I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
(
I
J
P
E
DS
)
Vo
l.
10
,
No
.
3
,
Sep
2
0
1
9
,
p
p
.
161
3
~
1
6
2
7
I
SS
N:
2088
-
8
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9
4
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DOI
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.
1
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.
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.
pp
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-
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6
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1613
J
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JP
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DS
Co
ntrol o
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p
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d in
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endzi
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rsity
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p
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rtme
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El
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IR
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Lab
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nfo
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ticle
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y:
R
ec
eiv
ed
Dec
7
,
2
0
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R
ev
is
ed
Feb
14
,
2
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Acc
ep
ted
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r
8
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2
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In
th
is p
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o
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is p
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te an
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ter
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y
m
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a
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sta
ti
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c
o
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rters
(c
h
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p
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r/i
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rter).
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n
t
h
e
p
h
o
t
o
v
o
lt
a
ic
c
o
n
v
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rsio
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c
h
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a
c
o
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tro
ll
e
r
fo
r
trac
k
in
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t
h
e
m
a
x
imu
m
p
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we
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p
o
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t
is
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e
sig
n
e
d
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sin
g
th
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d
irec
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p
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th
e
P
e
rtu
rb
a
n
d
o
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se
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v
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m
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d
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d
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ste
m
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th
e
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y
lo
g
ic.
T
h
e
sim
u
latio
n
wa
s
d
o
n
e
t
o
p
ro
v
e
th
e
v
a
li
d
it
y
o
f
th
e
stra
teg
y
a
n
d
o
f
th
e
c
o
n
tr
o
l
m
e
th
o
d
u
se
d
f
o
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th
e
c
o
n
tr
o
l
o
f
t
h
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p
o
we
r
g
e
n
e
ra
ted
b
y
t
h
e
h
y
b
ri
d
sy
ste
m
.
K
ey
w
o
r
d
s
:
W
in
d
tu
r
b
in
e
Do
u
b
ly
f
e
d
in
d
u
ctio
n
g
en
er
ato
r
Ph
o
to
v
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ltaic
Fu
zz
y
lo
g
ic
C
o
n
tr
o
l o
f
p
o
wer
Co
p
y
rig
h
t
©
2
0
1
9
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mo
h
am
m
ed
Ke
n
d
zi,
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
Sm
ar
t G
r
id
s
an
d
R
en
ewa
b
le
E
n
er
g
ies L
ab
o
r
ato
r
y
,
T
ah
r
i M
o
h
a
m
m
ed
B
ec
h
ar
U
n
iv
er
s
ity
,
Un
iv
er
s
ity
o
f
T
a
h
r
i M
o
h
a
m
ed
,
B
ec
h
ar
,
B
.
P 4
1
7
B
ec
h
ar
0
8
0
0
0
,
Alg
er
ia.
E
m
ail: k
en
d
zim
o
h
am
m
ed
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
R
en
ewa
b
le
en
er
g
ies
h
av
e
b
ec
o
m
e
v
er
y
p
r
o
m
is
in
g
s
o
u
r
ce
s
o
f
f
u
tu
r
e
en
er
g
y
r
eso
u
r
ce
s
in
th
e
wo
r
ld
,
p
r
im
ar
ily
b
ec
au
s
e
o
f
th
eir
o
wn
n
atu
r
e,
an
d
also
b
ec
au
s
e
o
f
th
e
d
im
in
is
h
in
g
r
eser
v
es
o
f
tr
ad
itio
n
al
r
eso
u
r
ce
s
(
o
il,
g
as,
etc.
)
.
.
)
,
Dem
o
g
r
ap
h
ic
an
d
ec
o
n
o
m
ic
g
r
o
wth
[
1
,
2
]
.
W
h
er
e
th
e
u
s
e
o
f
th
ese
s
o
u
r
ce
s
to
g
en
er
ate
elec
tr
icity
h
as b
ee
n
s
ee
n
s
in
ce
th
e
last
d
ec
ad
e
[
3
]
.
T
h
e
m
ain
ad
v
an
tag
e
o
f
r
en
ewa
b
le
s
o
u
r
ce
s
is
th
e
ab
s
en
ce
o
f
h
ar
m
f
u
l
em
is
s
io
n
s
.
On
e
way
to
g
en
er
ate
elec
tr
icity
f
r
o
m
r
en
ewa
b
le
s
o
u
r
ce
s
is
to
u
s
e
win
d
an
d
p
h
o
to
v
o
ltaic
po
wer
,
m
ain
ly
b
ec
au
s
e
it
is
clea
n
[
4
]
.
T
h
e
h
y
b
r
id
s
y
s
tem
is
ac
h
iev
ed
in
r
en
ewa
b
le
en
er
g
ies
co
n
s
is
tin
g
o
f
win
d
en
er
g
y
an
d
p
h
o
to
v
o
ltaic
(
PV)
en
er
g
y
f
o
r
p
ar
allel
p
er
f
o
r
m
an
ce
o
f
th
ese
two
s
o
u
r
ce
s
,
en
s
u
r
in
g
DFI
G
tr
ain
in
g
an
d
m
ax
im
izin
g
p
o
wer
g
en
er
ati
o
n
with
b
etter
ef
f
icien
cy
[
5
,
6
]
th
r
o
u
g
h
th
e
in
teg
r
atio
n
o
f
f
o
g
g
y
lo
g
ic
tech
n
o
lo
g
y
to
en
s
u
r
e
co
n
tr
o
l o
f
p
o
wer
s
Dep
o
s
ited
to
war
d
s
th
e
n
etwo
r
k
.
