TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 65
4
4
~ 655
0
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.497
2
6544
Re
cei
v
ed
No
vem
ber 2
8
, 2013; Re
vi
sed
Apr 2, 2014;
Acce
pted Jun
e
10, 2014
Single-winding Regulation Mode of Controllable
Reactor of Transformer Type
Yibin Liu,
Mingxing Tian,
Jianning Yin
Schoo
l of Auto
mation a
nd El
e
c
trical Eng
i
ne
e
r
ing, La
nzh
ou
Jiaoto
ng U
n
ive
r
sit
y
Lanz
ho
u, 730
0
70, Gansu pr
o
v
ince, Ch
ina, 1
365
94
658
40
Corresp
on
idn
g
author, e-mai
l
:
y
a
ner
w
u
min
g
@
12
6.com
A
b
st
r
a
ct
It is an i
m
por
tant part to s
e
lect the
reg
u
l
at
io
n mod
e
i
n
the desi
gn and man
u
facture
of
a
control
l
ab
le r
e
actor of transf
o
rmer type
(C
RT
). Based
on
the circ
uit e
q
u
a
tions
expr
ess
ed by
the s
e
lf
and
mutu
al
in
ducta
nce, the
pi
ece
w
ise express
i
o
n
s of the
in
sta
n
tane
ous c
u
rre
nt in w
o
rk w
i
n
d
in
g i
n
the s
i
n
g
le
-
w
i
ndin
g
re
gu
la
tion
mod
e
ar
e
obta
i
n
ed,
and
then
the
for
m
ula
for c
a
lcu
l
at
ing
the
RMS
o
f
each
h
a
r
m
on
ic
current
in w
o
rk
w
i
ndi
ng
is
der
ived
by F
o
uri
e
r series
d
e
co
mpositi
on. At
las
t, the
co
ntrol c
haracter
i
stics
of
CRT
an
d the c
u
rves of the
R
M
S of
harn
oni
c currents w
i
th
referenc
e to the o
u
tput p
o
w
e
r in thr
ee typi
ca
l
singl
e-w
i
nd
ing
regu
latio
n
mod
e
s are pres
ent
ed an
d thei
r a
d
vanta
ges a
n
d
disadv
anta
ges
are compar
ed
i
n
the sa
mpl
e
, w
h
ich prov
ides a r
e
ferenc
e for the desi
gn of CR
T
.
Ke
y
w
ords
:
co
ntroll
abl
e react
o
r of transformer type, singl
e-
w
i
ndin
g
reg
u
lat
i
on
mo
de, har
mo
nic curr
ent
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
Rea
c
tive bal
ance is very
important fo
r t
he se
cu
re
and econo
mical op
eration of the
power
syste
m
s[1]. By now, due to th
e
long-te
rm ef
f
o
rts of m
any
sci
entific
workers at h
o
me
and
abro
ad, there
are vario
u
s
kind
s of rea
c
t
i
ve-l
oad
com
pen
sation eq
uipment
s hav
e come into
use
[2-4], In 199
5, G.N.Aleksandrov, a Ru
ssi
an expe
rt,
came u
p
wit
h
the ba
sic
circuit di
agram
o
f
CRT[5], after
that many scholars d
o
furt
her
re
sea
r
ch
on it [6-9], an
d point o
u
t that CRT ha
s t
he
advantag
es
of fast re
spo
n
se a
nd
con
t
rollabl
e
harmonic
co
nte
n
ts, whi
c
h i
s
a rea
c
tive-l
oad
comp
en
satio
n
equipm
ent that can a
ppli
e
s to EHV tra
n
smi
ssi
on lin
es.
The key rea
s
on the h
a
rmonic
conte
n
ts of CR
T can b
e
co
ntrolled is that
there is a
rest
rictio
n am
ong regul
atio
n mode,
cont
rol ste
p
s,
cap
a
city of ea
ch
step a
nd ha
rmonic
co
nten
ts.
Referen
c
e [7
] presented
3 regul
ation
mode
s: st
ep
-singl
e-b
r
an
ch
mode, fixed-sin
g
le
-bran
c
h
mode, tran
sf
er-sin
gle-bra
n
ch m
ode, since all of th
em allow
onl
y one cont
ro
l windin
g
to be
regul
ated, th
ey can b
e
cal
l
ed as
sin
g
le-windi
ng regul
ation mod
e
. Referen
c
e [7]
did re
sea
r
ch
on
the
3 mode
s
in ca
se of negle
c
ting
th
e
coupli
ng
of the
cont
rol
windi
ng
s. Ho
wever, th
e n
on-
ignorable in
d
u
ctive co
upli
ng always ex
ists am
ong
t
he co
ntrol
wi
ding
s, and e
a
ch of the
co
ntrol
windi
ng current will seriously affect the o
t
hers, this
leads to a great
difficulty for the selection
of
the rated
cap
a
city of each
control win
d
in
g.
