In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
4
5
4
~1
4
6
0
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
3.14
5
4
-1
46
0
1454
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Voltage regula
t
ion and pha
se q
uantity
i
n
crea
se o
f two high-
p
o
wer 12-p
h
ase rectifiers
V
a
l
e
r
y
S
afon
ov
,
M
i
k
h
a
il D
z
i
u
b
a
D
e
part
emen
t
of E
lectri
c
P
o
w
e
r Gen
e
ratio
n
an
d
Su
pp
ly,
S
outh
Ural
S
tat
e
Univers
i
t
y
(national
res
e
arch uni
versity),
R
us
ia.
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
A
pr 17,
2
0
1
9
Re
vise
d Ju
l 2
2
,
201
9
A
c
c
e
pte
d
A
ug 3,
201
9
In
t
his
articl
e
,
we
p
res
e
nt
a
n
ew
m
et
ho
d
o
f
s
im
ultan
e
ou
sly
incr
easing
the
ph
ase
qu
ant
ity
a
nd
regu
lat
i
n
g
t
h
e
r
ect
ified
v
o
ltag
e
f
o
r
two
1
2
-
p
h
ase
h
i
gh
-
power
rect
ifi
e
rs
o
perati
ng
a
t
a
co
mmo
n
lo
a
d
.
Se
l
f
-excit
ed
v
olta
ge
i
nverters
sep
a
rately
f
orm
th
e
n
ecess
a
ry
v
o
ltag
e
s
f
o
r
v
o
lt
age
regu
latio
n
a
nd
f
o
r
in
creasin
g
th
e
phas
e
q
uan
tit
y
.
T
he
f
orm
e
d
vo
lt
age
is
i
nput
w
ith
t
he
h
el
p
o
f
a
com
m
o
n
bo
os
t
e
r
trans
f
orm
e
r.
S
eparat
in
g
th
e
i
n
v
e
rters
f
u
n
c
ti
ons
and
usi
ng
th
e
com
m
o
n
b
o
o
s
t
e
r
t
r
ansf
orm
e
r
m
a
kes
i
t
p
o
s
s
i
b
l
e
to
r
e
d
uce
t
h
e
inst
a
lled
po
wer
o
f
t
h
e
e
qui
pm
ent
signif
i
c
a
nt
ly
c
o
m
pared
to
s
imilar
ci
rcui
ts
w
hen
t
h
e
regu
lat
i
on
r
ange
o
f
t
h
e
rectified
vol
tag
e
i
s
u
p
t
o
5%
.
Calcul
at
i
ons
s
h
o
w
t
h
at
th
e
i
nvert
er
power
f
or
i
ncreas
ing
t
h
e
p
h
as
e
q
u
ant
i
t
y
i
s
abo
u
t
3
%
o
f
t
h
e
recti
f
ier
p
o
w
e
r.
T
he
c
i
r
cui
t
w
as
m
od
eled
i
n
M
a
tL
ab/S
im
u
l
in
k
and
t
h
e
elect
rom
a
gn
eti
c
p
ro
cess
e
s
i
n
t
he
r
ecti
f
ier
w
e
re
s
t
u
d
i
ed.
Th
e
p
r
opo
sed
m
e
th
od
m
a
kes
it
p
o
ssible
t
o
r
educe
th
e
total
harmoni
c
d
i
s
tort
i
o
n
o
f
t
h
e
net
w
ork
curren
t
a
nd
t
he
p
ul
sati
on
c
oeffici
ent
o
f
t
h
e
r
ect
if
ied
voltag
e
to
t
he
v
alues
ty
pi
cal f
o
r
24
-
phase recti
f
iers
.
K
eyw
ord
s
:
12-
phase
h
i
gh-
pow
er
r
ec
ti
f
i
e
r
bo
oste
r tra
n
sfo
r
m
e
r
self-e
xci
t
e
d
vo
lta
ge
i
nve
rter
s
vo
lta
ge r
eg
ula
t
i
o
n
u
nder
loa
d
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Mi
kh
a
i
l
Dz
iu
ba
,
D
e
pa
rtem
ent o
f
E
lec
t
r
i
c
P
o
w
e
r
G
e
ne
ration
and
S
u
p
p
l
y,
S
out
h U
r
al S
tate U
nive
rsity(
n
a
t
i
o
nal
rese
arc
h
un
i
versi
t
y)
,
76
Len
i
n pros
p
e
kt,
C
h
el
ya
bi
n
s
k,
Russia
.
Em
ail:
dzi
u
ba
m
a
@sus
u.ru
1.
I
N
TR
OD
U
C
TI
O
N
Ene
r
g
y
i
n
d
i
c
a
t
ors
at
t
he
p
o
i
n
t
o
f
c
o
mm
on
c
o
u
p
l
i
n
g
(P
CC)
o
f
pow
e
r
f
u
l
r
e
c
t
i
f
i
e
r
s
a
n
d
t
h
e
p
o
s
s
i
b
i
l
i
t
y
of
r
e
g
u
l
a
tin
g
(
s
ta
bil
i
zi
n
g
)
t
h
e
m
a
gn
it
u
d
e
of
t
he
r
ec
t
i
f
i
e
d
v
olt
a
g
e
ar
e
ve
ry
i
mp
or
t
a
nt
f
or
e
l
e
ctr
i
ca
l
e
q
u
i
pm
ent
w
ith
r
ect
ifiers.
V
a
rious
m
e
t
h
ods
a
r
e
u
se
d
to
r
e
g
u
l
a
t
e
t
h
e
ma
gn
i
tu
de
o
f
t
h
e
vo
l
t
a
g
e,
s
uc
h
a
s
s
te
p
re
g
u
l
a
ti
on
of
the
vol
ta
ge
o
f
t
h
e
tra
n
sfor
me
rs
u
n
d
e
r
l
oa
d,
s
a
t
ura
b
le
r
e
a
c
t
o
r
,
e
t
c
.
[
1,
2
]
.
T
he
m
ost
promi
s
i
ng
m
e
t
h
od
is
t
o
us
e
self-e
xci
t
e
d
v
o
l
t
a
ge
i
nvert
e
r
s
w
ith
a
D
C
l
i
nk
[
3-5].
Com
p
e
n
sa
te
d
r
e
c
t
i
f
ier
s
a
n
d
c
irc
u
its
w
it
h
a
lar
g
e
n
u
m
b
er
of
p
hases
ar
e
use
d
t
o
impr
ove
t
he
e
nerg
y
in
d
i
c
a
t
o
rs
a
t
P
CC
[6-1
1
]
.
A
c
t
i
v
e
f
i
l
t
e
r
s
c
o
n
n
e
c
t
e
d
i
n
s
e
r
i
e
s
a
n
d
para
l
l
e
l
a
t t
h
e
di
ffe
re
nt p
o
i
n
t
s
of
r
ec
t
i
fie
r
c
i
r
cui
t
s
[12,
13]
a
re
also use
d
for
t
his
purp
o
se.
S
e
pa
rate
t
ec
h
n
i
c
a
l
e
q
u
i
pme
n
t
is
u
se
d
t
o
r
eg
ula
t
e
the
re
ct
ified
vo
lta
ge
[
6,
8
]
a
nd
i
m
prov
e
the
e
n
erg
y
in
dic
a
t
o
rs
[
6],
[1
4-1
6
].
A
n
i
n
cre
a
se
o
f
the
t
o
ta
l
ins
t
al
le
d
c
a
p
a
c
i
t
y
of
t
he
e
qu
ipm
e
nt
l
e
a
d
s
t
o
a
n
inc
r
ea
se
i
n
cos
t
,
w
e
i
g
h
t
a
n
d
s
ize
of
t
he
e
qu
i
p
me
nt.
The
prob
lem
is
t
o
e
n
sur
e
the
re
q
u
i
r
e
d
pow
er
q
ua
li
ty
a
nd
the
vo
l
t
a
g
e
regu
la
ti
on r
a
n
g
e
w
hi
le
re
duc
i
ng t
h
e i
n
s
t
al
le
d
c
a
pac
ity
o
f the
e
qui
pme
n
t.
