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.
1, Mar
ch 20
19,
p
p.
522~
5
2
9
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
5
22-
52
9
522
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
Analysis and desi
gn of si
ngle pha
se voltage-frequency conve
r
ter
with optimized
P
I controll
er
M. As
n
a
1
,
H
.
S
har
eef
2
,
S.
N.
K
h
a
l
i
d
3
,
A. Al
D
o
s
a
ri
4
,
B.
Ham
ad
5
, M. Al
h
ammad
i
6
,
N
. Aldarmak
i
7
1
,
2,
4,
5
,
6,
7
D
e
p
a
rtm
e
n
t
of El
ectri
ca
l Engi
neer
i
n
g,
U
ni
ted Arab Emira
tes Univ
ersity
, Un
i
t
e
d
Arab
Emirat
e
s
3
Dep
a
rt
m
e
nt of E
l
ect
rical
P
o
w
er E
ngin
eering
,
Uni
versiti
Tek
n
o
l
o
g
i Malaysia,
M
a
laysia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
1
7
,
2
018
Re
vise
d N
ov
2
9
,
201
8
A
c
c
e
pte
d
D
ec 14,
2
0
1
8
Th
is
p
aper
p
ro
po
ses
a
n
e
w
vo
lt
age
f
r
equ
e
ncy
co
nvert
er
(
VF
C)
t
ha
t
con
v
erts
b
o
th
v
o
lta
ge
a
nd
fre
q
u
e
nc
y
to
t
h
e
r
e
q
uire
d
le
v
e
l
of
v
o
lta
ge
a
nd
f
re
q
u
e
nc
y
in
low
v
o
l
ta
ge
n
e
t
work
s
use
d
i
n
va
riou
s
c
o
un
tr
ie
s.
T
he
p
ro
po
se
d
c
o
nv
e
r
t
e
r
cou
l
d
be
u
s
e
d
as
a
u
n
i
v
e
rs
al
p
o
w
er
s
up
pl
y
for
s
e
ns
it
ive
AC
l
o
a
d
s.
T
he
c
o
nv
e
r
te
r
is
c
omp
o
se
d
of,
inp
u
t
v
ol
ta
ge
a
n
d
fre
q
ue
n
c
y
de
te
c
t
io
n
c
ir
c
u
it
r
y
,
f
u
l
l
b
ridge
boo
s
t
rect
i
f
i
e
r
a
n
d
a
DC
t
o
AC
i
nver
ter.
I
n
additio
n
,
t
o
i
m
prov
e
th
e
f
easibilit
y
a
n
d
p
erf
o
rm
ance
of
t
he
c
o
nvert
er,
sy
nch
r
on
ous
r
ef
erenc
e
bas
e
d
P
I
(
S
R
FP
I)
c
on
troller
is
a
d
o
pted
,
wh
ere
t
h
e
sy
st
em
b
ehave
s
si
m
i
la
r
to
a
DC-DC
con
v
e
r
ter.
T
he
p
aram
e
t
er
s
el
e
c
t
i
o
n
o
f
P
I
c
o
n
t
r
oller
is
d
o
n
e
u
s
i
n
g
a
recent
op
ti
mis
a
tio
n
t
ech
niq
u
e
called
L
i
g
h
tnin
g
S
e
arch
A
lg
orit
h
m
(
L
S
A
)
.
T
h
e
sim
u
l
a
tio
n
of
V
F
C
i
s
co
nd
uct
e
d
in
M
ATL
A
B/Sim
u
lin
k
env
i
ronm
ent
.
The
sim
u
l
a
tio
n
res
u
lts
sho
w
t
hat
LSA
based
P
I
c
ontrol
l
er
p
rovides
b
et
ter
ou
tput
vo
lt
age
regul
ati
o
n
w
ith
r
es
pect
t
o
th
e
ref
e
rence
va
l
u
e
und
er
v
a
rious
l
o
ad
a
nd
in
pu
t
co
nd
it
ions.
K
eyw
ord
s
:
Boos
t r
ecti
f
ier
Li
ght
ni
n
g
sea
rch
alg
o
ri
t
h
m
Op
ti
mi
sat
i
on
P
I
contro
l
l
er
S
ync
hr
on
o
u
s
refere
nce
fra
m
e
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:
Hussain S
hareef
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
Eng
i
ne
eri
ng,
U
n
i
t
e
d
A
r
a
b Em
irate
s
U
niv
e
rsi
t
y,
A
l
-A
in,
15
551,
U
nite
d
A
r
ab
E
m
i
r
a
tes.
Em
ail:
sha
r
ee
f@ua
e
u
.a
c.a
e
1.
I
N
TR
OD
U
C
TI
O
N
P
o
w
e
r
system
s
thr
o
u
g
h
o
u
t
t
h
e
w
o
rl
d
to
da
y
are
ma
i
n
l
y
b
a
s
e
d
o
n
ei
t
h
e
r
t
h
e
U
.
S
.
o
r
E
u
r
o
p
e
a
n
st
a
ndard
s.
D
iffe
rent v
o
l
ta
ge
s and fre
que
nc
ie
s can po
s
e rea
l
pro
blem
s for
the eq
ui
pme
n
t des
i
g
n
e
d
t
o op
e
r
ate
at
spec
ific
v
olta
ge
a
n
d
f
re
q
u
en
cy
.
I
n
fa
c
t
,
us
e
o
f
a
v
ol
t
a
ge
freq
u
e
n
c
y
c
onve
r
t
er
(
V
F
C)
i
s
an
a
l
t
e
rn
ati
v
e
to
overc
ome
thes
e
diffic
u
ltie
s.
D
iverse
t
ypes of
V
FCs
a
r
e
ava
i
la
b
l
e
n
o
w
,
f
o
r
e
x
a
m
p
l
e
t
r
a
n
s
f
o
r
m
e
r
b
a
s
e
d
v
o
l
t
a
g
e
con
v
er
t
e
rs
a
re
c
omm
only use
d
f
or
t
his
a
p
pl
ic
ati
on.
H
ow
ev
er
,
i
t
resul
t
s
in
i
nc
rea
s
e
d
p
ow
e
r
l
oss
a
nd
m
a
ke
s
t
h
e
system
b
ulky.
H
e
nc
e
a
t
r
a
n
sform
e
r
-
less
ba
s
e
d
V
F
Cs
h
as
a
ttrac
t
e
d
spe
c
i
al
a
t
t
e
n
t
i
on
due
i
t
s
h
igh
eff
i
ci
en
cy
,
minim
i
se
d co
st
a
nd size
of
t
he
syst
e
m.
A
V
F
C
m
a
inly
c
ons
i
s
ts
o
f
a
rectifier
and
a
n
i
nver
t
e
r
for
A
C
-DC
an
d
D
C
-
A
C
op
e
r
ati
o
n
respec
t
i
ve
ly
[1].
