TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5011 ~ 50
2
1
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.506
7
5011
Re
cei
v
ed
No
vem
ber 6, 20
13; Re
vised
Febr
uary 9, 2
014; Accepte
d
March 1, 20
14
Analysis of W
e
ak Positi
on in Overhead line under
Heavy Icing Condition by
Finite
Eleme
n
t Method
Liu Chao*
1
, Ruan Jia
ngjun
2
, Du Zhi
ye
3
, Du We, Liu Yang, Wa
ng Zhuo
Schoo
l of Elect
r
ical En
gin
eeri
ng, W
uhan U
n
i
v
ersit
y
, W
u
h
a
n
,
China
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: lcnha
lcnh
a@
163.com
*
1
, ruan30
8@1
26.co
m
2
, Duzhi
y
e@
126.com
3
A
b
st
r
a
ct
Trans
m
i
ssion tower is a
very important co
m
p
onent of power syst
em
, and heavy iced
transmissio
n
l
i
ne has beca
m
e
o
ne of
t
he
i
m
portant factors
aga
inst its s
a
fe
ty and st
abi
lity
in C
h
in
a'
s p
o
w
e
r
system thes
e years
but the
transmi
ssio
n
li
ne des
ign
ed fr
om trad
itio
nal
standar
d can't end
ure the
mo
re
w
o
rse enviro
n
m
e
n
t. In this paper, for pos
iti
oni
ng the w
eak
points of the trans
missi
on l
i
n
e
und
er he
avy
icin
g
accurate
ly and
providi
ng acc
u
rate pos
ition
a
l
para
m
et
er
s to onli
ne
mo
nit
o
rin
g
devic
es, the strain secti
o
n
mo
de
l is
bu
ilt t
o
a
nalys
is th
eir
mech
anic
a
l
pr
operti
es u
n
d
e
r
icing
a
nd w
i
nd
cond
itions. I
n
p
r
opos
ed
metho
d
,
the cou
p
li
ng ef
fect betw
een tow
e
r and l
i
nes
is consid
er
e
d
, then the w
e
a
k
tow
e
r is picked out by strai
n
section
mod
e
l
that is c
o
mbi
n
ed w
i
th
ei
ght t
o
w
e
rs. T
he
si
n
g
le
on
e-tow
e
r-tw
o
-lines
mod
e
l
of w
eak t
o
w
e
r is
built to si
mulat
e
an
d verify th
e w
eak po
int a
ccurately.
F
i
n
a
l
l
y the better w
a
y is defi
n
e
d
to
get the loc
a
tio
n
of
w
eak structure combi
ned w
i
th
the adva
n
tag
e
s
of both mo
de
ls.
Ke
y
w
ords
: tow
e
r-line
mo
del,
heavy ice
d
co
ver, finite el
e
m
ent method, u
n
bal
ance
d
tensi
on, w
eak poi
nt
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Icing is o
ne
of the comm
on natu
r
al p
henom
eno
n. Free
zin
g
rain
begin
s
to ice whe
n
encounte
r
ing
wire
s
and
to
wers,
and
ici
ng al
so
ha
pp
ens when
sn
ow
melts with
the
con
d
ition
that
the tempe
r
at
ure
rem
a
in
s
betwe
en mi
n
u
s
4 a
nd 0
[1]. Power transmi
ssion
li
ne pl
ays
a v
e
r
y
importa
nt role
in powe
r
system [2], damage of it
woul
d have gre
a
t impact on the
so
ciety. Durin
g
the 2008 S
p
ring Fe
stival, huge di
sa
ste
r
ca
used by
rare free
zin
g
rain a
nd sn
ow ha
ppe
ne
d in
Southern Chi
na, cau
s
ing
mass de
stru
ction to
powe
r
grid, whi
c
h made pe
ople
began to ref
l
ect
the de
sign
st
anda
rd
s of th
e po
we
r line
s
. Online m
oni
toring
device
for force
dete
c
tion al
so
ha
d
the attention.
Towe
rs-lin
es syste
m
of t
r
an
smi
ssi
on l
i
ne
i
s
coupl
ed system compo
s
ed
by
towe
rs,
insul
a
tor
strin
g
s a
nd
wire.
With differe
nt geog
ra
p
h
i
c
al
con
d
ition
s
, the span
differen
c
e, h
e
ight
differen
c
e an
d the co
rne
r
of each to
wer are differe
nt. Unre
asona
bl
e desi
gn of transmi
ssion li
ne,
like too large span difference
and
height difference,
will lead to
t
o
wer tension imbalance. The
imbalan
ce a
g
g
ravate
s whe
n
encounte
r
i
ng bad
weat
her
su
ch a
s
stron
g
wi
nd o
r
free
zing,
which
may cau
s
e t
o
we
r
bre
a
k,
tower
collap
s
e an
d lin
e fracture, ma
ki
ng a
significant imp
a
ct
o
n
peopl
e's p
r
o
d
u
ction a
nd living [4]. At th
e sam
e
ti
me, limited by the cal
c
ulatio
n con
d
ition
s
an
d
con
s
tru
c
tion,
the in
stallatio
n
lo
cation
of the tr
a
n
smissi
on line
towers
stre
ss dete
c
tion
device
can
not be a
c
curately installe
d in stress-concentratio
n
steel st
ru
ctures defin
ed a
s
we
ak
point
s. It
redu
ce the a
c
curacy of tower-li
ne sy
s
t
em s
t
ruc
t
ural failure predic
tion.