C
i
rcui
ts
f
or
p
h
a
se
s
pl
itt
i
ng
w
i
th
a
uto
t
ra
nsfor
m
e
r
s [7, 17, 18]
a
l
l
o
w
us to ma
i
n
ta
in t
h
e
v
o
l
t
a
ge q
ual
i
t
y
at
t
he
P
C
C
w
it
hi
n
the
sta
nda
rd
v
a
l
ues
(I
EC
6
1
0
00).
The
insta
lle
d
c
a
p
ac
it
y
of
t
ra
nsfor
m
e
r
e
qu
i
p
me
nt
i
n
s
u
c
h
schem
e
s
i
s
s
m
a
ll,
b
u
t
t
hey
d
o
not
h
a
v
e
a
g
a
lva
n
ic
i
s
o
la
t
i
on,
w
h
ic
h
is
m
anda
tor
y
f
or
h
i
gh-
pow
e
r
c
i
r
c
u
i
t
s.
I
n
add
i
tio
n,
e
i
t
h
e
r
a
ddi
ti
o
n
al
t
r
a
nsform
er
e
qu
ipme
n
t
o
r
a
v
o
l
t
a
g
e
re
gul
at
or
i
s
n
eed
ed
t
o
reg
u
l
a
t
e
t
h
e
v
olt
a
ge
ma
gni
tude
i
n h
i
g
h
-p
ow
er
circ
u
its.
A
spe
c
ial
re
g
u
la
ti
ng
trans
f
or
me
r
and
a
pas
s
ive
fi
l
t
e
r
c
on
ne
cte
d
t
o
it
[
1
0
]
i
s
use
d
t
o
r
e
gu
la
te
t
he
rec
t
i
f
i
e
d
v
o
lta
ge
a
n
d
r
educ
e
the
t
o
t
a
l
ha
rm
oni
c
dist
ort
i
on
(
T
H
D
)
of
t
he
v
ol
ta
ge
a
t
t
h
e
P
C
C.
T
h
i
s
sc
hem
e
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Volt
a
g
e
regu
la
ti
o
n
an
d p
h
a
s
e
qu
a
n
ti
ty
inc
r
ea
se
of
two
hi
gh-
po
wer 1
2
-
p
has
e
rec
t
i
fie
rs (Valery
S
a
f
o
nov)
1
455
pro
v
i
d
es
t
he
r
equ
i
re
d
l
e
ve
l
o
f
t
he
p
ow
er
q
ua
l
i
t
y
i
n
a
l
l
oper
a
ti
ng
m
o
des.
H
owever
,
th
is
t
ra
nsform
er
i
s
cho
s
en
a
t
a
f
u
l
l
p
o
w
e
r
t
r
a
n
s
f
e
r
r
e
d
t
o
t
h
e
l
o
a
d
,
w
h
i
c
h
l
e
a
d
s
t
o
a
d
d
i
t
i
o
na
l
e
n
e
r
gy
lo
sses
an
d
an
i
nc
rea
s
e
i
n
t
he
i
ns
tal
l
e
d
ca
paci
t
y
of t
h
e e
q
u
i
pm
ent.
C
i
rcui
ts
w
it
h
a
con
v
er
ter
w
i
t
h
a
D
C
l
i
nk
a
nd
w
i
t
h
D
C
direc
t
-
c
ur
r
e
nt
buse
s
f
or
r
egula
t
ing
t
h
e
rec
t
i
f
i
e
d
vol
tag
e
o
f
1
2
-p
hase
a
nd
2
4-p
h
a
s
e
r
e
c
tifie
rs
w
ere
st
u
d
i
e
d
i
n
a
r
t
i
c
l
e
s
[
6
]
.
T
h
e
p
o
w
e
r
o
f
s
u
c
h
f
i
l
t
e
r
s
i
s
l
i
mit
e
d
by
t
e
c
h
n
i
c
a
l
a
nd
e
co
no
mi
c
f
a
c
t
o
r
s
b
e
ca
use
of
t
h
e
e
xi
st
i
ng
el
em
e
n
ta
l
base
o
f
pow
er
e
le
c
t
ro
nics.
There
f
ore
,
t
he
r
ange
o
f
v
o
lt
a
g
e
re
g
u
l
a
tio
n
for
hig
h
-
pow
er
r
ecti
fier
s
i
s
l
imite
d
on
l
y
by
v
o
l
t
a
g
e
r
e
g
u
la
t
i
o
n
w
ithi
n
a
s
ing
l
e
sta
g
e
o
f
t
he
t
ap-
c
ha
nge
r
t
r
ansform
e
r.
B
oo
ster
t
ra
n
s
fo
rmers
are
u
s
ed
t
o
i
m
p
r
ov
e
t
h
e
e
n
e
r
gy
in
dic
a
t
o
rs
[
1
9
]
.
T
his
s
o
lu
ti
on
i
s
th
e
mos
t
e
ffe
c
t
i
ve
,
si
nc
e
t
h
e
i
ns
ta
lle
d
c
a
p
a
c
i
t
y
of
t
ra
nsform
er
e
qu
ipm
e
nt
i
s
re
d
u
ced
.
I
n
[2
0
,
21],
a
sche
me
w
a
s
sug
ges
t
ed for i
nc
r
e
a
s
i
ng the
p
h
as
e
qu
a
n
t
i
t
y
of tw
o
12-p
h
ase
re
cti
f
iers w
ith
a
to
ta
l
loa
d
u
p
to
t
he
24-p
h
a
s
e
r
e
gime
.
The
sc
hem
e
m
akes
it
po
s
si
b
l
e
to
i
m
p
ro
ve
e
ne
rgy
para
me
ters
a
n
d
vo
lta
ge
r
eg
ula
t
io
n
a
n
d
is
e
ffe
c
ti
ve
f
or
a
l
ar
ge
r
an
ge
o
f
v
o
l
t
a
g
e
re
gu
la
ti
o
n
(
mor
e
t
ha
n
25
%
o
f
t
he
n
o
m
inal
val
u
e)
.
H
o
w
e
ve
r,
i
f
vo
lta
ge
r
egu
l
a
tio
n
is
n
o
t
r
equ
i
re
d
,
t
r
a
n
s
fo
rm
er
e
quip
m
ent
an
d
co
nv
erter
s
w
ith
a
pow
er
o
f
abo
u
t
13
%
o
f t
h
e
re
ctifier
po
wer
a
r
e ne
eded
t
o
incre
a
se
t
he
pha
se
q
uan
t
ity
.
T
h
i
s
p
a
p
e
r
p
r
e
s
e
n
t
s
a
s
c
h
e
m
e
w
i
t
h
t
h
e
b
o
o
s
t
e
r
t
r
a
n
s
f
o
r
m
e
r
s
s
i
m
i
l
a
r
to
t
hose
c
o
nsi
d
ere
d
i
n
[1
9]
a
n
d
an
o
ri
g
i
na
l
arra
ngem
e
n
t
o
f
se
lf-e
xc
i
t
e
d
vol
ta
ge
i
nve
r
t
ers.
D
ue
to
t
h
i
s,
t
he
i
ns
tal
l
e
d
c
a
p
ac
i
t
y
of
t
he
e
q
u
ip
m
e
nt
w
a
s
r
e
duce
d
w
hi
le
m
ai
n
t
ai
ni
ng
the
qua
l
i
t
y
o
f
e
l
e
c
t
rica
l
e
n
er
gy
at
t
he
P
CC
a
n
d
the
con
t
ro
l
ra
nge
o
f
th
e
r
e
c
t
if
ie
d
v
o
l
t
a
g
e
.
2.
CIRCUIT DESCRIPTIO
N
A
circ
ui
t
of
t
w
o
1
2-p
h
a
s
e
r
ecti
f
ier
s
w
it
h
a
com
m
on
loa
d
a
n
d
a
d
e
v
i
c
e
f
o
r
regu
l
a
t
i
ng
t
h
e
re
ct
ifi
e
d
vo
lta
ge
m
a
g
n
i
t
ude
a
n
d
i
nc
rea
s
i
ng
t
h
e
rec
t
i
f
ie
r
phase
q
uan
t
it
y
a
re
s
how
n
in
F
i
g
ure
1.