T
h
is
co
n
tr
o
l
tech
n
o
lo
g
y
is
s
im
p
le
in
its
im
p
lem
en
tatio
n
an
d
its
r
elativ
ely
s
atis
f
ac
to
r
y
ef
f
icien
cy
(
f
o
r
s
o
m
e
ap
p
licatio
n
s
)
,
an
d
th
e
ea
s
e
o
f
o
p
er
atio
n
an
d
lo
w
co
s
t
o
f
th
ese
co
n
tr
o
ller
s
ar
e
th
e
m
ain
r
ea
s
o
n
s
f
o
r
its
s
u
cc
ess
[
7
]
.
Fu
zz
y
lo
g
ic
is
th
er
ef
o
r
e
o
n
e
o
f
th
e
im
p
o
r
tan
t
b
r
an
ch
es
o
f
ar
tific
ial
in
tellig
en
ce
am
o
n
g
all
in
tellig
en
t te
ch
n
iq
u
es,
t
h
e
s
im
p
lest
m
eth
o
d
o
f
co
n
tr
o
l to
b
e
im
p
lem
en
ted
in
p
r
ac
tice.
[
8
,
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
3
,
Sep
201
9
:
1
6
1
3
–
1
6
2
7
1614
T
h
e
wo
r
k
p
r
esen
te
d
in
t
h
is
p
ap
er
r
elate
s
to
t
h
e
im
p
lem
e
n
tatio
n
o
f
th
e
DFI
G
win
d
tu
r
b
i
n
e
co
n
tr
o
l
s
tr
ateg
y
an
d
th
e
s
u
p
p
ly
o
f
r
o
t
o
r
f
r
o
m
a
PV
g
e
n
er
ato
r
.
T
h
is
s
y
s
tem
is
co
n
tr
o
lled
b
y
f
o
g
g
y
lo
g
ic
tech
n
o
lo
g
y
.
T
h
e
r
eg
u
latio
n
o
f
th
is
p
ap
e
r
is
as
f
o
llo
ws:
I
n
Sectio
n
2
,
we
in
tr
o
d
u
ce
t
h
e
p
r
o
p
o
s
ed
m
ix
ed
s
y
s
tem
(
PV/
win
d
)
.
3
r
d
s
ec
tio
n
was
d
esig
n
ed
to
m
o
d
el
h
y
b
r
id
s
y
s
tem
co
m
p
o
n
e
n
ts
.
I
n
Sectio
n
4
,
a
co
n
tr
o
l
s
tr
ateg
y
is
p
r
esen
ted
.
I
n
Sectio
n
5
,
th
e
p
r
i
n
cip
l
e
o
f
p
r
ec
is
e
l
o
g
ical
c
o
n
tr
o
l
is
d
e
s
cr
ib
ed
an
d
u
s
ed
in
th
e
d
esig
n
o
f
m
is
ty
lo
g
ical
co
n
tr
o
ller
s
.
T
h
e
p
h
o
to
v
o
ltaic
s
y
s
tem
m
o
d
el
is
ac
h
iev
ed
in
Sectio
n
VI
.
I
n
Sectio
n
7
,
we
d
escr
ib
e
th
e
MPPT
s
tr
u
ctu
r
e
ap
p
lied
to
th
e
PV
s
y
s
tem
.
T
h
e
s
im
u
latio
n
r
esu
l
ts
an
d
co
n
cl
u
s
io
n
s
ar
e
s
u
m
m
ar
ized
in
t
h
e
last
s
ec
tio
n
s
2.
P
RE
S
E
NT
AT
I
O
N
O
F
T
H
E
H
YB
RID
SYS
T
E
M
(
P
H
O
T
O
VO
L
T
A
I
C/
W
I
ND)
T
h
e
h
y
b
r
i
d
p
o
wer
s
y
s
tem
co
n
tain
s
two
co
n
v
er
s
io
n
ch
ai
n
s
.
T
h
e
f
ir
s
t
ch
ain
is
a
wi
n
d
p
o
wer
co
n
v
er
s
io
n
s
y
s
tem
,
co
n
tain
i
n
g
a
DFI
G
co
n
n
ec
ted
d
i
r
ec
tly
to
th
e
n
etwo
r
k
s
.
T
h
e
s
ec
o
n
d
c
h
ain
is
a
p
h
o
to
v
o
ltaic
co
n
v
er
s
io
n
s
y
s
tem
.
T
h
e
p
o
w
er
g
en
er
ate
d
b
y
th
e
DFI
G
is
co
n
tr
o
lled
b
y
t
h
e
tech
n
i
q
u
e
o
f
th
e
f
u
zz
y
l
o
g
ic
.
T
h
e
PV
g
en
er
ato
r
is
u
s
ed
to
s
u
p
p
ly
t
h
e
DFI
G
r
o
to
r
,
wh
ile
t
h
e
r
est
o
f
th
e
g
en
e
r
ated
p
o
wer
is
in
jecte
d
in
to
th
e
g
r
id
.
Fig
u
r
e
1
s
h
o
ws th
e
b
lo
ck
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
p
o
wer
s
y
s
tem
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
t
h
e
h
y
b
r
id
p
o
wer
s
y
s
tem
3.
M
O
DE
L
I
NG
O
F
T
N
E
CO
N
VE
RS
I
O
N
H
YB
R
I
D
SY
ST
E
M
3
.
1
.
