Synchronised Measurement Technology for Analysis of Transmission Lines Faults

Transcription

1 roeedings of the th Hwii Interntionl Conferene on System Sienes - Synhronised Mesurement Tehnology for nlysis of Trnsmission ines Fults Vldimir Terzij The University of Mnhester terzij@ieee.org Mlden Kezunovi Texs &M University kezunov@mil.ee.tmu.edu bstrt new numeril lgorithm for the nlysis of single line to ground fults on short overhed trnsmission lines is presented in this pper. It is bsed on synhronised smpling t two line terminls nd n urte fult model inluding the ring phenomen nd tower footing resistne t the fult point. The ore of the lgorithm is n effiient non-reursive prmeter estimtion method. dynmi r model is inluded in the fult model to represent the r s intertion with the externl network. The lgorithm urtely estimtes the r voltge mplitude, tower footing resistne, nd the fult lotion, simultneously. The lgorithm is derived in the time domin, nd is bsed on the synhronized quisition of urrents nd voltges t both line terminls. Cse studies bsed on simulted dt re presented to demonstrte the effetiveness of the new method.. Introdution Fult lotors determine the distne to the fult using mesurements from the lol line terminl(s). In modern power systems, whih re designed to exploit the existing ssets optimlly, the importne of loting fults quikly nd preisely is beoming ritilly importnt. rompt nd urte lotion of the fults in lrge-sle trnsmission system n elerte the system restortion, redue the outge time nd improve the system relibility [-]. Gret efforts hve been mde in the pst developing vrious lgorithms for improved fult lotion estimtes [-5]. One-terminl lgorithms using the lol voltges nd urrents re proposed in [-3]. The ury of this type of lgorithm is normlly dversely ffeted by the fult resistne, nd ompenstion tehnique is proposed to llevite this effet [3]. To improve the ury of estimtion, the uthors of [-5] hve designed speil one-end lgorithms pplible to the phse to ground fults. method for prllel line fult lotion using one-end dt is reported in [6]. eferene [7] presents n pproh using the pre-fult nd fult urrent phsors t one end of the line for estimting the fult lotion ssuming the soure impednes to be vilble. Fult lotion tehniques employing the mesurements t two- or multi-ends of the line hve been proposed in [8-5]. Unsynhronized mesurements re utilized for estimting the fult lotion nd the unsynhroniztion ngle between the mesurements t the two terminls of the line [8-]. lumped line model is used in [8] where the shunt pitne for long lines is ompensted in n itertive wy. eferene [9] is lso bsed on the lumped model nd the shunt pitne of the line is negleted. The tehnique presented in [] first obtins the unsynhroniztion ngle by solving qudrti eqution nd then derives the fult lotion, ignoring the distributed prmeter effets while onsidering the shunt dmittne of the line. Synhronized mesurements hve been utilized in [- 5]. eferene [] formultes the fult lotion problem bsed on the trvelling wve equtions onsidering losses. The BCD prmeters of the line is utilized in [3] for deriving the fult lotion bsed on the lumped line model. Synhronized voltge mesurements from multi-ends of the lines re utilized to find the fult lotion ssuming tht the soure impednes re known without onsidering the shunt pitne in []. method bsed on the fult generted trnsients nd the trvelling wve theory is presented in [5]. In this pper new two-terminl synhronized smpling numeril lgorithm for the nlysis of single line to ground fults on short overhed trnsmission lines is presented. Bkground desribing developments in synhronized smpling tehnology nd previous lgorithm developments re disussed in Setion. Informtion bout the previous work is given in Setion 3. The trnsmission line modelling nd relted lgorithm development is presented in Setion. The new lgorithm itself is presented in Setion 5, where s the lgorithm test results nd onlusions re given in Setion / $6. IEEE