As the mutu
a
l
cou
p
ling b
e
twee
n the in
sulator, tower
and
wire, ext
e
rnal fa
cto
r
s i
n
volved
icing g
r
avity, wind a
nd et
c., it is difficult to
determin
e
the initial sh
a
pe of the tower-li
ne mo
del,
and so is the
numeri
c
al a
nalysi
s
. In literatu
r
e [1] and [9], based
on mech
ani
cs p
r
in
ciple
s
the
authors
used
the finite el
e
m
ent meth
od
that apply
e
d
icing
loa
d
o
n
wi
re n
ode
s. Cal
c
ulation
o
f
icing l
oad i
s
compl
e
x. Wh
enever th
e i
c
ing thickn
ess is chan
ged,
the load
on
node
s
will ne
ed
recalculation,
and there i
s
a deviation in
the resul
t. In
[14] it proposed to establi
s
h icing el
eme
n
ts
whi
c
h sh
ared
node
s with wire el
ement
s on wi
re
su
rface. Avoidi
ng the com
p
lex mecha
n
ical
cal
c
ulatio
ns, i
t
can ea
sily control the i
c
i
ng
thickn
ess,
icing h
e
tero
geneity and
uneven d
e
-i
ci
ng.
This pap
er
d
e
scrib
ed
the
relevant prin
ciples of
the fi
nite eleme
n
t
mech
ani
cs a
nalysi
s
of to
wer-
line mod
e
l fo
r tran
smi
s
sio
n
line. It buil
ded u
p
ov
e
r
a
ll strai
n
segm
ent finite ele
m
ent me
cha
n
ics
analysi
s
mod
e
l of overhea
d transmissio
n line towe
r
line system. T
h
rou
gh si
mul
a
tion, it inden
tify
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5011 – 50
21
5012
the stru
cturel
y weak to
wer in strain seg
m
ent.
Combi
ned with a
ccurate an
alysi
s
in one
-tower-
two-lin
es m
o
de, the wea
k
points in the wea
k
towe
r coul
d be p
o
sition
ed. Propo
sed meth
od
combi
ned the
analysi
s
cha
r
acte
ri
stics of strain
segm
ent model an
d one-to
we
r-t
wo-li
n
e
s
mod
e
l,
simplifing
the
analy
s
is pro
c
e
s
s an
d eff
e
ctively im
p
r
oving the
a
c
curacy
and
efficien
cy of
th
e
mech
ani
cal st
ructu
r
e a
naly
s
is of the ici
n
g tower-lin
e system.
2. Mechanic
s Finite Element An
aly
s
is Theor
y
of
To
w
e
r
-
Line
Sy
stem
2.1. Cons
titu
tiv
e
Equation
Towe
r m
e
cha
n
ics an
alysi
s
is
stru
ctural str
ength i
s
sue,
whi
c
h m
eets the ba
si
c eq
uation
s
of elasti
city. Elasticity, also kn
own a
s
t
he theo
ry
of elasti
city,
is mainly
ab
out the
stress, strain
and di
spl
a
ce
ment of the
obje
c
t wh
en f
a
ctors
su
ch
as exte
rnal f
o
rce o
r
a te
mperature
ch
ange
acted on it, so as to address the stre
n
g
th and st
iffness pro
b
lem
s
of structu
r
al
or mech
ani
cal
desi
gn. Sin
c
e
the mate
rial
con
c
e
r
ne
d
wi
th is i
s
otr
opi
c, according
to
the theo
ry of
ela
s
tic-pla
s
tic
mech
ani
cs, controllin
g equ
ations in
clu
d
e
d
two gro
u
p
s
of equation
s
as follo
ws:
Differential e
quation
s
of mech
ani
cal eq
uilibriu
m
0
0
0
yx
xz
x
xy
y
z
y
yz
xz
z
X
xy
z
Y
xy
z
Z
xy
z
(1)
Material con
s
titutive
equations
1
[(
)
]
1
[(
)
]
1
[(
)
]
2(
1
)
2(
1
)
2(
1
)
xx
y
z
yy
x
z
zz
x
y
yz
yz
xz
x
z
xy
x
y
E
E
E
E
E
E
(2)
x
,
y
,
z
yz
T
=
zy
T
,
x
z
T
=
zx
T
and
x
y
T
=
yx
T
of Equ
a
tion (1)
are
st
ress
comp
one
nts
of different
dire
ction
s
, X, Y, Z are the phy
sical
comp
one
nts
of the unit volume in th
ree
coo
r
din
a
te di
rectio
ns;
x
,
y
,
z
,
yz
,
x
z
and
x
y
of Equ
a
tion (2) are
strain
comp
o
nents of
different di
re
ction
s
, rep
r
e
s
entin
g rel
a
tions
of di
spla
ceme
nt and
strain
of any
points
within
the
obje
c
t when
deform
a
tion o
c
curs to it;
E
and
represent
the Young's
m
odulu
s
of elasticity and
Poisson'
s ratio, meeting Hookela
w
. For con
c
rete
tower-li
ne st
ru
cture
system, takin
g
the ab
ove
two formul
as
as solving eq
uation
s
, base
d
on the
finite element m
e
thod, we
ca
n bulid up e
n
tity
model
with the help of business software ANSYS [15
]. It provides
elelment
s of different types
with differe
nts de
gre
e
s
of freed
om for m
odelin
g va
rio
u
s
stru
ctures,
whi
c
h would
be intro
d
u
c
ed
in
the next chap
ter. We co
uld
define
the propertie
s
of the material an
d take the the initial value of
strain
an
d
direct fo
rce of
sysytem a
s
kn
own
pa
ram
e
ter to
figure o
u
t un
kno
w
n
variabl
es of e
a
c
h
node
su
ch
a
s
stre
ss,
disp
lacem
ent a
n
d
strain. It could b
e
u
s
e
d
to judg
e the
relia
