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.
414~
4
2
2
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
4
14-
42
2
414
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
A
d
aptive fuzzy sliding m
o
de b
ased M
PPT controll
er for a
photovoltaic wate
r
pum
ping syste
m
S
a
b
a
h
Mi
qo
i
,
A
b
d
e
l
g
h
a
n
i
E
l
O
ug
l
i
,
B
e
lk
a
s
s
e
m
T
i
dh
a
f
N
a
ti
onal
S
c
ho
o
l
of
App
l
i
e
d S
c
i
e
nces
,
M
oh
ammed
First
U
n
i
v
ersity,
M
o
r
occo
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Sep 6,
2018
Re
vise
d O
c
t
2
7
,
2018
A
c
c
e
pte
d
D
ec 4,
201
8
Th
e
app
l
i
catio
n
s
o
f ph
oto
volt
a
ic en
e
rgy
are
s
t
e
a
di
ly
i
n
c
reasi
n
g
.
However,
th
e
out
put
p
o
w
er
o
f
a
ph
o
t
ovo
lt
a
i
c
s
y
stem
i
s
inf
l
uen
ced
b
y
th
e
meteorolog
i
cal
c
onditions
(
te
mpe
r
at
ure
and
irradi
ati
o
n),
wh
i
c
h
ca
n
aff
ect
t
h
e
pro
duct
i
o
n
a
nd
e
ffici
ency
o
f
t
h
e p
hot
ov
oltai
c
p
anel
e
n
e
rgy
.
S
o
t
o
e
ns
ure
that
th
e
ph
ot
ovolt
a
ic p
anel
p
ro
du
ces
i
ts
m
axim
um
p
o
w
e
r
po
ssi
b
l
e
at
a
ny
tim
e
and
regard
less
o
f
the
e
x
tern
al
c
on
di
tio
n
s
,
we
u
s
e
t
he
e
q
u
i
p
m
e
nt
cal
l
e
d
M
PPT
(m
axim
u
m
power
poi
nt
t
ra
ck
er).
S
lid
ing
m
o
de
c
o
n
t
r
ol
i
s
recogni
z
ed
b
y
its
sta
b
il
ity
a
n
d
ro
bu
stne
ss
a
n
d
wid
e
ly
u
se
d
in
n
on
-l
in
e
a
r
s
y
s
te
ms
bu
t
represen
ts
a
dis
a
dv
ant
a
g
e
b
ecaus
e
o
f
th
e
ch
att
e
ring
phen
o
m
e
n
a
.
So
i
n
o
r
der
t
o
o
v
e
r
c
o
me
t
hi
s
p
r
o
b
l
e
m
a
n
d
i
m
p
ro
ve
t
hi
s
c
o
ntro
l
,
w
e
op
te
d
to
a
dd
t
o
i
t
t
h
e
adap
tiv
e
f
u
zzy
c
o
n
t
r
ol
w
hich
w
ill
ad
apt
th
e
s
w
it
c
h
i
n
g
gai
n
.
Thi
s
con
t
ro
ll
er
i
s
nam
e
d
A
F
S
M
C
(adap
tiv
e
fu
zzy
s
lid
in
g
m
ode
c
on
tro
l
)
and
wil
l
b
e
c
om
pared
th
e
s
l
i
d
in
g
m
ode
c
o
n
tro
l
l
e
r
S
M
C
i
n
o
rd
er
t
o
se
e
t
h
e
di
ff
e
r
en
ce
an
d
to
t
he
P&O
(per
t
u
rb
&
o
bserve)
met
h
od
t
o
vali
date
t
hi
s
cont
ro
l
l
er.
O
u
r
s
y
s
t
e
m
con
s
ists
o
f
a
photo
v
o
l
t
a
ic
p
anel
a
D
C-DC
b
oo
st
c
on
verter
a
n
d
a
cen
tri
f
u
g
a
l
p
u
m
p
w
i
t
h
a
D
C
m
o
t
o
r
.
A
l
l
s
i
m
u
l
a
t
i
o
n
s
a
r
e
c
a
r
r
i
e
d
o
u
t
u
n
d
e
r
M
A
TL
AB/
S
IMULINK
an
d
t
h
e
e
x
tract
ed
r
es
ults
s
h
o
w
the
effi
c
i
en
cy
o
f
t
h
e
AF
SM
C
co
nt
ro
l
l
er
a
n
d
c
on
f
i
rm
t
hat
t
h
e
new
m
e
th
od
s
hav
e
i
mp
ro
v
e
d
e
n
e
r
g
y
ef
ficien
cy an
d
p
rod
u
ct
ion
.
K
eyw
ord
s
:
Ad
a
p
t
i
v
e
c
ont
ro
l
AF
S
M
C
D
C
m
ot
or
D
C
-D
C bo
os
t
con
v
er
t
e
r
Fu
zz
y
co
nt
rol
MPP
T
P&O
Phot
o
v
o
lta
ic
PV
SMC
Wa
te
r
p
u
m
p
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:
S
a
bah M
i
q
o
i
,
Lab
o
ra
t
o
r
y
of
Embe
d
d
ed E
le
c
t
ro
nic S
y
st
e
m
s
and Re
ne
w
a
b
l
e
Energ
y
,
N
a
ti
ona
l S
c
ho
ol o
f
A
p
p
lie
d S
c
ience
s
,
Moha
m
m
e
d F
i
rst U
n
ivers
i
t
y
,
BP
717
60
0
00
O
u
jda
Mar
o
c
،BV
M
o
ha
me
d V
I
BP
717,
O
ujda
6
0
0
0
0
, Morocco.
Em
ail:
sa
ba
h.
miq@
gm
ai
l
.
co
m
1.
I
N
TR
OD
U
C
TI
O
N
The
a
ppl
ica
t
i
o
n
a
n
d
de
ve
lopm
en
t
o
f
p
h
o
t
o
vol
tai
c
e
ne
rgy
is
i
ncre
asin
g
a
l
l
ov
e
r
t
he
w
orl
d
.
P
hot
o
v
o
lta
ic
pum
pi
n
g
i
s
o
n
e
of
t
he
p
rom
i
si
ng
a
pp
l
i
cat
i
o
n
s
f
or
t
h
e
u
se
o
f
p
hot
ovo
lt
ai
c
en
ergy
,
p
a
rt
i
c
u
l
arl
y
i
n
rura
l
are
a
s
t
h
at
h
ave
a
su
bs
ta
nt
ia
l
am
o
u
n
t
o
f
i
n
sola
ti
on
a
n
d
ha
v
e
n
o
ac
cess
to
a
n
el
ect
ric
g
r
i
d
[
1
]
.
