ELECTRICAL TRACTION, AND ITS SECURITY VOLUME: 16 |NUMBER: 2 |2018 |JUNE
T ack Occupancy De ec ion Using Ra io o
Open-Ci cui Impedance o Sho -Ci cui Impedance
Lubomi IVANEK 1, Pe ORSAG 1, Vladimi MOSTYN 2, Ka el SCHEE 3
1Depa men o Elec ical Enginee ing, Facul y o Elec ical Enginee ing and Compu e Science,
VSB–Technical Uni e si y o Os a a, 17. lis opadu 15, 708 00 Os a a, Czech Republic
2Depa men o Robo ics, Facul y o Mechanical Enginee ing, VSB–Technical Uni e si y o Os a a,
17. lis opadu 15, 708 00 Os a a, Czech Republic
3P ni signalni a.s., Bohuminska 368/172, 712 00 Os a a, Czech Republic
lubomi .i [email p o ec ed], p[email p o ec ed], ladimi .mos [email p o ec ed], sc[email p o ec ed]
DOI: 10.15598/aeee. 16i2.2662
Abs ac . This pape deals wi h he change o he
a io o he open ci cui impedance o sho -ci cui
impedance o he elec ic ac ion depending on he
dis ance o he ac ion ehicle om he beginning o
he sec ion. This a io is calcula ed in o de o es-
ima e he ac ion ehicle speed and he dis ance a
which he ack occupancy can be indica ed. The e o e,
he impedance moduli and he impedance phases o he
open ack ci cui and he impedance o he occupied
ack (sho -ci cui impedance) is compa ed a di e en
sho -ci cui dis ances. The impedances a io a ies
wi h changing wea he condi ions. I is di e en in d y
wea he han in he ain. The e o e, in p ac ical use,
he ack occupancy indica o mus always be upda ed
and he a io mus always be ecalcula ed o he new
si ua ion. In his pape , he impedances a io is calcu-
la ed o speci ic pa ame e s measu ed in he sec ion o
he ack in O lo a. The dis ance be ween a e e ence
poin (place o sho ci cui ails) om a measu ing
poin is o he impedance module a io o F=10 abou
218 m.
Keywo ds
Impedance, occupied ack, ail, ac ion, wo-
po .
1. In oduc ion
This pape is aimed a es ima ing how he pa ame-
e Fo ailway ac ion is changed depending on he
leng h o he occupied sec ion. Fis he a io o he in-
pu impedance o he unoccupied ack ci cui sec ion
o he inpu impedance o he occupied ack pa s o
he same ac ion sec ion. Inpu impedance measu e-
men s can be used o he occupancy de ec ion o he
examined sec ion i a io Fis la ge enough. This pa-
pe uses da a measu ed a he ac ion in O lo a as
a model example. Thus, he dependence o F(x)on
he a iable xwas calcula ed based on he esul s o
he measu emen o he insula ed sec ion o he ac-
ion in he O lo a.
The a io F(x)o he open-ci cui inpu impedance
Z0 o he sho -ci cui inpu impedance ZSon he
leng h xo he examined sec ion was calcula ed.
The impedance o open-ci cui Z0is de ined as he
impedance o he open ail sec ion o a leng h l0.
F om he alue x=l0wi h inc easing dis ance x(i.e.
dis ance om he measu ing poin ), he open-ci cui
impedance is no longe changing. We di ided his con-
s an open-ci cui impedance alue Z0by he inpu
impedance o he sho -ci cui ZS(x) o he di e en
leng hs xo he sec ions o ob ain he desi ed depen-
dence F(x)as a unc ion o he a iable x.
The ac ions a e a highly a iable sys em om an
elec ical poin o iew. This conce ns he di e ences
in he ack layou on di e en acks and a di e en
loca ions, as well as he dependence o ack pa ame-
e s on wea he condi ions. The space be ween he ails
is o en di y, he dis ance o he ails om ea h is di -
e en . F equen ly, he ails a e in di ec con ac wi h
g a el, which ills he space be ween hem. The g a el
may be s eaked wi h ege a ion ha ouches he ails.
