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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
,
p
p
.
2
1
8
3
~
2
1
9
6
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
7
.
i
3
.
p
p
2
1
8
3
-
2
1
9
6
2183
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Energ
y
optimiza
t
io
n of an elec
tric
v
ehicle charg
ing
s
tatio
n using
a
hybrid ST
A
-
G
WO
M
PP
T
s
trate
g
y
Sa
m
ia
Am
r
o
un
i
1,
2
,
Sa
id Ais
s
o
u
3
,
Ra
f
ik
M
edj
o
ud
j
1
,
E
ly
a
zid A
m
iro
uche
3
,
Na
bil
B
eny
a
h
ia
4
,
Abdelh
a
k
im
B
elk
a
id
5
1
La
b
o
r
a
t
o
i
r
e
LI
TA
N
Éc
o
l
e
su
p
é
r
i
e
u
r
e
e
n
S
c
i
e
n
c
e
s
e
t
T
e
c
h
n
o
l
o
g
i
e
s
d
e
l
’
I
n
f
o
r
mat
i
q
u
e
e
t
d
u
N
u
mér
i
q
u
e
R
N
7
5
,
B
e
j
a
i
a
,
A
l
g
é
r
i
e
2
D
e
p
a
r
t
me
n
t
o
f
A
u
t
o
ma
t
i
o
n
,
M
o
u
l
o
u
d
M
a
mm
e
r
i
U
n
i
v
e
r
si
t
y
o
f
Ti
z
i
-
O
u
z
o
u
,
Ti
z
i
-
O
u
z
o
u
,
A
l
g
e
r
i
a
3
La
b
o
r
a
t
o
i
r
e
d
e
M
a
i
t
r
i
s
e
d
e
s
En
e
r
g
i
e
s
R
e
n
o
u
v
e
l
a
b
l
e
s
(
L
M
ER
)
,
F
a
c
u
l
t
é
d
e
T
e
c
h
n
o
l
o
g
i
e
,
U
n
i
v
e
r
s
i
t
é
d
e
B
e
j
a
i
a
,
B
e
j
a
i
a
,
A
l
g
é
r
i
e
4
ESM
E
R
e
sea
r
c
h
La
b
,
I
v
r
y
-
su
r
-
S
e
i
n
e
,
F
r
a
n
c
e
5
La
b
o
r
a
t
o
i
r
e
d
e
T
e
c
h
n
o
l
o
g
i
e
I
n
d
u
st
r
i
e
l
l
e
e
t
d
e
l
’
I
n
f
o
r
mat
i
o
n
(
LTII
)
,
F
a
c
u
l
t
é
d
e
Te
c
h
n
o
l
o
g
i
e
,
U
n
i
v
e
r
si
t
é
d
e
B
e
j
a
i
a
,
A
l
g
é
r
i
e
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
u
l 2
4
,
2
0
2
6
R
ev
is
ed
Au
g
1
7
,
2
0
2
6
Acc
ep
ted
Au
g
2
4
,
2
0
2
6
Th
is
p
a
p
e
r
p
re
se
n
ts
a
h
y
b
ri
d
e
lec
tri
c
v
e
h
icle
c
h
a
rg
i
n
g
sta
ti
o
n
p
o
we
re
d
b
y
b
o
t
h
a
P
V
so
u
rc
e
a
n
d
th
e
u
ti
li
ty
g
rid
,
i
n
c
o
r
p
o
ra
ti
n
g
a
n
e
n
e
rg
y
m
a
n
a
g
e
m
e
n
t
stra
teg
y
t
h
a
t
p
rio
r
it
ize
s
th
e
u
ti
li
z
a
ti
o
n
o
f
so
lar
e
n
e
rg
y
wh
il
e
e
x
p
o
rti
n
g
su
rp
lu
s
p
o
we
r
to
th
e
g
rid
d
u
r
i
n
g
p
e
rio
d
s
o
f
lo
w
c
h
a
rg
in
g
d
e
m
a
n
d
.
T
o
e
n
h
a
n
c
e
t
h
e
p
e
rfo
rm
a
n
c
e
o
f
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
,
a
h
y
b
rid
c
o
n
tro
l
stra
teg
y
i
n
teg
ra
ti
n
g
th
e
g
re
y
wo
lf
o
p
ti
m
ize
r
(G
WO)
a
n
d
t
h
e
su
p
e
r
-
twisti
n
g
a
lg
o
r
it
h
m
(S
TA)
is
p
r
o
p
o
se
d
.
T
h
e
G
WO
p
e
rfo
rm
s
ra
p
id
g
l
o
b
a
l
e
x
p
lo
ra
ti
o
n
t
o
a
c
c
u
ra
tely
i
d
e
n
ti
f
y
t
h
e
m
a
x
imu
m
p
o
we
r
p
o
i
n
t,
w
h
e
re
a
s
th
e
S
TA
e
n
su
re
s
p
re
c
ise
,
ro
b
u
st,
a
n
d
c
h
a
tt
e
rin
g
-
fre
e
trac
k
in
g
u
n
d
e
r
st
e
a
d
y
-
sta
te
o
p
e
ra
ti
n
g
c
o
n
d
it
io
n
s.
Th
e
p
r
o
p
o
se
d
s
y
ste
m
wa
s
m
o
d
e
led
i
n
M
ATLAB/S
imu
li
n
k
a
n
d
v
a
li
d
a
ted
u
n
d
e
r
a
d
y
n
a
m
ic
irrad
ian
c
e
p
ro
fil
e
c
h
a
ra
c
teriz
e
d
b
y
b
o
t
h
a
b
r
u
p
t
a
n
d
g
ra
d
u
a
l
v
a
riatio
n
s
.
