ene gies
A icle
Two-Te minal Algo i hm Analysis o Unsymme ical
Faul Loca ion on 110 kV Lines
Zuzana Buk iso a *, Ja osla a O sago a , Da id Topolanek and Pe Toman
Depa men o Elec ical Powe Enginee ing, B no Uni e si y o Technology, Technicka 12, 61600 B no,
Czech Republic; [email p o ec ed].cz (J.O.); opolanek@ u b .cz (D.T.); [email p o ec ed].cz (P.T.)
*Co espondence: [email p o ec ed].cz; Tel.: +420-606-202-347
Recei ed: 5 Ma ch 2019; Accep ed: 25 Ma ch 2019; Published: 27 Ma ch 2019


Abs ac :
This wo k analyses a wo- e minal algo i hm designed o loca e unsymme ical aul s on
110 kV powe ansmission lines. The algo i hm p ocesses synch onized ol age and cu en da a
ob ained om bo h ends o he p o ec ed ansmission line and calcula es he dis ance o he aul .
I is based on decomposing he equi alen ci cui in o he posi i e-, nega i e- and ze o-sequence
componen s and inding he poin whe e he ou pu ol ages o he igh and he le side o he
ansmission line a e equal. Compa ed o he con en ional dis ance elay loca o , he accu acy o
his me hod is highe and less in luenced by he aul esis ance, he pa allel-ope a ed line e ec
and line asymme y, as discussed in his wo k. I is, howe e , e y sensi i e o he synch oniza ion
accu acy. The ma hema ical model o he powe sys em was c ea ed in he PSCAD (Powe Sys ems
Compu e Aided Design) en i onmen and he compu a ional algo i hm was implemen ed in
Ma hema ica so wa e.
Keywo ds: unsymme ical aul loca ion; wo- e minal algo i hm; sequence componen s
1. In oduc ion
To loca e a aul du ing single-phase aul s in a 110 kV line, a aul loca o , which is one o he
unc ions o dis ance p o ec ion, is cu en ly used. The basic pa ame e s o a p o ec ed line a e se in
he elay and used o compu e he aul dis ance and usually o ini ia e he loca o unc ion as well.
Basically, a e he pick up o he ip o he dis ance p o ec ion, a sho -ci cui loop is de e mined
and he cu en s and ol ages measu ed in his loop a e used o he sho -ci cui loop eac ance and
esis ance calcula ion. A e ha , a aul loop and i s impedance
ZL
h ough he measu ed phase
cu en s and ol ages a e de e mined. I a g ound aul loca ion is calcula ed, i is necessa y o ake
accoun o alues o he esidual compensa ion ac o s R
E
/R
1
,X
E
/X
1
as well. The compu a ional
algo i hm used o he aul impedance
ZL
de e mina ion is based on he solu ion o he sho -ci cui
loop using he alue o he ol age measu ed a he p o ec ion connec ion poin , he cu en in
he o wa d di ec ion ( o he aul ) and he cu en in he backwa d di ec ion (back o he poin o
measu emen ). In he case o a single-phase aul in phase i(i= 1, 2, 3) i will be:
ZL =ULi
ILi−kEIE
. (1)
The aul dis ance is e alua ed om he eac ance o he aul
XL
, which is he imagina y
componen o he aul impedance
ZL
. Thus, he co ec e alua ion o he single-phase aul dis ance
is always s ongly dependen on he eac ance pe kilome e
XL
and esidual compensa ion ac o
kE
o he p o ec ed line se in he dis ance elay.
Since mos o he 110 kV lines a e no ully ansposed, aul loca o e o s a e o en caused by
unequal impedance alues o he phase-g ound loops and mu ual impedances o hese loops. Ano he
Ene gies 2019,12, 1193; doi:10.3390/en12071193 www.mdpi.com/jou nal/ene gies
Ene gies 2019,12, 1193 2 o 14
e o can be caused by non-homogenei y o he ansmission line. Non-homogenei y means ha he
line pa ame e s a e no cons an o he whole line leng h bu a y in indi idual sec ions. Typical
examples a e changes in c oss-sec ion o di e en g ound wi e conduc i i y. Nega i e e ec o he aul
esis ance on aul loca ion is desc ibed in [
1
,
2
]. In sys ems wi h pa allel-ope a ed lines, he accu acy
o he aul loca ion is also g ea ly in luenced by mu ual impedances. In gene al, he g ound wi e
conduc i i y and he sho -ci cui con ibu ion o he pa allel line powe supply will ha e he majo
in luence on he loca o e o a e.
Many esea che s ha e ocused hei a en ion on possible e o elimina ion. The p oposed
algo i hms di e depending on he inpu da a hey ha e a ailable and he me hod o calcula ion.
The me hods can be di ided in o h ee main g oups:
