TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 1, Janua
ry 201
5, pp. 20 ~ 2
5
DOI: 10.115
9
1
/telkomni
ka.
v
13i1.672
4
20
Re
cei
v
ed Se
ptem
ber 25, 2014; Revi
se
d No
vem
ber
4, 2014; Acce
pted De
cem
b
er 12, 201
4
A Decoupling Structure of Controllable React
or of
Transformer Type
Yu He*, Hua
t
ai Chen
Po
w
e
r Su
ppl
y
Comp
an
y of Bai
y
in, Ba
i
y
in, 7
309
00, Ch
ina
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 4697
21
978
@
qq.com
A
b
st
r
a
ct
In ord
e
r to
ma
ke contr
o
ll
abl
e
reactor
of tra
n
sf
ormer type
(CRT) working
of safety, rel
i
abl
e a
n
d
compe
n
satio
n
effect is obvio
u
s
, the princi
ple
of “hi
gh i
m
pe
danc
e, w
eak coup
lin
g
”
must be satisfie
d in
th
e
desi
gn of
CRT
structure.
T
he
ma
gn
etic i
n
teg
r
ation tec
h
n
o
lo
gy use
d
i
n
the
desi
gn
of the o
n
tolo
gy of C
R
T
i
n
this p
a
p
e
r, a
deco
upl
in
g i
n
tegrate
d
c
o
re s
t
ructure is
pr
o
pose
d
. T
h
is
p
aper
als
o
c
a
lc
ulates
the
le
ak
ag
e
reactanc
e an
d current of
dec
o
upli
ng structur
e.
Ke
y
w
ords
:
co
ntroll
abl
e react
o
r of transformer type, ma
gn
e
t
ic integrati
on, equ
ival
ent circ
uit
Copy
right
©
2015 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 di
agram
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”
.
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
rcui
t [10-12]; Ge
nerally th
i
s
structu
r
e also can be
e
a
sily
extended
to
the
stru
cture of the multiple
control windi
n
g
s,
provide
s
a
refe
ren
c
e f
o
r the furth
e
r application
o
f
magneti
c
inte
gration te
chn
o
logy.
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TELKOM
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A Deco
uplin
g
Structure of Controllabl
e
Rea
c
tor of T
r
ansfo
rm
er Type (Yu He)
21
2. A Dec
oupl
ing Structu
r
e of CRT
In magn
etic i
n
tegratio
n te
chnolo
g
y, the
dec
ouplin
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.
Figure 2. De
couplin
g Struct
ure of CRT
In Figure 2, t
he ce
nter
col
u
mn and
upp
er and l
o
we
r
yoke a
r
e lo
w relu
ctan
ce, e
a
ch
side
of column o
pene
d the g
ap. The ce
nter col
u
mn
wound a
r
ou
nd
the work wi
nding a
nd work
windi
ng is co
nstituted by t
w
o
windin
g
s
of parall
e
led.
Each
cont
rol
windi
ng al
so
con
s
tituted
by
two win
d
ing
s
of parallele
d and this t
w
o wi
ndin
g
s woun
d aro
u
nd in up an
d lowe
r colu
mn
respe
c
tively. Becau
s
e
hav
e air
gap i
n
side of colum
n
of this d
e
co
u
p
ling
stru
cture, the mag
n
e
t
ic
flux
gene
rate
d
by
ea
ch co
ntrol windin
g
are clo
s
ed
th
roug
h the
ce
nter
colum
n
and itself col
u
mn
and
coul
d no
t through
col
u
mns
wo
und
arou
nd oth
e
r
control
win
d
ing
s
, so thi
s
stru
cture me
ets
the de
cou
p
lin
g of control
winding
s.
Thi
s
stru
cture is symmetrical
of
up a
nd lo
we
r se
ction
s
, on
its
uppe
r
se
ctio
n is
co
ncern
ed, there a
r
e
five colu
m
n
s, so the m
a
gnetic flux
g
enerated
by work
windi
ng only
have 1/4
cro
s
s-lin
ke
d with
each cont
rol
windi
ng, whi
c
h meets th
e
desi
gn p
r
in
ci
ple
“high i
m
ped
a
n
ce
” of CRT.
Also be
ca
use wo
rk
wi
n
d
i
ng an
d control win
d
ing
s
a
ll con
s
tituted
by
two
windi
ng
s in p
a
rall
el,
thus, the
effect of
re
acti
ve po
wer co
mpen
sation
i
s
g
r
eat
of t
h
is
decouplin
g st
ructu
r
e.
3. Calculatio
n of Leak
age
Inductan
c
e
Becau
s
e of symmetry of deco
upling
structure,
the follow an
alysi
s
and calculatio
ns only
for one
small
basi
c
unit a
s
sho
w
n in Fig
u
re 3.