S
imu
lati
o
n
re
su
lt
s
d
e
m
o
n
stra
te
a
c
o
n
v
e
r
g
e
n
c
e
ti
m
e
o
f
2
-
3
m
s,
re
sid
u
a
l
p
o
we
r
o
sc
il
latio
n
s
b
e
lo
w
0
.
1
%
,
a
n
d
a
n
a
v
e
ra
g
e
trac
k
in
g
e
fficie
n
c
y
o
f
9
9
.
3
8
%
.
Co
m
p
a
re
d
with
c
o
n
v
e
n
ti
o
n
a
l
M
P
P
T
tec
h
n
iq
u
e
s,
th
e
p
ro
p
o
se
d
S
TA
-
G
WO
a
p
p
r
o
a
c
h
sig
n
ifi
c
a
n
t
ly
su
p
p
re
ss
e
s
ste
a
d
y
-
s
tate
o
sc
il
latio
n
s,
a
c
c
e
lera
tes
c
o
n
v
e
rg
e
n
c
e
,
a
n
d
p
re
v
e
n
ts
M
P
P
trac
k
in
g
fa
il
u
re
u
n
d
e
r
ra
p
i
d
irrad
ia
n
c
e
flu
c
tu
a
ti
o
n
s
th
ro
u
g
h
th
e
g
l
o
b
a
l
o
p
ti
m
iza
ti
o
n
c
a
p
a
b
il
it
y
o
f
G
WO.
Th
e
se
fin
d
in
g
s h
ig
h
l
ig
h
t
th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
th
e
p
r
o
p
o
se
d
h
y
b
rid
M
P
P
T
stra
teg
y
i
n
imp
r
o
v
i
n
g
t
h
e
ro
b
u
stn
e
ss
,
e
n
e
rg
y
c
o
n
v
e
rsi
o
n
e
f
ficie
n
c
y
,
a
n
d
g
rid
i
n
teg
ra
ti
o
n
c
a
p
a
b
il
it
y
o
f
PV
-
p
o
we
re
d
EV
c
h
a
rg
in
g
sta
ti
o
n
s,
m
a
k
in
g
it
a
p
ro
m
isi
n
g
so
lu
ti
o
n
fo
r
n
e
x
t
-
g
e
n
e
ra
ti
o
n
su
sta
in
a
b
le ch
a
rg
i
n
g
i
n
fra
stru
c
tu
re
.
K
ey
w
o
r
d
s
:
E
lectr
ic
v
eh
icles
E
V
ch
ar
g
in
g
s
tatio
n
s
Gr
ey
wo
lf
o
p
tim
izer
M
PPT
Ph
o
to
v
o
ltaic
s
y
s
tem
s
Su
p
er
twis
tin
g
alg
o
r
ith
m
T
h
is i
s
a
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
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Said
Ais
s
o
u
L
ab
o
r
ato
ir
e
d
e
Ma
itrise
d
es E
n
er
g
ies R
en
o
u
v
elab
les (
L
ME
R
)
,
Facu
lté
d
e
T
ec
h
n
o
l
o
g
ie
Un
iv
er
s
ité
d
e
B
ejaia
B
ejaia
,
Alg
ér
ie
E
m
ail:
s
aid
.
aiss
o
u
@
u
n
iv
-
b
ejaia
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
g
r
o
wth
o
f
elec
tr
ic
v
eh
icle
s
(
E
Vs),
co
u
p
led
with
th
e
ex
p
an
d
in
g
d
e
p
lo
y
m
e
n
t
o
f
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
c
e
s
,
h
as
b
e
c
o
m
e
a
k
e
y
d
r
iv
e
r
i
n
r
e
d
u
c
i
n
g
g
r
e
e
n
h
o
u
s
e
g
a
s
e
m
is
s
i
o
n
s
a
n
d
d
e
p
e
n
d
e
n
c
e
o
n
f
o
s
s
i
l
f
u
el
s
[
1
]
,
[
2
]
.
Ph
o
to
v
o
ltaic
(
PV)
en
er
g
y
p
la
y
s
a
p
r
o
m
in
en
t
r
o
le
o
win
g
to
ab
u
n
d
an
t
s
o
lar
en
er
g
y
r
eso
u
r
ce
s
,
th
e
co
n
tin
u
o
u
s
d
ec
lin
e
in
m
o
d
u
le
co
s
ts
,
an
d
its
ea
s
e
o
f
in
teg
r
atio
n
in
to
elec
tr
ical
in
f
r
astru
ctu
r
e
[
3
]
.
T
h
is
tr
en
d
is
r
ef
lecte
d
in
th
e
r
em
ar
k
ab
le
g
r
o
wth
o
f
in
s
talled
PV
ca
p
ac
ity
,
wh
ich
r
o
s
e
f
r
o
m
ar
o
u
n
d
4
0
GW
in
2
0
1
0
to
m
o
r
e
th
a
n
2
.
2
6
T
W
b
y
th
e
en
d
o
f
2
0
2
4
,
b
ef
o
r
e
ex
ce
ed
i
n
g
2
.
9
T
W
in
2
0
2
5
[
4
]
.