Th
en
o
u
r
sy
st
em
c
o
n
s
i
s
ts
o
f
a
p
hot
ovo
l
t
a
i
c
p
an
el
t
h
a
t
su
ppli
e
s
en
e
r
gy
t
o
the
w
at
er pump v
i
a a
D
C
/
D
C
c
onve
rte
r
and a
D
C
m
ot
or
.
A
m
ong
the
bene
fits
o
f
us
ing
a
pho
to
v
o
l
t
a
i
c
s
ourc
e
i
s
t
h
at
i
t
i
s
fre
e
a
n
d
sus
t
ai
n
a
b
l
e
f
u
e
l
s
o
u
rc
e;
t
h
e
r
e
li
gh
t
-
w
e
ig
ht
,
al
th
ough
P
V
sy
st
e
m
s
ma
y
e
x
p
a
nd
ov
e
r
l
a
rg
e
a
r
eas; n
o
i
s
e fre
e
opera
t
i
on
d
ue
t
o t
h
e a
b
se
nc
e
of
l
a
r
ge
r
o
t
a
ting
m
a
ch
i
n
e
r
y
;
t
he
p
oss
i
b
i
l
i
t
y
o
f
a
p
p
lic
at
ion
c
l
o
se
t
o
t
h
e
po
i
n
t
o
f
u
se
;
ea
se
o
f
insta
lla
t
i
on
;
p
r
e
d
i
c
t
a
bl
e
a
v
ai
l
a
bi
l
ity
i
n
cert
a
in
g
eog
r
ap
hi
c
a
l
re
gio
n
s;
a
n
d
s
y
s
t
e
ms
r
e
q
ui
re
r
el
a
t
iv
el
y
l
itt
l
e
r
eg
ul
ar
ma
int
e
na
nce
.
I
n
s
p
i
te
o
f
a
ll
t
h
e
s
e
ad
va
nt
a
g
es,
PV
s
ystem
is
k
n
o
w
n
f
or
t
he
n
o
n
l
inea
r
c
u
r
r
ent-v
o
lta
ge
a
nd
p
o
w
e
r-
vo
lta
ge
c
ha
rac
t
e
r
is
t
i
c
s
w
h
i
c
h
d
e
p
e
n
ds
o
n
t
h
e
va
ria
tio
ns
i
n
t
e
mp
e
r
at
ure
and
so
lar
irra
di
a
t
ion,
t
he
ref
o
r
e
t
he
p
hot
ovo
lt
ai
c
sy
st
em
d
o
e
s
no
t
p
r
odu
c
e
i
t
s
m
a
x
i
m
u
m
e
n
e
rgy
all
t
h
e
t
i
m
e
wh
i
c
h
l
e
ad
s
to
l
o
w
e
ffi
ci
e
n
cy.
Th
ere
is
a
u
niq
u
e
p
o
i
n
t
on
the
P-
V
(Pow
er-V
o
lta
ge
)
cha
r
ac
t
e
ristic,
k
n
ow
n
a
s
t
he
M
P
P
(
m
a
xim
u
m
pow
e
r
p
o
i
n
t
)
w
h
er
e
t
h
e
ph
o
t
ovo
lta
ic ce
ll prod
uces
i
t
s
ma
x
i
m
um
p
ow
e
r
. There
f
o
re,
t
h
e
P
V
s
y
s
t
e
ms
r
eq
ui
re
a
n
e
q
ui
pme
n
t
t
o
trac
k
t
h
e
MP
P
at
a
l
l
t
im
e,
r
e
g
ardle
s
s
o
f
t
he
t
em
pera
t
u
r
e
a
n
d
s
o
l
a
r
i
r
radia
t
io
n.
A
s
ignif
i
c
a
nt
num
ber
o
f
M
P
P
T
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
Ad
ap
tive
fu
zzy sl
id
ing
m
o
de
base
d
MPPT
c
o
n
t
ro
l
l
e
r
fo
r a p
h
o
t
ovo
l
ta
i
c
w
a
t
e
r p
u
m
p
in
g system
(Sab
a
h
Miq
o
i
)
41
5
con
t
ro
l
s
y
s
t
em
s
ha
ve
be
e
n
de
v
el
o
p
ed
f
or ye
a
rs,
starti
ng
w
i
t
h
s
i
m
p
l
e
t
ec
h
n
i
q
u
e
s
suc
h a
s
v
ol
ta
ge or
c
u
rre
nt an
d
H
ill
c
l
i
m
b
i
ng
,
Inc
r
em
ental
in
d
u
cta
n
c
e
a
nd
Per
t
ur
b
a
n
d
O
b
ser
v
e;
th
ose
a
r
e
t
h
e
con
v
e
nt
ion
a
l
con
t
ro
l
tech
n
i
q
u
es
[
2].
O
n
t
he
o
the
r
h
a
n
d,
unc
o
n
ve
nti
ona
l
te
ch
n
i
q
u
es
s
u
ch
a
s
fuzz
y
lo
gi
c
,
a
rt
ifi
c
i
a
l
ne
u
r
al
n
e
t
wo
rk
a
n
d
sl
idi
n
g
mo
d
e
c
o
n
t
r
ol
,
wh
i
c
h
ca
n
p
r
o
v
id
e
mo
re
s
t
a
b
i
li
ty
a
nd
ro
bu
stn
e
ss,
h
av
e
b
een
w
i
d
e
l
y
u
s
e
d
a
nd
deve
l
ope
d.
The
s
l
id
ing
m
ode
c
on
t
r
o
ller
is
m
uc
h
k
now
n
for
i
t
s
ro
b
u
s
t
ne
ss
a
n
d
st
ab
il
i
t
y
and
i
s
w
i
l
d
l
y
u
s
ed
i
n
non
line
a
r
sys
t
e
m
s
and
es
pec
i
al
ly
on
aircr
a
f
t
c
ontrol
[3].
H
owever
t
h
is
c
o
n
t
rol
l
e
r
r
epr
e
sents
a
disa
dva
nta
g
e
calle
d
the
c
h
a
t
t
e
ri
ng
phe
n
o
m
e
na
r
e
s
ul
t
i
ng
from
t
h
e
h
i
g
h
osc
illa
t
i
ons
a
ro
un
d
the
sli
d
i
n
g
s
u
rfa
c
e
.
To
overc
ome
t
h
is
di
sa
d
v
a
n
ta
ge
w
e
have
t
rie
d
t
o
de
vel
o
p
t
h
e
sl
i
d
i
ng
mo
de
c
on
t
r
o
l
l
er
by
r
e
plac
i
ng
t
h
e
s
w
it
c
h
in
g
ga
i
n
by
a
n
ada
p
t
i
ve
f
uzz
y
gai
n.