T
he
r
e
c
tifie
r
conve
rt
s
t
h
e
in
pu
t
v
o
l
tage
i
n
t
o
t
h
e
D
C
l
in
k
v
o
l
t
a
g
e
an
d
i
nver
t
er
p
e
r
for
m
s
the
co
nver
s
io
n
o
f
t
h
e
D
C
l
in
k
vo
lt
ag
e
t
o
a
c
on
st
a
n
t
lo
ad
volt
a
g
e
.
In
a
ddi
ti
o
n
t
o
th
e
po
wer
ci
rc
u
i
t
,
f
e
e
db
ac
k
con
t
rol
circu
i
t
i
s
use
d
t
o
reg
u
la
t
e
t
he
l
oad
v
o
l
t
a
ge
t
o
a
se
t
r
e
fe
renc
e
va
l
u
e.
T
he
m
aj
or
c
ha
l
l
e
nge
s
in
a
n
inve
r
t
er
d
e
s
i
g
n
ar
e
the
c
o
nt
rol
o
f
out
pu
t
vol
t
a
g
e
a
nd
curre
nt
s
i
g
n
a
ls
r
e
g
ardles
s
of
t
he
l
oa
d
t
ype
t
o
w
h
ic
h
i
t
i
s
c
o
nn
ec
te
d.
N
um
erous
c
o
nt
rol
t
e
chni
qu
es
h
a
v
e
b
een
d
o
c
u
m
ent
e
d
fo
r
co
n
t
rolli
ng
t
ypi
ca
l
s
i
n
gle
pha
se
v
o
lta
ge
s
ource
i
n
v
er
t
e
r
s
t
ha
t
inc
l
ude
s
L
C
R
e
s
ona
nce
c
ontr
o
l
[2],
s
l
i
d
i
ng-
mode
c
o
n
t
r
ol
[
3],
re
pe
t
i
ti
v
e
c
o
n
t
rol
[4]
a
n
d
sy
nc
hr
on
ou
s
refere
nce
frame
c
o
n
tro
l
[
5].A
m
ong
w
h
ich
sync
hr
ono
us
r
efere
n
ce
f
r
a
m
e
b
a
s
e
d
s
p
a
c
e
v
e
c
t
o
r
P
W
M
c
o
n
t
r
o
l
,
c
o
mmo
n
l
y
u
s
ed
i
n
t
h
re
e
p
h
a
se
i
nv
e
r
t
e
rs
a
re
n
o
w
w
id
el
y
ap
pli
e
d
i
n
si
n
g
l
e
pha
se
i
n
v
er
te
rs
due
t
o
i
t
s
bet
t
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Ana
l
y
s
i
s
and
des
i
g
n
of
s
i
n
g
l
e
-p
ha
se
v
o
lt
ag
e
-
fre
q
u
e
n
c
y
c
o
n
ver
t
e
r
wit
h
opt
imi
z
ed
PI c
o
nt
ro
l
l
e
r (M.
Asn
a
)
52
3
st
ead
y
st
at
e
an
d
dyn
ami
c
p
erf
o
rma
n
ce
[
6].
Hen
c
e
,
t
h
e
i
n
v
e
rt
e
r
c
a
n
b
e
m
ode
le
d
a
s
a
D
C-D
C
b
u
c
k
or
bo
ost
co
nver
t
e
r
.
P
r
evio
us
r
e
s
ear
ches
r
e
porte
d
in
[
7]
,
[8
]
val
i
date
s
t
h
at
p
ro
p
o
rt
io
na
l
an
d
i
n
tegra
l
(
P
I)
contro
ller
ha
ve
go
o
d
c
ontr
o
l
p
e
rform
ance
d
u
r
in
g
so
ur
ce
and
l
o
ad
d
is
t
u
rba
n
c
e
s.
B
e
s
ide
s
,
P
I
c
ontr
o
l
l
er
e
na
b
l
e
s
t
o
ach
ie
ve
z
er
o
st
e
a
dy-s
t
ate
err
o
r
a
t
t
he
f
un
dam
e
nta
l
f
re
que
nc
y
o
f
t
he
c
on
ve
rte
r
[9].
I
n
a
P
I
c
ontroller,
f
inding
the
gain
parameters K
p
a
nd K
i
is
a
c
om
ple
x
t
a
s
k to e
n
s
ur
e the
bes
t
p
e
r
form
a
n
c
e
of ove
ra
ll s
y
s
t
e
m
.
PI contro
l
l
ers can be
tu
ne
d
ei
the
r
m
a
nua
l
l
y
or
u
s
i
n
g
r
ule-ba
se
d
m
e
th
o
d
s
suc
h
a
s
Z
i
e
g
l
e
r
N
i
c
h
o
l
s
t
e
c
h
n
i
q
u
e
.
B
u
t
t
h
e
s
e
m
e
t
h
o
d
s
a
r
e
it
e
r
a
t
i
v
e,
t
im
e
c
o
n
s
um
i
n
g,
a
n
d
s
om
et
im
es
p
rod
u
ce
l
arge
o
v
e
rsh
o
o
t. A
p
a
rt
f
r
o
m
t
h
ese
t
r
adi
tio
na
l
m
e
t
h
ods,
sever
a
l
i
n
tel
l
i
g
e
nt
op
t
i
m
isa
tio
n
tec
h
n
i
que
s
can
b
e
use
d
t
o
s
o
lv
e
t
h
e
com
p
l
e
xi
t
y
i
n
c
o
mp
u
t
at
i
ona
l
pr
oced
ure
in
tu
nin
g
co
n
t
ro
lle
r pa
ram
e
te
rs so a
s
to a
c
h
ieve
an op
tim
al sys
tem
de
s
ig
n [1
0
]
, [11].
Rec
e
n
t
l
y
,
num
er
ous s
tud
i
e
s
have
d
isc
u
sse
d
he
urist
i
c
op
t
i
m
isat
io
n
me
th
ods
t
ha
t
inc
l
ude
s
ge
n
et
ic
a
l
gor
it
hm
(
G
A
)
[
12]
,
P
a
rticle
S
w
a
r
m
O
p
t
i
m
i
sa
tio
n
(
P
SO
)
[13],
[14
]
f
or
i
m
p
rov
i
ng
P
I
D
contro
ll
ers.
I
n
[1
5]
P
SO
h
as
b
e
e
n
u
t
i
l
i
s
e
d
f
or
P
I
contr
o
l
l
e
r
op
tim
iza
t
i
o
n
i
n
s
i
n
g
l
e
p
h
ase
i
nver
t
e
r
s.
H
ow
ever,
th
i
s
m
et
h
o
d
fa
i
l
s
to
p
r
o
v
i
de
b
e
s
t
pa
i
r
o
f
co
n
t
rol
par
a
me
ters
due
t
o
ear
l
y
c
o
nve
r
g
ence
.
