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Appl
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wer
E
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(
I
J
AP
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)
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
,
p
p
.
6
6
6
~
6
7
5
I
SS
N:
2252
-
8
7
9
2
,
DOI
:
1
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1
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i
3
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pp
666
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675
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In
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e
q
u
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li
t
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p
o
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r
in
jec
ted
in
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o
t
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r
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e
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ially
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n
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e
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u
a
li
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d
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re
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q
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a
d
ra
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DQ
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o
n
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tec
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q
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e
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u
sin
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ra
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d
f
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in
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g
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c
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e
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ted
P
V
sy
ste
m
.
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e
DQ
c
o
n
tro
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m
e
th
o
d
sim
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v
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n
d
re
a
c
ti
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p
o
we
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b
y
tran
sfo
rm
i
n
g
th
re
e
-
p
h
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se
sig
n
a
ls
in
t
o
a
r
o
tati
n
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re
fe
re
n
c
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m
e
.
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h
il
e
P
I
c
o
n
tro
ll
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rs
a
re
wid
e
l
y
u
se
d
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th
e
y
o
ften
str
u
g
g
le
wit
h
n
o
n
-
li
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a
rit
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n
d
lo
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LCs
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h
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ir
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ise
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th
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m
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a
k
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th
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m
m
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ffe
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ti
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n
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e
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m
ic
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o
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i
ti
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e
sy
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m
u
n
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lu
d
e
s
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g
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n
e
ra
ti
o
n
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EVs
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a
n
d
n
o
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-
li
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e
a
r
lo
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d
s.
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rfo
rm
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n
c
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m
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tri
c
s
su
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s
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tal
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rm
o
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ic
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isto
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ti
o
n
(THD),
v
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lt
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g
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il
it
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,
a
n
d
p
o
we
r
fa
c
to
r
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re
a
n
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ly
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lt
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t
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o
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ll
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rs sig
n
ifi
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n
tl
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imp
r
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v
e
p
o
we
r
q
u
a
li
ty
a
n
d
sy
ste
m
re
sp
o
n
se
.
K
ey
w
o
r
d
s
:
B
id
ir
ec
tio
n
al
E
V
ch
ar
g
er
DQ
co
n
tr
o
l
E
V
ch
ar
g
in
g
Fu
zz
y
co
n
tr
o
l
Plu
g
-
in
elec
tr
ic
v
eh
icle
T
h
is i
s
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n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
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se
.
C
o
r
r
e
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p
o
nd
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A
uth
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r
:
Han
u
m
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Dep
ar
tm
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o
f
E
lectr
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an
d
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lectr
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ics E
n
g
in
ee
r
i
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g
,
Go
v
er
n
m
en
t Po
ly
tech
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ic
Ku
s
tag
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Kar
n
atak
a,
I
n
d
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E
m
ail:
h
an
u
m
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s
ag
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1
3
8
@
g
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co
m
1.
I
NT
RO
D
UCT
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O
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Po
wer
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ality
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in
p
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s
u
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ter
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tr
o
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u
cin
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co
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tech
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iq
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es
[
1
]
,
[
2
]
.
I
n
t
r
o
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atin
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tio
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ltag
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
I
mp
leme
n
ta
tio
n
o
f f
u
z
z
y
in
DQ
co
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tr
o
l o
f P
V
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ter
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p
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icles
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667
co
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s
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ib
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FAC
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S
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ev
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ik
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DSTA
T
C
OM
[
3
]
,
[
4
]
.
E
lectr
ical
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g
in
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s
ar
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co
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ce
r
n
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d
with
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o
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ith
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C
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[
5
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[
8
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Nu
m
e
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s
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ted
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[
7
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[
9
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-
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1
2
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d
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tech
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[
1
3
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[
1
9
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Oth
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is
cu
s
s
ed
in
[
2
0
]
-
[
2
7
]
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
i
-
co
s
ap
p
r
o
ac
h
is
ev
alu
ated
u
n
d
e
r
a
v
ar
iety
o
f
lo
ad
i
n
g
co
n
d
itio
n
s
,
in
clu
d
in
g
non
-
lin
ea
r
an
d
E
V
lo
ad
s
.
