A. Borghetti, M. Bosetti, M. Di Silvestro, C.A. Nucci and M. Paolone

Transcription

1 Contnuou-Wavelet Tranform for Fault Locaton n Dtrbuton Power Network: Defnton of Mother Wavelet Inferred from Fault Orgnated Tranent A. Borghett, M. Boett, M. D Slvetro, C.A. Nucc and M. Paolone Abtract-- The aer reent a fault locaton algorthm for dtrbuton network baed on wavelet analy of the voltage waveform of the travelng wave recorded at a bu durng the fault. In artcular, the rooed rocedure mlement the contnuou wavelet tranform combned wth the ue of mother wavelet nferred from the fault-orgnated tranent waveform. The erformance of the rooed algorthm are analyzed for the cae of the IEEE 34-bu tet dtrbuton ytem and comared wth thoe acheved by ung the Morlet mother wavelet. Keyword: Fault locaton, ower qualty, dtrbuton network, contnuou wavelet tranform, mother wavelet. I. INTRODUCTION OWER Qualty of dtrbuton network, wth artcular Preference to the number and duraton of hort and long nterruton, trctly deendent to the annual number of network fault n dtrbuton network and to the relevant retoraton tme. The avalablty of accurate fault locaton technque can reult n mortant reducton of retoraton tme [1]. The fault locaton roblem ha been extenvely nvetgated and everal aroache have been rooed n the lterature n order to relace earchng technque baed on equental wtchng maneuver. Thee aroache can be groued nto the followng two man categore: ) method baed on medance meaurement (e.g. []-[4]); ) method baed on the analy of fault-orgnated voltage and current travelng wave (e.g. [5]-[8]). It worth mentonng that exert ytem, often baed on the ue of neural network, have been alo rooed (e.g. [9]-[11]). Imedance meaurement method eentally rely on the evaluaton of the fault medance at ower frequency, whch carred out by analy of voltage and current gnal recorded at the lne termnal. Tranmon lne are the tycal alcaton feld of th technque: the conderable lne length and the mle network toology allow for a good accuracy achevement. Concernng the accuracy of thee method, t affected by the Th work a art of a reearch rogram uorted by CESI, Italy. A. Borghett, M. Boett, M. D Slvetro, C.A. Nucc and M. Paolone are wth the Deartment of Electrcal Engneerng, Unverty of Bologna, Bologna, Italy (e-mal: {alberto.borghett; mauro.boett; mauro.dlvetro; carloalberto.nucc: maro.aolone}@mal.ng.unbo.t). Preented at the Internatonal Conference on Power Sytem Tranent (IPST 7) n Lyon, France on June 4-7, 7 fault medance value and t decreae when dtrbuton network characterzed by the reence of hort lne wth a radal toology are dealt wth. For uch a cae, the adoton of method baed on the travelng wave theory ha been rooed, although ther mlementaton call for both a more comlex meaurement and gnal analy technque. Thee method rely on the analy of the hgh-frequency comonent of the voltage and current tranent orgnated by the fault, whch roagate along the lne. For th uroe, the ue of Wavelet-baed analy ha been recently rooed [6,7,1]. The method reented n th aer can be condered belongng to category ). It baed on the extenon of the algorthm reented n [1] n whch voltage tranent generated by the fault are montored and analyzed by mean of a Contnuou Wavelet Tranformaton (CWT), n order to detect ecular frequence whch characterze the fault. Thee frequence can be ued to nfer the fault locaton, aumng the network toology and lne conductor geometry known. In order to mrove the method erformance, and to overcome ome lmtaton of the relevant algorthm [1], th aer rooe a method mrovement baed on the contructon of mother wavelet drectly nferred from the recorded faultorgnated voltage tranent. The nfluence of uch a rocedure on the fault locaton accuracy analyzed, and the reult are comared wth thoe obtaned by ung a tandard mother wavelet, namely the o-called Morlet mother wavelet. The aer tructured a follow. Secton II decrbe the nformaton that can be nferred from fault-orgnated travellng wave and the adequacy of dfferent gnal roceng technque that can be adoted to analyze fault tranent takng nto account ther ecular charactertc. Secton III llutrate the algorthm for the defnton of tranent-baed mother wavelet and Secton IV how ome alcaton makng reference to the IEEE 34-bu dtrbuton ytem. II. THE PROPOSED TRAVELING-WAVE APPROACH The rooed aroach baed on the correlaton between fault locaton and ome charactertc frequence aocated to fault-orgnated travelng-wave ath along the network. Thee charactertc frequence can be dentfed by mean of adequate gnal analy technque aled to the voltage or current waveform recorded at an obervaton ont, tycally located at the lower voltage termnal of the tranformer

