TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 65
2
6
~ 653
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.467
6
6526
Re
cei
v
ed O
c
t
ober 8, 20
13;
Revi
se
d Apr
28, 2014; Accepted June 6,
2014
Application of Magnetic Integrated Technology in
Controllable Reactor of Transformer Type
Jianning Yin*, Mingxing Tian, Guoha
n Yin
Schoo
l of Auto
mation & Electr
ical En
gin
eeri
n
g, Lanzh
ou Ji
a
o
tong U
n
iv
ersity,
Lanz
ho
u Gans
u 730
07
0, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
y
i
n
2
0
0
8
093
0
7
@1
63.com
A
b
st
r
a
ct
T
here is th
e magn
etic cou
p
l
i
n
g
a
m
o
ng co
ntrol w
i
ndi
ngs
of control
l
ab
le re
actor of transfo
rmer ty
p
e
(CRT
),
the de
coup
lin
g integr
ated mag
netic
techn
o
l
ogy
is
ap
pli
e
d
to t
h
e
structure
des
i
gn
of C
R
T
in
t
h
is
p
a
p
e
r
. To
re
a
liz
e th
e de
co
up
li
n
g
am
on
g th
e co
n
t
rol
wi
nd
in
gs w
e
pr
op
ose
a
magn
et
ic int
egrate
d
structu
r
e
of CRT
by providi
ng l
o
w
magn
etic
resista
n
ce
mag
netic
circuit for cont
rol w
i
ndi
ngs
magn
etic flux. T
h
e
w
i
ndin
g
l
eaka
ges
of this str
u
cture
are c
a
l
c
ulate
d
, it
s i
n
ductanc
e-trans
former
eq
uiv
a
l
ent circu
i
t is
als
o
establ
ishe
d, a
nd th
e
equ
atio
n of th
e c
o
u
p
li
ng
de
gree
of
control
w
i
ndi
n
g
s a
n
d
no-
loa
d
curr
ent w
i
th
t
h
e
latera
l colu
mn
air gap si
ze are de
duc
ed. T
he si
mu
latio
n
mode
l for a CRT
is fabricated w
i
t
h
MAT
L
AB/SIMULINK. Simul
a
ti
on a
nd
ana
lysi
s results sh
ow
s that w
hen i
n
c
r
easi
ng the
air
gap, the
mag
n
e
tic
coup
lin
g betw
e
en the c
ontrol
w
i
ndin
g
s dec
r
e
ases a
ppar
entl
y
, the utili
z
a
ti
o
n
ra
tio of w
i
nd
i
ngs curre
nt is
also
raise
d
. T
he simu
lati
on resu
lts verify the effectiven
ess of
this metho
d
by
control
lin
g the
latera
l colu
mn
air
gap si
z
e
to
ach
i
eve the p
u
rp
o
s
e of deco
upl
in
g.
Ke
y
w
ords
:
co
ntroll
abl
e react
o
r of transformer type, ma
gn
e
t
ic
integrati
on, simulati
on a
n
a
l
ysis, utili
z
a
ti
on
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
In the EHV
transmissio
n
system, in
orde
r to
solv
e the p
r
obl
e
m
of re
activ
e
po
wer
balan
ce, rea
c
tive power
comp
en
satio
n
device m
u
st be in
stalle
d [1-3]. Co
ntrollabl
e re
act
o
r of
transfo
rme
r
type (CRT
) is
a new
m
u
lti-winding
rea
c
tive power
com
pen
sation d
e
v
ice; the wo
rking
prin
ciple di
ag
ram of CRT i
s
sh
own as Fi
gure 1 [4
-6].
1
Th
2
Th
N
Th
N
u
2
u
1
u
0
i
2
i
N
i
1
i
BW
i
u
1
CW
2
CW
N
CW
1
a
2
a
11
c
12
c
21
c
22
c
1
c
N
2
c
N
1
L
2
L
N
L
Figure 1. The
Working P
r
in
ciple
Diag
ram
of CRT
In Figure 1,
the pu
rpo
s
e of the
rea
c
tive
po
we
r
cap
a
city with
contin
uou
s
smooth
adju
s
tment of
CRT ca
n
b
e
achi
eved by adju
s
ting
th
e
size of
condu
ction
angl
e of
the
anti-p
a
ral
l
el
thyristors seri
es in control windi
ng loop,
and the
cu
rrent harm
oni
c conte
n
t is sm
all of CRT [7,
8].