T
h
e
r
e
f
o
r
e
,
t
h
e
a
i
m
o
f
t
h
i
s
r
e
s
e
a
r
c
h
i
s
t
o
d
e
v
e
l
o
p
a
V
F
C
t
h
a
t
c
a
n
c
o
nver
t
1
2
0
V
/
6
0
H
z
(U
.S
l
ow
vo
lta
ge
s
ta
nda
rd)
to
2
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/5
0H
z
(Europe
/A
sia
l
o
w
vo
l
t
a
g
e
sta
n
dar
d
)
a
nd
vice
v
e
r
sa.
More
over,
a
h
e
u
r
i
sti
c
op
tim
isa
tio
n
c
a
lle
d
L
i
gh
t
n
i
n
g
Se
arc
h
A
lg
ori
t
hm
(
LSA
)
i
s
a
d
o
p
t
e
d
i
n
t
u
ni
ng
P
I
c
on
tro
l
ler
t
o
e
nha
nc
e
perform
ance
a
nd
e
f
f
ic
ie
nc
y
o
f
overa
ll
s
ys
te
m
.
L
S
A
i
s
a
m
e
ta
h
eu
r
i
st
i
c
s
op
ti
mi
sati
on
t
ech
ni
q
u
e
b
ase
d
o
n
t
h
e
b
e
h
a
vi
ou
r
o
f
l
i
g
htn
i
ng
.
It
i
s
use
d
t
o
solv
e
c
o
mp
l
e
x
p
r
o
b
l
e
ms
r
e
lated
t
o
c
on
tro
l
p
a
r
am
eter
o
p
tim
isa
t
ion
[1
6].
Com
p
ar
ed to
G
A
a
n
d
PS
O, it is com
p
u
ta
t
i
o
n
a
l
l
y
e
ffic
i
e
n
t
,
sim
p
le
and
has
hig
h
er
con
ve
rgenc
e
r
ate
[17]
.
The
pape
r
is
d
i
v
i
d
ed
a
s
fo
ll
ow
s:
S
ec
t
i
o
n
2
d
e
s
c
r
i
b
es
t
he
p
r
opos
ed
t
op
olog
y;
s
e
c
ti
on
3
p
ro
vi
d
e
s
th
e
ana
l
ys
is
o
f
S
R
F
base
d
P
I
c
ontr
o
l
s
y
ste
m
;
sec
tio
n
4
g
i
ve
s
de
t
a
i
l
e
d
s
t
u
d
y
o
f
LS
A
opt
i
m
i
s
a
tio
n
tec
h
niq
u
e
;
sect
io
n
5
repr
esen
ts
t
he
s
imula
t
io
n
re
su
lts
t
o
veri
fy
t
he
t
he
or
et
ica
l
d
iscuss
io
ns
r
e
g
a
r
di
ng
o
u
t
p
ut
v
ol
ta
ge
con
t
ro
l u
nder
v
a
r
y
ing
in
pu
t a
n
d loa
d
c
o
n
d
i
tio
ns.
F
i
nal
l
y sec
tio
n 6
co
nc
lu
de
s
t
h
is w
ork.
2.
SY
S
T
E
M
D
ESCRIPTIO
N
The
pro
pose
d
s
yste
m
is
d
e
p
i
c
ted
i
n
F
i
gure
1.
A
s
se
en
i
n
the
F
i
g
ure,
t
h
e
c
o
nver
t
er
c
o
n
f
i
gura
t
io
n
com
p
rises
of
a
f
u
ll
br
id
ge
d
i
ode
r
e
c
t
i
f
ier,
a
c
on
ve
nt
i
o
n
a
l
bo
os
t
c
o
n
v
er
t
e
r
a
nd
a
sin
g
l
e-pha
se
v
o
lta
ge
s
our
c
e
in
verter
. A
fu
l
l
bri
dge
d
i
o
de
r
ecti
f
ier i
n
it
ia
ll
y re
ct
ifies t
h
e
su
p
p
l
y vo
l
t
a
g
e
. In
c
a
s
e
o
f
c
on
ve
rt
in
g
120
V/6
0
Hz
t
o
23
0V
/
50H
z
,
a
s
te
p
u
p
c
o
nve
r
t
er
i
s
nee
d
e
d
t
o
m
a
in
t
a
in
a
c
ons
t
a
n
t
D
C
li
nk
v
o
l
t
a
g
e
r
eq
ui
re
d
by
t
h
e
i
nve
rt
e
r
.
Th
is
c
a
n
b
e
a
c
h
ie
ve
d
us
i
n
g
a
b
oos
t
c
o
nve
r
t
er
w
here
t
he
o
ut
p
u
t
v
ol
t
a
g
e
i
s
re
g
u
l
a
t
e
d
by
c
o
n
t
r
oll
i
ng
t
h
e
dut
y
c
y
cl
e D o
f
swi
tc
h
S
0
. F
o
r a c
onv
e
n
tio
nal
bo
ost c
o
nverte
r
,
t
h
e
vol
ta
ge
g
a
i
n i
s
gi
v
en
b
y:
(1)
wher
e D is the
dut
y
cycle,
V
dc
i
s
the D
C
l
i
n
k vo
l
t
age
an
d
V
in
is the
i
n
put
v
ol
tage
.
F
i
gure
1.
P
rop
o
se
d
si
n
g
l
e
ph
ase
vo
l
t
a
g
e
-
fr
e
que
nc
y
con
v
er
te
r
To
h
a
v
e
a
smo
o
th
c
ont
inu
o
u
s
i
np
ut
c
u
rrent
,
t
h
e
fil
t
e
r
i
n
d
u
c
t
o
r
L
o
w
i
th
a
n
appr
opria
te
v
a
l
ue
m
ust
b
e
cho
s
en.
In
a
d
d
i
t
i
on,
a
p
re
-c
ha
rge
d
i
ode
i
s
k
e
pt
p
ar
a
lle
l
t
o
t
he
boo
st
i
nd
uct
o
r
to
i
ni
t
i
a
l
ly
c
h
a
rg
e
th
e
D
C
l
i
n
k
ca
paci
ta
nce
pri
o
r
to
c
onve
r
t
er
s
tart-
up.
F
o
l
l
o
w
e
d
b
y
t
he
b
o
o
s
t
st
a
g
e,
s
in
gle
ph
as
e
f
u
ll
b
rid
g
e
i
nv
e
r
t
e
r
con
v
e
rt
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
52
2 –
52
9
52
4
the
D
C
l
i
nk
v
o
l
t
a
g
e
t
o
pure
A
C
v
ol
ta
ge
w
i
t
h
r
e
q
u
ired
freque
nc
y
u
s
in
g
un
ip
o
l
ar
p
u
l
se
w
idt
h
m
od
ula
t
io
n
(P
WM).