2 feedng the dtrbuton network. A. Fault-orgnated travelng-wave ath and aocated charactertc frequence Fault-orgnated travelng wave roagate along the network and reflect at lne termnaton, juncton between feeder and lateral, and the fault locaton. The relevant reflecton coeffcent deend on the lne urge medance, on the medance of ower comonent connected to the network termnaton and on the fault medance value. A certan number of ath, covered by the travellng wave, can be aocated to obervaton ont m, where the fault-orgnated travelng wave are meaured. Aumng a network toology characterzed by a man feeder and ome lateral, the number of ath equal to the number of network lateral lu the number of feeder-lateral juncton. A an examle, fgure 1 how a fault locaton laced between bue 81 and 814 of the frt ecton of the man feeder of the IEEE 34-bu dtrbuton ytem [13]. For uch a fault locaton, four dfferent ath can be dentfed and ath #1, #3 and #4 can be aocated to the obervaton ont laced n correondence of the bu 8 (medum voltage de of the feedng ubtaton). Fg. 1. Examle of ath covered by the travellng wave aocated to a fault locaton laced between bue 81 and 814 of the frt ecton of the man feeder of the IEEE 34-bu dtrbuton ytem [13]. Each ath can be aocated to a number of charactertc frequence, one for each of the travelng-wave roagaton mode [14,15] 1. Aumng the network toology and travellng wave eed for the varou roagaton mode are known, frequency f, of mode through ath can be evaluated a-ror a v f, = (1) nl where v the travellng eed of the -th roagaton mode, L the length of the -th ath and n ( the number of tme needed for a gven travellng wave to travel along ath before attanng agan the ame olarty at obervaton ont m. Next ecton devoted to a revew of gnal analy 1 A bref ummary on modal analy, were the man quantte ued n th aer are defned, reorted n the Aendx. technque that can be adoted for the dentfcaton of the frequency value f, by the analy of recorded tranent waveform: -1 value are ued to dentfy the faulted ecton and the remanng one ued to dentfy the fault dtance between obervaton ont m and the fault locaton [1]. B. Sgnal analy technque for charactertc frequency dentfcaton of travelng-wave ath The dentfcaton of charactertc frequence f, aocated wth the fault locaton can be accomlhed by ung one the arorate gnal analy technque, whoe choce deend on the charactertc of the fault tranent gnal. Thee gnal are comoed by the uermoon of the tatonary ndutral frequency waveform (low frequency comonent of large duraton) and the tranent dturbance caued by the fault (hgh frequency comonent of hort duraton). The reultng gnal therefore characterzed by a contnuou ectrum due t tme-varant roerte. The arorate gnal analy technque hould atfy the two followng requrement: () large temoral reoluton at hgh frequence and () large frequency reoluton at low frequence. The ue of tme-frequency rereentaton (TFR) allow for the adjutment of the gnal ectrum veru tme [16]. A gnal TFR lnk a one-dmenonal tme gnal x ( t ) nto a b-dmenonal functon of tme and frequency, Tx ( t, f ). Tycal examle of lnear TFR are the Short Tme Fourer Tranform (STFT) and the Wavelet Tranform. A known, STFT a wndowed Fourer tranform n whch the obervaton nterval dvded nto a gven number of ubnterval. For each ubnterval, STFT comuted accordng to the followng equaton: + jωτ TSTFT ( t, f ) = x( τ ) w( t τ) e dτ () where w( τ ) the wndowng functon that defne the length of the ubnterval. Smlarly to the Fourer Tranform, the man charactertc of the STFT that the tme-frequency reoluton contant and equal to the duraton of each ubnterval. Therefore, t not the more arorate tool for the analy of fault gnal. The wavelet tranform, on the other hand, a TFR whch allow a good frequency reoluton at low frequence and a good tme reoluton at hgh frequence [17]. In artcular, t allow for the analy of hgh frequency comonent very cloe to each other n tme and low frequency comonent very cloe each other n frequency. Thee roerte are ndeed artcularly utable for the tudy of tranent waveform roduced by fault. The rooed fault locaton aroach baed on the ue of a Contnuou Wavelet Tranform (CWT). The CWT of gnal x ( t ), a known, the ntegral of the roduct between x ( t ) and the o-called daughter-wavelet, whch are tme tranlated and cale exanded/comreed veron of a fnte energy