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TELKOM
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Vol. 13, No. 1, Janua
ry 2015 : 20 – 2
5
22
Figure 3. The
distributio
n g
r
aph of ma
gn
etic field inten
s
ity
In Figure 3,
h is h
e
ight of
iron
co
re
wi
ndo
w, z i
s
e
quivalent h
e
i
ght of win
d
in
g,
co
r
is
radiu
s
of ce
n
t
er colu
mn, a is equivalent
width of
work win
d
ing, b is equivale
nt width of cont
rol
windi
ng, c is
distan
ce b
e
tween two
windi
ngs,
is length
of air gap.
Set
i
0
is current of work windi
ng,
i
1
is curre
n
t of co
ntrol win
d
ing,
make in
side
of center
colum
n
to ze
ro refere
nce. Based
on A
m
pere ci
rcuit law, in 0
~
a
area
s, the current incre
a
s
e
linearly along
x
di
re
ction, t
he ma
gneti
c
f
i
eld inten
s
ity
also
incre
a
se
linea
rly, form
ula of m
agnet
ic
field intensity is follow:
x
za
i
N
a
x
H
H
0
0
0
ax
(
1
)
In
a
~
a
+
c
are
a
s, b
e
cau
s
e t
here
is no
current in
crea
se,
so
ma
gnetic
field inten
s
ity
remai
n
unchan
ged, the formul
a is
follow:
z
i
N
H
H
0
0
m
cx
(
2
)
In
a
+
c
~
a+
b+c
areas,
sin
c
e the reverse cu
rre
nt of c
ontrol win
d
i
ng, the mag
netic field
intensity de
crease linea
rly, so the formul
a if follow:
c)
(a
x
bz
i
N
H
H
1
1
m
bx
(
3
)
Acco
rdi
ng to the magn
etic f
i
eld inten
s
ity di
strib
u
tion of
the magneti
c
field determi
nes the
magneti
c
ene
rgy, in 0~a a
r
eas, the form
ula of magnet
ic ene
rgy is follow:
2
0
0
2
0
2
a
0
2
2
2
0
2
0
0
a
0
2
ax
0
a
)
i
(N
8z
πa
μ
zdx
πx
x
a
z
i
N
2
μ
dV
H
2
μ
W
(
4
)
In
a
~
a+
c
ar
ea
s
,
2
0
0
2
0
c
a
a
2
2
0
2
0
0
c
)
i
(N
2z
)
c
2
1
π(ac
μ
zdx
πx
z
i
N
2
μ
W
(
5
)
In a+c~a
+
b
+
c area
s,
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TELKOM
NIKA
ISSN:
2302-4
046
A Deco
uplin
g
Structure of Controllabl
e
Rea
c
tor of T
r
ansfo
rm
er Type (Yu He)
23
dV
H
2
μ
W
c
b
a
c
a
2
bx
0
b
(
6
)
Since excitin
g
cu
rre
nt is very small,
so pape
r igno
re it’s effect,
there is
0
0
1
1
i
N
i
N
,
formula (6)
can re
write a
s
follow:
2
1
1
2
0
2
1
1
2
0
b
)
i
(N
zb
]
b
c)
c)[2b(a
π(a
μ
)
i
(N
4z
]
b
c)
π[2b(a
μ
W
2
1
1
2
4
4
0
2
1
1
3
3
0
)
i
(N
8zb
]
c)
(a
-
c)
b
π[(a
μ
)
i
(N
3zb
]
c)
(a
-
c)
b
π[(a
μ
2
1
1
2
2
2
0
2
1
1
3
3
0
)
i
(N
4zb
]
b
c)
[2b(a
c)
π(a
μ
)
i
(N
3bz
]
c)
(a
c)
b
c)[(a
π(a
μ
(
7
)
Magneti
c
ene
rgy of the wh
ole are
a
is fol
l
ow:
2
1
σ1
2
0
σ0
c
b
a
i
L
2
1
i
L
2
1
W
W
W
(
8
)
Simultaneo
us formula 4, 5, 7 and 8, we
can get follow:
2z
)
c
2
1
π(ac
μ
8z
πa
μ
N
L
2
0
2
0
2
0
σ0
(
9
)
zb
]
b
c)
c)[2b(a
π(a
μ
N
4z
]
b
c)
π[2b(a
μ
N
L
2
0
2
1
2
0
2
1
σ1
2
4
4
0
2
1
3
3
0
2
1
8zb
]
c)
(a
c)
b
π[(a
μ
N
3zb
]
c)
(a
c)
b
π[(a
μ
N
2
2
2
0
2
1
3
3
0
2
1
4zb
]
b
c)
[2b(a
c)
π(a
μ
N
3bz
]
c)
(a
c)
b
c)[(a
π(a
μ
N
(
1
0
)
In formula (1
0),
0
L
and
1
L
is leaka
ge indu
ct
ance of work
windi
ng and
control win
d
i
n
g
r
e
spec
tively.