This m
e
t
h
o
d
is ca
l
l
e
d
A
da
pt
ive
F
u
z
z
y
S
l
i
d
i
ng
Mo
de
C
on
tro
l
A
F
S
M
C.
In
t
hi
s
p
a
p
e
r,
a
p
hot
ovo
lt
ai
c
wa
t
e
r
p
u
m
pi
ng
sy
st
e
m
,
wa
s
st
u
d
i
e
d
a
n
d
t
he
m
athem
a
t
i
ca
l
m
odel
l
i
n
g
of
its
e
q
u
ipm
e
n
t
s
is
r
epre
sen
t
ed
[
4]
.
The
differe
nt
M
P
P
T
te
ch
ni
que
s
use
d
h
a
v
e
also
b
ee
n
s
t
ud
i
e
d
an
d
ana
l
yz
ed
and
al
so com
p
a
re
d.
T
he syste
m
ha
s bee
n
test
e
d
and a
s
se
sse
d
us
i
n
g MA
TL
A
B
/
S
imu
l
in
k.
2.
PV WATER PUM
PING
S
YS
T
E
M
DE
S
I
G
N
:
O
u
r
sys
t
em
c
o
n
sists
of
a
ph
o
t
ov
o
lta
ic
p
a
n
e
l
a
D
C-
D
C
b
oo
st
c
on
ve
rt
er
a
nd
a
cen
t
r
i
f
u
g
a
l
pu
mp
w
it
h
a
D
C
m
ot
or
. F
igure
1 show
s t
h
e
equi
va
le
nt c
ir
cui
t
of
the
sys
t
em
i
n all.
F
i
gure
1.
E
qu
iva
l
e
n
t circ
u
i
t
o
f
the
s
y
s
t
e
m
The
sys
t
em
’s avera
g
e
m
ode
l
is g
iv
e
n
in
th
e
(1
):
pv
mL
F
W
a
F
W
a
LL
L
pv
pv
L
11
aa
a
a
aa
a
aa
LL
22
2
21
a
V
Ri
V
V
V
V
di
R
i
dt
L
L
L
L
L
dV
i
i
dt
C
C
di
R
V
k
iω
dt
L
L
L
dV
i
ii
dt
C
C
C
kk
dω
k
iω
dt
j
j
j
u
u
(
1
)
Where
u
i
s
t
h
e
co
nt
ro
l
i
nput
.
L,
R
L
a
n
d
i
a
re
t
he
s
elf-i
n
duc
t
a
nc
e,
r
e
s
i
s
tanc
e
and
c
u
rrent.
R
i
s
t
h
e
re
si
st
an
c
e
c
h
a
ra
ct
eri
z
i
n
g
IGB
T
l
o
s
t
.
C
and
C
a
re
t
he
i
np
u
t
a
n
d
t
he
o
u
t
pu
t
ca
pac
i
t
a
nc
e
re
spect
i
v
ely.
V
i
s
the d
i
ode
f
orw
a
rd vo
lta
ge
. Th
e
state
r
epr
e
senta
t
io
n o
f
t
he
s
ys
t
em
is w
r
itte
n a
s
:
L
fω
mL
f
ω
a
LL
pv
1
pv
pv
1
a
aa
aa
a
L
aa
2
22
1
2
R
11
00
V
LL
L
Ri
V
V
1
L
00
0
0
ii
L
i
C
0
VV
C
R
1k
d
00
0
ii
LL
L
0
dt
i
VV
11
0
00
0
C
ωω
CC
k
0
k
k
j
00
0
jj
u
(2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
41
4 –
42
2
41
6
The
sys
t
em
ca
n
be
re
presente
d
as:
xA
.
x
b
x
d
u
(3
)
Where :
L
p
v
a
a
i
V
x
i
V
ω
L
1
a
aa
a
22
2
R1
1
00
LL
L
1
00
0
0
C
R
1k
00
LL
L
11
00
0
CC
k
k
00
0
jj
A
mL
f
ω
a
L
2
Ri
V
V
L
0
0
i
C
0
bx
fω
pv
1
1
V
L
i
C
d
0
0
k
j
(4
)
3.
MPPT M
ETHODS
3.1.
P&
O
To
v
al
i
d
ate
o
u
r
p
rop
o
se
d
M
P
P
T
c
ontro
ller
w
e
h
a
v
e
c
h
ose
n
t
o
c
o
mp
are
it
t
o
th
e
P
&
O
me
t
hod
d
u
e
t
o
the fac
t
t
ha
t
i
t
i
s
w
e
ll kn
ow
n
a
nd c
o
mm
un
l
y
use
d in
t
he
i
nd
us
t
r
y.
The
op
e
r
a
t
i
n
g
pri
n
ci
p
l
e
of
t
hi
s
al
gor
ithm
is
s
how
n
i
n
F
igur
e
2,
a
nd
can
b
e
e
x
p
l
ain
e
d
a
s
f
o
l
lo
ws:
th
e
vo
lta
ge of t
h
e
P
V
panel is d
i
s
t
ur
bed
the
n
w
e
c
a
lcu
l
a
t
e t
h
e p
o
w
e
r pr
ov
ide
d
by t
h
e P
V
pan
e
l
at t
i
m
e
k,
a
nd t
h
e
n
it
is
c
om
pare
d
t
o
t
he
p
re
vio
u
s
one
o
f
the
m
o
m
e
nt
(
k-
1
)
.
If
t
he
d
i
ffer
e
n
ce
is
pos
iti
v
e
t
ha
t
is
t
he
p
o
w
er
incre
a
ses,
it
m
eans
t
h
a
t
we ar
e
a
p
proac
h
i
n
g MP
P and t
h
e
v
a
ria
t
i
o
n
of
t
h
e
dut
y c
y
cle
i
s
m
ain
t
a
i
ne
d i
n
th
e
sam
e
direc
t
i
o
n.
O
n
the
o
t
her
ha
nd,
i
f
t
h
e
d
i
ffere
n
ce
i
s
n
e
g
a
t
i
v
e
tha
t
i
s
t
h
e
p
o
w
e
r
d
e
c
r
e
a
s
e
s
,
w
e
a
r
e
m
o
v
i
n
g
a
w
a
y
from
the
MP
P
.
S
o
, w
e
have
to
re
verse
the
di
r
ecti
o
n of
t
he c
han
g
e
in
t
h
e
d
ut
y
cy
cl
e
.
F
i
gur
e 2.
P
&O
flow
c
ha
rt
3.2.