When e alua ing he occupancy o he sec ion, elec i-
cal pa ame e s o he ack change wi h he wea he
condi ions and he ime a iabili y o he ope a ing
condi ions mus also be aken in o accoun . The e-
o e, de e mining he pa ame e s o ail ac ion is
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a e y complex ask. The ime- a ying condi ions o
al e na ing cu en s (injec ed in o ails o ack ci -
cui s p o ec ion) in p ac ical applica ions equi e he
egula calib a ion o de ices, he unc ion o which is
based on he e alua ion o he ac ion elec ical pa-
ame e s. In his model example we do no ake in
he accoun he impedance be ween he wheels o he
ac ion ehicle which could inc ease he ans e se o
longi udinal impedance o he sec ion o ailway line.
The occupancy o ail oad acks by he ain wheels
and axles should be de ec ed, o example, nea he
ailway c ossing. The e o e, secu i y de ices mus ec-
ognize i he sec ion is occupied. I is o en also e-
qui ed o de e mine he speed o an app oaching e-
hicle. The occupied sec ion appea s o us as a sho -
ci cui in he place whe e he ac ion ehicle is loca ed
( he low impedance o ails sho ci cui h ough he
wheels and axles o he ac ion ehicle is neglec ed).
A ca ego y o he "Ea ly De ec ion" sys em is app o-
p ia e [1] o he de ec ion o he posi ion and speed
o a ain be o e ailway c ossing. These de ices a e
moun ed a he c ossing poin only and do no use any
emo e senso s. The e a e mul iple p inciples in his
ca ego y - o example, ada sys ems using Dopple ’s
p inciple o speed measu emen , Time-Domain Re lec-
ome y [2] - ansmi ing impulse o ack ci cui and
measu ing ansmission delay a e i s e lec ion, and
e en acous ic sys ems based on he ho n sound anal-
ysis. A e y good p inciple o de ec ing he ain’s
posi ion and speed, also included unde he "Ea ly De-
ec ion" ca ego y, is o measu e he wa e o m o he
impedance o he ack ci cui , which is sho ed by he
on and o he axles o he incoming ain. This p in-
ciple is al eady in use, bu i s sa e use is g ea ly ham-
pe ed by he high le el o in e e ence o he measu ing
signals caused by elec ic ac ion d i es o ains, by
he ansmission o signaling by means o ack ci cui s
and o he sou ces o elec ical in e e ence. Howe e ,
wi h he de elopmen o as Digi al Signal P ocesso s
(DSPs), i is possible o cons uc a measu ing de ice
esis an o his in e e ence and o accu a ely analyze
he sho -ci cui impedance o he ack ci cui .
The sensi i i y o he me hods compa ing he
changes in he impedance o he occupied and unoc-
cupied ack can be judged by he wa e o m o he
impedances a io F(x)measu ed on he open ack Z0
and he impedance on he sho -ci cui ed ack ZS.
Acco ding o his a io, we can deduce he place o he
sho -ci cui and ul ima ely he speed o he app oach-
ing ehicle. Ob iously, a a ce ain c i ical dis ance
lk, he a io is so small ha we will no egis e he
a i ing ehicle. The dependence o he a io F(x)on
he dis ances x om he measu ing poin can be de-
sc ibed by he analy ical unc ion and implemen ed in
he DITO (De ice o Indica ing o he T ack Occu-
pancy) de ice o de ec ing ack occupancy. Bo h he
modulus a io F(x)and i s phase can be e alua ed.
The second eason o de ec ion o he open-ci cui o
sho -ci cui impedance a io F(x)a e equen ime
changes o bo h impedances, caused in pa icula by
changes in he conduc i i y o he subsoil and ack
sleepe s [3]. While he open-ci cui impedance luc u-
a es g ea ly wi h he conduc i i y o he subsoil, he
sho ci cui impedance a ies ela i ely li le. How-
e e , i is possible o c ea e a calib a ion cu e o
he simula ion o he posi ion and speed o he ehi-
cle on he ack ci cui due o changes in he module
and phase o he impedance a io F(x). Calib a ion is
pe o med on he basis o he measu emen o an un-
occupied sec ion, i.e., when he e is no ehicle on he
ack.