2 roeedings of the th Hwii Interntionl Conferene on System Sienes -. Bkground eent dvnes in Informtion nd Communitions Tehnology (ICT) hve led to signifint developments in the use of intelligent systems for power system monitoring, ontrol nd protetion. Supported by the Globl ositioning System (GS), Synhronised Mesurement Tehnology (SMT) is fst beoming key tehnology in this re. Its min omponents re: Synhronised/hsor Mesurement Units (SMU/MU), Dt Conentrtors (DC), pplition softwre (S) nd its supporting ommunition networks (CN). In Fig. typil Wide re Monitoring, rotetion nd Control (WMC) rhiteture bsed on SMT is presented. Fig. illustrtes how phsor/smple informtion is olleted. In Fig., phsor/smple informtion (nd other eletril nd non-eletril vribles) is olleted from the network by MUs nd forwrded over different ommunition medi to the DCs. Two DCs forwrd seleted informtion to the Super DC, whih is onneted to the el Time Monitoring entre. Seleted WMC pplitions n be run diretly t this (top) level, long with the Dt rhiving. The objetive of this pper is to propose new numeril lgorithm for nlysis of fults on trnsmission lines bsed on SMT nd synhronised smpling. 3. revious work revious efforts were imed t implementing urte fult lotion lgorithms for short lines represented with lumped prmeters nd long lines represented with distributed prmeters [] For short lines, the fult lotion is lulted diretly using minimum squre estimte method, s follows []: x = where N m m=, b, k = N p=, b, m=, b, k= B m m B m = υ ms υm lmp lmp d [( rmp + ) i ps i Bm = {( rmp p=, b, lmp [ i ps ( k ) lmp + )[ i p ps ( k )]} ps () m=,b, () ( k )] p ] m=,b, (3) where k is the smple point, is smple period, subsripts S, stnd for the vlues from sending end nd reeiving end of the line. For long lines, ording to Bergeron s equtions, the voltge nd urrent profiles long the line re expressed s follows []: υ j, k = [ υ Δx + [ i j, k j, k + υ j, k+ j, k + i j, k = [ υ j, k υ j Z Δx + [ i j, k+ j, k ] Z Z ] + [ i Δx ] i, k + j, k ] + [ i j, k j, k j, k + ] j, k + ] () (5) Fig. : Generi rhiteture of WMC system. where Δx = is the distne tht the wve trvels l with smpling period ; l Z = is the surge impedne. Subsript j is the position expressed s disrete point on the line nd k is the smple point. The finl lotion is obtined by n indiret method presented in []. The impt of prllel lines on the fult lotion hs been tken into ount in []

3 roeedings of the th Hwii Interntionl Conferene on System Sienes - Methods presented in [],[] gve sound bse for extending the strtegy of using the synhronized smpling pproh by modelling the fult lotion more relistilly nd opening by this quite new options for detiled fult nlysis. The ssumption tht fults re just pure metlli (bolted) fults is not lwys vlid, prtiulrly during ring fults, or fults inluding fult resistne. In the next Setion of the pper this issue will be ddressed. New opportunities for estblishing methods for detiled fult nlysis, e.g. inluding detetion of the nture of the fults,i.e. ring (trnsient) or non-ring (permnent) fults, whih is nother importnt spet of fult lotion proess, will be shown.. Modelling of fulty trnsmission lines The simplest pproh to fult modelling is to model the fult s pure metlli (bolted) fult. Sttistilly, fults re predominntly ring fults; pproximtely 8% of ll fults re followed by n r, whih ontributes to the resistive omponent of the fult impedne. The fult pth lso inludes the tower footing resistne nd ny other resistne t the fult point. n urte fult lotion lgorithm must onsider ll resistne omponents: the r nd the tower footing resistne, whih re onneted in series. Fig. shows