电气化铁道动力供电系统模拟_英文_

第5卷第3期2005年6月

交通运输系统工程与信息

Journal of T ranspo rtati on System s Engineering and Info r m ati on T echno logy V o l 15N o 13June 2005

文章编号:100926744(2005)0320093215

交通科学与工程

Traction Power System Si m ula tion

i n Electr if ied Ra ilways

T .K .Ho 1,Y .L .Ch i 1,L .K .Siu 2,L .Ferreira

3

(1.D epartm ent of E lectrical Engineering ,Hong Kong Po lytechnic U niversity ,Hong Kong ,Ch ina ;2.Kow loon 2Canton R ail w ay Co rpo rati on ,Hong Kong ,Ch ina ;3.Schoo l of C ivil Engineering ,Q ueensland U niversity of T echno logy ,

A ustralia )

Abstract :　E lectricity has been the m aj o r source of pow er in mo st rail w ay system s .R eliable ,efficient and safe pow er distributi on to the trains is vitally i m po rtant to the overall quality of rail w ay service .L ike any large -scale engineering system ,design ,operati on and p lanning of tracti on pow er system s rely heavily on computer si m ulati on .T h is paper review s the m aj o r features on modelling and the general p ractices fo r tracti on pow er system si m ulati on ;and introduces the developm ent of the latest si m ulati on app roach w ith discussi ons on si m ulati on results and p ractical app licati ons .R em ark s w ill also be given on the future challenges on tracti on pow er system si m ulati on .Key words :　electrified rail w ays ;computer si m ulati on ;tracti on pow er system CLC nu m ber :　U 223.6

电气化铁道动力供电系统模拟

何天健1,池云莉1,邵乐基2,L .Ferreira 3

(1.香港理工大学电气工程系,中国香港;2.九龙区铁路公司,中国香港;3.昆士兰技术大学民用工程系,澳大利亚)

摘要:　电力是现今大部份铁道系统的动力来源Λ可靠、有效率及安全的电力输送对整

体铁道服务质素尤为重要,跟其它大型工程系统一样,铁道供电系统的设计,运作及筹划相当倚重计算机仿真Λ本文将回顾铁道供电系统仿真的模型及一般常规,并通过模拟结果例子及实际应用,介绍最新的模拟方式发展Λ本文亦对铁道供电系统仿真的未来挑战作出评论Λ

关键词:　电气化铁道;计算机模拟;动力供电系统中图分类号:　U 223.6

收稿日期:2005204218

何天健(1966-),男,中国香港人,香港理工大学电机工程系副教授,主要研究方向为铁路系统传真,铁路牵引与供变电技术,交通控制模型等Λ

0　I n troduction

E lectricity has becom e the p ri m ary sou rce of tracti on pow er in m odern rail w ays .A ll m etro system s are now operated by electricity in one

fo r m o r ano ther .W h ile the diesel o r coal driven train s are still heavily u sed in som e coun tries ,they

are

often

li m ited to

long 2distance

comm u tati on

and o r

freigh t

tran spo rtati on .

E lectricity u tilisati on is the trend of rail tran spo rtati on,ju st the sam e as fo r social advancem en t.N o t on ly does it p rovide a reliab le pow er sou rce and enab le robu st train p erfo r m ance,it is also an environm en tally friendly m ean s to con sum e energy.Sm oke and po llu tan ts from com bu sti on engines are si m p ly no t accep tab le fo r op erati on s in enclo sed environm en t,p articu larly in m etro system s.

E li m inating the need to carry fuel on board m ay be seen as ano ther advan tage of u sing electricity fo r rail w ay tracti on.How ever,the pow er distribu ti on along the rail w ay lines and the equ i pm en t to facilitate pow er tran s m issi on ju st po se ano ther m ajo r engineering p rob lem in stead.

Indeed,the advan tages of electric tracti on pow er do no t com e w ithou t a h itch.

E lectrom agnetic incom p atib ility w ith the signalling system s w as the early p rob lem and is still raising m ajo r concern s.In som e cases, p hysically sep arated system s fo r tracti on pow er and signalling have to be adop ted,such as the4-rail arrangem en t in the L ondon U nderground [1].W ith advanced pow er electron ics tracti on drive system,har m on ics m ay be generated, w h ich is sign ifican t enough to con tam inate the electricity supp lied to o ther u sers.O ther concern s include safety(touch vo ltage on rails),operati on (overloading,system fau lt and po ssib le equ i pm en t failu res),p ro tecti on(ligh tn ing and vandalis m),m ain tenance(rail co rro si on due to stray cu rren t,pan tograph and overhead line in teracti on)and p lann ing(line ex ten si on s, sho rter headw ay o r h igher speed).

W ith the inevitab ly h igh cap ital co st in a rail w ay system,the study on tracti on pow er system starts from the design stage.Sizes and locati on s of the feeding sub stati on and ratings of the pow er equ i pm en t to cater fo r the expected traffic vo lum e are am ong the first questi on s from electrical engineers.Energy co st is also i m po rtan t fo r the op erato rs in the nego tiati on of electricity tariff.T he range of variati on s of pow er and vo ltage at certain po in ts of the pow er netw o rk,robu stness to ab so rb fau lts and capab ility to handle regenerated energy(from regenerative b rak ing)are the key issues in op erati on s. Fu rther,the p ro jected u sage,as w ell as the po ssib ility and ex ten t of overloading,of the pow er system equ i pm en t,p rovides the u sefu l info r m ati on on m ain tenance w o rk.

