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.
4, D
e
c
e
m
ber
201
9,
pp.
1823~
18
32
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1823-1832
1823
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
Modelling
of three
phase svpwm
AC-AC converter using unity
power factor control
Sa
id
a
h
1
, Hari
S
u
tik
s
no
2
,
Ba
mb
an
g Pu
rwah
yu
d
i
1
,
T
a
u
f
i
k
3
1
Dep
a
rt
m
e
nt of Elect
rical En
g
ineer
in
g,
Bh
ayang
k
a
ra
U
ni
versity
,
Su
ra
b
a
ya,
Ind
one
s
i
a
2
Dep
artm
en
t
of
El
e
c
t
rical
En
g
i
n
eerin
g,
S
ekol
ah
Tin
ggi T
ekn
i
k
Su
ra
ba
ya
(STTS)
,
Su
r
a
b
a
y
a
,
I
nd
on
e
s
ia
3
Dep
artm
en
t
o
f
Elect
rical
En
g
i
n
eer
in
g,
C
al P
o
l
y S
t
ate Uni
v
ersit
y,
S
an
Lu
i
s
Obis
p
o
,
C
alif
ornia,
U
S
A
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
O
c
t
8
,
2018
Re
vise
d N
ov
1
9
,
201
8
Ac
ce
p
t
ed
M
a
y
2
9
,
2
019
Thi
s
p
a
p
er
i
nt
ro
duces
t
he
m
odelling
of
a
n
ovel
t
h
r
ee
ph
ase
AC-A
C
co
nv
erte
r
with
i
n
d
irect
u
se
o
f
a
capaci
tor
as
D
C
vo
lt
age
link
.
Th
e
pro
pos
e
d
c
on
ve
rte
r
has
h
i
g
h
e
ff
i
c
ien
c
y
b
ecaus
e
i
t
u
s
es
S
p
ace
Vect
or
P
W
M
(
S
V
PWM)
t
e
chn
i
qu
e
at
bot
h
rect
ifi
c
ie
r an
d i
n
v
e
rter s
ta
g
e
s t
o
o
perat
e
t
he pu
l
s
e
wi
d
t
h
mo
du
lati
on
in
IGBT
switches
.
T
h
e
n
ov
e
l
c
onv
e
r
ter
is
e
q
u
i
pped
wit
h
a
pow
er
f
ac
t
o
r
cont
rol
to
s
hape
t
he
r
ectifier
input
curr
e
n
t
wa
ve
form
t
o
be
s
inu
s
oida
l
an
d
to
b
e
in
ph
ase
w
i
t
h
t
he
i
np
ut
volt
a
ge.
To
k
eep
t
h
e
D
C
v
o
l
t
ag
e
st
abl
e
,
t
h
e
co
nv
ert
e
r
ut
ilizes
P
I
con
t
ro
ll
e
r
s.
S
im
u
l
ati
o
ns
a
re
c
o
n
d
u
cted
f
or ou
t
pu
t v
olta
g
e
f
rom
120
to
3
00
Vo
lt
s
wit
h
output
f
requ
en
cy
r
angi
ng
f
rom
30
H
z
to
6
0
H
z
.
T
h
e
simul
a
tion
resu
lt
s
show
t
hat
the
conv
erter
i
s
a
bl
e
to
m
aintain
st
abl
e
t
h
e
D
C
vo
lt
age
and
curren
t
.
F
u
rth
e
rmo
r
e,
t
he
m
od
e
l
d
em
onstrat
es
t
he
b
e
nef
its
o
f
pro
p
o
s
ed
c
on
ve
rter
i
n
term
s
o
f
acq
uiri
ng
h
i
g
h
i
npu
t
po
w
e
r
f
acto
r
and
si
nu
soidal curren
t
w
ave
f
o
r
m
at the o
ut
pu
t sid
e
o
f t
h
e i
n
v
e
rter.
K
eyw
ord
s
:
AC-AC converter
P
i
c
ontr
o
lle
r
P
o
w
e
r fac
t
or
con
tro
l
SV
P
W
M
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:
Sai
d
ah
,
D
e
pa
rtem
ent o
f
E
lectr
i
c
a
l E
n
gi
nee
r
in
g,
Bha
y
a
n
gkar
a
U
ni
ver
s
ity,
Ahm
a
d Ya
ni 1
14,
S
ura
b
aya,
Jaw
a Tim
u
r, In
d
o
n
es
ia.
Em
ail:
sa
i
d
ah
@u
b
h
ara
.
a
c
.id
and sa
ida
hba
isa
@
gma
i
l
.
com
1.
I
N
TR
OD
U
C
TI
O
N
A
C
p
ow
er
s
o
u
r
c
e
s
ar
e
f
r
e
que
n
t
l
y
n
e
e
d
e
d
i
n i
n
d
u
s
t
r
y
to
o
p
e
r
ate
d
ev
ice
s
,
w
ith d
iffere
n
t
am
p
l
itu
de a
n
d
fre
que
nc
y
fr
o
m
t
ha
t
pro
v
i
d
e
d
b
y
t
he
g
r
i
d.
A
p
ow
er
e
l
e
ctr
o
n
i
c
ci
rc
u
it
kn
ow
n
as
a
t
hre
e
-phase
A
C-A
C
con
v
er
t
e
r
is
u
se
d
t
o
c
o
n
ve
rt
a
f
i
x
e
d
A
C
v
o
l
ta
ge
t
o
a
va
ri
able
A
C
v
o
lta
ge
w
i
t
h
a
d
jus
t
able
freq
u
e
n
c
y
.
Som
e
c
o
mmo
n
ap
pli
c
a
t
io
n
s
o
f
su
ch
c
onv
ert
e
r
t
h
at
a
re
w
i
d
ely
u
s
ed
i
n
i
n
dus
t
r
y
i
n
cl
u
d
e
ad
j
u
sta
b
le
-spee
d
d
rive
s,
A
C
–A
C
tra
n
s
m
issi
on,
u
n
i
n
t
err
uptib
le
p
o
w
er
s
uppl
ies
(U
P
S
)
a
nd
r
e
new
a
ble
e
n
erg
y
c
o
nver
s
io
n
sys
t
e
m
s
[1
]
.
H
o
w
e
ve
r,
t
he
v
aria
ble
sp
e
e
d
d
ri
ve
s
ys
tem
s
f
or
i
n
d
u
c
t
i
o
n
m
o
tor
s
co
ns
t
i
tu
te
a
n
i
m
p
o
rt
ant
ar
ea
of
A
C
–
A
C
con
v
er
sio
n
s
ue
t
o
the
fac
t
t
ha
t
it
cur
r
en
t
l
y
a
c
c
ou
n
t
s
f
o
r
ab
ou
t
50%
o
f
e
l
e
c
t
r
i
c
i
t
y
c
onsu
m
ptio
n
[
2
].
Th
e
mo
s
t
p
opu
l
a
r
of
a
p
p
ro
a
c
h
fo
r
AC
-AC
c
o
n
v
e
rt
er
m
o
d
e
l
l
i
n
g
i
nvol
v
e
s
t
h
e
use
of
a
D
C-l
i
n
k
c
o
m
p
on
en
t
by
e
mpl
oyi
ng
eit
h
er
a
c
apac
i
t
or
(
as
a
D
C
v
o
lta
ge
s
o
u
rc
e)
o
r
a
n
i
nd
uc
tor
(a
s
a
DC
c
u
rre
nt
s
ou
rc
e).
Th
i
s
t
yp
e
o
f
c
on
v
e
rter
i
s
w
i
de
ly
u
sed
in
i
nd
us
try
an
d
i
s
k
n
o
w
n
a
s
a
n
i
n
d
i
rec
t
f
re
que
ncy
c
on
ve
rter
w
it
h
a
D
C
e
ne
rgy
s
t
orage
ele
m
ent,
and
has
be
e
n
inve
st
i
g
ate
d
e
x
t
ens
i
ve
l
y
f
or
m
a
n
y
yea
r
s
[3].
T
h
i
s
AC-AC
c
o
n
v
erter
has th
e
ma
i
n
a
d
v
an
ta
ge
t
ha
t
bo
th
r
ecti
f
ica
t
i
on
a
nd
i
n
verte
r
a
re
l
arge
l
y
s
e
p
a
r
ate
d
f
or
c
o
n
tr
ol
p
r
o
ce
ss.
O
n
the
o
t
her
ha
nd,
t
he
a
p
p
ro
a
c
h
has
in
here
nt
d
r
a
w
b
ac
k
of
h
a
v
i
n
g
D
C
l
i
n
k
en
e
r
g
y
s
tora
ge
c
om
po
ne
nt
t
h
a
t
i
s
relat
i
ve
l
y
l
ar
ge
i
n
ph
ys
i
c
a
l
v
o
l
ume
.