S
elf-
exc
i
te
d
v
o
l
t
a
ge
in
verter
s S
V
I
1
a
n
d
S
V
I
2 re
gu
la
te t
he
vo
l
t
a
ge a
nd pa
ss
o
n t
h
e ne
c
e
s
s
ary
acti
v
e
po
wer
fro
m
t
h
e
po
we
r ne
t
w
o
r
k
or
r
ec
ti
f
i
e
r
b
use
s
t
hr
ou
g
h
t
h
e
c
on
verte
r
.
S
V
I3
i
nc
rea
s
e
s
t
he
p
h
ase
q
u
a
n
tit
y
of
t
he
t
w
o
12-
pha
se
r
e
c
tif
ier
up
t
o
the
mode
o
f
a
24-
phase
r
ecti
f
ier.
I
f
the
inve
r
t
er
e
lem
e
n
t
s
ar
e
i
d
ea
l
,
t
he
n
S
V
I3
does
n
o
t
c
ons
ume
a
c
t
i
v
e
pow
er
and
ca
n
w
o
rk
w
i
t
h
a
ca
pac
iti
ve
e
ne
rg
y
acc
umula
t
or.
Boo
s
ter
tra
n
s
f
o
r
m
e
r
s
w
i
t
h
a
s
p
e
c
i
a
l
d
e
s
i
g
n
i
n
p
u
t
t
h
e
vo
lta
ge
s
dE
1
a
nd
dE
2,
f
orm
e
d
b
y
S
V
I
1-S
V
I3a
n
d
LC-
f
i
l
te
rs
F
1-F
3
,
int
o
t
he
s
w
itc
h
i
n
g
c
ircu
its.
The
w
i
n
d
i
n
g
end
s
of t
h
e
boo
ster
transf
o
rme
r
s in F
igures
1
and
2 ha
ve
t
he
s
a
m
e
de
s
i
g
na
t
i
on.
More
de
t
a
ile
d
sche
me
s o
f
bo
o
ste
r
t
ra
nsform
ers T1
s
how
n i
n
F
i
gur
e 2(a)
a
nd
T
2
sh
ow
n
i
n
F
igure
2
(
b
)
use
d
a
re
s
h
o
w
n
i
n
F
i
g
u
re
2
.
The
e
n
d
s
o
f
w
i
n
d
i
n
gs
w
i
t
h
num
ber
o
f
t
h
e
w
i
n
d
i
n
g
t
u
r
n
s
w
,
w
1
a
n
d
w
2
respe
c
t
i
ve
l
y
a
re
i
n
d
ic
ate
d
b
y
the
s
y
mb
ol
"
*"
.
The
inp
u
ts
(
A
1
,
B
1,
C
1)
o
f
t
h
e
prima
r
y
w
i
ndi
ng
s
of
t
he
b
oos
ter
trans
f
or
me
rs
a
re
c
on
n
e
cte
d
t
o
the
hi
g
h
v
ol
tage
i
np
u
t
s
of
t
he
p
o
wer
t
r
ansf
orm
e
r
s
.
T
he
i
nput
s
(A,
B,
C
)
ar
e
con
n
ec
ted
to
t
he
p
ow
er
n
e
t
w
o
rk,
the
ou
tpu
t
s
(a1,
b1,
c
1)
a
r
e
c
o
n
n
e
c
t
ed
t
o
t
h
e
S
V
I3
c
on
verte
r
,
w
h
ic
h
incre
a
ses
t
h
e
p
h
a
s
e
q
u
a
n
ti
ty,
and
the
o
u
t
p
u
t
s
(a
,
b,
c
)
are
con
ne
c
t
ed
t
o
S
V
I1
a
nd
S
V
I2,
w
h
ic
h
r
e
gu
la
t
e
s
the
vo
lta
ge.
F
i
gur
e 1.
The
circ
u
i
t
o
f tw
o
1
2
-
phase
re
c
ti
fiersw
it
h a
com
m
on lo
ad
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
145
4
– 1
460
1
456
(a)
(b)
F
i
gure
2.
D
etai
led
sc
hem
a
tic
o
f b
o
o
ster
t
ran
s
form
er
s T1 a
nd T2
The
se
co
n
d
ary
w
i
nd
ing
s
o
f
b
ooste
r
tra
n
s
f
orm
e
rs
T
1
and
T2
a
re
c
o
n
n
ec
te
d
in
s
uc
h
w
a
y
as
t
o
prov
i
d
e
a
phase
s
h
i
ft
o
f
the
first
harm
on
i
c
o
f
the
curr
ent
by
+
7
.5
a
nd
-7.
5
d
e
g
re
es,
re
spect
ive
l
y.
F
or
t
his,
t
he
n
um
be
r
of
w
ind
i
ng t
u
rns
must sat
is
fy
the
r
e
l
a
tio
n.
.
°
.
°
.
(
1
)
The
va
r
i
an
t
o
f
t
he
b
oos
ter
tra
n
sfor
me
rs
T
1
a
nd
T
2
s
how
n
i
n
F
ig
u
re
2
i
s
n
o
t
the
o
n
l
y
one
poss
i
b
l
e.
I
t
is
i
mp
orta
nt
t
ha
t
t
h
e
first
h
a
rmonic
s
o
f
t
h
e
sec
o
nda
r
y
w
in
din
g
s
c
urre
nts
of
t
he
b
oos
ter
tran
sfor
me
rs
a
r
e
op
p
o
site
i
n
p
h
a
s
e
w
h
en
S
VI3
is
opera
t
i
n
g
.
3.
MATHE
M
A
T
ICAL MODEL
I
n
t
h
i
s
s
e
c
t
i
o
n
,
i
t
i
s
e
x
p
l
a
i
n
e
d
t
h
e
r
e
s
u
l
t
s
o
f
r
e
s
e
a
r
c
h
a
n
d
a
t
t
he
s
a
m
e
t
i
m
e
i
s
gi
ven
th
e
com
p
rehe
nsive
disc
uss
i
o
n
.
Re
su
lt
s ca
n be pr
e
se
nte
d
in F
i
gu
r
e
s,
graphs, tab
les an
d o
t
hers t
hat m
a
ke
t
he rea
der
un
dersta
n
d
easil
y [2,
5]. The
di
s
cuss
io
n
can
b
e
ma
de in
se
v
e
ra
l
sub-cha
p
t
e
rs.
Wh
en
a
sse
ssi
n
g
t
h
e
in
st
all
e
d
c
a
p
a
ci
ty
o
f
a
d
dit
i
on
a
l
t
ran
s
fo
rmer
e
qui
pme
n
t
in
t
he
c
ircui
t
s
how
n
in
Figure
1,
t
he
i
nsta
lle
d
c
a
p
ac
itie
s
of
b
o
o
s
t
er
t
rans
fo
r
m
e
r
s
w
e
r
e
t
a
k
e
n
i
n
t
o
a
c
c
o
u
n
t
.
T
h
e
c
a
l
c
u
l
a
t
i
o
n
s
a
r
e
m
a
d
e
in ac
c
or
da
nce
w
ith
[
2
2
].
The
de
pen
d
e
n
c
e
o
f
t
h
e
boo
ster
t
ra
nsform
er
pow
er
on
the
re
gu
l
a
ti
on
ma
gnit
ude
aU
/U
(
U
–
adde
d
v
o
lta
ge,
U
– pha
se
to gro
u
nd
vo
lta
ge
o
f
the
gri
d
)
is
"
(
2
)
The
i
n
sta
l
l
e
d
p
o
w
e
rs
a
re
equa
l to.
S
a
d
E
aI
,
S
a
d
E
aI
,
S
"
a
d
E
"
aI
"
for one of
the
p
h
ases
o
f
t
h
e
prima
r
y
w
i
n
d
i
n
g
a
nd
the
com
p
o
n
e
n
ts
o
f
the
se
c
o
nda
ry
w
in
di
n
g
o
f
bo
os
t
e
r
tra
n
sf
orme
r
respe
c
t
i
ve
l
y
.
The
cur
r
ents
o
f
the
w
i
nd
i
n
g
s
a
r
e
d
e
t
e
r
m
i
ne
d
by
t
h
e
l
o
a
d
a
nd
are
e
qual
t
o
I
I
K
,
w
h
er
e
I
–
pha
se
c
urrent
s
how
n
i
n
F
i
gur
e
1
and
K
–
tra
n
sf
orm
a
tion
ra
tio.