•T a elling wa e-based me hods,
•A i icial in elligence-based me hods,
•Impedance-based me hods.
1.1. T a elling Wa e- and A i icial In elligence-Based Me hods
T a elling wa e-based compu a ional me hods a e usually based on he co ela ion be ween
he o wa d and backwa d wa es ha a el alongside he ansmission line. When a aul occu s,
he wa es a el om he poin o he aul o bo h ends o he ansmission line. The aul is hen
iden i ied using he ansien -s a e analysis. Some s udies [
3
,
4
] sugges c ea ing a da abase o a ious
aul scena ios o make he ansien analysis easie .
These me hods can wo k wi h one- o mul iple- e minal da a. The accu acy o hese algo i hms is
mainly dependen on he da a sampling a e. Fo he aul de ec ion, he wa ele ans o m p o es o
be e y eliable.
In elligen echniques help o imp o e e iciency o he aul de ec ion and classi ica ion.
The ad an age o using neu al ne wo k is i s abili y o ecognize a pa e n and ca ego ize he da a.
Acco ding o [5], he mos used echniques based on he a i icial in elligence a e:
•Expe Sys em Techniques,
•A i icial Neu al Ne wo ks,
•Fuzzy Logic Sys ems.
Recen ly, a use o ime- ime (TT) ans o m in signal p ocessing has been discussed [
6
]. Re e ence [
7
]
p oposes o apply TT- ans o m o se ies-compensa ed lines, which p o ed o be e icien e en when
p ocessing a signal in luenced by high noise. In [
8
], he TT- ans o m and a aul classi ica ion based
on suppo ec o machine (SVM) is used o loca e aul on a hyb id line. Al hough his echnique
p ocesses ansien ol age signal ob ained om only one end, he aul was iden i ied and loca ed wi h
a high accu acy.
1.2. Impedance-Based Me hods
The basic p inciple o he impedance-based algo i hms o he aul loca ion calcula ion is simple.
The p o ec ion elay uses posi i e and ze o sequence impedances and measu ed ol ages and cu en s
o de e mine he dis ance o he aul by calcula ing he impedance, as desc ibed by Equa ion (1). These
me hods a e simple and commonly used and hei accu acy can be signi ican ly imp o ed i da a om
mul iple e minals is acqui ed.
Algo i hms ha use only local measu emen da a a e called single-ended (o one- e minal)
algo i hms. These me hods a e o en implemen ed, e.g., in mic op ocesso -based p o ec i e elays
[9,10]
.
Thei ad an ages a e simplici y due o hei lack o communica ion equi emen s. Howe e , he accu acy
o hese me hods is g ea ly in luenced by aul esis ance, load low and sou ce impedances. In [
11
],
a single-ended echnique, which is based on using he cu en and ol age measu emen s a local e minal
and an es ima ed sho -ci cui capaci y o he emo e sys em, is p oposed. Al hough his me hod is no
una ec ed by he p oblems men ioned abo e, he e o s we e wi hin accep able limi s.
Ene gies 2019,12, 1193 3 o 14
Two- e minal algo i hms wo k wi h he measu emen s om bo h ends o he ansmission
line. These algo i hms can be u he di ided in o me hods using synch onized o unsynch onized
measu emen s. I is also possible o p ocess da a om mul iple e minals o imp o e he accu acy o
he calcula ion.
Using he synch onized wo- e minal ol age and cu en phaso s, he calcula ion o he aul
loca ion is signi ican ly imp o ed [
1
]. The da a collec ed om digi al eco de s is e alua ed in a cen al
compu e using specialized so wa e. Wi h he elecommunica ions de elopmen , he synch oniza ion
and as and eliable measu ed phaso da a exchange a e becoming easie and he e o e i is possible
o implemen hese algo i hms di ec ly in o he p o ec ion. The ad an ages o hese me hods a e:
•
Elimina ion o aul loca ion e o s caused by inaccu acies in esidual compensa ion
ac o s de e mina ion,
•Supp ession o an e o caused by he aul esis ance,
•Reduc ion o he e ec s o mu ual coupling and line asymme y.
The impedance-based me hods a e cu en ly he mos widely used me hods o aul loca ion and
wi h he de elopmen and ins alla ion o he phaso measu emen uni s (PMUs) o digi al elays wi h
global posi ioning sys ems, he echniques based on he undamen al powe equency componen s
can be imp o ed. The bigges ad an age o hese echniques, p oposed e.g., in [
12
–
14
], is ha he e o