I
n
un
i
p
o
l
a
r
P
WM,
th
e
ga
te
s
ig
na
ls
f
or
d
ri
vin
g
t
he
s
w
itc
h
i
n
g
d
e
vic
e
s
a
re
g
en
e
r
ate
d
b
y
c
o
mp
arin
g
th
e
sinus
o
i
da
l
refe
renc
e
signa
l
w
i
th
a
tria
n
g
u
l
ar
c
a
rrier
.
A
l
so
t
h
e
a
m
p
l
i
t
ude of out
pu
t
vo
l
t
age
and i
t
s
fun
d
am
enta
l
fre
que
nc
y
is
c
o
n
tr
ol
l
e
d by
the
re
fer
e
nce
/
mo
d
u
la
t
i
on
sig
n
a
l
a
s p
e
r
t
he
gi
v
en
r
elat
io
n
:
(2)
wher
e
modu
la
t
i
o
n
i
n
d
e
x
,
m
a
i
s
d
efi
n
ed
a
s
th
e
rat
i
o
o
f
amp
lit
ud
e
o
f
r
e
f
e
r
e
n
ce
,
A
re
f
t
o
am
plit
ud
e
o
f
c
arr
i
e
r
signa
l
,
A
carrier
.
Ma
gn
i
t
u
d
e
of
o
u
t
pu
t v
o
l
t
a
g
e
V
o
can
b
e
o
b
ta
ine
d
as
:
(3)
The
low
p
a
ss
LC
f
i
lte
r
at
t
he
o
u
t
pu
t
e
n
d
f
ilt
ers
the
u
n
w
a
n
t
ed
v
o
l
t
a
ge
a
n
d
curr
ent
ha
rm
o
n
i
c
s
ge
nera
t
e
d
by
t
h
e
in
verter
to o
b
t
a
i
n a
pure
si
nu
soi
d
a
l
ou
t
pu
t v
o
lta
ge
w
avef
orm
.
3.
SYNCH
RON
O
US
R
EFE
R
ENCE FRA
M
E
BASED PI CO
N
T
ROLLER
S
ynchr
on
o
u
s
r
e
fe
renc
e
fram
e
(S
RF
)
contro
l
in
t
hree
p
ha
se
s
ys
tem
r
eq
ui
re
s
re
p
r
es
ent
a
ti
o
n
of
t
h
r
ee
pha
se
v
aria
ble
s
a
s
t
w
o
e
q
u
i
v
a
len
t
o
r
t
ho
g
o
n
a
l
vec
t
ors.
H
ow
e
v
er,
i
t
i
s
h
a
r
d
t
o
a
do
pt
t
hi
s
t
e
c
hniq
u
e
i
n
s
i
n
g
l
e
pha
se
c
o
nverte
r
s
sin
c
e
it
r
e
qu
ires
a
t
l
e
as
t
tw
o
ort
h
og
o
n
al
v
ec
t
o
r
s
from
a
s
ing
l
e
p
h
ase
qua
n
tit
y.
T
o
ge
ner
a
t
e
orthogonal
vectors,
d
iff
e
rent
t
echniques
can
b
e
used
[
18]-[20].
I
n
t
h
is
s
tud
y
,
t
h
e
m
o
s
t
c
om
m
on
m
e
t
h
od
i
s
use
d
,
i
n
w
hi
c
h
a
tim
e
de
l
a
y
bl
oc
k
in
tro
duc
es
a
phase
s
hif
t
o
f
9
0
°
w
ith
r
espec
t
t
o
fu
nd
a
m
ental
freq
u
e
n
c
y
o
f
re
fe
ren
c
e
sig
n
a
l
.
On
ce
,
t
h
e
t
w
o
o
r
t
hogon
a
l
p
h
a
se
s
a
r
e
g
e
n
e
ra
t
e
d
,
th
e
co
nv
ert
e
r
ca
n
b
e
m
od
ell
e
d
in
syn
c
hro
n
o
u
s
r
efere
n
c
e
f
r
a
m
e
.
U
s
ing
(4),
o
r
t
ho
go
na
l
s
i
g
n
a
l
s
ob
ta
ine
d
u
n
d
er
g
o
es
P
ar
k
T
r
ansform
a
ti
o
n
(
DQ
Tra
n
sf
orma
tio
n)
s
o as
t
o ob
ta
in s
ig
na
ls
i
n s
y
nchr
on
o
u
s r
e
fe
renc
e fram
e
.
(4)
The
r
ef
ore,
t
he
A
C
qua
n
t
i
t
ie
s
i
n
s
ta
ti
o
n
ary
re
fer
e
nce
fra
m
e
beco
m
e
D
C
ve
c
t
ors
i
n
r
o
t
a
t
i
n
g
αβ
refere
nce
fr
ame.
T
hus the
c
o
n
t
ro
ll
e
r
de
s
i
g
n
b
ecom
e
s
as simple
a
s
DC
-
D
C
con
v
er
ter.
4.
OPTIMIS
A
T
I
ON OF
PI
C
O
N
T
R
OLLER
Mu
l
t
i
l
o
op
c
o
n
t
r
o
l
syste
m
ca
n
e
ffec
tive
l
y reduc
e o
u
tp
ut vo
l
t
a
ge
var
i
a
tio
n and pr
ov
ide
be
tt
er
t
ra
nsie
n
t
respo
n
se
u
nder
l
i
ne
ar
a
n
d
no
n
-
li
nea
r
loa
d
co
nd
i
t
i
o
ns [2
1
].
A
s
s
how
n
i
n
F
ig
ure
2,
i
nve
r
t
er
out
p
u
t
v
o
l
t
a
g
e
V
o
a
n
d
i
nduc
t
o
r
c
u
rre
n
t
I
o
w
il
l
f
o
rm
a
n
o
u
t
e
r
v
o
lta
ge
lo
op
a
n
d
in
ner
c
u
rre
nt
l
o
o
p
r
espec
t
i
v
e
l
y,
e
a
c
h
g
o
v
erne
d
b
y
a
P
I
c
ontroller
f
o
r
m
i
ni
m
i
s
i
ng
s
tea
d
y
s
t
a
t
e
er
ror
with
r
espec
t
t
o
refere
n
c
e
si
gn
al.
The
v
o
l
tage
r
efe
r
enc
e
w
ou
ld
d
e
t
e
r
m
i
ne
t
he
d
es
ire
d
o
utpu
t
vo
l
t
age
r
e
qu
ire
d
wher
eas
c
urre
nt re
f
er
ence
is d
e
te
rmine
d
by o
u
ter
v
o
l
t
a
g
e
l
o
op.
