Study on Shunt State of Track Circuit Based on Transient Current

Transcription

1 Sudy on Shun Sae of Track Circui Based on Transien Curren QI Huan,ZHANG You-peng, ZHAO Bin School of Auomaic & Elecrical Engineering anzhou Jiaoong Universiy anzhou 737,China Absrac: - Track circui is considered o be one of he means of rain deecion, is shun sae ofen misjudged due o he shun malfuncion Aim a he influence of shun malfuncion on he shun sae of rack circui, a deecion mehod for he shun sae of rack circui according o he ransien curren was proposed And he ime response of rack circui was obained by he precise ime-inegraion mehod The runcaion error is efficienly decreased by inerlacing he volage and curren nodes along he x-axis Taking he boundary condiions of rack circui in adjusing and shuning sae, changes of he receiving end curren was simulaed The resuls show ha he precise ime-inegraion is uncondiional sabiliy, which is an effecive mehod for analysis of rack circui and he ransien curren when a rain enering or clearing a rack secion, which can be regard as an imporan informaion for he shun sae of rack circui Key-Words: rack circui; shun sae; ransien curren; precise ime-inegraion mehod; sabiliy Inroducion In railway signaling sysems, he shun sae of rack circui is a rack secion occupied by rain, which is deeced frequenly according o he elecrical shuning deecion principle [] When a rain eners a rack secion, i creaes a shor-circui by he shun resisance ha consiss of he maerial resisance of he wheels and he conac resisance beween wheel and rail, hus conducing he curren from one rail o he oher insead of flowing hrough he relay a he receiving end of he secion (Fig) This shuns he relay sufficienly o cause i o release and indicae a rain s occupancy However, in some secions, he shun resisance goes oo high due o rails become rusy or diry, which making he signal ampliude a receiving end is greaer han he drop value of he relay, and he signal fails o indicae he presence of he rain in he secion and gives false informaion advising approaching rains ha he secion is clear This siuaion is called a shun malfuncion, which is he main cause of a fail o deec a rain in a rack secion and can lead o serious adverse effec on railway ranspor safey and efficiency And according o he saisical daa released by Chinese railway deparmen, here were abou 8 housand shun malfuncion happening in he Chinese railways [6] The majoriy of his faul was caused by excessive shun resisance[9] So i s necessary o sudy on shun sae of rack circui rail rail Transmier Curren direcion Wheels and axle Receiver Fig Basic srucure of rack circui (occupied) In order o agains his phenomenon, alhough here has been numerous aemps o preven shuning malfuncion, such as use of he rail surface derusing machine or supersonic arc spraying equipmen[],[3], which requires periodically inspeced and shoren rails uiliy longeviy In some of hem[4],[5], rain presence is deeced by combining wih he axle couner rain deecion echnology or poor shuning early warning sysem, ec These mehods require he addiional equipmen, high cos; furhermore, he axle couner is vulnerable o he inerference of eernal facors (he rack sae, weaher, and oher environmenal condiions) Some oher soluions use impulse rack circui, which needs o replace he equipmen of rack circui, a large amoun of consrucion [6],[7] Summing up, all hese mehods, wihou a oal eradicaion could be obained, sill needs o rely on arificial adminisraion As shun malfuncion have poenial E-ISSN: 4-66X 399 Volume 4, 5

2 repercussion on signalling and raffic conrol, herefore, i is necessary o research on he deecion mehod of shun sae of rack circui Based on he essence change of rack circui sae is he abrup change of characerisic impedance [8] In oher words, his is he process of he ransien signal wihin rack circui To realize reliable deecion of he rack circui s shun sae, a ransien response analysis o he receiving end curren signal is proposed in his paper In order o analyze ransien curren of rack circui when a rain eners a rack secion a ransien model of rack circui is esablished based on uniform ransmission line heory Up o now, he common approach for ransien analysis of lossy ransmission line is using numerical soluion mehod, Such as Fas Fourier