caused by a ia ions in he sou ce and aul impedances is elimina ed. Ex ensi e placing o he PMUs
is, howe e , e y limi ed by he high ins alla ion cos s and he e o e, some wo ks ocus on de eloping
an op imal PMU placemen s a egy [
12
]. Mo eo e , he de eloped echniques a e o en in luenced by
o he ac o s, such as need o high da a sampling a e [14].
Re e ence [
13
] p oposes a me hod ha u ilizes synch onized ol age and cu en da a de i ed a
bo h ends o he ansmission line and exp esses he ol age ac oss he aul in e ms o he measu ed
da a. This wo k is based on simila p inciple and i will be discussed la e in his ex . Compa ed
o [
13
], howe e , he exac e alua ion o he aul dis ance is no pe o med. Ins ead, he accu acy o
he analyzed algo i hm is imp o ed by using no only posi i e-, bu nega i e-sequence componen s as
well. Then, he leas squa e me hod is applied o ind he poin o he aul .
Some pape s [
15
–
17
] y o emo e he need o ob aining synch onized da a. Re e ence [
15
]
sugges s modi ying he echnique in oduced in [
13
] by conside ing only he magni udes o he ol age
a he aul poin . This assump ion allows o use unsynch onized phaso s o measu ed ol ages and
cu en s and emo e he e o caused by he unsynch onized da a. Me hods desc ibed in [
16
,
17
] a e
based on a simple assump ion ha a aul impedance is pu ely esis i e. Finding a solu ion o his
condi ion is hen used o ind he synch oniza ion angle.
Al hough hese algo i hms enable o use he unsynch onized measu emen s, which is a big
imp o emen , he main aim o his wo k is o ind a usable me hod o he aul loca ion on 110 kV lines
in he Czech Republic, which a e sho and o en pa allel-ope a ed. Me hods p oposed in [
15
–
17
] do no
deal wi h he e ec o he pa allel line. In his wo k, he e ec o mu ual coupling is ully conside ed.
The es o he pape is o ganized as ollows: Sec ion 2desc ibes he basic p inciple o he
algo i hm. Sec ion 3discusses he model used o es ing he me hod and esul s o a ious scena ios.
Sec ion 4gi es he conclusions.
2. Desc ip ion o he Analyzed Algo i hm
Fi s ly, a me hod using he one- e minal app oach will be desc ibed o ou line a basic p inciple
o he p oposed impedance-based algo i hm and he e o s ha can occu . The pa allel-ope a ed
line e ec is desc ibed he e as well. La e in his sec ion, an analyzed wo- e minal algo i hm will
be discussed.
Ene gies 2019,12, 1193 4 o 14
2.1. Basic Desc ip ion o he One-Te minal Algo i hm
Figu e 1displays a si ua ion when a single-phase aul wi h a aul esis ance R
occu s in a
ansmission line. The aul is loca ed in he dis ance dmeasu ed om he loca o a he x-poin ,
he o al line leng h is l. Using his example, an idea o one- e minal algo i hm e o s can be gi en.
Ene gies 2018, 11, x 4 o 15
2.1. Basic Desc ip ion o he One-Te minal Algo i hm
Figu e 1 displays a si ua ion when a single-phase aul wi h a aul esis ance R occu s in a
ansmission line. The aul is loca ed in he dis ance d measu ed om he loca o a he x-poin , he
o al line leng h is l. Using his example, an idea o one- e minal algo i hm e o s can be gi en.
Figu e 1. A simpli ied aul y ansmission line scheme.
An equi alen ci cui is o med by he in e connec ion o impedance sequence componen
ci cui s and he aul esis ance—see E o ! Re e ence sou ce no ound.. The indexes o he posi i e,
nega i e and ze o-sequence componen s a e 1, 2 and 0, espec i ely. I he Ki chho ’s ci cui laws
a e applied in indi idual loops o he equi alen ci cui , an e alua ion o he aul dis ance d using
he cu en x
Iand ol age x
U a io used by he loca o placed a he x-poin can be done:
()
1 2 0 1x 1L 2x 1L 0x 0L 0x 1L 0x 1L
1x 2x 0x
x
x 1x2x0x 1x2x0x
U U U dIZ IZ IZ IZ IZ
UU U
U
IIII III
+++ + + + −
++
==
++ ++ , (2)
()()
1 2 0 1L 1x 2x 0x 0x 0L 1L
x
x1x2x0x
..UU U dZI I I IdZ Z
U
IIII
+++ ++ + −
=++ . (3)
I 0L 1L E 1L
3
Z
ZkZ−= (whe e 0L
Z
and 1L
Z
a e line impedances pe uni leng h o a ze o- and
posi i e-sequence componen , espec i ely, and E
k is a esidual compensa ion ac o ) is assumed,
hen:
0x E 1L 1 2 0 1 2 0 xEx
1L 1L E
xx1x2x0x x1x2x0x
31
IkZ U U U U U U
UI
dZ dZ k
I I II I I II I
 
