The Application of the Wavelet Transform of Travelling Wave Phenomena for Transient Based Protection

Transcription

1 The Applicatio of the Wavelet Trasfor of Travellig Wave Pheoea for Trasiet Based Protectio X Z Dog 1, M A Redfer, Z Bo 3 ad F Jiag 4 (1) Tsigha Uiversity, Beijig, PR Chia (e-ail: dxz@ail.eea.tsigha.ed.c) () Uiversity of Bath, Bath, UK (e-ail: M.A.Redfer@bath.ac.k) (3) Alsto T&D, Protectio ad Cotrol, Stafford, UK, (e.ail: zhiqia.bo@tde.alsto.co) (4) Sigapore Polytechic, Sigapore. (e.ail: jiagfa@sp.ed.sg ) Abstract The key poit of trasiet based protectio is the ability to extract the trasiet copoets fro the sapled wavefors ad the process these to detect qickly the occrrece of a power syste falt ad the accrately deterie the falt s locatio i the power syste etwork. This paper presets a aalysis of the characteristics of falt geerated travellig wave trasiet pheoea sig the wavelet trasfor. The characteristics of both the forward ad reverse travellig waves are extracted sig the Modls Maxia (MM) of the wavelet trasfor. The advatages of the techiqes are that they are siple ad direct i their aalysis ad ths are able to deterie clearly the characteristics of the travellig waves trasiets ad hece deterie the type of falt ad its locatio. The paper provides the theoretical fodatio for falt detectio ad locatio sig wavelet trasfors to aalyse trasiets ad illstrates their applicatio. Keywords Trasiets, Neric Relayig, Trasissio Lies, Travellig Wave, Wavelets ad Modls Maxia. characteristics of the varios TWT, ad the Wavelet aalysis of both the power syste voltage ad crret sigals to preset a basic aalysis of varios falt characteristics. It provides the fodatio for TWT based protectio ad falt locatio techiqes. II. CHARACTERISTICS OF THE TRAVELLING WAVE TRANSIENTS (TWT). A. Basic Characteristics of TWT A falt occrrig o a trasissio lie will geerate both voltage ad crret travellig waves. These will travel alog the lie til they eet a discotiity o the lie, sch as falt poit ad bsbar. At this poit, both a reflectio ad a refractio of the wave will occr. This geerates additioal waves which will propagate throgh the power syste. I. INTRODUCTION. The accrate extractio ad characterisatio of travellig wave trasiet copoets provides the fodatio for the travellig wave based protectio ad falt locatio systes. Travellig waves are high freqecy sigals geerated by sdde chages to the power syste. By their atre, the Forier trasfor ad other covetioal atheatical ethods caot copletely represet these trasiet sigals i both their freqecy characteristics ad the tie that they occr. As a reslt, the extractio ad represetatio of the characteristics of the travellig waves trasiets have bee a proble ad therefore the falt locatio ad protectio techiqes which se these aalysis techiqes caot offer a ideal perforace. The wavelet trasfor is a aalysis ethod that ses both the tie ad the freqecy doai. It is ot oly sitable for aalysis of travellig wave trasiets, bt also provides a tool for the extractio ad represetatio of travellig wave trasiets (TWT). Based o the theories describig travellig wave propagatio, this paper ses the basic Fig.1. Falt geerated Travellig Wave o a Sigle-Phase Trasissio Lie. Fig.1 shows a diagra for a solid falt o a sigle-phase trasissio lie. The voltage ad crret travellig wave at both eds of the lie M ad N ca be expressed as:- ) + α e( ) α e( e( ) + αe( ) + αe( ) αe( ) +... i =, Z + = α e( ) +... C (1) 1