To
a
dd
re
ss
t
h
e
af
o
r
emen
t
i
on
ed
i
s
s
u
e
w
it
h
t
h
e
p
h
y
s
i
c
a
l
s
i
z
e
o
f
t
he
D
C
li
n
k
c
ompo
ne
nt,
so
m
e
r
esearche
r
s
hav
e
deve
l
ope
d
o
t
h
e
r
type
s
of
A
C-A
C
c
on
ver
t
e
r
s
w
itho
u
t
u
s
i
n
g
t
he
D
C-
li
n
k
c
om
po
ne
nt.
The
s
e
c
o
nve
r
t
ers
ar
e
ca
l
l
e
d
a
d
ire
c
t
power-
f
re
qu
e
n
cy
c
on
ver
t
e
r
.
The
r
e
a
r
e
m
a
n
y
d
i
r
ec
t
pow
er
freque
nc
y
c
o
n
v
erte
r
t
o
p
o
l
o
gi
es
w
ith
the
mos
t
c
om
mon
one
i
s
the
Ma
t
r
ix
C
o
nve
rter
(
M
C
).
T
hi
s
co
nver
t
e
r
has
n
o
D
C
e
n
er
gy
s
tor
a
ge
e
le
me
nts
a
n
d
bas
i
ca
ll
y
c
o
n
s
i
s
t
s
o
f
a
n
a
rra
y
of
s
t
a
tic
p
ow
e
r
s
w
i
tches
c
o
n
n
e
c
t
ed
b
etwee
n
t
he
s
our
ce
a
n
d
l
o
a
d
t
er
mina
ls
.
F
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
2
3
– 1
832
1
824
g
ood
p
e
r
fo
rman
c
e
d
i
r
e
c
t
f
re
qu
e
n
c
y
c
o
n
v
e
rters
mu
st
h
av
e
smal
l
ca
pac
i
t
o
rs
a
nd
in
d
u
ct
or
s,
s
uc
h
as
t
h
o
s
e
u
sed
in
t
h
e
ir
h
i
gh
fre
que
nc
y
c
o
m
pone
n
t
f
i
lte
rs
o
r
sm
all
re
g
e
ner
a
tive
A
C
e
n
er
gy
s
tor
a
ge.
H
o
w
e
ver
M
C
h
as
s
om
e
di
sa
d
v
a
n
ta
ges.
T
he
v
o
lta
ge
t
ransfe
r
ra
tio
i
s
l
i
m
ited
to
0
.8
66
t
o
o
b
ta
in
s
in
uso
i
da
l
o
u
t
p
ut
w
a
v
e
f
or
ms
[
4-
6].
It
a
ls
o
re
q
u
ir
es
m
ore
se
mic
ond
uc
tor
de
v
i
ce
s
c
o
m
p
are
d
t
o
co
n
v
en
t
io
n
a
l
A
C
–A
C
i
n
d
i
rec
t
c
o
nver
t
e
r
s.
M
o
reo
v
e
r,
M
C
i
s
s
en
si
tiv
e
t
o
d
istu
rb
an
ce
s
at
t
he
i
np
ut
v
o
l
t
a
g
e
to
t
he
s
yst
e
m
[7].
T
he
M
C
has
bee
n
obs
e
r
ved
to p
osses
s
hi
g
h
e
r
l
e
vel of T
ota
l
H
a
r
m
oni
c
D
i
st
ortio
n
(TH
D
)
c
om
p
a
r
ed
t
o
in
di
re
ct
c
onv
erte
rs [8
]
.
To
a
c
c
o
m
p
lis
h
t
h
e
mos
t
d
e
s
ira
b
le
o
pe
rati
o
n
,
t
he
A
C-A
C
c
onve
rter
s
mus
t
b
e
a
b
l
e
t
o
ge
nera
t
e
l
oad
vo
lta
ge
s
w
i
th
a
rbit
r
a
ry
a
m
p
li
tu
de
a
nd
freque
nc
y,
p
ro
d
u
ce
s
i
n
uso
i
d
a
l
s
our
ce
a
nd
loa
d
c
ur
rent
s
f
u
rt
h
e
r
i
m
p
l
yi
ng
th
e
pro
v
i
sion
o
f
un
i
t
y
p
ow
er fac
to
r
for
a
ny l
o
a
d
, ac
c
o
mmo
d
a
t
e
b
id
i
r
e
c
t
i
on
a
l
power
f
l
o
w
th
ro
ug
h
the
con
v
er
t
e
rs,
an
d
fi
nal
l
y
a
sim
p
l
e
a
n
d
c
ompa
ct
p
ow
er
c
irc
u
i
t
[
9
]
.
V
a
r
ious
m
e
t
hods
a
re
u
se
d
by
re
se
arc
h
ers
t
o
impro
v
e
pow
e
r
f
ac
tor,
r
egul
a
t
e
i
nver
t
e
r
o
u
t
p
u
t
v
o
l
ta
ge
a
nd
m
a
i
n
t
a
i
n
D
C
v
o
l
t
a
g
e
a
t
t
h
e
d
e
s
i
r
e
d
v
a
l
u
e
.
The
rese
arc
h
ers
pr
e
v
i
o
usly
u
sed
f
ilter
s
o
n
the
ne
t
w
ork
si
de
t
o
o
b
ta
in
u
n
i
t
y
power
f
ac
t
o
r
[10
,
1
1
]
.
Th
e
r
e
a
r
e
al
so
rese
arc
h
ers
wh
o
use
t
h
e
tec
h
niq
u
e
o
f
n
on
l
i
n
ear
b
ackste
p
pi
ng
c
o
n
tro
l
[
12,
13],
combine
d
P
ID
a
nd
P
I
C
ontr
o
l
[1
4]
a
n
d
V
o
l
t
a
ge
O
rien
te
d
C
o
n
t
ro
ls
(
V
O
C
)
w
i
t
h
e
stim
at
io
n
o
f
a
c
t
ive
po
w
e
r
and
rea
c
t
i
ve
p
ow
er
[
1
5
].
w
hi
le
the c
o
nt
r
o
l
m
e
t
h
o
d
o
f
t
h
is pa
p
er only c
ons
ist
s
o
f a
P
I
c
on
t
r
o
l
t
o
m
ain
t
a
i
n a st
a
b
l
e
D
C vol
t
a
ge
an
d
u
n
i
t
y
p
o
w
er
fa
ct
or c
on
t
r
ol
s
o the
mode
l
o
f
the
A
C-A
C
co
nve
r
t
er
b
ecom
e
s
sim
p
ler.
Thi
s
p
a
p
e
r
d
e
s
c
r
i
b
es
a
p
ropose
d
t
h
r
e
e
p
h
a
se
A
C-AC
c
o
n
v
e
rt
e
r
t
o
c
o
n
v
e
rt
220
V
o
lts,
50
H
z
i
npu
t
in
to
a
v
ar
i
a
ble
vol
tage
from
120
to
3
0
0
V
o
lts
w
ith
v
ar
ia
ble
fre
que
ncy
fro
m
20
H
z
–
60
H
z
w
hich
h
a
v
e
ne
ver
bee
n
d
i
s
c
u
sse
d
in
p
r
e
v
i
ous
p
a
p
ers.
T
h
i
s
c
o
n
v
erter
be
l
o
ngs
t
o
t
h
e
i
n
direc
t
c
on
ver
t
e
r
t
ype
a
nd
i
t
is
s
ui
ta
b
l
e
to
opera
te
a
sy
nc
h
r
on
ous
m
o
t
ors
(
i
n
d
uc
t
i
o
n
m
o
t
ors)
w
it
h
va
r
i
ous
l
oa
ds
w
he
re
e
x
p
e
c
te
d
s
p
eed,
th
us
f
re
que
nc
y
and
var
i
a
b
l
e
vol
ta
ge
a
re
n
e
e
d
ed.
T
h
e
pro
pos
ed
A
C-
A
C
c
o
nve
rter
i
s
e
q
ui
p
p
ed
w
ith
pow
e
r
f
ac
t
o
r
c
o
n
t
r
o
ller
to
kee
p
a
u
n
i
t
y
pow
er
f
ac
tor
a
nd
obta
i
n
s
i
n
u
s
o
i
da
l
i
n
p
u
t
c
u
rrent
f
rom
t
h
e
gri
d
a
s
w
e
l
l
as
s
i
n
u
s
o
i
da
l
ou
pu
t
curr
ent.
