TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 4988 ~ 49
9
5
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.432
3
4988
Re
cei
v
ed Se
ptem
ber 4, 2013; Re
vi
sed
Februar
y 5, 2
014; Accepte
d
March 7, 20
14
Electromagnetic-thermal Scale Model of Gas-Insulated
Bus Bars
Li Hongtao*,
Shu Naiqiu, Li Ling, Peng Hui, Li Zipin
Schoo
l of Elect
r
ical En
gin
eeri
ng, W
uhan U
n
i
v
ersit
y
,
No.8, Don
g
h
u
n
an Ro
ad, Ho
ng
shan D
i
strict, W
uhan 4
3
0
072
, China
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 5pro@
163.co
m
A
b
st
r
a
ct
Know
led
ge of the
he
at
diss
ip
at
ion
ab
ility of
gas-i
nsul
ated
bus b
a
rs (GIB) is par
a
m
o
u
n
t in th
e
desi
gn stag
e. T
o
reduce th
e
capita
l cost, a scale
mo
del w
h
ich h
a
s the i
d
entica
l
el
ectro
m
a
g
n
e
tic-ther
ma
l
character
i
stics
of a full sc
al
e
GIB is desig
ne
d in th
is
p
aper.
T
he scal
i
ng
re
latio
n
shi
p
s of t
he p
o
w
e
r loss
es,
convecti
on h
e
a
t transfer, radia
n
t heat tra
n
sfer
and th
e
r
ma
l eq
uil
i
bri
u
m are
ana
ly
zed bas
ed o
n
the
gover
nin
g
e
q
u
a
tions
an
d no
n
-
di
mens
io
nal c
o
rrelati
ons.
C
u
rrent de
nsities,
pow
er loss
es, convectiv
e
h
e
a
t
transfer coeffic
i
ents an
d te
mperatur
e distrib
u
tions i
n
con
d
u
ctor and ta
nk
of t
he prototype an
d the sc
ale
mo
de
ls u
nder
different
loa
d
c
u
rrents
are c
o
mp
are
d
by
F
E
M (F
inite E
l
e
m
ent Meth
od). T
he
effectiven
es
s of
scale
mo
dels i
s
valid
ated by t
he co
mp
aris
o
n
betw
een calc
u
l
ated a
nd test results.
Ke
y
w
ords
:
scale
mod
e
l,
gas-insu
l
ate
d
bus bars
(GIB
), temper
ature rise te
st, non-di
me
n
s
ion
a
l
correlati
ons, fin
i
te ele
m
ent me
thod (F
EM)
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
The cu
rrent-carryin
g cap
a
city is
of critica
l
importan
c
e to the desig
n of gas-i
nsulat
ed bu
s
bars (GIB), whi
c
h i
s
det
ermin
ed by
the maxi
mu
m permi
ssibl
e
tempe
r
ature [1]. The h
eat
gene
ration
a
nd di
ssipatio
n in
GIB, in
cludi
ng
po
wer l
o
sse
s
,
convectio
n
a
n
d radiation,
are
compl
e
x p
r
ob
lems. T
h
e
r
efo
r
e, inve
stigati
on o
n
el
ect
r
o
m
agneti
c
-th
e
rmal
cha
r
a
c
teristics of
GIB i
s
necessa
ry in unde
rsta
ndin
g
the improve
m
ent
of desig
n and man
u
fa
cture p
r
o
c
e
sses [2, 3].
Tempe
r
at
u
r
e
rise t
e
st
is
t
he most
di
r
e
ct
an
d co
nvincibl
e mea
n
s in inve
stig
ating the
electroma
gne
tic-the
r
mal chara
c
te
risti
c
s
of
GI
B. Tests have be
e
n
ca
rrie
d
out
to analyze t
he
temperature
rise
cha
r
a
c
teri
stics of the G
I
B [4].
Long term te
st of b
u
ried
GIB is
pre
s
ente
d
in
[5].
Ho
wever, th
e tests u
s
in
g full scal
e
GIB ar
e dee
med to be
co
stly and time co
nsumi
ng.