S
l
i
d
in
g m
o
d
e
c
on
trol
S
l
i
d
in
g
M
o
d
e
C
o
n
t
r
ol
i
s
a
no
nl
i
n
ea
r
c
ont
ro
ll
er
b
as
e
d
on
t
h
e
v
a
r
i
a
ble
s
t
ruc
t
ure
co
ntr
o
l
(V
S
C
).
T
he
adva
n
t
a
g
e
s
of
t
h
e S
M
C
are
var
i
o
u
s: H
igh
pre
c
i
s
i
o
n
,
good
sta
b
il
i
t
y
,
sim
p
l
i
c
i
t
y
,
in
varia
n
c
e
,
robus
tne
ss.
The
de
si
g
n
o
f
the
c
o
ntrol i
s
b
ased
o
n
tw
o impor
tan
t
s
t
e
ps; firs
t,
t
h
e
c
h
o
i
c
e
of t
he
s
l
i
di
ng surfac
e
s(x)
=
0
w
hi
c
h
d
et
ermi
n
e
s
t
h
e
t
r
a
j
ec
t
o
ry
t
h
a
t
th
e
c
o
nt
rol
sh
ould
fo
ll
ow
,
seco
nd,
d
e
t
e
r
m
i
ne
t
he
c
o
n
tr
ol
l
a
w
s
tha
t
hel
p
m
ain
t
a
i
n
a
nd s
t
ab
i
l
ize
t
h
is co
n
tro
l
o
n
t
h
e
sli
d
in
g
sur
f
ac
e
[5],[6]:
‐
Th
e c
h
o
i
ce
of th
e
sli
d
i
n
g
su
rfa
ce
:
Th
e M
P
P i
s
d
et
ermi
n
e
d
wh
en :
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
Ad
ap
tive
fu
zzy sl
id
ing
m
o
de
base
d
MPPT
c
o
n
t
ro
l
l
e
r
fo
r a p
h
o
t
ovo
l
ta
i
c
w
a
t
e
r p
u
m
p
in
g system
(Sab
a
h
Miq
o
i
)
41
7
pv
pv
P
0
V
(5)
Th
ere
f
o
r
e
,
t
h
e
sl
i
d
in
g
su
rf
ac
e i
s
d
e
f
i
n
ed
a
s:
2
pv
pv
p
v
pv
pv
p
v
pv
pv
pv
PI
R
I
sI
V
0
VV
V
(
6)
-
The de
t
e
rm
in
a
t
i
o
n
o
f
the
c
o
n
t
rol law
:
The
co
n
t
ro
l
la
w
c
onsis
ts
o
f
t
w
o
par
t
s
:
t
he
f
ir
st
one
c
a
l
led
the
e
q
u
i
v
a
l
en
t
con
t
ro
l,
i
t
he
lp
s
ma
inta
in
s
the
ope
ra
ti
o
n
p
o
i
nt
i
n
the
sli
d
ing
s
u
rfa
ce,
t
he
s
ec
on
d
on
e
is
t
h
e
s
wi
t
c
hi
ng
c
ont
rol
a
n
d
p
r
ovi
d
e
s
t
h
e
st
a
b
il
iza
t
i
on
o
f
the
c
on
tro
l
l
e
r [7],
[
8]:
eq
n
uu
u
(7)
The
e
q
uiva
l
e
n
t
c
on
tro
l
w
as
f
irst
s
u
gge
st
ed
b
y
S
l
o
t
i
n
e
a
n
d
L
i
[
9
]
and
is
d
eter
mine
d
b
y
t
h
e
fo
l
l
ow
i
n
g
co
nd
iti
on
:
TT
ss
sx
A
.
x
b
x
d
0
xx
u
(
8)
We
con
si
der
d=0,
to sim
p
l
i
fy
t
he
c
alc
u
la
t
i
o
n
s
,
the
equ
i
va
le
nt c
ont
rol
b
e
c
o
me
s:
T
eq
T
s
A.
x
x
s
b
x
x
u
(9)
The
sw
i
t
c
h
in
g
con
t
ro
l
ca
n be
a
l
ine
a
r
fu
nc
t
i
o
n
of
the
sl
idi
n
g
s
urfac
e
,
it
i
s
gi
ven b
y
:
ns
k.
s
g
n
s
u
(
1
0
)
ks is a
pos
iti
ve
c
ons
tan
t
de
t
er
mined
b
y
t
he
c
ons
truc
ter.
Th
us the
S
M
C
c
on
tro
l
ler
i
s
:
T
s
T
s
A.
x
x
uk
.
s
g
n
s
s
bx
x
(
11
)
St
a
b
ili
z
a
t
i
on
stu
dy:
W
e
c
h
o
se t
o
u
s
e
a
fu
n
c
tio
n
n
ame
d
Ly
a
pu
nov g
i
v
e
n
by
:
2
1
2
Vs
(
1
2
)
The
deri
va
ti
ve
o
f t
h
is fu
n
c
t
i
o
n
is:
Vs
s
0
0
s
(13
)
3.3.
A
d
apt
i
ve
fu
z
z
y
slid
in
g
mod
e
con
trol
D
e
spite
t
he
r
o
bus
t
n
ess
of
t
he
s
l
i
d
i
n
g
m
ode
c
on
tro
l
,
it
c
a
us
es
d
r
a
wbac
ks.
The
m
a
i
n
d
isa
dva
n
t
age
i
s
the
c
h
a
t
ter
i
n
g
phe
n
o
m
e
no
n
c
a
use
d
b
y
the
h
i
gh
osc
i
ll
a
tio
ns
a
rou
n
d
t
h
e
sli
d
in
g
s
u
rface
.
In
a
dd
i
t
i
on,
t
o
ac
hie
v
e
a
fa
s
t
c
on
ve
rge
n
c
e
a
nd
m
ore
s
t
ab
i
l
i
t
y
,
i
t
i
s
re
c
o
mm
ende
d
t
o
u
se
h
igh
va
lue
s
o
f
sw
i
t
c
h
i
n
g
ga
in.
H
o
w
e
ve
r
,
t
he
hi
ghe
r the
ga
in
the
m
ore
osc
illa
ti
on
s ther
e a
r
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
:
41
4 –
42
2
41
8
F
i
gure
3(
a)
r
e
p
r
e
sen
t
s
the
o
u
t
p
ut
p
ow
er
u
sing
t
h
e
s
l
i
d
i
ng
m
o
de
c
o
n
t
rol
l
er
f
or
d
iffer
e
nt
s
ol
ar
i
rrad
i
a
t
i
o
n
l
e
vel
s
o
f
800
,
100
0
a
n
d
60
0
and
a
fi
x
e
d
t
e
mpera
t
u
r
e
.