Fo
r
an
y
p
o
wer
c
o
n
tr
o
ller
s
in
th
e
p
o
wer
s
y
s
tem
th
e
v
o
ltag
e
an
d
f
r
eq
u
en
c
y
co
n
tr
o
l
is
p
r
im
ar
y
.
Fre
q
u
en
cy
c
o
n
tr
o
l
i
s
m
ad
e
p
o
s
s
ib
le
u
s
in
g
th
e
p
h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
,
wh
ile
v
o
ltag
e
co
n
tr
o
l
is
d
ev
elo
p
e
d
u
s
in
g
th
e
v
o
ltag
e
r
eg
u
latio
n
c
o
n
tr
o
ller
.
Usu
ally
,
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
(
PI
)
c
o
n
t
r
o
ller
s
ar
e
u
s
ed
in
th
e
v
o
ltag
e
an
d
t
h
e
cu
r
r
e
n
t
co
n
tr
o
l
lo
o
p
u
s
ed
in
th
e
co
n
t
r
o
ll
er
s
.
T
h
e
v
o
ltag
e
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
li
n
g
(
PC
C
)
is
co
n
tr
o
lled
b
y
th
e
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
(
PI)
co
n
tr
o
ll
er
.
Simu
ltan
eo
u
s
ly
,
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
DC
b
u
s
ca
p
ac
ito
r
is
m
an
ag
ed
b
y
estab
lis
h
in
g
th
e
r
ef
er
en
ce
f
o
r
th
e
d
i
r
ec
t a
x
is
co
m
p
o
n
e
n
t w
ith
in
th
e
v
o
ltag
e
r
eg
u
latio
n
co
n
tr
o
ller
.
T
h
e
r
esu
lts
will b
e
an
aly
ze
d
f
o
llo
win
g
th
e
s
u
b
s
titu
tio
n
o
f
th
e
PI
co
n
t
r
o
ller
with
a
f
u
zz
y
c
o
n
tr
o
ller
.
2.
M
E
T
H
O
D
T
h
e
b
lo
c
k
d
ia
g
r
am
f
o
r
th
e
d
ir
ec
t
-
q
u
ad
r
at
u
r
e
(
DQ
)
c
o
n
tr
o
lle
d
s
o
lar
in
te
g
r
ated
elec
tr
ic
v
eh
icle
in
th
e
g
r
id
is
as
g
iv
e
n
in
Fig
u
r
e
1
.
P
h
o
to
v
o
ltaic
(
PV
)
p
o
wer
is
in
t
eg
r
ated
t
o
th
e
g
r
id
t
h
r
o
u
g
h
th
e
g
r
id
s
id
e
i
n
v
er
ter
.
T
h
e
PV
s
y
s
tem
is
in
teg
r
ated
with
a
b
o
o
s
t
co
n
v
er
ter
,
w
h
ich
is
co
n
tr
o
lled
th
r
o
u
g
h
a
f
ee
d
f
o
r
war
d
lo
o
p
f
o
r
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT
)
,
as
illu
s
tr
ated
in
t
h
e
d
iag
r
am
.
T
h
e
MPPT
co
n
tr
o
l
r
eg
u
lates
th
e
PV
v
o
ltag
e
at
t
h
e
m
a
x
im
u
m
p
o
we
r
p
o
i
n
t.
T
h
e
p
u
ls
es
ar
e
s
u
b
s
eq
u
en
tly
o
u
t
p
u
tted
.
T
h
e
b
o
o
s
t
c
o
n
v
er
ter
s
u
b
s
eq
u
en
tly
m
o
d
if
ies
th
e
v
o
ltag
e
to
alig
n
with
th
e
r
eq
u
ir
ed
DC
lin
k
s
p
ec
if
icatio
n
s
.
Su
b
s
eq
u
e
n
tly
,
t
h
e
DC
co
n
n
ec
tio
n
tr
an
s
m
its
th
e
s
ig
n
al
to
a
DC
to
AC
co
n
v
er
te
r
.