bility of the
sy
st
em.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis of
Weak Po
sition i
n
Ove
r
he
ad li
ne
und
er Hea
vy Ici
ng Cond
ition by… (Liu
Chao
)
5013
2.2. To
w
e
r Steel Stru
ctur
e Model
BEAM188 el
ement i
s
usually used on
tower stee
l structure m
o
deling [18]. As what i
s
sho
w
n
in Fi
g
u
re
1(a), it i
s
a
two
-
no
d
e
s-3-D
linea
r finite strain
element. It h
a
s
six o
r
se
ven
degree
s of freedom
at ea
ch n
ode, in
cl
uding t
r
an
sl
a
t
ions in th
e
x, y, and z
dire
ction
s
an
d
rotation
s a
b
o
u
t the x, y, and z
dire
ction
s
and
a opt
io
n
a
l deg
ree
of freed
om of
wa
rping. It ha
s t
he
ability to wit
h
stand the t
ensi
on, com
p
ressi
on, bending, twi
s
ti
ng and shear. Based on
the
Timoshen
ko
beam the
o
ry, the plane of
cro
s
s-se
ctio
n of the ele
m
ent ke
ep
s undi
storted
a
fter
deform
a
tion. The ela
s
tic, creep a
nd pla
s
tic mate
rial
model a
r
e su
pporte
d, and
also throug
h the
definition
of cross-sectio
n and se
ctional
dire
ct
ion defi
ned
p
o
int,
cross-se
ction si
mulation can
b
e
achi
eved. Th
e simulatio
n
functio
n
cove
rs a variet
y of material
s, su
ch a
s
steel a
r
ch sectio
n, and
is suitable fo
r analysi
s
of the an
gle ba
r material
m
o
del of towe
r.
As sh
own in
Figure 1(b),
b
y
setting the real constant
s of BEAM188 element, we
can simulate the
sh
ape and cros
s-secti
on
size of L-sha
ped an
gle ba
r.
(a) Bea
m
18
8 element
(b) mo
del of L-shap
ed an
g
l
e bar
Figure 1. 3-D
Linea
r Finite
Strain Beam
Element
2.3. Wire and Ground
Wire Model
As a flexible comp
one
nt, wire a
nd grou
nd wire
have the cha
r
a
c
teri
stic
s that they are not
subj
ecte
d to
bendi
ng m
o
ments
or stress a
nd
only
with
stand
te
nsio
n. They
can
be
preci
s
ely
pro
c
e
s
sed in
accordan
ce
with the structure of t
he si
ngle cable. F
o
r the cro
s
s-se
ctional
size
of
the cabl
e is very small co
mpared with
the length of
the cabl
e, its flexural
stiffness is so sm
all
that it can
be
igno
red. Th
e
cabl
e mate
ri
al co
mp
lies with
Hooke's law.
U
nde
r it
s o
w
n
weig
ht, it
has
geom
etri
c shap
e of a
caten
a
ry [9]. Comp
ared
wi
th the gen
era
l
cabl
e st
ru
cture
s
an
d b
r
id
ges
Lasso,
wire a
nd g
r
ou
nd
wi
re have
small
e
r
stiffnes
s, b
i
gger span,
d
e
flection
an
d
a hig
her de
gree
of nonlinea
rit
y
. The specifi
c
bilinea
r stiffness ma
trix chara
c
te
risti
c
s of LINK10 element ma
kes it
a pole elem
e
n
t which is o
n
ly under p
r
essure or
te
nsio
n In the axial dire
ctio
n. Openni
ng
th
e
tensio
n-o
n
ly option, if the
unit is u
nde
r
pre
s
sure
, stiffness
will di
sa
ppea
r, so a
s
to simulat
e
th
e
natural
relax
a
tion pro
p
e
r
ties of wi
re an
d grou
nd wi
re. LINK10 el
ement ha
s fu
nction of solving
non-li
nea
r, stress stiffenin
g
and larg
e deform
a
ti
on probl
em
s, makin
g
it an ideal elem
ent
to
analo
g
wire a
nd gro
und
wire of transmi
ssion lin
e.
2.4.
Insulator Strings Model
Size of i
n
sula
tor
string
s
an
d the
wire
co
nne
ction fittin
g
s i
s
m
u
ch
smaller compa
r
ed
with
size of T
o
wer-Line
sy
stem,
so
their influ
n
ce
fo
r
me
ch
anics
analy
s
is of th
e T
o
wer-Line
struct
ure
is insig
n
ifica
n
t. Ignoring gravity of conn
ection fi
ttings
and insulato
r string
s, they can be a
nalo
ged
by the ri
gid
conne
cting
ro
d elem
ent LI
NK8. Th
e ele
m
ent with
two no
des an
d
three
deg
ree
s
of
freedo
m co
ul
d be used for
the link of tower bea
m elem
ent and the wire ca
ble ele
m
ent.
To effectively calculate
stress and
defo
r
ma
tion
cau
s
ed by sp
an, height differe
nce a
nd
uneven l
oad
of multi-sp
an To
we
rs-L
ines
sy
ste
m
, we
used B
EAM188 el
e
m
ent to an
a
l
og
transmissio
n tower, LI
NK1
0
eleme
n
t to analog
wire
and g
r
oun
d
wire
and LI
NK8 elem
ent
to
analo
g
insul
a
tor strin
g
s a
n
d
con
n
e
c
tion fittings.
Con
s
i
derin
g the co
upling of To
wer-Line
syste
m
,
we
coul
d cre
a
te overall
e
n
tity model. Beam el
em
e
n
t cross-se
cti
on of
the tra
n
smi
ssi
on to
wer
model i
s
"
L
" sh
ape
d, e
c
centri
cly
con
necte
d.