Ho
wever, b
e
c
au
se it h
a
s multiple con
t
rol win
d
ing
s
,
there i
s
a
magneti
c
cou
p
ling am
ong
the
control win
d
i
ngs, which le
ads to the subsequ
ent
control wi
ndin
g
input will make
s the control
windi
ng
current utilization
rate is decli
n
e of have b
een put into operated, in
order to improve the
control winding current utilization and m
a
ke the
CRT
reliabl
e work,
reference [9] pointes out that
the st
ru
ctural
desi
gn
of the
CRT
mu
st foll
ow th
e
de
s
i
gn
p
r
in
c
i
p
l
es
of “
h
ig
h impe
da
n
c
e
an
d
w
e
a
k
c
o
up
lin
g”
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Applicatio
n of Magnetic Int
egrate
d
Te
ch
nolog
y
in Con
t
rollable
Rea
c
tor of… (Ji
a
n
n
ing Yin)
6527
In this pa
per,
aiming at th
e pro
b
lem of
magneti
c
cou
p
ling am
ong
the co
ntrol
wi
nding
s,
the integrate
d
magnetic
structure
of CRT which is ba
sed on the m
agneti
c
integration techn
o
l
ogy
is p
r
op
osed,
this st
ru
cture
achi
eves the
decoupl
i
ng
of the control
windi
ng
s by
providin
g a l
o
w
relu
ctan
ce m
agneti
c
ci
rcuit [10-1
2
]; The
simulatio
n
ex
ample
of the
relation
shi
p
b
e
twee
n jamb
air
gap
size an
d deg
ree
of
cou
p
ling fo
r
this st
ru
ct
ure
sho
w
s that
the structu
r
e
can
we
ak t
he
magneti
c
co
upling amon
g
the control
windi
ng
s,
improve
utilization of the
windi
ng
current.
Gene
rally thi
s
stru
cture al
so
ca
n be
e
a
sily ext
end
e
d
to the
stru
cture
of the
multiple
cont
rol
windi
ng
s, pro
v
ides a refe
re
nce for th
e further a
ppli
c
ati
on of magneti
c
integration tech
nolo
g
y.
2. Magnetic I
n
tegr
ation S
t
ruc
t
ure o
f
CRT
In magn
etic i
n
tegratio
n te
chnolo
g
y, the
decouplin
g in
tegrated
met
hod
whi
c
h provides a
low
relu
ctan
ce
magn
etic can achieve the
de
cou
p
ling of multi-windi
ng
s [13]
. this metho
d
is
applie
d to th
e structu
r
al d
e
sig
n
of CRT
,
and a
ki
nd
of integrate
d
magneti
c
st
ru
cture
of CRT
is
prop
osed an
d
sho
w
n a
s
Figure 2.
1
BW
2
BW
1
CW
2
CW
3
CW
4
CW
1
a
2
a
1
Th
2
Th
3
Th
4
Th
0
N
0
N
1
N
2
N
3
N
4
N
0
1
2
3
4
11
c
12
c
21
c
22
c
31
c
32
c
41
c
42
c
0
Figure 2. Integrated M
agn
etic Structu
r
e
of CRT
In Figu
re
2, a
1
, a
2
are two
ports of th
e
worki
n
g
win
d
in
g, and
p
a
rall
e
l
ed to
the
po
wer g
r
id,
the po
we
r
grid voltage
be
tween
the t
w
o po
rts;
ij
c
(
i
=1,2,3,4;
j
=
1
,2)is
the
j
-th
po
rt of
control
windi
ng
i
CW
, the anti-parallel
thyristo
rs a
r
e u
s
ed
in
serie
s
with b
o
th
po
rts
of each cont
rol
windi
ng, rea
c
tive power
of
CRT
can
be
adju
s
ted
by thyristo
rs.