Con
s
e
quently
, scale mo
de
ls, whi
c
h hav
e the advant
age
s of good
practi
cability
and econom
y,
have bee
n wi
dely employe
d
to simulate
the perfo
rma
n
ce of ma
ny appa
ratu
s [6-8]. Howeve
r, the
scaling m
e
th
ods
of multi-physi
cal field
pro
b
le
m
s
ca
nnot be
re
alized
by traditi
onal lin
ear
scaling
method, whi
c
h
a
r
e prove
d
to
be ch
allen
g
ing
ta
s
ks. Ci
rcuital
an
d ki
nematic scali
ng relation
shi
p
s
of the rail
gu
n syste
m
, wh
ich i
s
an
ele
c
tromag
netic-mech
ani
cal p
r
oble
m
, are i
n
vestigate
d
a
nd
verified by nu
meri
cal sim
u
l
a
tion [9]. The literature [10
]
has ca
rri
ed
out a gro
und
simulatio
n
test
to study
the t
herm
a
l p
r
obl
e
m
of
spa
c
e
c
rafts un
de
r the
co
ndition
of
microgravity based
on
a fl
uid-
thermal
scale
model and h
eat flow com
pen
sation te
chniqu
e.
In this pap
er,
scaling m
e
th
od of ele
c
tro
m
agneti
c
-th
e
rmal pro
b
lem i
n
GIB is inve
stigated.
The scali
ng
relation
shi
p
s of powe
r
lo
sses a
nd ra
diant heat transfe
r are d
e
rived fro
m
the
governi
ng
eq
uation
s
, whil
e the
scali
n
g
of
conve
c
tio
n
he
at tra
n
sf
er i
s
analy
z
e
d
with
the
he
lp of
non-dime
nsio
nal correl
ations. 1/4-scal
e
mo
del
s of
the
singl
e- and
three-pha
se
GIB
are
establi
s
h
ed. The finite ele
m
ent method
(FEM)
i
s
used to solve t
he co
uple
d
e
l
ectro
m
ag
neti
c
-
fluid-the
r
mal
probl
em in
G
I
B. The cal
c
ulated results of the scale
model
s a
r
e
comp
ared
with
those of the p
r
ototypes
a
n
d
the experime
n
tal data.
2. Scaling method
GIB is m
a
inly
com
p
o
s
ed
of
alumin
um
en
clo
s
ure, cond
uctor,
epoxy
resi
n in
sul
a
to
rs
and
insul
a
ting g
a
s (SF
6
)
.
Th
e
c
r
o
s
s
s
e
c
t
io
ns
o
f
s
i
ng
le
- a
nd th
r
e
e-
ph
as
e
G
I
B a
r
e sh
own
,
r
e
s
p
ec
tive
ly
,
in Figu
re
1(a
)
and Fi
gu
re 1
(
b). In th
e the
r
mal a
nalysi
s
of GIB, the h
eat
tran
sfer mech
ani
sm
s are
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TELKOM
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An Approa
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Based on
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…
(Xiang Li)
4989
con
d
u
c
tion, convectio
n
an
d radiatio
n. The heat ge
ne
rated in the
condu
ctor a
n
d
the enclo
su
re is
transfe
rred from the interi
or su
rfa
c
e to the exte
rnal
surfa
c
e by condu
cti
on. Natural conve
c
tive
heat tran
sfer,
which is
cau
s
ed by the d
e
n
sity differen
c
e of the fluid
,
exists
at the interface of the
SF
6
gas and
the con
d
u
c
to
r and that of the SF
6
gas and the en
cl
osu
r
e. The
r
m
a
l radiatio
n h
eat
transfe
r from
the encl
o
sure
surfa
c
e to th
e su
rro
undi
n
g
air an
d bet
wee
n
the con
ducto
r an
d the
encl
o
sure i
s
signifi
cant, e
s
pe
cially wh
e
n
the te
mperature differen
c
e in
cre
a
ses.
To the authors’
kno
w
le
dge, a
pproxim
ately 60% of
the h
eat gen
erate
d
in the GIB i
s
di
ssi
pated t
o
the surrou
n
d
ing
air by radi
atio
n.
(a) Singl
e-ph
ase GIB
(b) T
h
re
e-p
h
a
s
e GIB
Figure 1.
Schematic
Diag
ram of Single
-
pha
se a
nd T
h
ree
-
p
h
a
s
e G
I
B
Figure 2.