three-phse representtion of single line to ground ring fult on trnsmission line. It is ssumed tht urrent nd voltge mesurements re synhronously quired t both line terminls nd trnsmitted to the entrl Intelligent Eletroni Devie (IED) where they re proessed by n pproprite numeril lgorithm to determine the fult distne, l, r voltge mplitude, U, nd the tower footing resistne, F. potentil limittion of suh n pproh might be some unexpeted problems with the synhronistion. It is ssumed tht the synhronistion is idel, otherwise, some errors in fult nlysis would be identified. Fig. : Three-phse representtion of the fulted line. The fult r hs highly nonliner nture, using distortions in the voltge nd urrent wveforms long the trnsmission line. The r voltge wveform n be modelled s pure squre wve [6-7]: u () t U sgn( i ) = (6) This prtil r voltge model is used to further develop the new numeril lgorithm. Model (6) hs just one unknown model prmeter: the r voltge mplitude U. Other r models inlude number of different prmeters, but it will be shown tht model (6) is urte enough for developing new lgorithms for overhed lines protetion. Using the symmetril omponents pproh, the left line terminl voltge u n be expressed s follows: di di u = ( i + K i ) + + K + u F (7) dt dt where,, nd re positive nd zero sequene line resistne nd indutne, respetively, i nd i re left line terminl urrent nd its zero sequene omponent during the fult, u F is fult voltge, nd K = ( ) K ( ) nd = re the ompenstion oeffiients to ount for the zero-sequene urrent flowing through the line. These oeffiients n be lulted in dvne nd they remin onstnt. The fult urrent i is the sum of the urrents flowing to the fult from both of the line terminls (see Fig. ): i = i (8) lso, the fult voltge u F n be expressed s: u = U sgn( i ) + i (9) F F Substituting equtions (8) nd (9) into eqution (7) gives: di di u = ( i + K i ) + + K + dt dt () U sgn( i ) + ( i ) F The line prmeters n be expressed s produts of the line length nd per unit length vlues. Eqution () then beomes: di di u = r ( i + K i ) l + l K + l + dt dt () sgn( i ) U + ( i ) F 3

4 roeedings of the th Hwii Interntionl Conferene on System Sienes - where: l is the unknown distne from the left line terminl to the fult lotion, U is the unknown r voltge mgnitude nd F is the unknown fult resistne. Eqution () n then be rewritten in the following simplified form: u = l + U + 3 F () Coeffiients, nd 3 n be identified from eqution (): [ ] di di i K i l K dt dt = r (3) [ i ] sgni = sgn = () = i = i 3 (5) In eqution (),, 3 nd u n be mesured t both line terminls. The unknown prmeters n be rrnged in the vetor x, s follows: [ l ] T x = U F (6) where T denotes mtrix trnsposition. Thus, the generi prmeter model of the problem n be expressed s follows: T T [ ] [ l U ] = u = (7) 3 F x where is 3 oeffiient model mtrix. Finlly, to tke into ount the unertinties in the proess nlysed, rndom noise, μ, should be dded to (7) (this noise hs norml distribution with mthemtil expettion equl to ): T u = x + μ (8) Expression (8) is the generi mthemtil model of the mesured voltge on the fulted phse. This is the strting point for designing suitble tehnique for estimting the fult distne, r voltge mplitude nd tower footing resistne. Sine the model is liner, liner prmeter estimtion tehniques n be implemented here. The model order, s defined by the number of unknown model prmeters, is 3, so the option of pplying non-reursive estimtor is eptble for future rel-time proessing. This will be shown in the next Setion of the pper, in whih the pplition of non-reursive est Error Squres estimtion method is presented. For the lultion of the first order derivtives of urrents, the polynomil interpoltion pproh ws used. 5. est error squres prmeter estimtion If the input signls re uniformly smpled with the