Co
re column
a
r
o
und th
e
worki
ng
windi
ng an
d
iron yo
ke u
p
and do
wn
a
r
e lo
w mag
n
e
tic re
si
stan
ce, side le
gs
arou
nd
cont
ro
l
windi
ng
s a
r
e
gapp
ed to
in
cre
a
se th
e
re
luctan
ce,
so
t
hat a
large
p
a
rt of
mag
net
ic flux
whi
c
h
is
gene
rated by
the
co
ntrol wi
nding
s con
s
titutes
a cl
o
s
e
d
loop throug
h
the low m
agn
etic re
si
stan
ce
magneti
c
circuit with its
column,
while
only a
small
amou
nt of
magneti
c
flux
flowing
thro
ugh
magneti
c
circuit
in
oth
e
r co
ntrol windi
ng
s,
whic
h will wea
k
th
e
di
re
ct
coupli
ng a
m
ong
th
e con
t
rol
windi
ng
s, be
cau
s
e the
worki
ng
windi
ngs a
r
o
und
the uppe
r a
nd lower
ce
nter column
are
con
n
e
c
ted in
serie
s
, the inputs of su
b
s
eq
uent co
ntrol win
d
ing
s
will lead to the increa
sin
g
of
workin
g
wing
ding
cu
rrent,
so th
at the
m
agneti
c
flux
g
enerated
by t
he
wo
rkin
g
winding
will
al
so
raise, in turn, this will effect the control
wi
nding
cu
rrent whi
c
h ha
s bee
n put into operate
d
. We
define
it a
s
an indire
ct cou
p
ling; this de
gree of co
upli
ng is small. If we don’t con
s
ide
r
the indirect
cou
p
ling, the
couplin
g am
ong the co
ntrol windin
g
s o
f
this structu
r
e is small, a
nd the prin
ci
ple
“we
a
k
cou
p
lin
g” amo
ng different control windi
ng
s is a
c
hieve
d
.
3. The Calcu
l
ation of Cou
p
ling Degre
e
Acco
rdi
ng to Ohm'
s law of
magnetic ci
rcuit,
the equi
valent magne
tic circuit of magneti
c
integratio
n structure of the CRT
sho
w
e
d
in Figure 2 is
sho
w
n a
s
Fig
u
re 3.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
26 – 653
3
6528
0
R
0
R
1
R
2
R
3
R
4
R
0
0
i
N
0
0
i
N
1
1
i
N
2
2
i
N
3
3
i
N
4
4
i
N
0
0
1
2
3
4
Figure 3. Equivalent magn
etic circ
uit of
magneti
c
inte
grated
stru
ctu
r
e
In Figure 3,
0
R
is the magn
etic re
sista
n
ce of center
column;
1,2,3,4)
(i
R
i
is ma
gnetic
resi
stan
ce
(in
c
ludi
ng relu
ctance of ai
r g
ap)
of the
sid
e
col
u
mn
aro
und
cont
rol
winding
i
CW
;
0
N
is
the half turns
of working wi
nding;
i
N
is the turn
s of control windin
g
i
CW
. M
a
k
e
R
R
R
R
R
4
3
2
1
, in case of without consi
derin
g the indire
ct
cou
p
lin
g among
con
t
rol windi
ng
s, the degre
e
of
cou
p
ling bet
ween control
winding
1
CW
and co
ntrol win
d
ing
2
CW
is:
)
δ
μ
(
μ
)
2r
(h
2
μ
l
μ
R
R
R
k
0
co
0
0
0
0
12
(
1
)
Whe
r
e,
0
μ
and
μ
is perm
eability of the air ga
p and core resp
ectively;
l
is the cal
c
ul
ative
length(i
n
cl
udi
ng the
ce
nte
r
colum
n
hei
ght an
d len
g
t
h of the i
r
on
yoke
) of th
e
ce
nter
col
u
m
n
magneti
c
re
si
stan
ce;
δ
is the size of air ga
p for side col
u
mn;
h
is the h
e
ight of side colum
n
;
co
r
is
the radiu
s
of the co
re colu
mns.
In a similar
way, the de
gree of
cou
p
ling bet
wee
n
cont
rol wi
nding
3
CW
and co
ntrol
windi
ng
4
CW
is:
)
δ
μ
(
μ
)
2r
(h
2
μ
l
μ
k
0
co
0
0
34
(
2
)
And,
0
k
k
k
k
24
23
14
13
(
3
)
It can be
see
n
from the
fo
rmula
(1
) an
d
(2) th
at the
degree of
co
upling
amon
g
cont
rol
windi
ng
s de
crea
se
s with t
he increa
sin
g
of air gap for the side colu
mn whe
n
wit
hout co
nsi
dering
the indire
ct couplin
g amon
g control win
d
ing
s
.