We used he pa ame e alues om Tab. 1 o all he
calcula ions in his pape based on he impedances o
he ac ion ci cui s measu ed on he ack in O lo a
[3]. In he calcula ions, we eplaced he measu ed sec-
ion using a Π wo-po ne wo k. F om he impedance
o open-ci cui Z0and impedance o sho -ci cui ZS
(measu ed on he isola ed sec ion o he ailway line),
he ansmission ma ix cascading coe icien s Eq. (1)
and he ac ion pa ame e s we e i s calcula ed.
A=



Z0
Z0−ZS
ZS Z0
Z0−ZS
1
Z0(Z0−ZS) Z0
Z0−ZS




.(1)
Tab. 1: Open-ci cui and sho -ci cui impedance.
Impedance Z0
open-ci cui
Impedance ZS
sho -ci cui
(Hz) Z0(Ω) 0(◦) (Hz) ZS(Ω) S(◦)
74.76 13.25 −5.775.86 0.85 47.6
Pe -uni -leng h pa ame e s o he Πelemen [3] a e
calcula ed om he elemen s o he cascade coe icien
ma ix on he basis o Eq. (2) and Eq. (3) and a e
p esen ed in Tab. 2. He e, o compa ison, he mea-
su emen s a he equency o 275 Hz a e also gi en.
Z=A12 =R+jωL, (2)
Y=A11 −1
A12
=G+jωC. (3)
Tab. 2: Pe -uni -leng h pa ame e s o Πelemen .
(Hz)
R
(Ω·km−1)
G
(S·km−1)
L
(H·km−1)
C
(F·km−1)
75 1.05e+00 1.40e-01 2.61e-03 3.68e-05
275 1.56e+00 1.51e-01 2.06e-03 6.46e-06
The pa ame e s o di e en ypes o acks a y con-
side ably, as can be seen in he li e a u e [3], [4], [5],
[6], [7], [8] and [9]. We u he used he pa ame e s
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om Tab. 2 o c ea e a sample model case o a pa -
icula ailway ack. Fo his model case, we ha e
ound ou he a io o he open-ci cui and sho -ci cui
impedance measu ed a he inpu o he ack ci cui
Eq. (10).
2. De e mining Open-Ci cui
Impedance
As s a ed in he in oduc ion, he DITO se ings o
modi ied a ic condi ions a e co ec ed ( e-calib a ed)
a p ede e mined in e als based on he measu emen s.
The calib a ion is pe o med when he sec ion is no oc-
cupied. The ques ion is, how long he dis ance o he
sec ion o ailway line om he sou ce can be measu ed
o ob ain he inpu impedance o an open ci cui using
al e na ing cu en wi h a equency o 75 Hz o 275 Hz.
Thus, a wha sho es dis ance l0 he inpu impedance
changes minimal (wi h a equi ed ole ance), o exam-
ple, when he ail ci cui is powe ed by a 5A cu en
sou ce. The powe supply is ca ied ou a he mea-
su ing poin be ween he wo ails o he same ack as
shown in Fig. 1.
Oscilloscope
Ampli ie
Signal Gene a o
Powe Supply
Fig. 1: Block diag am o measu ing ac ion pa ame e s.
The wo-po ne wo ks a e he passi e and longi udi-
nally symme ical ones. Thus, in he case o he ailway
ac ion, he image pa ame e s o uni o mly dis ibu ed
line can be used o calcula e he inpu impedance. The
open-ci cui impedance is calcula ed om he inpu
ol age and cu en a ios Eq. (4), Eq. (5) and Eq. (6).
U10 =U20 cosh(γx),(4)
I10 =U20
Z
sinh(γx) =
=
U10
cosh(γx)
Z
sinh(γx) = U10
Z
anh(γx),
(5)
Z0=Z
anh(γx),(6)
whe e:
•U10 is he open-ci cui ol age a he inpu a he
poin o measu emen , i.e., a he beginning o he
es sec ion,
•U20 is he ol age a he end o he unoccupied
sec ion (a a dis ance o x=l0),
•Z is he image (cha ac e is ic) impedance
Z =qZ
Y,
•γis he p opaga ion cons an γ=Z·Y,
•xis he dis ance om he measu ing poin ( he
beginning o he sec ion).