I
n
th
is
c
o
n
tex
t,
in
teg
r
atin
g
PV
s
y
s
tem
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
2183
-
2
1
9
6
2184
in
to
E
V
c
h
ar
g
i
n
g
s
tatio
n
s
is
a
r
elev
an
t
s
o
lu
tio
n
f
o
r
d
ec
ar
b
o
n
izin
g
th
e
tr
an
s
p
o
r
t
s
ec
to
r
wh
ile
lim
itin
g
r
elian
c
e
o
n
th
e
elec
tr
ical
g
r
id
.
H
o
wev
e
r
,
f
u
lly
ex
p
lo
itin
g
th
ese
in
f
r
astru
ctu
r
es
d
e
p
en
d
s
h
ea
v
ily
o
n
th
e
ab
ilit
y
o
f
t
h
e
PV
g
en
er
ato
r
t
o
d
eliv
er
m
ax
im
u
m
p
o
wer
d
esp
ite
clim
atic
v
ar
iatio
n
s
.
I
n
d
ee
d
,
PV
ce
lls
ex
h
ib
it
in
h
e
r
en
tly
n
o
n
lin
ea
r
c
h
ar
ac
ter
is
tics
th
at
ar
e
s
tr
o
n
g
ly
d
ep
en
d
en
t
o
n
s
o
lar
ir
r
ad
ian
ce
an
d
tem
p
er
a
tu
r
e:
v
ar
iatio
n
s
in
ir
r
ad
ian
ce
m
ain
l
y
af
f
ec
t
th
e
g
en
er
ated
c
u
r
r
en
t,
wh
ile
tem
p
er
atu
r
e
f
l
u
ctu
atio
n
s
af
f
ec
t
t
h
e
o
u
tp
u
t
v
o
ltag
e
,
ca
u
s
in
g
a
co
n
tin
u
o
u
s
s
h
if
t
o
f
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
MPP)
[
5
]
.
C
o
n
s
eq
u
en
tly
,
m
ain
tain
in
g
o
p
tim
a
l
ef
f
icien
cy
r
e
q
u
ir
es
a
p
er
m
an
en
t
ad
ju
s
tm
en
t
o
f
th
e
o
p
er
at
in
g
p
o
i
n
t
in
o
r
d
er
to
co
n
tin
u
o
u
s
ly
ex
tr
ac
t
th
e
m
ax
im
u
m
av
ailab
le
p
o
wer
[
6
]
.
I
n
E
V
ch
ar
g
in
g
ap
p
licati
o
n
s
,
wh
er
e
en
er
g
y
av
ailab
ilit
y
an
d
co
n
v
er
s
io
n
ef
f
icien
cy
ar
e
cr
itical,
th
is
f
u
n
ctio
n
is
g
en
er
ally
p
er
f
o
r
m
ed
b
y
a
DC
/D
C
co
n
v
er
ter
co
n
tr
o
ll
ed
b
y
a
m
ax
im
u
m
p
o
wer
p
o
in
t
t
r
ac
k
in
g
(
MPPT)
alg
o
r
ith
m
.
B
y
d
y
n
am
ically
ad
ju
s
tin
g
th
e
co
n
v
er
ter
'
s
d
u
ty
cy
cle,
t
h
e
MPPT
alg
o
r
ith
m
k
ee
p
s
t
h
e
PV
s
y
s
te
m
n
ea
r
th
e
MPP
an
d
th
u
s
im
p
r
o
v
es
o
v
er
all
ef
f
icien
c
y
[
7
]
.
Ov
er
th
e
p
ast
f
ew
d
ec
ad
es,
a
lar
g
e
n
u
m
b
er
o
f
MPPT
tech
n
iq
u
es
h
av
e
b
ee
n
p
r
o
p
o
s
ed
.
T
h
ey
ca
n
b
e
g
r
o
u
p
ed
in
to
th
r
ee
m
ain
f
am
ilies
:
co
n
v
en
tio
n
al
tec
h
n
i
q
u
es,
ar
tific
ial
-
in
tellig
en
ce
-
b
a
s
ed
ap
p
r
o
ac
h
es,
an
d
b
io
-
i
n
s
p
ir
ed
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
ea
ch
o
f
f
er
in
g
ad
v
a
n
tag
es
b
u
t
also
lim
itatio
n
s
th
a
t
r
estrict
th
eir
p
er
f
o
r
m
an
ce
u
n
d
er
r
ap
id
ly
v
ar
y
in
g
ir
r
ad
ian
ce
co
n
d
itio
n
s
[
8
]
.
C
o
n
v
en
tio
n
al
tec
h
n
iq
u
es,
n
o
tab
l
y
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O
)
an
d
i
n
cr
em
en
tal
co
n
d
u
cta
n
ce
(
I
NC
)
,
r
em
ai
n
w
id
ely
u
s
ed
o
win
g
to
th
eir
s
im
p
licity
o
f
im
p
lem
e
n
tatio
n
[
6
]
,
[
9
]
.
Ho
wev
e
r
,
th
eir
p
er
f
o
r
m
an
ce
d
eg
r
a
d
es
u
n
d
er
d
y
n
am
ic
clim
atic
c
o
n
d
itio
n
s
d
u
e
to
r
elativ
ely
s
lo
w
co
n
v
er
g
en
ce
,
p
er
s
is
ten
t
o
s
cillatio
n
s
ar
o
u
n
d
th
e
MPP,
an
d
h
ig
h
s
en
s
itiv
ity
to
th
e
ch
o
ice
o
f
p
er
tu
r
b
atio
n
s
tep
,
wh
ich
ca
n
lead
to
s
ig
n
if
ican
t e
n
er
g
y
lo
s
s
es.