T
he
c
on
ver
t
e
r
o
ffer
s
hi
g
h
e
fficie
n
c
y
b
e
c
a
use
i
t
u
ses
S
pa
ce
V
e
c
t
or
P
WM
(
S
V
P
W
M)
t
o
ha
ndle
t
h
e
pu
lse
w
i
dt
h m
o
d
u
la
ti
on i
n
its
IG
B
T
sw
it
c
h
com
po
ne
nt
s.
2.
MODEL
O
F
AC-
AC
C
ON
VERTER
2.1.
Prop
osed
A
C-AC c
o
nver
ter mod
e
l
F
i
gure
1
sh
ow
s
t
h
e
pr
op
ose
d
t
hr
ee
P
h
ase
A
C
-
A
C
c
o
n
v
e
r
ter
mode
l
.
Th
e
c
o
n
v
erter
is
a
n
i
n
di
r
e
c
t
con
v
er
t
e
r
wi
th
D
C-Li
nk
ca
pa
cit
o
r
as
t
he
e
n
e
r
gy
st
ora
g
e
e
l
em
ent.
T
he
c
o
nver
t
er
m
odel
con
s
is
ts
o
f
a
r
e
c
t
i
f
ier
,
DC-Li
nk
ca
pa
cit
o
r
an
d
a
n
i
n
v
e
r
ter
t
h
a
t
i
m
p
lem
e
n
t
s
the
Spa
ce
Vec
t
o
r
M
odu
l
a
ti
on
(
SV
M
)
t
e
c
h
ni
qu
e
.
T
h
e
S
V
M
c
ontro
l
t
echn
i
que
i
s
u
s
e
d
f
or
b
o
t
h
th
e
r
ecti
f
ier
a
n
d
inve
r
t
e
r
f
eed
in
g
t
h
e
in
du
ct
io
n
mo
to
r.
T
h
e
S
VM
tech
n
i
q
u
e
is
c
hose
n
due
t
o
i
t
s
m
o
re
p
re
val
e
nt
u
se
t
h
a
n
all
ot
he
r
con
v
e
n
t
i
o
n
a
l
te
ch
ni
qu
e
s
a
s
th
e
t
e
ch
nique
offe
rs
i
m
p
ro
ve
d
D
C
b
us
u
t
i
liz
atio
n,
l
ow
e
r
h
a
r
m
onic
s
,
le
ss
sw
it
c
hin
g
l
o
sses,
a
nd
h
i
gh
er
overa
ll
co
n
v
er
t
e
r’s
e
ffi
c
i
en
cy
[
16
]-[
1
9
]
.
The
mai
n
t
ask
o
f
t
h
e
S
VM
t
ech
ni
q
u
e
i
s
t
o
ca
l
c
ul
at
e
th
e
d
u
t
y
c
y
c
les
a
n
d
de
fi
n
e
t
he
sw
it
c
h
i
n
g
pa
tte
rn.
I
n
t
he
p
ro
p
o
se
d
co
n
v
er
t
e
r
a
n
d
as
i
l
l
ustra
t
e
d
i
n
F
i
g
u
re
1
,
t
h
e
nov
e
lty
l
i
e
s
o
n
th
e
uni
ty
p
o
w
er
f
a
c
t
o
r
con
t
ro
l
em
p
l
o
y
e
d
i
n
t
he
c
on
v
e
rter
t
ha
t
w
i
l
l
m
aint
a
i
n
t
h
e
in
put
pow
er
f
ac
t
o
r
to
t
he
r
e
c
ti
fi
er
s
tage
c
lose
t
o
o
n
e
.
Conse
que
n
tly,
the
pow
er
f
ac
tor
con
t
rol
k
e
e
p
s the
so
urce
cur
rent
in
the
sam
e
phase
a
s the
vol
t
a
ge.
F
i
gure
1. P
rop
o
se
d
of A
C-A
C
c
o
nverter
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
Mo
del
l
i
n
g
o
f
t
h
ree
p
hase
sv
p
w
m
ac
-ac
conv
erter us
i
ng u
n
i
t
y
po
wer f
a
c
t
or
c
ontro
l (Sa
i
d
a
h
)
1
825
2.2.
U
n
i
t
y p
o
wer
fact
or c
on
t
r
ol
U
n
i
t
y
p
o
w
e
r
fa
c
t
or
o
c
c
u
rs
w
h
e
n
the
di
ffe
re
n
c
e
be
tw
ee
n
v
o
l
t
a
ge
a
ng
le
V
a
nd
c
urr
e
n
t
a
ngl
e
I
is
z
e
r
o
degre
e
s.
I
n
o
t
h
e
r w
o
r
d
s, it is e
st
a
b
lis
hed
w
h
e
n
vo
l
tage
an
d
c
ur
re
nt w
ave
f
orm
s
are
i
n
phas
e
.
F
i
gure
2.
E
qu
i
v
ale
n
t c
i
r
c
u
i
t
o
f
the
co
n
v
e
r
ter
from
the
a
c
sourc
e si
d
e
Th
e
c
u
rrent
r
e
g
ul
at
o
r
c
an
b
e
re
al
i
z
e
d
b
y
ma
k
i
ng
a
c
al
cul
a
ti
on
p
roc
e
ss
to
g
ene
r
a
t
e
t
h
e
de
sire
d
PWM
vo
lta
ge,
so
t
ha
t
t
h
e
c
u
rre
nt
f
l
o
w
i
ng
in
t
he
i
nd
uc
tor
ca
n
b
e
d
e
t
erm
i
ned,
a
s
sh
ow
n
i
n
F
ig
ure
2.
I
n
a
pow
e
r
con
v
er
t
e
r,
i
f
it
is
a
ss
ume
d
t
ha
t
t
h
e
sam
p
lin
g
peri
od
is
T
s,
t
h
e
i
n
d
u
ct
or
r
esi
s
ta
nce
is
n
e
g
l
i
g
ib
le,
and
the
sourc
e
in
put
v
o
l
t
a
ge
a
t
t
h
e
sam
p
l
i
ng
in
terva
l
i
s
c
o
n
s
i
d
ere
d
c
o
n
st
a
n
t,
t
h
en
t
he
c
u
r
rent
f
l
o
w
i
ng
in
t
he
i
nd
uc
tor
c
a
n
be
deter
m
i
n
ed
acc
ord
i
n
g
t
o the
e
qua
t
i
o
n
as
fo
l
l
ow
s:
s
n
s
n
n
PWM
n
T
t
i
T
t
i
L
t
i
L
t
V
t
V
)
(
)
(
)
(
)
(
(
1
)
wher
e:
)
(
n
t
V
is
t
he
s
ource
v
ol
ta
ge
a
t t
=
tn
)
(
n
PWM
t
V
is t
he
P
WM
v
o
l
ta
ge o
n
t
h
e
A
C
si
d
e
of t
he
c
on
ver
t
e
r
Eq
uat
i
on (1)
ca
n be
w
ritt
e
n
a
s:
)]
(
)
(
[
)
(
)
(
n
s
n
s
n
n
PWM
t
i
T
t
i
T
L
t
V
t
V
(
2
)
H
e
re
i
t
a
ppear
s
t
h
a
t
t
he
m
a
g
nit
ude
o
f
the
i
n
d
u
c
t
or
c
ur
ren
t
t
hat
w
i
l
l
f
low
at
time
t
=
t
n
+
T
s
ca
n
be
deter
m
i
n
ed
by
givi
n
g
t
he
P
WM
vol
ta
ge
a
c
c
ord
i
n
g
t
o
t
h
e
ins
t
a
n
ta
n
e
o
u
s
c
urre
nt
e
q
u
a
t
io
n
pr
op
ort
i
o
n
a
l
t
o
t
h
e
vo
lta
ge.
Th
is
c
urr
e
nt
s
e
t
t
i
ng
pro
v
i
d
es
t
he
p
ossib
i
lit
y
t
o
obta
i
n
a
si
nus
o
i
da
l
c
u
rr
ent
w
a
vefor
m
w
it
h
a
pow
e
r
fa
ct
or e
q
u
a
l
t
o one
. If the
c
u
r
r
en
t
i
s
a sinusodal
a
nd
has a
p
h
ase
e
q
u
a
l
t
o
its
v
olt
a
g
e
,
t
h
en
t
h
e
r
ef
eren
c
e
c
u
rre
n
t
ma
y be
define
d
as:
)
(
)
(
T
t
kV
T
t
i
n
s
n
(
3
)
w
h
e
r
e
k
is
a
c
o
n
sta
n
t
w
hos
e
m
a
gni
tude
d
epe
n
ds
on
th
e
curr
ent
t
o
b
e
st
re
amed
.