M
o
del o
f
t
he
t
urbin
e
T
h
e
ae
r
o
tu
r
b
in
e
is
co
m
p
o
s
ed
o
f
th
r
ee
p
ales
o
f
len
g
th
R
o
n
o
n
e
tr
ee
,
a
tu
r
b
in
e
an
d
a
g
ea
r
b
o
x
with
a
g
ain
G
.
T
h
e
g
en
er
at
o
r
s
h
af
t is
m
o
d
eled
b
y
th
e
f
o
llo
win
g
e
q
u
atio
n
[
1
0
]
:
m
e
c
g
e
m
m
e
c
d
J
dt
f
CC
=
−
−
(
1
)
,,
a
e
r
a
e
r
m
e
c
g
a
e
r
t
u
r
t
u
r
G
C
P
C
C
G
=
=
=
(
2
)
W
h
er
e:
J
is
th
e
to
tal
in
er
tia
o
f
r
o
tatin
g
p
ar
ts
(
k
g
•
m
2
)
;
f
is
th
e
v
is
co
u
s
f
r
ictio
n
co
ef
f
icien
t;
C
em
is
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
o
f
th
e
g
en
er
ato
r
(
N
•
m
)
;
C
g
is
th
e
m
ec
h
an
ical
to
r
q
u
e
in
th
e
o
u
tp
u
t
o
f
th
e
m
u
lt
ip
lier
;
C
aer
is
th
e
ae
r
o
d
y
n
am
ic
to
r
q
u
e
o
f
th
e
t
u
r
b
in
e;
G
is
th
e
m
u
ltip
lier
g
ain
;
Ω
mec
is
g
en
er
ato
r
s
p
ee
d
;
Ω
tur
is
t
h
e
s
p
ee
d
o
f
th
e
tu
r
b
in
e
.
I
n
th
e
wi
n
d
tu
r
b
in
e
m
o
d
el,
th
e
ae
r
o
d
y
n
am
ic
p
o
wer
o
u
tp
u
t is g
iv
e
n
as
f
o
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
n
tr
o
l o
f th
e
p
h
o
to
elec
tr
ic
g
en
era
to
r
fo
r
u
s
ed
in
feed
in
g
o
f
th
e
in
d
ep
e
n
d
en
t…
(
Mo
h
a
mm
ed
K
en
d
z
i
)
1615
(
)
3
;
2
a
e
r
p
C
s
v
P
=
(
3
)
W
h
e
r
e
ρ
is
th
e
ai
r
d
en
s
it
y
(
K
g
/
m
3
)
,
v
is
t
h
e
wi
n
d
s
p
e
e
d
(
m
/s
)
,
an
d
C
p
is
t
h
e
p
o
we
r
c
o
e
f
fic
ie
n
t
.
T
h
e
p
o
we
r
c
o
ef
f
icien
t
C
p
p
r
es
en
ts
t
h
e
p
o
r
ti
o
n
o
f
w
in
d
p
o
w
e
r
c
a
p
t
u
r
e
d
b
y
t
h
e
t
u
r
b
i
n
e
.
I
t
d
ep
en
d
s
o
n
two
p
a
r
a
m
et
er
s
,
n
am
el
y
ti
p
s
p
ee
d
r
a
ti
o
λ
a
n
d
p
itc
h
a
n
g
le
o
f
t
h
e
b
la
d
es
β
:
[
1
1
,
1
2
]
:
(
)
(
)
(
)
(
)
(
)
0
.
1
0
.
5
0
.
0
0
1
6
7
2
s
i
n
0
.
0
0
1
8
4
3
2
1
8
.
5
0
.
3
2
p
C
+
=
−
−
−
−
−
−−
(
4
)
W
h
e
r
e:
λ
is
t
h
e
s
p
ee
d
r
a
ti
o
is
d
e
f
i
n
e
d
as
t
h
e
r
a
ti
o
b
etw
ee
n
t
h
e
li
n
ea
r
s
p
e
e
d
o
f
t
h
e
b
la
d
es
an
d
t
h
e
wi
n
d
s
p
ee
d
;
β
is
th
e
o
r
ie
n
t
ati
o
n
a
n
g
le
o
f
t
h
e
b
la
d
es
.
3
.
2
.
M
o
delin
g
o
f
DF
I
G
T
h
e
P
ar
k
m
o
d
e
l
o
f
th
e
m
a
c
h
i
n
e
is
d
esc
r
i
b
e
d
b
y
t
h
e
f
o
ll
o
wi
n
g
e
q
u
ati
o
n
s
[
1
3
,
14]
:
T
h
e
e
le
c
tr
ic
eq
u
a
ti
o
n
s
:
(
)
(
)
s
d
s
d
s
s
d
s
q
s
s
q
s
q
s
s
q
s
d
s
r
d
r
d
r
s
r
d
r
q
r
r
q
r
q
r
s
r
q
r
d
r
d
dt
d
dt
d
dt
d
dt
vi
R
vi
R
vi
R
vi
R
=
+
−
=
+
−
=
+
−
−
=
+
+
−
(
5
)
T
h
e
f
l
u
x
eq
u
ati
o
n
s
:
s
sr
ds
dr
ds
s
sr
qs
qr
qs
r
sr
dr
ds
dr
r
sr
qr
qs
qr
ii
LM
ii
LM
ii
LM
ii
LM
=+
=+
=+
=+
(
6
)
T
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
eq
u
atio
n
:
(
)
sr
e
m
d
r
q
r
q
s
d
s
s
p
M
C
i
i
L
=−
(
7
)
wh
er
e:
R
s
is
th
e
s
tato
r
r
esis
tan
ce
,
R
r
is
th
e
r
o
t
o
r
r
esis
ta
n
ce
,
L
s
is
th
e
s
tato
r
in
d
u
cta
n
ce
,
M
sr
is
m
u
tu
a
l
in
d
u
ctan
ce
,
ϕ
ds
,
ϕ
qs
a
r
e
r
esp
ec
t
iv
ely
th
e
d
ir
ec
t
an
d
q
u
ad
r
atu
r
e
f
lu
x
es
o
f
th
e
s
tato
r
,
ϕ
dr
,
ϕ
qr
ar
e
r
esp
ec
tiv
ely
th
e
d
ir
ec
t
an
d
q
u
ad
r
atu
r
e
f
lu
x
es
o
f
th
e
r
o
t
o
r
,
i
ds
,
i
qs
ar
e
r
esp
ec
ti
v
ely
d
ir
ec
t
a
n
d
q
u
ad
r
at
u
r
e
s
tato
r
cu
r
r
e
n
ts
,
i
dr
,
i
qr
ar
e
r
esp
ec
tiv
ely
d
ir
ec
t
an
d
q
u
ad
r
atu
r
e
r
o
t
o
r
cu
r
r
en
ts
,
p
is
n
u
m
b
er
o
f
e
v
en
p
o
les,
ω
r
,
ω
s
ar
e
an
g
u
lar
s
p
ee
d
s
r
esp
ec
tiv
ely
o
f
th
e
r
o
to
r
an
d
s
tato
r
.