We
can
s
ee
th
at
t
h
e
m
o
r
e
we
i
n
c
rea
s
e
th
e
gai
n
,
the m
o
re
there
is osc
i
lla
t
i
ons,
and
t
h
e h
i
gher
t
h
e pow
er
prod
uct
i
on.
O
n
t
h
e
o
t
h
e
r
h
and,
i
f
w
e
c
on
side
r
F
i
gure
3(
b)
w
hic
h
r
epre
sen
t
s
t
h
e
o
u
t
p
u
t
p
o
w
e
r
f
o
r
a
o
n
e
-
d
a
y
s
e
e
Figure
9,
w
e
can
s
ee
t
ha
t
if
w
e
incre
a
se
t
h
e
g
ai
n
the
r
o
b
u
stnes
s
of
t
h
e
c
on
tro
lle
r
i
n
c
r
ea
ses
a
s
w
ell
as
t
he
osc
illa
t
i
o
n
s
w
h
ich
m
a
ke
s
t
h
e
c
o
n
t
ro
lle
r
uns
ta
bl
e
.
F
or
a
s
ma
l
l
g
ai
n
o
f
0
.5
d
es
pi
te
i
ts
s
ta
b
i
l
i
t
y
it
is
l
e
s
s
rob
u
st
and
pr
od
uces
l
e
s
s
ene
r
gy c
o
mpar
ed
t
o
o
t
he
r ga
i
n
.
(a
)
(b
)
F
i
gure
3.
C
om
par
i
s
on
of o
ut
p
u
t
p
o
w
e
r
for
di
ffe
ren
t
ga
i
n
S
o
, to
f
i
n
d
a
b
a
l
a
nce
be
tw
e
e
n the
sta
b
ili
t
y
a
n
d
the r
ob
us
t
n
e
ss
w
e
op
t
e
d
to u
s
e
a
n
a
da
pti
v
e gai
n
, sinc
e
a
c
ons
t
a
n
t
-
g
ai
n
fe
e
dbac
k
c
o
n
tr
ol
l
e
r
is
n
o
t
a
ble
to
p
ro
perl
y
tra
ck
t
he
M
P
P
due
t
o
the
c
o
n
s
t
a
n
t
c
ha
n
g
e
o
f
th
e
w
e
a
t
he
r.
F
igure
4
show
t
he a
dap
t
ive f
u
zz
y
con
t
ro
l.
F
i
gur
e 4
.
the
a
dap
t
ive
fuzz
y con
t
ro
l
Th
is
c
on
tro
lle
r
com
b
i
n
e
s
t
he
s
lid
i
ng
mo
de
c
onc
e
p
t
w
i
t
h
f
u
z
z
y
c
o
n
t
r
o
l
s
t
rateg
y
t
o
de
si
g
n
an
a
da
pt
iv
e
fuz
z
y
s
l
i
d
i
ng
m
ode
c
ontr
o
l
l
e
r
,
t
he
a
dap
t
iv
e
fuz
z
y
w
i
ll
s
erve
t
o
g
e
n
er
ate
a
d
ap
t
i
v
e
s
w
itc
h
i
n
g
g
a
i
n.
A
s
we
esta
bl
ishe
d
i
n
(
7), the c
o
ntr
o
l
law
co
ns
ists of
tw
o co
n
t
rols a
n
e
qu
i
v
ale
n
t
c
o
n
t
r
o
l tha
t
we
ar
e n
o
t
cha
n
gi
n
g
,
and
a
sw
i
t
c
h
i
ng
co
ntr
o
l t
h
a
t
c
onta
i
n
s
t
he
m
od
i
f
i
e
d gai
n
.
A
s
s
how
n
o
n
t
h
e
F
ig
ure
5
the
in
p
u
t
s
i
gna
ls o
f
the
f
u
zz
y
l
o
gic
c
ontr
o
l
are
t
h
e
slid
in
g
sur
f
ac
e
s
and i
t
s
deri
va
ti
ve
d
s
/
d
t
,
the ou
t
p
u
t
o
f
i
s
t
h
e
sw
itc
hi
n
g
gai
n
ks.
The
f
uz
z
y
r
ul
e
s
ar
e
give
n
in t
h
e
fol
l
ow
in
g f
o
rm
[9]
:
R
u
le j
: I
F
i
s
A
and
is
A
; THEN
ks is
B
A
a
nd
B
a
re
r
e
s
p
ect
iv
el
y
t
h
e
i
n
p
u
t
a
n
d
ou
t
p
u
t
f
u
zzy
s
et
s.
B
y
usi
ng
t
h
e
c
ent
r
e
av
e
r
ag
e
defuz
z
i
fica
t
i
o
n
m
e
thod,
th
e
o
ut
p
u
t va
l
u
e
of
t
he
fuz
z
y
s
ys
te
m
is
as
f
o
llow:
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
Ad
ap
tive
fu
zzy sl
id
ing
m
o
de
base
d
MPPT
c
o
n
t
ro
l
l
e
r
fo
r a p
h
o
t
ovo
l
ta
i
c
w
a
t
e
r p
u
m
p
in
g system
(Sab
a
h
Miq
o
i
)
41
9
1
1
()
n
i
j
j
ji
s
n
i
j
ji
yA
k
A
(14
)
Where
μ
A
the
membe
r
shi
p
i
s
funct
i
on
va
lue
o
f
a
lin
g
u
i
s
t
i
c
va
riab
le
a
nd
y
d
e
f
i
n
e
a
c
r
i
s
p
v
a
l
u
e
at
w
h
ic
h the
o
u
t
put
m
e
m
be
rship
func
t
i
o
n
μ
B
a
chieves its m
a
ximum
μ
B
1
.
The
(24)
ca
n
b
e
expre
ssed a
s
fo
l
low
:
T
s
ky
(
1
5
)
Where
y
i
s
a
n
adj
u
s
t
a
b
l
e
p
a
r
am
eter
v
e
c
tor,
ξ
i
s
a
fuz
z
y
ba
si
s
f
un
ct
i
on
v
e
ctor,
and
ξ
∏
∑∏
j = 1,
2,
3.
.
.
m.