Th
i
s
r
e
f
ere
n
ce
curr
ent
d
o
e
s
n
ot
c
han
g
e
ra
pi
d
l
y
com
p
are
d
t
o
th
e
sa
mp
li
n
g
p
e
r
i
o
d
.
Th
e
r
ef
o
r
e,
t
h
e
c
u
rren
t
can
b
e
p
r
ed
i
c
t
e
d
thr
o
u
g
h
the
p
re
vi
o
u
s
va
lue
ap
proa
c
h
,
as show
n
in F
ig
ure
3,
a
s:
T
T
T
t
i
t
i
t
i
T
t
i
s
s
n
n
s
n
.
)
(
)
(
)
(
)
(
(
4
)
Or
)
(
)
(
2
)
(
s
n
n
s
n
T
t
i
t
i
T
t
i
(
5
)
ac
cord
in
g t
o
e
qua
t
i
o
n
(
3),
the
refere
nce
current o
f
eq
ua
ti
on
(
5
) c
a
n be
e
xpr
essed
as fol
l
o
w
s
:
)
(
)
(
2
)
(
s
n
n
s
n
T
t
kV
t
kV
T
t
i
(
6
)
V
V
X
L
V
pw
m
Vp
w
m
I
li
n
e
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
1
823
–
1
832
1
826
B
y
c
ombi
n
i
n
g
e
qua
tio
ns
(
2)
a
nd
(
6
)
,
t
he
r
e
f
er
ence
v
o
lta
ge
can
b
e
obta
i
n
e
d
as:
)
(
)
(
)
(
)
2
1
(
)
(
'
n
s
s
n
s
n
s
n
t
i
T
L
T
t
V
T
kL
t
V
T
kL
t
V
(
7
)
Eq
uat
i
o
n
(
7
)
d
e
no
t
e
s
t
h
e
P
W
M
vo
l
t
a
g
e
to
b
e
r
a
ise
d
s
o
th
a
t
t
he
c
u
r
re
nt
f
lo
w
i
ng
i
n
th
e
in
du
c
t
o
r
i
s
k
∙
V
(
t)
.
F
i
gu
r
e
4
.
show
s
t
h
e
c
u
r
r
e
nt
r
e
g
u
l
a
t
o
r
d
ia
gr
a
m
o
f
P
W
M
co
n
v
er
te
r
w
i
t
h
i
n
put
v
o
l
t
a
ge
V
(
t
)
,
c
hann
e
l
c
u
r
r
e
nti(
t)
,
a
n
d
k
fa
c
t
or
.
Th
is
c
ur
r
e
nt
r
egu
l
at
or
i
s
r
e
aliz
ed
i
n
th
e
ca
lc
ula
t
i
o
n
pr
oc
ess
b
y
u
sin
g
a
m
i
cr
opr
ocess
o
r
,
t
oge
t
h
e
r
w
it
h
t
h
e
P
W
M
si
gna
l
ge
ne
r
a
t
i
o
n
p
r
o
ce
ss
.
Wi
th
t
he
c
ur
r
e
n
t
r
egu
l
a
t
or
t
he
c
u
r
r
e
n
t
w
a
vef
o
r
m
w
il
l
be
t
he
s
a
m
e
a
s
t
he
v
o
lta
ge
-
s
hape
d
s
i
nus
o
i
d
a
l
w
a
ve
f
o
r
m
a
nd
w
ith
t
he
s
a
m
e
pha
se
.
F
i
g
u
r
e
4
il
l
u
s
t
ra
t
e
s t
h
e
v
ector
d
i
a
gram
o
f t
h
e
syste
m
.
Figure
3.
T
he
r
efere
n
ce
curr
ent a
t
t
he e
n
d
of e
ach
p
eri
o
d
F
i
gur
e
4.
V
e
c
tor
di
a
g
r
a
m
of
t
he
c
on
ver
t
e
r
f
r
o
m
the
AC
so
u
r
ce
s
id
e
3.
RESU
L
T
S
A
ND DIS
C
U
S
S
I
ON
The
pro
p
o
sed
AC-AC
con
v
e
r
t
e
r
perform
ance
i
s
simu
late
d
wit
h
M
a
t
l
a
b
/S
imul
i
nk
sof
t
w
a
r
e
.
I
n
t
he
sim
u
la
ti
on,
t
he
t
hr
ee
-
phase
s
our
ce
v
o
l
t
a
g
e
i
s
s
e
t
a
t
22
0
V
/
5
0
H
z
,
t
h
e
D
C
v
o
lt
ag
e
i
s
100
0
Vol
t
s
an
d
t
h
e
sa
mpl
i
n
g
f
r
e
q
u
e
ncy
i
s
10
kH
z.
T
he
d
es
ir
ed
A
C
o
u
tp
ut
v
o
lta
ge
v
ar
ie
s
w
ith
v
ar
iab
l
e
fr
e
que
nc
y
a
n
d
di
f
f
e
r
ent
loa
d
i
m
p
eda
n
c
e
.
The
si
m
u
la
t
i
on
i
s
d
o
n
e
o
n
t
he
o
u
t
pu
t
vo
l
t
a
g
e
f
r
om
1
20
t
o
3
00
V
o
l
t
sw
i
t
h
o
ut
p
u
t
fr
eq
u
e
ncy
be
in
g
var
i
e
d
f
r
o
m
2
0
t
o
60
H
z
,
w
hil
e
o
bse
r
v
i
n
g
t
he
p
ow
er
f
ac
tor
,
D
C
v
o
l
ta
ge
a
nd
c
ur
r
e
nt,
t
h
e
o
u
t
p
ut
v
ol
t
a
ge
a
n
d
cur
r
en
t w
a
vef
o
r
m
s.
T
he
r
ecti
f
ier
i
n
the
s
i
m
ula
t
i
on f
o
l
l
o
w
s
the
r
e
qu
ir
e
m
e
n
ts
o
f
thr
ee-
pha
se v
olt
a
ge
s
our
c
e
22
0 V
/
50 H
z
w
it
h
a
m
pl
i
t
u
d
e
2
x 22
0
=
3
1
1
V
olts,
D
C
V
ol
ta
ge o
f
100
0 V
o
l
t
s,
a
n
d
t
he
s
am
plin
g
fr
e
qu
e
n
cy
i
s
10
kH
z.
T
o
e
v
a
l
ua
te
t
he
p
e
r
for
m
a
n
ce
of
t
he
p
r
o
p
o
se
d
c
o
n
v
e
r
ter
,
six
diff
erent
cases
were
s
imulate
d
a
nd
a
n
al
yze
d
.
P
r
evio
us
r
esea
rche
r
s
c
on
d
u
c
t
ed
e
val
u
a
t
i
o
ns
o
f
c
o
n
v
er
t
er
p
erf
o
r
m
a
n
ce
f
or
o
n
l
y
o
n
e
ca
se.
Ta
ble
1
li
st
t
he
i
nver
t
e
r
s
pe
cif
i
ca
tio
ns
f
or
e
ach
o
f
the
s
e
c
a
ses.
Tab
l
e
1.
I
nver
t
er
s
pec
i
f
i
cat
i
o
n
s
Ca
se
Out
put
Volta
g
e
Am
pli
t
ude
V
o
lt
ag
e
O
u
tput
F
r
e
que
n
c
y
Lo
ad
1
220
Vol
t
311
V
o
lt
30
H
z
6
+
j
8
o
h
m
2
250
Vol
t
353
V
o
lt
50
H
z
10
+
j
10
ohm
3
120
Vol
t
170
V
o
lt
60
H
z
6
+
j
8
o
h
m
4
120
Vol
t
170
V
o
lt
50
H
z
10
+
j
10
ohm
5
120
Vol
t
170
V
o
lt
30
H
z
6
+
j
8
o
h
m
6
300
Vol
t
424
V
o
lt
30
H
z
10
+
j
10
ohm
Ca
se
1
.
D
C
vol
t
age
so
urc
e
1
0
0
0
Volt
s,
volt
age am
pl
it
ude
of i
n
v
e
r
t
e
r
ou
tp
u
t
31
1 Vol
t
s,
ou
t
p
u
t
fre
que
nc
y
30
H
z
and lo
ad i
m
pe
d
a
n
ce 6
+
j 8
ohm
.
S
i
m
u
l
a
t
i
o
n
r
esul
ts
a
r
e
s
how
n
in
F
i
g
ur
es
5
–8.