The
volta
ge
o
f
the
prima
r
y
w
i
n
d
in
g
is
c
reate
d
by t
h
e
S
V
I
3
c
o
nve
r
t
er
t
o
incre
a
se
t
he
p
hase
q
uan
t
ity
I
U
si
n
7
.
5
°
a
nd on
e
of the
S
V
I
1 or S
VI
2 conve
r
t
ers
to
c
on
trol the
v
ol
ta
ge
U
"
a
a
U
. The pha
se shift be
t
w
e
e
n
t
hese
c
omp
one
n
t
s
of
t
he volta
ge
i
s 90
e
.
degree
s,
henc
e t
h
e
w
i
n
d
i
n
g
v
olta
ge
is
sin
7.
5
°
.
(
3
)
The
w
i
n
d
i
n
g
v
ol
t
a
ges of sec
onda
r
y
w
in
di
n
g
par
ts
s
h
o
w
n
i
n F
i
gue
r
2
a
re equal
.°
°
,
"
.
°
°
(
4
)
Whe
n
p
e
rfor
m
in
g
t
h
e
ca
l
c
u
l
a
tio
ns,
it
w
as
a
ssume
d
t
h
a
t
t
h
e
phase
s
hi
ft
b
etw
e
en
p
ha
se
c
urre
nt
a
n
d
vo
lta
ge
i
s
15
e
l
.
degr
ees
a
n
d
t
he
r
ec
ti
fie
r
p
o
w
er
i
s
equa
l
P
6
U
I
c
o
s
1
5°
.
Ta
kin
g
i
n
t
o
ac
c
o
u
n
t
(
2-4),
w
e
get
the
rela
t
i
v
e
(norm
a
lize
d
t
o
the
rec
tif
i
e
r
pow
er
)
insta
l
le
d
ca
paci
t
y
o
f
tw
o
t
h
re
e-phase
b
oos
ter
tra
n
sform
e
rs
in t
he
f
orm
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Volt
a
g
e
regu
la
ti
o
n
an
d p
h
a
s
e
qu
a
n
ti
ty
inc
r
ea
se
of
two
hi
gh-
po
wer 1
2
-
p
has
e
rec
t
i
fie
rs (Valery
S
a
f
o
nov)
1
457
.
°
.
°
.
°
°
°
.
(
5
)
To
e
sti
m
at
e
th
e
i
n
st
a
l
l
e
d
po
we
r
o
f
c
onvert
e
r
s
SVI1
,
S
V
I2
,
an
d
S
VI3,
i
t
was
assum
e
d
tha
t
t
he
con
v
er
t
e
rs
w
er
e
re
pl
a
c
e
d
b
y
idea
l
v
o
l
t
a
g
e
s
ourc
e
s.
F
or
o
n
e
o
f
t
he
p
ha
se
s
of
t
h
e
c
on
ve
r
t
e
r
S
V
I
3
inst
all
e
d
pow
er
is.
.
°
2
(
6
)
The
ca
l
c
ul
a
t
i
o
n
use
d
t
he
r
at
io
I
I
/n
f
or
t
he
h
a
r
monic
s
o
f
the
netw
ork
c
u
rrent
f
or
a
t
hree
-
pha
se
b
rid
g
e
c
i
r
c
u
it
i
n
w
hi
c
h
t
he
s
w
itc
h
i
n
g
proce
sse
s
w
e
re
n
ot
t
a
ke
n
i
n
t
o
a
c
c
o
u
n
t
.
It
w
as
a
ls
o
t
a
ken
i
n
t
o
ac
cou
n
t
t
ha
t
t
h
e
cur
r
ent
s
o
f
t
h
e
1
1
th
a
n
d
13
t
h har
m
on
ics
ar
e
la
r
g
er th
a
n
t
h
e
o
t
her harm
on
ics
i
n
S
V
I
3.
F
or
one
pha
se
o
f t
h
e
SV
I1 a
nd S
V
I2 c
on
v
e
rter
s,
the
i
nsta
l
l
ed
capa
c
i
t
y
i
s
°
.
(
7
)
Ta
k
i
n
g
i
n
t
o
ac
cou
n
t
(
5-6),
w
e
g
e
t
t
he
r
e
l
a
t
i
v
e
(n
orm
a
lize
d
t
o
t
he
r
ect
i
f
ier
pow
er)
ins
t
al
l
e
d
c
a
p
ac
it
y
of
t
hre
e
-
p
h
a
se
c
on
verter
s S
V
I1,
SV
I
2
, a
nd S
V
I3 in
t
h
e
for
m
°
.
°
°
(
8
)
Ca
lcu
l
a
t
i
o
ns
o
f
the
i
n
s
t
a
l
l
e
d
p
o
w
e
r
of
t
he
t
rans
for
m
e
r
e
qui
pm
en
t
a
n
d
the
i
n
s
t
a
lle
d
p
o
w
e
r
of
t
he
con
v
er
t
e
rs
f
or
a
n
al
terna
tiv
e
c
i
rcu
i
t
[2
3]
a
r
e
m
ade
in
t
he
s
am
e
w
a
y
.
I
n
eac
h
ca
se
,
the
de
pe
n
d
ence
i
s
deter
m
i
n
ed
b
y the
ex
press
i
o
n
"
.
°
°
.
(
9
)
The
dependences
(
5
,
9
)
of
t
he
boo
ster
t
ra
nsfo
r
m
e
r
s
po
w
e
r
on
t
h
e
v
ol
tage
r
egul
a
t
ion
dep
t
h
k
a
for
a
circuit
w
i
th
a
g
e
n
e
r
al
vol
tage
r
egul
a
t
ion
and
phase
quantity
i
n
crea
s
e
(
re
d
)
[
23]
a
nd
fo
r
a
ci
rc
ui
t
w
i
t
h
s
e
p
a
r
ate
converters
for
phase
quantity
i
ncrea
s
e
and
fo
r
vol
tage
r
e
gulat
i
on
(blue)
a
re
s
how
n
in
F
igure
3
(
а
)
.
S
i
milar
dependences (
8
,
9)
fo
r the tot
a
l
converte
r
s po
w
e
r
a
r
e
show
n
in
F
i
gure
3
(
b).
(a)
(b)
F
i
gure
3.
T
he de
p
e
n
denc
e o
f
the
b
o
o
s
t
er
tra
nsf
o
rme
r
s pow
e
r
(a)
and
t
h
e
c
o
n
v
e
r
ter
pow
er
(
b)
Taki
ng
i
nt
o
a
c
c
o
unt
t
h
e
a
ssump
t
i
on
s
mad
e
a
b
o
v
e
,
t
h
e
ext
e
rn
al
c
h
a
r
ac
t
e
ri
sti
c
s
fo
r
t
h
e
co
nsi
d
ered
schem
e
a
re c
alcula
te
d
i
n
the
s
tan
d
a
r
d w
a
y [22]
a
nd
h
a
v
e
the
for
m
,
(
10)
wh
ere
U
–rec
t
i
fie
d
v
ol
ta
ge
i
n
i
d
le
m
o
d
e
w
i
t
hou
t
re
gu
l
a
t
i
o
n
,
I
–r
ect
ifie
d
c
u
rre
nt
,
an
d
x
–
s
w
i
t
c
h
i
n
g
circ
u
i
t
resis
t
a
n
ce.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
145
4
– 1
460
1
458
4.
SIMU
L
A
TION
MODEL
ING
To
m
ode
l
t
h
e
pow
er
s
u
p
p
ly
s
ys
tem
,
w
e
use
d
а
t
hr
ee-
w
i
n
d
i
n
g
c
o
nve
rter
t
ransfor
m
er
w
ith
windings
vo
lta
ge
o
f
10
kV
a
nd
62
0
V
,
pow
er
o
f
1
0
M
W,
a
s
hor
t-c
i
r
c
u
i
t
o
f
vo
lta
ge
8
.4%
an
d
short-c
i
r
c
u
i
t
pow
e
r
83 k
W
.
The
fr
e
que
nc
y
of
p
o
w
e
r
s
upp
l
y
i
s
50
H
z
.
