J. Elctromagntic Analysis & Applications, 00,, ** doi:0.436/jmaa.00.08 Publishd Onlin Novmbr 00 (http://www.scirp.org/journal/jmaa) Invstigation of Powr Factor Bhavior in AC Railway Systm Basd on Spcial Traction Transformrs Mohsn Kalantari, Mohammad Javad Sadghi, Syd Sad Fazl, Siamak Farshad Railway Enginring School, Univrsity of Scinc & Tchnology, Thran, Iran. Email: Mohsn.Kalantar83@gmail.com, J_Sadghi@rail.iust.ac.ir, {Fazl, Farshad}@iust.ac.ir Rcivd August 0 th, 00; rvisd Sptmbr 5 th, 00; accptd Sptmbr 8 th, 00. ABSTRACT Th singl-phas traction load has ssntially an unbalanc charactristic at th Point of Common Coupling (PCC), which injcts harmonic into th utility grid. In this papr, th ffct of harmonic distortion and unbalanc loading ar invstigatd simultanously for lctrical railway systms. Spcial traction transformrs (i.. singl-phas, V/V, Wy-Dlta, Scott, and L Blanc) ar usd btwn th utility grid and th traction load. For analysis, diffrnt dfinitions of powr factors ar considrd, which ar prsntd by IEEE Std.459. Th dtaild simulation study is mad with MATLAB/SIMULINK program to rprsnt th impacts of harmonic componnts and unbalanc loading on th powr factor bhavior in th Elctrical Railway systms. Kywords: Powr Factor, Traction Transformr, Unbalanc Loading. Introduction Rcnt tchnological advancs hav bn mad with rspct to srious problms (.g. population growth continuously, nvironmntal pollution, nrgy shortags, and inadquat transportation capacity) in xisting railway systms. Nowadays, du to many advantags such as big transport capacity, nrgy-saving, and nvironmnt-frindly lctrifid railway systm is considrd as a propr substitution for th obsolt and disl systms. Th singl-phas lctric supply of lctrifid railway is providd via singl-phas or thr-phas traction substations. Th lctric locomotivs ar basically considrd singl-phas loads in which th load conditions and spds altr during vry short span of tim. Bsids, non-linarity, asymmtrical, and non-sinusoidal ar othr charactristics of such singl phas loads. This rsults in an unbalanc and harmonic load to th utility grid mor than bfor. Spcial traction transformrs (.g. V/V, Wy-Dlta, L-Blanc, and Scott) ar usually applid to fd th traction loads and thrfor, to rduc th unbalanc problm. Th bst connction of transformr for a particular utility grid is slctd basd on diffrnt lctrical paramtrs and physical conditions such as primary cost, maintnanc condition, ncssary rsrvation in utility grid, th ffcts of harmonic and ngativ squnc on th utility grid and powr factor valu in powr systm. Harmonic and ngativ squnc componnts of voltag and currnt viwd from PCC hav bn valuatd in svral paprs [-5]. Howvr, th powr factor has not bn analyzd focusd sufficintly in th Elctrical Railway systms as a powr quality indx. In ordr to dtrmin th powr factor bhavior at PCC, four dfinitions ar prsntd by IEEE Standard 459-000 [6]. Chang Ping and his collagus hav studid th ffcts of harmonic distortion and unbalanc loads on th diffrnt powr factor dfinitions in railway systms rgarding th following assumptions [7]. a) Th Elctrical Railway load is takn as a RL on and th harmonic componnts valus ar injctd arbitrary amplitud and sparatly. b) Thy hav studid sparatly th ffcts of harmonic distortion and unbalanc loads on th powr factor bhavior for thr transformr connctions (i.. V/V, Scott and L Blanc). c) In th harmonic analysis, only th harmonic componnts 3, 5 with th sam and unral valus ar considrd. d) In analyzing th powr factor bhavior, lading
stats ar considrd. Howvr such cass occur sldom in th Elctrical Railway systms. Th aformntiond assumptions ar not abl to xprss th xact natur of th Elctrical Railway Systms. Thrfor, this papr is aimd at valuating th powr factor bhaviors of th utility grid in various trms of unbalanc positions and harmonic distortion, using th ral load modl [8]. Finally to calculat th powr factors in diffrnt conditions of th Elctrical Railway systms, a suitabl dfinition is introducd for aformntiond spcial transformr connctions.. Powr Factor Dfinitions On of th significant indxs in dfining th powr quality of th utility grid is th load powr factor and th fding systm. Powr factor is gnrally dtrmind by a spcific dfinition considring balanc loading without harmonics on th load sid of substation. Howvr, in practic th powr factor is affctd by harmonic distortion and also unbalanc loading. Svral powr factor dfinitions ar prsntd to apply th ffcts of non-sinusoidal and unbalancd conditions in lctrical railways. In this part, calculating mthods for th powr factor is prsntd [6]. Th impacts of th harmonics and unbalanc loading ar simulatd and studid in sction 5. Th activ powr is