A com p rehen sive study on the tracti on pow er system has to be carried ou t even befo re the system is bu https://www.360docs.net/doc/5811517897.html, pu ter si m u lati on is conceived as the on ly viab le m ean s to enab le such study. Si m u lati on s of differen t app roaches and scales are u sed ex ten sively to investigate vari ou s k inds of system studies.Si m u lati on m odels and techn iques on rail w ay tracti on system s w ere first develop ed th ree decades ago.Since then,they have m atu red th rough a num ber of evo lu ti on s on m odel accu racy and com pu tati onal efficiency and served the pu rpo ses of vari ou s app licati on s fo r rail w ay engineers,operato rs and researchers.How ever, the developm en t of tracti on pow er system si m u lati on seem ed to com e to a gradual halt ten years ago becau se of the satu rati on of app licati on requ irem en ts.In recen t year,driven by the increasingly dem anding requ irem en ts on system reliab ility and availab ility,service quality and traffic dem and from p lann ing view po in t and coup led w ith the po ssib le need of real2ti m e app licati on s from operati on view po in t,new developm en t in si m u lati on app roach and u tilisati on of advanced com p u ting techn iques have su rfaced.

T h is paper ai m s to review the m odels, difficu lties and app licati on s of tracti on pow er system si m u lati https://www.360docs.net/doc/5811517897.html, parison s are then m ade on the si m u lato rs w ith the traditi onal and the latest app roaches of pow er flow calcu lati on, fo llow ed by the discu ssi on s of inco rpo rating the advan tages of m odern com pu ting hardw are and softw are to enhance the app licab ility of the si m u lato rs.

1　Traction Power Supply System s

T he tracti on pow er system is,in its si m p lest

49交通运输系统工程与信息2005年6月

fo r m ,a huge electrical circu it .T he pow er supp ly m ay be in single o r m u lti p le sou rces and the

feeding arrangem en ts vary in differen t system s .T he com p licati on s ,as illu strated later ,m o stly com e from A C tracti on pow er supp lies .T he loads in the electrical circu its are the train s w h ich are m oving and dem anding differen t levels of pow er

acco rding to their op erati onal m odes and sp eeds .A train m ay becom e a sou rce if regenerative

b rak ing is allow ed .

In o rder to attain steady 2state so lu ti on of the electrical circu it ,the sou rces ,feeding netw o rk s and loads m u st be p roperly m odelled ,w h ich is no si m p le task ,given the varieties of supp ly system s and operati on conditi on s .T h is secti on exam ines the featu res of tracti on pow er system s and discu sses the con siderati on s and difficu lties in m odelling .

1.1　Power Suppl ies 1.1.1　DC supp lies

DC rail w ays are operated at relatively low er vo ltages .600V ,750V and 1.5kV are the typ ical figu res [2].T he DC tracti on pow er com es from track side rectifier sub stati on s linked to the A C distribu ti on netw o rk .Each feeding sub stati on covers a secti on of track bu t there is no r m ally no iso lati on betw een adjacen t secti on s ,w h ich i m p lies a m u lti p le 2sou rce system .T he secti on length is sub stan tially

sho rter

becau se of the low er distribu ti on vo ltage level

.It shou ld be no ted that the tracti on cu rren t can be as h igh as a few

thou sand am peres .O verhead catenary o r a th ird rail (o r even track side sliding con tact ),w ith runn ing rail retu rn ,is em p loyed to distribu te pow er to train s .F ig .1show s a typ ical DC supp ly netw o rk fo r a b ranched tw o 2road service .Sw itchgear and iso lato rs on A C side and circu it b reakers on DC side are in stalled fo r p ro tecti on and fau lt m anagem en t

.F ig .1　B ranched tw o 2road netw o rk w ith DC supp ly

DC rail w ays are u sually less su scep tib le to electrom agnetic in terference even though har m on ics from the rectifier sub stati on s o r tracti on equ i pm en t requ ire p rop er filtering .L eakage cu rren t th rough the runn ing rails how ever cau ses co rro si on on the rails .T he rail 2to 2earth conductivity ,w h ich deter m ines the am oun t of leakage cu rren t ,dep ends on so il p roperties and the earth ing structu re in the su rroundings .T he h igh retu rn cu rren t th rough the rails also develop s vo ltage on rails ,w h ich

m ay be hazardou s to personnel w o rk ing clo se to the rails .

D esp ite being a m u lti p le 2sou rce system ,DC tracti on pow er system does no t cau se too m any difficu lties to the so lu ti on calcu lati on p rocess in si m u lati on (train s m ay becom e sou rces w ith regenerative b rak ing to tu rn the circu it in to a m u lti 2sou rce system anyw ay )becau se of the si m p le feeding arrangem en t .W hen the locati on s of train s and resistance of rails and overhead cab les are know n ,it is on ly tedi ou s to estab lish

5

9第3期T racti on Pow er System Si m ulati on in E lectrified R ail w ays

the electrical circu it in o rder to so lve fo r the vo ltages and cu rren ts in the circu it.B ranches and m u lti2track lines are comm on in rail w ays and they ju st m ake the electrical circu it m o re com p licated.

A pp rop riate netw o rk partiti on ing w ill certain ly reduce the com p u tati onal dem and of the so lu ti on p rocess.

A s som e sub stati on s are equ i pp ed to receive pow er from the DC system and release it back to the A C side so as to ab so rb the excessive fed2back energy from regenerative b rak ing,the b i2 directi onal flow of pow er shou ld be inco rpo rated in the m odels.How ever,the i m po rtan t featu re is that recep tive sub stati on s allow pow er flow in one directi on(from A C to DC)m o st of the ti m e and they on ly p er m it reversal of pow er flow w hen it is necessary.

1.1.2　A C supp lies

Pow er fo r A C rail w ay tracti on is ob tained from u tility supp ly system,at tran s m issi on o r sub2tran s m issi on vo ltage level,th rough tracti on feeding sub stati on s.25kV tracti on netw o rk at50 o r60H z is the m o st comm on ly adop ted system. T he rail line is u sually divided in to a num ber of iso lated feeding secti on s and each secti on is fed by a single2phase supp ly from a tran sfo r m er w ith in the secti on.Pow er is carried to the train s th rough overhead catenary and cu rren t takes the rails as retu rn path s.H igh catenary vo ltage allow s low er tracti on cu rren t and s m aller pow er lo ss w h ile the secti on length(o r distance betw een adjacen t feeding tran sfo r m ers)can be kep t relatively long, typ ically over10km.A djacen t secti on s are supp lied by differen t p hases of a32phase netw o rk and they are sep arated by track neu tral. P rovisi on s of iso lato rs and s w itchgear are necessary fo r track neu tral and parallel secti on s to enab le con tinual feeding in cases of failu res and ou tages by iso lating certain fau lty equ i pm en t o r secti on o r even reconfigu ring to a differen t feeding netw o rk.