3 functon ψ () t, called mother wavelet. Th tranform, whch equvalent to a calar roduct, roduce wavelet coeffcent C( a, b ) that rereent the TFR b-dmenonal functon of tme and frequency Tx ( t, f ). Coeffcent C( a, b ) can be een a mlarty ndexe between the gnal and the ocalled daughter wavelet located at oton b (tme hftng factor) wth otve cale a + 1 * t b C( a, b) x( t) dt a ψ = a (3) where * denote comlex conjugaton. Equaton (3) n frequency doman read (e.g. [18]): * F C a, b = aψ a ω X ω (4) ( ( )) ( ) ( ) where F( C( a, b )), X ( ω ) and Ψ ( ω) are the Fourer tranform of C( a, b ), x ( t ) and ψ () t reectvely. If the center frequency of the mother wavelet ψ ( t) F, then the one of ψ ( at) F a. Therefore, dfferent cale a allow the extracton of dfferent frequence. If the CWT backward tranformaton,.e. the gnal recontructon, mut be guaranteed, the choce of the number and acng of cale a hould comly wth ecfc contrant. For our uroe, the gnal recontructon not needed and therefore the CWT ectrum can ue lnear or logarthmc cale of any dered denty. If needed, a hghreoluton ectrum can be generated for a narrow range of frequence. The analyzed art () t of recorded gnal x ( t ), correondng to a voltage or current fault-tranent, characterzed by a hort duraton, of a few mllecond. Such a duraton correond to the roduct between amlng tme T and number of amle N. Therefore, n the numercal mlementaton of the CWT aled to gnal ( t ), the element of matrx C( a, b ) of (3) are gven by 1 N 1 ( ) ( ) * n T C a T T ψ ( nt ), = a n= a (5) where roduct T correond to the tme hftng factor b of the CWT exreed a a multle of amlng tme T. The um of the quared value of all coeffcent belongng to the ame cale, whch wll be denoted a CWT gnal energy Ecwt ( a ), dentfe a calogram whch rovde the weght of each frequency comonent [19]: N 1 E ( ) ( (, )) cwt a = C a nt (6) n= By nectng the relatve maxmum eak of the obtaned calogram Ecwt ( a ), the charactertc frequence f, aocated wth the fault locaton can be dentfed. C. A frt alcaton examle: balanced old fault A a frt examle, the rooed fault locaton rocedure aled to the cae of a three-hae old fault at bu 81 of the IEEE 34-bu dtrbuton ytem [13] decrbed n the Aendx and llutrated n fgure A1. Three travellng-wave roagaton ath are aocated wth the condered fault at bu 81. They are characterzed by a common extremty, namely bu 8. The other three ath-termnal correond to bu 81 (ath #1), bu 88 (ath #) and bu 81 (ath #3). In order to aocate a charactertc frequency to each of the three ath, we can ee the fault a a te-functon ource trggered by the fault occurrence. The fault-generated te wave travel along the network and reflected n correondence to the above-mentoned extremte of the ath. Each extremty characterzed by a voltage reflecton coeffcent: extremte where a ower tranformer connected can be condered a oen crcut and the relevant reflecton coeffcent cloe to +1; extremte that correond to a juncton between varou lne are characterzed by a negatve reflecton coeffcent; the reflecton coeffcent of the extremty where the fault occurrng cloe to -1, a the fault medance value lower than the charactertc medance of the lne. Therefore, the reultant voltage tranent oberved at bu 8 the um of three quare wave, each one relevant to a ecfc ath. Each quare wave characterzed by a man frequency gven by (1), where each coeffcent n deend on the gn of the reflecton coeffcent of the two ath extremte, namely n equal to or to 4 f the reflecton coeffcent have the ame or oote gn, reectvely. Table I how the theoretcal frequency value obtaned by alyng (1) to the condered examle. TABLE I. CHARACTERISTIC AND CWT-IDENTIFIED FREQUENCIES RELEVANT TO THE PROPAGATION PATHS FOR A THREE PHASE SOLID FAULT LOCATED AT NODE 81 OF FIGURE A.1. THE RESULTS MAKE REFERENCE TO THE MORLET MOTHER WAVELET. THE ANALYSIS REFERS TO PROPAGATION MODE 1 OF TABLE A.I. Theoretcal frequence f, CWT dentfed length frequency (travelng wave refer to (km) roagaton mode 1 of Table A.1) x x x Table I alo how the frequency value obtaned by alyng the CWT-analy to the voltage tranent at bu 8 a reroduced by an EMTP-RV mulaton (ee the Aendx). The CWT analy aled to the voltage tranent recorded at the medum voltage de of the feedng ubtaton (bu 8), carred out by ung the Morlet mother wavelet.