4. Equiv
a
len
t
Circuit o
f
CRT
0
2
0
R
N
0
L
1
a
2
2
0
R
N
1
2
0
R
N
0
N
1
L
1
N
11
c
0
N
2
L
2
N
21
c
4
2
0
R
N
3
2
0
R
N
0
N
3
L
3
N
31
c
0
N
4
L
4
N
41
c
0
2
0
R
N
0
L
2
a
12
c
22
c
32
c
42
c
Figure 4. Inductan
c
e
-
tra
n
sformer Eq
uivalent Circuit
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Applicatio
n of Magnetic Int
egrate
d
Te
ch
nolog
y
in Con
t
rollable
Rea
c
tor of… (Ji
a
n
n
ing Yin)
6529
Acco
rdi
ng to
the esta
blished meth
od
of equivale
nt circuit for integrate
d
magneti
c
comp
one
nt, with the
num
ber
of turn
0
N
for referen
c
e,
the ind
u
cta
n
ce
-tra
nsfo
rmer e
quivale
nt
circuit of magnetic integ
r
a
t
ed stru
cture of CRT
showed in Figure 2 now is sho
w
n as Fig
u
re
4
[14].
In Figure 4,
0
L
is the le
akage
indu
ctan
ce h
a
lf of the wo
rking
win
d
ing;
i
L
is the le
aka
g
e
indu
ctan
ce o
f
cont
rol wi
nding
i
CW
, all transfo
rme
r
s
are
ide
a
l transfo
rme
r
, o
n
ly act
s
as
impeda
nce transfo
rmatio
n. Based on th
e equivalent
ci
rcuit sh
own in Figure 4, the relatio
n
shi
p
of
no-lo
ad
cu
rre
n
t RMS
with
the si
ze
of th
e air ga
p ca
n be
cal
c
ul
ated
when
the
control
windi
ng
turns
of CRT are
imp
u
ted
0
N
is:
0
0
0
co
0
2
0
0
0
00
2
ωω
)
δ
μ
(
μ
)
μ
2r
(h
l
2
μ
AN
4
ωωμ
U
i
(
4
)
Whe
re,
0
U
is RMS of powe
r
grid voltag
e;
A
is the cro
s
s se
ctional a
r
e
a
of co
re
col
u
mns;
ω
is
angul
ar fre
q
u
ency.
It can be
se
e
n
from fo
rmul
a (4
) that no
-load
curre
n
t
00
i
increa
se
s wit
h
the raise of
the
size of air ga
p
δ
for side
col
u
mn.
5. Calculatio
n of Leak
age
Inductan
ce
The ma
gneti
c
integrated
structu
r
e
of CRT sh
own
a
s
Figure
2 are
symmetri
c
,
th
erefo
r
e,
it is base
d
on
the working
windi
ng
1
BW
and control wi
ndin
g
1
CW
as an exam
ple that to cal
c
ulate
the leakage i
ndu
ctan
ce, which i
s
sh
own
as Figu
re 5.
Figure 5. Magnetic Fiel
d Intensity Di
stri
bution
The Figu
re 5
is the co
re
cross-sectio
na
l view and a
magneti
c
field intensity di
stributio
n
figure of wo
rking
windin
g
1
BW
and control
windi
ng
1
CW
. In Fi
gure 5,
h
is the height of iro
n
core
wind
ow;
z
is the
equivale
nt h
e
ight of
windi
ng;
a
is the
in
su
lation di
stan
ce of working
windi
ng to
the ce
nter
co
lumn;
b
is the thickne
s
s of
workin
g wi
ndi
ng con
s
ide
r
canceling tu
rn
insul
a
tion;
d
is
the thickn
ess of control
wi
nding
co
nsi
d
e
r
can
c
eli
ng t
u
rn i
n
sulation
;
e
is the i
n
sulation di
stan
ce
o
f
control wi
ndin
g
to the si
de
colum
n
;
δ
is the
size of air
ga
p. Setting the line l as l
e
a
k
age ma
gneti
c
flux distributi
on boun
da
ry of working
wi
nding an
d co
ntrol win
d
ing,
c
is the distan
ce of wo
rki
n
g
windi
ng to the boun
dary,
m
is the dista
n
ce of control winding to the
boun
dary.