2 = α e( ) +... ) + α e( ) α e( e( ) + α e( ) + α e( ) α e( ) +... i( t) =, Z + C () healthy lie sectios ad the propagatio to the falted lie sectio; the differet propagatio velocities for aerial ode ad grod ode; the propagatio losses of the wave; the shtig effects de to the bsbar to earth capacitace; ad the presece of iterferece or oise. All these factors case coplicatios for techiqes sed for the travellig wave based falt locatio[3,6] ad protectio[4] systes. Where:-, represet voltage ad crret qatities at ed M ad N respectively; α ad α are the reflectio coefficiets at eds M ad N respectively. τ ad τ are the tie for the wave to travel to the eds M ad N respectively. Zc is the wave resistace; positive is the forward wave ad egative is the reverse wave e(t) is the sper-iposed voltage sorce of the falt etwork [1] As show i Fig.1 ad eqatios (1) ad (), the basic characteristics of falt geerated travellig wave trasiets ca be sarised as:- 1) The wave characteristics chage sddely with the arrival of sccessive waves at the bsbar. This arks the occrrig of the falt ad the travellig tie for the jorey fro the falt to bsbar etc. ) The agitde of the sdde chage depeds o the agitde of the voltage at the falt istat - e(t). For later waves, it also depeds o the reflectio ad refractio coefficiets at the discotiity ad the atteatio characteristics of travellig wave[]. 3) The polarity of the sdde chage depeds o the polarity of the falt voltage at the falt istat ad the discotios characteristics of the wave ipedace. Geerally speakig, the polarity of travellig wave has the followig characteristics:- a). Reflected voltage ad crret waves fro the falt poit will have the sae polarity as the icidet waves. b). The iitial voltage or crret waves have the sae polarity at both eds of the lie. c). For the reflected positive wave fro the bsbar ad the reflected egative wave fro the falt poit, their iitial wave ad reflected wave have the sae polarity. B. Wavelet Trasfor ad Modls Maxia. The Wavelet descriptio of travellig wave is derived fro the Base Wavelet fctio ad describes the irreglar characteristics of the trasiet travellig wave. Asse the fctio f(t) represets the travellig wave (voltage, crret or directio) ad the Ψ t represets base Wavelet the Wavelet descriptio of travellig wave, or Wavelet trasfor W s f t is give i Eq.(3) below[5]: W s f t = f t Ψ s t 3 Where ψ s t = ψ t/s /s represets the basic Wavelet s is the scale paraeter or scalig factor. The Wavelet is the dyadic Wavelet whe s = j j Z the correspodig wavelet trasfor is the Dyadic Wavelet trasfor. The dyadic wavelet trasfor possesses a iportat characteristic i that the aplitde of the wavelet trasfor s Modls Maxia MM, is ot odified by traslatios. Therefore this trasfor is sitable for patter idetificatio ad detectig siglarities i the sigal. Becase the B-splie fctio ad its derivatives ca be readily calclated, ad it has the least spport i all of the polyoial splie fctios, the qadratic B-splie fctio has bee proved to be a optial fctio to hadle sigals cotaiated by oise[5]. This techiqe is therefore sed to extract travellig wave sigals. The odls axia, MM, of wavelet trasfor is defied as ε >0, W s, f t ad is sed to extract the axia vales i the easred sigals withi the tie period (t-ε, t+ε). The MM procedre is sed to idetify the axi sigals i the oitored data ad provides both the vale of these axi sigals ad the tie of their occrrece. These are the stored for the ext stage of the aalysis. Sice the ipt wavefors are redced to a table of these easreets, this draatically siplifies the idetificatio of the discotiities associated with the travellig wave trasiets. The vole of data that eeds to be processed is draatically lower tha that sed by alterative approaches. The above basic characteristics lay the fodatio for the TWT protectio. However, cosiderig falt detectio, the extractio of the falt geerated TWT is frther coplicated by the coplig betwee three phases; the refractio fro o-etallic falt; the refractio fro

3 The odls axia of the reslts fro sig the Wavelet trasfor ca copletely describe the origial fctio (or sigal), ad ca also be sed to recostrct the origial fctio[5]. I additio, the se of the odls axia of wavelet ca also eliiate the ajority of ay oise i the origial sigals. C. Procedre for Aalysis sig Wavelets to describe Travellig Waves. 1) Perfor Wavelet trasfor o easred wavefors. ) Obtai the MM of reslts fro sig the wavelet trasfor. three phase voltage travellig wave. 3) Store the vales of the axia ad the tie whe they occr. 4) Aalyse the reslts of the MM, to idetify the travellig wave trasiets ad to check the validity of the reslts to esre that they defie travellig wave trasiets associated with power syste falt coditios. Other types of sigals will also have a MM sigatre ad therefore ca be extracted fro the record. III. THE MODULUS MAXIMA REPRESENTATION OF VARIOUS TRAVELLING WAVES A. MM represetatio of Voltage Travellig Wave. a phase voltage for scales, of wavelet trasfor ad The etwork show i Fig. was sed to illstrate the techiqe. This shows a 500kV trasissio syste with a a phase to earth falt o the lie sectio MN. The falt iceptio agle is 45 o ad falt path resistace is 50Ω. Fig.. The Test 500kV Trasissio Lie Syste. Fig.3 shows the three phase voltages ad reslts of sig the Wavelet trasfor o the wavefors recorded for the phase a travellig wave voltage sigal ad its MM, the trasforatio was carried ot 4 ties sig the differet wavelet trasfors. Fro Fig.3, it is observed that:- 1) The Wavelet trasfors reach a axia whe the falt travellig wave arrives at the easreet poit ad is represeted by etc.. The sdde chage poit correspods to the tie whe the travellig wave arrives at the bsbar. MM of a phase voltage corrspodig to scales Fig.3. Three Phase Voltages ad Phase a Wavelet Trasfor. 3