Flo
w
Ch
art of Scaling on GIB
The flo
w
cha
r
t of scalin
g
on GIB is
sh
own i
n
Fi
gu
re 2. First of a
ll, the temperature
rise
mech
ani
sm o
f
GIB is a
nal
yzed to
build
the ma
the
m
a
t
ical mo
del
s;
se
con
d
ly, derive the coupl
ed
field scalin
g
relation
shi
p
s
by analy
z
ing
the
simila
rit
y
of tempe
r
a
t
ure
rise in
GIB theoretically;
thirdly, discu
ss the pa
ra
meters of scale model
a
c
cording to the scali
ng rel
a
tionship
s
; finally,
asse
ss the
correctn
ess a
nd rob
u
st
n
e
ss of scale m
odel by FEM
and
test re
sults, if the scale
model cann
ot satisfy the experim
ental re
quire
ment
s, the paramete
r
s sh
ould b
e
furthe
r modifie
d
.
3. Simi
larit
y
Anal
y
s
is
3.1. Similarity
of Po
w
e
r L
o
sses
The follo
win
g
assu
mption
s are ma
de i
n
the a
nal
ysi
s
proce
s
s: di
splacement
cu
rre
nt is
negle
c
ted; th
e current flo
w
ing
in the
condu
ctor
is sinusoidal; the
relu
ctivity is co
nsi
dered
a
s
c
o
ns
tant.
A
,
－
A
method
is e
m
ployed
to investig
ate
the e
ddy
cu
rre
nt p
r
oble
m
, and th
e
ed
d
y
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TELKOM
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KA
Vol. 12, No. 7, July 201
4: 4988 – 49
95
4990
curre
n
t field
is divided i
n
to eddy
cu
rre
nt V
1
and
non-eddy
current re
gion
V
2
. Governing
equatio
ns of the two re
gion
s are d
e
scrib
ed as [11]:
e
1
(
)
(
)
()
()
in V
((
)
(
)
)
0
TT
t
TT
t
A
AA
J
A
(
1
)
s2
(
)
(
)
in V
AA
J
(
2
)
Whe
r
e
ν
is the reluctivity,
A
is the ma
g
netic vecto
r
p
o
tential,
σ
is the co
ndu
ctivity,
t
is the time,
Φ
is the el
ectri
c
scal
ar
potential,
J
e
and
J
s
a
r
e, resp
ectively, the eddy
current den
sity and
sou
r
ce cu
rren
t density,
T
is the temperat
ure.
Joul
e he
at loss
P
c
in th
e co
ndu
ctor
and e
ddy cu
rre
nt loss
P
t
in the en
clo
s
ure a
r
e
expre
s
sed a
s
:
2
s
c
V
1
2(
)
Pd
v
T
J
(
3
)
2
e
t
V
1
2(
)
Pd
v
T
J
(
4
)
Acco
rdi
ng to
the equatio
ns mentio
ne
d above,
the
similarity cri
t
erion
s
of the power
losse
s
are
su
mmari
zed a
s
:
2
2
s
12
3
22
22
s
45
2
c
t
ΠΠ
Π
ΠΠ
Jl
ll
tA
A
Jl
A
P
lP
，，
，
，
(
5
)
3.2. Similarity
of Heat Tr
a
n
sfer
The tra
d
ition
a
l scaling
of natural
co
nvecti
on i
s
ba
sed on th
e co
ntinuity equat
ion, the
Navier-Stoke
s eq
uation
an
d the e
ner
gy equatio
n. Ho
wever, it i
s
kn
own th
at scali
ng relation
shi
p
s
of natural con
v
ection h
eat tran
sfer
ca
n h
a
rdly be
fulfilled in m
u
lti-ph
ysical fiel
d p
r
oblem
becau
se
it is difficult t
o
find o
u
t an
app
rop
r
iate
fluid
media.