The
0
i
is the current of working wi
ndin
g
,
1
i
is the curren
t of control winding, sel
e
ct
the
insid
e
edge
of the center
colum
n
as th
e zero re
fe
re
nce. Acco
rdi
ng to the Ampere’
s la
w, there
are:
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TELKOM
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26 – 653
3
6530
In the area
a
~
b
, magnetic fi
eld strength i
n
crea
se
s line
a
rly along th
e x directio
n, the
expre
ssi
on of
magnetic fiel
d stren
g
th is:
x
zb
i
N
b
x
H
H
0
0
0
bx
(
5
)
In the area
c
b
a
~
b
a
, becau
se
wi
thout the in
crea
se
of cu
rrent, mag
net
ic field
intensity rem
a
ins u
n
chan
g
ed, the expr
e
ssi
on of mag
netic field strength is:
z
i
N
H
H
0
0
m
cx
(
6
)
Magneti
c
ene
rgy also
can
be expre
s
sed
by the following formul
a, in the area
a
~
b
,
2
0
0
4
4
2
0
2
b
a
2
2
2
0
2
0
0
b
a
2
ax
0
1
)
i
(N
a
4
1
b)
(a
4
1
zb
π
μ
zdx
2
ππ
x
b
z
i
N
2
μ
dV
H
2
μ
W
(
7
)
In the area
c
b
a
~
b
a
,
2
0
0
2
2
0
c
b
a
b
a
2
2
0
2
0
0
2
)
i
(N
b)
(a
2
1
c)
b
(a
2
1
z
π
μ
zdx
2
ππ
z
i
N
2
μ
W
(
8
)
The mag
netic energy of the
leaka
ge re
act
ance in the
whol
e distri
bu
ted regio
n
is:
2
0
0
2
1
i
L
2
1
W
W
W
(
9
)
Acco
rdi
ng to
simultan
eou
s Equation
(7),
(8),
(9),
we
can obtai
n the
leakage i
ndu
ctan
ce
of the workin
g windi
ng
1
BW
is:
2
2
2
0
0
2
2
2
2
0
0
0
b
a
2
1
c
b
a
2
1
z
π
N
μ
a
4
1
b)
(a
4
1
zb
N
2
ππ
L
(
1
0
)
In a similar
way, the leaka
ge indu
ctan
ce of the control windi
ng
1
CW
is:
2
2
2
1
0
4
4
2
2
1
0
1
d)
(e
2
1
m)
d
(e
2
1
z
N
2
ππ
e
4
1
d)
(e
4
1
zd
N
2
ππ
L
(
1
1
)
Other
control
windin
g
lea
k
age ind
u
cta
n
c
e can
be
ca
lculate
d
acco
rding to the f
o
rmul
a
(11
)
. After th
e lea
k
a
ge i
n
d
u
ctan
ce
s
of t
he
windi
ng
s
are
calcul
ate
d
, the
windi
n
g
s
cu
rrent
ca
n be
simulate
d accordin
g to indu
ctor-tra
nsfo
rmer eq
uivale
nt circuit sho
w
n in Figu
re
4 of CRT.
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TELKOM
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ISSN:
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Applicatio
n of Magnetic Int
egrate
d
Te
ch
nolog
y
in Con
t
rollable
Rea
c
tor of… (Ji
a
n
n
ing Yin)
6531
6. Example Calcula
t
ion and Simulation
The st
ru
cture
para
m
eter
of CRT
are
sh
o
w
n in T
able 1
,
the turns
of workin
g wi
ndi
ng
1
BW
is
1600
N
0
, each
cont
rol wi
ndin
g
s t
u
rn a
r
e im
pu
ted to 1600 t
u
rn
s, the working
windi
ng
rated
voltage RMS
is
3
500/
U
0
kV
.
