) are the products o this tie-scale transoration, which are represented as a bi-diensional unction. Basically being (t) the recorded transient signal, W(u,s) are calculated by (15), leading to a tie-scale representation. The squared odulus o these coeicients deines a tie-scale energy density [14]. Hence, integrating this energy density along the tie by each requency, the intensity per unit scale is obtained. W, () E (s) W u s du Applying () to (15), the discrete version is obtained. W N 1, (3) E (s) W t s 0 The E W (s) unction is called scalogra and represents the weight o each scale coponent. In a classical CWT bi-diensional graphic, like Fig. 3, peaks can be seen in translations and dilations where the wavelet has a best correlation with analyses signal.

4 v d is the direct axis coponent. [c di ] is used here to detect the initial transient instant because coeicient related to transient signals are apliied and that related to noral conditions are kept with low agnitude. Henceorth, when [c di ] exceeds a deterined threshold, the transient is detected and recorded. 3 Siulations and Results (a) (b) Fig. 3. a) Signal and other wavelet being scaled by s1, s and translated by u1, u. b) bi-diensional illustration o signal W(u,s). 3.1 Siulation Model To evaluate the perorance o the proposed ethodology, siulations o the 69 kv real lie syste illustrated in Fig. 4 were done using ATP [5]. Such syste is radial and transits an average power o 14 MVA to an equivalent load. Total length o the line is 8.9 k, divided in three transpositions located at 4.8, 14 and 3. kiloetres respectively. Each line section was odelled using the J. Marti s [11] requencydependent line odel. Thus, the tie-intervals when the initial wave-ront back to the easuring point, is estiated by easuring the tie between peaks at the scale that has axiu value in the E W (s) unction. Park s Equation and Transient Detection The above ethod needs a way to detect the starting tie o the transient and the relevant waveors. In order to do that, the Park equation is used to reer the voltages ro a stationary three-phase (abc) reerence to a rotating (0dq) reerence syste (). Hence, the power requency signals are reoved allowing the transient tie detection [8] v 0 va vd cos t cos t cos t v b (4) v q v c sin t sint sin t 3 3 The subscripts 0, d and q are the zero, direct and quadrature axes coponents. is the power requency o the syste. Here, only the voltage o the direct axis will be considered to transient detection using the dierence coeicients vd nvd n1 cdi n. (5) t Where: t is the tie step; n is the saple nuber; Fig. 4. Three-phase syste odelled in ATP. Letters ro A to E are the line sections and 1,, 3 are the transpositions. 3. Applied Faults Digital siulations were perored or three-phase aults. They were located along the line in steps o 5 k ro the Bus 1, and the ault resistance was varied ro 0 to 30 with steps o 10. A sapling requency o 1 MHz, have been used to easure the phase-voltages. Ater inishing the siulations in ATP, the signals were analysed with the proposed algorith through Matlab. 3.3 Results and Analysis Fig. 5 shows as an exaple o the three-diensional graphic obtained ater analysing a ault located at 5 k. It is the squared odulus o the CWT carried out on the voltage o the irst aerial ode, representing its energy density distribution. A scale s is selected by (3) as the one whose energy is axiu. Then, aking a ast Fourier transor o the W(u,s ), the requency o peaks repetition can be calculated. Twice the requency with axiu spectru is adopted as the estiated requency that characterizes the ault distance at the analysed ode.

5 Fig. 5. Squared Modulus o the ault voltage-transient generated by a 5 k ault distance with 0 o ault resistance. Error! No se encuentra el origen de la reerencia. shows the estiated and calculated requencies or each ault distance. Calculated requencies are given by: c c (6) x Where c is the speed o light ( k/s), and x is the real ault distant ro siulations. The wave-propagation speed was assued as equal or all three odes v i =c. Coparing with the calculated requencies, the sallest errors correspond to aults located in the irst part o the line. A 6.3% higher requency error was estiated or aults located at 0 k. However, at 5 k the estiated requency is slightly lower, producing an oscillation around these distances. Fig. 6 and Fig. 7 illustrates the values ebodied in Table 1. Fig. 7. Frequency Error. In Table and Fig. 8 are shown the real and estiated ault distance. Fault Distance [k] Estiated Fault Distance [k] Distance Error [%] 5 5,0 0, ,05 0, ,08 0,8 0 18,83 4,05 5 6,33 4,6 8,9 8,99 0,31 Table Real and Estiated Fault Distances. Fault resistance: 0, 10, 0, 30. Fault Distance [k] Estiated Frequency [Hz] Calculated Frequency [Hz] Frequency Error [%] , , , , , ,3 Table 1 Calculated and Estiated Characteristic Frequencies. Fault resistance: 0, 10, 0, 30. Fig. 8. Distance Error. 4 Conclusions Fig. 6. Calculated and estiated requencies. An approach or ault location on transission lines was presented in this paper. Only the phase-voltages signals onitored in one terinal are used, aiing at siplicity. In order to detect the transient signal, all three phases are onitored by the direct axis voltage obtained through Park s equation. Then, the transient-signal is saved or an o-line analysis. A other wavelet is inerred ro the signal to have a good correlation, and the CWT is carried out to identiy a characteristic requency. This requency is used to estiate a distance.

