TELKOM
NIKA
, Vol.11, No
.3, March 2
0
1
3
, pp. 1377 ~ 1382
ISSN: 2302-4
046
1377
Re
cei
v
ed O
c
t
ober 1
0
, 201
2; Revi
se
d Ja
nuary 14, 20
1
3
; Acce
pted Janua
ry 2
5
, 20
13
T
e
mperature Rise Comp
arison of Switchgear in SF
6
, N
2
,
and Air
Feng Hao*
,
Zhang Ju
nmin
School of
Auto
mation Sci
enc
e and El
ectrica
l
Engi
neer
in
g, Beih
ang U
n
iv
e
r
sit
y
, Beij
ing
10
019
1, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: fl
y
i
n
g
.fh20
06
@
y
ah
oo.com.c
n
A
b
st
r
a
ct
Based
on th
e
heat co
nd
uctio
n
eq
uatio
n, flui
d flow
gover
ni
ng e
quati
on
an
d rad
i
atio
n h
e
a
t
transfer
equ
atio
n, a
mu
lti-physics
cou
p
le
d
ma
th
e
m
at
ical mode
l
is e
s
tablis
hed,
th
e convecti
on hea
t
transfer
pro
b
l
e
m
betw
een so
lid
and fl
uid
is solve
d
by w
a
ll
function.
T
h
e
three di
mens
i
ona
l ther
ma
l fi
eld i
n
a typ
e
of
sw
itchgear fill
e
d
respectiv
e
ly
w
i
th
SF6, N2,
and
air are c
a
l
c
ulate
d
an
d an
aly
z
e
d
t
o
disc
u
ss the feasib
ilit
y of
usin
g air
or N
2
as the s
ubs
titution of SF
6
by the
finit
e
volu
me metho
d
. T
he resu
lts show
that th
e
temp
eratur
e fi
elds i
n
three
g
a
ses are s
i
mil
a
r in the
sw
itchge
ar. T
he temp
eratur
e
rise
of current-carr
y
in
g
loo
p
is the h
i
g
hest in SF
6 a
n
d
is the l
o
w
e
st in the a
i
r. So the co
nclus
i
on
coul
d be
ma
de
that air or N2
ca
n
repl
ace SF
6 as
the insul
a
tin
g
gas of sw
itc
hgear on the
pers
pective of te
mp
erature ris
e
.
Ke
y
w
ords
:
temp
eratur
e rise,
sw
itchgear
, SF
6
, N
2
, air
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Gas in
sulatio
n
technol
ogy has be
en gen
erally applie
d
in medium voltage switch
gear for
its enha
ncem
ent of reliabili
ty and dimin
u
tion of fl
oor
area
of swit
chgea
r. Du
e to the admi
r
a
b
le
insul
a
ting p
r
operty, SF
6
become
s
the
most fre
q
u
ently use
d
insul
a
ting ga
s in
swit
chg
ear.
Ho
wev
e
r, SF
6
is green
hou
se g
a
s,
so d
e
c
re
asi
ng a
nd
even forbi
ddi
ng the u
s
e
of SF
6
is surely
to
be the trend
in
the development of switch
gea
r [1]. Air
and N
2
are both inexpen
sive and
environ
menta
l
, so it is si
gni
ficative of ma
king
air
and
N
2
a
s
the
su
b
s
titution of S
F
6
in switchgear.
A lot of rese
arch about searchin
g the sub
s
titution o
f
SF
6
has be
en carrie
d ou
t both domestic
and overse
as. Referen
c
e [
2
] discus
se
s the bre
a
kdo
w
n prop
erty to explore the fe
asibility of usi
ng
N
2
and mixtu
r
e of N
2
an
d SF
6
as the
sub
s
titution of SF
6
. Refere
nce [3] discu
s
ses the i
n
sulat
i
on
prop
erty of N
2
or C
4
F
8
, to find out wh
eth
e
r they coul
d be the su
bstit
u
tion of SF
6
.
Tempe
r
atu
r
e rise dire
ctly
reflects
the sa
fety
performa
n
ce of
switch
gear,
so it is one of
the significant factors of
analyzing the
feasibility of
substitution of SF
6
. Howe
v
e
r, refe
ren
c
es
based on the
perspe
c
tive of temperatu
r
e rise
of se
archin
g the su
b
s
titution ga
s
of SF
6
are ra
rely
to be s
e
en.