4. The Equiv
a
lent Cir
c
uit
of Ba
sic Unit
0
X
1
X
m
X
0
I
1
I
0
4
1
u
m
I
Figure 3. The
equivalent ci
rcuit of ba
sic
unit
Figure 3 i
s
e
quivalent
circuit of T type, in Fi
gu
re
3, we ig
no
res the resi
stan
ce
of wo
rk
windi
ng, cont
rol windi
ng a
nd
ex
citation
re
sista
n
ce
. In orde
r to e
n
s
ure the
ma
g
netic flux
ch
a
i
n
relation
shi
p
remain
s the
same, the voltage of the p
r
imary si
de is
u
0
/4 in equiv
a
lent ci
rcuit, all
para
m
eters o
f
circuit are re
turn to the sid
e
of work win
d
ing [14].
In Figure 3,
m
I
i
s
exc
i
tation current,
1
X
is imp
u
ted value of
leakage
rea
c
t
ance of control
windi
ng,
1
I
is im
puted value o
f
current of control wi
ndi
n
g
. Acco
rdin
g to the magne
tic Ohm'
s law,
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TELKOM
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Vol. 13, No. 1, Janua
ry 2015 : 20 – 2
5
24
we can get:
ω
4N
u
R
I
2
0
0
m
m
(
1
1
)
In formula (11),
m
R
is ma
gn
etic resi
stan
ce (in
c
lu
di
ng
magneti
c
resistan
ce of
center
colum
n
,
iron
y
o
ke an
d sid
e
colum
n
).
Acco
rdi
ng to equivalent
circuit, we can g
e
t follow form
ula:
m
m
σ1
1
m
m
σ0
0
0
1
0
m
Z
I
Z
I
0
Z
I
Z
I
u
4
1
I
I
I
(
1
2
)
Based o
n
formula (1
2), we
can calculate
:
σ1
σ0
0
σ0
m
1
Z
4Z
u
Z
4I
I
(
1
3
)
1
m
0
I
I
I
(
1
4
)
5. Calculatio
n for Exampl
e
The pa
ramet
e
rs
of iron co
re is
sho
w
ing
as Tabl
e 1, turn
s of wo
rk
windi
ng is
1600
0
N
,
turns of all
co
ntrol win
d
ing i
s
120.
Table 1. The
para
m
eters o
f
iron co
re
paramete
r
value(cm)
paramete
r
value(cm)
a
23
h
125
b
1
z
110
c
16
δ
3mm
co
r
39.5
r
μ
2000
Acco
rdi
ng to
value of T
abl
e 1, we
can
calcul
ate the
currents of all
windi
ng
s a
r
e
sho
w
a
s
Table 2.
Table 2. Cal
c
ulation value
s
of current
no-load
CW1short
ci
rcuit CW1~CW2
short
cir
c
uit
CW1~CW3 short
cir
c
uit
CW1~CW4 short
cir
c
uit
current of BW/A
2.3219
36.3253
72.6505
108.9758
145.3011
current of
1/2CW
1
0
15.8407
15.8407
15.8407
15.8407
current of
1/2CW
2
0
0
15.8407
15.8407
15.8407
current of
1/2CW
3
0 0
0
15.8407
15.8407
current of
1/2CW
4
0 0
0
0
15.8407
We can be
seen that this st
ru
cture
ca
n not only re
alize the d
e
couplin
g between the
control windi
ng,
but also the
compe
n
sation
effe
ct
i
s
ve
ry goo
d
according
to
the
cal
c
ulati
on
results in Table 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Deco
uplin
g
Structure of Controllabl
e
Rea
c
tor of T
r
ansfo
rm
er Type (Yu He)
25
6. 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
de
couplin
g struct
ure h
a
s
been
prop
osed. O
n
the ba
sis
of the cal
c
ulati
on
of the lea
k
a
ge ind
u
cta
n
ce of the wi
n
d
ing
s
an
d
e
quivalent
circuit is e
s
tabli
s
he
d, we
get
th
e
f
o
llowin
g
con
c
lu
sion
s:
(1) The “wea
k
coupli
ng” d
e
sig
n
re
qui
re
ment
amo
ng control
wi
ndi
ngs of
CRT can
be reali
z
e
d
by
providin
g a lo
w relu
ctan
ce
magneti
c
ci
rcuit.
(2)
Wh
en the
air ga
p of si
de column
b
e
com
e
s
bigg
er, the de
gre
e
of co
upling
among
co
ntrol
windi
ng
s becomes
small
e
r.
(3) Th
e meth
od of
de
cou
p
l
i
ng am
ong
co
ntrol
windi
ng
s by adj
ustin
g
the air ga
p of
sid
e
colum
n
of
magneti
c
inte
grated
stru
ctu
r
e of CRT is
effective.
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