4 ) Differet scales of MMs (M 1, M, M 3 ad M 4 ) reflect agitdes ad positios of travellig wave copoets for differet freqecy badwidth. 3) The polarity of MM is idetical to the polarity of sdde chage of the travellig wave. 4) The agitde of MM depeds o two factors:- (a) crret sigal travellig wave. (a) the aplitde of the sdde chage of the travellig wave; (b) gradiet of the sdde chage. The aplitde of the sdde chage de to the travellig wave depeds o the istataeos agitde of the voltage at the falt poit whe the falt occrs. The gradiet depeds o the travellig wave atteatio characteristics, the falt positio, syste cofigratio ad lie paraeters. The basic characteristics of these axia i the MM sigal are idetical to that associated with travellig wave trasiets. The derivatio of the MM is based o the Wavelet trasfor. They ca be expressed as:- f ( v, v, v, i, i, i ) g(ax( w f ( v, i )) j = a, b c (3) a b c a b c s j j, Where f is the set of travellig wave ad g is the set of MM. The followig poits ca be see fro the wavefors show i Fig.3:- 1) The travellig wave appears o both falted ad healthy phases whe falt occrs. ) After the Wavelet trasfor, the MM process idetifies the iitial voltage travellig wave, the reflectio waves fro the falt poit the reflected waves fro reote ed bsbar the reflected waves fro eighborig lie bsbar ad the grod odal copoets. 3) The MMs of the reflected wave ad the iitial wave have the sae polarity. 4) The MMs of the reflected voltage wave fro the eighborig bsbar ad the iitial wave have the sae polarity. 5) Falts ivolvig earth prodce grod odal travellig waves. Becase of the differet velocities of the grod ode ad the aerial ode travellig waves, there are sdde chages i the voltage wavefor ad correspodig chages i the grod odal travellig wave he MM prodced by the chages will coplicate the extractio of the waves. (b) Modls axia M 1 M M 3 ad M 4. Fig.4 Mode α Crret Travellig Wave ad the Wavelet Trasfor. B. MM represetatio of crret travellig wave. Fig.4 shows the wavefor of odal crret ad its MMs. With referece to Eqatio (1), it is observed that:- 1) The agitde of the iitial wave is greater tha that of the reflected waves fro the falt poit ad other discotiity poits, sch as a bsbar. Their MMs also follow this patter. See poit as show i Fig. 4. ) The polarity of the MM of the reflected wave fro the falt poit is the sae as that of the iitial wave. Its aplitde is or ties of that of the iitial wave. or represet the atteatio of these sigals. See poit as show i Fig.4. 3) The polarity of the MM of the reflected wave fro eighborig bsbar is the sae as that fro the falted poit, ad its aplitde is the iverse of the forer (poit as show i Fig.4). 4) The polarity of the MM wave reflected fro the reote ed bsbar is of the opposite polarity to that fro the falt poit. Its aplitde is proportioal to (poit as show i Fig.4). 4

5 There is o grod ode travellig wave sig the α ode crret travellig wave ad hece there is o eqivalet to poit as show i Fig.3. C. MM represetatio for the forward travellig wave. The cobiatio of travellig voltage ad crret waves provides a clear idicatio of the directioality of a falt. This is very iportat for power lie protectio. The forward travellig wave reflects oly travellig waves fro reote bsbar, ad ca be expressed as:- (a) Forward travellig wave at ed M. 1 = ( ( t) Z ci ( )) (5) M. forward + t Whe derivig forward travellig wave, both voltage ad crret se the odal travellig wave i order to cacel the oise iterferece of the grod odal wave. Figs 5(a) ad 5(b) show the Wavelet trasfor ad its MM of the forward travellig wave. As show i the figre, the reflectio wave fro eighborig bsbar L, poit is stregtheed whe the forward travellig wave is extracted sig MM. (b) MM of forward travellig wave, M 1 M M 3 ad M 4. D. MM represetatio of reverse travellig wave. The reverse travellig wave which cotais the reflectios of the wave fro the falted lie, cotais iforatio of falt locatio[3,6] ad fors the basis for travellig wave distace easreet[4] ad positioal protectio[7]. The reverse travellig wave at poit M ca be expressed as: (c). Reverse travellig wave at ed M. 1 = ( Z ci ( )) (6) M. iverse t Figs 5 (c) ad (d) show the reverse travellig waves ad the distribtio of their MMs. The figre shows the iitial travellig wave, the reflected wave fro the falt poit ad the reflected wave fro the reote bsbar Here, the reflected wave fro the eighborig bsbar L does ot appear, ad therefore, the reverse travellig wavefors oly cotai the waves coig after the iitial wave will be the reflected wave either fro the falt poit or fro the reote ed bsbar[7]. I the syste cofigratio sed here, the reflected wave fro the falted poit will be of the sae polarity as that of the iitial wave, ad that fro the reote bsbar will be of the opposite polarity to the iitial wave. This ca easily be sed for falt locatio, distace ad positioal protectio. (d) MM of reverse travellig wave, M 1 M M 3 ad M 4. Fig.5 α Modal Travellig Wave ad Distribtio of MM. 5