composd of th fundamntal and harmonic componnts. Ths componnts ar dfind as bllow rspctivly: P V I cos () PH V cos h hih h () h P P P H V I cos h h h (3) Th ractiv powr is composd of th fundamntal and harmonic componnts too. Ths componnts ar dfind as bllow rspctivly: Q V I sin (4) Q V I sinh (5) BH h h h S P Q D b b Bb Bb S P Q D c c Bc Bc c (9) (0) Thn, arithmtic apparnt powr (S A ) and powr factor ( A ) ar calculatd basd on th aformntiond quations: S S S S () A a b P Pa Pb P c A () P S A (3) Obviously, S A is th dirct sum of thr singl-phas apparnt powrs, so that it cannot compltly dmonstrat th ffcts of load unbalanc. If th activ, ractiv and distortion powrs ar considrd individually from ach othr, vctor apparnt powr (S V ) and apparnt powr factor ( V ) ar dfind as: whr SV P QB DB (4) V P S V (5) P Pa Pb P c (6) QB QBa QBb QBc (7) DB DBa DBb DBc (8) Figur shows th diffrnc btwn SA and SV. S A S V S V S c D c Q Q Q V I sin (6) B BH h h h h Distortion Powr (D B ) is dfind basd on Budanu s rul and it is calculatd via th following quation: S b D b P c D a P b Q b S a Q c D S P Q B B (7) As a rsult, pr phas apparnt powr is dfind as: S P Q D a a Ba Ba (8) P a Q a Figur. Arithmtic (S A ) and Vctor (S V ) apparnt powrs, unbalancd non-sinusoidal conditions.
Th ffctiv apparnt powr (S ) and ffctiv powr factor ( ) of th thr-phas is calculatd through th following quations: Va Vb Vc V (9) 3 whr I Ia Ib Ic (0) 3 S P S () 3V I () Th ffctiv apparnt powr has bn introducd to dtrmin th powr-lin losss causd by unbalancd loads [9]. In ordr to valuat th loading charactristic of th Elctrical Railway, it is ncssary to introduc a suitabl powr factor dfinition among, A and V. Finally, fundamntal powr factor is dfind as: whr cos tan P a b Q c c (3) Q Q Q Q (4) P P P P (5) a b This dfinition is basd on only fundamntal componnt and thrfor, harmonic distortion can not affct on its valu. 3. Traction Transformr Spcially connctd transformrs such as singl-phas, V/V, Wy-Dlta, Scott, and L-Blanc transformrs ar usd to convrt a thr-phas supply into on or two singl-phas supplis. Ths transformrs ar commonly usd in th lctro locomotiv traction systms. In all quations, K=N /N is dfind as no-load turn ratio. 3.. Singl Phas Connction Th singl phas traction transformr configuration is shown in Figur. For a singl phas traction transformr, thr is only on trminal at th scondary sid. This typ of connction causs th worst unbalanc loading condition in Elctrical Railway systm. Whn powr supply is providd through AB phass, th currnt and voltag rlationships btwn primary and scondary of th Singl phas transformr ar: V ab V a V b kvt (6) I a IT k (7) Figur. Singl phas connction [0]. Figur 3. V/V connction [0]. I b Ia IT k (8) 3.. V/V Traction Connction I c 0 (9) Th configuration of V/V traction transformr is shown in Figur 3. It is composd of two singl-phas transformrs which fd by two phas voltags (i.. AB and CB) and th currnt and voltag rlationships ar as blow: V ab V a V b kvt (30) Vbc Vb Vc kv M (3) V ca V c V a k V M VT (3) I a IT k (33) I b Ia Ic IT I M k (34) I c I M k 3.3. Wy-Dlta Connction (35) Th Wy-Dlta transformr, anothr spcially connctd transformr consisting of thr two-winding transformrs is usd in lctric railways. Th currnt and voltag rlationships obtaind from Figur 4 ar as follows: V ab V a V b k VT V M (36) Vbc Vb Vc kv M VT (37)
Figur 4.Wy-Dlta connction []. 3.4. Scott Connction V ca V c V a kv M VT (38) I a IT IM k (39) I b IT I M k (40) I c IM IT k (4) Th Scott traction transformr consists of two singl-phas transformrs, M and T, and its diagram circuit is dmonstratd in Figur 5. This connction transforms thr-phas to a two-phas supply and thrfor, it can b rducd th dgr of voltag imbalanc causd by singl-phas traction loads. Th magnituds of th voltag at th scondary sids ar qual but th phas angl of T transformr is 90 in lad of M. Th currnt and voltag rlationships of th Scott transformr ar calculatd as follows: k V ab V a V b 3VT V M (4) V bc V b V c kv M (43) k Vca Vc V a 3VT V M (44) I a I T (45) 3k I I I 3 b M T I I I 3 c M T 3.5. L Blanc Bonnction k (46) k (47) Th winding of th primary sid of L Blanc transformr is dsignd in a dlta ( ) connction form and on th scondary sid, two windings (T and M) ar usd which contain unbalancd structur as shown in Figur 6. This connction transforms thr-phas to a two-phas supply similar to th Scott connction and thrfor, it can b also rducd th dgr of voltag imbalanc causd by singl-phas traction loads. Th currnt and voltag rlationships of th primary and scondary of th L Blanc transformr ar as follows: 3 3 V V V k V V 4 ab a b T M (48) Figur 5. Scott connction [0]. Figur 6. L Blanc connction [0].