4 Such a functon one of the everal mother wavelet rooed n the lterature (e.g. [-5]) and t adoton jutfed by the mlarty to tycal voltage fault-tranent waveform. It defned by a Gauan-wndowed comlex nuod t / F t = (7) ψ () t e e π The CWT-analy erformed n a tme wndow of m and refer to roagaton mode 1. The ecfc charactertc of roagaton mode along the lne of the condered network are gven n Table A.1 of the Aendx. Fgure how the obtaned gnal energy value ( ) cwt E a. A t can be een from fgure, the CWT analy able to dentfy the frequence related to ath #1 and the one related to the lateral branch between bu 8 and bu 81 (ath #3), whlt t unable to dentfy ath #, between bu 8 and bu 88. The frequency aocated wth the econd ath hdden by the other frequence due to the large flter amltude related to the adoted mother wavelet. The locaton error defned a 1 ν e% = L* (8) CWT L* n* f*, where L * the length of ath * between the obervaton bu and the fault locaton, ν the roagaton eed of mode CWT, n * equal to 4 and f *, the CWD-dentfed frequency relevant ath *. The locaton error for the condered fault acheved by the CWT analy equal to 1.9%. CWT gnal energy (.u.) Morlet Mother wavelet Theoretcal frequence Frequency Fg.. Reult of the CWT analy of the mode 1 of the voltage tranent recorded at node 8 for a three-hae old fault at node 81. The value are n er-unt wth reect to the maxmum. III. DEFINITION OF MOTHER WAVELETS INFERRED FROM FAULT-ORIGINATED TRANSIENTS A. Proerte of mother wavelet A known, the CWT allow for the adoton of arbtrary mother wavelet rovded that have to comly wth the admblty condton + Ψ ( ω) Cψ = dω < (9) ω Suffcent condton to atfy (9) are: + a) mean value of ψ ( t) equal to zero, namely htdt () = ; b) fat decreae to zero of ψ () t for t ±. Therefore, a feable mother wavelet ha at leat one zero value. If the mother wavelet atfe alo the o-called orthogonalty condton, the gnal can be recontructed from the CWT tranform coeffcent, a (e.g. [17]) + + () 1 (, ) da db f t = C a b ψ, () ab t C (1) ψ a The orthogonalty condton not requred for the CWT analy of the rooed fault locaton aroach, but needed n cae of tme-doman fault locaton aroache (e.g. [7]), baed on recontructon of the fault tranent gnal related to each charactertc frequency. B. Defnton of mother wavelet nferred from faultorgnated tranent A above mentoned, the CWT can be condered a a flterng roce baed on the calar roduct between the daughter wavelet and the analyzed gnal. The maxmzaton of uch a calar roduct related to the mlarty between the mother wavelet and the gnal telf, and, therefore t aear arorate to buld the mother wavelet by ung art of the fault tranent waveform telf. The rocedure develoed to buld uch a mother wavelet, whch comle wth condton (9), comoed by the followng te. 1. Beng ( t ) the fault tranent waveform, () t extracted a the ntal art of ( t ). Functon () t ued to buld the mother wavelet ψ ( t) and t tart from the faultoccurrence tme wth a duraton t that correond to the mnmum exected frequency content of the analyzed gnal.. ( t ) then normalzed wth t maxmum value. 3. In order to atfy condton a), ( t ) further normalzed to obtan a mean value equal to zero. ψ t buld a a ere of everal k t-hfted 4. Fnally, ( ) ( t ) multled by a an exonental decay, characterzed by tme contant τ, n order to atfy condton b): t ψ () t = ( t+ k t) + ( t k t) e τ (11) k wth () () t t t t = (1) t ; t t C. Alcaton examle: balanced old fault In th ecton decrbed the alcaton of the above rooed rocedure for the cae of a three-hae old fault located n correondence of node 814 of the IEEE 34-bu