A
p
p
l
y
i
ng a
n
a
da
pt
ive
co
n
t
ro
l
w
e
get
t
he
fo
l
l
o
w
i
ng eq
ua
t
i
o
n
:
T
s
ky
(16)
A
c
cordi
n
g
to
t
he
u
n
i
versa
l
a
ppr
ox
im
at
i
o
n
t
h
e
o
rem
[10],
there
ex
is
ts
a
n
op
tim
al
p
a
r
am
eter
y
tha
t
sat
is
fie
s
:
**
T
s
ky
(17)
Where
y
i
s
t
h
e
e
s
t
i
m
a
t
i
o
n
o
f
y
∗
,
a
nd
ε
is
t
he
a
ppro
x
i
ma
t
i
o
n
e
rror
del
i
mi
ted
b
y
|
ε
|
E
,
E
is
a
pos
it
ive
co
ns
t
a
nt
.
S
t
abi
liz
a
tio
n
stud
y
:
The
Lya
p
u
n
ov
fu
nc
ti
o
n
i
s def
i
ne
d as
f
o
l
l
o
w
i
ng
[1
0]:
2
11
22
T
Vs
y
y
(
1
8
)
Where
y
y
∗
y
a
nd
γ
i
s
a posi
tive
c
o
nstan
t
.
**
TT
T
ss
s
kk
k
y
y
y
(19
)
To
e
n
s
u
r
e t
h
at
t
h
e
c
ont
rol
l
er i
s s
t
ab
l
e
t
h
e
de
r
i
v
ati
v
e
of Ly
a
pu
nov
f
un
ct
ion
mu
s
t
b
e
lo
wer
t
h
an
z
e
r
o
:
T
Vs
s
y
y
(
20
)
s
eq
s
eq
..
u
k
s
g
n
s
.u
k
s
g
n
s
TT
T
ss
s
A
x
bx
u
d
A
x
bx
d
xx
s
sA
x
b
x
d
b
x
x
(
21
)
C
ons
ide
r
i
ng t
h
at
x
A
.
x
b
x
u
d
0
F
r
om 31
beco
m
e
s:
s
ks
g
n
s
T
s
sb
x
x
(
22
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
41
4
–
422
42
0
W
e
ap
p
ly
to:
s
ks
g
n
s
(
)
s
g
n
s
TT
TT
T
ss
V
s
b
x
yy
s
b
x
y
yy
xx
(
23
)
V
|
|
ξ
|
|
(24)
Let t
h
e
ada
p
tiv
e
rule
b
e:
1
ξ
T
s
ys
b
x
x
(
25
)
The
n
w
e w
i
ll h
a
ve:
0
T
s
Vs
b
x
s
x
(26)
Due
to
f
a
c
t
tha
t ε
is pos
iti
ve
V
i
s
und
e
n
ia
bly
n
e
gat
i
v
e
w
h
i
c
h
pr
o
v
e
s
t
he
s
tab
i
l
i
t
y
o
f
t
he
s
ys
te
m.
F
i
gur
e
5.
I
npu
t
fuzz
y
m
e
m
b
er
sh
ips
F
i
gur
e
6.
O
utp
u
t
f
u
z
z
y
m
em
b
e
r
s
hips
The
f
u
zz
y
r
u
l
e
s
ar
e
su
m
m
a
r
i
z
e
d
i
n
t
he
T
a
b
le
1
.
A
nd
m
e
m
b
er
sh
ip
f
un
c
t
ion
s
f
o
r
t
h
e
i
nput
s
a
nd
s
a
r
e
r
e
pr
e
s
ente
d
i
n
F
i
g
ur
e
6.
F
or
t
he
o
ut
put
o
f
t
h
e
f
u
z
z
y
s
ys
tem
k
s
seve
n
eq
ui
dis
t
an
t
l
y
pl
a
c
e
d
s
in
gl
et
ons
a
r
e
use
d
,
as
s
how
n
i
n
F
igur
e
7.
T
he
m
em
ber
s
hi
p
f
unc
tio
ns
a
r
e
c
atego
r
i
z
e
d
b
y
l
i
n
g
u
i
st
ic
v
a
l
ue
s
N
e
gat
i
v
e
Bi
g
(
N
B)
,
N
e
gati
v
e
Me
d
ium (
N
M)
,
N
e
gat
i
v
e
S
ma
ll (
N
S
)
,
Zer
o
(
Z
R)
,
P
o
s
iti
ve Sm
a
ll
(
P
S
)
, Posi
tive
Me
di
u
m
(
P
M
)
an
d
Po
s
i
tiv
e
Big
(P
B
).
Tab
l
e
1.
F
uzz
y
r
ule
s
s \
N
B
N
M
Z
R
P
M
PB
Z
R
P
M
PS
Z
R
N
S
N
M
PS
P
S
Z
R
N
S
N
M
N
B
PM
Z
R
N
S
N
S
N
M
N
B
P
B
Z
R
NS
N
M
NB
N
B
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
Ad
ap
tive
fu
zzy sl
id
ing
m
o
de
base
d
MPPT
c
o
n
t
ro
l
l
e
r
fo
r a p
h
o
t
ovo
l
ta
i
c
w
a
t
e
r p
u
m
p
in
g system
(Sab
a
h
Miq
o
i
)
42
1
4.
RESULT
S
The
P
V
w
a
t
er
pum
p
i
ng
s
y
s
t
e
m
h
as
b
ee
n
m
ode
l
l
ed
a
n
d
s
i
m
ulate
d
u
s
i
ng
MATLAB
/
SIMULI
NK
and
the
pro
p
o
s
ed
c
ontr
o
l
l
ed
A
F
S
M
C
w
as
c
omp
a
red
t
o
b
ot
h
t
h
e
S
lid
ing
m
o
d
e
c
on
t
r
ol
a
n
d
t
he
P
&O
a
lg
ori
t
hm
t
o
see
it
s
be
nefi
t
s
i
n
e
x
tra
c
t
i
n
g
t
he
m
ax
im
um
pow
e
r
a
n
d
a
l
s
o
t
o
v
a
l
i
d
ate
the
fu
nc
ti
o
n
a
l
i
t
y
of
t
his
c
o
ntr
o
ller
.
Tab
l
e
2 re
prese
n
ts
t
he
pa
r
am
eter
s
of
t
he
P
V
w
a
t
e
r pum
pin
g
sys
t
e
m:
Tab
l
e
2. S
ystem
par
a
m
e
ters
PV
p
a
n
e
l
T
E
500CR
B
oost c
onve
rte
r
D
C m
o
tor
Wm
pp
=
55w
a
tts
R
L
=0
.5
Ω
R
a
=
1
.
254 Ω
Vm
pp
=
17,
50V
L
=
6
.
8
1
0
-3
H
L
a
=
28
10
-3
H
Im
pp
=
3
,
10A
C
1
=6
.2
1
0
-3
F
k
1
=
0
.
1kg.m
2
.r
ad
/
s
ec
V
o
c=
21,
7V
C
2
=
2
.