A num ber of feeding arrangem en ts are availab le,including direct supp ly w ith o r w ithou t retu rn conducto rs,boo ster tran sfo r m er(

B T)and au to tran sfo r m er(A T)system s.Several con siderati on s,such as pow er tran s m issi on efficiency,vo ltage regu lati on and in terference supp ressi on,have to be taken on the adop ti on of the su itab le feeding arrangem en t fo r a p articu lar tracti on pow er system.

D irect connecti on of the tran sfo r m er secondary to the catenary and rails is the m o st straigh tfo r w ard m ean s of pow er feeding. Sign ifican t rail2to2earth leakage cu rren t is the m ajo r draw back of th is feeding arrangem en t becau se of the inevitab le rail2to2earth i m p edance. Co rro si on on rails is no longer an issue becau se of A C cu rren t.How ever,the i m balance betw een the supp ly cu rren t on the overhead cab le and the retu rn cu rren t on the rails(the difference betw een the tw o being the rail2to2earth leakage cu rren t), coup led w ith the physical separati on betw een overhead cab le and rails,is often one of the m ain cau ses of electrom agnetic in terference to the lineside telecomm un icati on equ i pm en t.A s show n in F ig.2,the additi on of a retu rn conducti on,in parallel w ith the catenary and connected to the rails at regu lar in tervals,help s reduce the leakage cu rren t,bu t on ly to a certain ex ten t

.

F ig.2　D irect feeding w ith return conducto r

B T feeding p rovides ano ther m ean s of in terference reducti on by fo rcing the cu rren t to flow in the retu rn conducto r rather than in the rail. How ever,it is at the exp en se of poo rer vo ltage regu lati on becau se of additi onal i m pedance of B T s.H aving allow ed pow er to be tran s m itted at the vo ltage tw ice as h igh as the op erating vo ltage,A T feeding i m p roves system efficiency. In terference supp ressi on is ano ther advan tage of A T feeding.In additi on,A T feeding p rovides

69交通运输系统工程与信息2005年6月

better vo ltage regu lati on and allow s longer in terval betw een tran sfo r m ers[3],w h ich is essen tial fo r service reliab ility of long2distance rail lines,if no t ju st the cap ital co st.Bo th B T s and A T s are p laced at regu lar in tervals w ith in a feeding secti on.Illu strated in F igs.3and4,B T feeding op erates by balancing cu rren ts on the tw o w indings of the tran sfo r m ers w h ilst A T relies on vo ltage balancing.B y in troducing B T s o r A T s w ith in the feeding secti on,the cu rren t is fo rced to retu rn via the retu rn conducto rs.Such m an i p u lati on of cu rren t retu rn path is how ever at the expen se of m o re conducto rs(m o stly overhead)along the lines and m o re com p licated cu rren t distribu ti on s.

T he additi onal equ i pm en t w ith B T and A T feeding p resen ts ex tra m odelling w o rk s in the si m u lati on.T he electrical param eters of the equ i pm en t are often availab le from m anufactu rers o r op erato rs bu t they have to appear as com p lex num bers(e.g.i m p edance in stead of resistance) becau se of the A C natu re.T he scale and com p lex ity of com pu tati on requ ired is then inflated sign ifican tly.It is also necessary to exam ine the cu rren t distribu ti on in the conducto rs along the line as the m u tual i m p edances am ong the conducto rs,as w ell as the adm ittances to the ground,p lay i m po rtan t parts in the steady2state so lu ti on.T rain po siti on relative to the locati on s of B T s o r A T s ho lds keys to cu rren t distribu ti on and differen t train po siti on s m ay lead to differen t circu it configu rati on s.O ne con so lati on from m odelling view po in t is that the feeding sub stati on s here are no t in terfaces betw een A C and DC system s,as in DC rail w ays.T he com p licati on of pow er flow directi on does no t ex ist in A C supp lies even w ith excessive pow er recovered from regenerative b rak ing.

1.2　L oads

In a typ ical in ter2stati on run,a train accelerates from a stati on to the m ax i m um p er m issib le sp eed,m ain tain s the speed and b rakes to a com p lete stop at the nex t stati on.It therefo re goes th rough a w ide range of speeds,differen t op erati on m odes and hence the pow er dem and m ay vary sign ifican tly w ith in a sho rt peri od of ti m e.T rain speed and operati on m ode are the decisive facto rs of the i m m ediate am oun t of pow er requ ired by the train as a load.T hey are how ever deter m ined by the tracti on equ i pm en t characteristics,train w eigh t,aerodynam ics, track geom etry and drive con tro l.T he electrical rep resen tati on of the train s in the circu it as a variab le load(and som eti m es sou rce)requ ires carefu l m odelling in the si m u lati on.

W ith the m oving train s,the configu rati on of the electrical circu it keep s changing and the so lu ti on relevan t to one in stan t m ay no t be valid to the nex t.If it is necessary to attain the details of the tracti on pow er system behavi ou r and train in teracti on,the electrical circu it has to be updated and the new circu it so lu ti on is to be re2 calcu lated at every regu lar ti m e in terval over a long sp an of ti m e.T rain m ovem en t si m u lati on is the basic accom pan ied functi on to p rovide train po siti on,speed and operati on m ode fo r the pu rpo ses of estab lish ing the electrical circu it.T he pow er netw o rk so lu ti on p rocess,u sually w ith m an i p u lati on of large2scale m atrix equati on s,at each ti m e in terval thu s i m po ses trem endou s com p u tati onal dem and to the si m u lati on.In fact, the pow er netw o rk so lu ti on is al w ays the m o st ti m e2con sum ing step of a w ho le system si m u lati on in rail w ays[4].