5 x1 4 dtrbuton ytem. Fgure 3 how the voltage waveform of the roagaton mode 1 oberved at the node 8 and the electon of the art of the fault tranent waveform ( t ) ued to buld the mother wavelet hown n fgure 4. Fgure 5 how the CWT analy by comarng the reult obtaned by ung the fault-nferred and Morlet mother wavelet. The dentfed frequence, a well a the relevant ath, are reorted n Table II. Mode1 Voltage (kv) Tme () Fg. 3. Fault voltage tranent waveform of the roagaton mode 1 oberved at node 8 of the IEEE 34-bu dtrbuton ytem for a three hae old fault n 814; the electon of () t ued to buld the mother wavelet. 1 CWT Mother Wavelet Amltude [.u.] t e τ Samle x 1 4 Fg. 4. Tranent-baed mother wavelet bult from ( t ) of fgure 3; τ =1-1. CWT gnal energy (.u.) Tranent-baed mother wavelet Morlet mother wavelet Theoretcal frequence Frequency Fg. 5. Comaron between the reult of the CWT analy erformed wth Morlet and wth fault-nferred mother wavelet of mode 1 of the voltage tranent recorded at node 8 for a three-hae old fault at node 814. The value are n er-unt wth reect to the maxmum. A for the cae llutrated n revou ecton, the CWT analy referrng to the Morlet mother wavelet able to detect only the frequence aocated wth the frt and econd ath whle the frequency eak aocated wth the thrd ath aear hdden by the econd eak. On the contrary, the CWT referrng to the tranent-nferred mother wavelet allow the dentfcaton of all the three frequence. TABLE II. CHARACTERISTIC AND CWT IDENTIFIED-FREQUENCIES RELEVANT TO THE PROPAGATION PATHS FOR A THREE PHASE SOLID FAULT LOCATED AT NODE 814 OF FIGURE A.1. THE ANALYSIS REFERS TO THE PROPAGATION MODE 1 OF TABLE A.I. length (km) Theoretcal frequence f, (travelng wave refer to roagaton mode 1 of Table A.1) CWT dentfed frequency Tranentbaed mother wavelet Morlet mother wavelet x x x IV. APPLICATION EXAMPLES OF THE CWT-BASED ALGORITHM FOR FAULT LOCATION IN DISTRIBUTION NETWORKS The revou examle make reference to the cae of balanced old fault. In what follow, the erformance of the rooed algorthm are evaluated for the cae of: a) unbalanced fault, b) varable value of fault medance; c) dfferent exonental decay tme of the mother wavelet and d) dfferent fault locaton wthn the IEEE 34-bu dtrbuton ytem. A. Unbalanced fault Let conder a hae-to-ground old fault located n correondence of node 81 of fgure A.1. For th fault locaton, three charactertc frequence can be dentfed. The charactertc of each ath are the ame llutrated n Table I. Fgure 6 how the CWT analy erformed makng reference to the roagaton mode 1 oberved n correondence of node 8 and the comaron between the reult obtaned by ung the fault-nferred and Morlet mother wavelet. Alo for the cae of unbalanced fault, the rooed aroach utably combned wth the ue of tranent-baed mother wavelet, allow for the dentfcaton of all the charactertc frequence, a reorted n Table III. B. Effect of the fault medance In th ecton the effect of the fault medance on the accuracy of the fault locaton algorthm aeed. A hae-to-ground fault ha been aumed at node 86 of the IEEE 34-bu dtrbuton ytem. Such a bu ha been elected n order to analyze a fault locaton characterzed by a ngle ath. Three dfferent fault medance have been condered, namely, 1 and 1 Ω and the reult are hown n Table IV. Such a Table reort alo the locaton accuracy, d, calculated a the dfference between the length of the ath