Table 1. The
Structu
r
al Parameter
paramete
r
value(cm)
paramete
r
value
(cm)
a
1
h
125
b
19
z
110
c
7
d
10
co
r
3.95
r
μ
2000
e
1
m
6
In Table
1,
r
μ
is
relative p
e
rm
eability of core, other pa
ra
meters
whi
c
h
rep
r
e
s
e
n
t ph
ysical
meanin
g
s a
r
e
same a
s
Fig
u
re 5.
Set the size
of air gap of
side column
s aro
und fou
r
cont
rol wi
n
d
ing
s
are e
q
ual, the
cro
s
s-se
ction
a
l are
a
of sid
e
colu
mn is
equal to
the
cro
s
s-se
ction
a
l are
a
of ce
nter column,
the
para
m
eter values i
n
Ta
ble
1 plug i
n
type
(10
)
can
b
e
cal
c
ulate
d
to
the lea
k
ag
e i
ndu
ctan
ce of
the
workin
g wi
ndi
ng
i
BW
(
1,2
i
) is
2.036H
L
0
; the le
aka
ge in
duct
ance of the
control
windi
n
g
1
CW
is
0.6725H
L
1
; the lea
k
ag
e indu
ctan
ce
of the control win
d
ing
2
CW
is
0.5299H
L
2
; th
e
l
e
ak
ag
e
indu
ctan
ce o
f
the control
win
d
ing
3
CW
is
0.3708H
L
3
; the le
akage
i
ndu
ctan
ce
of the
cont
rol
windi
ng
4
CW
is
0.2116H
L
4
. Ba
sed
on MA
TL
AB R200
9b
p
l
atform, we can buil
d
simul
a
tion ci
rcuit
according
to
Figu
re 4,
short-circuit th
e contro
l
win
d
ing in
turn,
the current
RMS of
wo
rking
windi
ng
and
control
windi
ng
can
be
m
easure
d
[1
5,
16]. The
Ta
b
l
e 2, T
able
3
and
Ta
ble
4
of
followin
g
are
simulatio
n
values of wi
ndin
g
s when ai
r g
ap
0
δ
,
3mm
δ
,
7mm
δ
re
spe
c
ti
v
e
ly
.
Table 2 Th
e Simulation Value when Air Gap
0
δ
No-load
current
CW
1
short-
circuit
CW
1
~CW
2
short
-
circuit
CW
1
~CW
3
short
-
circuit
CW
1
~CW
4
short
-
circuit
Curre
nt of
BW/A
33.43
36.36
54.47
62.90
160.70
Curre
nt of
CW
1
/A
0 13.76
49.25
56.87
145.30
Curre
nt of
CW
2
/A
0 0
49.54
57.21
146.20
Curre
nt of
CW
3
/A
0 0
0
24.28
152.60
Curre
nt of
CW
4
/A
0 0
0
0
153.60
Table 3. The
Simulation Value when Air Gap
3mm
δ
No-load
current
CW
1
short-
circuit
CW
1
~CW
2
short
-
circuit
CW
1
~CW
3
short
-
circuit
CW
1
~CW
4
short
-
circuit
Curre
nt of
BW/A
60.64
68.93
86.69
106.40
164.60
Curre
nt of
CW
1
/A
0 45.36
70.21
86.19
133.30
Curre
nt of
CW
2
/A
0 0
72.28
88.73
137.20
Curre
nt of
CW
3
/A
0 0
0
75.43
146.40
Curre
nt of
CW
4
/A
0 0
0
0
151.60
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
26 – 653
3
6532
Table 4. The
Simulation Value when Air Gap
7mm
δ
No-load
current
CW
1
short-
circuit
CW
1
~CW
2
short
-
circuit
CW
1
~CW
3
short
-
circuit
CW
1
~CW
4
short
-
circuit
Curre
nt of
BW/A
86.84
96.43
112.00
131.30
169.00
Curre
nt of
CW
1
/A
0 62.38
79.67
93.28
120.20
Curre
nt of
CW
2
/A
0 0
84.06
98.42
126.80
Curre
nt of
CW
3
/A
0 0
0
96.42
138.70
Curre
nt of
CW
4
/A
0 0
0
0
148.40
In Table 2, Table 3 a
n
d
Table 4, BW is
workin
g windi
ng,
1,2,3,4)
(i
CW
i
is control
windi
ng. It ca
n be
see
n
fro
m
the sim
u
lat
ed data
abov
e three ta
ble
s
that control
windi
ng
3
CW
an
d
4
CW
put
into ope
ration will
im
pact on
th
e curre
n
ts of
1
CW
an
d
2
CW
, th
i
s
i
s
b
e
c
a
us
e th
er
e
i
s
indire
ct
cou
p
l
i
ng b
e
twe
en t
hem. It can
b
e
con
c
lud
ed f
r
om th
e
com
pare
with
sim
u
lated
data t
hat
in
the ca
se o
f
other param
eters
a
r
e sa
me
exa
c
tly,
with the
air-g
ap in
crea
se
s, the loa
d
current
also i
n
cre
a
se
s, whi
c
h
is f
u
lly con
s
i
s
te
nt with the
result of fo
rm
ula (4). Th
e
curre
n
t utiliza
t
ion
curve
s
of
co
ntrol wi
ndin
g
1
CW
can b
e
obtai
ned a
c
cordin
g to the sim
u
lated data, t
he cu
rve
s
of
different si
ze
of air-g
ap are
sho
w
n a
s
Figure 6.