2　M odell i ng

T h is secti on discu sses the featu res in the tracti on pow er si m u lati on m odels w h ich requ ire carefu l con siderati on s.

2.1　Power suppl ies and feed i ng networks

2.1.1　DC supp lies

T he pow er sou rce at the sub stati on is assum ed to be a con stan t(u sually vo ltage)sou rce w ith equ ivalen t sou rce resistance.W hen the pow er system calcu lati on does no t com e up w ith a so lu ti on becau se of excessive over2vo ltage at the sub stati on o r cu rren t flow ing in oppo site directi on (u sually resu lted from regeneravivetive b rak ing),

79

第3期T racti on Pow er System Si m ulati on in E lectrified R ail w ays

the sub stati on m ay be re2m odelled as a passive load to allow pow er to go back to the supp ly system,p rovided that the sub stati on is suppo sed to be capab le of do ing so.

O nce the train po siti on s are know n,the resistances betw een train s are tho se of the overhead lines(o r con tact w ires)and the rails sep arating the train s if the resistance p er un it length of these conducto rs is assum ed to be con stan t.In p ractice,the resistances of the conducto rs are cu rren t2dep enden t[5]even though the variati on is no t disp ropo rti onate.Such dep endency can be inco rpo rated in the si m u lati on m odel fo r better accu racy bu t the so lu ti on p rocess m ay take m o re ti m e w ith m o re iterati on s.

R ail2to2earth leakage cu rren t is ano ther issue leading to com p licati on.T he leakage is a distribu tive p henom enon along the rail and it can be m odelled w ith a fin ite2elem en t app roach,in w h ich the rail is divided in to a num ber of elem en ts of equal length and a certain po rti on of the cu rren t flow ing th rough each elem en t leak s th rough the rail2to2earth resistance w h ile the rem ain ing carries on to the nex t elem en t.A s a resu lt,the rails have to be rep resen ted by a num ber of resistances in series,in stead of one resisto r on ly,in tersected w ith the rail2to2earth resistances in betw een.A s rail2to2earth leakage cu rren t does no t directly affect train in teracti on s th rough the pow er system,the ju stificati on of its inclu si on in the si m u lati on m odel is thu s deter m ined by the app licati on s of the si m u lato r.

2.1.2　A C supp lies

Feeding sub stati on s are still m odelled as con stan t vo ltage sou rces.A dditi onal conducto rs (m o stly overhead)and lineside equ i pm en t(B T s o r A T s)can be rep resen ted by app rop riate i m p edances and m u tual inductances in the electrical circu it.How ever,the m odelling of the m u tual inducti on am ong the p arallel conducto rs requ ires the fin ite2elem en t app roach again.T he p hysical sizes,relative resistivity,per m eab ility and geom etry of the conducto rs,relative p er m ittivity of the m edium,cu rren t distribu ti on and earth ing conditi on s are essen tial in th is m u lti2 conducto r m odel[3].Fu rther,as the rail is of un ique shap e,calcu lati on of i m pedance,w h ich is cu rren t and frequency dependen t,is far from easy.It can be treated as a single cylindrical steel conducto r,upon sub stan tial p re2p rocessing com p u tati on,w ith differen t cro ss2secti on areas fo r a w ide range of frequencies[5].R ail2to2earth leakage cu rren t can be conven ien tly included in th is fin ite2elem en t app roach,w h ich is a bonu s. W ith the distribu ted elem en ts,the num ber of com ponen ts in the electrical circu it becom es very h igh and the circu it is qu ite com p licated even befo re the train s are in serted.

In o rder to reduce the scale of com pu tati on requ ired,conducto rs w ith the sam e longitudinal vo ltages can be com b ined(e.g.the tw o rails)as one.T here are still at least th ree along2the2line conducto rs w ith B T and A T feeding,as show n in F ig.3and F ig.4

.

F ig.3　BT

feeding

F ig.4　A T feeding

2.2　L oads

T rain s,as loads,can be si m p ly m odelled as passive and pow er2con sum ing elem en ts in the electrical circu it to rep resen t its functi on as a pow er sink.In the case of A C rail w ays,the load shou ld con sist of the resistive and reactive com ponen ts to illu strate its pow er facto r. How ever,such si m p licity does no t reflect the dependence of pow er dem and on train sp eed and

89交通运输系统工程与信息2005年6月

operati on m ode,as w ell as vo ltage2sen sitive natu re of the load.

O ne app roach is to derive the train cu rren t and tracti on effo rt requ ired,given the train speed and operati on m ode,from the tracti on equ i pm en t characteristics(availab le from the op erato rs o r m anufactu rers),fo llow ed by estab lish ing a vo ltage2i m p edance(T heven in equ ivalen t circu it) o r cu rren t2adm ittance(N o rton equ ivalen t circu it) m odel[6],w h ich is p iecew ise linear.T he equ ivalen t circu it m ay con tain a hypo thetically negative i m pedance to indicate the pow er2sink ing p roperty of the load.D etailed tracti on equ i pm en t characteristics con tain ing tracti on p erfo r m ance w ith in a range of vo ltage variati on can be adop ted to m odel the vo ltage2dep enden t perfo r m ance of the load.T he data are u sually m ade ready p ri o r to the si m u lati on and sto red in the si m u lato r as look2up tab les fo r easy and ti m e2efficien t referencing.

A no ther app roach is to w o rk back from the ou tp u t m echan ical pow er.F rom the requ ired tracti on effo rt to su stain a certain sp eed o r to p roduce accelerati on,the ou tpu t pow er can be calcu lated from the train w eigh t,track geom etry, o ther train m ovem en t param eters and pow er lo sses.Given the efficiency of the tracti on system,the inp u t electrical pow er is attained and an equ ivalen t circu it w ith respect to the pow er dem and can again be u sed to rep resen t the load. It is a si m p ler app roach bu t it relies on com p rehen sive m odelling of all po ssib le pow er lo sses du ring train m ovem en t.