6 *, between the obervaton bu and the fault locaton, and the CWT-dentfed length of the ame ath. A t can be een, the accuracy of the rooed algorthm not nfluenced by the dfferent fault medance value. CWT gnal energy (.u.) Tranent-baed mother wavelet Morlet mother wavelet Theoretcal frequence Frequency Fg. 6. Comaron between the reult of the CWT analy erformed wth Morlet and fault-nferred mother wavelet of the mode 1 of the voltage tranent recorded at node 8 for a hae-to-ground old fault at node 81. The value are n er-unt wth reect to the maxmum. TABLE III. CHARACTERISTIC AND CWT IDENTIFIED FREQUENCIES RELEVANT TO THE PROPAGATION PATHS FOR A PHASE-TO-GROUND SOLID FAULT LOCATED AT NODE 81 OF FIGURE A.1. THE ANALYSIS REFERS TO THE PROPAGATION MODE 1 OF TABLE A.I. length (km) Theoretcal frequence f, (travelng wave refer to roagaton mode 1 of Table A.1) CWT dentfed frequency Tranentbaed mother wavelet Morlet mother wavelet x x x TABLE IV. CHARACTERISTIC AND CWT IDENTIFIED FREQUENCIES RELEVANT TO THE PROPAGATION PATHS FOR A PHASE-TO-GROUND FAULT LOCATED AT NODE 86 OF FIGURE A.1. THE RESULTS MAKE REFERENCE TO THE TRANSIENT BASED MOTHER WAVELET. THE ANALYSIS REFERS TO THE PROPAGATION MODE 1 OF TABLE A.I. Theoretcal Fault frequence f, CWT dentfed d Imedance frequency (travelng wave refer to (m) (Ω) roagaton mode 1 of Table A.1) C. Influence of the mother wavelet exonental decay tme In th ecton the nfluence of the exonental decay tme τ of the mother wavelet exreed by (11) analyzed. In artcular, four dfferent value of τ have been condered, namely: 1-7, 1-8, 1-9 and 1-1. The relevant CWT analy of the voltage tranent recorded at node 8 for a three-hae old fault at node 814 reorted n fgure 7. The reult how that the ncreae of the exonental decay tme of the mother wavelet reult n a decreae of the erformance of the algorthm n the dentfcaton of charactertc frequence of large amltude. CWT Sgnal Energy [.u.] 1, 1,8,6,4, τ =1e-7 τ =1e-8 τ =1e-9 τ =1e Frequency [khz] Fg. 7. Comaron between the reult of the CWT analy erformed wth dfferent mother wavelet exonental decay tme. Analy erformed n the mode 1 of the voltage tranent recorded at node 8 for a three-hae zeromedance fault at node 814. The value are n er-unt wth reect to the maxmum. D. Extended fault locaton analy reult The lat analy erformed wth the rooed algorthm the dentfcaton of ngle/three hae fault locaton occurrng at everal the bue of the IEEE 34-bu dtrbuton ytem. The reult relevant to the three hae fault are reorted n Table V whle the reult of ngle hae fault n Table VI. Both table reort alo the locaton accuracy, d, calculated followng the ame rocedure decrbed n revou ecton IV.B. It can be oberved that the rooed algorthm erform atfactorly for any of the aumed fault locaton. V. CONCLUSIONS The aer ha reented an mrovement veron of a fault locaton algorthm, revouly develoed by the author, baed on the analy of fault-generated travellng wave by mean of the contnuou wavelet tranform. The mrovement ha been realzed by mean of the arorate defnton of mother wavelet nferred from fault tranent waveform. The defnton of thee mother wavelet allow ndeed to overcome ome lmtaton of the orgnal algorthm, whch were related to the ue of tandard mother wavelet. In artcular, the ue of tandard mother wavelet doe not allow to dentfy all the frequence of the fault-orgnated travellng wave, and the relevant ath, aocated wth a ecfc fault locaton. Th ha been confrmed by mean of an extenve analy carred out on the IEEE 34-bu dtrbuton ytem. A comrehenve evaluaton of the erformance of the rooed algorthm ha been reented for dfferent tye of fault and for dfferent locaton and the overall effectvene of the rooed algorthm ha been roved. Future reearch effort wll be devoted to the orthogonalzaton roce of tranent-nferred mother wavelet, n order to allow for the recontructon of the tranent gnal for each charactertc frequency. Th exected to mrove of the algorthm accuracy by mean of roer ntegraton of the rooed algorthm wth tmedoman fault locaton aroache [6].