88
10
-3
F
k
2
=
0
.
0114
kg.
m
2
/se
c
2
Isc=
3
,
5A
j=
0.
004
kg.m
2
N
s
=
3
6
k
=
0
.
333
V
.
s
e
c
/
r
a
d
F
i
r
s
t
l
y
w
e
m
a
d
e
t
h
e
c
o
m
p
a
r
i
s
o
n
f
o
r
a
f
i
x
e
d
t
e
m
p
e
r
a
t
u
r
e
o
f
2
5
°
C
a
n
d
var
i
a
b
l
e
s
o
l
ar
i
rr
adia
t
i
o
n
s,
a
s
show
n
in
F
i
gur
e
7,
in
o
rder
t
o
see
cl
ose
l
y
t
h
e
de
fer
e
nce
a
n
d
t
h
e
a
dv
a
n
t
a
ge
o
f
ad
d
i
n
g
t
he
f
uz
zy
a
da
p
t
ive
t
o
t
h
e
S
M
C
,
w
e
h
a
v
e
e
x
t
r
a
c
t
e
d
t
h
e
p
o
w
e
r
f
o
r
t
h
r
e
e
d
i
f
f
e
r
e
n
t
v
a
l
u
e
o
f
t
he
s
olar
i
rradia
tio
n
,
F
igure
8
sh
o
w
s
th
e
varia
t
i
o
n of t
he
o
u
t
p
u
t pa
ne
l p
o
w
e
r
.
F
i
gure
7.
S
olar
i
rra
d
i
a
t
i
o
n
F
i
gur
e 8.
P
ow
e
r
v
aria
t
i
on f
o
r fix
e
d
tem
per
a
t
u
re
a
nd
va
ria
b
le
i
r
r
ad
ia
ti
o
n
A
c
cordi
n
g t
o
t
he
F
i
gure 8,
w
e
ca
n
see
t
h
at
t
he
p
r
opose
d
m
eth
o
d
A
F
SMC
is
b
e
t
te
r
t
h
an
t
he othe
r
t
w
o
me
tho
d
s.
C
ompa
red
to
t
he
P
&O
t
he
S
M
C
a
nd
A
F
S
M
C
a
r
e
w
a
y
be
tt
e
r
a
nd
p
rod
u
c
e
m
or
e
pow
e
r
.
If
w
e
com
p
are
the
S
M
C
an
d
AF
SM
C,
w
e
no
te
t
hat
t
h
e
AF
SMC
i
s
s
li
gh
t
l
y
h
i
gher
tha
n
t
he
S
M
C
a
n
t
h
er
e
are
few
e
r
osc
illa
t
i
o
n
s
a
n
d
w
e
c
an
c
o
n
c
lu
de
t
ha
t
o
u
r
prop
ose
d
m
etho
d
is
m
o
re
e
ffic
i
e
n
t
.
A
f
terw
a
r
d,
w
e
m
a
de
t
he
com
p
aris
on
of
t
he
t
hre
e
m
etho
ds
u
si
ng
the
w
e
ather
data
f
or
a
o
n
e
s
p
e
c
i
fic
da
y,
F
ig
ure
9
show
s
the
d
a
ta
o
f
tem
p
era
t
ur
e a
nd irra
dia
t
i
o
n
seque
n
tia
l
l
y
for
t
h
i
s
da
y
.
F
i
gure
9
.
S
olar
i
rradia
t
i
on da
ta
for a
day
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
:
41
4 –
42
2
42
2
We
h
ave
e
x
tra
c
te
d
t
h
e
va
ria
t
io
n
of
t
he
o
ut
pu
t
p
o
w
e
r
for
th
ose
s
o
l
ar
i
rr
adia
t
i
o
n
s
an
d
t
e
m
p
era
t
ure
data,
as
i
t
is
s
how
n
in
F
i
g
ure
10.
W
e
a
l
so
e
xtra
cte
d
t
he
M
o
t
or
D
C
s
p
e
e
d
s
e
e
F
i
g
u
r
e
1
1
.
A
n
d
w
e
c
a
n
s
e
e
t
h
a
t
A
F
S
M
C
has le
ss
o
sc
i
llat
i
on a
n
d
t
h
ere
is no
de
v
i
a
tio
n
of t
h
e
c
ur
ve
,
l
i
ke
t
he
one
w
e
ca
n see
on
t
h
e
S
M
C
c
u
rve.
F
i
gure
1
0
.
P
V
pow
er
v
aria
ti
o
n
F
i
gure
1
1
.
M
otor
D
C spee
d v
a
r
i
a
t
i
o
n
A
ll
t
h
o
s
e
re
su
l
t
s
s
how
c
le
arl
y
t
he
s
u
p
e
r
ior
ity
a
n
d
e
ff
i
c
ien
c
y
o
f
the
pro
p
o
se
d
c
ontr
o
lle
r
A
F
S
M
C
c
o
mp
a
r
ed
t
o
t
h
e
SM
C
and
th
e
P&O.
f
u
r
t
h
ermo
re
t
h
e
re
a
re
f
e
w
er
o
s
c
i
l
l
a
t
i
ons on
t
h
e pro
pos
ed
c
o
n
t
r
o
ll
er
c
urv
e
w
h
ic
h pr
o
v
e it
s stab
il
ity a
nd
go
o
d
pe
r
form
anc
e
.
5.
CONCL
U
S
ION:
I
n
t
his
w
o
r
k
w
e
did
the
st
u
dy
of
a
p
h
o
t
o
vol
taic
w
a
t
er
pump
i
ng
s
ys
t
e
m
t
h
e
n
w
e
mode
lize
d
a
n
d
si
m
u
late
d
th
is
s
yste
m
usi
n
g
MA
TLA
B
/
SIMU
LI
N
K
simula
t
o
r,
n
ext
w
e
have
d
eve
l
o
p
e
d
a
n
e
w
m
axim
um
p
o
w
e
r
poi
nt
t
rac
k
e
r
c
a
l
l
e
d
A
F
S
M
C
a
d
apt
i
ve
f
uz
zy
s
lid
i
ng
mo
d
e
c
o
ntr
o
ll
e
r
,
this
c
o
n
t
ro
l
l
er
i
s
ba
se
d
o
n
t
h
e
rob
u
st
m
eth
o
d
s
lid
i
ng
m
ode.
We
h
ave
a
d
d
e
d
t
o
t
h
i
s
las
t
t
h
e
a
da
p
t
i
ve
f
uzz
y
m
et
ho
d
i
n
o
rder
t
o
am
el
i
o
rate
t
h
e
perform
ance
o
f
t
h
e
SM
C
an
d
to
o
v
e
rc
om
e
t
h
e
c
h
a
t
teri
ng
p
h
en
ome
n
a
.