Fi s o all, we a e in e es ed in he cons an open-
ci cui impedance alue Z0 o x=l0, whe e l0is he
limi ing (c i ical) leng h o he segmen . A dis ance
l0 he open-ci cui impedance a he inpu is no longe
changing wi h an inc easing x-coo dina e. The open-
ci cui impedance alues Z0a e hen c ucial o de e -
mining he a io F(x). F om he calcula ed wa e o m
o he open-ci cui impedance module alues Z0a e
isible in Fig. 2 up o 600 m in leng h and in Fig. 3 up
o 3000 m ( o 75 Hz). I is clea ha i he measu ed
sec ion is longe han 2500 m, we can expec a cons an
(s eady) inpu impedance alue o he unoccupied sec-
ion (open ci cui ).
Measu ed sec ion leng h (m)
0 100 200 300 400 500 600
Open-ci cui impedance
modulus (Ω)
0
200
400
600
800
1000
Fig. 2: Dependency o he unoccupied module Z0on he leng h
o he measu ed sec ion.
The impedance module sha ply dec eases - see Fig. 2.
I se les a he alue 4. Fo small alues o x, he g aph
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is d awn wi h a high inpu alue o he open-ci cui
impedance module. The si ua ion is mo e clea ly seen
om he g aph o he dis ances om 500 m o 3000 m,
see Fig. 3. Figu e 4 shows mo e complica ed depen-
dence o he phase inpu impedance o he unoccupied
sec ion.
Measu ed sec ion leng h (m)
500 1000 1500 2000 2500 3000
Open-ci cui impedance
modulus (Ω)
0
5
10
15
Fig. 3: De ail o he module Z0 o dis ance om 500 m.
Measu ed sec ion leng h (m)
0 500 1000 1500 2000 2500 3000
Open-ci cui impedance
modulus (Ω)
-10
-5
0
5
10
15
Fig. 4: Dependence o he Z0phase o he unoccupied sec ion
on he leng h o he measu ed sec ion.
The shape o he cu e shows a capaci i e cha ac e
a i s , which is logical o sho pa allel conduc o s
wi h a low ans e se conduc i i y. A abou 1500 m,
he ci cui is in esonance, and he cha ac e o he
ci cui is u he changed o induc i e. The induc-
i e na u e o he cu en loops, which a e closed o e
he ans e se conduc ion be ween he ails, is al eady
clea ly applied he e.
The DITO de ice will "calib a e" he new pa ame-
e s a in e als when he sec ion is unoccupied. Thus,
a cons an open-ci cui impedance alue is conside ed
when calcula ing he a io F(x). This impedance alue
is measu ed when he ins umen is calib a ed. When
he leng h o he measu ed sec ion inc eases, i does
no change much. In he example modeled he e we
chose Z0= (3.42 + 0.74j) Ω (designa ed o 3000 m).
3. De e mining he Impedance
o he Occupied Ci cui
In he case o he p esence o a ac ion ehicle in
he measu ed sec ion, he ails o he occupied acks
a e shun (a e eplaced by sho -ci cui ing). The in-
pu impedance o he measu ed sec ion dec eases wi h
he ehicle app oaching o he measu ing poin . The
sho -ci cui inpu impedance is again calcula ed om
he a io o sho -ci cui ol age o he sho -ci cui
cu en Eq. (7), Eq. (8) and Eq. (9).
U1S=Z I0
2Ssinh(γx) =
=Z
I1S
cosh(γx)sinh(γx) =
=Z I1S anh(γx),
(7)
I1S=I0
2Scosh(γx),(8)
ZS=Z anh(γx),(9)
whe e:
•I1Sis he inpu sho -ci cui cu en a he mea-
su ing poin , i.e., a he beginning o he es sec-
ion unde in es iga ion,
•I0
2Sis he cu en in he place o he sho -ci cui .
The g aphical dependencies o he sho -ci cui
impedance ZSon he ehicle’s dis ance om he mea-
su ed poin ( om he beginning o he sec ion) a e,
a 75 Hz, shown in Fig. 5 o he module and Fig. 6 o
he phase.