4.
CO
NT
RO
L
ST
R
AT
E
G
Y
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
ar
e
wr
itten
in
th
e
Par
k
m
o
d
el
as f
o
llo
ws [
1
5
,
16
]:
s
d
s
d
s
q
s
q
s
q
s
d
s
d
s
q
s
s
V
i
V
i
P
Q
V
i
V
i
=+
=−
(
8
)
B
y
t
h
e
o
r
ie
n
t
ati
o
n
o
f
th
e
s
tat
o
r
f
lu
x
al
o
n
g
t
h
e
ax
is
d
,
w
e
h
a
v
e
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
3
,
Sep
201
9
:
1
6
1
3
–
1
6
2
7
1616
0
,
q
s
d
s
s
==
(
9
)
an
d
,
0
q
s
s
d
s
V
V
V
==
(
1
0
)
T
h
e
(
8
)
b
ec
o
m
es:
s
qs
qs
qs
ds
s
Vi
P
Q
Vi
=
=
(
1
1
)
B
y
co
m
b
i
n
i
n
g
(
5
,
6
,
a
n
d
1
1
)
,
(
1
1
)
b
ec
o
m
es:
s
s
q
r
s
s
s
s
d
r
s
ss
M
M
Vi
P
L
V
Q
Vi
LL
=−
=
−
+
(
1
2
)
B
y
s
u
b
s
tit
u
t
in
g
(
6
)
f
o
r
(
5
)
a
n
d
u
s
i
n
g
(
9
)
,
th
e
r
o
t
o
r
v
o
lta
g
e
ca
n
b
e
r
e
wr
itt
en
as
f
o
ll
o
ws:
dr
rr
d
r
d
r
r
s
q
r
qr
s
rr
q
r
q
r
r
s
d
r
s
g
dt
gg
dt
di
v
i
L
i
RL
di
MV
v
i
L
i
RL
L
=
+
−
=
+
+
+
(
1
3
)
W
h
er
e
:
2
1
rs
M
LL
=−
;
1
s
r
g
=−
5.
F
UZ
Z
Y
L
O
G
I
C
CO
N
T
RO
L
5
.
1
.
P
rinciple o
f
f
uzzy
lo
g
ic
m
et
ho
d
T
h
e
p
r
in
cip
le
o
f
f
u
zz
y
c
o
n
t
r
o
l
is
b
ased
o
n
th
e
f
o
llo
win
g
th
r
ee
b
lo
ck
s
:
Fu
zz
if
icatio
n
o
f
in
p
u
t
v
ar
iab
les
wh
ich
ar
e
d
ef
i
n
ed
b
y
lin
g
u
is
tic
v
ar
iab
les
(
f
u
zz
y
s
ets
o
r
s
u
b
s
ets),
th
en
th
e
I
n
f
er
en
ce
wh
er
e
th
ese
v
ar
iab
les
ar
e
c
o
m
p
a
r
ed
with
p
r
ed
ef
in
e
d
s
ets
to
d
eter
m
in
e
ap
p
r
o
p
r
iate
r
esp
o
n
s
e.
An
d
f
i
n
ally
d
ef
u
zz
i
f
icatio
n
,
to
co
n
v
er
t
th
e
s
u
b
s
et
f
u
zz
if
ic
atio
n
in
v
alu
es,
u
s
in
g
th
e
ce
n
tr
o
id
d
ef
u
zz
if
icatio
n
.
T
h
e
b
as
ic
s
tr
u
ctu
r
e
o
f
o
u
r
f
u
zz
y
co
n
t
r
o
ller
is
s
h
o
wn
i
n
Fig
u
r
e
2
[1
7
,
1
8
]
.
Fig
u
r
e
2
.
I
n
ter
n
al
s
tr
u
ctu
r
e
o
f
a
f
u
zz
y
c
o
n
tr
o
ller
W
ith
:
R
(
t
)
is
th
e
r
e
f
er
en
ce
s
i
g
n
al,
u
(
t)
is
t
h
e
c
o
m
m
an
d
s
i
g
n
al
,
y
(
t
)
is
th
e
o
u
t
p
u
t
o
f
t
h
e
s
y
s
te
m
to
b
e
c
o
n
tr
o
ll
e
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
n
tr
o
l o
f th
e
p
h
o
to
elec
tr
ic
g
en
era
to
r
fo
r
u
s
ed
in
feed
in
g
o
f
th
e
in
d
ep
e
n
d
en
t…
(
Mo
h
a
mm
ed
K
en
d
z
i
)
1617
5
.