I
t
is nec
e
ssary
t
o tu
ne P
I cont
ro
ll
er p
a
r
amet
ers
i
n
o
rd
e
r
t
o
ob
ta
i
n
rob
us
t pe
rform
a
nc
e of t
he pro
po
sed
con
v
er
t
e
r
ov
e
r
a
w
ide
ra
nge o
f oper
a
t
i
ng
co
n
d
i
tio
ns.
W
i
t
h
o
u
t
t
he
p
rope
r
selec
t
i
o
n
of
P
I
c
onst
a
n
t
s,
s
yste
m
b
e
h
a
vi
ou
r
b
eco
me
s
un
sta
b
l
e
.
B
e
si
des
the
classi
cal
m
ethod
of
t
un
ing,
a
b
e
t
te
r
w
a
y
to
t
u
n
e
P
I
c
on
t
r
o
l
le
r
is
t
o
use
t
h
e
op
t
i
m
i
sa
t
i
o
n
t
ec
hn
iqu
e
s
d
i
sc
usse
d
in
liter
a
ture.
In
t
h
i
s
pape
r,
a
m
e
t
a
heur
ist
i
c
o
p
t
i
m
i
sa
tio
n
tec
h
n
i
qu
e
c
a
l
l
ed
Ligh
t
ni
ng
S
e
a
r
c
h
A
l
g
o
r
i
t
h
m
(LSA)
i
s a
d
opt
e
d
fo
r
t
uni
ng
v
ol
ta
ge
a
n
d
c
urre
n
t
P
I
co
ntr
o
l
l
ers.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Ana
l
y
s
i
s
and
des
i
g
n
of
s
i
n
g
l
e
-p
ha
se
v
o
lt
ag
e
-
fre
q
u
e
n
c
y
c
o
n
ver
t
e
r
wit
h
opt
imi
z
ed
PI c
o
nt
ro
l
l
e
r (M.
Asn
a
)
52
5
L
O
A
D
T
i
m
e
D
el
ay
OS
G
T
i
m
e
D
el
ay
OS
G
dq
dq
αβ
αβ
θ
θ
I
d
I
q
V
q
V
d
C
u
rre
nt
C
ont
rol
l
e
r
Vo
l
t
a
g
e
Con
t
r
o
l
l
e
r
I
α
I
β
V
β
V
α
V
dr
e
f
V
qr
e
f
I
qr
e
f
I
dr
e
f
dq
αβ
M
d
M
q
V
in
M
a
PW
M
S
1
–
S
4
I
o
V
o
θ
Bo
o
s
t
Re
c
t
i
f
i
e
r
In
v
e
r
t
e
r
C
d
C
o
L
o
F
i
gure
2. S
ynchro
n
o
u
s r
e
fe
renc
e fram
e
c
ont
rol struc
t
ure
for
prop
ose
d
c
on
verter
4.1.
C
on
ce
pt
of
LS
A
LS
A
i
s
a
no
v
e
l
o
pt
imisa
t
io
n
t
e
c
hni
que
s base
d on
t
he p
hen
o
m
enon
of
l
i
ght
n
i
ng
.
It
a
d
opt
s
t
h
e
c
o
n
c
ept
of
s
te
p
lea
d
e
r
p
r
opa
ga
t
i
o
n
u
s
i
n
g
t
he
f
a
s
t
pa
rtic
les
cal
le
d
p
r
oj
ec
ti
les,
f
or
m
i
ng
a
bina
ry
t
re
e
struc
t
u
r
e
of
s
tep
leade
r
.
T
h
r
e
e
type
s
of
p
ro
jec
tile
s
use
d
a
re
(
a)
t
he
t
r
a
ns
i
t
i
o
n
pro
j
ec
ti
les
t
h
at
c
r
eat
e
t
h
e
fi
rst
l
e
ade
r
p
op
u
l
a
t
ion
(b)
the
spac
e
p
r
ojec
t
i
les
t
h
a
t
t
ry
t
o
bec
o
me
t
he
l
ea
der
a
nd
(
c
)
t
he
l
ea
d
pr
oje
c
t
ile
t
ha
t
re
pr
ese
n
ts
t
he
p
ro
j
ecti
l
e
fo
u
nd from
the
be
st
p
osit
io
ne
d ste
p
l
eade
r
s.
T
he de
t
a
i
l
e
d LS
A a
lgor
it
hm
step
s
ar
e
g
i
v
e
n
i
n [1
7]
.
4.2.
Prob
le
m D
e
scrip
t
ion
I
n
t
he
c
on
t
r
ol
l
e
r
struc
t
ur
e
s
how
n
i
n
F
i
gure
2,
e
rror
i
n
d
q
v
o
lt
ag
es
a
nd
c
u
rren
t
i
s
f
e
d
to
r
e
s
p
e
c
t
iv
e
PI
con
t
ro
l
l
ers.
H
e
n
c
e
f
o
u
r P
I
c
ontro
ll
e
r
s ne
e
d
to
be tune
d
b
y
LS
A
opt
imisa
t
io
n to o
b
t
ai
n be
tt
er
re
s
ults.
The
ke
y e
l
e
m
ent
s
r
equire
d fo
r
solv
i
n
g
an
y o
p
t
i
misa
t
i
o
n
pro
blem
are
a.
Input Vector
b.
O
b
jec
t
i
v
e
Func
ti
o
n
c.
O
p
t
i
m
i
sa
ti
on
Cons
tra
i
n
t
s
St
e
p
s i
n
vol
ving
i
n
LS
A a
r
e
s
t
at
ed
as
f
o
ll
o
w
s:
a.
Se
t
the
LS
A
p
a
ra
me
ters
n
a
m
e
l
y
n
u
mbe
r
o
f
iter
a
tio
ns
T
,
p
o
p
u
l
at
io
n
size
N
,
dime
nsio
n
of
i
n
p
u
t
v
e
c
t
or
D
and
cha
n
ne
l
t
i
m
e
.
b.
Ini
t
i
a
lise
th
e
p
r
ojec
tile
v
ec
to
r
con
t
ai
n
i
n
g
s
t
e
p
l
eade
r
s
tha
t
n
eed
t
o
b
e
o
p
t
i
m
i
s
e
d
.
Eac
h
p
arti
cl
e
in
t
he
po
p
u
l
a
tio
n
corre
sp
onds
t
o
P
I
c
ons
ta
n
t
s K
p
a
nd
K
i
.
The e
xpressi
on be
l
o
w
repr
esen
ts t
he
i
np
u
t
ve
c
t
o
r,
Z
ij
.
(5)
wher
e
a
<
X
ij
<
b
,
i
n
w
h
i
c
h
a
a
n
d
b
a
r
e
l
o
w
e
r
a
n
d
u
p
p
e
r
b
o
u
n
d
s
t
h
a
t
r
e
p
r
e
s
e
n
t
s
t
he
o
ptim
isa
t
i
o
n
c
o
nst
r
ai
nt
s.
c.
