Digital Fault Locator for Double End Fed Transmission Lines

Transcription

1 Europea Assoctio or the Developmet o Reewable Eergies, Eviromet ad Power Quality (EAEPQ) Iteratioal Coerece o Reewable Eergies ad Power Quality (ICREPQ ) Las Palmas de Gra Caar (Spai), th to th April, Digital Fault Locator or Double Ed Fed Trasmissio Lies R. Micheletti Departmet o Eergy ad Systems Egieerig Uiversity o Pisa Largo L. Lazzario, 6 Pisa (Italy) Tel. (+9 ) 79, Fax (+9 ) 7 roberto.micheletti@dsea.uipi.it Abstract The paper presets a digital ault locator by dyamic system parameter estimatio or a double ed ed trasmissio lie. The method uses about /6 cycle o recorded ault data ad does t require ilterig o dc oset ad high-requecy compoets. The system dieretl equatios are based o a lumped parameter lie model, Thevei equivalets at both eds o the lie ad a ukow ault resistace. The accuracy is demostrated by a represetative set o tests results obtaied with computer simulatio. Key words Fault locatio, Trasmissio lies, Parameter estimatio.. Itroductio Trasmissio lie aults must be located quickly ad accurately i order to repair the aulted sectio, restore power delivery ad reduce outage time as soo as possible. Thereore the developmet o ast ad accurate ault locatio techiques has become a highly importat research area. Several papers have bee published i recet years o ault locatio methods. Most o them ivolve two mai approaches. Oe is based o the travellig wave theory. Whe a lie ault occurs a sudde chage i voltage or i curret at the ault poit geerates high requecy compoets. Fault geerated travellig waves appear as disturbaces superimposed o the power requecy sigals; by processig these sigals, recorded by the relays, it is possible to determie the ault distace. However this method depeds o the travellig wave propagatio, that is a complex pheomeo diicult to aalyze perectly; this is critical to the accuracy o the ault locatio []-[]. The other approach relies o iormatio supplied by the lie currets ad voltages at some observatio poits o a eergized system withi the irst istats ater ault iceptio []. I both cases the recordigs o voltage ad curret costitutes the iitl data or a estimatio problem leadig to ault locatio. Most ault locatig devices measure impedace, or more exactly reactace, betwee the short circuit ad the ed o the lie where they are istalled. The measured reactace provides a exact distace to the aulted poit whe the ault resistace is zero. This latter, uortuately is ot zero i actual aults, causig the impedace to devte rom its true value. This is because the curret that lows through the ault resistace is slederly shited i phase with respect to the curret measured at the ed o the lie, due to the eect o the preault load curret. As a result, the ault resistace is recogized as a apparet impedace with both resistive ad reactive compoets, which is resposible or a error i the ault locatio. The error may be positive or egative, depedig o the directio o the load curret. May algorithms that correct this error were preseted []-[]. Further publicatios o ault locacatio ca be oud i []-[]. I this paper aother way o producig ast ad accurate ault locatio is proposed. The lie is represeted as a lumped parameter circuit. The system model icludes Thevei equivalets with resistaces ad iductaces at both eds o the lie ad a ukow ault resistace. A method o dyamic parameter estimatio will be used i this paper to id ault distace. The ault locatio is quickly obtaied by comparig the respose o the actual system with that o the lumped parameter model. The model s parameters are varied util a adequate RE&PQJ, Vol., No.9, May