2.3　Power network solution

W ith the m odels of pow er supp ly and tracti on equ i pm en t availab le,the circu it of the electrified rail w ay line is estab lished fo r the calcu lati on of vo ltages and cu rren ts at vari ou s po in ts of in terest.T he m o st direct app roach is to fo r m u late a m atrix equati on from the electrical circu it u sing either m esh o r nodal analysis[6].T he so lu ti on is attained from so lving th is m atrix equati on w ho se coefficien t m atrix size depends on the num ber of train s and com p lex ity of the netw o rk.T h is app roach is m o re su itab le fo r com p lex electrical netw o rk s becau se it is often easier to iden tify nodes than loop s in non2p laner netw o rk s.F rom a p rogramm ing persp ective, au tom atic netw o rk set2up p rocedu res and advanced netw o rk graph techn iques are desirab le in the i m p lem en tati on,w ith the u se of the nodal app roach.

T he coefficien t m atrix in the pow er netw o rk so lu ti on is sparse,banded and symm etric fo r a si m p le tw o2track netw o rk.W hen the netw o rk con sists of b ranches and loop s,the bandw idth of the coefficien t m atrix increases and the sp arsity deteri o rates.F ig.5show s the circu it rep resen tati on of a typ ical DC tracti on pow er netw o rk w ith b ranches.It is no t difficu lt to see that the rail w ay tracti on pow er netw o rk is characterised by secti on s of ladder type netw o rk s infrequen tly cro ss2connected.Fo r th is characteristic topo logy,the sparse m atrix techn ique coup led w ith efficien t m atrix eli m inati on m ethods leads to an exp editi ou s netw o rk so lu ti on,since it does no t suffer from the fill2in s that the direct inversi on of the coefficien t m atrix requ ires.It has to be stressed again that if the fin ite2elem en t app roach is adop ted to m odel the conducto rs,the electrical circu it netw o rk w ill be fu rther com p licated and the size of the m atrices w ill be driven up con siderab ly.

W ith the coefficien t m atrix being po sitive defin ite (PD),symm etric and sparse,m any sparse m atrix eli m inati on techn iques tailo red fo r PD m atrices, such as L L T decom po siti on and Cho lesky decom po siti on,are app licab le.Fo r sparse m atrix so lu ti on techn iques,the essence is equati on2 o rdering.T here are generally tw o types of o rdering m ethods nam ely,static and dynam ic o rdering.T yp ical exam p les of static o rdering fo r long and th in ladder typ e netw o rk s include the Cu th ill and M cKee algo rithm[7]and reverse Cu th ill and M cKee algo rithm[8],w h ich m ake u se of the p rop erty that the zero elem en ts situated befo re the first non2zero elem en t on any row al w ays

99

第3期T racti on Pow er System Si m ulati on in E lectrified R ail w ays

rem ain zero .Fo r dynam ic o rdering ,the m in i m um degree algo rithm p rovides an efficien t alternative fo r so lving the netw o rk m atrix .T h is is actually a heu ristic algo rithm to find an o rdering fo r the coefficien

t m atrix w h ich suffers

from low fill 2in s w hen it is facto red .T he m in i m um degree algo rithm

is p articu larly su itab le fo r so lving

m edium to large netw o rk s ,in w h ich there are 200nodes and m o re .Fo r s m aller netw o rk s ,the m in i m um

degree

algo rithm

becom es

a

less

efficien t op ti on since a sign ifican t po rti on of the overall p rocessing ti m e is u sed in the sym bo lic facto risati on p rocess

.

F ig .5　T he equivalent circuit of a typ ical pow er netw o rk w ith branches

Partiti on ing the electrical netw o rk in to several s m aller ,m o re m anageab le sub 2circu its by

node sp litting [9]

is one of the comm on m ethods to enhance si m u lati on efficiency .T h is techn ique ,

also know n as diakop tics [10]

,invo lves tearing a given netw o rk in to a num ber of indep enden t p arts and pu tting the so lu ti on s of the divided p arts together to fo r m the so lu ti on of the o riginal p rob lem .T he natu ral tearing po in ts in tracti on pow er netw o rk are the b ranches becau se the coefficien t m atrix of an iso lated b ranch is h igh ly sparse .How ever ,the num ber and size of the to rn p arts depend on netw o rk topo logy and num ber of

train s on the b ranches respectively [11]

.2.4　I n tegra tion with tra i n m ove m en t

T racti on pow er system si m u lato r on ly p rovides a steady so lu ti on fo r a given train conditi on .In o rder to estab lish vo ltage and cu rren t p rofiles over ti m e at certain po in ts of the pow er netw o rk w h ile train s are m oving in the rail w ay system ,it is essen tial to in tegrate the m ovem en t si m u lato r .

T ak ing in to accoun t the track geom etry ,signalling con strain ts ,ti m etab le o r headw ay conditi on s ,tracti on equ i pm en t behavi ou r and civil engineering speed restricti on s ,a train m ovem en t si m u lato r derives the sp eed ,po siti on and op erati on m ode of each train at each and every specific ti m e in tervals .O ne of the key facto rs in train m ovem en t is inevitab ly the tractive effo rt p roduced by the tracti on m o to rs .Perfo r m ance of the tracti on m o to rs is a functi on of train vo ltage and cu rren t w h ich are in tu rn calcu lated by the tracti on pow er system si m u lato r acco rding to train sp eed ,po siti on and operati on m ode .A s a resu lt ,in teracti on s betw een pow er system and train m ovem en t si m u lato r are necessary fo r the con siderati on of dynam ic train behavi ou r .

3　Si m ula tion and Appl ica tion s

Tw o si m u lati on app roaches on the m odels described are discu ssed here ,one w ith the 001交通运输系统工程与信息2005年6月

the o ther w ith a new m ethod of p robab ilistic calcu lati on w h ich p rovides an alternative p ro spective.Som e exam p les of si m u lati on resu lts are show n here to illu strate the differences in their functi onalities.A num ber of app licati on s of tracti on pow er system si m u lati on are then given to dem on strate its value in p ractice.