Transform (FFT), Numerical Inverse aplace Transform (NIT) or Finie Difference Time Domain (FDTD), [9-], ec However, for coupled lines of rack circui, using FFT or NIT, which may be need a large number of frequency dae poins o ensure he accuracy of simulaion resuls And FDTD mus ensure he sabiliy of he algorihm Ref[3],[4] shows ha he precise imeinegraion mehod is an efficien and accurae approach for he ransien analysis of lossy ransmission line, which no only improves he soluion accuracy, bu also he sabiliy propery of he inegraion algorihm So, his mehod for analysis he curren response of he shun sae of rack circui is proposed in his paper This paper is organized as follows Secion gives an overall background and inroduces he problem Secion gives a descripion of rack circui ransien model Secion 3 gives he calculaion mehod for he ransien curren of rack circui based on he precise ime-inegraion Secion 4 gives he simulaion analysis Finally, Secion 5 gives he conclusion 6 Track Circui Transmission ine Model In accordance wih he characerisics of rack circui, when you analyze he ransien response of he rack circui, he rail line is equivalen o uniform disribued parameer circui, which composed of hree wires includes wo rails and he ground The rail has a longiudinal impedance and muual inducance, he ground as a conducor which has a large cross-secion area and he impedance is zero Based on uniform ransmission line heory, he rail line model is considered as disribued model ha is made of numerous iny unis x, he equivalen model of he per-uni as shown in Fig Here R is he rail resisance, Ω/km ; is he rail inducance, H/km ; M is he muual inducance beween he rails, H/km ; g is he leakage conducance beween he rail wih he ground,( Ω km ) - ; g is he leakage conducance beween he rails, ( Ω km ) - ; C is he leakage capaciance beween he rail wih he ground, F/km ; C is he leakage capaciance beween he rails, F/km ; x is he disance o he erminal of rail line, km ; i (, i ( is he curren in wo rails, respecively, A ; u ( is he volage o ground in wo rails, respecively, V - R R M g g g i( x C i( x C C Fig The equivalen model of he rail line railⅠ u( x - ground - u( x railⅡ For he model, under he Kirchhoff s volage and curren aws, he disribuions of volage and curren on he rail line can be expressed as Eq when = Ri ( M () = Ri ( M () = gu ( g[ u ( u (] C [ ] C (3) = gu ( g[ u ( u (] C [ ] C (4) The above parial differenial equaions can be described in marix form as: = ( Ri () = G C ( x l x ) () E-ISSN: 4-66X 4 Volume 4, 5

3 where l is he lengh of he rail line; u ( =[ u ( ]T ; i ( =[ i ( i ( ] T ; u (, is he volage and curren marix along he rail line, respecively; R are he per-uni lengh marix of resisance and inducance; G C are he per-uni lengh marix of conducance and capaciance R g g g R = R ; G = g g g ; M C C C = M ; C = C C C ; I is clear ha he change of volage and curren along he rail line a any ime can be described by he soluions of he above ransmission line equaions Therefore, o solve he ransmission line equaions is he basis for he ransien analysis of rack circui 6 Time Response of Track Circui Track circui is a lossy ransmission line The precise ime-inegraion mehod enables one o overcome he difficuly of aking ino accoun he open or shor boundaries by radiional mehods In addiion, he benefi of he ime domain model accouns for arbirary iniial condiions[5],[6] So his provides an efficien numerical approach o solve he ransien response of rack circui 3 Space Discreizaion of Transmission ine Equaions In his secion one crucially needs o solve he ransmission line equaions of rack circui, as shown in Eq() Firs, by implemening he discreizaion in he space coordinae(x) o Eq() The classical discree mehod where he samples of boh volages and currens are aken a he same poins[3] In addiion, volages and currens parial derivaive respecively used forward difference and backward difference, which causes runcaion error is: l '' Ry [ ] = ± y( i ) M ξ (3) To reduce he runcaion error, he volage and curren is sampled by inerlacing he volage and curren nodes along x-axis in his paper (as shown in Fig3) i (v ) v i v i i M- v M- i M- v M (i M ) Fig 3 Inerval sampling of volage and curren We divide he ransmission line ino M- secions each of lengh