++ ++
=+ + = + +
 
++ ++


, (4)
whe e he ol age a he aul poin can be w i en as:
()()()()
1 2 0 1x 1y 2x 2y 0x 0y Ex Ey
33 3U U U RI I RI I RI I RI I++= += + = + = + . (5)
Applying hese equa ions, he impedance measu ed by he loca o a he x-poin is:
Ex Ey
xEx
1L E
xxx
.1
II
UI
dZ k R
III
+

=++

 (6)
and simila ly, o he loca o placed a he y-poin :
()
yEyExEy
1L E
yyy
.1
UIII
ldZ k R
III

+
=− + +



. (7)
I he line pa ame e s 1L
Z
and E
k, aul esis ance R and he ea h cu en s Ey
I and Ex
I
acqui ed om bo h ends a e known, he Equa ions (6) and (7) can be used o p ecisely calcula e he
aul dis ance. I hese alues a e no ob ained, he loca o algo i hm co ec ion me hod will always
be jus an es ima ion and he e o e po en ially able o ac ually inc ease he loca o e o . E en mo e
complica ed si ua ion occu s o he pa allel-ope a ed lines, when he equi alen ci cui con ains also
he pa allel-line sequence impedances—in he E o ! Re e ence sou ce no ound. d awn in ed.
Figu e 1. A simpli ied aul y ansmission line scheme.
An equi alen ci cui is o med by he in e connec ion o impedance sequence componen ci cui s
and he aul esis ance—see Figu e 2. The indexes o he posi i e, nega i e and ze o-sequence
componen s a e 1, 2 and 0, espec i ely. I he Ki chho ’s ci cui laws a e applied in indi idual loops
o he equi alen ci cui , an e alua ion o he aul dis ance dusing he cu en
Ix
and ol age
Ux
a io
used by he loca o placed a he x-poin can be done:
Ux
Ix
=U1x +U2x +U0x
I1x +I2x +I0x
=U1 +U2 +U0 +dI1xZ1L +I2xZ1L +I0xZ0L +I0xZ1L −I0xZ1L
I1x +I2x +I0x
, (2)
Ux
Ix
=U1 +U2 +U0 +d.Z1L.I1x +I2x +I0x+I0xdZ0L −Z1L
I1x +I2x +I0x
. (3)
I
Z0L −Z1L =
3
kEZ1L
(whe e
Z0L
and
Z1L
a e line impedances pe uni leng h o a ze o- and
posi i e-sequence componen , espec i ely, and
kE
is a esidual compensa ion ac o ) is assumed, hen:
Ux
Ix
=d Z1L +I0x3kEZ1L
Ix!+U1 +U2 +U0
I1x +I2x +I0x
=dZ1L1+kE
IEx
Ix+U1 +U2 +U0
I1x +I2x +I0x
, (4)
whe e he ol age a he aul poin can be w i en as:
U1 +U2 +U0 =3R I1x +I1y=3R I2x +I2y=3R I0x +I0y=R IEx +IEy. (5)
Applying hese equa ions, he impedance measu ed by he loca o a he x-poin is:
Ux
Ix
=d.Z1L1+kE
IEx
Ix+R
IEx +IEy
Ix
(6)
and simila ly, o he loca o placed a he y-poin :
Uy
Iy
=(l−d).Z1L 1+kE
IEy
Iy!+R
IEx +IEy
Iy
. (7)
I he line pa ame e s
Z1L
and
kE
, aul esis ance R
and he ea h cu en s
IEy
and
IEx
acqui ed
om bo h ends a e known, he Equa ions (6) and (7) can be used o p ecisely calcula e he aul
dis ance. I hese alues a e no ob ained, he loca o algo i hm co ec ion me hod will always be
jus an es ima ion and he e o e po en ially able o ac ually inc ease he loca o e o . E en mo e
Ene gies 2019,12, 1193 5 o 14
complica ed si ua ion occu s o he pa allel-ope a ed lines, when he equi alen ci cui con ains also
he pa allel-line sequence impedances—in he Figu e 2d awn in ed.
Ene gies 2018, 11, x 5 o 15
Figu e 2. The equi alen ci cui o pa allel-ope a ed ansmission lines.
F om he ci cui diag am i is clea ha he posi i e and he nega i e sequence componen s o
he impedance measu ed by he loca o emain he same, bu he ze o sequence does no . This is
caused by he common pa h o he ea h cu en o bo h ansmission lines o med by he g ound
and he g ound wi e. The mu ual coupling is symbolized in he ze o-sequence componen by ou
addi ional induced ol age sou ces. Two o hem a e pa o he ze o-sequence componen o he
aul ed sec ion. These ol ages a e induced by he ze o-sequence cu en 0x pa
I o he pa allel line:
0A 0M 0x pa
..UdZI=, (8)
()
0B 0M 0x pa
..UldZI=− . (9)
The emaining wo ol age sou ces a e loca ed in he ze o-sequence componen o he heal hy
line and a e induced by he ze o-sequence cu en 0x
I o he aul y line:
0C 0M 0x
..UdZI=, (10)
()
()
0D 0M 0x
..UldZII=− − . (11)
Vol ages can be subs i u ed o p oduc o cu en s ha induce hese ol ages and mu ual ze o
sequence impedance 0M
Z
acco ding o Equa ions (8)–(11). Then, he equi alen ci cui o he ze o-
sequence impedance can be modi ied, as shown in Figu e 3.
The loca o placed a he x-poin calcula es he impedance as
()
1x 2x 0xx
x1x2x0x
1 2 0 1x 1L 2x 1L 0x 0L 0x 1L 0x 1L 0x pa 0M 0y 0L
1x 2x 0x
UU U
U
IIII
U U U dIZ dIZ dIZ dIZ dIZ lI Z l dIZ
II I
++
=++
+++ + + + − + −−
=++
, (12)
()
xE yE 0x pa 0M 0y 0L
xEx
1L E
xxxxx
.1 ()
II
I
ZIZ
UI
dZ k R l l d
I
III I
+