Heatin
g and dissip
ating proce
s
s is a co
mplic
ate p
h
ysical process combine
s
con
ductio
n
,
conve
c
tion a
nd radiatio
n, and it could
be anal
yzed by mathematical modeli
n
g
and numeri
c
al
cal
c
ulatio
n. Ho
weve
r
,
it is dif
f
icult to carry
out this calculation
becau
se of the com
p
licate 3D
model of the swit
chg
ear a
nd the larg
e
g
r
id num
bers i
n
nume
r
ic
cal
c
ulatio
n.
In this pap
er,
based on th
e heat cond
u
c
tion eq
uatio
n, fluid flow g
o
vernin
g eq
u
a
tion and
radiatio
n he
a
t
transfe
r eq
u
a
tion, the mu
lti-physi
cs
co
upled m
a
the
m
atical m
ode
l is e
s
tabli
s
h
ed,
and wall function is used to solve the convecti
o
n
heat transfer problem betwe
en the solid and
the gas. After the simulatio
n
and cal
c
ula
t
ion of the th
ermal field re
spe
c
tively in
SF
6
, N
2
and
air,
the 3D distri
bution of th
ermal field resp
ec
tively in three gases ha
s been
obtained. Then
compari
s
on and analysi
s
of the cal
c
ul
ating re
sults has been
done to discuss t
he feasibility
o
f
usin
g N
2
and
air as the
sub
s
titution of SF
6
on the basi
s
of temperatu
r
e ri
se.
2. Mathema
t
i
cal Model
[4]
The gen
eration of heat in
switchge
ar i
s
ca
used by heat loss of resi
stan
ce
s. The heat
transfe
rred in
the co
ndu
cto
r
s i
s
mai
n
ly b
y
cond
uc
tio
n
. Heat tra
n
sfe
r
s from
co
ndu
ctors to the g
a
s
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02-4
046
TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1377 – 1
382
1378
by conve
c
tio
n
and ra
diati
on, and finall
y
transfe
rs to the ambie
n
t air outsid
e
the swit
ch
gear
throug
h the e
n
clo
s
u
r
e.
2.1. Thermal Gov
e
rning Equation
s
The k-
turbu
l
ence model i
s
introd
uced in the heat transfer a
nd fluid flow, includi
ng the
mass, mome
ntum, ene
rgy con
s
e
r
vation
equation
s
, k equation
an
d
equation.
The gove
r
ni
ng
equatio
ns
ca
n be written i
n
con
s
e
r
vatio
n
form [5] as follows e
qua
tion (1). So the variabl
es
of
velocity, temperatu
r
e, k an
d
can be solved usi
ng the nume
r
i
c
al
method.
()
()
(
)
div
V
d
i
v
g
rad
S
t
(1)
Whe
r
e
is the universal variabl
e whi
c
h is
ex
pre
s
sed a
s
temperature,
velocity,
pre
s
sure, k a
nd
res
p
ec
tively;
V
is the velocity vect
or;
i
s
the co
efficient of dif
f
usion;
S
is t
h
e
sou
r
ces,
whi
c
h in
clu
de t
he Joule’
s lo
ss
and
radi
a
t
ion heat flu
x
from the condu
ctor to t
he
encl
o
sure.
The Jo
ule’
s loss is express
ed by the fol
l
owin
g equati
on:
2
I
R
.
(2)
Whe
r
e
i
s
th
e Joul
e’s lo
ss,
I
is
the c
u
rrent,
R
is
the res
i
s
t
ance.
In the switch
gear, the rad
i
ation from the cond
ucto
r to the enclo
sure is ca
use
d
by th
e
temperature
differen
c
e b
e
twee
n the con
ducto
r su
rfa
c
e and the
en
clo
s
ure.
The
heat tran
sfe
r
by
radiatio
n is calcul
ated by Stefan-Boltzman’s la
w a
s
follows.
)
(
4
2
4
1
1
T
T
A
. (3)
Whe
r
e
T
1
an
d
T
2
are the
condu
cto
r
surface tempe
r
ature and e
n
clo
s
u
r
e tem
peratu
r
e
r
e
spec
tively, A
1
is the con
ducto
r surfa
c
e are
a
,
is the con
d
u
c
tor
emissivity co
nstant
[6],
σ
is
the Stefan-Bo
ltzman
con
s
tant,
i
s
the radiation h
eat flux.