T
h
e
g
r
id
is
s
u
b
s
eq
u
en
tly
c
o
n
n
ec
ted
to
t
h
e
AC
v
o
ltag
e.
T
h
is
s
y
s
tem
in
co
r
p
o
r
ates
b
o
th
lin
e
ar
an
d
n
o
n
-
lin
ea
r
l
o
ad
co
m
b
in
atio
n
s
.
T
h
e
in
v
er
ter
is
r
eq
u
ir
e
d
to
m
an
ag
e
p
o
wer
q
u
ality
ch
allen
g
es
ar
is
in
g
f
r
o
m
th
e
co
m
b
in
atio
n
o
f
lin
ea
r
a
n
d
n
o
n
-
lin
ea
r
lo
ad
s
.
T
h
e
d
-
q
-
tec
h
n
iq
u
e
is
u
s
ed
in
th
e
in
v
eter
to
p
er
f
o
r
m
th
e
ac
tiv
e
p
o
wer
f
ilter
o
p
er
atio
n
.
T
h
e
d
-
q
tech
n
iq
u
e
is
d
er
iv
ed
f
r
o
m
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es.
T
h
e
d
-
q
is
d
ir
ec
t
a
n
d
q
u
ad
r
atu
r
e
ax
is
.
T
h
e
d
a
n
d
q
co
m
p
o
n
e
n
ts
ar
e
p
er
p
en
d
icu
lar
to
ea
ch
o
th
e
r
.
T
h
e
s
et
v
o
ltag
e
is
co
m
p
ar
ed
ag
a
in
s
t
th
e
m
ea
s
u
r
ed
v
o
ltag
e.
T
h
i
s
v
o
ltag
e
r
ep
r
esen
ts
th
e
v
o
ltag
e
er
r
o
r
.
T
h
e
wac
e
f
o
r
m
is
p
r
o
ce
s
s
ed
b
y
th
e
PI
co
n
tr
o
ller
.
T
h
e
co
r
r
esp
o
n
d
in
g
cu
r
r
en
t
is
p
r
o
d
u
ce
d
in
th
is
co
n
tex
t.
T
h
is
f
ac
ilit
ates th
e
r
eg
u
latio
n
o
f
th
e
DC
lin
k
wit
h
in
th
e
in
v
e
r
ter
s
y
s
tem
.
T
h
e
d
ir
ec
t a
x
is
cu
r
r
en
t is
d
eter
m
in
ed
u
s
in
g
th
e
f
o
r
m
u
la
p
r
esen
ted
in
(
1
)
.
∗
=
∗
.
;
∗
=
∗
.
∗
=
∗
.
}
(
1
)
W
h
er
e,
=
=
=
}
(
2
)
wh
er
e
,
,
an
d
ar
e
th
e
in
s
tan
tan
eo
u
s
v
o
ltag
e
, a
n
d
th
e
m
ag
n
itu
d
e
is
.
=
{
2
3
(
2
+
2
+
2
)
}
1
2
(
3
)
Fo
r
q
u
ad
r
atu
r
e
c
u
r
r
en
t
r
ef
er
e
n
ce
is
ca
lcu
lated
as in
(
4
)
.
∗
=
∗
.
;
∗
=
∗
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∗
=
∗
.
}
(
4
)
W
h
er
e
,
,
an
d
ar
e
u
s
in
g
th
e
f
o
r
m
u
la
s
tated
in
(
5
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
6
6
6
-
675
668
=
−
+
√
3
=
√
3
+
−
2
√
3
=
−
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3
+
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2
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3
}
(
5
)
T
h
e
ac
tu
al
co
n
tr
o
l is
r
ep
r
esen
t
ed
in
F
ig
u
r
e
1.