2
.
Reg
ula
t
ing
po
wer
by
f
u
zz
y
lo
g
ic
T
h
e
f
u
zz
y
co
n
tr
o
ller
is
b
a
s
ically
non
-
lin
ea
r
s
tatic
in
p
u
t/
o
u
tp
u
t
p
lo
t
as
s
h
o
w
in
Fig
u
r
e
3
,
th
e
co
n
tr
o
ller
ac
tio
n
ca
n
b
e
wr
itten
in
th
e
f
o
r
m
:
..
ee
u
k
e
k
e
=
+
(
1
4
)
Fig
u
r
e
3
.
Fu
zz
y
lo
g
ic
r
eg
u
lato
r
T
h
e
f
u
z
zy
o
u
tp
u
t
is
:
.
u
y
k
u
=
(
1
5
)
W
h
e
r
e:
k
e
is
t
h
e
g
ai
n
o
f
t
h
e
p
o
wer
e
r
r
o
r
(
P
s
o
r
Q
s
)
,
k
Δ
e
is
t
h
e
g
ai
n
o
f
t
h
e
v
a
r
ia
ti
o
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ed
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re
f
s
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re
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e
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e
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k
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W
h
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r
e:
P
is
th
e
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ef
e
r
e
n
c
e
s
tat
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r
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we
r
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,
Q
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ef
e
r
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e
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cti
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tat
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)
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k
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−
−
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1
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5
.
3
.
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a
nd
a
pp
lica
t
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o
n o
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a
f
uzzy
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djustm
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f
t
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in a
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G
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,
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f
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f
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ts
a
n
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co
n
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ct
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d
f
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m
th
e
f
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g
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it
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n
r
u
l
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u
le
(
i
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i
f
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s
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h
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f
is
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i
=
1
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5
T
a
b
le
1
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p
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i
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l
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les
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as
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m
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er
s
h
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p
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w
h
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r
e
:
NB
is
n
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ati
v
e
b
i
g
,
NS
is
n
eg
ati
v
e
s
m
all
,
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o
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i
ti
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ll
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d
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v
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ig
.
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h
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r
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n
y
m
s
ar
e
l
ab
els
o
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f
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zz
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ets
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n
d
t
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ir
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o
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d
i
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em
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r
s
h
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p
f
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n
c
ti
o
n
s
a
r
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d
ep
ict
e
d
i
n
Fi
g
u
r
e
4
,
[
1
9
]
.
T
o
c
o
n
t
r
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l
t
h
e
s
tat
o
r
p
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in
a
DF
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G
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h
a
v
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s
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e
b
l
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ck
d
ia
g
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m
o
f
F
ig
u
r
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5
s
im
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la
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t
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f
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ig
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r
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ab
le
1
.
o
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f
p
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ase
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v
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m
e
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h
i
p
f
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cti
o
n
s
e
Δ
e
NB
NS
ZE
PS
PB
NB
ZE
ZE
PB
PB
PB
NS
ZE
ZE
PS
PS
PS
ZE
PS
ZE
ZE
ZE
NS
PS
NS
NS
NS
ZE
ZE
PB
NB
NB
NB
ZE
ZE
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
694
I
n
t J
Po
w
E
lec
&
Dr
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Sy
s
t,
Vo
l.
10
,
No
.
3
,
Sep
201
9
:
1
6
1
3
–
1
6
2
7
1618
Fig
u
r
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4
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Me
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ip
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f
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M
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d
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as
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in
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g
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r
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6
.
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u
r
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6
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E
q
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iv
alen
t
d
iag
r
am
o
f
a
r
ea
l
p
h
o
to
v
o
ltaic
ce
ll [
2
0
]
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I
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t J Po
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&
Dr
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s
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I
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N:
2
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8
694
C
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W
h
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r
e:
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o
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s
a
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ti
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r
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n
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o
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/
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o
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o
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s
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g
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0
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f
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m
p
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at
u
r
e.
6
.
1
.
M
o
delin
g
o
f
t
he
ph
o
t
o
v
o
lt
a
ic
co
ntinuo
us
bu
s
T
h
e
ev
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l
u
t
io
n
o
f
t
h
e
p
h
o
t
o
v
o
lt
aic
DC
b
u
s
v
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lt
a
g
e
is
g
i
v
en
b
y
t
h
e
f
o
l
lo
wi
n
g
e
q
u
at
io
n
:
1
pv
pv
c
pv
dt
vi
c
=
(
2
1
)
T
h
e
cu
r
r
e
n
t
i
n
th
e
p
h
o
t
o
v
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l
tai
c
DC
b
u
s
co
m
es
f
r
o
m
a
n
o
d
e
f
r
o
m
w
h
i
ch
tw
o
c
u
r
r
en
ts
f
l
o
w:
pv
pv
hac
c
i
i
i
=−
(
2
2
)
W
h
er
e:
I
cpv
is
t
h
e
c
u
r
r
e
n
t
o
f
th
e
p
h
o
to
v
o
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c
co
n
t
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u
o
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s
b
u
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;
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hac
is
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e
c
u
r
r
e
n
t
o
f
th
e
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o
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p
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r
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t
h
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p
ac
it
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o
f
th
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p
h
o
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v
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l
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c
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o
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s
.