Ca
lcu
l
a
t
e
t
h
e
fit
n
ess
va
lue
f
o
r
ea
ch
p
ar
tic
le
i
n
t
h
e
p
o
p
u
l
a
t
i
o
n
u
s
i
ng
the
o
b
jec
t
iv
e
func
ti
on
de
fi
ne
d
i
n
(
6).
In
S
RF
P
I
c
o
n
t
r
ol
ler
,
R
MS
E
of
i
n
v
er
t
e
r
o
u
t
p
u
t
v
o
l
t
a
ge
i
s
take
n
a
s
the
o
b
jec
t
iv
e
fu
nc
ti
on
to
m
easure
t
h
e
per
f
orm
a
nce
i
n
dex.
(6)
wh
ere V
dr
e
f
is the
r
efere
n
ce
vol
t
a
ge
,
V
d
i
s
the m
e
a
s
ured
o
u
t
pu
t v
o
l
t
a
g
e
an
d
n
is t
he num
ber
of
s
am
pl
e
s
.
d.
Modi
f
y
the initi
al input
m
at
r
i
x,
Z
ij
in te
rm
s
of
d
i
r
ect
io
n,
posi
tio
n
and
va
l
u
e
a
s
p
er the
r
elati
o
n,
(
7
)
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nt
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P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
52
2 –
52
9
52
6
(8)
wh
ere
P
i
S
new
is
t
he ne
w
spa
ce
part
icle
P
i
S
r
epre
sents ol
d spac
e
part
i
c
le
P
L
new
i
s
the ne
w
lea
d
pa
r
ti
c
l
e
P
L
is t
he
o
l
d
le
a
d
part
icle
µ i
s
s
h
a
pi
ng
f
act
o
r
σ
i
s t
h
e sc
al
e fa
ct
o
r
e.
R
e
peat ste
ps
3
a
nd
4 u
n
til
the
itera
t
i
o
n
c
ou
n
t
r
ea
che
s
m
aximum
va
l
u
e
.
5.
S
I
M
U
LA
T
I
O
N
A
N
D
R
ES
UL
TS
To va
l
ida
t
e the
ope
rat
i
on of p
rop
o
sed vol
tag
e
f
r
e
que
nc
y
c
onve
r
t
er,
the sys
t
e
m
is
b
u
i
lt i
n
MA
TLA
B
S
i
m
u
l
i
n
k
e
nv
ir
onme
n
t
as sho
w
n
i
n
F
i
g
u
re
3.
F
i
gure
3. S
imulat
i
on m
o
d
e
l o
f
vol
t
a
ge frequ
e
n
cy c
o
n
v
erter
The
simu
la
ti
o
n
has
b
e
en
c
arr
i
ed
o
ut
f
or
0
.3s
a
t
a
s
am
pl
in
g
t
i
me
o
f
1µs.T
h
e
s
p
ec
i
f
i
c
a
t
i
o
ns
f
or
t
he
si
m
u
lat
i
on ar
e li
ste
d
o
n
t
h
e
T
a
ble
1.
Tab
l
e
1. S
imulati
o
n pa
ram
e
ter
s
o
f
vo
l
t
a
g
e
fr
eque
nc
y con
v
e
r
ter
Pa
r
a
m
e
t
e
rs
V
alue
s
I
n
p
u
t Volta
g
e
, V
i
120
V
rm
s
Output
V
olt
a
g
e
,
V
o
230
V
rm
s
Output
P
ow
e
r
800
W
DC
L
ink
V
o
lta
g
e
,
V
dc
350
V
I
n
p
u
t
In
duc
t
a
nce
,
L
i
6
m
H
DC
L
ink C
a
p
a
c
i
t
a
nce
, C
d
2
.
5
m
F
Filt
e
r
I
nduc
t
a
n
c
e
, L
o
3
.
8
m
H
F
i
l
t
er
C
ap
aci
t
a
n
c
e
,
C
o
8
µ
F
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Ana
l
y
s
i
s
and
des
i
g
n
of
s
i
n
g
l
e
-p
ha
se
v
o
lt
ag
e
-
fre
q
u
e
n
c
y
c
o
n
ver
t
e
r
wit
h
opt
imi
z
ed
PI c
o
nt
ro
l
l
e
r (M.
Asn
a
)
52
7
O
p
t
i
m
a
l
pa
ram
e
te
rs
f
or
P
I
c
o
ntr
o
l
l
e
r
u
s
i
n
g
L
S
A
i
s
im
pl
e
m
e
n
ted
w
i
t
h
MA
TLA
B
mfile
c
o
d
e
an
d
i
t
i
s
lin
k
e
d
with
S
im
ul
i
n
k.
P
aram
ete
r
s of
L
SA
for
s
imul
ati
o
n ar
e liste
d be
lo
w.
Num
b
er
of
it
er
ations, T
=
20
P
opu
l
a
tio
n
siz
e
, N
= 10
N
u
m
b
er
of
dim
e
nsi
ons,
D
= 8
The
o
p
tim
i
s
e
d
val
ue
o
f
K
p
an
d
K
i
obta
i
ne
d
aft
e
r sim
u
l
a
ti
on
a
r
e
tabu
late
d
in
T
ab
le
2
.
Table
2
.
PI
Pa
ram
e
ter
s
PI C
ontrolle
r
K
p
K
i
P
I
D
1
91.
7
51.
1
P
I
D
2
93.
7
9.
3
P
I
D
3
80.
5
20.
4
PID
4
78.
4
28.
1
F
i
gure
4
de
pi
cts
t
h
e
c
o
n
v
er
genc
e
c
u
r
v
e
for
o
p
t
i
m
i
s
at
io
n
in
w
h
i
c
h
ro
ot
m
ea
n
sq
ua
re
e
r
r
or
h
as
reduc
e
d
t
o
nea
r
l
y
z
e
r
o va
lue
after
perfor
mi
n
g
20
ite
rat
i
on
s.
F
i
gure
4. P
e
r
fo
rm
ance
error
curve
To
e
xa
mi
ne
t
h
e
p
er
form
ance
o
f
VFC
wi
t
h
o
p
tim
i
s
e
d
P
I
con
t
ro
l
l
er
un
d
e
r
v
a
ryi
n
g
lo
ad
a
n
d
i
np
ut
c
on
di
t
i
o
n
s,
the f
o
l
l
ow
i
n
g sit
u
a
tio
ns
w
ere
ana
l
yse
d
.
a.
The
loa
d
h
as
v
a
r
ied
fr
om
R
t
o
R
L
l
oa
d,
t
he
o
u
t
pu
t
vo
l
t
age
a
nd
c
urre
nt
r
e
s
po
nse
u
nder
t
h
i
s
c
o
n
d
it
io
n
is
pl
otte
d in
F
ig
u
r
e
5.