Measu ed sec ion leng h (m)
0 500 1000 1500 2000 2500 3000
Sho -ci cui impedance
modulus (Ω)
0
1
2
3
4
Fig. 5: Dependence o he ZSmodule on he ehicle’s dis ance
om he measu ing poin .
Measu ed sec ion leng h (m)
0 500 1000 1500 2000 2500 3000
Sho -ci cui impedance
modulus (Ω)
30
35
40
45
50
Fig. 6: Dependence o he ZSphase on he ehicle’s dis ance
om he measu ing poin .
4. Calcula e he Ra io F(x)
Ra io F(x)exp esses he p opo ion o cons an open-
ci cui inpu impedance (i will be measu ed on an un-
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occupied ack a de ined in e als, always o he same
leng h o he segmen ) o he a iable sho -ci cui
impedance Eq. (10). The g aphical ep esen a ion o
a io F(x)is shown in Fig. 5 ( o he module) and
Fig. 6 ( o he phase).
F(x) = ZS(x)
Z0(lk)=1
anh(γx) anh(γlk).(10)
The anh alue o he posi i e a gumen anges om
0 o 1. I can be said ha when he a gumen o a io
F(x)is equal o 2.5 he anh alue is e y close o
1, wi h he a gumen , equal o 0. I needs no being
conside ed in his case. The e o e, he lowe limi o
his a io may heo e ically be 1, bu p ac ically i is
g ea e .
The ela ionship can also be adjus ed o Eq. (11):
F(x) = 1
anh(γx) anh(γlk)=
=cosh(γ(lk+x)) + cosh(γ(lk−x))
cosh(γ(lk+x)) −cosh(γ(lk−x)).
(11)
The module alues F(x)in ela ion o he sho -
ci cui dis ance a e shown in Fig. 5 and Fig. 7 and he
a io phase alues F(x)in Fig. 8.
Based on he au oma ic measu emen o he open-
ci cui impedance a egula in e als on an unoccu-
pied ack, pa ame e s R,L,C,Ga e ecalcula ed
and he ins umen calib a ed o changed condi ions,
e.g. wea he .
Rolling s ock dis ance (m)
0 500 1000 1500 2000 2500 3000
Ra io F modulus (-)
0
50
100
150
200
Fig. 7: Dependence o he module a io F(x)on dis ance xo
he ehicle om he measu ing poin .
Rolling s ock dis ance (m)
50 100 150 200 250 300 350 400 450 500
Ra io F modulus (-)
0
10
20
30
40
50
Fig. 8: Module a io F(x)- de ail om 50 m o 500 m.
Rolling s ock dis ance (m)
500 1000 1500 2000 2500 3000
Ra io F modulus (-)
0
1
2
3
4
5
Fig. 9: Module a io F(x)- de ail om 500 m o 3000 m.
Rolling s ock dis ance (m)
0 500 1000 1500 2000 2500 3000
Ra io F a gumen (°)
-40
-35
-30
-25
-20
-15
Fig. 10: Dependence o he phase a io F(x)on he ehicle’s
dis ance om he measu ed si e.
The a io o module F(x)a he selec ed e e ence
alue Z0= (3.42+0.74j) Ω eaches a alue o abou 10
in abou 218 m. This a io, a i s glance, dec eases by
1.595 a 1.5 km, 1.34 a 1.9 km, 1.013 a 4.66 km, bu
hen again sligh ly inc eases om 29.7 km. I s abi-
lizes a alue 1.034. The limi dis ance l1a which he
DITO de ice is s ill able o egis e he sho -ci cui ing
o he ails on he basis o he module’s alues F(x)oc-
cu s a he a io F(x)>1.3(a 75 Hz). In his model
example his alue is achie ed in dis ance l1= 2000 m.
A a g ea e dis ance whe e he a io F(x)and he in-
pu impedance do no change du ing he sho -ci cui .
Thus, a io F(x)<1.3canno be used o he speed
es ima e and o he ack occupancy indica ion. In
his case, i is possible o use he ela i ely signi ican
change in he phase o he a io F(x).