Wi
re
and
groun
d
wire of t
r
a
n
smi
ssi
on li
n
e
s
establi
s
h a
cable elem
ent caten
a
ry mod
e
l, and
the prestre
s
s could
be determi
n
ed acco
rdin
g to
the installatio
n
Actinoba
cill
us st
re
ss [15]
.
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TELKOM
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KA
Vol. 12, No. 7, July 201
4: 5011 – 50
21
5014
3. Anal
y
s
is o
f
Weak Point of Strain
Se
gment Mod
e
l of To
w
e
r
-
Line Sy
stem
3.1. Cate
nar
y
Structure
In this pape
r, we use
d
the
catena
ry formula in line d
e
sig
n
manu
al
to simulate the wire
and groun
d wire stru
ctu
r
e.
The 50
0kV
o
v
erhea
d wi
re
s are fou
r
-spl
it stru
cture. T
o
simplify the
modelin
g proce
s
s,
four-split
wire
s could
be eq
uivalent to a
wire. T
he
formulor
of cal
c
ulating e
quivalent diam
ete
r
are
as
follows
[21]:
eq
Sd
dD
D
(3)
S
is split number;
D
is se
paratist diamete
r
;
d
is the diamet
er of the ea
ch
wire.
The co
ndu
cto
r
caten
a
ry eq
uation is a
s
follows [16]:
2
00
00
0
0
0
0
2
(2
)
(
)
[sinh
s
in
h
]
[
s
inh
s
inh
]
1
(
)
22
2
2
h
h
h
lx
l
x
l
x
h
y
LL
(4)
In the equatio
n, the param
eter
0
h
L
can be calcul
ated a
s
follows:
0
0
0
2
sinh
2
h
l
L
(5)
l
——ho
r
izonta
l
distan
ce of the two suspe
n
sio
n
point
s
；
h
——verti
cal d
i
stan
ce of the
two su
spe
n
si
on point
s
；
——ratio of g
r
avity per unit
length of
wire and cro
s
s-section
a
l are
a
of wire
；
0
——st
r
e
ss of
the wire lo
we
st point (the
cross-sectio
n tensi
on of wire per unit
)
；
Coo
r
din
a
tes
of each di
screte node on
caten
a
ry line
coul
d be obta
i
ned acco
rdi
n
g to th
e
formula (5), value
of
is related to the
wire m
odel
and value of
0
shoul
d be th
e avera
g
e
annu
al ope
rat
i
ng stre
ss.
3.2. Finite Element Mod
e
l of the To
w
e
r-line Sy
stem
In this pa
per,
we
sele
cted
a micro
c
lim
ate Strain
se
gment of a
5
00kV lin
e in
Central
Chin
a to buil
d
up finite el
ement mod
e
l
,
which i
n
cl
u
ded 8 to
wers and seven span
s, numb
e
r
ing
from 1
82#
to
189
#. The
182#
an
d 18
9# to
wer we
re
strai
n
to
wers.
Co
nsi
d
e
r
ing th
at hei
ght
differen
c
e a
n
d
uneve
n
spa
n
we
re of
sig
n
ificant affe
ct to Tower fo
rce, coo
r
din
a
te
s value
s
of e
a
ch
tower in the
model
we
re t
a
ke
n from
th
e actu
al lin
e
para
m
eters.
Each to
we
r
consi
s
ted
of two
kind
s of ste
e
l material
s,
Q235 an
d Q345. Th
e forme
r
one
wa
s usually use
d
as a
u
xiliary
material
s, an
d the latter o
ne was u
s
u
a
ll
y used
as
m
a
in materi
als.
Both of them
have “L
”-sh
a
ped
cro
s
s-
se
ct
ion
,
as wa
s sh
o
w
n in Figu
re
1(b
)
.
Mat
e
rial
param
eters of the strain
are a
s
follows in
Table 1.
Table 1. The
Physical Prop
erties of Mate
rials
Entity
To
w
e
r
Wir
e
Grou
nd w
i
re
Ty
p
e
Q345
Q235
LGJ-400/
35
GJ
-80
Cross-section ar
ea (mm
2
)
/
/
661.74
79.39
Elastic modulus
（）
Mpa
206000
206000
65000
181300
Densit
y
(
t/mm
3
)
7.85e-9
7.85e-9
3.1e-9
7.94e-9
Poisson's ratio
0.3
0.3
/
/
Y
i
eld strength
（）
Mpa
345
235
97.73
443.97
In the mod
e
l, each an
gle
bar of th
e to
wer wa
s
equi
valent to an
element, an
d
the wh
ole
insul
a
tor
stri
ngs were
eq
uivalent to
a
n
elem
ent. F
o
r the
wi
re
and
gro
und
wire, th
ey were
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TELKOM
NIKA
ISSN:
2302-4
046
Analysis of
Weak Po
sition i
n
Ove
r
he
ad li
ne
und
er Hea
vy Ici
ng Cond
ition by… (Liu
Chao
)
5015
equivalent to
hea
d-tail-co
nne
cted
ele
m
ents
of 4.5
meters lo
ng
acco
rdin
g to
its initial
sh
ape.
There
were t
o
tally 208
62
eleme
n
ts
a
nd 1
470
9 no
des in th
e fi
nite elem
ent
model
of
strain
segm
ent. Fin
i
te element model of To
wer-lin
e strai
n
segm
ent system are
sh
own in Fig
u
re 2.