1
1.
5
2
2.
5
3
3.
5
4
0
10
20
30
40
50
60
70
80
90
100
T
he num
b
e
r
of
c
ont
r
o
l
w
i
n
d
i
ng
be
i
n
g
c
ond
uc
t
e
d
T
he
ai
r
ga
p i
s
7
m
m
T
he
ai
r
ga
p i
s
3
m
m
T
he ai
r
gap
i
s
0
%
/
Figure 6. Curves of Cu
rre
n
t
Utilization Ratio
In the Figu
re
6, the ab
scissa i
s
a
n
integ
e
r
whi
c
h m
e
a
n
s the
num
b
e
r of
cont
rol
windi
ng
for bei
ng full
y con
d
u
c
ted.
We
can
se
e
from
cu
rves
that the
cu
rrent utiliz
ation
ratio
of cont
rol
windi
ng incre
a
se
s with th
e raisi
ng of the air gap,
if the air-ga
p
of side col
u
mn is bigge
r,
th
e
degree
of co
upling amon
g
cont
rol windi
ngs wo
uld
b
e
sm
all
e
r, whi
c
h i
s
fully co
nsi
s
tent with
the
result of form
ula (1) a
nd f
o
rmul
a (2
), therefo
r
e,
the
size of the
a
i
r ga
p of si
de
colu
mn
can
be
increa
sed in
orde
r to achieve the co
ntrol
win
d
ing
"weak
cou
p
ling" purp
o
se. The cu
rre
nt
utilization o
n
the rise with in
put numbe
r o
f
control
windi
ng increa
sin
g
.
7. Conclusio
n
In this a
r
ticle,
the de
cou
p
li
ng integ
r
ated
magneti
c
technolo
g
y is a
p
p
lied to the
st
ructu
r
e
desi
gn of
CRT, a CRT m
a
gnetic i
n
teg
r
a
t
ed struct
u
r
e
has
bee
n p
r
o
posed. On
th
e ba
sis of th
e
cal
c
ulatio
n of
the lea
k
ag
e
indu
ctan
ce of
the win
d
ing
s
and e
quivale
nt circuit i
s
e
s
tabli
s
he
d, the
simulatio
n
a
n
a
ly
sis
of this
stru
ctu
r
e
on
t
he MATLA
B
have b
een
don
e, we
g
e
t the follo
wi
ng
con
c
lu
sio
n
s:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Applicatio
n of Magnetic Int
egrate
d
Te
ch
nolog
y
in Con
t
rollable
Rea
c
tor of… (Ji
a
n
n
ing Yin)
6533
(1) T
he “we
a
k
couplin
g” d
e
sig
n
re
quire
ment amon
g
control wi
nd
ings of
CRT can
be
reali
z
ed by p
r
oviding a low
relu
ctan
ce m
agneti
c
circuit
.
(2)
Wh
en the
air ga
p of
si
de column
b
e
com
e
s
bigg
er, the d
egre
e
of co
uplin
g
among
control
windi
ngs be
com
e
s sm
aller,
and
the utilization
rate
of
windi
ng
curre
n
t a
r
e al
so
high
er.