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.
2
.
Cho
pp
er
bo
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s
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er
T
h
e
b
o
o
s
t
e
r
c
o
n
v
e
r
te
r
co
n
t
r
o
l
s
th
e
e
le
ct
r
ic
al
p
o
we
r
in
DC
ci
r
c
u
its
wit
h
g
r
e
at
f
l
ex
ib
ilit
y
an
d
h
ig
h
ef
f
ic
ie
n
c
y
.
I
t
c
o
n
s
is
ts
o
f
c
ap
ac
i
to
r
s
,
i
n
d
u
cta
n
ce
,
an
d
s
wit
c
h
es;
al
l t
h
ese
d
ev
ic
es
co
n
s
u
m
e
n
o
ac
ti
v
e
p
o
we
r
.
Fig
u
r
e
7
.
E
lect
r
ical
B
o
o
s
t c
o
n
v
er
ter
Sch
em
e
[
2
1
]
Du
r
i
n
g
o
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e
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ati
o
n
o
f
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e
c
h
o
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r
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f
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it
h
a
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o
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Ts
)
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d
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n
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s
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)
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h
e
r
e:
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e
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ch
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α
∈
[
0
,
1
]
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
3
,
Sep
201
9
:
1
6
1
3
–
1
6
2
7
1620
Fig
u
r
e
8
.
Per
io
d
s
o
f
clo
s
in
g
an
d
o
p
en
i
n
g
a
s
witch
.
Ap
p
l
y
i
n
g
K
ir
ch
h
o
f
f
'
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l
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t
o
t
h
e
s
c
h
e
m
e
o
f
f
i
g
u
r
e
7
,
w
e
o
b
ta
in
t
h
e
f
o
l
lo
wi
n
g
s
y
s
te
m
s
o
f
e
q
u
at
io
n
s
[
2
2
]:
Fo
r
t
h
e
1
st
p
e
r
i
o
d
α
.T
s
:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
1
2
1
0
20
i
iL
c
c
L
LL
Li
t
t
t
t
dt
t
tt
dt
t
L
t
R
i
dt
dv
i
c
i
i
dv
i
c
i
di
vv
=
=
−
=
=
−
=
=
−
−
(
2
3
)
Fo
r
t
h
e
2
nd
p
e
r
i
o
d
(1
-
α
)
.
T
s
:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
1
2
1
0
20
0
i
iL
c
L
c
L
LL
Li
t
t
t
t
dt
t
t
t
t
dt
t
L
t
t
R
i
dt
dv
i
c
i
i
dv
i
c
i
i
di
v
v
v
=
=
−
=
=
−
=
=
−
−
(
2
4
)
T
o
f
i
n
d
a
v
al
id
d
y
n
am
i
c
r
ep
r
es
en
t
ati
o
n
f
o
r
t
h
e
w
h
o
l
e
p
e
r
i
o
d
T
s
,
we
g
e
n
e
r
al
ly
u
s
e
t
h
e
f
o
l
lo
wi
n
g
ex
p
r
ess
i
o
n
:
(
)
(
)
(
)
(
)
1
1
s
s
s
s
s
T
T
d
x
d
x
d
x
dt
T
T
T
d
t
d
t
−
=+
−
(
2
5
)
Ap
p
l
y
i
n
g
t
h
e
r
e
lat
io
n
(
2
5
)
t
o
th
e
s
y
s
te
m
s
o
f
e
q
u
ati
o
n
s
(
2
3
)
a
n
d
(
2
4
)
,
w
e
f
i
n
d
t
h
e
E
q
u
at
io
n
s
th
at
g
o
v
er
n
th
e
s
y
s
te
m
o
v
er
a
n
e
n
ti
r
e
p
e
r
i
o
d
ar
e
o
b
t
ai
n
e
d
:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
1
0
2
0
0
0
1
1
1
i
s
s
i
L
s
i
L
s
s
s
L
L
s
s
i
L
L
s
i
L
L
dv
c
T
T
i
i
T
i
i
dt
dv
c
T
T
i
T
i
i
dt
L
T
T
v
R
i
T
v
v
R
i
dt
di
=
−
+
−
−
=
−
+
−
−
=
−
+
−
−
−
(
2
6
)
B
y
ar
r
a
n
g
i
n
g
t
h
e
t
er
m
s
o
f
t
h
e
p
r
ec
ed
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g
e
q
u
at
io
n
s
,
(
s
o
t
h
at
w
e
ca
n
i
n
te
r
c
o
n
n
ec
t
th
e
B
o
o
s
t
wit
h
th
e
o
t
h
er
s
im
u
la
ti
o
n
b
l
o
c
k
s
)
,
we
o
b
tai
n
t
h
e
d
y
n
a
m
i
c
m
o
d
eli
n
g
o
f
th
e
B
o
o
s
t
co
n
v
e
r
t
er
:
(
)
(
)
(
)
(
)
1
0
02
0
1
1
i
Li
L
L
LL
i
t
dt
t
dt
L
R
i
dt
dv
i
i
c
dv
i
ic
di
v
v
=−
=−
=
+
+
−
−
(
2
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
n
tr
o
l o
f th
e
p
h
o
to
elec
tr
ic
g
en
era
to
r
fo
r
u
s
ed
in
feed
in
g
o
f
th
e
in
d
ep
e
n
d
en
t…
(
Mo
h
a
mm
ed
K
en
d
z
i
)
1621
6
.
3
.