Becau
s
e
the
temperature
gra
d
ient o
n
the
outer
su
rface
of con
d
u
c
tor and e
n
cl
osure is n
o
t obvio
us, the
scalin
g of average
temperature
on
con
d
u
c
tor an
d enclo
su
re i
s
fulfilled app
roximately by analyzing th
e rate of hea
t transfer, wh
ile
the exact di
stribution of t
he conve
c
tive heat tra
n
sf
er coefficie
n
t is not q
u
ite
necessa
ry. With
rega
rd to
sin
g
le-p
ha
se GI
B, the equivalent thermal
con
d
u
c
tivity
λ
e
is used t
o
cal
c
ul
ate the
conve
c
tion
h
eat tran
sfe
r
Q
scc
between th
e cond
ucto
r a
nd the
en
clo
s
ure i
n
(6) [4],
and th
e radia
n
t
heat tran
sfer
Q
scr
betwee
n
the con
d
u
c
tor and the en
cl
osu
r
e is exp
r
essed in (7).
ec
e
scc
ei
co
0.2
3
2
0.2
vc
f
e
i
c
o
f
p
e1
f
1
f
ff
2-
=
ln
/
--
CG
r
P
r
C
TT
Q
DD
gT
T
D
D
C
(
6
)
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TELKOM
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ISSN:
2302-4
046
An Approa
ch
for Assessin
g
Harm
oni
c Em
ission Le
vel
Based on
Ro
bust Partial
…
(Xiang Li)
4991
44
ce
sc
r
c
o
co
co
ei
ei
11
1
TT
QD
D
D
(
7
)
Whe
r
e
Gr
1
and
Pr
1
are the
Gra
s
hof
num
ber
and th
e P
r
andtl
numb
e
r
of SF
6
,
C
1
is a con
s
tant,
D
ei
and
D
co
a
r
e the inne
r diam
eter of en
closure an
d out
e
r
diameter of
con
d
u
c
tor respectively,
T
c
,
T
e
and
T
f
are the tempe
r
atu
r
e of co
ndu
ctor, encl
o
sure and SF
6
, res
p
ec
tively.
g
is the gra
v
ity
accele
ration
,
ρ
f
, C
p
,
λ
f
and
μ
f
are, resp
e
c
tively, the density, sp
e
c
ifi
c
heat, therm
a
l con
d
u
c
tivity
and dyn
a
mic visco
sity of SF
6
,
δ
is Stefan-Bolt
zman
n co
nsta
nt,
ε
co
and
ε
ei
are t
he emi
ssivity of
outer surfa
c
e
of cond
ucto
r and inn
e
r surf
ace of en
clo
s
ure.
For three
-
ph
a
s
e GIB, the convectio
n
he
at transfe
r
Q
tc
c
and ra
diant
heat tran
sfe
r
Q
tcr
are
expre
s
sed a
s
[12]:
1.
25
0.
6
0
.
7
5
2c
o
c
e
tc
c
1.25
0.
6
ei
co
co
ei
3C
2.2
l
n
1
2.4
2.4
pD
T
T
Q
DD
DD
(
8
)
44
ce
tcr
c
o
co
c
o
ei
ei
3
11
1
TT
QD
D
D
(
9
)
Whe
r
e
p
is th
e pre
s
sure of SF
6
.
Q
ec
and
Q
er
a
r
e the
natu
r
al
co
nvection
h
eat tran
sf
e
r
a
nd radia
n
t he
at tran
sfer be
tween
the encl
o
sure
and the ambi
ent air, whi
c
h
are de
scrib
e
d
as:
ec
eo
e
a
0.
3
0.
3
32
ve
a
e
o
a
p
a
a2
2
2
a2
eo
eo
a
a
-
CG
r
P
r
C
QD
h
T
T
gT
T
D
C
h
DD
-
(
1
0
)
44
er
eo
e
o
e
a
QD
T
T
(
1
1
)
Whe
r
e
h
is th
e conve
c
tive heat tran
sfer
coeffici
ent,
T
a
is the ambie
n
t temperatu
r
e,
Gr
2
and
Pr
2
are the Grashof numbe
r a
nd Prandt
l n
u
mbe
r
of ambient air,
C
2
is a con
s
tant,
D
eo
is the outer
diamete
r
of
e
n
clo
s
u
r
e,
ρ
a
, C
pa
,
λ
a
an
d
μ
a
are, re
spe
c
tively, the d
ensity, spe
c
ific h
eat, the
r
m
a
l
con
d
u
c
tivity a
nd dynami
c
viscosity of air.