T
h
e
s
u
m
o
f
d
ir
ec
t a
n
d
q
u
a
d
r
atu
r
e
ax
is
c
o
n
tr
o
l c
u
r
r
e
n
t is
g
iv
en
in
(
6
)
∗
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;
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=
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;
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;
}
(
6
)
T
h
e
cu
r
r
en
t
f
r
o
m
th
e
(
6
)
is
r
ef
er
r
ed
with
th
e
s
u
p
p
ly
cu
r
r
en
t
an
d
th
e
d
u
ty
c
y
cle
is
cr
ea
te
d
f
r
o
m
th
at
th
e
p
u
ls
es
ar
e
g
en
er
ated
.
T
h
is
is
g
iv
en
to
th
e
co
n
v
e
r
ter
.
T
h
is
co
n
tr
o
ls
th
e
p
o
wer
f
ac
to
r
an
d
q
u
ality
o
f
t
h
e
s
u
p
p
ly
.
Fig
u
r
e
2
s
h
o
ws th
e
f
lo
w
d
iag
r
am
.
Fig
u
r
e
1.
T
est s
etu
p
f
o
r
test
in
g
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
(
d
er
iv
ed
f
r
o
m
[
2
6
]
)
Fig
u
r
e
2
.
C
o
n
tr
o
l b
lo
c
k
d
iag
r
a
m
o
f
DQ
m
eth
o
d
(
d
er
iv
ed
f
r
o
m
[
2
7
]
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
I
mp
leme
n
ta
tio
n
o
f f
u
z
z
y
in
DQ
co
n
tr
o
l o
f P
V
b
a
s
ed
in
ve
r
ter
w
ith
p
lu
g
in
elec
tr
ic
ve
h
icles
(
Ha
n
u
mesh
)
669
2
.
1
.
P
I
co
ntr
o
ller
im
plem
ent
a
t
io
n
T
h
e
2
µs
tim
e
s
tep
PI
c
o
n
tr
o
l
ler
is
h
er
e
to
co
n
tr
o
l
th
e
DC
lin
k
v
o
ltag
e.
T
h
e
d
is
cr
ete
PI
co
n
tr
o
ller
eq
u
atio
n
s
p
ec
if
ic
to
th
e
Vd
c
e
r
r
o
r
is
g
iv
en
in
(
7
)
.
T
h
e
v
alu
e
s
f
o
r
KP
an
d
KI
ar
e
tu
n
ed
u
s
in
g
th
e
MA
T
L
AB
-
b
ased
ar
b
itra
r
y
tu
n
in
g
m
eth
o
d
.
=
(
+
−
1
)
×
(
7
)
2
.
2
.
F
uzzy
lo
g
ic
i
m
plem
ent
a
t
io
n
T
h
e
lo
g
ic
o
f
f
u
zz
y
co
n
tr
o
l
is
im
p
lem
en
ted
at
th
e
DC
lin
k
c
o
n
tr
o
l
p
ar
t
o
f
th
e
DQ
co
n
tr
o
ller
.
Her
e
,
th
e
r
u
les
ar
e
f
o
r
m
e
d
ac
co
r
d
in
g
t
o
t
h
e
r
esu
lts
ac
h
iev
ed
.
Her
e
,
t
h
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
ar
e
f
o
r
m
ed
lik
e
N
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n
eg
ati
v
e
v
alu
e
,
P
-
p
o
s
itiv
e
v
alu
e
,
a
n
d
Z
-
ze
r
o
v
alu
e.
E
r
r
o
r
is
th
e
v
alu
e
m
ea
s
u
r
ed
d
ir
ec
tly
f
r
o
m
th
e
c
o
m
p
ar
ato
r
.
T
h
e
c
h
-
er
r
o
r
is
th
e
s
am
p
les
o
f
0
.
1
m
s
f
r
o
m
th
e
co
m
p
ar
ato
r
.
T
a
b
le
1
s
h
o
ws
th
e
f
u
zz
y
r
u
le
with
a
3
×
3
in
f
er
en
ce
s
y
s
tem
.
T
ab
le
1
.
F
u
zz
y
r
u
le
with
3
×
3
i
n
f
er
en
ce
s
y
s
tem
Er
r
o
r
/
c
h
-
e
r
r
o
r
N
Z
P
N
N
P
Z
Z
P
N
Z
P
N
Z
P
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
MA
T
L
AB
Simu
lin
k
s
o
f
t
war
e
was
u
tili
ze
d
t
o
c
o
n
d
u
ct
th
e
s
im
u
latio
n
s
tu
d
ies
o
f
th
e
s
u
g
g
ested
s
y
s
tem
th
at
is
d
ep
icted
in
Fig
u
r
e
1
.