In this pap
er,
takin
g
into
a
c
count
of the
indu
ctive co
upling
amo
n
g
the cont
rol widin
g
s,
the formula
s
for calculati
ng the RMS
of
each ha
rmonic
cu
rre
n
t
and the cu
rre
nt harm
o
n
i
c
coeffici
ents a
r
e given, and
then the variation tr
end
s
of the output power
an
d the curve
s
of the
RMS of
ha
rn
onic current
s
with
referen
c
e to the
outp
u
t po
wer in
the th
ree
typical si
ngle
-
wi
nd
ing
regul
ation mo
des a
r
e p
r
e
s
e
n
ted, this will
provide
s
a referen
c
e fo
r the desi
gn of a CRT.
2. Instantane
ous Cur
r
en
t of Wor
k
ing
Winding
The basi
c
circuit diagram
of a CRT
i
s
illustrated
in Figure
1, where,
1
W
is the
hi
gh-
voltage work windi
ng,
a
n
d
2
W
,
3
W
,…,
n
W
are
co
ntro
l win
d
ing
s
. In
additio
n
, ea
ch control
win
d
ing
is equi
pped
with a cu
rren
t-limiting rea
c
tor (
2
X
,
3
X
,…,
n
X
) an
d a thyristor
swit
ch (
2
T
,
3
T
,…,
n
T
)whi
ch
co
nsi
s
ts of two thyri
s
tors in pa
rall
el but
in opp
o
s
ite directio
ns. Assume th
at the voltage of
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Single-windi
n
g
Reg
u
lation
Mode of Co
ntrollabl
e
Re
act
o
r of Tra
n
sfo
r
m
e
r Type (Yi
b
in Liu)
6545
the grid i
s
sh
own a
s
)
cos(
2
1
1
t
U
u
, and the starting
point du
ring
each pe
riod i
s
the time wh
en
the voltage of the grid re
ached maximu
m.
..
.
1
u
2
W
3
W
n
W
2
X
2
T
3
T
n
T
3
X
n
X
3
i
2
i
n
i
1
i
1
W
Figure 1. Basic Circuit Di
a
g
ram of CRT
Includi
ng
1
W
,There a
r
e
n
windi
ngs in the CRT illustrated
in Figure 1. Assume that
all
the pa
ram
e
ters of all
wi
nding
s
are
referred to
1
W
. Negl
ectin
g
th
e iro
n
satu
ra
tion an
d all
resi
stan
ce, th
e in
stantan
eo
us
circuit
equ
ati
ons for all
of the
windi
n
g
s
whil
e all
the
1
n
co
nt
rol
windi
ng
s a
r
e
sho
r
t-circuite
d are give
n b
y
(1),
wh
ere,
k
L
is
th
e se
lf-
i
n
d
u
c
ta
nc
e o
f
k
W
(
1
≤
k
≤
n
),
kq
M
is the
mutua
l
-indu
ctan
ce
betwe
en
k
W
and
q
W
,
k
L
x
is the i
ndu
ct
ance of
k
X
, while
k
X
is the
c
u
rrent-limiting reac
tor
c
o
nnec
ted with
k
W
as mentioned a
bove.
n
n
n
p
u
i
L
)
(
(
1
)
Whe
r
e,
n
n
n
n
n
n
n
n
n
L
L
M
M
M
M
L
L
M
M
M
M
L
L
M
M
M
M
L
x
3
2
1
3
x3
3
32
31
2
23
x2
2
21
1
13
12
1
L
,
t
p
d
d
,
n
n
i
i
i
i
3
2
1
i
,
0
0
0
1
u
n
u
.
Assu
me
that there are
1
h
(
1
≤
h
≤
n
)control wi
ndi
ngs
are
invol
v
ed in the o
p
e
ration, a
nd
only one of th
em is b
e
ing
regulate
d
, wh
ose tri
gge
red
angle i
s
eq
ua
l to
(
0
<
<
2
π
), whil
e the
other
2
h
are sh
ort-circuited d
u
ring the p
e
ri
od. Si
nce the
symmetry of curre
n
t wavef
o
rm in
1
W
,
we ju
st have to work out th
e expre
ssi
on
for the instant
aneo
us
curre
n
t in
]
2
π
,
0
[
.