3 V bc V b V c kv M (49) 3 3 V ca V c V a k VT V M 4 (50) 4. Traction Load I a I T (5) 3k I I I 3 b M T k (5) I c IT IM k (53) 3 To considr th ffcts of th harmonics on th utility grid, a.5-mw thyristor rctifir locomotiv (ratd at 5 KV) ar assumd [3]. It is modld as two half-controlld thyristor bridg rctifirs in sris as shown in Figur 7. Transformr ratio is ::. All locomotivs paramtrs ar convrtd to a 5 KV bas. Whn two or mor such locomotivs ar running togthr hauling a singl train, thy ar assumd to hav idntical firing angls. This assumption allows two locomotivs to b modld as a singl locomotiv of doubl or manifold th ral siz, which is asily obtaind for xampl by halving th inductancs, and doubling th capacitanc and also doubling th load currnt. Figur 8 shows th traction load currnt and its harmonics spctrum. This simulation rsults rprsnt that th odd harmonic ordr of th traction load currnt compard to vn on as an xpctd. 5. Simulation Rsult This sction analyss th calculatd rsults for diffrnt powr factor dfinitions which stm from ntwork simulation. Rgarding th diffrnt functions of various transformrs, this invstigation is prformd in four cass considring various connctions. Furthrmor, th powr factor bhavior is also takn in to account and simulatd basd on unbalanc indx from zro to 00 prcnt. Th simulatd ntwork block diagram is considrd according to Figur 9. In this diagram, th traction loading typ and applid connction transformrs affct rmarkably on th calculation rsults. To compar th rsults, fiv typs of transformrs with th sam turn ratio ar utilizd in th block of Traction transformr. In load block, th ral load modl of th Elctrical Railway is assumd which was uttrly dscribd in th prvious part. Not that th ncssary input data is shown in Tabl. Load Currnt (A) Harmonic Magnitud 600 400 00 0-00 -400 Figur 7. DC traction load [8]. -600 0.5.5 Tim (ms) x 0 4 50 00 50 00 50 0 3 5 7 9 3 5 7 9 Harmonic Ordr Figur 8. Traction load currnt and its harmonic ordr. Figur 9. Simulatd block diagram. Tabl. Th ncssary input data Symmtrical Voltag Sourc Short-Circuit Capacity on th primary (thr phas) sid Transformr capacity 69 KV 736 MVA 5 MVA Turn ratio no load (N:N) 69:7.5
Tabl illustrats th load conditions for four analyzing cass. Cas shows th balancd load at th both scondary sids of substation. In practic, it should b notd that th load balancing in scondary sid (two-phas) is not th sam in primary sid (thr-phas). In addition, practically du to moving of train, ths two loads ar not quatd and thy ar sldom balancd. This imbalanc is laboratd in th cas. Sinc th thyristor convrtr is usd as a traction load modl for th mntiond cass, th amount of powr factors ar low rangd (from 9 to 6, rfr to Tabl 3). Thrfor, for improving th powr factor valus practically, som mthodology such as compnsation in th utility grid, GTO convrtr, and IGBT convrtr ar takn into account. Cass and ar listd in Tabl aftr improving th powr factors by compnsation mthod in trms of cass 3 and 4. Powr factor valus in th primary (thr-phas) sid of th Traction substation ar shown as a simulation rsults in Tabl 3. Ths rsults ar catgorizd as following: A: Cas Th thr phas sids of Scott and L Blanc connctions ar balancd and thrfor, th calculatd powr factors of, A and V for thss two connctions in cas ar qual whil th powr factor valu of shows a slight diffrnc compard with ths factors du to load harmonics distortion. In singl phas, V/V and Wy-Dlta connctions, th powr factor valus ar diffrnt from ach othr and ar not th sam. This charactristic rprsnts th undsird ffcts of unbalanc loading, rsultant from asymmtrical structur of ths connctions on th powr factor rsults. In lctrifid railway systms, th ratio of th ngativ squnc currnt to th positiv on is highr than th usual powr utility