Heat transf
e
r on the
con
ducto
r an
d e
n
clo
s
u
r
e
su
rface
s
in
stea
dy state follo
ws th
e
thermal e
quili
brium e
quatio
ns.
sc
c
s
c
r
c
tc
c
t
c
r
ct
e
c
e
r
s
i
ngl
e-phas
e
cas
e
t
h
r
ee-phas
e
cas
e
QQ
P
QQ
PP
Q
Q
(
1
2
)
The simil
a
rity indexes of convective he
at transfe
r are summ
ari
z
e
d
as follo
ws:
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046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 4988 – 49
95
4992
0.
8
0
.
6
0.
4
0
.
2
0.6
0
.
7
5
0
.9
ff
p
67
8
0.
2
tcc
e
c
fs
c
c
scr
t
c
r
er
c
91
0
1
1
1
2
co
co
e
o
cc
c
c
c
13
14
15
1
6
1
7
scc
s
c
r
t
c
c
e
r
e
c
Π
,
Π
,
Π
,
Π
,
Π
,
Π
,
Π
,
Π
,
Π
,
Π
,
Π
,
Π
t
lC
pl
l
QQ
Q
QQ
Q
P
ll
l
P
PP
P
P
P
Q
QQQ
Q
(
1
3
)
3. Scale Model Design
Usi
ng the
sa
me materi
al, all the scale f
a
ctors
of the
material p
a
ra
meters are set to 1
.
The
scale f
a
ctors
of the po
we
r lo
sse
s
, heat
transfe
r, ga
s
den
sity and
load
cu
rre
nt are
summ
ari
z
ed as:
ct
scc
f
t
c
c
scr
t
cr
ec
er
f
22
0.
6
0
.
4
0.
6
0
.
7
5
0.
9
2
1
.
5
0.
417
,
,
,
,
PP
I
l
Ql
Q
p
l
Ql
Q
l
Ql
Q
l
lt
l
I
l
p
l
KK
K
K
KK
K
K
K
K
KK
K
K
KK
K
K
KK
K
K
K
K
K
K
,
,
,
，，
，
(
1
4
)
Con
s
id
erin
g the re
stri
ction of experiment
al
conditio
n
s
and fabri
c
atio
n, a 1/4-scale
model
is feasi
b
le fo
r the tests.
As the dime
nsio
nal
scale
factor is 4,
the other scale fa
ctors are
cal
c
ulate
d
as:
f
e
s
c
c
t
cc
s
c
r
t
c
r
er
ec
Q
4
1
6
8
1.
78
0.
87,
4
,
16
14
tI
p
h
QQ
Q
Q
Q
KK
K
K
KK
KK
K
K
K
K
，，
，
，
(
1
5
)
In this
way, the scali
n
g relationships of
convect
i
on and radi
at
ion can
be fulfilled
simultan
eou
sl
y without hea
t flow comp
e
n
satio
n
. The
crite
r
ion
s
of
Π
1
-
Π
16
are ful
f
illed, and
Π
17
is
approximatel
y fulfilled. Dimensi
on pa
rameters
of the full scale
and the 1/4-scal
e GIB are
comp
ared in
Table 1.
T
able 1.
Dimensio
n Paramet
e
rs of F
u
ll Scal
e and 1/
4-scal
e
GIB
Full scale (single
-
phase)
Full scale (three-
phase)
1/4 scale (single-phase)
1/4 scale (three-
phase)
D
ci
/mm
150
65
37.5
16.25
D
co
/mm 180
85
45
21.25
D
ei
/mm
470
492
117.5
123
D
eo
/mm
500
508
125
127
3. Calculation and Validation
The structu
r
e
of GIB is deemed
sym
m
etrical.
In this sectio
n, in orde
r to re
duce the
comp
utation
co
st with
out
the lo
ss of
accu
ra
cy, two-dime
nsio
nal (2-D) fin
i
te model
s
are
employed to
descri
be the f
u
ll scal
e a
nd
the 1/4-scale
GIB in the
sol
u
tion procedu
re, as
sh
own
in
Figure 3. Th
e FEM is ap
plied to solve
the cou
p
led
electroma
gne
tic-fluid
-
therm
a
l pro
b
lem [1
3,
14]. Steady-state temperature
rise, cu
rrent den
sity
a
nd conve
c
tive heat tran
sfer
coeffici
ent
of
the 1/4-scale
model
s are
comp
ared wit
h
those
of the prototyp
e
s
.