Figure 2(a) i
s
a 3-D finite element mo
d
e
l of a
typical
tower
used i
n
the strain
segment, Fig
u
re
2(b
)
i
s
a
full
model
diag
ra
m of the
entire st
rain
se
gm
ents
of tran
smissi
on li
ne
s. The l
a
rge
s
t span
of strain
seg
m
ent attains
863m, lo
cate
d betwe
en 18
4 # and 1
85
# towe
r. The
maximum hei
ght
differen
c
e is
61.3m, locate
d betwe
en 18
6 # and 18
7#
tower.
(a) ty
pic
a
l sin
g
le towe
r mo
del
(b) strain se
ct
ion
model
Figure 2. Finite Element Model of Tra
n
smissi
on Lin
e
3.3. External
Force Load
Since the
co
nce
r
ne
d obj
e
c
t is me
ch
ani
cal p
r
op
ertie
s
of transmisson line
s
an
d
towers,
we mainly co
nsid
ere
d
the effect of icing
gravit
y and wind. Acco
rdi
ng to the formula of line d
e
sig
n
manual, external force load
of the model coul
d be calculated a
s
follows:
(1)
Wind lo
ad
on wire a
nd
grou
nd wi
re
Whe
n
the sp
an of wire a
n
d
grou
nd wi
re
is
H
l
, the wind load is
cal
c
ula
t
ed as follo
ws:
22
3
0.
62
5
(
2
)
(
)
s
i
n
1
0
xs
c
c
H
h
Wd
l
K
v
(6)
In the
con
d
ition
with i
c
ing,
unit le
ngth
wind
loa
d
of
wire
p
r
od
uce
d
by h
o
ri
zont
al wi
nd
coul
d be calculated by the followin
g
formula:
22
-
3
1
0.
6
2
5
(
2
)
(
)
s
in
10
,
/
sc
h
g
dK
N
m
(7)
In the co
ndition with
out ici
ng, unit lengt
h wind
l
oad
o
f
wire p
r
od
uced by ho
rizon
t
al wind
can b
e
cal
c
ul
ated by the following fo
rmul
a:
22
-
3
2
0.6
2
5
(
)
s
i
n
10
,
/
sc
h
g
dK
N
m
(8)
In the equatio
n,
the param
eter
h
K
could be
calculated a
s
follows:
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5011 – 50
21
5016
)
(
s
h
h
h
K
(9)
h
——hei
ght from the gro
u
n
d
or wate
r surface to win
d
;
s
h
——ref
ere
n
ce height of wi
nd sp
eed of the line
s
；
——the coefficient rel
a
ted to surfa
c
e
rou
ghne
ss. For g
eneral landli
n
e it takes 0.1
6
；
d
——diamete
r of wire o
r
ground
wire
；
s
c
——wi
r
e sha
pe co
efficient
；
c
——the win
d
load adju
s
tm
ent factor of
wire
s’ effect o
n
tower in 5
0
0
kV line
；
——the p
r
escriptive desi
g
n
wind spee
d at high ba
seli
ne hs
，；
with the unit of m/s
h
K
——hig
h
coef
ficient of
vari
ation of
the
wind
spe
ed at the
wi
re
s ave
r
age
h
e
ight h
.
In
con
d
ition that
h
is equivalten
to
s
h
, value of
h
K
is
1
；
——wi
r
e ice thickne
s
s
，；
wit
h
the unit of mm
H
l
——horiz
ontal s
p
an of tower
，；
with the
unit of m
——the an
gle
betwee
n
win
d
dire
ction an
d wire axial.
(2)
Wind lo
ad
on tower
Wind lo
ad pe
rpen
dicular to
the surfa
c
e o
f
the structu
r
e
can be
cal
c
ul
ated as follo
ws:
2
1.6
tz
T
c
v
Fk
k
k
A
(10)
k
——wi
nd loa
d
sha
pe coefficient, whi
c
h i
s
usually 1.3;
z
k
——wi
nd pre
s
sure va
riatio
n coeffici
ent of height
；
T
k
——wi
nd loa
d
adju
s
tment factor
；
c
A
——tod wi
n a
r
ea.
(3) Ici
ng loa
d
on wire and g
r
oun
d wi
re
Icing loa
d
on
wire a
nd g
r
ou
nd wire pe
r u
n
it length ca
n
be cal
c
ulate
d
as follo
ws:
g
3
= 9.8×0.9
πδ
(
d
+
δ
)×
10
-3
，
N/m
(11)
Cal
c
ulating
wind lo
ad
and
icing
loa
d
o
n
wi
re
and
gro
und
wire
per
unit len
g
th, we can
cal
c
ulate loa
d
on element a
c
cordi
ng to the length.
Dev
i
ding the load
on element b
y
two, we can
get nod
e loa
d
on two sid
e
s
of elem
ent. In the
sam
e
way, nod
e lo
ad on to
we
r
element al
so
can
be obtain
ed.
For to
wer fo
u
ndation
s
a
r
e
deeply bu
rie
d
in the
soil
a
nd po
ure
d
wit
h
co
ncrete, they ca
n
be con
s
ide
r
e
d
to be
rigi
d
con
n
e
c
tion in
the st
ru
ctur
e
.
In the finite
element m
o
d
e
l, all de
gre
e
s
of
freedo
m of tower fou
ndatio
n node
s were
app
lied the
constraints val
ue of ze
ro.
3.4. Strain Segment-line Model Simulation Results
The
purpo
se
of this pa
pe
r i
s
to i
dentif
y st
ru
cturally we
ak poi
nts of tower-line
syste
m
throug
h a
nal
ysis
of the m
e
ch
ani
cal p
r
o
pertie
s
of th
e
towe
r-li
ne
system un
de
r
the condition
of
icing. Con
s
id
ering the
effect of lateral
wind lo
ad
s, by changi
ng combinatio
n of icing thickn
e
s
s
and wind sp
e
ed,
we ca
n
b
u
ild
up re
cycl
able cal
c
ulat
e program of
the strain
se
ction to a
naly
z
e
force of to
wer-lin
e syst
em model.