smpling frequeny f s, then disrete presenttion of time, hving index m is given by t = t m = mt s. ssuming tht N smples, whih belong to dt window of size T dw, re simultneously proessed, then suitble eqution (8) n be written for eh time step within the dt window. In this wy, N equtions will be obtined for N smples. These n be presented in the following ler mtrix form: - mesurement vetor of voltge smples: T [ u t ) u ( t ] = [ u u ] T u = (9) ( N ) А АN - oeffiients of suitble model mtries: [ i + K i ] di di r + l + K dt dt t ) = () [ + ] + di di r i Ki l + K t N ) dt dt [ sgn[ i ] sgn[ ] ] T i = () t ) t N [ i i ] T = () 3 t ) tn ) For given dt window, the following holds: T T [ ] x + μ = x μ u = 3 + ) (3) where is oeffiient model mtrix. The optiml prmeter estimtes re obtined by using the est Error Squres (ES) estimtion method:

5 roeedings of the th Hwii Interntionl Conferene on System Sienes - T T ( ) u x = () T T where ( ) is the left pseudo-inverse mtrix of the model mtrix. The model order n (here n = 3) is determined by the number of unknowns. The inversion of 3x3 mtrix is trivil tsk, even for ordinry hrdwre pltforms, so the lgorithm ould be implemented in future IEDs. In the bove lgorithm, the ury of lssil fult lotors hs been signifintly improved by tking the r voltge into onsidertion. Furthermore, the new lgorithm provides mens of deteting ring fults to id dptive uto-relosure. In the lgorithm derivtion, the pitive nture of the line ws negleted, so the presented solution n be pplied to short lines (lines of length less thn km). The differene between this lgorithm nd the present stte of the rt is tht, due to the lgorithm being derived in the time domin, it is ble to estimte the fult resistne nd indite the presene of fult r s well s estimting the fult distne. The effets of the fult r on the ury of the lgorithm re ssessed; the lgorithm is rigorously tested for vrying r voltge wveform shpes nd r elongtion effets. s the lgorithm ws derived in the time domin, it hs fster onvergene time thn those derived in the spetrl domin. The lgorithm is bsed on synhronised dt smpling t both line terminls. 6. lgorithm testing The lgorithm performne ws investigted by simulting different kinds of fults on km long overhed trnsmission line. In ppendix I the single line digrm of the simulted line nd its prmeters re given. Single line-to-ground ring nd rless fults were simulted t different lotions long the line. In eh se the fult ineption time ws set t t = 3 ms nd the tower footing resistne F ws vried in the rnge of - Ω. It ws ssumed tht the line ws loded before the fult ineption. The smpling frequeny ws f s = 3 Hz. The dt window size ws T dw = ms (N = 8 smples per dt window). The seletion of the bove prmeters re typil when testing lgorithms for fult lotion/nlysis. Fults t km, 5 km, nd 9 km from the left line terminl, both with nd without rs, will be presented. The lgorithm ws rigorously tested using the following riteri: ) omprison between one- nd two-port lgorithms nd b) ssessment of the suitbility of the proposed lgorithm for dptive utorelosure. 6.. Comprison between one- nd two-port lgorithms The ury of the proposed lgorithm is ompred with tht of orresponding lgorithm using single line terminl dt. 9 km ring fult is used to demonstrte the fetures of the two-port lgorithm. The T simulted voltges nd urrents from both line terminls re to estimte the unknown model prmeters of (6). In Figs. 5 nd 6 the simulted urrents nd voltges from the left line terminl re presented, respetively. These input dt nd those from the right line terminl ontin the informtion bout the unknown prmeters being estimted by the proposed lgorithm. From Fig. 7, it is obvious tht the new two-port lgorithm gives more urte estimtion of the distne fult. From Fig. 8, it n be onluded tht the one port lgorithm does not reh stble estimte of the r voltge mplitude; it nnot, therefore, be used s relible riterion for ontrolling the uto-relosure. It is ssumed tht the uto-relosure would be bloked if the r is not deteted t the fult lotion; the r voltge mplitude is used to indite the presene of n r). From the bove test it n be onluded tht twoport lgorithms offer higher ury nd greter potentil for different pplitions. dptive utorelosure issues re explored in the next Subsetion. i, i, i 3 [ k ] i i 3 - i Fig. 5: Simulted left line terminl urrents. 5