2 match is obtaied with the actual system respose. This procedure permits to estimate ot oly the ault distace but also the ault resistace which may be or may ot be o iterest.. System model The most complete represetatio o the system model icludes ot oly the series impedaces but also the parallel parameters o the lie. Geerally the shut coductace is eglected due to its very small cotributio to the shut admittace; moreover, or trasmissio lies less tha about km log, the eect o the earth capacitace o the power requecy compoet is very small ad is usually eglected. Furthermore either the high requecy trasiet compoets due to the capacitace, immedtely ater a ault occurs, eect i a egative way the estimatio process i a model without capacitace represetatio is used ad the samplig rate o the sigals is at least twice the highest requecy o the observed trasiet compoets. Thereore i this aalysis it has ot bee take ito accout the shut admittace o the lie. The overall system model is show i ig., where both eds o the lie are represeted by three-phase Theveis equivalets or trasiet. V a ad V b are the istataeous voltages o the Thevei equivalets at the measuremet ad remote eds o the lie, respectively. Similarly Z a (p) ad Z b (p) are the the operatioal impedaces (p=d/dt) o the Thevei equivalets at the measuremet ad remote eds o the lie, respectively. Z(p)=(R+Lp) ad R are the operatioal lie impedace per kilometer ad the ault resistace, respectively, while l is the total lie legth. Fig. Preault circuit Fig. Circuit describig ault caused varbles I the ault occurs at distace l rom the measurig poit, the preault siusoidal voltage at ault locatio V ad the ault caused currets ca be expressed, i terms o R ad l, both i steady-state systems ad uder trasiet systems coditios. I particular the operatioal impedaces o the Thevei equivalets behid the measuremet poit are elimted by isertig the observable voltage V a. The expressio o V ca be writte V = V - lr-jlωl I a a v )= V si(ωt+θ ) () where V ad are uctio o V a, Ia ad l. Moreover the expressios o the ault caused currets ca be writte i terms o V, R ad l. Fig. Faulted system coiguratio All types o aults that are likely to occur o a threephase power system ca be led back to the study o a sigle phase equivalet circuit i which the relatio betwee the parameter o the equivalet system ad real system, that depeds o the type o ault ( phase, phase-phase, phase-groud), is obtaied by approprtely alterig the sequece etwork s itercoectio. By applicatio o the superpositio priciple to ig., the ault voltages ad currets ca be resolved ito preault (ig. ) ad ault caused compoets (ig. ) i )=C e +C e +C si(ωt)+c cos(ωt) pt pt a a a a a i )=C e +C e +C si(ωt)+c cos(ωt) pt pt b b b b b () where C a, C a, C a, C a, C b, C b, C b, C b, p, p are uctio o V, R ad l. I the parameter estimatio process the voltage V a ad the curret I a i the model are the kow iputs derived rom the recorded data o the real circuit while the curret i a, ormig the model output, is compared with the correspodig curret obtaied rom the the RE&PQJ, Vol., No.9, May

3 recorded real lie ault caused curret i order to id the ukow parameters l ad R.. Estimatio Algorithm The equatio describig the ault caused curret i a ) ca be expressed as a uctio o the parameters l, R ad time t i a ) = i a (l, R, t) () Expadig i a ) i a Taylor series i the eighborhood o give values l*, R * o parameters l, R gives i ) i ) i ) i ) l R a a a a l R () The total square error is miimized by solvig the partl derivatives o (7) relative to l ad R evaluated at l* ad R * E E l R There results ater rearragemet i a s) l s= ar s a s s= a s + R R i )-i ) i a s) i a s) l l i ) l+ (8) (9) where the higher order terms o the expasio are igored ad =l*, R *). The priciple o operatio o the estimatio techique is based, as above metioed, o the compariso betwee the real values o the ault curret at measuremet ed o the lie ad the estimatio values o the model