The ci
rcuit eq
uation
s
for all
of the windin
g
s in
]
,
0
(
can be rewritten a
s
:
1
1
1
)
(
h-
h-
h-
p
u
i
L
(
2
)
Whe
r
e,
1
h
L
,
1
h
i
,
1
h
u
are
the subm
atri
xes of
n
L
,
n
i
,
n
u
re
spectively, whi
c
h
ca
n b
e
o
b
tained
b
y
r
e
mo
ving
th
e e
l
e
m
en
ts
o
f
n
L
,
n
i
,
n
u
that co
rre
s
po
ndin
g
to
the
re
gulate
d
and
op
en-ci
rcuite
d
windi
ng
s.
From
(2), the
differential eq
uation for the
work wi
ndin
g
curre
n
t is deri
v
ed as:
1
,
1
1
1
d
d
h
L
u
t
i
(
3
)
Whe
r
e,
1
-
,
1
1
h
L
is the first eleme
n
t of the first co
lumn of
1
1
h-
L
, and
1
1
h-
L
is the inverse matrix of
1
h-
L
.
Since the initi
a
l condition in this time segment is
0
0
1
t
i
, from (3),
1
i
is figure out as (4).
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
44 – 655
0
6546
)
sin(
2
1
-
,
1
1
1
t
L
U
i
h
(
4
)
In the same
way, the circuit equat
ion f
o
r wo
rk win
d
i
ng cu
rrent in
]
2
π
,
(
can be rewritten
as:
h
L
u
t
i
,
1
1
1
d
d
(
5
)
Whe
r
e,
h
L
,
1
1
is the
first el
ement
of the first
col
u
mn
of
1
h
L
, and
1
h
L
is the inverse
matrix of
h
L
, and
h
L
is the subm
atrixes of
n
L
,which
can
be
obtained
by removing th
e eleme
n
ts
of
n
L
tha
t
corre
s
p
ondin
g
to the ope
n-ci
rcuited
co
ntrol wi
nding
s. Since th
e final value of
the forme
r
time
s
egment is
the initial c
o
ndition of
the c
u
rrent time s
e
gment,from(5),
1
i
can be figure out as (6).
sin
)
2
2
(
)
sin(
2
1
-
,
1
1
,
1
1
,
1
1
1
h
h
h
L
U
L
U
t
L
U
i
(
6
)
3. Formulas for Cal
c
ulati
ng Harmonic
s
The waveform of
1
i
is symmetric
amo
ng 4 qua
rter period
s
, wh
ich contain
s
only
fundame
n
tal and od
d harmonics. He
nce,
1
i
can b
e
expressed a
s
a F
ourie
r serie
s
l
i
ke this.
]}
)
1
2
sin[(
{
1
1
2
1
k
k
t
k
b
i
(
7
)
Whe
r
e,
)
3
2
1
(
)
d(
]
)
1
2
sin[(
)
(
π
4
2
π
0
1
1
2
，
，
，
k
t
t
k
t
i
b
k
(
8
)
From
(4
), (
6
),
(8
), the
RMS
of the
)
,
3
,
2
,
1
(
1
2
k
k
th ha
rmonic current
in the
wo
rk
windi
ng
can b
e
derive
d
as (9
):
)
(
)
1
1
(
)
2
π
(
1
π
,
1
1
,
1
,
1
1
1
2
k
h
h
k
h
k
f
L
L
f
L
U
I
(
9
)
Whe
r
e,
)
,
4
,
3
,
2
(
]
2
sin
1
)
1
(
2
sin
[
1
2
1
)
(
2
sin
2
)
(
1
k
k
k
k
k
k
f
f
k
(
1
0
)
The fo
rmul
a(9)
cla
r
ifies th
e relation
shi
p
not
only b
e
twee
n the
RMS of
ea
ch current
harm
oni
c a
n
d
trigg
e
re
d a
n
g
le, but
also
betwe
en th
e
harm
oni
c
co
mpone
nts an
d the
pa
rame
ters
of self and m
u
tual indu
cta
n
ce,
w
hi
ch is
very importan
t
for the desig
n of CRT.