6 roeedings of the th Hwii Interntionl Conferene on System Sienes - u, u, u 3 [ kv ] - u u 3 u Fig. 6: Simulted left line terminl voltges. l [ km ] Two ort One ort elongtion. It ws ssumed tht the r elongted t rte of m/s s obtined from the nlysis of rel r. In Fig. 9 the elongted r voltge u, its estimted mplitude, nd the ontrol signl inditing tht the fult is trnsient re presented. The exellent trking bilities of the lgorithm re obvious. The utorelosure ontrol signl C hs true (logil ) vlue, so the uto-relosure is relesed; onversely, for n rless fult, it hs flse (logil ) vlue, so the uto-relosure is bloked. Simultneously to the r voltge mplitude, the unknown fult distne (9 km) nd tower footing resistne F (3 Ω) re estimted (see Figs. nd ). The equivlent tests were rried out for other fult lotions on the line, nd resistnes F. In eh se the lgorithm hs given urte results. For the equivlent test but without n r, the lgorithm detets the rless fult, s presented in Fig.. Here the estimted r voltge mplitude is zero. Consequently, the uto-relosure ontrol signl is flse. In [7], more detils bout the onept of dptive uto-relosure re given Fig. 7: Estimted fult distne. Estimted u 3 u [ kv ] - u C o n t r o l S i g n l u [ kv ] - Two ort - One ort u Fig. 8: Estimted r voltge mgnitude. C t [s] Fig. 9: Estimted r voltge mgnitude for 9 km ring fult Fult nture detetion l [ km ] 9 9 If the r model inludes the r voltge, the bove lgorithm n be used to sertin the nture of the fult. By evluting the estimted r voltge mplitude it is possible to distinguish between ring (trnsient) nd non-ring (permnent) fults. In this test, n dditionl r phenomenon is inluded: r Fig. : Estimted fult distne for 9 km ring fult. 6

7 roeedings of the th Hwii Interntionl Conferene on System Sienes - F [ Ω ] Fig. : Estimted fult resistne. u [ kv ] u = Estimted u fult ineption time t =.3 s - C t [s] Fig. : Estimted r voltge mgnitude for 9 km rless fult Sensitivity to synhronistion errors The bove results were presented under the ssumption tht the relys t the two line terminls were perfetly synhronised. In this Subsetion the sensitivity of the lgorithm to synhronistion errors is investigted. For this, n ring fult ws simulted t km from the left line terminl. The r voltge mplitude ws U = kv, nd fult resistne F ws Ω. The first row of Tble I shows the level of synhronistion error, expressed s ngle θ in degrees. The stedy-stte error in the estimtion of eh unknown prmeter is presented. Obviously, very high level of ury hs been hieved. TBE I: SENSITIVITY TO SYNCHONISTION EOS. C o n t r o l S i g n l 7. Conlusions In this pper new time domin dptive estimtion numeril lgorithm for the nlysis of single line to ground fults on short overhed trnsmission lines, bsed on synhronized phsors tehnology nd the implementtion of prmeter estimtion theory, hs been presented. It ws derived bsed on some erlier work by the uthors briefly desribed in the pper. It hs been demonstrted tht the ury of fult lotors n be signifintly improved by relistilly modelling the ring fult. It ws shown tht the fult nture (permnent metlli or trnsient ring) n be effiiently determined. The importne of fult r modelling ws investigted nd it ws proved tht relisti r modelling n improve the qulity of fult lotors nd lgorithms for the nlysis of fults on trnsmission lines. The proposed solutions is limited to short trnsmission lines, so the lgorithm for fult lotion, developed in the erlier reserh by the uthors, is still superior solution for long lines. 