F
igur
es 5
a
nd
6
s
h
ow
t
ha
t
D
C
C
ur
r
e
n
t
a
nd
D
C
V
o
l
t
a
ge
a
r
e bo
th s
ta
ble
r
e
spec
tive
l
y w
i
t
h
s
t
e
ad
y
sta
t
e
D
C
vo
l
tage
o
f
10
0
0
V
o
l
t
s
.
T
h
e
so
ur
ce
c
ur
r
e
nt
a
n
d
vol
tage
o
f
the
r
ectif
ier
have
t
he
s
a
m
e
pha
se
a
s
show
n
a
t
F
ig
ur
e
7.
,
w
hich
r
esul
t
s
i
n
un
i
t
y
p
o
w
e
r
fa
c
t
or
.
T
h
e
r
e
c
tif
ier
s
our
c
e
vo
l
t
age
a
m
pl
i
t
ude
o
f
3
1
1
V
o
l
ts
a
t
fr
eq
ue
nc
y
50
H
z
is
s
uc
c
e
ssfu
l
ly
c
onv
e
r
t
e
d
to
3
11
Vol
t
s
a
t
3
0
Hz
f
re
qu
en
cy
si
nus
o
i
da
l
o
u
tp
ut
w
ave
f
or
m
,
a
s
dep
i
c
t
e
d
i
n
F
i
gur
e
8.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
M
ode
l
lin
g
o
f
three
p
hase sv
p
w
m
ac-
a
c conv
e
r
te
r us
ing u
n
ity po
w
e
r
f
a
c
t
or
cont
ro
l
(
S
a
i
d
a
h
)
1
827
F
i
g
u
r
e
5
.
D
C
c
u
r
r
e
nt,
c
ase
1
F
i
gur
e
6.
D
C
vol
ta
ge,
c
a
se
1
F
i
gur
e
7.
A
m
p
li
t
u
de
o
f
vo
lta
g
e
a
nd
cur
r
ent
a
t
i
np
ut
of
r
e
c
ti
f
i
e
r
,
ca
s
e
1
F
i
gur
e
8.
A
m
p
l
i
t
u
de
o
f
v
o
lta
g
e
a
nd
c
u
r
r
e
nt
a
t
ou
t
p
u
t
of
i
n
v
e
r
te
r
,
ca
s
e
1
Ca
se
2
.
D
C
vol
t
age
so
urc
e
1
0
0
0
Volt
s,
volt
age am
pl
it
ude
of i
n
v
e
r
t
e
r
ou
tp
u
t
35
3 Vol
t
s,
ou
t
p
u
t
fre
que
nc
y 5
0
H
z
and
lo
ad
i
m
pe
d
a
n
ce
10 + j
10
ohm
.
Si
mu
l
a
ti
on
r
e
s
u
l
t
s
a
re
p
r
e
sent
e
d
i
n
F
i
gu
res
9
–
12
.
As
o
b
s
erv
e
d
i
n
t
h
e
p
r
evi
o
u
s
c
a
s
e,
t
h
e
r
esu
l
t
shows
s
t
ab
le
D
C
cur
r
ent
a
n
d
DC
V
ol
ta
ge
a
t
1
0
0
0
V
o
lt
a
s
ill
ustra
ted
in
F
igur
e
s
9
a
n
d
10
r
e
spec
ti
ve
l
y
.
The
sour
c
e
c
ur
r
e
nt
a
nd
v
o
lta
ge of t
h
e
r
ecti
f
ier
ha
ve
t
he sam
e
ph
ase
,
w
h
ic
h
a
g
a
i
n
pr
o
v
e
s
t
he u
nit
y
pow
er
f
a
c
t
or
,
as
show
n
i
n
F
igur
e
11.
T
he
r
e
c
ti
f
i
er
s
our
ce
v
o
lta
ge
a
mpl
i
t
u
d
e
o
f
3
11
V
o
l
t
s
a
t
f
r
e
q
u
e
nc
y
50
H
z
i
s
agai
n
c
o
n
v
er
te
d
w
e
ll
t
o
3
5
3
V
ol
ts
a
t
t
h
e
sam
e
f
r
e
que
nc
y
5
0
H
z,
a
s
see
n
in
F
igur
e
1
2
,
w
h
i
l
e
t
h
e
o
u
t
p
u
t
c
ur
r
e
nt
w
a
vef
o
r
m
i
s
si
nus
o
i
dal
a
s
d
es
ir
e
d
.
F
i
g
u
r
e
9
.
D
C
c
ur
r
e
nt,
c
ase
2
F
i
gur
e
1
0
.
D
C
vo
ltage
,
case
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
1
823
–
1
832
1
828
F
i
gur
e
1
1
.
Ampl
itu
de
o
f
vol
ta
ge
a
nd
cur
r
en
t
a
t
iin
pu
t
o
f
rec
t
i
fi
e
r
, ca
s
e
2
F
i
gur
e
1
2
.
Ampl
itu
de
o
f
vol
ta
ge
a
nd
cur
r
en
t
a
t
o
u
tp
u
t
o
f
i
n
v
e
rt
e
r
,
c
a
s
e
2
Ca
se
3
.
D
C
vol
t
age
so
urc
e
1
0
0
0
Volt
s,
volt
age am
pl
it
ude
of i
n
v
e
r
t
e
r
ou
tp
u
t
17
0 Vol
t
s,
ou
t
p
u
t
fre
que
nc
y 6
0
H
z
and lo
ad i
m
pe
d
a
n
ce 6
+
j 8
ohm
.
S
i
m
u
l
a
t
i
o
n
r
esul
ts
a
s
pr
esen
t
e
d
i
n
F
ig
ur
e
s
1
3
–
16
aga
i
n
s
h
ow
sta
b
le
D
C
cur
r
ent
a
n
d
D
C
V
o
l
ta
ge
a
t
10
0
0
V
o
lt
as
ill
us
t
r
ate
d
i
n
F
i
gur
e
s
1
3
an
d
14
r
e
s
pe
c
t
i
v
e
l
y.
T
he
u
nit
y
pow
er
f
ac
t
o
r
ha
s
a
l
s
o
b
een
a
c
h
i
e
ve
d
be
t
w
ee
n
t
h
e
s
our
c
e
c
ur
r
e
nt
a
nd
v
olta
ge
o
f
t
h
e
r
ect
i
f
ier
a
s
s
h
o
w
n
i
n
F
igur
e
1
5
.
The
r
e
cti
f
ier
so
ur
ce
v
ol
t
a
ge
a
m
pli
t
u
d
e
o
f
311
V
o
l
t
s
a
t
f
r
e
que
ncy
50
H
z
i
s
c
o
n
v
er
t
e
d
to
1
70
V
o
lts
a
t
the
sam
e
f
re
qu
e
n
cy
6
0
Hz,
as
d
e
pi
c
t
ed
i
n
F
i
gu
re
1
6
. , wh
ile
a
g
a
in
achiev
i
ng
th
e
d
esired
s
in
u
soid
a
l
out
put
c
u
r
re
n
t
w
a
v
e
f
o
r
m.
F
i
gur
e
1
3
.
D
C
cur
r
e
nt,
ca
se
3
F
igur
e
1
4
.
D
C
vo
ltage
,
case
3
F
i
gur
e
1
5
.
Ampli
t
u
d
e
o
f
v
o
l
ta
ge
a
nd
cur
r
en
t
a
t
i
n
p
u
t
o
f
rec
t
i
fi
e
r
, ca
s
e
3
F
i
gur
e
1
6
.
Ampl
itu
de
o
f
vol
ta
ge
a
nd
cur
r
en
t
a
t
o
u
tp
u
t
o
f
i
n
v
e
rt
e
r
,
c
a
s
e
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
M
ode
l
lin
g
o
f
three
p
hase sv
p
w
m
ac-
a
c conv
e
r
te
r us
ing u
n
ity po
w
e
r
f
a
c
t
or
cont
ro
l
(
S
a
i
d
a
h
)
1
829
Ca
se
4
.
D
C
vol
t
age
so
urc
e
1
0
0
0
Volt
s,
volt
age am
pl
it
ude
of i
n
v
e
r
t
e
r
ou
tp
u
t
17
0 Vol
t
s,
ou
t
p
u
t
fre
que
nc
y 5
0
H
z
and
lo
ad
i
m
pe
d
a
n
ce
10 + j
10
ohm
.
Si
mu
l
a
ti
on
r
es
u
l
t
s
a
re
s
ho
wn
i
n
th
e
Fi
gu
re
1
7
–20
.
F
i
g
u
r
e
1
7
sho
w
s
s
t
a
b
l
e
D
C
c
u
r
r
e
n
t
a
n
d
F
i
g
u
r
e
1
8
show
s
D
C
v
ol
ta
ge
i
s
s
t
a
b
le
a
t
1
0
0
0
V
o
l
ts.