I
n
T
ab
le
2
,
th
e
s
im
u
latio
n
s
p
ec
if
icatio
n
s
ar
e
p
r
esen
ted
f
o
r
y
o
u
r
p
e
r
u
s
al.
T
h
e
p
o
wer
is
b
ein
g
g
en
er
ate
d
b
y
th
e
PV
s
y
s
tem
h
er
e.
T
h
r
o
u
g
h
th
e
u
s
e
o
f
th
e
in
v
er
ter
,
th
is
DC
is
co
n
v
er
ted
in
t
o
AC
.
W
h
en
o
p
e
r
atin
g
i
n
c
o
n
v
e
n
tio
n
al
m
o
d
e,
t
h
e
in
v
er
ter
is
co
n
t
r
o
lled
b
y
a
DQ
c
o
n
tr
o
ller
in
c
o
n
ju
n
ctio
n
with
a
PI
co
n
tr
o
ller
,
a
nd
by
u
t
ilizin
g
a
DQ
co
n
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ller
in
c
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u
n
ctio
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u
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y
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e
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o
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o
s
ed
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eth
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d
.
T
h
e
p
h
o
t
o
v
o
ltaic
(
PV)
p
o
we
r
g
en
er
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n
is
d
ep
icted
i
n
Fig
u
r
e
3
.
I
n
th
is
ex
am
p
le,
th
e
P
V
p
o
wer
is
o
b
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ed
f
r
o
m
an
ir
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ia
n
ce
o
f
0
.
4
k
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,
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en
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ec
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4
k
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.
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h
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r
ly
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ch
ch
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u
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Fig
u
r
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3
,
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ich
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em
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ates
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m
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ar
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PI
an
d
DQ
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a
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cise m
an
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ab
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2
.
R
atin
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Fig
u
r
e
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Fig
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.
Z
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I
SS
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2
2
5
2
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9
2
I
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p
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,
Vo
l.
14
,
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.
3
,
Sep
tem
b
er
20
25
:
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6
6
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675
670
T
ak
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g
PI
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n
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f
o
r
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m
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ar
is
o
n
,
th
e
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u
zz
y
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co
n
tr
o
ller
ex
h
ib
its
a
lo
wer
lev
el
o
f
r
ip
p
les.
Fig
u
r
e
5
d
ep
icts
th
e
p
o
wer
m
e
asu
r
ed
at
lin
ea
r
lo
ad
f
o
r
y
o
u
r
r
ef
er
en
ce
.
T
h
is
was
a
r
ep
r
esen
t
atio
n
o
f
th
e
p
o
wer
s
h
if
t
th
at
is
tak
in
g
p
lace
in
th
e
lin
ea
r
lo
ad
.
T
h
e
co
m
p
ar
is
o
n
o
f
p
o
wer
at
th
e
p
o
in
t
o
f
PC
C
b
etwe
en
PI
an
d
D
Q
co
n
tr
o
l
an
d
f
u
zz
y
co
n
t
r
o
l
is
d
ep
icted
in
Fig
u
r
e
6
.
T
h
e
p
o
w
er
f
ed
to
th
e
g
r
id
is
r
ep
r
esen
ted
b
y
th
e
n
eg
ativ
e
p
o
wer
.
W
h
ile
th
e
p
o
wer
th
at
is
s
en
t
to
th
e
g
r
id
i
n
f
u
zz
y
D
Q
co
n
tr
o
ller
s
is
6
5
k
W
,
t
h
e
p
o
w
er
th
at
is
s
en
t
to
th
e
g
r
id
in
PI
co
n
tr
o
l
DQ
is
6
0
kW
.
T
h
e
p
o
wer
r
esp
o
n
s
iv
en
ess
i
s
im
p
r
o
v
ed
b
y
u
s
in
g
a
f
u
z
zy
co
n
tr
o
ller
with
a
DQ
s
y
s
tem
.