Acco
rdi
ng to
line desi
g
n
manual a
s
well as lo
cal
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis of
Weak Po
sition i
n
Ove
r
he
ad li
ne
und
er Hea
vy Ici
ng Cond
ition by… (Liu
Chao
)
5017
meteorologi
cal con
d
ition
of several years, the
cal
c
ulation was
divided into
16 group
s, a
s
is
sho
w
n in Ta
b
l
e 2:
Table 2. The
Load
ed Data
Grou
p numbe
r
Icing
thicknes
（
mm
）
Wind
speed(m/s)
1
0
0
～
30
2
2
0
～
30
·
·
·
·
·
·
·
·
·
14
26
0
～
30
15
28
0
～
30
16
30
0
～
30
Und
e
r ce
rtai
n
clim
atic condition
s,
si
mula
tion
re
sults of di
spl
a
cem
ent a
n
d
stress
distrib
u
tion
of the st
rain
se
gment-li
ne m
odel a
r
e
sh
o
w
n in
Fig
u
re
3 an
d Fig
u
re
4. By cal
c
ulat
ing
stre
ss on ea
ch bar,
we ca
n obtain ratio
of actual
stress and yiel
d
stre
ss,
whi
c
h can
be u
s
e
d
to
determi
ne instability of st
rain
segm
ent
line-tower
system. If the rati
o i
s
bi
gger than 1,
strain
segm
ent line
-
tower
syste
m
sho
u
ld b
e
consi
dered a
s
failure fo
r safe ope
ration
of power g
r
i
d
s.
Loadi
ng diffe
rent combin
a
t
ions of icin
g
thickn
es
s a
nd win
d
sp
e
ed, we could
get cro
s
sov
e
r
failure data
of strain
seg
m
ent line (in
the condi
tio
n
that strain
segme
n
t line is impen
di
ng
stru
ctural da
mage
).
Figure 3. Displacement Di
stributio
n of Strain Sectio
n-l
i
ne
Figure 4. Stress Di
stributi
on of Strain Section
-
line
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5011 – 50
21
5018
Table 3. The
aggregatio
n o
f
critical failu
re data
Icing
thickness
（
mm
）
Wind speed
（
m/s
）
Element num. of
w
e
ak points
To
w
e
r num.
of
w
e
ak points
Actual str
e
ss
（
kN/m
2
）
Ratio
12
16
8944
188#
-57933
0.1679
14
16
4641
185#
-59529
0.1725
16
12
8944
188#
-56970
0.1651
18
12
8944
188#
-58513
0.1696
20
10
8944
188#
-46276
0.1341
22
12
8944
188#
-59647
0.1729
26
14
8944
188#
-66969
0.1941
28
16
8944
188#
-71977
0.2086
Data of ice thickne
s
s and
wind
spe
ed
list
ed in Ta
bl
e 3 are th
e input load
s
when the
tower st
ruct
u
r
e
wa
s cro
s
sover failure. Du
ring th
e
simul
a
tion
pro
c
e
ss,
we
found
out t
hat
increa
sing either wind sp
e
ed
or
icin
g
thi
c
kne
ss of
ce
rtain crossove
r failure data,
stre
ss of we
ak
points li
sted i
n
the table would in
cre
a
se
a lot
and excee
d
the yield stre
ngth of
the angle b
a
r,
and in th
e
sa
me time di
spl
a
cem
ent of n
ode
s on th
e
wea
k
p
o
ints
wa
s mu
ch l
a
rger th
an b
e
fo
re,
whi
c
h me
ant
the angl
e ba
r wa
s st
ru
cturally destroy
e
d
. This
wo
uld
se
riou
sly affect the
safe
and
stable
op
erati
on of th
e tran
smissio
n
lin
e
s
. In th
e
cal
c
ulation
of ea
ch cli
m
ate
co
n
d
ition, be
ca
u
s
e
the icin
g thi
c
kne
ss i
n
cre
a
se
s 2
mm
or
wind
sp
e
ed in
crea
se
s 2m/s, the
acq
u
ire
d
cli
m
ate
threshold
just
app
roximate
on the
real t
h
re
shol
d an
d
the a
c
qui
red
ratio
wa
s un
able to b
e
g
e
t
clo
s
e to 1.
As ca
n be
se
en from T
abl
e 3, whe
n
the
ice thic
kn
ess increa
se
s, the criti
c
al valu
e of the
wind sp
eed d
o
se not
mo
n
o
tonically
de
cre
a
se,
whic
h mea
n
s
critical failu
re i
c
i
ng thickn
ess
and
wind spee
d of the strain
segm
ent line
are non
-line
a
r relatio
n
shi
p
, and the trend is compl
e
x.
E
v
en somet
i
mes
whe
n
ic
e t
h
ic
kne
ss i
n
cr
ea
se
s,
ma
x
i
mum wind
spe
ed t
hat
t
h
e t
r
an
smi
sso
n line
can with
stan
d increa
se in
steadly.
For
example, wh
en the thickn
es
s of the ice cover in
cre
a
se
s
from 22mm t
o
26mm, its maximum afforda
b
le wi
nd
load increa
ses from 1
2
m/
s to 14m/s. T
h
is
situation
is m
a
inly du
e to t
he diffe
rent
d
i
rectio
n of
th
e ici
ng l
oad
and
win
d
lo
a
d
which
cau
s
es
internal
imb
a
l
ance ten
s
io
n
to offset. Thi
s
p
a
rtly expl
a
i
ns
why ta
kin
g
de
-i
cing
op
eration
s
in th
e
con
d
ition
of strong
win
d
(melting i
c
e
with DC to
re
d
u
ce
ici
ng thi
c
kne
s
s of
the
line) may
ca
use
damag
e to the origin
ally stable tower-lin
e system.