=++ + −−

 . (13)
Figu e 2. The equi alen ci cui o pa allel-ope a ed ansmission lines.
F om he ci cui diag am i is clea ha he posi i e and he nega i e sequence componen s o he
impedance measu ed by he loca o emain he same, bu he ze o sequence does no . This is caused
by he common pa h o he ea h cu en o bo h ansmission lines o med by he g ound and he
g ound wi e. The mu ual coupling is symbolized in he ze o-sequence componen by ou addi ional
induced ol age sou ces. Two o hem a e pa o he ze o-sequence componen o he aul ed sec ion.
These ol ages a e induced by he ze o-sequence cu en I0x pa o he pa allel line:
U0A =d.Z0M.I0x pa , (8)
U0B =(l−d).Z0M.I0x pa . (9)
The emaining wo ol age sou ces a e loca ed in he ze o-sequence componen o he heal hy
line and a e induced by he ze o-sequence cu en I0x o he aul y line:
U0C =d.Z0M.I0x, (10)
U0D =(l−d).Z0M.I0x −I . (11)
Vol ages can be subs i u ed o p oduc o cu en s ha induce hese ol ages and mu ual
ze o sequence impedance
Z0M
acco ding o Equa ions (8)–(11). Then, he equi alen ci cui o he
ze o-sequence impedance can be modi ied, as shown in Figu e 3.

Ene gies 2019,12, 1193 6 o 14
The loca o placed a he x-poin calcula es he impedance as
Ux
Ix=U1x+U2x+U0x
I1x+I2x+I0x
=U1 +U2 +U0 +dI1xZ1L+dI2xZ1L+dI0xZ0L+dI0xZ1L−dI0xZ1L+lI0x pa Z0M−(l−d)I0yZ0L
I1x+I2x+I0x
, (12)
Ux
Ix
=d.Z1L1+kE
IEx
Ix+R IxE +IyE
Ix
+lI0x pa Z0M
Ix
−(l−d)I0y Z0L
Ix
. (13)
Fo he loca o placed a he y-poin can be w i en as:
Uy
Iy
=(l−d).Z1L 1+kE
IEy
Iy!+R IEx +IEy
Iy
+lI0y pa Z0M
Iy
−(l−d)I0x Z0L
Iy
. (14)
I is ob ious ha due o he numbe o quan i ies ha in luence he impedance calcula ion, i is
much mo e e ec i e o use wo- e minal algo i hms.
Ene gies 2018, 11, x 6 o 15
Fo he loca o placed a he y-poin can be w i en as:
()
()
Ex Ey
yEy0y pa 0M
0x 0L
1L E
yyyyy
.1 ()
II
UI IZ
IZ
ldZ k R l ld
IIIII
+

=− + + + −−



. (14)
I is ob ious ha due o he numbe o quan i ies ha in luence he impedance calcula ion, i is
much mo e e ec i e o use wo- e minal algo i hms.
.
Figu e 3. A ze o-sequence componen equi alen ci cui o pa allel-ope a ed ansmission lines.
2.2. Two-Te minal Algo i hm
The equi alen ci cui used o wo- e minal algo i hms is displayed in E o ! Re e ence sou ce
no ound.. The ansmission line be ween he sou ce and he aul poin is subs i u ed by he
dis ibu ed pa ame e line model wi h se ies impedances and shun admi ances. The comple e
equi alen ci cui consis s o indi idual sequence componen ci cui s connec ed o he aul esis ance
R .
Figu e 4. An equi alen ci cui o a single-phase aul .
To calcula e he aul loca ion, indi idual sequence componen ol ages a he aul poin (whe e
i = 1, 2, 0) a e de e mined. These ol ages ep esen he ou pu ol ages o he espec i e ansmission
line model and can be calcula ed using he inpu alues o cu en s in
xi
I
and ol ages in
xi
U a he
x-poin :
ou in in
x x x
cosh( . ) sinh( . )
ii i i ii i
UU U dlIZ dl
γγ
== − , (15)
o using he inpu alues o cu en s in
yi
I and ol ages in
yi
U a he y-poin :
Figu e 3. A ze o-sequence componen equi alen ci cui o pa allel-ope a ed ansmission lines.
2.2. Two-Te minal Algo i hm
The equi alen ci cui used o wo- e minal algo i hms is displayed in Figu e 4. The ansmission
line be ween he sou ce and he aul poin is subs i u ed by he dis ibu ed pa ame e line model
wi h se ies impedances and shun admi ances. The comple e equi alen ci cui consis s o indi idual
sequence componen ci cui s connec ed o he aul esis ance R .
To calcula e he aul loca ion, indi idual sequence componen ol ages a he aul poin
(whe e
i= 1, 2, 0
) a e de e mined. These ol ages ep esen he ou pu ol ages o he espec i e
ansmission line model and can be calcula ed using he inpu alues o cu en s
Iin
ix
and ol ages
Uin
ix
a he x-poin :
Ui =Uou
ix=Uin
ixcosh(γid.l)−Iin
ixZi sinh(γid.l), (15)
o using he inpu alues o cu en s Iin
iyand ol ages Uin
iya he y-poin :
Ui =Uou
iy=Uin
iycosh(γi(1−d).l)−Iin
iyZi sinh(γi(1−d).l), (16)
whe e
γi=pZiL.YiL
is he p opaga ion cons an and
Zi = ZiL
YiL
is he cha ac e is ic impedance o
he p o ec ed ansmission line (i= 1, 2, 0 o he posi i e-, nega i e- and ze o-sequence componen o
he line impedance pe uni leng h ZiLand he line admi ance pe uni leng h YiL).
I
Ui =Uou
ix=Uou
iy
, hen he aul loca ion dcan be de e mined. Fo his pu pose, he
posi i e-sequence componen can be used because i s pa ame e s
γ1=pZ1L.Y1L
and
Z1 = Z1L
Y1L
a e known and hei calcula ion is no in luenced by he soil esis i i y.
Ene gies 2019,12, 1193 7 o 14
Ene gies 2018, 11, x 6 o 15
Fo he loca o placed a he y-poin can be w i en as:
()
()
Ex Ey
yEy0y pa 0M
0x 0L
1L E
yyyyy
.1 ()
II
UI IZ
IZ
ldZ k R l ld
IIIII
+