T
h
e
gr
i
d
r
esista
n
c
e
i
s
a
bo
u
t
12%
o
f
the
re
si
s
t
anc
e
o
f
t
h
e
sw
it
c
h
i
n
g
c
i
r
c
ui
t.
T
he
l
oa
d
pow
e
r
w
a
s
a
ss
ume
d
t
o
be
1
9
M
W
.
T
h
us
,
t
h
e
l
o
a
d
c
u
r
r
e
n
t
i
s
2
0
k
A
,
a
n
d
t
h
e
rec
t
i
f
i
e
d
vol
tag
e
i
n
t
h
e
i
d
le
m
ode
i
s
9
5
0
V
.
The
in
d
u
c
t
anc
e
o
f
th
e
equ
a
l
i
z
i
ng
r
ea
ct
o
r
s
wa
s
as
su
me
d
to
b
e
6
.
6
mH
,
w
h
ic
h
en
sure
s
tha
t
t
her
e
i
s
no
pu
lsa
t
ion
o
f
t
he
r
ect
i
f
ie
d
c
urre
n
t
.
At
t
he
g
ive
n
l
oa
d,
t
he
d
ura
t
ion
o
f
t
he
swi
t
c
h
i
n
g
p
r
o
c
e
ss
i
s
a
b
out
15
e.
d
eg
re
es.
Th
e
c
h
o
s
en
p
a
r
amet
ers
o
f
t
h
e
mo
d
e
l
a
r
e
typi
ca
l
fo
r
po
we
r
su
pp
ly
systems
for
electrol
ys
is
p
lants.
I
t
w
a
s
a
s
s
u
m
e
d
t
h
a
t
t
h
e
b
o
o
s
t
e
r
tra
n
sform
e
rs
a
nd
diode
s
w
e
re
i
deal.
The
con
v
er
sio
n
f
ac
tor
for
the
boos
t
e
r
transfor
me
r is
3
.
The
mo
du
la
t
i
o
n
freq
u
e
n
c
y
o
f
the
se
lf-e
xc
i
t
e
d
v
ol
tage
i
nve
r
t
ers
was
1
0
0
0
H
z.
T
he
p
ara
m
e
t
ers
o
f
t
he
in
put
L-sha
pe
d
fi
lte
rs w
e
r
e eq
ual
for S
V
I1,
S
V
I2,
and S
V
I
3
L1
=
L
2 =
L3 = 0.
1
m
H and
C1 = C2 = 2000 mF
,
С
3
=
5
00
m
F
r
e
s
p
ect
i
v
el
y
.
T
hi
s
en
sur
e
d the transm
is
sion
r
ati
o
a
t
t
h
e
fu
n
d
a
m
enta
l harm
o
n
i
c K
1
=
K
2 =
0.
987,
K
3
=
1
.
005,
a
t
the
mo
du
la
ti
on
freq
u
e
n
c
y
1
k
H
z
,
t
h
e
fr
eque
nc
y
o
f
t
he
c
on
se
cu
t
i
ve
r
e
s
on
anc
e
o
f
t
h
e
in
pu
t
r
e
s
i
s
t
a
n
c
e
i
n
t
h
e
i
d
l
e
m
o
d
e
f
1
=
f
2
=
3
5
6
H
z
,
f
3
=
7
1
2
H
z
,
a
n
d
TH
D
of
t
he
v
o
l
t
a
ge
a
t
t
h
e
fi
l
t
er
e
n
t
ranc
e
KTHD1
=
KTHD
2
=
4
.67
%,
K
THD3
=
4
2
.
96
%.
S
i
mulat
i
o
n
of
t
h
e
p
ow
er
s
up
p
l
y
sys
t
e
m
w
ith
t
he
a
bo
ve
p
ara
m
eters
w
as
p
erf
o
rmed
i
n
Ma
tLab
/Sim
u
l
i
nk.
(a)
(b)
F
i
gure
4
. The
time depe
ndences
o
f curre
nt
s
The
time
depe
nde
nce
s
o
f cur
r
e
nts
I1
a
n
d
I
2 show
n in F
i
g
ure 1 fo
r
o
n
e
p
h
a
s
e of t
he
1
2-ph
ase
re
cti
f
i
e
r
(dashe
d
l
i
ne,
s
o
l
i
d
l
i
ne)
an
d
t
h
e
ne
tw
ork
c
u
rr
ent
I
(
d
ash-d
o
tte
d
li
ne)
a
r
e
show
n
in
F
ig
ure
4
(
a).
SV
I3
p
rov
i
des
a
n
a
dd
it
io
n
a
l
i
n
put
v
o
l
t
a
g
e
to
e
a
c
h
o
f
th
e
12-p
h
a
se
r
ec
ti
fi
e
r
s
uch tha
t
t
he
d
io
des sw
i
t
c
h
in
g proc
es
ses of one
o
f
t
h
e
r
e
c
t
i
f
i
e
r
s
a
r
e
s
h
i
f
t
e
d
r
e
l
a
t
i
v
e
t
o
t
h
e
p
r
o
c
e
s
s
e
s
i
n
t
h
e
o
t
h
e
r
r
e
c
ti
f
i
er
b
y
1/24
of
t
he
n
e
t
w
o
r
k
vol
tage
p
e
r
i
od.
H
a
r
m
onic
ana
l
ys
i
s
o
f
t
h
ese
c
u
rre
nt
s
s
how
s
tha
t
T
H
D
i
s
7
.
8
%
for
the
c
u
r
r
ents
I
1
an
d
I2
a
nd
is
1
.4%
f
o
r
the
curr
ent
I.
T
he
1
1t
h
an
d
1
3
t
h
c
urre
n
t
h
ar
m
oni
c
s
r
e
m
a
i
n
in
t
he
n
e
tw
or
k
c
u
rr
ent
I,
but
t
he
ir
m
a
g
n
itu
de
i
s
sign
ifica
n
tl
y
reduc
e
d
w
he
n S
V
I3 is ope
rat
i
n
g
.
The
c
u
rre
nts
I
1
’
an
d
I2’
o
f
t
he
s
ec
on
dar
y
w
i
n
di
n
g
s
of
t
h
e
b
o
o
s
t
er
t
rans
f
o
r
m
ers
(sol
id
l
ines)
and
the
in
put
c
ur
ren
t
I
’
of
t
he
S
V
I
3
(
d
ashe
d
li
ne)
ar
e
show
n
in
F
igure
4(b)
.
H
a
r
m
onic
a
n
a
l
y
s
is
o
f
t
h
ese
c
u
rre
nt
s
sh
o
w
s
th
at
t
h
e
c
u
r
re
n
t
s I1
’ a
n
d
I2
’ o
f
th
e
win
di
n
g
s
are
oppo
si
t
e in
p
ha
se
an
d
t
h
e
in
put
curre
n
t
I
’
co
nt
a
i
ns on
l
y
t
h
e
11t
h
and
13
th
h
a
r
mo
ni
c
.
The
re
cti
f
ied
vo
lta
ge,
con
s
truc
t
e
d
a
t
p
ha
se
s
h
i
ft
b
e
t
w
e
en
t
he
i
n
p
u
t
vo
l
t
age
s
o
f
the
p
o
w
e
r
trans
f
or
me
rs,
equa
l
t
o
4
d
egr
e
es
(
da
shed
l
i
n
e)
a
nd
15
e.
d
egre
e
s
(
s
ol
id
l
i
n
e)
i
s
sh
ow
n
i
n
F
ig
ure
5.
S
p
e
ctral
a
n
al
y
s
i
s
o
f
t
h
e
d
e
p
e
nd
en
ce
s
sh
o
w
s
th
at
i
n
t
h
e
re
c
t
i
f
i
e
d
vo
lt
ag
e
,
w
h
e
n
t
he
pha
se
qua
n
tit
y
of
t
he
r
e
c
tif
i
e
r
incre
a
ses,
t
he 1
2t
h ha
rm
on
i
c
re
m
a
i
ns,
gra
dua
ll
y dec
r
ea
s
i
n
g
i
n
m
a
gnit
u
d
e
.
5.