x =l/(m-), a he beginning and end poins, he parial derivaive of he volage and curren o x is approximaed by he forward differenial and backward difference respecively While a each discree poin k ( k =,, M ), he cenered difference scheme is used So we can obain he following quesions: d uk() ik() ik () = C C Gu k () d (4) d ik() uk () uk() - = Ri k () d (4) where: k=, M-, u () k u ( ; () k ( d um() im() im () = C C Gu M () d (43) d i() u() u() - = Ri () d (44) For he same lengh of ransmission line, his mehod effecively reduced he space sep lengh o be compared wih mehod in Ref[7], and he cenered difference causes runcaion error is: l ''' Ry [ ] = y( ξ ) i 6 (M ) (5) which is significanly smaller han Eq3 3 Time Precise Inegraion for Solving he Transmission ine Equaions For Eq(4) we can describe in marix form as : dx = HX F (6) d Τ X = [ u, u, u um, i, i i M ] ; Τ F = [,, C im /, u /,,,] ; H where: 3 as shown in ne page We can obain he soluion of Eq(6) as: X( ) = exp( H ) X() exp[ H ( τ) F ( τ)]dτ (7) where X () represen he sae iniial value In order o saisfy he demands of he precise inegraion, he ime be divided ino a series of small ime sep: j = jh, j =,,, when = j,here is: jh j X( ) = X = exp( H jh) X() exp[ H ( jh τ) F( τ)]dτ j (8) Suppose h is sufficienly small, inhomogeneous F can be approximaed as a consan wihin he ime-inerval ( j, j ), so we have: j j j j X( j ) = X = exp( H ( h))[ X H F ] H F j j j T [ X H F ] H F, j =,, (9) = E-ISSN: 4-66X 4 Volume 4, 5

4 H C G C C C C C C G = R R For he marix T can be compued by he precise inegraion Based on he ideniy T= exp( H ( h)) = exp[ H ( h/ m)] m m = N, = h/ m = h/ N where:, h is sufficienly small Wihin he ime, aking he four-order Taylor expansion, he exp( H ) can be approximaed as: 3 4 exp( H ΗΗΗ ) I H ( ) / ( ) / 3! ( ) / 4! = I Ta () For T = exp( H ( h)) = ( I Ta ) N, which can be N N analysis ino T = ( I Ta) ( I Ta ), he oal decomposiion of N imes, which is equivalen o perform he following saemen: for( i= ; i< Ni ; ) Ta= Ta Ta Ta ; Then, we can ge T = I Ta Since is very small, Eq() wihin he accuracy range of he compuer, which can be regard as he exac soluion of exponenial funciont 33 Sabiliy Analysis of he Precise Time Inegraion Mehod Considering he soluion of he homogeneous equaion of Eq6, we have a recursive scheme as n n X = e H X () The sabiliy of he precise inegraion mehod can be deermined wih so-called Fourier mehod, which is idenified wih he follow inequaliy: i e λ () where λ i is all he eigenvalues of H Apparenly, as long as Re( λi ), he inequaliy () can be saisfied Since he ime-sep is a posiive real, for he inequaliy can be saisfied only if Re( λi ) Tha is o say, he ime-sep size does no exer an influence on he sabiliy of he scheme, and he Eq is deermined only wih he sign of Re( λ i ) So, he ime precise inegraion mehod is uncondiionally sable regardless of he ime-sep size 6 Simulaion Analysis Due o he shun sae of rack circui is based on he adjusing sae, for furher analysis of he ransien curren when rain eners he rack secion, he firs hing is calculaed he adjusing sae 4 Analysis of he Adjusing Sae The simple equivalen circui of rack circui as shown in Fig4, where in he beginning wih he volage source U s and Z s ac as inernal resisance; he erminal is conneced wih he load impedance Z, i () is he received curren; Rf is he equivalen shun resisance The differen working saes of rack circui correspond o differen boundary condiions When he rack secion is unoccupied, rack circui in he adjusing sae E-ISSN: 4-66X 4 Volume 4, 5

5 beginning i () Z s Us i () i () railⅠ i () M erminal K ground u () i () M f l railⅡ Fig4 The equivalen circui of rack circui R f x i () A his poin, K disconnecs he conac, he beginning and erminal boundary condiions of rack circui are as follows: beginning: u() = F[ i(), US()] = U s () i () Z s, where: i () = i () = i () ; erminal: i () = im() = F[ u M()] = um()/ Z = ( um() u M())/ Z; Consider he iniial condiion X () =, he space and ime sep size is respecively: M=; h =e-3s N= and he main parameers of rack circui are shown in Table Table : he main parameers of rack circui Parameer name Rail ype Supply volage Inernal resisance engh The load Parameer value P6 3 V Ω Km 7 Ω Fig5 shows he curren response a he receiving end