=− + + + −−



. (14)
I is ob ious ha due o he numbe o quan i ies ha in luence he impedance calcula ion, i is
much mo e e ec i e o use wo- e minal algo i hms.
.
Figu e 3. A ze o-sequence componen equi alen ci cui o pa allel-ope a ed ansmission lines.
2.2. Two-Te minal Algo i hm
The equi alen ci cui used o wo- e minal algo i hms is displayed in E o ! Re e ence sou ce
no ound.. The ansmission line be ween he sou ce and he aul poin is subs i u ed by he
dis ibu ed pa ame e line model wi h se ies impedances and shun admi ances. The comple e
equi alen ci cui consis s o indi idual sequence componen ci cui s connec ed o he aul esis ance
R .
Figu e 4. An equi alen ci cui o a single-phase aul .
To calcula e he aul loca ion, indi idual sequence componen ol ages a he aul poin (whe e
i = 1, 2, 0) a e de e mined. These ol ages ep esen he ou pu ol ages o he espec i e ansmission
line model and can be calcula ed using he inpu alues o cu en s in
xi
I
and ol ages in
xi
U a he
x-poin :
ou in in
x x x
cosh( . ) sinh( . )
ii i i ii i
UU U dlIZ dl
γγ
== − , (15)
o using he inpu alues o cu en s in
yi
I and ol ages in
yi
U a he y-poin :
Figu e 4. An equi alen ci cui o a single-phase aul .
I he igh sides o he Equa ions (15) and (16) a e equal, hen i is possible o use only he
equa ions o he posi i e-sequence ol age a he aul poin
Uin
1x cosh(γ1d.l)−Iin
1xZ1 sinh(γ1d.l)−Uin
1y cosh(γ1(1−d).l) + Iin
1yZ1 sinh(γ1(1−d).l) = 0. (17)
Assuming
γ1=γ2=pZ1L.Y1L
and
Z1 =Z2 = Z1L
Y1L
, o inc ease he calcula ion eliabili y,
he nega i e-sequence ol age is used as well
Uin
2x cosh(γ1d.l)−Iin
2xZ1 sinh(γ1d.l)−Uin
2y cosh(γ1(1−d).l) + Iin
2Z1 sinh(γ1(1−d).l) = 0. (18)
Fo each equa ion, a de ia ion om ze o o a ious alues o dcan be de e mined
ε1(d)=Uou
1x −Uou
1y , (19)
ε2(d)=Uou
2x −Uou
2y . (20)
A e ob aining he de ia ions o posi i e- and nega i e-sequence componen and applying he
leas squa e me hod, a simple unc ion F is c ea ed. This unc ion eaches i s minimum in he dis ance
d, which co esponds o he aul poin :
F(d) = |ε1(d)|2+|ε2(d)|2. (21)
The ou pu o his algo i hm is he alue o dis ance dwi h he minimal F(d) alue.
2.3. Synch oniza ion
To co ec ly calcula e he dis ance o he aul dusing his algo i hm, i is necessa y o measu e
he inpu cu en s and ol ages a x- and y-poin s synch onously. This, howe e , is mos ly impossible
in cu en 110 kV dis ibu ion ne wo ks. The dis ance p o ec ion loca o s do no use mu ual ime
synch oniza ion; he e o e, he da a eco ds mus be addi ionally synch onized be o e pe o ming
he calcula ions. This can be done wi h use o he ansien da a eco ds in he ime domain, e.g.,
Ene gies 2019,12, 1193 8 o 14
cap u ing he momen o he ansien incep ion (a su icien da a sampling a e equi ed). Ano he
me hod is based on he phaso co ec ion by es ima ing he inpu quan i ies mu ual phase shi . Using
his es ima ed phase shi alue, he co esponding quan i ies a e shi ed by angle
δ
-synch oniza ion
ope a o . I Iin
xis he synch onizing quan i y, hen:
•Phaso co ec ion a he x-poin : Iin
x=Iin
x∠(α−α),Uin
x=Uin
x∠(β−α),
•Phaso co ec ion a he y-poin : Iin
y=Iin
y∠(ϕ−ϕ+δ),Uin
y=Uin
y∠(γ−ϕ+δ),
whe e
α
,
β,γ
,
ϕ
a e he angles o he unsynch onously eco ded phaso s and
δ
is he synch oniza ion
ope a o de e mined by he phase shi o he cu en s Iin
xand Iin
y.
Conside ing he 110 kV dis ibu ion ne wo ks ope a ion, he phase shi be ween he inpu
cu en s can be de e mined using he sho -ci cui impedances
Zxs
and
Zys
ep esen ing he p o ec ed
line load, as shown in a simpli ied diag am in Figu e 5. Acco ding o [
1
], o es ima e he synch oniza ion
ope a o
δ
, he inpu cu en and ol age da a cap u ed du ing he no mal ope a ion o du ing he
aul (o hei combina ion) can be used. The same p inciple o he synch oniza ion in [13] is used.
Ene gies 2018, 11, x 8 o 15
Figu e 5. A simpli ied equi alen ci cui o a single-phase aul .
Ano he me hod is, as men ioned abo e, based on ansien obse a ion. To analyze he