M
o
delin
g
t
he
cho
pp
er
f
ilte
r
A
f
ilter
is
u
s
ed
to
elim
in
ate
th
e
h
ar
m
o
n
ics
g
en
er
ated
b
y
t
h
e
ch
o
p
p
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r
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h
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o
l
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tio
n
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f
th
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f
ilter
v
o
ltag
e
is
g
iv
en
b
y
th
e
f
o
llo
wi
n
g
eq
u
atio
n
[
1
3
]
:
fhac
fhac
fhac
fhac
fhac
dt
di
vi
RL
=+
(
2
8
)
W
h
er
e:
R
fha
c
is
th
e
ch
o
p
p
e
r
f
i
lt
er
r
esis
t
an
ce
;
L
fha
c
is
c
h
o
p
p
e
r
f
i
lte
r
i
n
d
u
ct
a
n
ce
.
6
.
4
.
Cho
pp
er
co
ntr
o
l
Ad
ju
s
tin
g
o
f
th
e
v
o
ltag
e
ac
c
o
r
d
in
g
to
th
e
d
esire
d
p
o
wer
(
r
ef
er
en
ce
)
is
n
ec
ess
ar
y
to
c
o
n
tr
o
l
t
h
e
en
er
g
y
p
r
o
d
u
ce
d
b
y
th
e
GP
V
p
h
o
to
v
o
ltaic
g
en
er
ato
r
with
a
m
o
d
if
icatio
n
o
f
th
e
v
ar
i
ab
le
co
n
tr
o
l
o
f
th
e
ch
o
p
p
e
r
(
p
e
r
io
d
ic
r
atio
α
)
an
d
s
er
v
o
co
n
t
r
o
l
o
f
th
e
i
f
h
ac
f
ilte
r
cu
r
r
e
n
t
(
if
h
ac
)
.
I
n
o
u
r
s
tu
d
y
,
th
e
s
witch
o
f
t
h
e
co
n
v
er
ter
is
co
n
tr
o
lled
b
y
a
Pu
ls
e
wav
e
Mo
d
u
latio
n
L
ar
g
e
(
PW
M)
s
ig
n
al,
with
a
f
ix
ed
f
r
eq
u
en
c
y
f
s
an
d
a
cy
clic
r
atio
α
v
a
r
iab
le.
T
h
e
t
w
o
o
p
er
ati
n
g
p
h
as
es
o
f
t
h
e
s
w
it
ch
S
m
u
s
t
b
e
s
t
u
d
i
ed
t
o
e
x
t
r
ac
t
t
h
e
c
o
n
tr
o
l
l
aw
o
f
th
e
p
h
o
to
v
o
l
t
aic
g
e
n
e
r
a
to
r
p
o
wer
o
u
tp
u
t
[
2
3
]:
•
S
hac
is
cl
o
s
e
d
(
0
<t<α
T
s
):
(
)
1
fh
a
c
fh
a
c
p
v
d
c
fh
a
c
fh
a
c
dt
di
v
v
i
R
L
=
−
−
(
2
9
)
•
S
hac
is
o
p
en
(
α
Ts
<t<T
s
)
:
(
)
1
fh
a
c
fh
a
c
d
c
fh
a
c
fh
a
c
dt
di
vi
R
L
=
−
+
(
3
0
)
T
e
r
m
(
2
9
)
a
n
d
(
3
0
)
r
e
p
r
ese
n
t
t
h
e
e
q
u
ati
o
n
s
o
f
th
e
ch
o
p
p
e
r
a
n
d
i
ts
f
ilt
e
r
f
o
r
a
p
e
r
i
o
d
α
Ts
a
n
d
(
1
-
α
)
Ts
r
es
p
e
cti
v
e
ly
.
S
o
we
h
av
e
t
o
f
i
n
d
a
v
al
id
a
p
p
r
o
x
im
ate
d
d
y
n
a
m
ic
r
e
p
r
es
en
tat
io
n
f
o
r
b
o
t
h
ti
m
e
s
l
o
ts
.
F
o
r
th
is
a
n
d
f
r
o
m
eq
u
ati
o
n
(
2
5
)
we
c
o
n
s
i
d
e
r
th
at
t
h
e
v
a
r
ia
ti
o
n
o
f
t
h
e
d
y
n
am
ic
v
ar
ia
b
l
e
(
i
f
hac
)
is
o
f
lin
ea
r
f
o
r
m
,
s
o
t
h
e
d
e
r
i
v
a
ti
v
e
o
f
t
h
e
d
y
n
a
m
i
c
v
a
r
i
ab
l
e
(
i
f
hac
)
ca
n
b
e
d
e
f
i
n
e
d
a
cc
o
r
d
i
n
g
t
o
e
q
u
ati
o
n
(
2
5
)
o
v
e
r
t
h
e
tw
o
t
im
e
p
e
r
i
o
d
s
α
Ts
an
d
(
1
-
α
)
Ts
:
(
)
(
)
(
)
(
)
1
1
s
s
fh
a
c
fh
a
c
fh
a
c
s
s
s
T
T
dt
d
i
d
i
d
i
T
T
T
d
t
d
t
−
=+
−
(
3
1
)
B
y
r
ep
la
ci
n
g
(
2
9
)
an
d
(
3
0
)
b
y
th
e
ir
v
al
u
e
i
n
r
e
lati
o
n
(
3
1
)
w
e
o
b
tai
n
th
e
e
q
u
at
io
n
t
h
at
g
o
v
er
n
s
t
h
e
s
y
s
t
em
o
n
t
h
e
en
t
ir
e
p
er
i
o
d
:
(
)
1
fh
a
c
fh
a
c
p
v
d
c
fh
a
c
fh
a
c
dt
di
v
v
i
R
L
=
−
−
(
3
2
)
T
h
e
co
n
t
r
o
l
la
w
is
g
i
v
e
n
b
y
t
h
e
f
o
ll
o
wi
n
g
ex
p
r
ess
io
n
a
n
d
d
es
cr
i
p
t
e
d
i
n
Fi
g
u
r
e
9
:
fh
a
c
d
c
pv
vv
v
+
=
(
3
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
3
,
Sep
201
9
:
1
6
1
3
–
1
6
2
7
1622
Fig
u
r
e
9
.