RESULT
S
A
N
D
DISCU
SSIO
N
The
t
r
ans
f
ormer
e
q
u
i
pm
en
t
p
o
w
e
r
i
n
t
he
c
o
n
s
i
dere
d
case
i
s
s
ome
w
h
a
t
hi
g
h
e
r
du
e
to
c
on
st
ru
ct
io
n
o
f
the
bo
oste
r
t
r
ansform
e
r
.
T
he
t
o
t
al
pow
er
o
f
the
c
o
n
v
e
r
ter
s
i
s
m
uch
l
o
w
e
r
.
If
the
r
e
is
n
o
ne
ed
f
or
v
ol
ta
ge
regu
la
ti
on
i
n
t
he
c
irc
u
it,
a
n
i
n
cre
a
se
o
f
pha
se
q
uan
t
ity
i
s
ac
h
ie
ve
d
b
y
a
c
on
verte
r
w
h
o
s
e
p
o
w
e
r
is
3
%
of
t
he
rec
t
i
f
i
e
r
'
s
pow
e
r
,
ver
s
us
1
3%
i
n
t
h
e
a
l
terna
t
i
v
e
ver
s
i
on
[23]
.
This
i
s
beca
u
s
e
i
n
t
h
e
p
r
o
p
o
se
d
c
onstruc
ti
o
n
,
t
h
e
curr
ent
of
t
he
f
irst
h
arm
onic
doe
s
n
o
t
fl
ow
i
n
t
h
e
c
o
n
v
erter
.
W
he
n
t
h
e
de
pt
h
o
f
v
ol
tage
r
egu
l
at
i
on
i
n
c
r
ea
se
s,
th
i
s
r
ati
o
is re
d
u
ced,
bu
t i
n
a
n
y
c
ase
t
h
e
sche
me
under
cons
i
d
e
r
a
t
i
o
n
r
em
ains m
ore
profita
ble.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Volt
a
g
e
regu
la
ti
o
n
an
d p
h
a
s
e
qu
a
n
ti
ty
inc
r
ea
se
of
two
hi
gh-
po
wer 1
2
-
p
has
e
rec
t
i
fie
rs (Valery
S
a
f
o
nov)
1
459
F
i
gure
5
. The
t
ime dependences
o
f
re
ct
ified volt
a
ge
The
re
sults
o
b
t
aine
d
i
n
t
he
s
im
ulat
i
o
n
are
cons
is
te
nt
w
i
t
h
the
re
su
lts
o
f
[22]
i
n
mul
t
i
p
h
a
se
c
i
r
cui
t
s
bo
th
i
n
t
h
e
net
w
ork
curr
en
t
c
u
rve
a
n
d
in
t
h
e
r
ec
t
i
fie
d
v
ol
ta
ge
c
u
rve
.
T
h
e
r
ec
t
i
fie
d
v
ol
ta
ge
c
urve
s
ho
w
n
i
n
F
i
gure
5
doe
s
not
f
ul
l
y
c
oi
nc
i
d
e
w
i
t
h
t
he
c
la
ssi
c
a
l
c
urve
o
f
th
e
2
4-p
h
ase
r
ecti
f
ier
.
H
oweve
r
,
the
d
i
ffere
nce
in
the r
i
pp
le
c
oe
fficie
n
t
be
t
w
een
t
hem
is i
nsig
n
i
fica
n
t
.
A
harm
onic
a
n
aly
s
i
s
o
f
the
s
e
curre
nts
show
s
t
h
a
t
t
he
T
H
D
i
s
7.8
%
f
o
r
the
curr
ents
I
1
and
I2,
and
1.4%
f
or
t
he
c
urr
e
nt
I
.
A
sm
all
i
n
duc
ta
nc
e
o
f
t
he
s
w
i
t
c
h
i
ng
c
ir
c
u
it
a
n
d
shor
t
sw
i
t
c
h
in
g
ti
m
e
o
f
d
i
o
d
e
s
ar
e
ty
pic
a
l
for
re
cti
f
iers
a
t
l
o
w
vo
l
t
age
s
a
n
d
p
ow
e
r
.
Thus,
th
e
TH
D
o
f
t
h
e
gri
d
c
u
r
rent
i
s
5.0
4
%
in
[
7].
The
si
m
i
lar
coe
ffic
i
en
t
i
s
e
qu
al
t
o
0.7
8
%
i
n
[
1
0
],
w
her
e
t
he
c
l
a
ssi
ca
l
24
-phas
e
r
e
c
t
if
i
cat
ion
mo
de
i
s
si
mu
l
a
t
e
d
.
The
i
n
cr
ease
i
n
t
he
T
HD
of
t
he
g
rid
c
u
rr
ent
in
t
he
c
o
n
s
i
d
ere
d
s
chem
e
wi
th
r
es
pect
t
o
the
va
lue
i
n
[
10]
in
dic
a
t
e
s
t
h
a
t
t
he
1
1
t
h
a
n
d
1
3
t
h
ha
rm
on
i
c
s
i
n
t
he
n
etw
o
rk
c
u
r
re
nt
c
ur
ve
a
re
not
c
omp
l
e
t
ely
e
l
imina
t
e
d
i
n
t
h
e
schem
e
s
h
o
w
n
i
n
F
i
gur
e
1.
A
g
ene
r
al
a
na
lys
i
s
o
f
t
he
o
b
t
a
i
n
e
d
cu
r
v
e
s
s
h
o
w
s
tha
t
t
he
r
ecti
f
ier
ope
ra
ti
o
n
m
ode
is
c
l
o
se
t
o
t
h
e
ope
ra
ti
o
n
of
a 24-
phase
r
ec
tifier
.
The
p
r
o
p
o
se
d
sc
hem
e
s
how
n
in
F
ig
ure
1
m
a
ke
s
it
poss
i
bl
e
t
o
i
ncr
e
a
se
t
he
p
hase
q
ua
nti
t
y
a
nd
t
o
regu
la
t
e
t
he
o
ut
p
u
t
vo
l
t
age
of
t
he
r
ec
tifier
,
c
onsis
t
i
ng
o
f
t
w
o
p
ow
er
fu
l
12-p
h
ase
rec
tifie
rs
o
pera
tin
g
a
t
a
com
m
on
loa
d
.
In
t
h
i
s
sche
m
e
,
se
p
a
ra
t
e
i
n
v
e
r
ter
s
a
nd
co
m
m
on
tran
sform
e
r
equipm
en
t
i
n
cre
a
se
t
h
e
pha
se
qua
n
t
i
t
y
an
d r
e
gu
la
te
t
h
e
vo
l
ta
ge.
6.
CONCL
U
S
ION
I
n
t
he
c
o
n
s
i
de
red
sche
me
s
how
n
i
n
F
i
gure
1,
s
er
i
a
l
,
w
i
d
e-spre
ad
t
hree
-w
in
din
g
t
ra
nsf
o
rme
r
s
and
rec
t
i
f
i
e
r
bri
dge
s
are
use
d
a
s
a
12-
phase
r
ect
ifier
.
T
h
i
s
a
l
l
o
w
s
u
s
t
o
a
p
p
ly
t
he
p
ro
pose
d
s
o
l
u
t
i
o
n
o
n
t
he
a
lr
ead
y
in
sta
l
led
1
2
-p
h
a
se
r
ec
t
i
fie
r
.
T
hus,
it
is
p
ossi
ble
t
o
i
m
p
ro
ve
t
h
e
q
ua
li
ty
o
f
e
l
e
c
t
ric
i
t
y
w
it
ho
u
t
r
ep
lac
i
n
g
th
e
ma
in proc
e
ss e
q
u
i
pm
ent,
w
hic
h
pro
vi
des
si
g
n
i
f
ica
n
t
fina
nc
i
a
l
sa
v
i
ngs.
The
prop
ose
d
s
chem
e
m
a
ke
s
it
p
o
ssib
l
e
t
o
r
educ
e
the
t
o
ta
l
p
o
we
r
o
f
i
n
v
e
r
t
e
r
s
i
n
c
o
m
p
a
r
i
s
o
n
w
i
t
h
a
schem
e
i
n
w
h
i
c
h
t
h
ese
fu
nc
ti
ons
a
re
p
e
r
for
m
e
d
b
y
a
com
m
o
n
i
nve
r
ter.