2.2. Bounda
r
y
Conditions
Gene
rally, wall functio
n
a
nd the lo
w
Re (Reynold
s
numbe
r) k-
turbul
en
ce m
odel a
n
d
the conve
c
tio
n
heat transf
e
r co
efficient
can be appl
ied to deal with the soli
d-fluid bo
und
ary
con
d
ition
s
[7]. Compa
r
ed
with the low
Re mo
del wh
ich ne
ed
s increa
sing the
g
r
id den
sity, wall
function can redu
ce the gri
d
s in SF
6
gas adjace
n
t to the con
d
u
c
tors, so CPU ti
mes an
d me
mory
stora
ge ca
n be saved more
in computer [8, 9]. T
he initial temperatu
r
e of
the cond
uctors and th
e
encl
o
sure m
u
st be assu
med firstly if using t
he conve
c
tion h
eat transfe
r coeffici
ent [10].
Ho
wever, the
initial temperature can not
be consi
dere
d
in wall function. Therefo
r
e, we introdu
ce
wall function
to calculate the fluid flow
a
nd heat transfer on the solid-SF
6
gas b
ound
ary in this
pape
r.
In wall fun
c
tio
n
, the dimen
s
ionle
ss va
ria
b
les
of velocit
y
u
+
, distance
y
+
and te
mp
eratu
r
e
T
+
are re
sp
ectively defined by the followi
ng equ
ation
s
:
/
w
u
u
. (4)
w
y
y
v
. (5)
1/
4
1
/
2
()
(
)
/
W
Wp
TT
c
k
T
qc
. (6)
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TELKOM
NIKA
ISSN:
2302-4
046
Tem
peratu
r
e
Rise Com
p
a
r
i
s
on of Swit
ch
gear in SF
6
, N
2
, and Air (F
eng Hao)
1379
Wall functio
n
assum
e
s a logarith
m
ic bo
unda
ry
layer adja
c
ent the con
d
u
c
tors, in which
the
u
+
and
T
+
sati
sfy the basi
c
loga
rith
mic equ
ation
s
. So the wal
l
shea
r stress
w
and the
heat
flux
q
w
from wall given
by followin
g
equ
ations
(7
) an
d (8
) are rel
a
ted to SF
6
g
a
s flo
w
th
r
o
u
gh
the
logarith
m
ic e
quation
s
.
P
W
P
t
w
y
u
u
. (7)
P
W
P
t
W
y
T
T
q
. (8)
Whe
r
e
T
W
,
T
P
and
u
w
,
u
p
are the tem
p
eratu
r
e an
d the velocity o
n
wall a
nd in
the gas
r
e
spec
tively;
is the fluid
den
sity; c
p
is the spe
c
ific h
eat at co
nsta
nt pre
s
sure;
v
is
th
e
k
i
nematic
v
i
sco
sit
y
;
c
is the turbulent
model con
s
t
ant;
t
is the turbule
n
t viscosity;
t
is the turbule
n
t hea
t
c
o
nduc
tivity.
Con
s
e
quently
,
q
w
can be obtained a
c
cording to the equation
s
(4
)-(8). And
t
and
t
can
be expre
s
sed
as follows eq
uation
s
(9
)-(1
0).
p
t
p
y
u
.
(9)
p
tL
p
y
T
. (10)
Whe
r
e
L
is the Prandtl
numbe
r;
is the gas h
e
a
t cond
uctivity;
is the dynami
c
v
i
sco
sit
y
.
3. Simulation Computati
on
3.1. Geometr
y
Model of the S
w
i
t
chg
e
ar
The main compon
ents
of the switchgea
r ar
e b
u
s ba
r, circuit brea
ker,
current
transfo
rme
r
,
and a th
ree
-
p
o
sition i
s
olati
on switch. Th
e switch
gea
r
has th
ree
ph
ase
s
, an
d ea
ch
pha
se i
s
coordinate
with e
a
ch
other. T
h
e bu
s ba
r
a
n
d
thre
e-p
o
siti
on isolation
switch
are
located
in the lower p
a
rt of the cyli
nder,
circuit b
r
ea
ke
r and
current tran
sfo
r
mer
are l
o
ca
ted in the up
per
part of the cyl
i
nder, an
d the
cable
wire i
s
extract
ed
on the top of the cylinde
r. The
rate current of
the swit
chg
e
a
r
is 200
0A, ra
te voltage
is 40.5kV, and t
he frequ
en
cy is 50
Hz.
Each pha
se
of the switch
gear is ind
e
p
ende
nt with each other
, a
nd they share th
e
same
structu
r
e, so on
e p
hase could
o
n
beh
alf of
the othe
r two
duri
ng the
calcul
ation. In
this
p
a
p
e
r
,
the mi
ddle ph
ase is the study obj
ect. It
s mod
e
l
and comp
on
ent
s i
n
cu
rre
n
t-ca
rryin
g lo
op
are as sho
w
n
in Figure 1.