7 TABLE V. CHARACTERISTIC AND CWT IDENTIFIED FREQUENCIES OF THREE PHASE SOLID FAULTS IN SOME NODES OF THE IEEE 34-BUS DISTRIBUTION SYSTEM REPORTED IN FIGURE A.1. THE RESULTS MAKE REFERENCE TO THE TRANSIENT-INFERRED MOTHER WAVELET. CWT dentfed Fault locaton Theoretcal freq d frequency node (m) TABLE VI. CHARACTERISTIC AND CWT IDENTIFIED FREQUENCIES OF PHASE- TO-GROUND FAULTS IN SOME NODES OF THE IEEE 34-BUS DISTRIBUTION SYSTEM REPORTED IN FIGURE A.1. THE RESULTS MAKE REFERENCE TO THE TRANSIENT-INFERRED MOTHER WAVELET. CWT dentfed Fault locaton Theoretcal freq d frequency node (m) VI. APPENDIX A. Summary on modal analy of tranmon lne and defnton of man quantte It worth notng that the roagaton of travellng wave n multconductor lne, nvolve the reence of dfferent roagaton eed. Therefore, the dentfcaton of uch frequence carred out earately for the varou roagaton mode. Equaton (A1) (A.3) brefly recall the o-called modal tranformaton, through tranformaton matrce [ T e ] and [ T ], adoted for voltage and current reectvely. h dv h [ Z'][ Y '][ V ] dx = h d I h [ Y '][ Z'][ I ] = dx h m [ V ] = [ Te ][ V ] h m [ I ] = [ T][ I ] (A.1) (A.) m dv m [ ] [ V ] dx = γ (A.3) m d I m [ γ ] [ I ] = dx Where: uercrt h and m denote hae and modal varable; [ Z '] and [ Y '] are the medance and admttance matrxe n er unt of length; [ γ ] the dagonal matrx of the common egenvalue of roduct [ Z '][ Y '] and [ Y '][ Z '] n whch γ = α + jβ are the roagaton contant of mode characterzed by the attenuaton contant α and the hae contant β. The hae velocty of mode gven by: ω v = (A.4) β Calculaton of matrxe [ T e ] and [ T ], whch mut be real n order to be adoted n a tme-doman alcaton, erformed ung the EMTP [15]. B. Data of the adated IEEE 34-bu dtrbuton ytem In th aer, the fault tranent are obtaned makng reference to the IEEE 34-bu dtrbuton ytem [13]. The model of the tet network ha been mlemented n the EMTP-RV envronment [7] (ee fgure A.1). The IEEE 34-node tet feeder comoed by branche characterzed by dfferent conductor confguraton. In order to mlfy the mulaton reult, the followng aumton have been made: () all the branche of the network are comoed by overhead lne whch conductor confguraton the ID #5 reorted n the fgure 1 of [13] (three-hae lu neutral) (ee fgure A.-a); () the network load are aumed located n correondence of the lne termnaton and connected by mean of dtrbuton tranformer. Concernng the ower dtrbuton tranformer, they are rereented by mean of the arallel of a 5 Hz tandard model and a Π of caactance n order to rereent, n a frt aroxmaton, t reone to tranent at a frequency range around 1 khz (ee fgure A.-b). The arameter adoted for the 5 Hz art of the tranformer model are the followng: 5 MVA 15/4.9 kv V c =9% for the ubtaton; 1 MVA 4.9/.4 kv V c =4% for the load and.5 MVA 4.9/4.9 kv V c =8% for the load.