Simulation p
a
ram
e
ters of the
prototype
an
d the
scale
model
s a
r
e
g
i
ven in
Tabl
e
2. Th
e a
nal
ysis
presente
d
in thi
s
pap
er i
s
based on the
followin
g
assumption
s:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Approa
ch
for Assessin
g
Harm
oni
c Em
ission Le
vel
Based on
Ro
bust Partial
…
(Xiang Li)
4993
a)
The GIB is infinitely long.
b)
Radi
ation effect of the SF
6
gas is di
sreg
arde
d.
The den
sity, visco
sity and
con
d
u
c
tivity o
f
the SF
6
gas and air a
r
e te
mperature d
e
pend
ent, whil
e
the spe
c
ific h
eat is co
nsi
d
e
r
ed a
s
co
nsta
nt.
(a) F
u
ll s
c
ale
three
-
pha
se
(b)Full scale
singl
e-
pha
se
(c) 1/4-scale
singl
e-
pha
se
(d) 1/4
-
scal
e
singl
e-
pha
se
Figure 3.
Fin
i
te Element Model
s of
the Full Scale an
d 1/4-scal
e GIB
Table 2.
Sim
u
lation Para
meters of Full
Scale and 1/
4-scal
e GIB
par
amet
er
s
Full s
c
a
l
e
(si
ngl
e-
ph
as
e)
Full s
c
a
l
e
(th
r
ee
-p
ha
se
)
1/4
s
c
al
e
(si
ngl
e-
ph
as
e)
1/4
s
c
al
e
(th
r
ee
-p
ha
se
)
I
/A
500
0
200
0
625
250
t
/ms
20
20
1.2
5
1.2
5
SF
6
p
r
e
s
s
u
re
/
M
pa
0
.
35
0
.
35
0
.
08
75
0
.
2
T
a
/
23
23
23
23
(a) F
u
ll scale
singl
e-p
h
a
s
e
bus b
a
r
(b) 1/4
-
scal
e
singl
e-p
h
a
s
e
bus b
a
r
(c) Full scale
three
-
ph
ase bus b
a
r
(d) 1/4
-
scal
e
three
-
p
h
a
s
e b
u
s ba
r
Figure 4.
Current De
nsit
y Distributio
n
s
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046
TELKOM
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KA
Vol. 12, No. 7, July 201
4: 4988 – 49
95
4994
(a) F
u
ll scale
singl
e-p
h
a
s
e
bus b
a
r
(b) 1/4
-
scal
e
singl
e-p
h
a
s
e
bus b
a
r
Figure 5.
Convective He
at Tran
sfer
Coe
fficient on
Surfaces of the GIB
(a) F
u
ll scale
singl
e-p
h
a
s
e
bus b
a
r
(b) 1/4
-
scal
e
singl
e-p
h
a
s
e
bus b
a
r
(c) Full scale
three
-
ph
ase bus b
a
r
(d) 1/4
-
scal
e
three
-
p
h
a
s
e b
u
s ba
r
Figure 6.
Te
mperature
Di
stributio
n on
Con
d
u
c
tors a
nd Enclo
s
u
r
e
The current
den
sity of th
e scale mod
e
ls
shares t
he sam
e
distribution
s
wit
h
the
prototype
s
, a
nd the
value
s
of the
scale
model
s a
r
e
a
c
curately
2 ti
mes larger th
an tho
s
e
of t
h
e
prototype, which demo
n
st
rates
the sca
ling
rel
a
tion
ships
of ele
c
tromagn
etic fie
l
d, as
sho
w
n
in
Figure 4. Co
mpari
s
o
n
bet
wee
n
conve
c
tive heat tr
an
sfer
coeffici
e
n
ts on th
e en
clo
s
ure external
surfa
c
e
of ful
l
scale
an
d
1/4-scal
e
GIB is
sh
ow
n i
n
Fig
u
re
5.