W
e
h
av
e
co
mp
a
r
ed
t
hi
s
me
t
hod
t
o
th
e
S
M
C
a
n
d
the
P
&
O
in
o
rder
t
o
val
i
d
ate
t
h
is
c
on
t
r
ol
ler
.
T
he
e
x
t
r
a
c
t
ed
r
e
s
ul
t
s
w
h
e
th
er
o
f
t
h
e
po
we
r
s
hows
t
h
e
r
o
b
u
s
t
n
e
s
s
a
n
d
e
f
f
i
c
i
e
n
c
y
o
f
t
h
i
s
m
e
t
h
o
d
.
I
n
f
u
t
u
r
e
w
o
r
k
,
w
e
h
o
p
e
t
o
be
a
ble
t
o
a
p
p
l
y
t
hi
s
me
t
h
od
i
n
r
e
a
lity
and
co
n
f
irm
th
e
effic
i
e
n
cy
o
f th
is co
n
t
rol
l
er.
REFE
RENCES
[1
]
Ab
do
urra
ziq
S,
A
bd
ou
rra
z
i
q
M
A,
a
n
d
D
ara
b
C
,
“
P
ho
to
volt
a
ic
w
ater
p
u
m
p
i
ng
sys
t
em
a
ppli
cation
in
M
o
r
oc
c
o
,”
I
n
Ele
ctr
o
m
e
ch
anica
l
an
d
Power
S
y
s
t
e
m
s
(
S
IE
LMEN)
,
”
2
0
17
Int
e
r
n
a
tiona
l
C
o
nf
e
r
e
n
ce
o
n
Oct
1
1
,
pp.
2
71-27
4.
IEEE,
2017.
[2]
D
o
l
a
r
a
A
,
F
a
r
a
n
d
a
R
,
a
n
d
L
e
v
a
S
,
“
E
n
e
r
g
y
c
o
m
p
a
r
i
s
o
n
o
f
s
e
v
e
n
M
P
P
T
t
ec
hniq
u
e
s
f
o
r
P
V
sy
stem
s,”
J
o
u
r
nal of
Ele
ctr
o
ma
gne
tic
A
n
a
l
y
s
is
an
d A
p
p
l
ic
ati
ons,
Se
p
2
8
;
1(
03):1
52
,
2009
.
[3]
R
a
o
D
V
an
d
G
o
T
H
,
“
A
u
to
m
a
ti
c
l
a
nd
in
g
s
y
s
t
e
m
d
es
i
g
n
u
s
in
g
s
l
id
in
g
m
o
d
e
c
on
tro
l
,”
Aer
o
s
p
a
c
e
S
c
i
e
nc
e
and
Te
c
h
n
o
l
o
g
y
,
J
a
n
1
;
32
(
1
)
:
1
8
0-
7
,
2
0
1
4
.
[4]
Bel
lia H, Y
ou
c
e
f
R, an
d
Fat
i
ma
M
,
“A
d
e
t
a
ile
d
mo
de
l
i
n
g
o
f
ph
o
t
o
volta
ic
m
od
u
l
e
usin
g M
A
TLAB,
”
N
R
I
A
G J
o
ur
na
l
of
Astr
on
omy
a
n
d
Ge
o
phy
sic
s
,
Ju
n 1
;
3
(
1
):53
-6
1,
2
0
1
4
.
[5]
Ut
k
i
n
VI
,
“
S
li
d
i
ng
m
od
e
c
o
n
t
ro
l
de
si
gn
p
r
inc
i
p
l
es
a
nd
a
pplica
t
i
o
n
s
t
o
e
lectric
driv
es,”
IEEE tran
sac
t
i
ons on
indus
t
rial
e
l
ectr
oni
c
s
.
F
e
b
;
4
0
(
1):2
3
-
3
6
,
1
99
3.
[6]
Slo
t
i
n
e JJ
and
Li
W
,
“
A
ppli
e
d
n
o
n
line
a
r c
ontr
o
l
.
En
glew
o
o
d
Cli
f
fs
,”
NJ:
P
ren
t
i
c
e
hal
l; 19
91
Jan
.
[7]
R
e
k
i
ou
a
D
,
A
c
h
o
u
r
A
Y
,
a
n
d
R
e
ki
ou
a
T
,
“
T
r
a
c
k
in
g
p
o
we
r
p
h
ot
o
v
o
l
t
a
ic
s
ystem
w
ith
s
l
i
d
i
ng
m
od
e
contr
o
l
st
r
a
t
e
g
y
,
”
En
e
r
gy
P
r
o
ced
ia
, J
an 1
; 3
6
:21
9
-
3
0
, 2
01
3.
[8]
An
us
uyad
e
vi
R
,
Pa
n
d
i
a
ra
ja
n
S
,
a
n
d
B
h
a
ra
thi
J.M
,
“
M
a
xim
u
m
P
o
we
r
P
o
in
t T
r
a
c
k
i
ng o
f
D
C
T
o
DC
Bo
ost
Co
nverte
r
Using
Sl
i
d
ing
M
ode
C
on
tr
o
l
,
”
Inte
r
nati
onal J
o
u
r
n
a
l
of Powe
r El
ect
r
o
n
i
cs an
d Dr
iv
e Syste
m
s
(
I
JP
EDS)
,
Ja
n
1
;
3
(
3):32
1
-7
,
2
013
.
[9]
Cerm
an
O
a
n
d
H
u
š
e
k
P
,
“
A
da
p
t
ive
f
u
zzy
s
li
di
n
g
m
od
e
c
o
ntr
o
l
f
o
r
electr
o
-h
yd
rau
l
i
c
s
er
vo
m
echa
n
ism
,
”
Exp
e
rt
System
s with
Applica
t
ion
s
, S
e
p
1
;3
9
(
1
1
):10
26
9
-
7
7
,
20
12
[10]
S
o
lta
np
our
M
.R,
Kho
oba
n
M
.
H,
a
n
d
K
hal
g
h
a
n
i
M
.R
,
“
A
n
op
t
i
ma
l
a
n
d
i
n
t
elligent
con
t
r
o
l
strat
e
gy
f
o
r
a
class
o
f
no
nl
ine
a
r
sy
s
t
ems
:
a
da
ptive
f
u
z
z
y
sl
id
i
n
g
m
ode
,”
J
o
u
r
n
a
l
o
f
V
i
b
r
ation
and
C
ontr
o
l
,
Ja
n;
2
2
(
1):1
59
-7
5
,
20
16.
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