Face
d
with
th
ese
li
m
itatio
n
s
,
r
esear
ch
h
as
p
r
o
g
r
ess
iv
ely
tu
r
n
ed
to
war
d
in
tellig
en
t
a
p
p
r
o
ac
h
es
ca
p
ab
le
o
f
im
p
r
o
v
in
g
MPP
tr
ac
k
in
g
in
d
y
n
am
ic
en
v
ir
o
n
m
e
n
ts
.
Am
o
n
g
th
ese,
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
(
FLC)
h
av
e
attr
ac
ted
p
ar
ticu
lar
in
te
r
est
o
win
g
to
th
eir
a
b
ilit
y
to
h
an
d
le
th
e
n
o
n
lin
e
ar
ities
o
f
th
e
PV
g
en
e
r
ato
r
with
o
u
t
a
p
r
ec
is
e
m
ath
em
atic
al
m
o
d
el
[
1
0
]
.
B
y
ex
p
l
o
itin
g
lin
g
u
is
tic
r
u
les,
th
ese
m
eth
o
d
s
o
f
f
er
ap
p
r
ec
iab
le
r
o
b
u
s
tn
ess
ag
ain
s
t
ir
r
ad
ia
n
ce
v
ar
iatio
n
s
an
d
s
y
s
tem
u
n
ce
r
t
ain
ties
.
T
h
eir
p
er
f
o
r
m
a
n
ce
n
e
v
er
th
eless
r
em
ain
s
h
ig
h
ly
d
ep
en
d
en
t
o
n
th
e
d
esig
n
o
f
t
h
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
an
d
r
u
le
b
ase,
wh
o
s
e
g
en
er
al
ly
em
p
ir
ical
tu
n
in
g
lim
its
th
eir
g
en
er
aliza
tio
n
ca
p
ab
ilit
y
an
d
m
o
tiv
ates
th
e
u
s
e
o
f
o
p
tim
izatio
n
tech
n
iq
u
es
to
au
to
m
ate
co
n
tr
o
ller
p
ar
am
eter
izatio
n
.
Ar
tific
ial
n
eu
r
al
n
etwo
r
k
s
(
ANN)
co
n
s
titu
te
an
o
th
e
r
wid
ely
s
tu
d
ie
d
f
am
ily
[
1
1
]
.
Du
e
to
th
eir
ab
ilit
y
to
lear
n
n
o
n
li
n
ea
r
b
eh
av
io
r
s
,
th
ey
q
u
ick
ly
esti
m
ate
th
e
MPP
f
r
o
m
m
ea
s
u
r
ed
e
lectr
ical
q
u
an
titi
es,
with
g
o
o
d
ad
a
p
tatio
n
to
wea
th
er
v
ar
iatio
n
s
.
Nev
er
th
eless
,
th
eir
p
er
f
o
r
m
an
ce
d
e
p
en
d
s
d
ir
ec
tly
o
n
th
e
q
u
alit
y
an
d
r
e
p
r
esen
tativ
en
ess
o
f
th
e
t
r
ain
in
g
d
ata.
Un
d
er
o
p
er
atin
g
co
n
d
itio
n
s
n
o
t
en
c
o
u
n
te
r
ed
d
u
r
in
g
tr
ain
i
n
g
,
th
eir
ac
cu
r
ac
y
ca
n
d
ec
r
ea
s
e
s
ig
n
if
i
ca
n
tly
.
Mo
r
eo
v
er
,
t
h
eir
co
m
p
u
tatio
n
al
co
s
t,
tr
ain
in
g
co
n
s
tr
ain
ts
,
an
d
lim
ited
in
ter
p
r
etab
ilit
y
s
till
r
estrict
th
eir
in
teg
r
atio
n
i
n
to
ce
r
tain
e
m
b
ed
d
ed
a
p
p
licatio
n
s
r
eq
u
ir
in
g
r
ea
l
-
tim
e
co
n
tr
o
l.
T
o
o
v
er
co
m
e
th
ese
lim
itatio
n
s
,
m
an
y
s
tu
d
ies
h
av
e
tu
r
n
ed
to
b
io
-
in
s
p
ir
ed
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
s
u
ch
as
g
en
etic
alg
o
r
ith
m
s
(
G
A)
[
1
1
]
,
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
P
SO)
[
1
2
]
,
g
r
e
y
wo
lf
o
p
tim
izer
(
GW
O)
[
1
3
]
,
[
1
4
]
.
T
h
ese
m
eth
o
d
s
s
tan
d
o
u
t
f
o
r
th
eir
ab
ilit
y
t
o
ef
f
icien
tly
s
ea
r
ch
f
o
r
th
e
g
l
o
b
a
l
p
o
wer
m
ax
im
u
m
,
p
ar
ticu
lar
ly
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
wh
er
e
s
ev
er
al
MPPs
ap
p
ea
r
,
th
er
eb
y
r
e
d
u
cin
g
th
e
r
is
k
o
f
co
n
v
er
g
en
ce
to
war
d
a
lo
ca
l
o
p
tim
u
m
.
T
h
is
p
er
f
o
r
m
an
ce
im
p
r
o
v
em
e
n
t,
h
o
wev
er
,
c
o
m
es
with
in
cr
ea
s
ed
alg
o
r
ith
m
ic
co
m
p
lex
ity
,
co
m
p
u
tatio
n
tim
e,
an
d
n
u
m
b
er
o
f
p
ar
am
eter
s
to
b
e
t
u
n
ed
,
wh
ich
ca
n
h
in
d
e
r
th
eir
u
s
e
in
em
b
ed
d
ed
s
y
s
tem
s
s
u
b
ject
to
r
ea
l
-
tim
e
c
o
n
s
tr
ain
ts
.