3.1　D eter m i n istic si m ula tion

In m o st app licati on s on op erati on and design, the fu ll details of in teracti on s am ong train s th rough the tracti on pow er system and betw een feeding system and train s are called fo r. Si m u lati on s under differen t operati onal conditi on s and traffic dem ands(o r‘w hat2if’scenari o studies),including no r m al and ex trem e,are requ https://www.360docs.net/doc/5811517897.html, p rehen sive m odels w ith the con siderati on s stated in the p revi ou s secti on s are requ ired in the si m u lati on and the netw o rk so lu ti on,how ever tedi ou s,is attained deter m in istically w ith respectab le accu racy.

T racti on pow er system si m u lati on is ti m e2 based and accom p an ied by a train m ovem en t si m u lato r.F rom all last know n train sp eeds and po siti on s,the pow er system si m u lato r estab lishes the pow er netw o rk w ith resp ect to the train po siti on s,track layou t and feeding arrangem en t; and so lves fo r the vo ltages and cu rren ts fo r one ti m e step.W ith the train vo ltages and cu rren ts p assed back to the train m ovem en t si m u lato r,it calcu lates the nex t train speeds and po siti on s. T he p rocess then repeats at every ti m e in terval. T h is rep etitive in teracti on betw een the pow er system and train m ovem en t si m u lato rs is illu strated in F ig.6.Softw are i m p lem en tati on is qu ite straigh tfo r w ard bu t still tedi ou s. N onetheless,system atic data m anagem en t and sub stan tial am oun t of data sto rage are strongly requ ired.

F igs.7and8show the sam p le resu lts of vo ltage and cu rren t variati on s at a feeding sub stati on in a typ ical DC m etro line w ith nom inal vo ltage of1.5kV.T hey indicate the loading at the sub stati on at a p articu lar traffic conditi on, and peak s and ranges of variati on s can

be

F ig.6　Interacti on betw een pow er system

and train movem ent si m ulato rs

iden tified easily.F igs9and10illu strate the vo ltage and cu rren t of a train as it m oves along the line and they allow m on ito ring of the train pow er dem and.T he resu lts from the pow er system si m u lati on al w ays co rrespond to the train m ovem en t.Fo r exam p le,cu rren t peak and vo ltage di p indicate accelerating train w h ilst a train in regenerative b rak ing is reflected by negative cu rren t flow and vo ltage rise

.

F ig.7　T rain vo ltage against

distance

F ig.8　T rain current against distance

T he ou tcom es from the pow er netw o rk si m u lato r are the exact vo ltages,cu rren ts and pow er flow p rofiles at all crucial po in ts in the netw o rk at every ti m e step over a peri od of ti m e.T hey are p roven to be very u sefu l fo r pow er engineers, rail w ay operato rs and m ain tenance personnel alike.How ever,as the resu lts com e from ti m e2

101

第3期T racti on Pow er System Si m ulati on in E lectrified R ail w ays

F ig .9　Substati on vo ltage against ti m

e

F ig .10　Substati on current against ti m e

con sum ing calcu lati on s and the ou tp u t data is

often vo lum inou s (w ith the size of the pow er netw o rk and num ber of train s )fo r analysis ,no t to m en ti on the po ssib ility of fu rther p rocessing and sto rage ,detail redundancy ,though an advan tage at ti m es ,is a draw back of th is deter m in istic app roach fo r certain app licati on s .Even though the resu lts give detailed accoun t of the electrical behavi ou r of the pow er system s and train s ,it has to be said that no t every detail is requ ired in m o st app licati on s .

M o st of the ex isting tracti on pow er system si m u lato rs

[6,12-15]

,as w ell as o ther comm ercially availab le p ackages [16]

,em p loy th is deter m in istic app roach .T hey are also equ i pped w ith reasonab le u ser in terfaces to enab le the inpu t (and ou tp u t )of the vast am oun t of data requ ired fo r (and p roduced by )the si m u lati on .N early all of them have been tailo r 2m ade to su it the p u rpo ses of p articu lar system s o r specific studies and hence som e of them m ay no t be p roperly docum en ted in p ub lic dom ain .

3.2　Probab il istic si m ula tion

A

new ly

developed

alternative

is

a

p robab ilistic app roach in w h ich the ou tcom es are

p robab ility den sity functi on s (pdf )of vo ltage o r pow er flow at certain po in ts of the pow er system ,indicating the ranges of variati on s of

such

param eters and hence the loading conditi on s ,on p robab ilistic basis w ith a si m p le and ho listic rep resen tati on ,w h ile sk i pp ing the tedi ou s p rocess of ex tracting the requ ired data from huge am oun t of si m u lati on resu lts .How ever ,the traditi onal

tracti on pow er si m u lato rs by deter m in istic

app roach are no t to be rep laced by tho se from th is

p robab ilistic app roach .T he p robab ilistic app roach indeed p rovides a differen t view po in t of in sigh t in to the tracti on pow er system behavi ou r and hence su its differen t pu rpo ses of app licati on s .

To bu ild the necessary pdfs ,train po siti on is the starting po in t and its ow n pdf is estab lished from

typ ical

speed p rofiles of in ter 2stati on

run s [17]

,w h ich can be generated by an off 2line

train m ovem en t si m u lato r .T he random sam p le draw n

from

the

train

po siti on

cum u lative

p robab ility functi on is u sed to deduce train speed and operati on m ode ,and hence the train pow er dem and is derived from the tracti on equ i pm en t characteristics .W ith the loading conditi on s (train s )know n ,the pow er netw o rk is so lved to p roduce the vo ltage ,cu rren t and pow er flow at certain po in ts .T he p rocess is repeated w ith sufficien t num ber of random sam p les of train po siti on and the resu lting p dfs are fo r m ed in M on te Carlo si m u lati on techn ique .T he p rocess is summ arised in F ig .11.M u lti p le train s of specific ti m etab les (o r headw ays )are pu t in to the calcu lati on

acco rding

to

their

suppo sed

sep arati on s so that the effects they i m po se on

each o ther can be inco rpo rated [18]

.