C
h
o
p
p
er
c
o
n
tr
o
l.
7.
ST
RUC
T
UR
E
O
F
T
H
E
M
P
P
T
CO
M
M
A
ND
B
Y
T
H
E
M
E
T
H
O
D
O
F
DIS
T
U
R
B
ANC
E
AND
O
B
SE
RVAT
I
O
N
«
P
& O
»
T
h
e
"P
&
O"
d
is
tu
r
b
an
ce
an
d
o
b
s
er
v
atio
n
m
eth
o
d
is
a
wid
ely
u
s
ed
ap
p
r
o
ac
h
in
th
e
s
ea
r
ch
f
o
r
Ma
x
im
u
m
Po
wer
Po
i
n
t
T
r
ac
k
in
g
(
MPPT)
b
ec
au
s
e
it
is
s
im
p
le
an
d
r
e
q
u
ir
es
o
n
ly
v
o
ltag
e
an
d
c
u
r
r
e
n
t
m
ea
s
u
r
em
en
ts
o
f
th
e
p
h
o
t
o
v
o
ltaic
p
an
els
v
p
v
an
d
ip
v
r
esp
ec
tiv
ely
.
I
t
ca
n
b
e
u
s
ed
to
d
ed
u
ce
th
e
p
o
i
n
t
o
f
m
ax
im
u
m
p
o
wer
ev
e
n
d
u
r
in
g
v
ar
iatio
n
s
in
illu
m
in
atio
n
an
d
tem
p
er
atu
r
e.
7
.
1
Ref
er
ence
curr
ent
ca
lcula
t
io
n by
pro
g
ra
m
o
f
t
he
M
P
P
T
co
m
ma
nd
Sev
er
al
alg
o
r
ith
m
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
th
e
r
ea
lizatio
n
o
f
th
e
MPPT
co
m
m
an
d
f
o
r
th
at
we
h
av
e
ch
o
s
en
th
e
f
o
llo
win
g
p
r
o
g
r
am
:
%
Sim
p
l
e
MP
P
"p
er
tu
r
b
a
n
d
o
b
s
e
r
v
e"
t
r
a
c
k
i
n
g
a
lg
o
r
it
h
m
% u
s
in
g
B
o
o
s
t
DC
-
DC
i
n
p
u
t
c
u
r
r
en
t
I
r
e
f
as t
h
e
co
n
t
r
o
l
v
ar
ia
b
le
%
Po
l
d
,
I
r
e
f
an
d
I
n
c
r
em
en
t
ar
e
i
n
iti
ali
ze
d
i
n
I
n
iti
ali
ze
MPPt
r
a
ck
I
r
e
f
.
m
% I
n
p
u
t:
p
o
w
er
P
t
o
b
e
m
a
x
i
m
ize
d
% O
u
t
p
u
t:
r
ef
er
en
ce
c
u
r
r
e
n
t
f
u
n
cti
o
n
y
=
f
cn
(
P
p
v
)
g
l
o
b
al
P
o
l
d
;
g
l
o
b
al
I
r
ef
;
g
l
o
b
al
I
n
cr
em
en
t;
I
r
ef
H
=
5
;
%
u
p
p
e
r
lim
it
f
o
r
t
h
e
r
e
f
e
r
e
n
c
e
c
u
r
r
e
n
t
I
r
ef
L
=
0
; %
l
o
we
r
li
m
it
f
o
r
th
e
r
e
f
e
r
e
n
c
e
c
u
r
r
e
n
t
Delt
aI
=
0
.
0
2
;
%
r
e
f
e
r
e
n
ce
c
u
r
r
e
n
t
i
n
c
r
e
m
e
n
t
P =
Pp
v
if
(
P
<
P
o
l
d
)
I
n
c
r
e
m
e
n
t
=
-
I
n
c
r
e
m
e
n
t;
%
c
h
an
g
e
d
i
r
ec
ti
o
n
i
f
P
d
e
cr
ea
s
ed
en
d
% i
n
c
r
e
m
e
n
t
c
u
r
r
en
t
r
e
f
e
r
en
ce
I
r
ef
=
I
r
ef
+I
n
cr
em
en
t*
Del
ta
I
;
% c
h
e
ck
f
o
r
u
p
p
e
r
li
m
it
if
(
I
r
e
f
>
I
r
e
f
H)
I
r
e
f
=
I
r
e
f
H;
E
n
d
% c
h
e
ck
f
o
r
l
o
we
r
li
m
it
if
(
I
r
e
f
<
I
r
e
f
L
)
I
r
ef
=
I
r
ef
L
;
E
n
d
% sa
v
e
p
o
w
e
r
v
a
lu
e
Po
l
d
=
P
;
% o
u
t
p
u
t
c
u
r
r
en
t
r
e
f
e
r
e
n
ce
y
=
I
r
e
f
;
8.
SI
M
UL
A
T
I
O
N
S AN
D
R
E
S
UL
T
S
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