At
the sam
e
tim
e
, no-lo
ad
cu
rre
nt will in
crease. So
rati
onal
sele
ctio
n of air
gap
size can n
o
t only
make
the
no
-load
current
small,
but a
l
so a
c
hi
eve t
he pu
rp
ose
of de
coupli
n
g amo
ng
co
ntrol
windi
ng
s.
(3) T
he m
e
th
od of de
co
up
ling amo
ng
control
wi
ndi
n
g
s by a
d
ju
sting the ai
r ga
p of sid
e
colum
n
of ma
gnetic inte
gra
t
ed stru
cture of CRT i
s
effective.
Referen
ces
[
1
]
T
i
an Jun,
Chen Qiao-f
u
,
Zhan
g Yu.
Adj
u
st
abl
e react
o
r
w
i
t
h
co
nt
rol
l
abl
e loa
d
of
mult
i-
w
i
ndi
n
g
tra
n
s
fo
rm
e
r
.
Electric Power Au
tomation Equipment
.
201
0;
3
0
(1):
32- 35.
[
2
]
Che
n
Wei-
xian
,
C
hen
He.
A
p
p
l
icat
io
n of
int
e
r-
phas
e sh
unt
r
e
act
o
rs i
n
EHV
and
UHV
t
r
ans
mission
li
ne
s
and su
ppr
essio
n
of
resona
nce
.
High Volta
ge
Engi
neer
in
g
.
2010;
36(
9):
218
7-21
92.
[
3
]
ZHANG Jian-
xing,
WANG
Xuan,
LEI
Xi,
et
al.
Overvi
e
w
of
Co
nt
roll
ab
l
e
Re
act
o
r.
Power System
T
e
chno
logy
.
2
006;
30:
2
69-2
72.
[
4
]
ZHANG You-p
eng,
DU Bi
n-
xi
ang,
T
I
AN Ming-xin
g
.
Rese
arch on C
o
mpe
n
s
at
ion D
egr
ee
of
Cont
rol
l
a
b
l
e
Shunt
React
o
r
I
n
st
alle
d i
n
U
H
V T
r
ansmissi
on L
i
n
e
w
i
t
h
L
o
ss Co
nsi
dere
d
.
Hig
h Vo
ltag
e En
gin
eeri
n
g
.
201
1;
37(9):
20
96-2
101.
[
5
]
CHEN H
e
,
CH
EN Weixia
n.
Sust
ain
ed C
ond
uct
i
on Met
hod
of
Cont
rol
l
a
b
le
React
o
r of
Mu
lt
iple P
a
ral
l
e
l
Branch T
y
pe.
High V
o
ltag
e E
ngi
neer
in
g
.
20
05;
31(4):
6
6
-6
8.
[
6
]
TI
AN Ming-
xi
n
g
,
LI
Qing-f
u
.
Magn
et
ic sat
u
r
a
t
i
on t
y
p
e
a
nd
t
r
ansf
o
rmer t
y
p
e
cont
ro
lla
bl
e
shunt
re
act
o
r.
High V
o
ltag
e E
ngi
neer
in
g
.
20
03;
29(7):
2
6
-2
7.
[
7
]
T
i
an Ming
xin
g
,
Li Qingf
u.
A cont
rol
l
ab
le re
act
o
r of
t
r
ansf
o
rmer t
y
pe.
I
EEE Transaction on Pow
e
r
DeliV
ery
.
200
4
;
19(4):
171
8-1
726.
[
8
]
Ming
xi
ng T
i
an.
Anal
ysis of
t
r
ansf
o
rmer
s on t
he conc
ept
of
elem
ent
ar
y
w
i
n
d
in
g.
Electrical
Engin
eeri
n
g
.
200
7;
89(7):
55
3-56
1.
[
9
]
T
i
an Ming
xi
ng.
Basic t
h
e
o
ret
i
cal res
earch
o
n
cont
ro
lla
bl
e
react
o
rs of
t
r
a
n
sf
ormer t
y
pe.
PhD t
hes
is.
Xi
’a
n:
Xi
’an Ji
a
o
t
ong U
n
iv
ersit
y
,
20
05.
[
10]
Che
n
Qia
n
h
o
n
g
.
Res
earch
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