T
h
e
sour
ce
c
u
r
r
e
nt
a
n
d
v
o
l
t
a
g
e
of
r
ect
if
ier
a
g
ai
n
s
h
ow
s
t
h
a
t
t
he
y
a
r
e
in
p
hase
a
s
show
n
at
F
i
g
u
r
e
19.
T
he
c
o
n
v
er
si
on
of
s
o
u
r
c
e
vo
l
t
a
g
e
w
i
t
h
a
m
p
l
i
t
u
d
e
o
f
3
1
1
V
o
l
t
s
a
t
5
0
H
z
take
s place successfully to sinu
s
o
id
al
1
7
0
V
o
l
t
s
a
t
5
0
H
z
a
s
p
r
esen
ted
in
F
igure
2
0
.
F
i
gur
e
1
7
.
D
C
cur
r
e
nt,
ca
se
4
F
igur
e
1
8
.
D
C
vo
ltage
,
case
4
F
i
gur
e
1
9
.
Ampl
i
t
u
d
e
o
f
v
o
l
t
a
ge
a
nd
c
u
r
r
e
nt
a
t
in
p
u
t
o
f
rec
t
i
fi
e
r
, ca
s
e
4
F
i
gur
e
2
0
.
Ampl
itu
de
o
f
vol
ta
ge
a
nd
cur
r
en
t
a
t
o
u
tp
u
t
o
f
i
n
v
e
rt
e
r
,
c
a
s
e
4
Ca
se
5
.
D
C
vol
t
age
so
urc
e
1
0
0
0
Volt
s,
volt
age am
pl
it
ude
of i
n
v
e
r
t
e
r
ou
tp
u
t
17
0 Vol
t
s,
ou
t
p
u
t
fre
que
nc
y 3
0
H
z
and lo
ad i
m
pe
d
a
n
ce 6
+
j 8
ohm
.
R
e
s
u
lts
o
f
t
h
is
c
a
s
e
are
in
a
g
r
ee
me
nt
w
it
h
t
h
e
pre
v
i
o
us
o
n
e
s.
A
s
illus
t
rat
e
d
i
n
F
i
g
ur
es
21
a
n
d
2
2
,
bo
t
h
D
C
c
u
r
r
e
nt
a
nd
D
C
v
olta
ge
a
r
e
s
t
a
b
l
e
.
T
he
s
our
ce
cur
r
ent
i
s
a
l
s
o
i
n
p
h
ase
w
i
t
h
t
he
s
o
u
r
c
e
vo
l
t
a
ge
o
f
r
ectifier
,
m
aki
n
g
t
h
e
in
pu
t
p
o
we
r
fac
t
or
u
n
i
t
y
,
see
Fi
g
u
re
2
3.
Si
nu
so
i
d
a
l
o
ut
pu
t
wav
e
fo
r
m
i
s
a
c
hi
e
v
e
d
a
ft
er
the
c
o
nve
rs
i
o
n
of
s
o
u
r
ce
v
o
lt
a
g
e
a
m
p
l
i
t
ude
o
f
r
ect
i
f
ier
a
t
3
1
1
Volt
san
d
5
0
Hz
t
o
17
0
V
o
l
t
s
a
t
30
H
z
t
ook
p
l
ace,
as
d
e
picted
i
n
Figu
re 2
4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
1
823
–
1
832
1
830
F
i
gur
e
2
1
.
D
C
cur
r
e
nt,
ca
se
5
F
i
gur
e
2
2
.
D
C
vo
ltage
,
case
5
Fi
g
u
r
e
23
.
A
m
p
lit
ud
e vo
lt
ag
e
a
n
d
c
u
rren
t
a
t
i
npu
t
of
r
e
c
t
if
ie
r
,
c
a
s
e
5
Figure
2
4
.
Amp
l
i
t
u
d
e v
o
l
t
a
g
e
and
curr
ent at
out
pu
t
of
i
n
v
e
r
ter,
c
ase
5
Ca
se
6
.
D
C
vol
t
age
so
urc
e
1
0
0
0
Volt
s,
volt
age am
pl
it
ude
of i
n
v
e
r
t
e
r
ou
tp
u
t
30
0 Vol
t
s,
ou
t
p
u
t
fre
que
nc
y 3
0
H
z
and
lo
ad
i
m
pe
d
a
n
ce
10 + j
10
ohm
.
S
i
mulat
i
o
n
r
e
sul
t
s
for
th
i
s
c
a
s
e
ar
e
cons
is
te
nt
w
i
t
h
those
obs
e
rv
ed
i
n
t
h
e
p
r
evi
o
u
s
c
a
s
es
.
St
ab
l
e
D
C
cu
rre
nt
a
nd
D
C
v
o
l
tag
e
a
r
e
s
how
n
i
n
F
igur
e
25
a
n
d
26,
a
n
d
uni
t
y
pow
er
f
ac
t
o
r
a
s
t
h
e
r
e
s
u
lt
o
f
i
n
p
h
ase
be
ha
v
i
or
o
f
sour
c
e
c
ur
r
e
nt
a
nd
v
o
l
t
a
ge
c
a
n
b
e
o
b
ser
v
e
d
i
n
F
i
g
u
r
e
2
7.
T
he
c
o
n
v
e
r
ter
is
a
l
s
o
a
b
le
t
o
con
v
e
r
t
succe
s
s
f
u
ll
y
31
1
Volts a
t 5
0
Hz a
t
the r
ecti
f
ier
to s
in
us
oid
a
l
30
0 Vol
t
s at
3
0
H
z
at
c
on
ve
r
t
er
’
s
outp
u
t
i
n
F
i
gur
e
28.
F
i
gur
e
2
5
.
D
C
cur
r
e
nt,
ca
se
6
F
i
gur
e
2
6
.
D
C
vo
ltage
,
case
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
M
ode
l
lin
g
o
f
three
p
hase sv
p
w
m
ac-
a
c conv
e
r
te
r us
ing u
n
ity po
w
e
r
f
a
c
t
or
cont
ro
l
(
S
a
i
d
a
h
)
1
831
Fi
g
u
r
e
27
.
A
m
p
lit
ud
e vo
lt
ag
e
a
n
d
c
u
rren
t
a
t
i
npu
t
of
r
e
c
t
if
ie
r
,
c
a
s
e
6
Figure
2
8
.
Amp
l
i
t
u
d
e v
o
l
t
a
g
e
and
curr
ent at
out
pu
t
of
i
n
v
e
r
ter,
c
ase
6
4.
CONCLUSION
Th
is
p
a
p
e
r
p
resen
t
s
a
pro
p
o
s
ed
t
hr
ee-
phase
A
C-AC
c
o
n
ve
r
t
er
u
s
i
n
g
a
ca
pa
ci
t
o
r
as
a
n
e
n
erg
y
s
t
o
r
age
e
l
e
m
e
n
t.
A
m
ode
l
of
t
he
p
r
o
p
o
se
d
c
o
n
v
e
r
ter
w
a
s
de
ve
l
o
ped
w
h
i
c
h
u
tili
ze
s
p
o
w
e
r
f
a
c
t
o
r
co
nt
rol
to
a
h
i
e
v
e
c
l
o
s
e
t
o
u
ni
ty
pow
er
f
ac
tor
.
T
he
p
r
o
po
se
d
co
nver
t
er
m
o
d
el
a
ls
o
i
n
cl
u
d
es
P
I
c
ontr
o
l
l
er
s
t
o
k
ee
p
t
h
e
DC
vo
l
t
age
s
t
ab
le.
The
pr
op
ose
d
A
C
-
A
C
c
on
ver
t
er
w
as
t
e
s
t
e
d
usi
n
g
s
i
m
ula
t
ion
t
o
p
r
o
duce
i
n
ver
t
e
r
o
u
t
pu
t
v
o
l
t
a
g
e
s
r
a
n
g
i
n
g
f
r
o
m
1
2
0
V
o
l
t
s
t
o
3
0
0
V
o
l
t
s
w
i
t
h
f
r
e
q
u
e
n
c
i
e
s
b
e
t
ween
3
0
-
6
0
Hz.
Simu
lati
on
resu
lts
o
f
s
i
x
di
ff
er
e
n
t
s
y
ste
m
s
cena
r
i
o
s
f
u
r
t
her
e
x
hib
i
t
the
ab
i
lit
y
o
f
p
r
o
po
sed
con
v
e
r
t
e
r
in
s
u
c
c
e
ssfu
ll
y
cha
ngi
ng
t
he
i
n
v
e
r
t
er
out
put
v
ol
t
a
g
e
a
t
di
f
f
e
r
en
t
fre
qu
e
n
c
i
e
s
a
n
d
v
a
ryi
ng
l
o
a
d
.