T
o
t
a
l
pow
er
i
s
reduc
e
d
f
r
o
m
20
%
to
13
% w
i
t
h
a
re
g
ula
t
i
o
n
range
o
f
5% of t
h
e
rec
t
i
f
ied
v
o
l
ta
ge.
U
s
in
g
s
i
mu
la
ti
on
i
n
MA
TLA
B
/
S
i
mul
i
nk,
w
e
ha
ve
s
how
n
t
h
a
t
t
he
e
le
c
t
ro
ma
gnet
i
c
proc
esses
in
t
h
e
pro
pose
d
sc
h
e
m
e are
close
t
o
t
he m
ode
o
f a
24-
pha
se r
ect
ifier
i
n re
lat
i
on
to
b
o
t
h
gri
d
a
nd
load.
REFE
RENCES
[1]
H.
X
u,
e
t
al.
,
"Coord
i
n
a
te
C
on
tro
l
S
t
r
ategy
f
o
r
Cu
rrent
S
t
a
bili
z
a
tion
i
n
a
n
Al
u
m
inu
m
S
me
lter
Incl
ud
in
g
on
L
oa
d
Tap Changer,"
En
erg
y
an
d P
o
we
r
En
g
i
neeri
n
g
, v
o
l
. 5
, p
p.
1
41
0-1
4
1
4
, 2
01
3.
[2]
C.
A
.
M
a
hrez
and
G.
d
e
P
r
éville,
"Gl
o
bal
curre
nt
r
egul
ation
a
n
d
A
h
com
p
ens
a
tio
n
f
o
r
alu
m
inu
m
e
lectro
lysis
su
bs
ta
ti
on,
"
2
0
1
5
17
th
E
u
r
opea
n
Con
f
er
ence on
P
o
wer El
ectr
onics a
nd A
pplica
t
i
o
n
s
(
E
PE'15
ECCE-Euro
p
e),
p
p
.
1-8
,
2
015
.
[3]
T.
H
.
Ng
uy
en,
e
t
a
l.
,
"
A
S
eri
e
s-Co
nn
e
c
t
e
d
T
opo
lo
gy
o
f
a
Di
od
e
R
ec
t
i
f
i
er
a
nd
a
V
o
ltag
e
-S
o
u
rce
Con
v
ert
e
r
f
o
r
an
HV
DC
T
ra
ns
m
i
s
s
ion
Sys
t
em,
"
IEEE T
r
an
sa
c
t
io
ns
on
Po
we
r
Ele
c
t
ro
nic
s
,
v
o
l
.
29
,
p
p
.
1
579
-15
8
4
,
A
pril
20
14
.
[4]
M
.
M
ako
s
ch
it
z,
e
t
al.,
"
C
o
n
trol
C
o
n
cep
ts
f
or
H
yb
rid
Re
ct
ifi
e
rs
Ut
il
iz
in
g
a
F
l
y
i
ng
C
on
ve
rte
r
C
e
l
l
Ac
tive
Cu
rre
nt
Inj
ection
Un
i
t
,
"
IE
EE
T
r
a
n
s
a
cti
o
n
s
o
n
Power
El
ectr
oni
cs
,
vol.
3
2
,
p
p
.
2
5
8
4
-
25
95,
Ap
r
il
2
0
17.
[5]
Y.
I
.
K
h
o
k
h
l
ov,
e
t
al.,
"
E
l
ect
ro
m
a
gn
eti
c
P
rocesses
i
n
P
o
w
e
r
Tra
n
sf
o
r
mers
wi
th
V
ect
or
C
ont
ro
l
,
"
J
o
urna
l Ru
ssia
n
El
ectr
i
cal En
gi
n
eer
ing
, vo
l
.
87
,
p
p
.
4
5-4
9
, 2
01
6.
[6]
Y.
I
.
K
h
o
khlo
v
,
et
a
l
.,
"
O
ut
put
a
n
d
p
o
w
er
p
er
fo
rm
ances
o
f
tw
elv
e-p
h
as
e
co
m
p
ens
a
ted
rectifier
s
w
ith
v
ect
o
r
con
t
ro
l,"
Bu
ll
etin o
f
t
h
e
South Ur
al St
a
t
e Uni
ver
sity S
e
r
i
es “Po
w
er E
ngin
e
er
in
g
,
v
o
l.
14
, p
p.
3
7-4
5
, 20
1
4
.
[7]
X.
Q
.
Ch
en
,
et
a
l.,
"Th
i
rt
y
-
Six
Pu
lse
Rectif
ier
S
c
h
e
me
B
ased
o
n
Z
igzag
A
u
t
o
-
Co
n
n
ected
T
ransf
o
rm
er,"
Ar
ch
ives
o
f
El
ectr
i
cal En
gi
n
eer
ing
, vo
l
.
65
,
p
p
.
1
17
-1
32
, Ma
r
ch
20
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
145
4
– 1
460
1
460
[8]
X.
G
.
M
a
,
et
a
l
.
,
"Th
e
V
ol
tage
O
u
t
put
C
haracte
r
i
s
t
i
cs
o
f
New
24
-P
uls
e
R
ect
ificat
io
n
Sy
st
em
under
Un
balan
c
ed
S
o
u
r
ce Vo
ltag
e," in
M
a
ter
i
als Scien
ce
an
d In
fo
rm
ation
T
echn
o
l
o
g
y
, P
ts 1
-8, pp
.
3
8
2
0
-
38
25
, 20
1
2
.
[9]
S.
F
ukuda,
e
t
a
l
.
,
"An
Auxiliary
-Supply-A
ss
i
s
ted
Harmoni
c
R
educ
ti
on
S
chem
e
f
or
1
2
-
P
u
l
s
e
Dio
d
e
R
ecti
f
iers,"
IEEE
T
r
a
n
sa
cti
o
n
s
o
n
P
o
wer
Electro
nics
,
v
o
l
.
2
3
,
pp.
1
2
7
0
-
12
77,
M
ay 2
00
8.
[10]
M
.
A
l
-
M
a
h
a
r
i
,
e
t
a
l
.
,
"
A
N
e
w
A
l
u
m
i
n
u
m
P
o
t
L
i
n
e
R
e
c
t
i
f
o
m
e
r
S
c
h
e
m
e
w
i
th
E
ff
ecti
v
e
H
a
rmo
n
i
c
S
upp
ression
Capability,"
Inter
n
a
t
io
na
l
Jou
r
nal
of P
o
wer Electr
o
n
i
cs a
n
d
Drive
Sys
t
em (
I
JPEDS
)
,
v
o
l
.
9,
n
o
4
,
pp.
1
57
3-1
5
8
3
,
Decem
ber
201
8.
[11]
V.
G
arg
,
e
t
al.,
"
24-P
u
ls
e
AC-DC
Con
v
ert
e
r
f
o
r
H
a
rm
on
ic
M
iti
g
at
io
n,
"
IET
Power
Electr
o
n
i
cs
,
v
o
l.
2
,
pp.
3
64
-37
4
,
July
2
00
9.
[12]
T.
R
ajesh
and
A.
N
irma
lkuma
r
"
A
S
h
unt
Act
i
ve
P
ower
F
il
t
e
r
f
o
r
1
2
P
u
ls
e
Con
v
ert
e
r
Us
in
g
S
o
urce
Curre
n
t
Det
ectio
n
Ap
pro
ach
,"
Int
e
rn
at
ional
Jo
ur
nal
of Power
E
l
ectron
i
cs
a
nd
Dr
ive S
y
st
e
m
(
I
J
P
ED
S
)
,
vol.
7,
pp.
2
25
-234
,
20
16
.
[13]
H.
F
uj
i
t
aand,
H
.
Akagi
,
"
The
un
if
ied
power
qual
i
t
y
cond
itioner:
T
h
e
i
ntegrat
i
o
n
o
f
series
acti
v
e
fi
lters
and
sh
unt
acti
v
e
filt
ers,"
PESC Record. 27t
h
A
n
nual IEEE
Powe
r Elect
ron
i
cs Speci
alists
Co
nf
erence
,
Baven
o
,
vo
l.
1
,
p
p.
4
9
4
-
50
1,
199
6.
[14]
X.
Q
.
C
henan
d
H
.
Qiu
.