The encl
o
sure is def
ined as the calcul
ation domain bo
unda
rie
s
, and
it
has b
een
set as ambi
ent temperature.
(a) Th
e external geom
etri
c model
(b)
Comp
one
nts in the
cu
rrent-carrying l
oop
Note:
1-cond
u
c
ting ro
d1, 2-c
ond
uctin
g
pl
ate, 3-contact fi
n
ger, 4-co
nd
ucti
ng b
a
n
d
, 5-mo
vabl
e co
nducti
n
g
pol
e, 6-fixed co
nducti
ng p
o
le,
7-con
ductin
g
rod2, 8-e
x
ter
n
a
l
bus
Figure 1. The
model of swit
chg
ear
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02-4
046
TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1377 – 1
382
1380
3.2. Parameter and Initial Condition
s
Acco
rdi
ng to
the Thomp
s
o
n
theory [11], increa
sin
g
the gas pre
s
sure could co
nsi
dera
b
ly
improve the i
n
sul
a
ting abili
ty of the insulating gas
in the swit
chgear. The insul
a
ting ability of
N
2
and air is ap
proximately 1
/
3 of
the one of SF
6
at the
same pre
ssure. So in order to make
sure
the three ga
ses ha
s the same insulatin
g
ability, and under the p
r
emise of lo
w gas p
r
e
s
sure
in
the switchge
ar, the initial
pre
s
sure of
N
2
and air is 0.25MPa, an
d the initial p
r
essu
re of SF
6
is
0.08MPa in
this pap
er.
The initial tempe
r
at
ures of the thre
e gases
are
all 20. Their
thermo
dynam
ic paramete
r
s can ref
e
r to referen
c
e [12].
The mate
rial
of the co
ndu
ctors i
n
the
cu
rre
nt
-carrying
loop, bu
shi
n
gs a
nd e
n
cl
o
s
ure a
r
e
cop
per, e
pox
y resin
and
steel respe
c
tively. Their therm
odynami
c
pa
ram
e
ters can
refer t
o
referenc
es
[12, 13].
Con
s
id
er the
skin coeffici
ent of every condu
cto
r
, the final calo
rific value of every
con
d
u
c
tor i
s
the pro
d
u
c
t of Joul
e’s l
o
ss an
d rel
e
vant ski
n co
efficient. The
power of m
a
jor
comp
one
nts
of current
-ca
r
rying loop at
20
℃
is li
sted
in Table1.
3.3. Grids
The hexah
ed
ral gri
d
is u
s
e
d
in the nume
r
ical
cal
c
ulati
on, and the to
tal grids
rea
c
h
1.2×1
0
6
in the cabi
net. The grid
s are as sho
w
n in Fig
u
re 2.
Table 1. Power loss of co
mpone
nts(20
℃
)
component
Power(W
)
conducting rod1
34.2
conducting rod2
43.8
conducting band
48.3
movable conducting pole
32.7
fixed conducting
pole
33.2
exter
nal bus
36.0
Figure 2. The
mesh of num
erical cal
c
ul
ation
3.4. Results and An
aly
s
is of
N
umerical Calculation
3.4.1. Thermal Field
The tempe
r
at
ure di
strib
u
tio
n
in three ga
ses is a
s
sho
w
n in Figure 3.
(a) SF
6
(b) N
2
(c
) air
Figure 3. Te
mperature fiel
d of
switchge
ar in thre
e ga
se
s
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Tem
peratu
r
e
Rise Com
p
a
r
i
s
on of Swit
ch
gear in SF
6
, N
2
, and Air (F
eng Hao)
1381
The rea
s
o
n
s cau
s
ed differen
c
e
s
of tempe
r
ature are the dive
rsity of resi
stance
values, the
si
ze of the
co
n
ducto
rs, a
nd
the co
ndi
tion
s of air flo
w
.
Con
d
u
c
tor
which
own a lo
wer
resi
stan
ce va
lue and a larger si
ze, gets a lower
te
mperature; o
n
the c
ontra
ry, it gets a higher
temperature.
Like the
co
n
ductin
g
ban
d
in Figur
e 3,
it has a hi
gh
resi
stan
ce va
lue and
a sm
all
size com
p
a
r
ed with oth
e
r co
ndu
cto
r
s in the
cu
rre
nt-carrying
loop,
so it gets a hig
her
temperature.