Note th
at the
co
nvective
heat
transfe
r coefficient
s of the scal
e
model
s have be
en
conve
r
ted b
y
multiply
ing its scale fact
or
whi
c
h
i
s
0.8
7
in
this pap
er. The conve
r
te
d
co
nvecti
ve heat
tra
n
sfe
r
coeffici
ent
is clo
s
e
to but
n
o
t
exactly the
same a
s
th
ose
of the p
r
otot
ype be
ca
u
s
e
of the ap
proximation ma
de
in the
scaling
of
conve
c
tion. Steady-state
temper
ature
distri
bution
on the
con
d
u
ctor(s) and encl
o
sure of
the
prototype
s
a
n
d
scal
e m
ode
ls a
r
e
given
in Figu
re
6. T
he tem
peratu
r
e
distri
bution
of scal
e m
o
d
e
l
corre
s
p
ond
s
well
with th
at of p
r
ototype.
Moreov
e
r
, th
e calculated
tempe
r
atures
are
compa
r
e
d
with the teste
d
tempe
r
atures of the
sin
g
le-p
ha
se
b
u
s
ba
r refe
rre
d
in [4], as shown in Tabl
e 3.
Clo
s
e ag
re
e
m
ent betwee
n
the cal
c
ul
a
t
ed temper
ature
s
an
d the
tested temp
eratu
r
e
s
ca
n
be
rega
rd
ed a
s
a good valid
a
t
ion for the scaling metho
d
prop
osed in this pa
per.
Table 3.
Co
mpari
s
o
n
bet
wee
n
Cal
c
ula
t
ed and Te
ste
d
Tempe
r
atu
r
e
Method
F
u
ll scale
1/4-
scale
I
=5000 A
I
=7000 A
I
=625 A
I
=875 A
T
c
T
e
T
c
T
e
T
c
T
e
T
c
T
e
Calculated
52.3 36.0 74.2
45.9
52.0
36.5
75.4
47.4
Tested
50 36 72
50
—
—
—
—
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Approa
ch
for Assessin
g
Harm
oni
c Em
ission Le
vel
Based on
Ro
bust Partial
…
(Xiang Li)
4995
4. Conclusio
n
In orde
r to avoid co
stly prototyping
in
the desi
gn of GIB,
a scaling m
e
thod is
investigate
d
to explore th
e electroma
g
netic-th
e
rm
al
characte
ri
stics of a full scale GIB. With
rega
rd to th
e scaling of
powe
r
lo
sses an
d he
at transfe
r, M
a
xwell’
s equ
ations a
nd
non-
dimen
s
ion
a
l correl
ation
s
are em
ploye
d
, respe
c
tively, to analyze
the scaling
relation
shi
p
s
of
power lo
sses and heat tra
n
sfer. Th
e 1/4-scal
e ele
c
tromagn
etic-th
e
rmal finite el
ement mod
e
l
s
of
singl
e- a
nd th
ree
-
ph
ase GI
B are d
e
si
gn
ed. T
he
co
rre
ctne
ss
of the
scaling m
e
th
odolo
g
y and t
h
e
simulatio
n
ca
lculatio
n i
s
v
a
lidated
by t
he
clo
s
e agreement
between
th
e cal
c
ulated re
sults
and
tested
re
sult
s. Th
e
scal
e mod
e
l p
r
opo
sed
in t
h
is
pap
er
can b
e
u
s
e
d
to stu
d
y the
electroma
gne
tic-the
r
mal chara
c
te
risti
c
s
of
GIB
p
r
ot
otype,
whi
c
h
sh
ows pra
c
t
i
cal sig
n
ifica
n
ce
and e
c
on
omi
c
al be
nefit.
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ces
[1]
Hedi
a H, H
enr
otte F
,
Me
y
s
B. Arrangem
e
n
t
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ph
ases and he
ating
c
onstrai
nts in
a
busb
a
r.
IEEE
T
r
ansactio
n
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n
Magn
etics
. 1999; 35(
3): 127
4--12
77.
[2]
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i
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u
ct
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s
t
e
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.
IEEE Transactions on Magnetics
. 2007; 43(
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36.
[3]
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h
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i
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hermal Probl
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ase
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agnetics
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r D
e
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ang GF
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