output []-[]. Thus the problem cosists i determiig the parameters l, R able to miimize the error betwee real sampled values ad estimatio values. I the iput quatities are sampled with samplig rate s, a set o samples is obtaied. The error, at istat ts, is expressed as e s ) = [i ar s ) i a s )] () i a s) R s= i )-i ) ar s a s i a s) i a s) R l s= i a s) + R R l+ This system ca be writte i compact orm c l + c R = b c l + c R = b () where i a s) ad i ar s) represet the sampled outputs o the model reerece ad the real system at the measurig poit at time ts. The total square error is give by s= E i )-i ) (6) ar s a s Substitutio o () ito (6) yields where cjk ad bj are kow values ad l ad R are the ukow o the liear system. Solutio o system () gives the correctios l ad R ecessary or updatig parameters l ad R or each iteratio step.. Computer Simulatio Results A 8 km trasmissio lie model was used or testig the ault locatio algorithm by computer simulatio. The model power system is similar to ig., with parameter data take rom a typical 7 kv trasmissio lie, give i Table. a s E= i ar s)-i a s) l s= l i a s) R R i ) (7) Table - 7 kv, MVA trasmissio lie model parameters Lie resistace Lie reactace.78 /km.8 /km To cover various situatios i actual power systems, computer simulatios have bee carried out extesively RE&PQJ, Vol., No.9, May

4 i order to determie the miimum data widow required to locatig a ault with good accuracy. The elaboratio or geeratig ew values o l ad R each iteratio step is carried out o a set o samples o the iput quatities, which are sampled with samplig ratio s = khz, correspodig to samples per period. The ault iceptio was selected such that both high requecy compoets ad dc oset i the recorded ault curret are preset. Fig. shows the waveorms o currets i a, i ar ad error i ar - i a ) or a ault distace o km ad ault resistace o Fig. 6 shows the ratio o estimate to true value o the distace agaist the data widow width or three values o the ault resistace (,, ) with a actual ault distace o km. The accuracy o the distace estimate is withi.7% i each case. Resistaces over have ot bee cosidered because might ot be detected as a ault at all because o the relatively small ault curret.. Curret (p.u.) x - Curret (p.u.) x - Curret (p.u.) x R = ohm R = ohm R = ohm Curret (p.u.) - Curret (p.u.) - Curret (p.u.) x x x x - Fig. 6 Eect o ault resistace o locatio accuracy at l= km Fig. Waveorms o currets i a, i ar ad error i ar - i a ) R = coverges to. km R = coverges to. km R = coverges to km Typical covergece characteristics are show i ig. or a ault distace o km ad ault resistace o The iitl estimates or ault distace ad ault resistace are chose ear zero; six iteratio steps are required to get to the covergece...6. l R.6.. l = km l = km l = 6 km..... x Iteratio Fig. Covergece o the estimatio algorithm R (= ) coverges to 9.87 l (= km) coverges to. km Fig. 7 Eect o ault locatio distace o locatio accuracy at R = l = km l = km l = 6 km coverges to.9 km coverges to. km coverges to 6. km RE&PQJ, Vol., No.9, May

5 Fig.7 shows estimates or several ault distaces,, ad 6 km with ault resistace; the l estimates are withi % accuracy i each case. Lie switchigs ad load chages may cause vartios i the actual value o the Thevei operatioal impedaces at the remote ed o the lie x - Fig. 8 Eect o errors i Zb(p) ad L o locatio accuracy at R = ad l = km Z b (p)=.6 o true value Z b (p)= true value Z b (p)= times true value L=. times true value coverges to. km coverges to. km coverges to. km coverges to. km Fig. 8 shows the eects o usig a value or Thevei impedace Z b (p) i the estimator that is 6% o the actual value used i the simulatio studies; i a secod test the Thevei impedace Z b (p) is assumed to be twice the actual value. The same igure shows also the eect o errors i the value o the lie impedace L, caused by vartios o earth resistivity alog the lie. As observed rom ig. 8 the l estimates o the ault distace, that was actually km with a ault resistace o, are withi.