8. eferenes [] M. Kezunovi nd B. erunii, Fult otion, Wiley Enylopedi of Eletril nd Eletronis Terminology, Vol. 7, pp 76-85, John Wiley, 999. [] K. Tkgi, Y. Yomkoshi, M. Ymur,. Kondow, nd T. Mtsushim, Development of new type fult lotor using the one-terminl voltge nd urrent dt, IEEE Trnstions on ower pprtus nd System, Vol., No. 8, ugust 98, pp [3]. Eriksson, M.M. Sh, nd G.D. okefeller, n urte fult lotor with ompenstion for pprent retne in the fult resistne resulting from remote-end infeed, IEEE Trnstions on ower pprtus nd Systems, Vol. S-, No., Februry 985, pp [] Q. Zhng, Y. Zhng, W. Song, nd D. Fng, Trnsmission line fult lotion for single-phse-to-erth fult on non-diret-ground neutrl system, IEEE Trnstions on ower Delivery, Vol. 3, No., Otober 998, pp [5] Q. Zhng, Y. Zhng, W. Song, nd Y. Yu, Trnsmission line fult lotion for phse-to-erth fult using one-terminl dt, IEE roeedings- Genertion, Trnsmission nd Distribution, Vol. 6, No., Mrh 999, pp. -. [6] J. Izykowski, E. osolowski, nd M. M. Sh, oting fults in prllel trnsmission lines under vilbility of omplete mesurements t one end, IEE roeedings- 7

8 roeedings of the th Hwii Interntionl Conferene on System Sienes - Genertion, Trnsmission nd Distribution, Vol. 5, No., Mrh,, pp [7] M. Djuri, Z. dojevi, nd V. Terzij, Distne protetion nd fult lotion utilizing only phse urrent phsors, IEEE Trnstions on ower Delivery, Vol. 3, No., Otober 998, pp. -6. [8] Novosel, D. G. Hrt, E. Udren, nd J. Gritty, Unsynhronized two-terminl fult lotion estimtion, IEEE Trnstions on ower Delivery, Vol., No., Jnury 996, pp [9].. Girgis, D. G. Hrt, nd W.. eterson, new fult lotion tehnique for two-nd three-terminl lines, IEEE Trnstions on ower Delivery, Vol. 7, No., Jnury 99, pp [] M. Shdev nd. grwl, tehnique for estimting trnsmission line fult lotions from digitl impedne rely mesurements, IEEE Trnstions on ower Delivery, Vol. 3, No., Jnury 998, pp. -9. []. Goplkrishnn, M. Kezunovi, S.M. MKenn, nd D.M. Hmi, "Fult lotion using distributed prmeter trnsmission line model", IEEE Trnstions on ower Delivery, Vol. 5, No., Otober, pp [] Y. H. in, C. W. iu, nd C. S. Chen, new MUbsed fult detetion/lotion tehnique for trnsmission lines with onsidertion of ring fult disrimintion prt I: theory nd lgorithms, IEEE Trnstions on power delivery, Vol. 9, No., Otober, pp ppendix In Fig. 3, the shemti digrm of kv, km long, overhed trnsmission line is presented. In Tbles II nd III, the prmeters of networks nd B nd the line prmeters re listed, respetively. Fig. 3: Single line digrm of the simulted fulted line. TBE II: METES OF NETWOKS ND B. rmeters Networks B U,MS [kv] 6 ϕ [ ] - [Ω] [H] , Ω , H TBE III: INE METES. rmeter p- nd n-sequene -sequene esistne, Ω/km Indutne mh/km [3] D. J. wrene,. Cbez, nd. Hohberg, Development of n dvned trnsmission line fult lotion system, rt I-Input trnsduer nlysis nd requirements, rt II-lgorithm development nd simultion, IEEE Trnstions on ower Delivery, Vol. 7, No., Otober 99, pp [] S.M. Brhm, Fult lotion sheme for multiterminl trnsmission line using synhronized voltge mesurements, IEEE Trnstions on ower Delivery, Vol., No., pril 5, pp [5] F. H. Mgngo nd. bur, urte fult lotion using wvelets, IEEE Trnstions on ower Delivery, Vol. 3, No., Deember 998, pp [6] Terzij V, Nelles D, "rmetrishe Modelle des ihtbogens und rmetershätzung uf Grund der simulierten und ehten Dten," (in Germn) TB 83/93, Univ. Kiserslutern, Kiserslutern, Germny, July 993. [7] M. Djuri, V. Terzij, " new pproh to the ring fults detetion for utorelosure in trnsmission systems," IEEE Trns. on ower Delivery, Vol., No, Ot. 995, pp