8 Load_ V_ AC_Feedng V_Reg_1.5 Load_838 V_838 V_8 V_85 V_86 Load_ V_83 V_Reg_ 856 V_ Load_ A? V_8 Load_8 Load_864 Load_84 Fg. A.1. IEEE 34-bu dtrbuton ytem mlemented n EMTP-RV. 8.9 VM V_84 8 V_ V_848 Load_848 Gven the lmted length of tycal dtrbuton network and the charactertc frequency content of fault tranent (wthn the order of few ten of khz), a contant arameter lne model (CP-lne model) adoted for the rereentaton of the overhead lne [15]. a) Tye of conductor Retance (5-6 Hz) [Ω/km] Outde dam [cm] Mean Radu [cm] Alumnum b).4nf + DY_1 1 C1 C3 +.nf 4.9/.4.7nF + VM + C P 848 Q Load Fgure A.. a)overhead lne conductor confguraton, b)tranformer model. The modal arameter of the CP-lne model referrng to the overhead lne confguraton hown n fgure A.-a are reorted n Table A.1 and the voltage tranformaton matrx n (A.5). The modal arameter are calculated aumng the ground retvty equal to 1 Ωm. TABLE A.I. VALUE OF THE MODAL PARAMETERS OF THE OVERHEAD LINE CONFIGURATION SHOWN IN FIGURE A.-B, GROUND RESISTIVITY EQUAL TO 1 ΩM. mode Proagaton r l c z c eed (Ω/km) (mh/km) (µf/km) (Ω) (km/) [ ] T e = (A.5) VII. REFERENCES [1] CIRED WG3 Fault management, Fault management n electrcal dtrbuton ytem, [] M. S. Sachdev, R. Agarwal, A technque for etmatng tranmon lne fault locaton from dgtal medance relay meaurement, IEEE Tran. on Power Delvery, vol. 3, n. 1, , January [3] K. Srnvaan, A. St.-Jacque, A new fault locaton algorthm for radal tranmon lne wth load, IEEE Tran. on Power Delvery, vol. 4, n. 3, , July [4] A.A. Grg, D.G. Hart, W.L. Peteron, A new fault locaton technque for two- and three-termnal lne, IEEE Tran. on Power Delvery, vol. 7, n. 1, , January 199. [5] G.B. Ancell, N.C. Pahalawatha, Maxmum lkelhood etmaton of fault locaton on tranmon lne ung travellng wave, IEEE Tran. on Power Delvery, vol. 9, n., , Arl [6] O. Chaar, M. Meuner, F. Brouaye, Wavelet: a new tool for the reonant grounded ower dtrbuton ytem relayng, IEEE Tran. on Power Delvery, vol. 11-3, , July [7] F.H. Magnago, A. Abur, Fault locaton ung wavelet, IEEE Tran. on Power Delvery, vol. 13, n. 4, , October [8] D.W.P. Thoma, R.E. Batty, C. Chrtooulo, A. Wang, A novel tranmon-lne voltage meaurng method, IEEE Tran. on Intrumentaton and Meaurement, vol. 47, n. 5, , October [9] S. Ebron, D.L. Lubkeman, M. Whte, A neural network aroach to the detecton of ncent fault on ower dtrbuton feeder, IEEE Tran. on Power Delvery, vol. 5, n., , Arl 199. [1] Z. Chen, J.C. Maun, Artfcal neural network aroach to ngle-ended fault locator for tranmon lne, IEEE Tran. on Power Sytem, vol. 15, n. 1, , February. [11] N. Kandl, V.K. Sood, K. Khoraan, R.V. Patel, Fault dentfcaton n an AC-DC tranmon ytem ung neural network, IEEE Tran. on Power Sytem, vol.7, n., , May. [1] A. Borghett, S. Cor, C.A. Nucc, M. Paolone, L. Peretto, R. Tnarell, On the ue of contnuou-wavelet tranform for fault locaton n dtrbuton ower network, Electrcal Power and Energy Sytem 8 (6) [13] IEEE Dtrbuton Plannng Workng Grou, Radal Dtrbuton Tet Feeder, IEEE Tran. on Power Sytem Vol. 6, No. 3, Augut 1991, [14] E. Clarke, Crcut analy of AC ower ytem, 1. New York: John Wley & Son; [15] H.W. Dommel, Dgtal comuter oluton of electromagnetc tranent n ngle and mult-hae network, IEEE Tran Power Aaratu Syt 1969;PAS-88(Arl):

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