The
1
2
k
th current
harmo
nic
co
efficient for th
e work wi
ndin
g
can b
e
deri
v
ed
)
(
)
(
π
)
(
1
1
,
1
,
1
1
,
1
1
1
2
1
2
H,
h
h
h
h
h
k
k
k
f
L
L
L
f
I
I
k
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Single-windi
n
g
Reg
u
lation
Mode of Co
ntrollabl
e
Re
act
o
r of Tra
n
sfo
r
m
e
r Type (Yi
b
in Liu)
6547
4. Analy
s
is o
f
Examples
Takin
g
CRT descri
bed
in [7]
as an
illu
stra
tion, th
e
3 si
ngle
-
wi
nd
ing regul
atio
n mod
e
s
are an
alyse
d
in the case of taking acco
u
n
t of t
he coupling of the control wi
ndin
g
s in this pap
er.
The
CRT
de
scribe
d in [7]
has 6
windi
ngs(in
c
ludi
ng
1
W
), the rated
voltage is
kV
3
500
N
U
.
Based
on
th
e self an
d m
u
tual imp
eda
nce
which
can b
e
conve
r
ted into
the
self
and
mu
tual
indu
ctan
ce a
nd the ind
u
ctance
of cu
rrent-limit
ing
reacto
rs
whi
c
h ca
n be
ca
lculate
d
by the
recursio
n alg
o
rithm,
n
L
can be
expediently obtaine
d,in this ca
se,
6
n
,Hence,
6
L
is
(unit:H)
453.99
452.48
452.32
452.22
452.16
450.98
452.48
462.89
452.57
452.48
452.41
451.17
452.32
452.57
482.61
452.64
452.57
451.27
452.22
452.48
452.64
524.34
452.67
451.36
452.16
452.41
452.57
452.67
538.36
451.40
450.98
451.17
451.27
451.36
451.40
452.83
6
L
Referrin
g to [
7
], a 5
-
digit
binary
co
de
i
s
u
s
e
d
to
re
pre
s
ent
the
state of e
a
ch
thyristor
swit
ch, the
r
e
is a
on
e-to
-one
co
rre
sp
o
nden
ce
between p
e
r
bit o
f
this code
in
se
quen
ce
from
high to l
o
w and
ea
ch
cont
rol
wi
nding
of CRT from
6
W
to
2
W
, where, “
0
”me
ans t
h
e
corre
s
p
ondin
g
control
wi
n
d
ing i
s
o
pen
-circuited,
and
the trig
gered
angle
of its thyristo
r i
s
eq
ual
to
90
;“
1
”mea
ns
short-circuite
d, and the trig
g
e
red
angl
e of the co
rre
sp
o
nding thyri
s
to
r is eq
ual
to
0
; “
1
”me
a
n
s
regulatio
n, the co
rrespon
ding trig
g
e
re
d angle falls some
whe
r
e
in between
those two.
Duri
ng the p
r
oce
s
s that the output po
wer of
CRT ch
ange
s from n
o
-loa
d to the rated, the
variation
ran
ge of outp
u
t power
can
b
e
divi
ded int
o
5 ste
p
s in
step-sin
g
le
-branch mod
e
,
16
step
s in fixed-sin
g
le
-bran
c
h mode, and
15 step
s
in transfe
r-sin
g
le-bran
c
h m
ode
in this ca
se.
Acco
rdi
ng to the above de
script
ion, the
regul
ating p
r
oce
s
se
s of the 3 ope
ration
modes
are a
s
follo
ws. The d
oubl
e arrow i
n
the processe
s indi
cate
s that the pr
ocess is
reversible,
whe
r
e, “
” p
r
e
s
ent
s a in
sta
n
taneo
usly
shifted pro
c
e
s
s of wi
nding
curre
n
ts, whil
e “
” mean
s
a smooth p
o
w
er
reg
u
latio
n
due to the chang
e of
trigg
e
red a
ngle of
the thyristor
switch.
(1) Step
-si
ngl
e-b
r
an
ch mo
de
11111
01111
00111
00011
00001
00000
5
4
3
2
1
(2) Fix
e
d
-
sing
le-b
ran
c
h mo
de
6
5
4
3
2
1
01011
01010
01001
01000
00111
00110
00101
00100
00011
00010
00001
00000
12
11
10
9
8
7
1011
1
10110
10101
10100
10011
10010
10001
10000
01111
01110
01101
01100
16
15
14
13
11111
11110
11101
11100
11011
11010
11001
11000
(3) T
r
an
sfe
r
-single-branch mode
10001
10000
0000
1
01000
000
1
0
00100
00
1
00
00010
0
1
000
00001
00000
6
5
4
3
2
1
11101
11100
00
1
11
11010
0
1
110
11001
11000
000
1
1
10100
00
1
10
10010
0
1
100
13
12
11
10
9
8
7
11111
11110
0
1
111
15
14
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
44 – 655
0
6548
Figure 3 sho
w
s the
pie
c
e
w
ise cu
rve
s
of
the RMS
of fundame
n
tal cu
rre
nt in
work
windi
ng
with
referen
c
e
to t
he tri
gge
red
angle
du
ri
ng
each step,na
mely,the
c
ont
rol ch
ara
c
te
ri
stic.