Mo
r
e
r
ec
en
t
ly
,
r
o
b
u
s
t
co
n
tr
o
l
s
tr
ateg
i
es,
n
o
tab
ly
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
,
h
av
e
em
er
g
ed
as
a
p
r
o
m
is
in
g
alt
er
n
ativ
e
o
win
g
to
th
eir
f
ast
co
n
v
er
g
e
n
ce
an
d
r
o
b
u
s
tn
ess
ag
ain
s
t
p
ar
am
etr
ic
u
n
ce
r
tain
ties
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
Ho
wev
er
,
th
eir
m
ai
n
d
r
awb
ac
k
lies
in
th
e
c
h
atter
in
g
p
h
e
n
o
m
en
o
n
,
wh
ich
ca
n
ca
u
s
e
co
n
tr
o
l
o
s
cillatio
n
s
,
in
cr
ea
s
ed
s
witch
in
g
l
o
s
s
es,
an
d
d
eg
r
ad
e
d
en
er
g
y
p
e
r
f
o
r
m
an
ce
.
T
o
m
itig
ate
th
is
lim
i
tatio
n
,
h
ig
h
er
-
o
r
d
er
s
lid
in
g
m
o
d
e
v
ar
ian
ts
,
in
p
ar
ticu
lar
th
e
s
u
p
er
-
twis
tin
g
alg
o
r
ith
m
(
STA)
,
h
av
e
b
ee
n
p
r
o
p
o
s
ed
t
o
r
ed
u
c
e
o
s
cillatio
n
s
wh
ile
p
r
eser
v
in
g
co
n
tr
o
ller
r
o
b
u
s
tn
ess
.
Desp
ite
en
co
u
r
ag
in
g
r
esu
lts
,
tu
n
in
g
th
e
p
a
r
am
eter
s
o
f
t
h
ese
ap
p
r
o
ac
h
es
r
em
ai
n
s
co
m
p
lex
an
d
h
ig
h
ly
d
ep
en
d
e
n
t o
n
o
p
er
atin
g
co
n
d
it
io
n
s
[
1
5
]
.
A
cr
itical
an
aly
s
is
o
f
th
ese
d
if
f
er
en
t
f
am
ilies
s
h
o
ws
th
at
n
o
s
in
g
le
MPPT
s
tr
ateg
y
alo
n
e
m
ee
ts
all
th
e
r
eq
u
ir
em
e
n
ts
o
f
m
o
d
er
n
PV
s
y
s
tem
s
.
T
h
is
co
m
p
lem
en
tar
ity
ex
p
lain
s
th
e
g
r
o
win
g
in
ter
est
in
h
y
b
r
id
ap
p
r
o
ac
h
es,
wh
ich
aim
to
co
m
b
in
e
th
e
ad
v
an
ta
g
es
o
f
s
ev
er
al
tech
n
iq
u
es
to
ac
h
iev
e
an
o
p
tim
al
tr
ad
e
-
o
f
f
b
etwe
en
co
n
v
e
r
g
en
ce
s
p
ee
d
,
t
r
ac
k
in
g
ac
c
u
r
ac
y
,
r
o
b
u
s
tn
ess
,
an
d
f
ea
s
ib
ilit
y
o
f
im
p
lem
en
t
atio
n
o
n
em
b
ed
d
e
d
p
l
a
t
f
o
r
m
s
.
I
n
t
h
i
s
p
e
r
s
p
e
c
ti
v
e
,
c
o
m
b
i
n
a
t
i
o
n
s
o
f
a
r
t
i
f
ic
i
a
l
i
n
te
l
l
i
g
e
n
c
e
a
l
g
o
r
i
t
h
m
s
,
b
i
o
-
i
n
s
p
i
r
e
d
m
e
t
h
o
d
s
,
a
n
d
r
o
b
u
s
t
c
o
n
t
r
o
l
t
e
c
h
n
i
q
u
e
s
,
s
u
c
h
a
s
P
SO
–
P
&
O
,
AN
F
I
S
–
PS
O
,
F
u
z
z
y
–
GW
O
,
o
r
A
N
N
–
S
MC
,
h
a
v
e
d
e
m
o
n
s
t
r
a
t
e
d
a
n
o
tab
le
im
p
r
o
v
e
m
en
t
in
co
n
v
e
r
g
en
ce
s
p
ee
d
a
n
d
tr
ac
k
in
g
ac
c
u
r
ac
y
.
Nev
er
th
eless
,
m
o
s
t
o
f
t
h
ese
s
tr
ateg
ies
s
till
f
ac
e
h
ig
h
alg
o
r
ith
m
ic
co
m
p
lex
ity
,
a
lar
g
e
n
u
m
b
er
o
f
p
ar
am
et
er
s
to
tu
n
e,
s
en
s
itiv
ity
to
in
itia
l
co
n
d
iti
o
n
s
,
an
d
a
co
m
p
u
tatio
n
al
lo
a
d
s
o
m
etim
es
in
co
m
p
atib
le
with
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
o
n
em
b
ed
d
e
d
s
y
s
tem
s
[
1
6
]
-
[
1
9
]
.
Am
o
n
g
th
ese
h
y
b
r
id
s
o
lu
tio
n
s
,
th
e
c
o
m
b
in
ati
o
n
o
f
GW
O
an
d
STA
is
o
f
p
a
r
ticu
lar
i
n
ter
est.