6 A 69 kv real lie transission syste was siulated, considering requency-dependent lines odels, three transpositions, an equivalent source and a load. The proposed ethod was applied taking account the inluence o threephase aults with dierent resistances. Results showed that the lower errors reerred to ault distances, were obtained in the irst part o the line. This can be explained by the inverse relationship between requency and distance. Thereore, the ethod is ore reliable or aults near the easureent point. Reerences [1] A. Borghetti, M. Bosetti, M. Di Silvestro, C. A. Nucci, M. Paolone. Continuous-Wavelet Transor or Fault Location in Distribution Power Networks: Deinition o Mother Wavelets Inerred Fro Fault Originated Transients IEEE Trans. On Power Systes. v. 3, no., May 008. [] A. Borghetti, S. Corsi, C. A. Nucci, M. Paolone, L. Peretto, R. Tinarelli, On the use o continuous-wavelet transor or ault location in distribution power systes Electrical Power and Energy Systes vol. 8, pp [3] A. Borguetti, M. Bosetti, C. A. Nucci, M. Paolone, A. Abur. Integrated use o Tie Frequency Wavelet Decopositions or Fault Location in Distribution Networks: Theory and Experiental Validation IEEE Trans. On Power Delivery, vol. 5, no. 4, 010. [4] A. D. Filoena, R. H. Sali, M. Resener, A. S. Bretas, Ground Distance Relaying With Fault-Resistance Copensation or Unbalanced Systes, IEEE Trans. On Power Delivery, vol. 3, no. 3, July 008. [5] Bonneville Power Adinistration, Alternative Transient Progras: ATP/EMTP, 00. [Online]. Available: [6] D. Spoor, J. G. Zhu, Iproved Single-Ended Traveling- Wave Fault-Location Algorith Based on Experience With Conventional Substation Transducers IEEE Trans. On Power Delivery, vol. 1, no. 3, July 006. [7] F. H. Magnago, A. Abur, Fault Location Using Wavelets IEEE Trans. On Power Delivery, vol. 13, no. 4, October 1998 [8] F. V. Lopes, d. Fernandes Jr. W. L. A. Neves. Fault Location on Transission Lines Based on Travelling Waes subitted to the International Conerence on Power Systes Transients in Del, the Neatherlands, June 14-17, 011. [9] J. Izykowski, R. Molag, E. Rosolowski, M. M. Saha. Accurate Location o Faults on Power Transission Lines With Use o Two-End Unsynchronized Measureents, IEEE Trans. On Power Delivery, vol. 1, no., April 006. [10]J. Izykowski, R. Molag, E. Rosolowski, M. M. Saha. Accurate Location o Faults on Power Transission Lines With Use o Two-End Unsynchronized Measureents, IEEE Trans. On Power Delivery, vol. 1, no., April 006. [11]J. R. Marti, Accurate Modeling o Frequency- Dependent Transission Lines in Electroagnetic Transient Siulations IEEE Trans. On Power Apparatus & Systes, vol. PAS-101, no. 1 January 198. [1] K. R. Caino de oliveira, R. H. Sali, A. Shuck Jr., A. S. Bretas Faulted Branch identiication on Power Distribution Systes Under Noisy Environent, subitted to the International Conerence on Power Systes Transients, Kyoto, Japan, June 3-6, 009. [13]Kasun Nanayakkara, A. D. Rajapakse, Randy Wachal. Fault Location in Extra Long HVdc Transission Lines using Continuous Wavelet Transor subitted to the International Conerence on Power Systes Transients, Det, the Netherlands, June 14-17, 011. [14]Mallat, Stéphane. A wavelet touro signal processing. Third Edition. Acadeic Press, dec, 008. [15]W. Threevithayanon, N. Hoonchareon. Fault Data Synchronization Using Wavelet or Iproving Twoterinal Fault Location Algorith In Power and Energy Engineering Conerence, Asia-Paciic 010.