A s there is no direct in teracti on betw een train m ovem en t and pow er system si m u lato rs in th is app roach ,the exact detail of the relati on sh i p betw een train vo ltage and speed m ay no t be fu lly reflected .A gain ,the p u rpo ses of the app licati on decide the level of details in the ou tp u t ,and thu s the si m u lati on app roach to be adop ted .

201交通运输系统工程与信息2005年6月

F ig .11　P rocessing from a train po siti on samp le to pow er system so luti on

T he resu lts from th is app roach basically give

the sam e info r m ati on on the tracti on pow er system behavi ou r over a p eri od of ti m e as in the deter m in istic app roach and they rely on the sam e m odelling con siderati on s in the calcu lati on .T he m ain difference is in the fo r m ats of ou tpu t p resen tati on .A s show n in the sam p le resu lts p resen ted here ,the sizab le data on the variati on s of a circu it p aram eter (vo ltage ,cu rren t o r pow er flow )is cap su lated in a single grap h of p robab ility den sity functi on w hereas the details of exact value at a specific po in t of ti m e are h idden .D esp ite the differen t in terp retati on s of ou tpu t ,com pu tati on dem and on tracti on pow er system si m u lati on is how ever very m uch si m ilar in bo th deter m in istic and p robab ilistic app roaches .T he general exp erience in th is app roach is that the M on te Carlo si m u lati on requ ires at least 10,000sam p les to estab lish reliab le p dfs .

P robab ilistic

app roach

is

no t

yet

as

comm on ly adop ted as the deter m in istic one bu t it serves its pu rpo ses as a supp lem en t to the fo r m er .

F ig .

12and F ig .

13are exam p les of

vo ltage and pow er dem and pdfs of a train in an A C rail w ay w ith A T feeding .W ith a nom inal supp ly vo ltage of 27.5kV ,the vo ltage sp reads over bo th sides of the nom inal value (and pow er p df sp illing on

bo th sides of 0MW ),w h ich indicates

that regenerative b rak ing is allow ed .F ig .14-F ig .

16com pare the pow er dem and pdfs at a feeding sub stati on under the sam e traffic conditi on s w ith the th ree differen t feeding arrangem en ts .A T feeding ,as exp ected ,p rovides better vo ltage regu lati on w ith a narrow er sp read in the p df .3.3　Appl ica tion s

T here

have

been

num erou s

p ractical

F ig .12　T rain vo ltage pdf

F ig .13　Pdf of active pow er dem and of a train

F ig .14　T rain vo ltage pdf of train w ith direct feeding

app licati on s of tracti on pow er system si m u lati on .Even though the ob jectives of the app licati on s m ay on ly focu s on a particu lar aspect of the pow er system ,the si m u lati on of the w ho le system is u sually needed to facilitate the fu ll functi on s of the aspect in questi on .System sizing on equ i pm en t and com ponen ts is an indispen sab le

3

01第3期T racti on Pow er System Si m ulati on in E lectrified R ail w ays

F ig .15　T

rain vo ltage pdf w ith BT feeding

F ig .16　T rain vo ltage pdf w ith A T feeding

step in the design stage .A s each rail w ay is

un ique in its traffic dem and ,track geom etry and operati on ,tests on pow er rating li m its o r capacities

[19]

and clai m ed p erfo r m ance

[20]

w ith

resp ect to the characteristics of the rail w ay system are com p u lso ry even befo re p rocu rem en t of the m ajo r equ i pm en t of the system .U n su rp risingly ,w ho le

system p erfo r m ance analysis w ith com p lete inco rpo rati on of train

m ovem en t

si m u lato r

[21]

to

exam ine

the

com p atib ility am ong differen t sub 2system s ,as w ell as their ow n functi onalities ,is al w ays one of the m ain p u rpo ses of si m u lati on .W h ile a fu ll system

analysis

w arran ts si m u lati on of

deter m in istic app roach ,the uncertain ty on som e system p aram eters at early stage of p lann ing m ay find the p robab ilistic app roach m o re su itab le . D ynam ic behavi ou r of the pow er system in the cou rse of operati on is ano ther m ajo r top ic of in terest .A s vo ltage stab ility is vital to con sisten t train p erfo r m ance ,a num ber of studies have investigated vo ltage fluctuati on s in differen t

system s [22-24]

under vari ou s op erati on conditi on s .

A pp licati on s ,such as studies on stray cu rren t [25]

,

touch vo ltage [26]and earth cu rren t [27]

,are also

found w ith good ex ten t of success ;w h ile analysis

on har m on ics [28],fau lt detecti on [29]

and electrom agnetic com p atib ility needs the tracti on pow er system si m u lati on as an aux iliary too l to supp ly background data .Fo r pow er engineers ,resu lts

from

p robab ilistic

si m u lati on

give

sufficien t indicati on s to peak dem and and vo ltage variati on s .O n the o ther hand ,rail w ay op erato rs

m ay need detailed si m u lati on resu lts w hen they need to investigate con tinuou s changes on vo ltage and cu rren t over a specific ti m e 2sp an .

In additi on to studies related to the pow er system ,tracti on pow er system si m u lati on has also com e to the aid of train operati on and

con tro l

.W hen train op erati on is m an i pu lated to fit particu lar ti m etab les o r schedu les ,the resu lting pow er dem and and o r energy con sum p ti on have to be checked fo r po ssib le saving and o r infringem en t of system con strain ts .Pow er system si m u lati on has been em p loyed to evaluate the i m pacts and m erits of re 2starting

regi m es of train queues [30]

and differen t coasting con tro l strategies to m eet run 2ti m e

requ irem en ts [31]

by si m p ly p roviding the data on the supp lied pow er and energy under specific train op erati on arrangem en ts .