of rack circui To demonsrae he validiy of he precise ime-inegraion compared is simulaion resul wih he finie difference ime domain (FDTD) his mehod(rd=5) his mehod(rd=3) FDTD(Rd=3) 5 5 /s Fig5 Curren response of he receiving end I can be seen ha he curren signal quickly comes o sabiliy wih ime passes, and he curren value becomes larger wih increased ballas Z resisance under oher parameers mainained a fixed value This is due o when ballas resisance increases; he leakage curren is reduced during he process of signal ransmission I is also seen ha he precise ime-inegraion mehod is agreemen wih he direc soluions by he FDTD mehod 4 Analysis of he Shun Sae From he above analysis, subsiuing he boundary and iniial condiions of adjusing sae ino Eq(9) We can ge he seady sae value of he volage and curren along he rail line, which can be used as he iniial condiion of he shun sae of rack circui, and furher analysis he curren response by combing wih he boundary condiion of shun sae When a rain peneraes he rack secion, is wheels and axles ac as a shun resisance R f, in Fig4, K connecs wih conac This ime, he beginning boundary condiion of rack circui is he same as he adjusing sae: u() = F[ i(), US()] = U s () i () Z s, where: i () = i () = i () ; While in he erminal of rack circui, curren flow o he receiver changed as: i () = im () Rf /( Rf Z) = F [ u M ( )] Rf / ( Rf Z) As is ofen he case, he shun resisance Rf is very small (4-5 Ω )[7], Rf << Z, so compared wih he adjusing sae, he receiving end of curren decreases obviously When he rain is arriving a he beginning and will leave he secion, he equivalen circui of rack circui as shown in Fig6 A his momen, he boundary condiions of rack circui in he beginning and erminal, respecively: u() = F[ i(), US()] = U s () i () Z s, where: i () = i () i f () = i () u ()/ R f ; i() = im() = F[ u M()] = um / Z = u / Z = ( u () u ())/ Z M M M beginning i railⅠ i () Z s U S K () i () f R f ground railⅡ i () M u () M erminal i () i () l x Fig6 The equivalen circui of rack circui When he rain leaving, in Fig6,open he Z E-ISSN: 4-66X 43 Volume 4, 5

6 conac and rack circui o he adjusing sae Normal Shun Secion Based on he above condiions, Fig7 indicaes he curren response of he receiver when a rain is shuning on he rails a =ms, where R f =6 Ω, R d =5 Ω km I can be seen ha, a =ms, because of shuning effec of R f, he ampliude of curren decreases dramaically, (here will be a fall edge), which is a ransien process of curren signal /s Fig7 Curren response of a rain enering he rack secion Fig8 shows when a rain passing hrough he rack secion, curren response of he receiver /s Fig8 Curren response of a rain leaving he rack secion I s also can be seen ha, a =4ms, he curren signal a he receiving end of rack circui increases sharply, (here will be a rising edge), which is a ransien signal From Fig7 and Fig8, i can be seen ha, in he momen of a rain enering or leaving he rack secion, here is a ransien signal As a resul, his can be used o deecion he shun sae of rack circui by idenifying signal ype of ransien curren (fall edge or rising edge) Shun Malfuncion Secion In he pracical applicaion, due o he complex working environmen, he deecion of rack circui s shun sae is easily effeced by ballas resisance, supply volage and shun resisance [8] The radiional mehod may be difficul o be used for rain deecion For example, Table shows he received curren ampliude under differen condiions Table he curren a receiving end wih f = Hz, l = km, R f = Ω R d /( Ω km ) U S /(V) R f ( Ω ) Adjusing sae shun sae i/(a) i/(a) I can be seen from Table ha he curren ampliude increases wih he increase of supply volage, ballas resisance and shun resisance Especially in he shun malfuncion secion, mainly due o he rus or dir of rail (or wheel) surface ha make he shun resisance beyond he sandard values[9] In such a siuaion, if we comparing he variaion of received curren ampliude wih a cerain hreshold, which may be difficul [] Fig9 shows he change of curren from he adjusing sae o he shun sae occurs a he wors condiions of shun model (in his case, consider he rail ype is P6, he supply volage is 5V, and wih he larges ballas resisance R d = Ω km and R f = Ω ) /s Fig9 Curren response in he bad condiion I can be seen ha, in shun malfuncion secion, he variaion of curren ampliude ( i ) is smaller han he variaion of curren ampliude in Fig 6 Tha may be cause a false judgmen if he rain deecion by he radiional mehod However, despie he variaion of curren ampliude ( i ) decreases, here sill is a ransien change process, a =8ms Therefore, he ransien characerisics of curren signal, which can be used for rain deecion, even in he shun malfuncion secion 5 Conclusion i E-ISSN: 4-66X 44 Volume 4, 5