T
he
r
efe
r
enc
e
v
o
l
ta
ge
i
s
ta
ke
n
a
s
2
3
0
V
/50
H
z
.
It
i
s
evident
from
t
h
e
wave
form
s
t
h
at
ou
tpu
t
v
ol
ta
ge
f
oll
o
w
s
r
e
f
er
ence
v
al
ue
(
2
30
V
/
50H
z
)
e
xact
l
y
a
ft
e
r
f
e
w
m
ill
ise
c
o
nd
s.
B
es
ides
t
he
w
a
ve
form
a
l
s
o
show
s
the
c
h
an
ge
i
n
the
pow
e
r
f
ac
t
o
r
after
a
n
a
dd
it
iona
l
RL
l
oa
d
is
c
onne
c
t
ed
at 0.
1
second.
F
i
gure
5.
E
ffe
c
t
of
l
o
a
d
c
han
g
e
s on
o
u
tp
ut v
o
lta
ge
a
n
d
c
urre
nt
w
a
v
e
form
of prop
ose
d
V
FC for a
step
ch
ange
fr
om
R
t
o
RL
l
oad
b.
The
effec
t
o
f
i
n
p
u
t
v
o
lta
ge
o
n
t
h
e
pro
pose
d
c
o
n
ve
rter
i
s
il
lu
st
r
a
te
d
i
n
F
i
gure
6.
I
n
th
i
s
case
,
t
he
i
n
p
u
t
vo
lta
ge,
V
in
is
c
han
g
e
d
f
rom
12
0V
/
6
0H
z
to
2
3
0
V
/
5
0
H
z
a
s
show
n
i
n
F
igu
r
e
6a
f
o
r
R
loa
d
.
Initia
ll
y
t
h
e
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
52
2 –
52
9
52
8
refere
nce
ou
t
vol
ta
ge
i
s
se
t
a
s
2
3
0
V
/
50H
z,
a
n
d
t
he
o
u
t
pu
t
v
o
lta
g
e
c
l
e
a
r
l
y
t
ra
ck
s
t
h
e
ref
e
ren
c
e
vo
lt
ag
e
as
dep
i
c
t
ed
i
n
F
i
g
u
r
e
6
c
.
W
he
n
V
in
i
s
c
h
ang
e
d
to
2
30
V/50
H
z
af
t
e
r
0
.
1
s
,
t
h
e
out
put
vol
ta
g
e
s
e
t
tl
e
s
to
t
he
new
re
fer
e
nce
v
a
l
u
e,
1
2
0
V
/
50H
z
as
s
how
n
in
F
ig
ure
6c
.
D
C
l
i
nk
v
ol
ta
g
e
i
s
regu
l
a
t
e
d
at
a
r
e
f
ere
n
c
e
val
u
e
of
3
5
0
V
w
i
t
h
a
s
lig
h
t
v
a
r
iat
i
o
n
,
as
d
e
p
ic
te
d
in
F
i
g
ure
6b
.
There
f
ore
,
f
r
o
m
F
i
gure
6
it
is
c
lear
t
h
a
t
syn
c
hro
n
o
u
s
r
efere
n
ce
fram
e
P
I
c
ont
r
o
l
l
er
s
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d
s
in
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egu
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a
t
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e
out
p
u
t
vo
lta
g
e
f
or
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a
r
ia
t
i
o
n
i
n
in
put
v
o
l
tage
w
hic
h
i
s
c
o
m
m
only
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oun
d
a
s
t
he
s
t
a
n
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ard
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l
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ag
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mai
n
s
lo
w
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t
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g
e
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l
y
i
n
vari
ous c
o
u
n
t
r
ie
s.
(a
)
(
b
)
(c)
F
i
gure
6.
E
ffe
c
t
of
i
n
put
v
olta
ge
var
i
a
tio
n
on
prop
o
sed
V
F
C. (a
) Input v
o
l
t
a
ge
w
ave
f
orm
(
b
) D
C
lin
k vo
l
t
age
(c) O
u
tp
ut v
o
lta
ge
r
espo
nse
6.
CONCL
U
S
ION
Th
is
p
aper
p
r
e
sen
t
ed
a
v
o
l
t
a
ge
frequ
e
n
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y
c
o
nver
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t
co
ul
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e
u
sed
in
p
ro
t
a
b
l
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lo
w
vo
lta
ge
V
F
C
.
It
e
mpl
oys
s
y
n
c
hr
o
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r
e
f
er
e
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ce
f
r
a
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b
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ed
P
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co
n
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ro
ll
er
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or
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u
t
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at
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y
r
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ula
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i
ng
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h
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ou
tpu
t
v
o
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ta
ge
i
n
ac
corda
n
c
e
w
ith
t
he
r
e
f
ere
n
ce
v
o
l
tage
.
LS
A
ba
sed
P
I
c
ont
r
o
ller
t
u
n
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ng
is
a
d
o
p
t
e
d
t
o
enha
nc
e
t
h
e
pe
rforma
n
ce
o
f
t
h
e
pro
pose
d
c
onve
rter.
In
a
d
d
i
tio
n,
s
i
m
u
l
ati
o
n
re
sul
t
s
su
cces
sfu
l
ly
s
u
pport
th
e
abi
l
i
t
y
o
f
t
h
e
con
v
e
r
ter
t
o
optim
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lly
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egu
l
a
t
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h
e
o
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t
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t
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o
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u
n
d
e
r
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a
ryi
n
g
l
o
ad
c
ondi
ti
o
n
s
a
n
d
i
n
put
c
o
ndit
i
o
n
s
.
ACKNOW
LEDG
E
MEN
T
S
Th
is
w
ork
w
a
s
su
pp
orte
d
b
y
t
he
U
n
i
t
e
d
A
r
ab
E
mira
t
e
s
U
n
i
v
er
si
t
y
(
U
A
E
U
)
u
n
d
e
r
G
r
a
n
t
3
1
N
3
4
8
-
1
6_7
_
S
URE+
20
18
REFE
RENCES
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Zio
gas,
e
t
al.,
"
O
p
t
i
m
u
m
sys
t
em
d
es
i
gn
o
f
a
t
hree
ph
ase
rec
t
i
f
i
e
r-inverter
type
o
f
freq
u
en
cy
c
h
a
ng
er
"
,
IEE
E
Tran
sac
t
io
ns
on
Ind
u
str
i
a
l
App
l
ic
a
t
ion
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5-1
2
2
5
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A
rg
o
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e
t
al.,
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A
co
nt
rol
m
e
th
o
d
f
or
s
i
ngle
p
h
ase
PW
M
in
verte
rs
,"P
r
oceedi
n
g
s
o
f
t
h
e
Inter
nati
onal Confer
ence
o
n
Po
wer
E
l
ectr
o
n
i
cs
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ve Systems
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t
al.