4　FurtherR Cha llenges

Si m u lati on

al w ays

relies

on

accu rate

m odelling of the functi on s and behavi ou r of the system to p roduce reliab le resu lts .In tracti on pow er system si m u lati on ,the m odels on vari ou s com ponen ts of the system are qu ite m atu re .D esp ite con tinu ing effo rt to pu rsue m o re accu rate and elabo rated m odels ,such as rail track ,rail

i m p edance ,m o to rs [32-34]

and even driver behavi ou r ,

the

ou tpu ts

from

the

ex isting

si m u lato rs are of accep tab le accu racy upon verificati on .T here are al w ays new system s o r set 2up s w h ich requ ire differen t m odelling and

M eglev is one exam p le [35-37]

.Fu rther developm en t on m odelling often enhances the level of details in the ou tp u t o r targets selected

investigati on ob jectives .

401交通运输系统工程与信息2005年6月

O n the o ther hand,com pu tati onal dem and is certain ly go ing up w ith m o re com p licated m odels. If it is desirab le to m ain tain the app licab ility of the si m u lato rs o r even to inco rpo rate them in to on2line con tro l softw are in an adviso ry ro le in the fu tu re,parallel p rocessing techn iques[38]to reduce com p u tati on ti m e and a carefu lly structu red app roach to softw are validati on are requ ired. Parallel p rocessing can be app lied to bo th hardw are and softw are.W ith hardw are,a num ber of p rocesso rs can be connected in a specific configu rati on and the difficu lty is to sp read the com pu tati on even ly to the p rocesso rs to ach ieve the m ax i m um th roughpu t.O n the configu rati on of p rocesso rs,there are m any po ssib le system s,based on differen t p aram eters such as con tro l m echan is m,m em o ry configu rati on and num ber of p rocesso rs.Since the m atrix is a22D data structu re,it can be easily m apped in to a linear o r a m esh array.

Even w ith a single p rocesso r,p arallel p rocessing is still po ssib le w ith the aid from softw are.PC s are still the comm on adop ted p latfo r m s fo r si m u lati on and their pop u lar In ter Pen tium III o r above p rocesso rs allow p arallel data p rocessing w ith in their structu re.T hey include S I M D(Single In structi on M u lti p le D ata) registers w here data p arallel op erati on s can be p erfo r m ed si m u ltaneou sly.Stream ing S I M D ex ten si on has p rovided a pow erfu l com pu tati on too l fo r p erfo r m ance i m p rovem en t.T he SSE registers are1282b it w ide and they can sto re floating2po in t values,as w ell as in tegers and characters.T here are eigh t SSE registers in a single p rocesso r,each of w h ich can be directly addressed u sing the designated nam es.U tilising the SSE registers in the tracti on pow er system si m u lati on softw are becom es a straigh tfo r w ard p rocess w hen su itab le too ls[39]are availab le.In the case of in tegers,eigh t162b it in tegers can be sto red and p rocessed in p arallel.Si m ilarly, p arallel m an i pu lati on of fou r322b it floating2po in t values also fit the1282b it registers.

W ith322b it float2po in t num bers rep resen tati on in the tracti on pow er si m u lato r,a m ax i m um com pu tati onal speed2up rati o of4is expected w ithou t any additi onal hardw are.In a p revi ou s study[40],a speed2up rati o of around3is ach ieved w ith LU decom po siti on of m atrix, depending upon the size of the m atrix.T he m ain reason fo r no t attain ing the m ax i m um speed2up of SSE m echan is m is the p rocessing overhead on pack ing data in to,as w ell as unpack ing data from,the1282b it fo r m at.T he num ber of p ack ing and unpack ing operati on s is p ropo rti onal to N2, w here N is the size of the m atrix.Softw are techn iques,such as loop ro lling and p re2fetch ing, have been app lied in a sub sequen t study[41]to i m p rove the sp eed2up rati o sligh tly.Fu rther w o rk s on em p loying assem b ly codes to accelerate the execu ti on of th is secti on of softw are p rogram are now undertaken.

5　Conclustion

T h is paper review s the key m odelling featu res in tracti on pow er system si m u lati on and h igh ligh ts the difficu lties w ith the supp ly system s and loads.R esu lts attained from tw o app roaches of si m u lati on,deter m in istic and p robab ilistic,are p resen ted to illu strate the diversity of ou tpu t fo r m ats.A w ide range of successfu l app licati on s, electrical2related o r o ther w ise,has also been in troduced b riefly here to dem on strate the versatility of the si m u lati on s.Ex ten sive w o rk on parallel p rocessing is iden tified as one of the p ri m ary directi on fo r fu rther developm en t on tracti on pow er system si m u lati on,particu larly w hen it is to be included in real2ti m e app licati on s. T racti on pow er system si m u lati on has been a w idely adop ted bu t un sung com p u ter2aided engineering too l fo r rail w ay pow er engineers fo r the last tw o decades.T h is paper co llectively summ arises the research effo rt and exp erience on the ex isting si m u lato rs and their underlying p rinci p les.W ith the advances in hardw are and softw are,new ly developed tracti on pow er system si m u lato rs m ay evo lve w ith fresh functi onalities

501

第3期T racti on Pow er System Si m ulati on in E lectrified R ail w ays

and featu res bu t the fundam en tals on m odelling and system con strain ts rem ain.A ccu rate,reliab le and efficien t si m u lati on is still critically essen tial fo r studies and analysis of all natu res at the design,op erati on and p lann ing stages of electrified rail w ay system s,w h ich is an in tegrated p art of rail w ay tran spo rtati on system engineering.

ACKNOWL ED GE M ENTS

T he au tho rs gratefu lly acknow ledge the generou s financial suppo rt p rovided by the R esearch Gran t Council of Hong Kong(Po lyU 5104 51E).T he au tho rs w ish to thank the referees fo r their valuab le comm en ts w h ich certain ly helped i m p rove the pap er sub stan tially.

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