Fig
u
r
e
7
s
h
o
ws
th
e
b
atter
y
S
OC
,
c
u
r
r
en
t
,
an
d
v
o
ltag
e.
T
h
e
SOC
in
cr
ea
s
es
f
r
o
m
0
to
0
.
3
s
ec
o
n
d
s
.
It
d
is
ch
ar
g
es
an
d
d
r
o
p
s
d
u
r
i
n
g
0
.
3
to
0
.
6
s
ec
o
n
d
s
.
T
h
e
n
,
d
u
r
in
g
0
.
6
to
1
s
ec
o
n
d
s
,
it
is
ch
ar
g
i
n
g
ag
ain
.
Fig
u
r
e
8
d
ep
icts
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD
)
o
f
th
e
v
o
ltag
e
f
o
r
th
e
PI
co
n
tr
o
ller
.
On
e
last
th
in
g
to
co
n
s
id
er
is
Fig
u
r
e
9
,
wh
ich
illu
s
tr
ates
th
e
cu
r
r
en
t
T
HD
f
o
r
th
e
PI
co
n
v
e
n
tio
n
al
co
n
tr
o
ller
.
Fig
u
r
e
1
0
d
ep
icts
th
e
T
HD
an
d
v
o
ltag
e
o
f
th
e
f
u
zz
y
DQ
co
n
t
r
o
ller
.
T
h
e
T
HD
f
o
r
th
e
f
u
zz
y
DQ
co
n
tr
o
ller
is
d
ep
icted
in
Fig
u
r
e
1
0
.
W
h
en
co
n
tr
asted
with
th
e
PI
co
n
tr
o
ll
er
,
th
e
cu
r
r
en
t to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
an
d
v
o
lta
g
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
th
e
f
u
zz
y
DQ
co
n
tr
o
ller
ar
e
d
e
em
ed
to
b
e
lo
wer
,
wh
ich
is
s
h
o
wn
in
Fig
u
r
e
1
1
.
Fro
m
th
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b
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er
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atio
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of
d
if
f
er
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n
t
s
im
u
latio
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s
,
it c
an
b
e
in
f
e
r
r
ed
th
at
th
e
f
u
zz
y
l
o
g
ic
-
b
ased
im
p
lem
en
tatio
n
is
ad
v
an
tag
eo
u
s
i
n
T
HD
r
ed
u
ctio
n
in
th
e
PC
C
o
f
th
e
p
o
wer
s
y
s
tem
.
B
o
th
cu
r
r
en
t
an
d
v
o
ltag
e
wav
e
f
o
r
m
clea
r
ly
r
ed
u
ce
s
th
e
T
HD
in
b
o
th
wav
ef
o
r
m
s
.
Fig
u
r
e
5
.
P
o
wer
m
ea
s
u
r
ed
at
li
n
ea
r
lo
ad
Fig
u
r
e
6
.
C
o
m
p
a
r
ativ
e
an
aly
s
i
s
o
f
f
u
zz
y
DQ
co
n
tr
o
l
an
d
PI
co
n
tr
o
l w
ith
r
e
g
ar
d
t
o
p
o
wer
at
PC
C
Fig
u
r
e
7
.
B
atter
y
SOC
,
cu
r
r
en
t
,
an
d
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
I
mp
leme
n
ta
tio
n
o
f f
u
z
z
y
in
DQ
co
n
tr
o
l o
f P
V
b
a
s
ed
in
ve
r
ter
w
ith
p
lu
g
in
elec
tr
ic
ve
h
icles
(
Ha
n
u
mesh
)
671
Fig
u
r
e
8
.
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
m
ea
s
u
r
ed
f
o
r
v
o
ltag
e
u
s
in
g
PI
co
n
tr
o
ller
Fig
u
r
e
9
.
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
m
ea
s
u
r
ed
f
o
r
cu
r
r
e
n
t
u
s
i
n
g
PI
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
6
6
6
-
675
672
Fig
u
r
e
1
0
.