"
Z
i
g
z
ag
C
onn
ected
A
ut
otran
s
f
o
rm
e
r-Bas
ed
2
4
-Puls
e
A
C-DCConvert
er,"
Internation
a
l
Jou
r
n
a
l
o
f
Em
er
gi
ng
El
ectr
i
c P
o
wer
Sys
t
ems
v
o
l
. 1
6, p
p
. 23
-
32
, F
ebru
ary 2
0
1
5
.
[15]
V.
S
h
e
e
l
va
n
t
,
e
t
a
l.
,
"
I
mp
ro
ve
m
e
n
tin
Ha
r
m
on
ic
R
e
d
uc
tion
o
f
a
Z
ig
zag Aut
oco
n
n
ect
ed Trans
f
o
rm
er
B
ased
1
2-P
u
l
s
e
Di
od
e
Bri
dge
R
ecti
f
ier
by
C
u
rrent
I
n
j
ection
a
t
DC
S
id
e,
"
IEE
E
T
r
a
n
s
a
c
tion
s
on
I
n
du
stry
Ap
p
lic
at
io
ns
,
vo
l.
5
3,
pp.
56
34
-564
4,
2
0
1
7
.
[16]
F
.
J
.
C
h
i
vite-Zabalza,
e
t
al
.,
"
A
24
-P
ul
se
V
oltag
e
S
ou
rce
d
C
o
nve
r
t
e
r
w
i
t
h
P
a
s
s
i
v
e
a
n
d
A
c
t
i
v
e
H
a
r
m
o
n
i
c
V
o
l
t
a
g
e
Inj
ection
,
"
IECO
N 20
06 - 3
2
n
d
An
nua
l Co
nfe
r
enceo
n IEE
E
Ind
u
s
t
rial El
ectroni
cs
,
V
o
l
s
1
-11,
p
p.
2
81
9-2
824
,
20
06
.
[17]
F.
J
.
Chivi
t
e-Zabal
za,
e
t
al.,
"
A
Si
mple
,
Passive
2
4-P
u
lse
AC-D
C
Co
nvert
er
w
i
t
h
In
herent
L
o
a
d
Balan
c
in
g
Us
ing
Harm
on
ic
V
olt
a
ge
I
n
j
ecti
o
n
,
"
200
5 IE
EE 3
6
t
h
Po
wer El
ectr
onic Sp
ecial
is
ts
Conferen
ce
,
IEEE
Po
we
r
El
ectro
n
i
cs
Sp
ecia
l
is
ts
Confer
ence R
ecord
s
, p
p. 7
6-8
2
,
20
0
5
.
[18]
F
.
J
.
Ch
i
v
ite-Zabalza,
e
t
al
.,
"
A
S
i
m
p
le,
P
a
s
s
i
v
e
24
-Pu
l
s
e
A
C-D
C
Con
v
erter
with
I
n
h
eren
t
Load
B
al
anci
ng,
"
IEEE
T
r
a
n
sa
cti
o
n
s
o
n
P
o
wer
El
ectr
onics
,
vol.
2
1
,
p
p
.
430-4
3
9
,
M
arch
200
6.
[19]
Yu.
I
.
K
ho
kh
lo
v,
e
t
a
l
.,
"
O
n
so
me
u
se
fu
l
q
u
a
li
tie
s
o
f
1
2-p
h
a
s
e
Converter
swith
a
c
ont
r
o
l
la
bl
e
E
n
semble
o
f
harm
o
n
ics
in
a
c
o
m
pens
ati
ng
Dev
i
ce
co
mm
o
n
f
o
r
s
i
x
-p
hase
U
n
i
ts
,
”
R
u
ssian Elect
ri
cal Enginee
r
i
n
g
,
vo
l.
8
4
,
pp.
54
2-5
48,
2
0
1
3
.
[20]
H.
Z
.
A
z
a
z
i
,
e
t
al.,
"
H
i
gh
P
ow
er
F
act
or
a
n
d
R
egu
l
at
ed
O
utp
u
t
Vo
lt
age
f
o
r
T
h
ree-P
h
as
e
AC-DC
Co
nv
erter
Usin
g
S
i
ng
le
-
S
w
i
tc
h
C
u
k
C
o
n
v
e
r
t
e
r
,
"
2017
Nineteenth I
n
ternational Mi
dd
le-Ea
s
t
Power Syst
ems
Co
nf
er
ence
,
pp
.
43
-5
1,
20
17
.
[21]
K.
D
arji,
et
a
l.,
"S
eries
V
o
l
t
age
In
jecti
o
n
St
rategy
f
o
r
Reacti
ve
P
ow
er
C
o
m
p
e
ns
ati
on
o
f
HVD
C
Rect
ifier
St
a
t
io
n
,
"
Pr
oceedi
n
g
s
of the
Fir
s
t
IEEE
Inter
n
a
t
i
onal
Co
n
f
eren
ce on
Po
wer Electr
onics
,
p.
4
,
20
16
.
[22]
G. S
. Zi
no
v
i
ev, "F
u
n
d
am
en
tals
of po
wer elect
ronics
"
Bo
ok
. - N
ov
osi
b
i
r
sk:
Publish
e
r NS
TU, 1999.
[23]
Yu
.
I.
K
ho
kh
l
ov,
e
t
al.,
"El
ectro
m
a
g
n
et
ic
p
roces
ses
i
n
non
-co
m
p
ensat
e
d
recti
f
ier
wit
h
t
h
e
i
ncreas
e
o
f
s
tage
m
o
t
ion
vect
or
c
on
tro
l
,
"
Sci
e
nce S
U
SU
. Sect
io
n of
tech
nica
l S
c
iences
: ma
teri
als o
f
t
h
e 67
th
scien
t
i
f
i
c
conferen
ce
,
pp
.
93
5-
94
1,
A
pril
2
0
1
5
.
B
I
OGRAPHIES
O
F AUTHO
RS
V
a
lery
I
.
Safonov
r
eceived
t
h
e
E.S
c
.
deg
r
e
e
s
in
E
l
ectro
ph
y
s
i
c
s
f
r
o
m
S
o
u
t
h
U
ral
S
ta
t
e
Un
ive
r
s
i
ty
,
Rus
s
ia
,
in
1
9
9
3
.
H
e
r
e
c
e
i
v
e
d
Ph
.D.
d
e
gre
e
i
n
R
a
dio
Ph
ys
i
c
s
f
ro
m
To
msk
S
t
a
t
e
U
n
iv
ersi
ty,
Russi
a,
i
n
1
997
.
Cu
rren
tl
y
h
e
i
s
an
a
s
s
i
s
t
a
nt
p
ro
fe
s
s
o
r
a
t
t
h
e
F
acu
lty
P
ower
E
ngi
neeri
ng
of
S
ou
th
U
ral
St
ate
Un
iv
ersity
.
Valery
i
s
co-aut
ho
r
o
f
s
e
veral
p
a
pers
o
n
n
onli
n
ear
o
p
t
i
cs
a
nd
pow
e
r
elect
ron
i
c s
y
stem
s
.
Mi
k
h
a
i
l
A.
D
z
i
uba
r
eceiv
e
d
the
E.S
c
.
deg
r
ees
i
n
Po
wer
En
g
i
neeri
ng
f
r
o
m
S
o
u
th
U
ra
l
St
at
e
U
n
iv
ersi
ty,
Ru
s
s
ia,
i
n
199
7
.
H
e received
P
h.D
.
d
e
g
ree
i
n
P
o
w
er
E
lect
ron
i
csf
r
om
S
ou
th
U
ra
l
Stat
e
U
n
iv
ersi
ty,
Russi
a,
i
n
2
005
.
Cu
rren
tl
y
h
e
i
s
an
a
s
s
i
s
t
a
nt
p
ro
fe
s
s
o
r
a
t
t
h
e
F
acu
lty
P
ower
E
ngi
neeri
n
g
S
o
u
th
U
ral
State
U
n
iv
ersity
.
Mikh
ail
has
m
a
ny
j
o
u
rna
l
and
co
nf
erence
pap
e
rs
i
n
p
o
wer
electro
ni
c
sy
s
t
ems.
Evaluation Warning : The document was created with Spire.PDF for Python.