equency componen s o he signal, he Fou ie ans o m is commonly used. The p oblem wi h
using Fou ie ans o m is ha i is no capable o de e mine when he pa icula equency changes.
To acqui e in o ma ion abou bo h ime and equency, a sho - ime Fou ie ans o m, which uses a
sliding window, can be applied. This echnique, howe e , limi s he equency esolu ion. Be e
solu ion is o use he wa ele ans o m [18]. The wa ele ans o m decomposes he signal in o
unc ions loca ed bo h in Fou ie and he eal- ime space. I is basically an in ini e se o a ious
ans o ms.
The p oblem wi h eco ds synch oniza ion using he ansien s udy is he unequal ime ha he
ansien needs o ge om he aul poin o he poin o measu emen . The ansien a i es soone
a he close e minal, so cap u ing he momen o he ansien incep ion a bo h e minals and
subsequen compa ison can be qui e inaccu a e. Fu u e esea ch will be ocused on his opic.
The synch oniza ion me hod should be chosen based on he da a a ailabili y. Howe e , he
p e e able one is he ansien analysis me hod. I he equi ed da a a e no a ailable, he
synch oniza ion ope a o needs o be calcula ed.
3. Analysis o he Two-Te minal Algo i hm Tes ing
3.1. Ma hema ical Model o a 110 kV Line
The p esen ed wo- e minal algo i hm was implemen ed in he Ma hema ica so wa e ( e sion
11.1.1.0, Wol am Resea ch, Champaign, IL, USA) o p ocess he ol ages and cu en s measu ed a
bo h ends o he 110 kV line modelled in PSCAD so wa e ( e sion 4.6.0.0, Mani oba HVDC Resea ch
Cen e, Winnipeg, MB, Canada). The ol age and cu en da a a e ob ained synch onously, which
means ha quan i ies mu ual ime shi is ze o. The c ea ed model consis s o wo non- ansposed
pa allel-ope a ed 110 kV lines wi h six conduc o s and one g ound wi e, as in Figu e 6. One side o
he owe ca ies he conduc o s o he i s line, he o he side ca ies he second line. The
ma hema ical model o his line is buil acco ding o he eal dis ibu ion pa allel-ope a ed 110 kV
line.
The ansmission line is modelled using he equency dependen line model. The soil esis i i y
is 50 Ωm, he leng h o he line is 27.88 km. The e a e six 240 AlFe4 conduc o s and a combined g ound
wi e wi h 48 ibe s (0.2 Ω DC esis ance and 18 mm diame e ). Line pa ame e s we e de i ed om
se ies impedance and shun admi ance ma ixes in PSCAD line cons an p og am ou pu ile. The
esul s a e lis ed in Table 1.
Figu e 5. A simpli ied equi alen ci cui o a single-phase aul .
Ano he me hod is, as men ioned abo e, based on ansien obse a ion. To analyze he equency
componen s o he signal, he Fou ie ans o m is commonly used. The p oblem wi h using Fou ie
ans o m is ha i is no capable o de e mine when he pa icula equency changes. To acqui e
in o ma ion abou bo h ime and equency, a sho - ime Fou ie ans o m, which uses a sliding
window, can be applied. This echnique, howe e , limi s he equency esolu ion. Be e solu ion is o
use he wa ele ans o m [
18
]. The wa ele ans o m decomposes he signal in o unc ions loca ed
bo h in Fou ie and he eal- ime space. I is basically an in ini e se o a ious ans o ms.
The p oblem wi h eco ds synch oniza ion using he ansien s udy is he unequal ime ha
he ansien needs o ge om he aul poin o he poin o measu emen . The ansien a i es
soone a he close e minal, so cap u ing he momen o he ansien incep ion a bo h e minals and
subsequen compa ison can be qui e inaccu a e. Fu u e esea ch will be ocused on his opic.
The synch oniza ion me hod should be chosen based on he da a a ailabili y. Howe e , he p e e able
one is he ansien analysis me hod. I he equi ed da a a e no a ailable, he synch oniza ion ope a o
needs o be calcula ed.
3. Analysis o he Two-Te minal Algo i hm Tes ing
3.1. Ma hema ical Model o a 110 kV Line
The p esen ed wo- e minal algo i hm was implemen ed in he Ma hema ica so wa e
( e sion 11.1.1.0, Wol am Resea ch, Champaign, IL, USA) o p ocess he ol ages and cu en s measu ed
Ene gies 2019,12, 1193 9 o 14