T
o
tal
h
ar
m
o
n
i
c
d
is
to
r
tio
n
m
ea
s
u
r
e
d
f
o
r
v
o
ltag
e
u
s
in
g
f
u
zz
y
co
n
t
r
o
ller
Fig
u
r
e
1
1
.
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
m
ea
s
u
r
e
d
f
o
r
cu
r
r
en
t u
s
in
g
f
u
zz
y
co
n
t
r
o
ller
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
d
em
o
n
s
tr
ates
th
e
ef
f
ec
tiv
en
ess
o
f
f
u
zz
y
lo
g
ic
c
o
n
tr
o
ller
s
o
v
e
r
tr
ad
itio
n
al
PI
co
n
tr
o
ller
s
with
in
th
e
DQ
co
n
tr
o
l
f
r
am
e
wo
r
k
f
o
r
g
r
i
d
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
.
I
n
s
ce
n
ar
io
s
in
v
o
l
v
in
g
p
lu
g
-
in
elec
tr
ic
v
eh
icles
(
PEVs)
an
d
n
o
n
-
lin
ea
r
lo
a
d
s
,
m
ain
tain
in
g
p
o
we
r
q
u
ality
b
ec
o
m
es
in
cr
ea
s
in
g
ly
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
I
mp
leme
n
ta
tio
n
o
f f
u
z
z
y
in
DQ
co
n
tr
o
l o
f P
V
b
a
s
ed
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ve
r
ter
w
ith
p
lu
g
in
elec
tr
ic
ve
h
icles
(
Ha
n
u
mesh
)
673
ch
allen
g
in
g
d
u
e
to
d
y
n
am
ic
a
n
d
h
ar
m
o
n
ic
d
is
tu
r
b
a
n
ce
s
.
W
h
ile
PI
co
n
tr
o
ller
s
o
f
f
e
r
s
im
p
licity
an
d
ar
e
wid
ely
u
s
ed
,
th
eir
p
er
f
o
r
m
a
n
ce
d
e
g
r
a
d
es u
n
d
e
r
n
o
n
lin
ea
r
an
d
tim
e
-
v
ar
y
in
g
co
n
d
itio
n
s
.
Fu
zz
y
co
n
tr
o
ller
s
,
b
y
co
n
tr
ast,
p
r
o
v
id
e
ad
ap
tiv
e
an
d
r
o
b
u
s
t
c
o
n
tr
o
l
with
o
u
t
r
eq
u
ir
in
g
an
e
x
ac
t
m
ath
em
atica
l
m
o
d
el.
Simu
latio
n
r
esu
lts
s
h
o
w
th
at
f
u
zz
y
lo
g
ic
s
ig
n
if
ican
tly
im
p
r
o
v
es
k
ey
p
e
r
f
o
r
m
an
ce
m
etr
ics
s
u
ch
as
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
v
o
ltag
e
s
tab
ilit
y
,
a
n
d
d
y
n
a
m
ic
r
esp
o
n
s
e.
T
h
ese
im
p
r
o
v
em
en
ts
lead
to
m
o
r
e
r
eliab
le
a
n
d
ef
f
icien
t
p
o
we
r
in
jectio
n
in
to
t
h
e
g
r
i
d
,
ev
e
n
u
n
d
er
c
o
m
p
lex
o
p
er
atin
g
co
n
d
i
tio
n
s
.
T
h
er
ef
o
r
e,
f
u
zz
y
lo
g
ic
c
o
n
tr
o
ller
s
p
r
esen
t
a
s
u
p
er
io
r
alter
n
ativ
e
to
PI
co
n
tr
o
ller
s
f
o
r
en
h
an
cin
g
p
o
wer
q
u
ality
in
m
o
d
er
n
PV
s
y
s
tem
s
,
esp
ec
ially
i
n
en
v
ir
o
n
m
en
ts
with
h
ig
h
v
ar
ia
b
ilit
y
an
d
n
o
n
-
lin
ea
r
b
eh
a
v
io
r
.
T
h
eir
in
teg
r
atio
n
in
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