6 IV. COMPARISON BETWEEN VOLTAGE AND CURRENT TRAVELLING WAVES. I order to copare the characteristics of falt voltage ad crret travellig wave, Fig.6 gives the ode of voltage ad crret travellig waves ad the distribtio of the forward ad reverse MMs at the scale 3. V. CONCLUSION The Modls Maxia of Wavelet trasfor provides a valable techiqe for extractig the characteristics of varios trasiet travellig waves geerated by a power syste falt. All the waves have odls axia after Wavelet trasfor, which icldes the reflected wave fro the falt poit, fro the eighborig bsbar, fro reote ed bsbar ad fro oise. (a) MM of voltage travellig waves. All the travellig waves, sch as voltage, crret ad directio waves, behave differetly ad this ca be sed to discriiate betwee travellig waves geerated at differet types of discotiity. (b) MM of crret travellig waves. The coo characteristic of varios waves is that the iitial wave has the sae polarity of MM as that of the wave reflected fro falt poit ad the aplitde of the MM of iitial wave is greater tha that of the correspodig reflected oes. (c) MM of forward travellig waves. (d) MM of r everse travellig waves. Fig.6. Copariso betwee the MM of Modal α Travellig Waves (scale 3 ). It ca be see fro the Fig. 6, that the reflectio fro eighborig bsbar ad that fro the falt poit caot be clearly idetified based o voltage travellig wave, poits ad. Also, the reflectio fro the eighborig bsbar ad that fro the falt poit caot be clearly idetified sig the crret travellig wave if there is a ope circit at the ed N bsbar [7]. The forward travellig wave is aplified by the wave fro the far-ed bsbar L. I this case the real falt iforatio is ot clear whe protectio is based o sig the travellig waves. The reverse travellig wave oly reflects the travellig wave fro the falt poit. This cotais the ost iportat iforatio abot the falt ad provides the ai basis for falt detectio ad idetificatio. ACKNOWLEDGMENTS The athors are gratefl for the spport of Godia Najig Atoatio CO., LTD., Chia, ad the Natioal Natral Sciece Fodatio of Chia (Grat No ad Grat No ). REFERENCES [1] GE Yaozhog. New Types Protective Relayig ad Falt Locatio Theory ad Techiqes. Xi`a: Xi`a Jiaotog Uiversity Press, Chia [] WU Weiha ad ZHANG Fagli. Nerical Calclatio of Ultra-Voltage of Electric Power Syste. Beijig: Sciece Press [3] DONG Xizho. Research of Applicatio of Wavelet Theory i the Protective Relayig of Trasissio Lie Based o Travellig Waves. Tiaji: Tiaji Uiversity, [4] Crossly P A ad McLare P G. Distace Protectio Based o Travellig Waves. IEEE PAS, 1983, 10(9): [5] Mallat S ad Hwag W L. Siglarity Detectio ad Processig with Wavelets. IEEE Tras. o Iforatio Theory, 199, 38(): [6] DONG Xizho, GE Yaozhog ad XU, Bigyi. Research of falt locatio based o crret travellig waves. Beijig: Zhoggo Diaji Gogcheg Xebao/Proceedigs of the Chiese Society of Electrical Egieerig, 1999, 19(4): [7] DONG Xizho, GE Yaozhog ad XU Bigyi. Falt positio relay based o crret travellig wave ad wavelets. Sigapore: Proceedigs of IEEE PES Witer Meetig, 000, Ja Fro the reslts show i Fig. 6, it is also show that all the travellig waves have a coo characteristic: the MM of the iitial wave has the sae polarity as that of the wave reflected fro falt poit; the aplitde of the MM of the iitial wave is also greater tha that of the correspodig reflected oes. 6