T
h
e
r
o
le
o
f
GW
O
is
to
d
eter
m
in
e
th
e
r
ef
er
e
n
ce
co
r
r
esp
o
n
d
in
g
to
th
e
g
lo
b
al
M
PP
,
wh
ile
th
e
STA
en
s
u
r
es
r
o
b
u
s
t
tr
ac
k
in
g
o
f
th
is
r
ef
er
en
ce
b
y
d
r
iv
i
n
g
th
e
p
o
wer
co
n
v
er
ter
[
2
0
]
,
[
2
1
]
.
T
h
is
ar
ch
itectu
r
e
m
ak
es
it
p
o
s
s
ib
le
to
s
ep
ar
ate
th
e
o
p
tim
izatio
n
an
d
co
n
tr
o
l
f
u
n
c
tio
n
s
,
ex
p
lo
itin
g
th
e
g
lo
b
al
e
x
p
lo
r
atio
n
ca
p
ab
ilit
y
o
f
GW
O
an
d
th
e
d
y
n
am
ic
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:
2088
-
8
6
9
4
E
n
erg
y
o
p
timiz
a
tio
n
o
f
a
n
elec
tr
ic
ve
h
icle
ch
a
r
g
in
g
s
ta
tio
n
u
s
in
g
a
h
yb
r
id
S
TA
-
GWO
…
(
S
a
mia
A
mro
u
n
i
)
2185
p
er
f
o
r
m
an
ce
o
f
t
h
e
STA.
Su
ch
f
u
n
ctio
n
al
co
m
p
lem
e
n
tar
ity
ad
d
r
ess
es
th
e
lim
itatio
n
s
id
en
tifie
d
in
ex
is
tin
g
ap
p
r
o
ac
h
es
an
d
c
o
n
s
titu
tes
a
p
r
o
m
is
in
g
s
o
lu
tio
n
f
o
r
s
im
u
ltan
eo
u
s
ly
im
p
r
o
v
in
g
MPPT
ac
cu
r
a
cy
,
c
o
n
v
e
r
g
en
c
e
s
p
ee
d
,
an
d
o
p
er
atin
g
s
tab
ilit
y
u
n
d
er
s
tr
o
n
g
ly
v
ar
iab
le
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
Am
o
n
g
th
e
s
o
lu
tio
n
s
lik
ely
t
o
m
itig
ate
g
lo
b
al
war
m
in
g
is
th
e
in
teg
r
atio
n
o
f
PV
s
y
s
tem
s
in
to
E
V
ch
ar
g
in
g
in
f
r
astru
ctu
r
e
[
2
]
,
[
2
2
]
.
I
n
t
h
is
p
ap
e
r
,
we
p
r
esen
t
a
s
tu
d
y
o
f
an
E
V
ch
ar
g
in
g
in
s
tallatio
n
lo
ca
ted
in
B
éjaïa
,
Alg
er
ia,
wh
o
s
e
ar
ch
itectu
r
e
is
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
m
ain
c
o
n
tr
ib
u
tio
n
o
f
th
is
wo
r
k
lies
in
o
p
tim
izin
g
th
e
p
o
we
r
o
f
th
e
P
V
p
ar
t.
Un
d
er
d
y
n
am
ic
ir
r
ad
ia
n
ce
co
n
d
itio
n
s
,
we
p
r
o
p
o
s
e
to
ex
p
lo
r
e
an
MPPT
alg
o
r
ith
m
b
u
ilt
ar
o
u
n
d
two
c
o
m
p
o
n
en
ts
:
en
er
g
y
m
an
ag
em
en
t
an
d
p
o
wer
o
p
tim
izatio
n
.
T
h
e
s
tu
d
ied
s
y
s
tem
in
clu
d
es
two
elec
tr
ical
en
er
g
y
s
o
u
r
ce
s
,
th
e
g
r
id
an
d
th
e
PV
g
en
er
ato
r
.
T
h
e
in
ter
f
ac
e
b
etwe
en
th
ese
two
s
o
u
r
ce
s
is
m
an
ag
ed
b
y
two
r
elay
s
(
K
pv
an
d
K
G
ri
d
)
,
an
d
f
o
u
r
s
ce
n
ar
io
s
ar
e
ex
am
in
e
d
.
Dep
en
d
in
g
o
n
th
e
av
ailab
ilit
y
o
f
th
e
s
o
lar
r
eso
u
r
ce
,
th
e
PV
s
o
u
r
ce
is
g
iv
en
p
r
i
o
r
ity
,
eith
er
to
ch
ar
g
e
th
e
E
V
b
atter
y
o
r
t
o
in
ject
en
er
g
y
in
to
th
e
g
r
id
;
o
th
er
w
is
e,
th
e
g
r
id
tak
es
o
v
er
t
o
e
n
s
u
r
e
ch
a
r
g
in
g
.
T
h
e
p
r
o
p
o
s
e
d
MPPT
ap
p
r
o
ac
h
co
m
b
in
es
th
e
STA
with
th
e
G
W
O
o
p
tim
izer
:
th
e
latter
q
u
ic
k
ly
lo
ca
tes
th
e
o
p
tim
al
o
p
er
ati
n
g
p
o
in
t,
wh
ile
th
e
STA
ac
ts
a
s
a
p
r
ec
is
io
n
r
eg
u
la
to
r
th
at
m
ain
tain
s
th
is
p
o
in
t
with
ac
cu
r
ac
y
an
d
s
tab
ilit
y
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
b
tain
ed
u
n
d
e
r
MA
T
L
AB
/Si
m
u
lin
k
p
r
o
v
i
d
e
v
alu
a
b
le
in
s
i
g
h
t
in
to
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
MPPT
co
n
tr
o
l a
n
d
h
ig
h
lig
h
t th
e
s
tr
en
g
th
s
o
f
th
is
h
y
b
r
id
a
p
p
r
o
ac
h
u
n
d
er
v
a
r
io
u
s
o
p
er
atin
g
c
o
n
d
iti
o
n
s
.