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"Fi
x
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swit
c
hi
ng
f
requ
e
n
cy
s
l
i
din
g
m
o
d
e
control
f
o
r
si
n
g
le-phase
u
nipol
a
r
inverters
"
,
IEE
E
T
r
a
n
sa
cti
o
n
s
o
n
P
o
wer
El
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t
al.,
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Z
ero-phase
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c
r
epet
itive
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or
a
s
in
gle-phas
e
P
W
M
i
n
v
ert
e
r"
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sacti
o
n
s
o
n P
o
wer
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ronics,
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o
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.
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an. 2
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Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
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86
94
Ana
l
y
s
i
s
and
des
i
g
n
of
s
i
n
g
l
e
-p
ha
se
v
o
lt
ag
e
-
fre
q
u
e
n
c
y
c
o
n
ver
t
e
r
wit
h
opt
imi
z
ed
PI c
o
nt
ro
l
l
e
r (M.
Asn
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M.
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R
y
an
a
nd
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D.
L
orenz,
"
A
s
ynchronous-fram
e
c
ontroll
e
r
fo
r
a
s
i
n
g
le-p
has
e
s
ine
wav
e
i
nve
rt
er"
,
P
roceedi
ngs
of
IEEE APEC
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1
3
-8
19
,
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e
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s
h
a
n
,
e
t
a
l
.
,
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A
D
-
Q
f
r
a
m
e
c
o
n
t
r
o
l
l
e
r
f
o
r
a
f
u
l
l
-
b
r
i
d
g
e
s
i
ngle
p
h
as
e
i
n
v
e
rter
u
s
e
d
i
n
s
m
a
ll
d
i
st
rib
u
t
e
d
po
wer
gen
e
ratio
n s
y
stem
s,"
P
r
oceedi
n
g
s
of
I
E
E
E
APEC
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eb.
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07,
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p
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41
-6
47
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u
n
,
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I
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t
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l
sy
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g
n
,
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n
t
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ems,
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2-4
1
,
2
0
0
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R.
O
rt
ega,
e
t
al
.,
"Con
tro
l
t
ech
niques
f
o
r
redu
ction
o
f
t
h
e
t
o
t
al
h
a
r
m
o
ni
c
d
i
s
t
o
r
tion
i
n
v
o
l
t
age
ap
pl
ied
t
o
a
s
i
ngle
-
ph
ase
inv
e
rter
w
ith
n
on
l
i
n
ear
l
oad
s
:
Revi
ew
."
R
e
n
ewa
b
le
an
d Su
sta
i
n
a
b
le
Ener
gy
Rev
i
e
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s
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l.
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Maswood,
a
nd
E
.
Al
-A
mmar,
"
Analysis
o
f
a
PWM
Volt
age
Sour
ce
Inv
e
rter
w
ith
P
I
Control
l
e
r
under
N
on-
ideal con
di
t
i
o
n
s",
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EE
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C
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93
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98
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010
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J.
H
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Z
h
ang
,
e
t
a
l
.,
"
S
e
lf
-organ
izing
g
e
neti
c
al
gorith
m
b
ased
t
un
in
g
of
P
ID
c
o
n
trol
le
rs"
,
Info
rma
t
io
n. Sc
ie
n
c
e
s
,
v
o
l
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9,
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–1
01
8,
2
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A.
K
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e
t
al.
,
"
Optimi
z
ed
P
I
D
C
ontro
ller
f
o
r
Both
S
i
n
gle
Ph
as
e
Inverter
a
nd
MPPT
S
EPIC
D
C/D
C
C
onvert
er
of
P
V
M
o
d
u
le",
I
EEE International Electr
i
c
Machines and Drives Confer
ence (IEM
D
C
)
,
pp.
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03
6-1
041
,
2
0
1
1
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[12]
Aru
n
k
u
m
a
r
G,
e
t al., "
P
aram
et
e
r
op
t
imi
zati
on o
f
t
hree ph
as
e
b
o
o
st
i
n
v
e
r
te
r
usin
g
g
e
ne
tic
a
l
go
rith
m
fo
r
line
a
r
l
oa
d
s
"
En
ergy Pr
oceedi
n
g
s
, vo
l
. 90
,
p
p
.
5
59
–5
65
,20
1
6
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T.
H
.
K
i
m
,
e
t
al.,
"
Robu
st
P
ID
c
on
tro
l
l
e
r
tu
ni
ng
b
ased
o
n
t
h
e
c
on
strai
n
ed
p
artic
l
e
s
warm
o
ptimi
zat
ion"
Automat
i
c
a
,
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al
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S
O
O
p
tim
izat
io
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F
o
r
So
lar
Sy
s
t
em
I
n
v
er
ter
Controller
And
Com
p
aris
o
n
B
et
ween
T
w
o
Co
ntro
lle
r Te
c
h
niqu
e
s
"
,
Jurn
a
l
T
ekno
l
o
g
i
.
7
8
.
1
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11
11
3/
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ait
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t
r
o
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eters
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e
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nn
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erter u
s
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g
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le s
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e
l
a
p
p
r
o
a
c
h
f
o
r
f
u
z
z
y
l
o
g
i
c
P
V
i
n
v
e
r
t
e
r
c
on
trolle
r
op
t
i
m
i
z
a
tio
n
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g
lig
h
t
n
i
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a
r
c
h
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ig
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n
g
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r
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m
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ati
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n
o
f
P
LL
a
lg
orit
h
m
s
f
or
s
ing
l
e
p
h
ase
g
r
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ecte
d
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u
s
t
ry Appli
c
a
t
io
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2
6
3
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.
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iob
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t
a
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l
.,
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N
ew
S
i
n
g
l
e-P
h
as
e
P
LL
S
t
ru
ctu
r
e
Bas
e
d
o
n
S
eco
nd
O
rde
r
G
en
eral
ized
I
n
t
eg
rator",
Power
El
ectro
n
i
cs
S
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eci
alists
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eren
ce,
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.
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C.
B
l
a
nco,
e
t
al
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"Q
uadrat
ure
S
i
g
n
al G
e
n
erato
r
bas
ed o
n All
-
P
a
s
s
F
ilt
e
r f
o
r
Single-P
h
ase
S
y
nchro
n
izatio
n"
[21]
N. M
.
Ab
del
-
Rahim
a
n
d J. E. Q
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ai
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aly
s
i
s
a
n
d
d
esi
g
n
of
a
mu
ltip
le
f
eed
bac
k
l
o
op
con
t
rol
strateg
y
f
o
r
si
ngle-
ph
ase v
o
l
t
age-s
o
u
r
ce UP
S
i
n
v
e
rters,"
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EE
T
r
a
n
sa
cti
ons o
n
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wer
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ectro
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i
cs
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l.
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l
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