grid. This fact lads to Tabl. Load condition Loading Catgory Cas Cas Cas 3 Cas 4 PT MW 4 6 4 6 Q ( MVAR ) T.4 3.6.4 3.6 PM MW 4 4 Q ( MVAR ) M.4..4. Fundamntal Activ & Ractiv powr Harmonic balanc loading Harmonic unbalanc loading Harmonic balanc loading Compnsation in Substation Harmonic unbalanc loading Compnsation in Substation Tabl 3. Simulation rsults Powr Factor Connction Schm Cas Cas Cas 3 Cas 4 94 94 57 57 Singl phas A 8 8 05 05 V 37 37 4 4 55 55 5 5 53 05 36 75 A 80 64 66 54 V/V V 40 38 3 8 48 49 54 45 Wy-Dlta Scott L Blanc 64 09 50 88 A 5 0 36 V 48 39 43 33 56 57 5 5 36 59 7 4 A 36 0 7 89 V 36 35 7 6 48 48 45 45 3 60 4 A 3 85 69 V 3 3 8 43 44 38 38
considrabl diffrnc btwn th powr factor valus. Th comparison of simulation rsults btwn th powr factor valus of th singl phas, V/V, and Wy-Dlta connctions indicat that th highr disparity btwn powr factor valus in singl phas connction compard to V/V and Wy-Dlta connctions. Similar to Scott and L Blanc connctions, thr is slight disparity btwn V and in singl phas, V/V and Wy-Dlta connctions. In othr words, load harmonics hav not considrably ffctiv on th powr factor valus. B: Cas Cas analyss th ffcts of harmonic distortion and unbalanc loading on th powr factor valus. Hr th unbalanc indx (UI) which is dfind in th following sction (rfr to quation 48), is almost 50%. Simulation rsults dmonstrat th following: Du to unbalanc loading, th powr factor valus ar diffrnt in all connctions. Sinc Scott and L Blanc connctions ar formd by a mor balancd structur, th disparity of powr factor valus of ths connctions ar lowr than th similar valus in singl phas, V/V and Wy-Dlta connctions. In th singl phas connction this diffrnc is rmarkabl and mor obsrvabl compard to othr than bcaus thy contain th most unbalancd position. Considring th fixd summation amount of powrs in singl-phas connction, simulation rsults in cass and ar qual. C: Cas 3 & 4 Th main goal of simulating th cass 3 and 4 is to study and analyss compnsatd powr factor mannr. Analyzing th simulation rsults show that: An improvmnt in th powr factor valus during compnsation causs rduction of powr factor disparity. Howvr, th unbalanc loading still hav a grat impact on th calculation rsults. If imbalanc loading is incrasd, th disparity is intnsifid accordingly. Th rsults of analyzing th four aformntiond cass show that, th rat of unbalancing in th utility grid is th most significant and ffctiv paramtr on th powr factor trnd. It should b notd that this imbalanc utility grid ar du to th imbalanc loading and also diffrnt transformr configurations. Thrfor, in ordr to calculat th ffcts of unbalanc loading on th utility powr factor in various connctions, th load summation must b considrd to b fixd. So assuming th qual initial loading on both sids of traction substation that is P T = P M = 6 MW & Q T = Q M = 3.6 MVAR. Th ffcts of complt balanc loading (two similar load on both sids), and th complt unbalanc loading (only on load on on sid of th traction substation) on th utility grid ar invstigatd for various connctions. Th unbalanc indx is dfind as follow: ST SM UI 00% (48) S S T M Figur 0 illustrats th simulation rsults in trms of changing unbalanc indx from zro (complt balanc loading) to 00 prcnt (complt unbalanc loading) with fixd summation loads in various connctions. As obsrvd in this figur: In all connctions, V and bhaviors ar almost indpndnt of unbalanc loading and hav fixd trnds. and A bhaviors ar both dpnd on unbalanc loading and unbalancd transformr structurs. So, whn unbalanc indx is mor than 0%, ths powr factors trnd starts to chang in Scott and LBlanc transformrs, dspit of thir balancd trat in railway systms. In 00% unbalanc indx (which th injction ngativ squnc currnt in to th utility grid hav a similar