Analyzing of simulatio
n
re
sults, we can
find out
that
in all critical f
a
ilure
situatio
ns, 188#
and 185
#
to
wer suffere
d
greater stre
ss
an
d stre
ss
ratio. M
e
a
n
whil
e, amo
n
g
several
sol
v
ing
pro
c
e
ss, the
wea
k
point m
a
inly focu
sed
on elem
ent 8
944 whi
c
h lo
cated on the 1
88# tower. T
h
is
mean
s that
unde
r differe
nt climatic
condition
s,
stress-con
ce
ntrated iro
n
ba
r in the
stra
in
segm
ent is
unchan
ged. I
t
can
com
e
to the pre
lim
inary con
c
lu
sion: for the
strain
segme
n
t
system, 18
8#
tower i
s
the
wea
k
tower of the strain
segm
ent, and elem
ent 8944 lo
cate
d
on
wea
k
tower h
a
s the mo
st concentrate
d stress, and i
s
also the
wea
k
point of the strain se
gme
n
t.
4. The Improv
ed Mechanical Analy
s
is
Metho
d
of Strain Segmen
t We
ak Point
The metho
d
introdu
ce
d a
bove ca
n used to find the wea
k
towe
r and
wea
k
point, but
recy
cled
cal
c
ulation of entire strain seg
m
ent model
woul
d co
st a lot of time. In orde
r to work
more
effectively, we try to analyze one
-towe
r-t
wo
-lin
e model
of the alre
ady fou
nd wea
k
tower,
who
e
s mod
e
l
is
sh
own in
Figure 5. In
t
he a
nalysi
s
,
we l
oad
ed th
e same
limat
e conditio
n
s
as
strain
segme
n
t model
ana
lysis, so a
s
t
o
figur
e out
mech
ani
cal p
r
ope
rtie
s of 1
88# to
we
r. O
n
e
cal
c
ulatio
n of the one-to
we
r-two-lin
e mo
del, usin
g hig
h
-pe
r
forman
ce com
puter, t
a
ke
s 8 min
u
tes,
and to
compl
e
te cal
c
ul
atio
n of all condit
i
ons
nee
ds
a
total of 30 ho
urs.
Com
pare
d
with the tim
e
co
st of strain
segm
ent mod
e
l of one cal
c
ulation,
60 mi
nutes, the former on
e is re
ally efficient.
It can be see
n
from Table
4 that the maximu
m stre
ss ratio occurs
on eleme
n
t 611 in all
critical failu
re
co
ndition
s,
whi
c
h m
ean
s the a
ngle
ba
r
corre
s
po
ndi
ng to
elem
en
t 611 i
s
th
e
weak
point of one-t
o
wel
-
two
-
line
model of 188
# towel.
By compa
r
ison, we can find o
u
t element 611
on
the on
e-to
wel
-
two
-
line
mod
e
l an
d ele
m
e
n
t 894
4 on
th
e strain
se
gm
ent mod
e
l
correspon
d to th
e
same
an
gle
bar. In
anoth
e
r
way, wea
k
p
o
ints
obta
i
ned from th
e two
differe
nt method
s
are
c
o
ns
is
tent.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis of
Weak Po
sition i
n
Ove
r
he
ad li
ne
und
er Hea
vy Ici
ng Cond
ition by… (Liu
Chao
)
5019
Figure 5. Stress
Dist
ributio
n of Wea
k
To
wer
Table 4. The
Aggre
gation
of Critical F
a
il
ure Data
Icing thickness
（
mm
）
Wind speed
（
m/s
）
Element num. of
w
e
ak point
Stress
（
N/m
2
）
Ratio
6
20
611
-5209113
3
0.151
20
20
611
-4573427
6
0.1326
24
22
611
-4701084
8
0.1363
26
10
611
-5596582
4
0.1622
30
14
611
-5224695
2
0.1514
Figure 6. The
Contra
st Dia
g
ram b
e
twe
e
n
Different M
odel
s’ Stress
As sho
w
n in
Figure 5, co
mpared with
the
st
rain
se
gment
re
sult
,
t
he max
i
mum st
re
ss
ratio occu
rs at the same region,
an
d the distrib
u
tion
s of the st
re
ss co
ncentrati
on are
a
are also
con
s
i
s
tent. Selectin
g 20
element
s ne
ar the lo
cation of the element 611
whe
r
e st
re
ss is
con
c
e
n
trated
to make a
contra
st betwe
en two m
ode
ls, we
can fin
d
out the val
ues of
stre
ss in
two mod
e
ls
h
a
ve little differen
c
e. Acco
rding to
a
naly
s
is above, we
can co
ncl
u
d
e
:
re
sults of
o
n
e
-
tower-two-lin
e model
a
c
cu
rately refle
c
t
singl
e tower
mech
ani
cal p
r
ope
rtie
s of the st
rain
se
g
m
ent
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5011 – 50
21
5020
model, an
d a
nalysi
s
of th
e forme
r
on
e
coul
d obtai
n
the sa
me re
sults
as th
e
strain
se
gme
n
t
model.