A
ll
o
f
t
h
e
se
w
er
e
a
c
hieve
d
by
t
h
e
pr
o
pos
ed
c
o
n
v
erter
wh
i
l
e
m
ain
t
a
i
n
i
ng
un
ity
p
o
w
er
f
a
c
t
or
,
sta
b
le
D
C
v
o
l
t
a
ge
a
nd
D
C
c
u
r
r
e
nt
,
a
n
d
s
i
nus
o
i
da
l
i
n
ver
t
e
r
ou
t
p
u
t
v
ol
t
a
ge
w
avef
or
m.
ACKNOWLEDGE
ME
N
T
S
The
a
u
thor
s
w
o
u
l
d
like
to
e
xpr
e
s
s
the
i
r
gr
ati
t
ude
t
o
G
o
d
,
b
elo
v
e
d
f
amil
y
,
a
nd
t
e
ach
ers.
S
p
e
c
i
al
tha
n
ks
a
r
e
due
t
o
t
h
e
D
i
r
e
ct
o
r
ate
G
e
ne
r
a
l
o
f
H
ig
her
Ed
uc
atio
n
(
D
i
r
e
kt
or
a
t
J
en
der
a
l
P
e
nd
idi
k
a
n
T
i
n
g
g
i)
t
ha
t
pr
ovi
de
d
the
f
u
ndi
ng
f
o
r
th
is
r
esea
r
c
h.
REFERE
NC
E
S
[1]
B. Wu
, “ Hig
h-p
o
wer Con
v
e
rt
ers and
AC
D
ri
v
e
s”
,
Pi
sc
atawa
y
,
NJ
:
I
EEE
/Wiley, 2
006.
[2]
Bo
ld
e
a
I
, Nas
a
r S
A
, “El
ectric
drives",
2n
d e
d
n. C
R
C
p
r
e
s
s
, Bo
ca
Rat
o
n, 2
00
6
.
[3]
K
o
l
a
r
JW,
F
r
ied
l
iT
,Krism
erF,
Roun
d
S
D
,
“
The
es
sen
ce
of
t
hree-p
h
a
s
e
A
C
/
AC
c
on
ve
rte
r
s
yste
m
s
”
,
In
: Pro
ceedi
n
g
s
o
f
p
o
wer elect
ronics
an
dm
o
tio
n
co
nt
rol co
nfer
en
ce
,
EPE-PE
M
C
’0
8,
Po
zna´
n,
P
o
l
a
n
d
,
p
p
2
7
–
42,
2008
[4]
T
h
o
m
as
F
ri
edli
and
J
o
h
a
nn
W
.
K
ol
ar,
“
C
om
prehen
si
ve
C
om
pari
so
n
o
f
Th
ree-P
h
ase
AC-A
C
M
a
trix
C
on
vert
er
a
nd
V
o
ltage
D
C-Li
n
k
Back-t
o-Back
C
o
n
v
e
rter S
y
s
t
e
ms
”,20
11.
[5]
J
o
h
a
nn
W.
K
ol
ar,
T
homas
F
ried
li,
J
o
s
e
Rod
rigu
ez and
P
a
tri
c
k W
.
W
h
eeler,
“
R
eview o
f
Th
r
ee
-P
h
a
se PW
M
AC–
AC
Co
nv
ert
e
r
To
polo
g
i
e
s”,
IE
EE T
r
a
n
s
a
cti
ons O
n
Indu
st
ri
a
l
El
ectr
o
ni
cs
, v
ol
. 58
,
n
o
.
11
, 20
1
1
.
[6]
H
u
l
u
si
Karaca
a
n
d
Ram
azanA
k
kay
a
,
“
M
od
eling,
S
im
u
l
ati
o
n
and
A
n
al
y
s
i
s
of
M
atri
x
Con
v
erter
Us
ing
M
a
tl
ab&
Simu
l
i
n
k
”
,
In
ternat
io
nal Jo
ur
nal o
f
M
o
d
e
lin
g
an
d
O
p
ti
miza
ti
on
,
v
o
l. 2
,
n
o
.
3
, 2
01
2
.
[7]
L
.
H
ub
er
a
n
d
D
.
Boroj
e
vi
c,
“
S
p
a
ce
vect
or
m
od
ulat
ed
t
h
r
ee-p
h
as
e
t
o
t
hree-p
h
as
e
m
a
tri
x
c
on
verter
w
ith
i
npu
t
po
wer
f
act
or co
r
rect
io
n
,
”
IE
EE Trans. I
n
d. Appl
,
vol.
31
,
no
.
6
,
1
995
.
[8]
C.K
a
laiselvi,
M.Bh
uv
anesw
a
ri,
A.
D
i
vyaV
i
n
o
th
R
aja,
“
Co
m
p
ariso
n
o
f
Th
re
e
P
h
ase
Vo
ltage
B
ack
t
o
Bac
k
Con
v
e
r
te
r
a
n
d
Ma
trix
C
on
ve
rte
r
”
,
Int
e
rn
ation
a
l Jour
na
l of
Inn
o
va
tive R
e
sear
ch in
Com
p
u
t
er a
nd Co
mmu
ni
cation
E
n
g
i
neer
in
g
,
v
o
l
. 2,
no
11
,
2
01
4
.
[9]
W
h
eeler P
W,
R
odri
g
u
ez
J, Clare J
C,
E
m
p
ring
ha
m
L,
W
e
i
n
s
te
jn
,
“
A
M
a
t
r
i
x
c
o
n
v
e
r
t
e
r
s
:
a
t
e
c
h
n
o
l
o
g
y
r
e
v
i
e
w
”
,
IEE
E
T
r
an
s In
d
E
l
ectron
,
vo
l
.
49
(
2
)
, p
p. 27
6
–
2
8
8
, 2
00
2.
[10]
K
.
K
avi
a
ras
u
,
T.
K
a
m
al
raj,“
A
n
Imp
r
ov
ed
S
i
n
g
l
e
P
h
ase
AC-A
C
Con
v
e
rt
er
W
ith
Q
uasi
-Z-So
u
rce
T
echn
i
qu
e”,
In
ter
natio
nal Jour
na
l F
o
r
T
echnolo
g
i
c
a
l
Res
e
ar
ch In
En
gin
eeri
ng
vo
l.
1
,
no
9
,
2014.
[11]
E
d
ison
R
.
C.
d
a
S
i
l
v
a
E
u
zeli
C.
d
os
S
an
to
s
Jr.
An
tô
n
i
o
I.
L
acer
da
,
“Cou
ple
d
-Ind
u
c
t
o
r
A
C-t
o
-AC
Co
nv
e
r
te
rs
Ha
v
i
n
g
I
m
pro
v
e
d
Inp
ut
Powe
r
F
a
c
t
o
r
, S
imp
l
e
Co
ntro
l, a
nd
V
a
r
ia
bl
e O
u
t
put F
requ
ency
”,
IEEE
,
20
1
0
.
[12]
A
.
Ai
t
e
l
m
a
hj
oub,
A
.
A
il
a
n
e,
A
.Ab
o
u
l
oiaf
a,
A
.
E
ssad
k
i
,
M
.
R
ach
ik
,
E
.Lab
riji,
“
A
N
on-l
i
n
ear
C
ontrol
ler
f
o
r
S
i
ngl
e
-
P
h
ase A
C
-AC Po
wer Con
v
ert
e
r to
m
eet U
PS
P
erform
ance
In
dex
”
,
2
0
1
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
2
3
– 1
832
1
832
[13]
Ab
derrahi
m
El
F
adi
l
i,
F
o
u
ad
G
i
r
i,
A
bd
elm
o
un
im
e
E
l
M
ag
ri,
Luc
Du
ga
rd
,
“Non
lin
e
a
r
c
on
tr
oller
f
o
r
Doubly
F
e
d
Induct
ion
M
o
tor
with
b
i-direct
i
o
n
a
l
AC/
D
C/AC
c
onv
erter”,
20
13
,
11
th IFAC Int
e
rnati
onal
W
o
r
k
sh
op on
Ad
ap
ta
tio
n a
nd
L
e
ar
ni
ng in Contr
o
l
an
d
S
i
g
nal
P
r
o
c
es
si
ng
July 3-5
, 2
013
. Caen
, F
r
ance
[14]
S
u
w
a
t
Kit
c
haro
en
wat
,
M
o
n
g
k
o
l
K
on
gh
irun
,
a
n
d
An
awach
S
ang
s
w
a
n
g
,
No
n-m
e
mbers
,
“
A
N
o
v
e
l
Si
ngle
P
h
ase
AC-
AC
C
on
ve
rte
r
w
ith
Powe
r
Fa
c
t
o
r
C
on
tro
l
”
,
Ect
i
T
r
an
sacti
ons
O
n
Elect
ri
ca
l
En
g., El
ectro
n
i
cs
,
And
Com
m
un
icati
ons,
vo
l.