% accuracy i each case ad are practically isesitive to vartios both o the Thevei operatioal impedace Z b (p) both o the lie impedace L.. Coclusio Zb(p) =.6 o true value Zb(p) = true value Zb(p) = times true value L =. times true value The paper has described a algorithm or the extremely rapid ad accurate locatio o aults o high voltage trasmissio lie. Useul estimates o ault distace are obtaied usig about /6 cycle o recorded ault data at the measuremet ed o the lie. The method does t require ilterig o dc oset ad high-requecy compoets rom the recorded sigals ad ca be used or ay type o ault o a three-phase trasmissio lie by approprtely alterig the sequece etworks itercoectio. No iormatio about ault resistace is required apriori or the algorithm to work. The sources o errors due to the parallel parameters o the lie have ot bee icluded i the aalysis. Computer simulatio tests idicate that ault locatio accuracy is relatively isesitive to ault resistace ad ault distace. Moreover durig these tests it has bee take ito accout the eect o the errors itroduced by measuremet istrumetatio. Reereces [] A.O. Ibe, B.J. Cory: "A travelig wave-based ault locator or two ad three terml etworks", Proc. o Power Idustry Computer Applicatio Coerece (PICA), Sa Fracisco, Calior, USA, May 6-, 98. [] Q. Jg, C. Xgxu, Z. Jichao: Travellig wave ault locatio o trasmissio lie usig wavelet trasorm Proc. o Power System Techology Coerece, POWERCOM 98, Beijig, Ch, Aug. 8-,998, pp. -7 [] M. Silva, M. Oleskovicz, D.V. Coury: A ault locator or trasmissio lies usig travelig waves ad wavelet trasorm theory 8 th IEE It. Coerece o Developmets i Power System Protectio, April -8,, Vol., pp. - [] M.T. Sat, M.E. Paithakar: "O lie digital ault locator or overhead trasmissio lies", Proc. IEE, Vol. 6, No., November 979, pp [] L. Eriksso, M. M. Saha, G.D. Rockeeller: " A Accurate Fault Locator with Compesatio or Apparet Reactace i the Fault Resistace Resultig rom Remote- Ed Ieed," IEEE Trasactios o Power Apparatus ad Systems, Vol. PAS-, No., pp. -6, 98 [6] K. Takagi, Y. Yomakoshi, M. Yamaura, R. Kodow, ad T. Matsushima: Developmet o a ew type ault locator usig the oe terml voltage ad curret data, IEEE Tras. Power App. Syst., vol. PAS-, pp , Aug. 98. [7] A. Girgis, D. Hart, W. Peterso: A ew ault locatio techique or two- ad three-terml lies, IEEE Tras. Power Delivery, vol. 7, pp.98 7, Ja. 99. [8] M. Abe, T. Emura, N. Otsuzuki, M. Takeuchi: Developmet o a ew ault locatio system or multi-terml sigle trasmissio lies, IEEE Tras. Power Delivery, vol., pp. 9 68, Ja. 99. [9] V. Cook.: Fudametal aspect o ault locatio algorithms used i distace protectio, Proc. IEE, Vol., Pt. C,. 6, September 986, pp [] A. Isaksso: Digital protective relayig through recursive least-square idetiicatio", Proc. IEE, Vol., Pt. C, No., September 988, pp. -9. [] M. Djurić, Z. Radojević, V. Terzija: Distace protectio ad ault locatio utilizig oly phase curret phasors, IEEE Tras. Power Delivery, vol., pp. 6, Oct [] D. Novosel, D.G. Hart, E. Udre, J. Garitty: Usychroized Two- Terml Fault Locatio Estimatio, IEEE Tras. o Power Delivery, Vol., No., Jauary 996. [] T.S.Sidhu, at alii: "Bibliography o Relay Literature, 7 IEEE Committee Report" IEEE Tras. Power Delivery, vol., pp. 88-, Ja.. [] G.G. Richards, O.T. Ta: "A accurate ault locatio estimator or trasmissio lies", Tras. IEEE, Vol.PAS, No., April 98, pp [] R. Micheletti: "Fast ad accurate ault locatio estimator or power lies", 6th IMEKO TC- Iteratioal Symposium: Itelliget Istrumetatio or Remote ad O-Site Measuremets, Brussels, - May 99, pp RE&PQJ, Vol., No.9, May