Thro
ugh
ab
o
v
e cal
c
ul
ation
of the
st
rain
segm
ent m
o
d
e
l an
d o
n
e
-
to
wer-two-lin
e
model
of
wea
k
to
wer, we
a
c
q
u
ire a kind of
more effective
met
hod for po
sitioning
stru
ctu
r
ally wea
k
p
o
i
n
t o
f
the strai
n
segment: Firstly calculate
results
of strain
se
gme
n
t model in
several cli
m
ate
con
d
ition
s
to
figure o
u
t the
wea
k
to
wer,
and the
n
buil
d
up o
ne-to
wer-t
wo-li
ne m
odel of the
weak
tower to obtai
n the pre
c
ise posit
io
n of we
ak poi
nt(an
g
l
e
bar).
5. Conclusio
n
Based
on
st
udy of me
ch
anics finite
e
l
em
ent a
naly
s
is on
overh
ead lin
e, pre
c
ise 1:1
model
s of
strain
segm
e
n
t and o
ne-tower-tw
o-lin
e syste
m
s
of 500
kV ov
erhe
ad lin
e
are
establi
s
h
ed i
n
this pa
per.
For th
e m
a
ximum of
win
d
spe
ed
and
ici
ng thi
c
kne
s
s
that might
occur
to this
ce
rtai
n line, m
e
ch
anics finite
e
l
ement
cal
c
ul
ating of th
e
model
s u
nde
r ma
ny different
con
d
ition
s
of combin
ation
of wind sp
eed and i
c
in
g thickne
ss
are do
ne. Throu
gh stu
d
i
e
s
mentione
d ab
ove, the following
con
c
lu
si
ons a
r
e obtai
ned:
(1) T
h
ro
ugh
simulatio
n
of strain
seg
m
e
n
t model and
one-to
we
r-t
wo-li
ne mo
de
l, result
s
of these two
model
s are found to be
consi
s
tent. So
it present
s a
relatively simple app
ro
ach for
positio
ning
structu
r
ally we
ak poi
nt of the strain
seg
m
ent.
(2) Th
rou
gh
simulatio
n
of
strain
seg
m
ent mod
e
l, th
e wea
k
to
we
r of
strai
n
se
gment i
s
found, whi
c
h
provide
s
tech
nical
sup
port
for anti-i
c
e di
sa
ster.
(3) Un
der different con
d
itio
ns
of wind sp
eed
a
nd i
c
ing
thickne
ss
co
mbination, th
e we
ak
tower is
not
fixed. The m
o
st da
nge
ro
u
s
to
wer
doe
s exist from
the pe
rspe
ctive of proba
bili
ty.
Cap
a
city to
withsta
nd l
o
a
d
s
of i
c
ing
a
nd
wind
in
the diffe
rent t
o
we
rs in
st
ra
in segm
ent
are
different.
(4) In the
stra
in segm
ent m
odel, for the
dire
ction diffe
ren
c
e of wi
nd
load and i
c
in
g load,
with the increase of cro
s
sover
wind speed, t
he co
rre
sp
ondi
ng cro
s
sove
r ici
ng thickne
s
s of
tower-lin
e sy
stem would i
n
crea
se rath
er than d
e
cr
ease. In som
e
con
d
ition
s
, it is structu
r
ally
stable
whe
n
the icing i
s
thick. On the
contra
ry
, in the deici
ng p
r
ocess, with
icing thi
c
kne
ss
decrea
s
in
g, certain tower o
f
the strain
se
gment may h
a
ve stru
cture damag
e.
(5) Th
rou
gh
simulatio
n
of strain segm
ent model an
d one-to
we
r-t
wo-li
ne mod
e
l
, weak
point
of
the whol
e strai
n
segm
ent syst
em can
be
p
o
siton
ed, whi
c
h provide
s
reliable
ba
si
s for
installatio
n
of stre
ss monito
ring devi
c
e.
Referen
ces
[1]
Li N
a
. Dra
w
fin
i
te el
eme
n
t an
al
ysis
an
d stru
cture o
p
timizati
on of c
a
b
l
es st
a
y
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V-sha
p
e
d
iron
to
w
e
r
.
Master Degr
ee
T
heses of Xi
’a
n
Univ
ersit
y
of T
e
chnolog
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[2]
W
angj
un Hu
an
g. Model
ing
an
d Simul
a
tion R
e
searc
h
on L
i
g
h
tnin
g Over vol
t
age of 50
0kV H
y
dro
e
lectr
i
c
Station.
T
E
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n Journ
a
l o
f
Electrical Eng
i
ne
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g
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2; 10(4): 619-
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4.
[3]
P Srikanth, Ash
w
a
n
i Kumar
Cha
nde
l. Inver
s
e
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r
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w
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r S
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aults Identific
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E
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urna
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ngi
neer
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9(1): 99-1
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[4]
Xi
ao
hui
Xi
ao, Jing W
u
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pin
g
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Key
B
r
idge Marriott. 4th IEEE Conf
erence on Automation
Scienc
e and
Engi
neer
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g, W
a
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[5]
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JC
. L
ong
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t
u
d
i
n
al
l
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ad
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n
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r
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on
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e
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a
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U
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ANG Ming, Z
HU W
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C
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er pe
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insul
a
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n
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o
n
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itio
n.
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h Volt
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en-hu
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n
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ge Eng
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[8]
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-li
a
ng, MA Jun, W
A
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a
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Lu Ji
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eng,
Liu
chu
n
, Ch
en H
o
n
g
-do
n
g
,
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i
nite e
l
eme
n
t calc
ula
t
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iced
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w
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r
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y
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h Vo
ltage En
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neer
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n
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u
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i
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eng, Z
h
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e
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ad
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y
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ngi
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h
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i
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n
g
，
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en
Hon
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ause
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of to
w
e
r fa
lli
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w
n
a
n
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ice
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n i
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an 5
00kV
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w
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r transmis
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，
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Evaluation Warning : The document was created with Spire.PDF for Python.