Hot gas fl
ows up
wardl
y
, so t
he upper p
a
rt of
the current
-ca
rryin
g loo
p's
temperature i
s
high
er than
one of the lo
wer p
a
rt.
3.4.2. Comp
arison and
Analy
s
is of Te
mperatu
r
e Rise in the Th
ree Gas
e
s
Dra
w
the temperatu
r
e valu
es in three ga
se
s into curv
es, as sho
w
n
in Figure 4. In Figure
4, X-axis is compon
ents n
u
mbe
r
s (th
e
orde
r is n
u
mb
ered from lower pa
rt to the uppe
r pa
rt of the
curre
n
t-carrying loop
), Y-a
x
is is the ratio
of co
mpon
en
ts' tempe
r
ature to the initial temperatu
r
e.
Figure 4. The
temperatu
r
e
of current carrying co
ndu
ct
or in thre
e ga
se
s
It could be se
en from Figu
re 4 that the tempe
r
ature d
i
stributio
ns of
the three ga
se
s are
simila
r. The tempe
r
ature ri
se in SF
6
is the high
est, a
nd is the lo
we
st in air.
The qua
ntity of heat tran
sferred from th
e con
d
u
c
tors to the gas in the three d
i
fferent
gases is supposed to be the same, so the only par
ameter that affects the gas
diffusion abilit
y i
s
thermal diffusivity. The gas diffusion abili
ty gets be
tter with the thermal diffusivity growi
ng larg
er,
so the heat
prod
uced by the curre
n
t-carryin
g loop
coul
d diffuse
more ra
pidly
.
Thus insula
ting
gas
with a higher the
r
mal
diffusivity has a lower tem
peratu
r
e ri
se
in the current
-ca
rryin
g loop
. It
coul
d be con
c
lud
ed that,
unde
r the premise of ce
t
e
ris pa
ribu
s, temperature
rise turns lo
wer
whe
n
ga
s get
s a high
er the
r
mal diffusivit
y
.
The exp
r
e
ssi
on of therm
a
l
diffusivity is
/(
)
p
ac
, where
is the
thermal diffus
i
vity
,
is
the thermal conduc
tivity,
c
p
is the sp
ecifi
c
h
e
a
t cap
a
city o
f
gas,
is
the dens
i
ty. After
cal
c
ulatio
n, the seq
uen
ce
of the three therm
a
l diffusi
vities is
6
2
SF
N
air
.So tempe
r
ature
rise of curren
t-ca
rrying lo
o
p
in SF
6
is
the highes
t; one in air is
the lowes
t. In s
u
mmary, from
the
perspe
c
tive o
f
temperatu
r
e
rise, u
s
ing N
2
and air a
s
the su
bstitutio
n
of SF
6
is
feas
ible.
4. Conclusio
n
In this pap
er,
the cou
p
led
mathemati
c
al
m
odel which
involves differential
equa
tions of
con
d
u
c
tion, conve
c
tion a
nd radiatio
n is establi
s
h
e
d
for calcula
t
ing the thermal field of
the
swit
chg
ear. Wall functio
n
is used to solve t
he convection heat transfe
r pro
b
l
e
m betwee
n
the
solid a
nd the
gas. Th
e finite volume met
hod is a
pplie
d to solve the
differential e
quation
s
for t
h
e
3D geom
etry model of the
swit
chg
ear. T
he thermal
field of the switchge
ar is si
mulated, and
th
e
distrib
u
tion of
temperatu
r
e
is obt
ai
ned re
spe
c
tively in SF
6
, N
2
, and
air
.
The result
s sh
ow that the
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distrib
u
tion
s of temperatu
r
e in the three gase
s
are si
milar
,
and the
temperatu
r
e rise in SF
6
is the
highe
st, and i
s
prove
d
to be the lowe
st in air
.
Af
ter co
mp
a
r
ing the t
herm
a
l field in the swit
chg
ear
respectively filled with SF
6
, N
2
and air,
it could be summed up that, from the persp
ective of
temperature rise, the temperatu
r
e ri
se in N
2
and air i
s
lowe
r than the one in SF
6
, hence u
s
i
n
g
N
2
and air a
s
the
sub
s
titution of SF
6
to be the insulating
gases in
swit
chg
ear i
s
fea
s
ible.
Akno
w
l
e
dge
ment
This work wa
s sup
p
o
r
ted by the National
Natural Science Found
ation of Chin
a unde
r
Grant No.5
1
1
7700
5.
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