11
,
n
o
.
1
20
13
[15]
F.J
.
M
aseda,
O
.
Barambones,
A.
J.
G
arrido
a
nd
I
.
Martija,
“A
S
en
sorless
AC-
D
C-
AC
C
onvert
er
w
i
t
h
S
liding
Mod
e
Con
t
roller
fo
r
In
d
u
ct
io
n M
o
tors
D
rives
”
,
2
014.
[16]
S
a
id
ah,
M
H
P
urno
m
o
,
M
A
s
h
a
ri,
“
High
P
erf
o
rm
ance
o
f
N
on
linear
A
ctiv
e
Re
ctifi
e
r
Vo
lt
age
and
P
o
w
e
r
Fact
or
Con
t
rol
Usin
g
F
eed
ba
ck
L
in
earizat
io
n”,
In
tern
a
tio
na
l R
eview of
E
l
ectrica
l E
ngin
eer
in
g
(
I
REE),
v
o
l.
8
,
no
2
,
pp
.
56
8-5
74,
20
13
.
[17]
S
a
id
ah,
B.
P
u
r
wahy
ud
i,
K
u
s
pija
ni
,
“
C
ontro
l
Strat
e
gy
f
or
P
WM
V
ol
t
a
ge
S
o
u
rce
Con
v
erter
U
s
i
n
g
F
u
zzy
L
o
g
i
c
f
o
r
Ad
ju
s
t
ab
le S
p
eed D
C M
o
t
o
r”,
IJP
E
D
S
,
vol.
8
,
p
p
.
5
1-5
8
,
201
7.
[18]
Ho
ng
wu
S
he,
H
u
a
L
i
n
,
B
i
He,
Xi
ngw
ei
W
a
n
g
,
L
imin
Yu
e,
a
nd
X
ing
A
n
,
“Im
p
le
m
e
nt
ati
o
n
of
V
o
l
tag
e
-Bas
ed
Com
m
u
t
a
ti
on
i
n
S
p
ace-Ve
ct
or-M
od
ul
ated
M
atri
x
Conv
erter”,
IEEE T
r
ansact
i
o
ns
on Indus
t
r
i
a
l
E
l
ect
ronics
,
v
o
l
.
5
9
, no
.
1,
20
12
.
[19]
S
a
id
ah,
M
H
P
u
r
no
m
o
,
M
As
hari,
“
A
dv
anced
C
o
n
t
rol
Of
A
ctiv
e
Rect
i
fier
Using
S
w
i
t
c
h
Fu
nctio
n
And
F
u
zzy
L
og
ic
F
o
r N
onli
n
ear Behav
io
ur Co
m
p
e
ns
ati
o
n
”
,
JAT
I
T
,
156
-
16
1,
2
0
1
2
.
B
I
OGRAPHIES
O
F AUTHO
RS
S
a
i
d
ah
r
eceiv
e
d
her
b
ach
el
or,
m
a
ster
a
nd
P
h
.
D
deg
r
ee
f
r
om
I
nsti
tut
Teknol
og
i
S
e
pu
luh
N
opem
b
er
(ITS)
S
urab
aya
i
n
1
9
8
5
,
2
00
5
an
d
20
13
r
esp
ecti
v
ely
.
S
h
e
h
a
s
been
t
h
e
f
acu
lty
m
e
m
b
er in Bhaya
n
gk
ara
Un
iv
ersit
y
i
n
S
u
rab
a
ya
s
in
ce
20
06
.
Her re
search in
t
erest
s
a
re on
th
e
us
e
of
ar
tificial
i
n
te
l
l
i
g
ent
f
o
r
po
wer el
ectron
i
cs
, con
t
ro
l an
d el
ectri
c d
r
i
v
es
app
licat
io
n
s
.
H
a
ri S
utik
sn
oreceiv
e
d
his b
a
ch
el
o
r
, m
a
st
er and
Ph.
D d
e
gree f
r
o
m
I
n
s
tit
u
t
Tek
n
o
l
ogi
S
e
p
ul
uh
N
opem
b
er
(ITS
)
S
u
r
abaya
in
1981,
2
0
0
1
and
20
1
3
r
esp
ectiv
ely.
H
e
j
o
i
ned
S
e
ko
lah
Ti
ng
gi
T
e
kni
k
Su
rabay
a
(
S
T
TS)
in
S
urabay
a si
nce 1
9
8
1
.
His
research
int
eres
t f
o
cus
e
s
o
n
t
he u
se of
art
i
f
i
c
i
al i
n
t
ell
i
gent
f
or
p
ower
e
lectro
ni
cs co
n
t
r
o
l
and
electr
ic
d
r
i
v
e
s
a
p
pl
ic
a
t
i
o
n
s
.
Bam
b
an
g P
u
rwa
h
yud
i
recei
ved
h
i
s
b
achel
or, m
a
s
t
er an
d
d
oct
o
r d
e
g
r
e
e
fr
o
m
I
ns
ti
tu
t
T
e
kn
ol
o
g
i
S
e
p
u
lu
h
N
o
p
e
mber
(IT
S)
S
urabay
a,
I
nd
on
esi
a
,
in
1
995
,
2
00
5
an
d 2
01
3 res
p
ecti
v
ely.
H
e h
a
s
jo
in
e
d
B
ha
y
a
ng
k
a
ra
Univ
e
rsi
t
y
S
u
ra
b
a
ya
,
In
do
ne
sia
, s
in
c
e
20
00
.
H
e
g
o
t
p
ub
li
cations
i
n
s
e
veral
National and In
ternat
ional journa
l
s
and
con
f
e
ren
ces. His areas
o
f
in
t
erest
are sim
u
lati
on
and
design
o
f power electroni
cs,
po
wer quality,
renewable
energy, a
nd art
i
f
ici
a
l
int
e
lligent
ap
pli
cati
on to
power
e
l
ectro
nics
a
nd
d
ri
ve.
T
a
ufik
r
eceiv
e
d
h
i
s
Bachel
or
o
f
S
c
ien
c
e
in
Electrical
E
n
g
i
n
eeri
ng
with
m
ino
r
i
n
Co
mp
ute
r
S
c
i
e
n
ce,
N
orth
e
r
n
A
r
izo
n
a
U
n
i
v
ersi
ty,
M
a
y
19
9
3
,
M
a
st
er
o
f
S
c
ien
ce
i
n
E
lectri
cal
E
ngin
eering
an
d
Com
p
u
t
er
S
cien
ce,
U
ni
versity
o
f
Il
li
nois
a
t
C
h
i
cag
o,
M
ay
1
9
95
,
an
d
Do
cto
r
o
f
E
ngin
e
eri
n
g
i
n
E
l
ectri
cal
E
ngi
neerin
g,
C
l
e
v
e
l
a
n
d
S
t
a
te
U
n
i
v
e
rs
it
y
,
M
ay
199
9
.
H
e
j
oi
ned
the
el
ectrical
en
gin
eerin
g
d
e
partm
e
n
t
a
t
Cal
P
o
ly
S
ta
t
e
U
n
i
versi
t
y
,
C
alif
ornia
,
U
S
A
i
n
1
999
w
h
ere
h
e
i
s
currentl
y
a
P
rofessor
and
Di
rect
or
o
f
E
l
ectri
c
P
o
wer
Institute.
H
e
i
s
S
eni
o
r
M
e
m
b
er
o
f
th
e
Instituteof
E
l
e
c
t
rical
a
nd
E
lect
ronics
E
ngineers
(IEEE),and
Me
m
ber
o
f
A
m
e
rican
S
ociet
y
o
f
E
ngi
neeri
n
g
Ed
u
cat
io
n
(AS
E
E
)
.
H
i
s
res
e
a
r
ch
i
nt
erests
e
n
c
om
pas
s
th
e
area
o
f
P
o
wer
Elect
ron
i
cs
,
P
o
wer S
y
s
t
ems
, S
m
a
rt
G
rid
,
Ren
ewabl
e
En
e
rgy
,
and
P
ow
er Qu
a
lity.
Evaluation Warning : The document was created with Spire.PDF for Python.