Fig
u
r
e
1
.
Sch
em
atic
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
A
ND
M
O
DE
L
L
I
NG
T
h
e
p
r
o
p
o
s
ed
ch
ar
g
in
g
s
tatio
n
is
b
ased
o
n
a
h
y
b
r
id
a
r
ch
it
ec
tu
r
e
in
teg
r
atin
g
a
PV
s
o
u
r
c
e
an
d
th
e
s
in
g
le
-
p
h
ase
elec
tr
ical
g
r
id
(
2
2
0
V,
5
0
Hz)
.
T
h
e
o
v
e
r
all
s
y
s
tem
ar
ch
itectu
r
e
is
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
is
co
n
f
ig
u
r
atio
n
aim
s
to
m
ax
im
i
ze
th
e
e
x
p
lo
itatio
n
o
f
s
o
lar
e
n
er
g
y
w
h
ile
en
s
u
r
in
g
c
o
n
tin
u
o
u
s
p
o
wer
s
u
p
p
ly
to
th
e
s
tatio
n
b
y
r
ely
in
g
o
n
th
e
elec
tr
ical
g
r
id
wh
en
p
h
o
to
v
o
ltaic
p
r
o
d
u
ctio
n
b
ec
o
m
es
in
s
u
f
f
icien
t.
T
h
e
PV
co
n
s
titu
tes
th
e
m
ain
p
o
wer
s
o
u
r
ce
.
T
o
en
s
u
r
e
o
p
tim
al
ex
p
l
o
itatio
n
o
f
th
is
s
o
u
r
ce
,
th
e
P
V
ch
ain
is
eq
u
i
p
p
ed
with
a
b
o
o
s
t
-
ty
p
e
DC
/DC
co
n
v
er
ter
,
co
n
tr
o
lled
b
y
a
n
MPPT
tech
n
iq
u
e
aim
ed
at
ex
t
r
ac
tin
g
,
at
ev
e
r
y
in
s
tan
t,
th
e
m
ax
im
u
m
p
o
wer
a
v
ailab
le
f
r
o
m
t
h
e
p
h
o
to
v
o
ltaic
g
en
er
at
o
r
.
T
h
e
r
eg
u
lated
d
ir
ec
t
cu
r
r
en
t
(
DC
)
elec
tr
ical
en
er
g
y
at
th
e
o
u
tp
u
t
o
f
th
e
b
o
o
s
t
co
n
v
e
r
ter
is
th
en
co
n
v
er
ted
in
to
alter
n
atin
g
cu
r
r
en
t
(
AC
)
en
er
g
y
b
y
a
DC
/AC
in
v
er
ter
co
n
tr
o
lled
u
s
in
g
t
h
e
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SP
W
M)
tech
n
iq
u
e
[
2
3
]
.
T
h
is
co
n
tr
o
l
m
eth
o
d
m
ak
es
it
p
o
s
s
ib
le
to
s
y
n
th
esize
an
AC
v
o
ltag
e
wh
o
s
e
wav
ef
o
r
m
is
v
er
y
clo
s
e
to
a
s
in
e
wa
v
e,
t
h
er
eb
y
r
ed
u
cin
g
t
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
an
d
im
p
r
o
v
in
g
th
e
q
u
ality
o
f
t
h
e
en
er
g
y
in
jecte
d
in
to
th
e
lo
a
d
o
r
th
e
g
r
i
d
.
T
h
e
in
v
er
ter
o
u
tp
u
t
is
co
n
n
ec
ted
t
o
an
is
o
latio
n
tr
an
s
f
o
r
m
er
,
wh
ic
h
p
r
o
v
id
es
g
alv
a
n
ic
is
o
latio
n
b
etwe
en
th
e
p
h
o
to
v
o
ltaic
ch
ai
n
an
d
t
h
e
elec
tr
ical
g
r
id
,
v
o
ltag
e
-
lev
el
a
d
ap
tatio
n
,
an
d
u
s
er
s
af
ety
.
T
h
e
en
er
g
y
f
lo
w
b
etwe
en
th
e
d
if
f
er
en
t
s
o
u
r
c
es
is
m
an
ag
ed
b
y
m
ea
n
s
o
f
two
s
tatic
s
witch
es,
d
en
o
ted
(
)
an
d
(
)
.
T
h
e
s
witch
(
)
co
n
tr
o
ls
t
h
e
co
n
n
ec
tio
n
o
f
th
e
p
h
o
to
v
o
ltaic
ch
ain
to
th
e
c
h
ar
g
in
g
s
tatio
n
.
W
h
en
clo
s
ed
,
th
e
en
e
r
g
y
p
r
o
d
u
ce
d
b
y
t
h
e
PV
p
an
e
ls
is
p
r
ef
er
en
tially
d
ir
ec
te
d
to
war
d
ch
ar
g
in
g
t
h
e
elec
tr
ic
v
eh
icle
wh
en
a
v
eh
icle
is
co
n
n
ec
ted
to
th
e
s
tatio
n
.