5. Conclusion
Ensu ing he sa e y o ain c ossings is cu en ly an in-
c easingly di icul challenge. Ea ly closu e o a c oss-
ing h ough signaling o ga es also b ings secu i y isks
om undisciplined d i e s and o en disp opo iona ely
hinde s anspo . The op imum ime- o-lock se ing
by signaling o ba ie equi es a eliable posi ioning
and speed sys em o he ain app oaching he c oss-
ing. One o he p inciples ha can be used o loca e
he ain and de e mine i s speed is o measu e he
wa e o m o he impedance o he ack ci cui sho -
ci cui ed by he app oaching ain.
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ELECTRICAL TRACTION, AND ITS SECURITY VOLUME: 16 |NUMBER: 2 |2018 |JUNE
In o de o p epa e he design o he equipmen o
his ac i i y, we p epa ed a me hodology o analyzing
he changes in he impedances a ios o he occupied
and unoccupied sec ion. F om hese backg ounds, de-
signe s o he occupancy indica ion sec ion judge how
o se he inpu o his de ice so ha i can unc ion
p ope ly. The esul s o his pape may be help ul in
doing so.
Acknowledgmen
This publica ion is suppo ed by p ojec SP2017/152
"Resea ch o an enna sys ems, diagnos ics and elia-
bili y o elec ical machines and equipmen " and by
p ojec TA04031780.
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Abou Au ho s
Lubomi IVANEK was bo n in F ydek Mis ek in
he Czech Republic. He g adua ed om he VSB–
Technical Uni e si y Os a a, Facul y o Mechanical
and Elec ical Enginee ing, ea ned his Ph.D. deg ee
om he Czech Technical Uni e si y in P ague,
Depa men o Theo e ical Elec ical Enginee ing. As-
socia e P o esso deg ee ecei ed a he VSB–Technical
Uni e si y o Os a a in he ield o Theo e ical Elec-
ical Enginee ing. His esea ch in ol es he wa es
p opaga ion and an ennas, ma hema ical modelling o
he elec omagne ic ield, s ay cu en unde elec ic
ac ions.
Pe ORSAG was bo n in P e o , he Czech
Republic in 1963. He ecei ed his M.Sc. deg ee
in Elec ical Machines and Elec ical D i es om
VSB–Technical Uni e si y o Os a a in 1988 and
Ph.D. deg ee om VSB–Technical Uni e si y o
Os a a in 1999. A p esen he is a senio lec u e
a VSB–Technical Uni e si y o Os a a. His ield
o in e es is elec omechanical sys ems diagnos ics,
powe e iciency o he adjus able speed d i es and
modelling o elec ical sys ems.
Vladimi MOSTYN was bo n in P ilepy in
he Czech Republic. He ecei ed he M.Sc. deg ee
c
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ELECTRICAL TRACTION, AND ITS SECURITY VOLUME: 16 |NUMBER: 2 |2018 |JUNE
in Elec ical Enginee ing in 1979 om he VSB–
Technical Uni e si y o Os a a, Czech Republic.
Since 1990, he has been an Assis an P o esso wi h
he Depa men o Robo ics and he ecei ed he
Ph.D. deg ee in 1996 in Con ol Enginee ing a he
same uni e si y. In 2006 he was appoin ed by he
p esiden o Slo ak Republic o deg ee P o esso in
b anch P oduc ion Sys ems wi h Indus ial Robo s
and Manipula o s a e a success ul accomplishmen
o he p ocess o awa ding a p o esso ship a he
Technical Uni e si y o Kosice, Slo ak Republic. Now
he is wo king as p o esso a he Depa men o
Robo ics a he Facul y o Mechanical Enginee ing
a he VSB–Technical Uni e si y o Os a a, Czech
Republic. He is he au ho o wo books and mo e han
80 a icles. His esea ch in e es s include obo ics,
simula ion o he complex mecha onic sys ems and
compu e aided sys ems. P o eso Vladimi Mos yn
is an Associa e Edi o o he jou nal MM Science
Jou nal and he membe o Czech Associa ion o
Robo ic Su ge y.
Ka el SCHEE was bo n in Opa a in he Czech
Republic. He ecei ed his M.Sc. om VSB–TUO in
1999. His esea ch in e es s include au oma ion o ail
anspo .
c
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