7 Aiming a he shun malfuncion problem, a ransien response analysis for he shun sae of rack circui based on he precise ime-inegraion mehod is proposed in his paper Combined wih he differen iniial and boundary condiions of rack circui, by numerical simulaing analysis he curren response from he adjusing sae o he shun sae The heoreical and simulaion resuls show ha he precise ime-inegraion algorihm is an effecive mehod for he analysis of shun sae of rack circui, and when a rain eners a rack secion, here is obviously ransien curren even in he wors condiions of shun sae So his is imporan informaion for he shun sae of rack circui 6 ACKNOWEDGEMENTS This projec is suppored by he China Railway Corporaion and Technology Research and Developmen Program (5X7-H) References: [] FHouze, Elecrical behaviour of he wheel-rail conacin, Elecrical Conacs & Inernaional Conference on,, 67-7 [] UO Yong, Simple Analysis and Soluion of Bad Track Circui Shuning, Railway Signaling & Commubicaion engineering, 4, (6):3 [3] HE Gui-yang, HUA Ze-xi, Soluion analysis for defecive shuning of rack circui, Railway Compuer Applicaion,, ():48-5 [4] I Ming, Invesigaion he axle couner o solve he bad shuning of rack circui, Railway Signaling & Commubicaion engineering, 3, (6):58-6 [5] MI Gen-suo, WANG Yan-kuai, WANG Wenbo, Applicaion of Radar Char in Poor Shuning Early Warning for Track Circui, Journal of he China Railway Sociey, 3, 35(): 66-7 [6] YUAN Xiao-jun, Research on Shun Malfuncion of Railway Track Circui, Railway Signal and Communicaion, 7, 43(4): -4 [7] DI Jing-jing, Sudy on he New Asymmeric Pulse Track Circui Technology, Xi'an Universiy of Archiecure &Technology, [8] ZHAO Bin, ZHANG You-peng, WEI ei, Analysis on he Time Responses of Track Circuis, Journal of he China Railway Sociey, 4, 36(9):68-7 [9] CRPaul, Analysis of Muliconducor Transmissionon ines, New York: Wiley Inerscience, 994 [] AOrlandi, CRPaul, FDTD Analysis of ossy Muliconducor Transmission ines Terminaed in Arbirary oads, IEEE Trans, On Elecromagneic Combaibiliy, vol 38, no 3, Aug 996, pp [] PGómez and FAUribe, The numerical aplace ransform: An accurae ool for analyzing elecromagneic ransiens on power sysem devices, InJElecPower Energy Sys,vol3,no 3,pp6 3,Feb/Mar9 [] P Moreno and A Ramírez, Implemenaion of he numerical aplace ransform: A review, IEEE Trans Power Del, vol 3, no 4, pp599 69, Oc 8 [3] ZHAO Jin-quan, MA Xi-kui, QIU Guan-yuan, A Precise Time-Inegraion for Analysis of Time-Domain Response o ossy Transmission ines, Microelecronics, 997, 7(3):8-85 [4] KONG Xiang-dong, ZHONG Wan-xie, Precise ime inegraion algorihm of siff equaion in nonlinear dynamic sysem, Journal of Dalian Universiy of Technology,, 4(6): [5] ZHAO Jin-quan, MA Xi-kui, QIU Guan-yuan A Precise Compuaion Mehod for he Time- Domain Response of Muliconducor Coupled Transmission ines, Journal of Circui and Sysems, 997, (3):3-7 [6] TANG Min, MA Xi-kui, A Precise Inegraion Algorihm for Transien Simulaion of Inerconnecs in High-Speed VSI, Journal of Elecronica, 4, 3(5): [7] Z Yong-xian, X Xue-song, and Y Jiang-song, Modeling and simulaion of ZPW-A joinless rack circui, Journal of Eas China Jiaoong Universiy, no3, pp64 68, 9 [8] C J Baker, Chapman, A Quinn, and K Dobney, Climae change and he railway indusry: a review, Proceedings of he Insiuion of Mechanical Engineers C: Journal of Mechanical Engineering Science, vol4, no3, pp59 58, [9] SUN Shang-peng, ZHAO Hui-bing, CHEN Dewang, ec, Research on Mehod for Calculaion of Shun Resisances of Track Circui Using Elecrical Conac Theory, Journal of he China Railway Sociey, 4, 36(3): 3-35 [] F Filippone, A Mariscoi, and P Pozzobon, The inernal impedance of racion rails for DC railways in he khz frequency range, IEEE Trans Insrum Meas, vol 55, no 5, pp 66 69, Oc 6 E-ISSN: 4-66X 45 Volume 4, 5