The numb
e
r i
n
each p
a
re
nthesi
s
in Figu
re 3 repr
esent
s the step nu
mber, whi
c
h i
s
the same
wi
th
what in th
e regulatin
g pro
c
e
s
ses
metio
ned a
bove.
The
corre
s
po
nding t
r
igge
red an
gle d
u
ri
ng
each step re
duces
from
90
to
0
in both
Figu
re 3(a)
and
F
i
gure
3(b),
which
is
different from
Figure 3(c). I
n
Figure 3(c),
the triggered
angle of the
i
th step re
du
ces from
a sp
ecific a
ngle
i
calle
d as
starting regul
atin
g angle that varie
s
amo
ng
different ste
p
s
. In this ca
se, the calcula
t
ed
values of
i
are given in Tabl
e 1.
Table 1. Start
i
ng Re
gulatin
g Angle of ea
ch Step in Transfe
r-sin
g
le-bran
c
h M
ode
i
1 2
3 4 5
6 7 8
9
10
11
12
13
14
15
)
(
i
90.0 7.19
27.1 29.1 31.8
90.0 3.90 23.1
25.0
90
3.40
22.4 90.0 3.20
90.0
(a) step
-sin
gl
e-b
r
an
ch
mo
de
(b) fix
ed-
sin
g
l
e
-b
ran
c
h mo
de
(c) tran
sfer-si
ngle-bran
ch
mode
Figure 3. RM
S of Fundam
ental
Cu
rrent vs Step Num
bers
Figure 3
(
b) shows that
th
e
output p
o
wer is inte
rmitten
t
when
the
CRT o
perating
in fixed-
singl
e-b
r
an
ch
mode,
whi
c
h is mainly
due to
t
hat
t
he cap
a
city assignm
ent of
ea
ch co
ntrol
windi
ng ca
n't satisfy the de
sign requi
rem
ent for cont
in
uation, in fact
, the c
apa
city of each control
windi
ng mai
n
ly depe
nd
s on the valu
e of its current
-limiting reacto
r.
He
nc
e, it is of great
importa
nce to
sele
ct a a
p
p
r
op
riate valu
e
for ea
ch
cu
rrent-limiting
re
actor in o
r
de
r to satisfy the
contin
uation
of output po
wer. Fi
gure
3(a
)
an
d Fig
u
re 3
(
c)
sho
w
s th
at the
output po
we
r is
contin
uou
s when CRT
op
erating
in ste
p
-si
ngle
-
b
r
an
ch m
ode
and
tran
sfer-si
n
g
l
e-b
r
an
ch
mo
de,
but the
re
gul
ation of
outp
u
t po
we
r mai
n
ly dep
end
s
on the
fou
r
th
and fifth
step
in thi
s
ca
se,
an
d
the cap
a
city
of the regul
ating co
ntrol
wi
nding
s in the
s
e two
step
s
are la
rge
r
tha
n
others,this i
s
unre
a
sona
ble
in the practi
cal appli
c
ation.
Figure 4
sho
w
s
re
spe
c
tively the variat
ion tend
en
cy of the RMS
of
the 5th,
7th, 11th,
13th h
a
rm
oni
c
curre
n
t and
the total h
a
rnoni
c
current
com
pon
ents (de
noted
a
s
H
I
) that p
o
u
r
ed
into power sy
stem with referen
c
e to the
RM
S of the fundame
n
tal cu
rre
nt in work
windi
ng.