a bo h ends o he 110 kV line modelled in PSCAD so wa e ( e sion 4.6.0.0, Mani oba HVDC Resea ch
Cen e, Winnipeg, MB, Canada). The ol age and cu en da a a e ob ained synch onously, which
means ha quan i ies mu ual ime shi is ze o. The c ea ed model consis s o wo non- ansposed
pa allel-ope a ed 110 kV lines wi h six conduc o s and one g ound wi e, as in Figu e 6. One side o he
owe ca ies he conduc o s o he i s line, he o he side ca ies he second line. The ma hema ical
model o his line is buil acco ding o he eal dis ibu ion pa allel-ope a ed 110 kV line.
Ene gies 2018, 11, x 9 o 15
Figu e 6. T ansmission line conduc o a angemen .
Table 1. Line pa ame e s.
Posi i e- and nega i e-sequence
impedance
()
121 1
j 3.513 j 11.096ZZ R X==+ = + Ω
Pe kilome e :
()
1L 2L 1L 1L
j 0.126 j 0.398 /kmZZ R X==+ = + Ω
Ze o-sequence impedance
()
00 0
j 7.165 j 32.369ZR X=+ = + Ω
Pe kilome e :
()
0L 0L 0L
j 0.257 j 1.161 /kmZR X=+ = + Ω
Posi i e- and nega i e-sequence
admi ance
()
75
12 1 1
jB 2.788.10 j 8.263.10 SYY G −−
==− = −
Pe kilome e :
()
86
1L 2L 1L 1L
j 10 j 2.964.10 S/kmYY G B −−
==− = −
Ze o-sequence admi ance
()
75
00 0
j 2.788.10 j 4.851.10YG B −−
=− = − Ω
Pe kilome e :
()
86
0L 0L 0L
j 10 j 1.740.10 S/kmYG B −−
=− = −
Residual compensa ion ac o 0L 1L
EREXE
1L
j 0.346 j 0.639
3.
ZZ
kkk
Z
−
==+=+
Using he c ea ed PSCAD model, i is also possible o calcula e he aul dis ance. To do his, he
Equa ion (1) is used simila ly o he common aul loca o . The compu a ional algo i hm is buil wi h
logical blocks and unc ions implemen ed in he PSCAD lib a y. I u ilizes ob ained cu en and
ol age da a p ocessed using he Fas Fou ie T ans o m. The ou pu o his calcula ion can be
compa ed o he ou pu o he p oposed algo i hm.
The simula ion da a a e s o ed in a Com ade ile o ma . The PSCAD so wa e con ains a
componen called RTP/COMTRADE Reco de , which is able o eco d he simula ed da a a sa e hem
as Com ade. The e o e, he da a can be u he iewed in a so wa e ha uses his o ma .
3.2. Impac o he Faul Resis ance
Se e al es s we e pe o med o assess he impac o he aul esis ance alue on he p oposed
algo i hm. The aul occu ed in he L1 phase in he dis ance o 4.49 km om he e minal a he x-
poin . The aul esis ance was changed up o 100 Ω, which appea s e y a ely in he 110 kV ne wo k
and e en a aul wi h such high esis ance was success ully localized, as seen in E o ! Re e ence
sou ce no ound., whe e he minimum o he unc ion
[
]
ln F( )d deno es he calcula ed aul loca ion.
Figu e 6. T ansmission line conduc o a angemen .
The ansmission line is modelled using he equency dependen line model. The soil esis i i y
is 50
Ω
m, he leng h o he line is 27.88 km. The e a e six 240 AlFe4 conduc o s and a combined
g ound wi e wi h 48 ibe s (0.2
Ω
DC esis ance and 18 mm diame e ). Line pa ame e s we e de i ed
om se ies impedance and shun admi ance ma ixes in PSCAD line cons an p og am ou pu ile.
The esul s a e lis ed in Table 1.
Table 1. Line pa ame e s.
Posi i e- and nega i e-sequence
impedance
Z1=Z2=R1+jX1=(3.513 +j 11.096)Ω
Pe kilome e : Z1L =Z2L =R1L +jX1L =(0.126 +j 0.398)Ω/km
Ze o-sequence impedance Z0=R0+jX0=(7.165 +j 32.369)Ω
Pe kilome e : Z0L =R0L +jX0L =(0.257 +j 1.161)Ω/km
Posi i e- and nega i e-sequence
admi ance
Y1=Y2=G1−jB1=2.788.10−7−j 8.263.10−5S
Pe kilome e : Y1L =Y2L =G1L −jB1L =10−8−j 2.964.10−6S/km
Ze o-sequence admi ance Y0=G0−jB0=2.788.10−7−j 4.851.10−5Ω
Pe kilome e : Y0L =G0L −jB0L =10−8−j 1.740.10−6S/km
Residual compensa ion ac o kE=Z0L−Z1L
3.Z1L =kRE +jkXE =0.346 +j 0.639
Using he c ea ed PSCAD model, i is also possible o calcula e he aul dis ance. To do his,
he Equa ion (1) is used simila ly o he common aul loca o . The compu a ional algo i hm is buil
wi h logical blocks and unc ions implemen ed in he PSCAD lib a y. I u ilizes ob ained cu en
and ol age da a p ocessed using he Fas Fou ie T ans o m. The ou pu o his calcula ion can be
compa ed o he ou pu o he p oposed algo i hm.