trnds in all connctions [3]), it is obsrvd that powr factor in various connctions lads to almost th sam amount namly. Th rfrnc [] has introducd powr factor as th load spcification indx which can rval th unbalanc loading impacts in th utility grid clarly. Howvr, powr factor is subjct to unbalanc loading and also diffrnt componnts of th activ, ractiv and distortion powrs. Thn, th unbalanc loading impact on th valu of is not clar xactly. On th othr hand, it is worth noting that th main function of th powr factor is to clarify various powr componnts rlations with ach othr. Although, th utility imbalanc is dtrmind rgarding th othr indxs such as ngativ squnc componnts. Thrfor, it can b obsrvd that utilizing powr factor dfinition V is suitabl for traction applications du to th ffcts of harmonics distortion and unbalanc loading in th utility grid. This dfinition not changs and has a fixd trnd vrsus unbalanc indx. Th valu of including only th fundamntal componnts and th harmonic distortion is disrgardd. So, thr is slight disparity btwn V and. Subsquntly, whn V calculation is difficult or impossibl, can b calculatd as a propr approximation instad of V in all unbalancd situation.
Singl Phas a v 0 0 40 60 80 00 V-V a v 0 0 40 60 80 00 Wy-Dlta a v 0 0 40 60 80 00 Scott a v 0 0 40 60 80 00 L Balanc a v 0 0 40 60 80 00 Figur 0. Powr factor valus vrsus UI. 6. Conclusions In this papr, th dtaild charactristic of th powr factor bhavior has bn simulatd and analyzd. To valuat th powr factor bhavior for a varity of applications, fiv spcial traction transformrs (i.. singlphas, V/V, Wy-Dlta, Scott, and L Blanc) hav bn compard in dtail, and its ffcts on th utility grid hav bn invstigatd. Simulation rsults ar diffrnt du to th unbalanc loading and asymmtry in transformr structurs. Using th singl-phas transformr culminats in th most troubl unbalanc circumstancs. Within th scop of thr phas transformrs, th V/V and Wy-Dlta impos undsird imbalancs on th utility grid compard to othr connctions. Having changd unbalanc indx from zro (complt balanc stat) to 00 prcnt, th and A ar considrably affctd assuming fixd activ and ractiv powrs, whil mor stability is obsrvd in V and dfinitions and thy dmonstrat lss failur subjct to asymmtric loading in both sids of traction substation. Consquntly, V powr factor is th most fficint utility du to bttr stability and covring harmonic ffcts in comparison with othr powr factors as discussd in last sction. It is worth nothing that, can b suitabl substitutions for V, whn its calculation is impossibl or challnging. REFERENCES [] H. E. Mazin and W. Xu, An Invstigation on th Effctivnss of Scott Transformr on Harmonic Rduction, Procdings of IEEE Powr Enginring Socity Mting-convrsation and Dlivry of Elctrical Enrgy in th st Cntury, Pittsburgh, 008, pp. -4. [] M. L Dng, G. N. Wu, X. Y. Zhang, C. L. Fan, C. H. H and Q. Y, Th Simulation Analysis of Harmonics and Ngativ Squnc with Scott Wiring Transformr, Intrnational Confrnc on Condition Monitoring and Diagnosis, Bijing, 008, pp. -4. [3] H. Q. Wang, Y. J Tian and Q. C. Gui Evaluation Of Ngativ Squnc Currnt Injcting into th Public Grid from Diffrnt Traction Substation in Elctrical Railways, Intrnational Confrnc on Elctricity Distribution, Pragu, 8- Jun 009, pp. -4. [4] H. E. Mazin and W. Xu, Harmonic Cancllation Charactristics of Spcially Connctd Transformrs, Elctric Powr Systms Rsarch, Vol. 79, No., 009, pp. 689-697. [5] S. R. Huang and B. N. Chn, Harmonic Study of L Blanc Transformr for Taiwan Railway Elctrification Systm, Procdings of IEEE Powr Enginring Socity Wintr Mting, Taichung, 3-7 January 000, pp. 45-50. [6] IEEE, IEEE Trial-Us Standard Dfinitions for th Masurmnt of Elctric Powr Quantitis undr Sinu-
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