The
curve
s
o
f
the RMS of
each ha
rno
n
ic
curre
n
t with referen
c
e
to the outpu
t powe
r
have a tre
n
d
of increa
se
in
both
step-singl
e-b
r
an
ch
mode a
nd
t
r
an
sfer-si
ngle
-
bran
ch mo
d
e
,
while they a
r
e steady in f
i
xed-si
ngle
-
b
r
anch mo
d
e
. Furthe
rmo
r
e,
the wavefo
rm disto
r
tion in
transfe
r-sin
g
l
e
-b
ran
c
h m
o
de is the
mo
st serio
u
s
amo
ng 3 mo
de
s, and the
wave
form di
stortio
n
in
fixed-sin
g
le
-b
ran
c
h mo
de i
s
mu
ch le
ss
than the
othe
r two. Analysing the tren
d
s
of the abov
e
curve
s
combi
n
ing with ea
ch step, we ca
n find that
it
will lead to large
r
harm
oni
c cu
rrent in work
windi
ng if a control wi
ndin
g
of large
r
ca
pacity is re
gul
ated.
0
50
100
150
200
I
1
/A
(1
)
(2
)
(3
)
(4
)
(5
)
0
50
100
150
200
I
1
/A
(1)
(2
)
(3
)
(4
)
(5
)
(6
)
(7)
(8)
(9
)
(
10)
(
11)
(
12)
(
13)
(14)
(1
5
)
(
16)
0
50
10
0
15
0
20
0
I
1
/A
(1
)
(2
)
(3
)
(4
)
(5)
(6
)
(7)
(8)
(9)
(10
)
(11
)
(12
)
(1
3
)
(1
4
)
(1
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Single-windi
n
g
Reg
u
lation
Mode of Co
ntrollabl
e
Re
act
o
r of Tra
n
sfo
r
m
e
r Type (Yi
b
in Liu)
6549
(a) 5th h
a
rm
o
n
ic current
(b) 7th h
a
rm
o
n
ic current
(c) 11th ha
rm
onic
curre
n
t
(d) 1
3
th harm
onic
curre
n
t
(e) total ha
rm
onic
cur
r
e
n
ts
H
I
Figure 4. RM
S of every Harmoni
c Curre
n
ts and
H
I
vs out
put Powe
r
4. Conclusio
n
(1) T
he RM
S of harmon
i
c cu
rrents i
n
wo
rk
windi
ng of all kin
d
s of si
ngle
-
windi
ng
regul
ation m
ode
i
n
the
case
of con
s
i
derin
g
the
couplin
g
am
o
ng cont
rol winding
s ca
n be
cal
c
ulate
d
by an unified formula.
(2) O
p
e
r
atin
g in the sin
g
le-windi
ng regulat
io
n mo
de, the cont
rol win
d
ing
of small
cap
a
city
sho
u
ld b
e
regul
ated to
red
u
c
e th
e h
a
rm
onic content
s in the
work win
d
ing
on
the
premi
s
e that the co
ntinuati
on of
the outp
u
t powe
r
hav
e been e
n
sured.
Ackn
o
w
l
e
dg
ements
This
study is
Suppo
rted by
Nation
al Natu
ral S
c
ien
c
e
Found
ation o
f
China
(51
1
6700
9),
Nation
al Nat
u
ral Scie
nce
Foundatio
n
of China (5136
7010
) a
nd Scien
c
e
and Te
chn
o
l
o
g
y
Program of G
ansu Provin
ce (130
4WCG
A181).
Referen
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[1]
Z
haoa
n W
a
n
g
, Jun Ya
ng, Ji
nj
un L
i
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an
d Var C
o
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e
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.
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ng: Mach
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h
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ongz
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ang Z
hen
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m
en
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o
mpe
n
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ntrol
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ution T
r
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n
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mer.
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ectric
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w
e
r A
u
tom
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q
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ang
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0
20
40
60
80
10
0
12
0
14
0
160
180
200
0
2
4
6
8
I
1
/A
I
5
/A
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60
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0
120
14
0
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I
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I
7
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100
120
14
0
160
180
200
0
1
2
I
1
/A
I
11
/A
0
20
40
60
80
10
0
120
14
0
16
0
18
0
20
0
0
0.
5
1
I
1
/A
I
13
/A
0
20
40
60
80
100
120
140
160
180
200
0
5
10
I
1
/A
I
H
/A
s
t
ep-
s
i
ngle-
br
anc
h m
ode
f
i
x
ed-
s
i
ngle-
br
anc
h m
ode
t
r
ans
f
e
r
-
s
ingle-
br
anc
h m
ode
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
44 – 655
0
6550
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umin
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n
, Du Xiz
h
o
u
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e
Co
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o
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hunti
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i
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i
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i
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eactor. Ph
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ansformer-t
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ersit
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Evaluation Warning : The document was created with Spire.PDF for Python.