C
o
n
v
er
s
ely
,
if
n
o
v
eh
icle
is
p
r
esen
t
an
d
PV
p
r
o
d
u
ctio
n
is
i
n
ex
ce
s
s
,
th
is
en
er
g
y
ca
n
b
e
in
jecte
d
in
to
th
e
elec
tr
ical
g
r
id
,
p
r
o
v
i
d
ed
th
at
th
e
s
witch
i
s
clo
s
ed
(
)
.
W
h
en
p
h
o
to
v
o
ltaic
p
r
o
d
u
ctio
n
b
ec
o
m
es
i
n
s
u
f
f
icien
t,
p
ar
ti
cu
lar
ly
d
u
r
in
g
p
er
io
d
s
o
f
l
o
w
s
u
n
lig
h
t,
h
ea
v
ily
o
v
er
ca
s
t
d
ay
s
,
o
r
at
n
i
g
h
t,
p
o
wer
s
u
p
p
l
y
p
r
i
o
r
ity
is
au
to
m
atica
lly
tr
an
s
f
er
r
e
d
to
t
h
e
elec
tr
ical
g
r
id
.
I
n
th
is
o
p
er
atin
g
m
o
d
e,
is
o
p
e
n
wh
ile
is
clo
s
ed
,
allo
win
g
t
h
e
g
r
id
to
s
u
p
p
l
y
th
e
en
e
r
g
y
n
e
ed
ed
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
2183
-
2
1
9
6
2186
en
s
u
r
e
co
n
tin
u
ity
o
f
th
e
E
V
ch
ar
g
in
g
s
er
v
ice.
T
h
is
s
tr
ateg
y
g
u
ar
an
tees
p
er
m
an
e
n
t
av
ailab
ilit
y
o
f
th
e
s
tatio
n
,
r
eg
ar
d
less
o
f
f
lu
ctu
atio
n
s
in
s
o
lar
p
r
o
d
u
ctio
n
.
T
h
u
s
,
th
e
p
r
o
p
o
s
ed
ar
c
h
itectu
r
e
en
s
u
r
es
ef
f
icien
t
p
o
wer
f
lo
w
m
an
ag
em
e
n
t
b
y
s
y
s
tem
atica
lly
p
r
io
r
itizin
g
th
e
u
s
e
o
f
PV
en
er
g
y
,
wh
ile
u
s
in
g
th
e
elec
tr
ical
g
r
id
as
a
b
ac
k
u
p
s
o
u
r
ce
wh
en
n
ec
ess
ar
y
.
T
h
is
ap
p
r
o
ac
h
im
p
r
o
v
es
s
elf
-
co
n
s
u
m
p
tio
n
o
f
th
e
e
n
er
g
y
p
r
o
d
u
ce
d
,
r
ed
u
ce
s
d
ep
en
d
en
ce
o
n
t
h
e
g
r
id
,
lo
wer
s
th
e
o
p
er
atin
g
co
s
ts
o
f
th
e
c
h
ar
g
in
g
s
tatio
n
,
a
n
d
c
o
n
tr
ib
u
tes
to
r
ed
u
cin
g
g
r
ee
n
h
o
u
s
e
g
as
em
is
s
io
n
s
.
T
h
e
d
if
f
er
e
n
t
o
p
er
atin
g
p
r
i
o
r
ities
o
f
s
witch
es
an
d
,
co
r
r
esp
o
n
d
in
g
to
th
e
v
ar
io
u
s
m
an
a
g
em
en
t
m
o
d
es,
ar
e
s
u
m
m
ar
ized
in
T
a
b
le
1
.
Fi
g
u
r
e
2
.
Ar
c
h
itectu
r
e
o
f
th
e
s
tu
d
ied
s
y
s
tem
T
ab
le
1.
R
elay
s
witch
in
g
lo
g
ic
K
pv
K
G
ri
d
R
e
s
u
l
t
s
0
0
0
1
0
P
V
t
o
EV
0
1
G
r
i
d
t
o
EV
1
1
P
V
t
o
G
r
i
d
2
.
1
.
P
V
m
o
delin
g
T
h
e
s
in
g
le
-
d
io
d
e
eq
u
iv
alen
t
m
o
d
el,
s
h
o
wn
in
Fig
u
r
e
3
,
is
o
n
e
o
f
th
e
m
o
s
t
co
m
m
o
n
ly
u
s
ed
ap
p
r
o
ac
h
es f
o
r
m
o
d
elin
g
p
h
o
to
v
o
ltaic
ce
lls
.
T
h
is
wid
e
ad
o
p
t
io
n
is
ex
p
lain
ed
b
y
its
r
elativ
e
ly
s
im
p
le
s
tr
u
ctu
r
e,
wh
ile
s
till
o
f
f
er
in
g
s
u
f
f
ici
en
t
ac
cu
r
ac
y
to
f
aith
f
u
lly
r
e
p
r
esen
t
th
e
elec
tr
ical
b
e
h
av
io
r
o
f
PV
ce
lls
.
B
y
ap
p
ly
in
g
Kir
ch
h
o
f
f
'
s
cu
r
r
e
n
t
law
to
t
h
e
eq
u
iv
ale
n
t
cir
c
u
it
p
r
esen
ted
,
th
e
ex
p
r
ess
io
n
o
f
th
e
v
a
r
io
u
s
cu
r
r
en
ts
f
l
o
win
g
in
th
e
p
h
o
t
o
v
o
ltaic
ce
ll is
wr
itten
as sh
o
wn
in
(
1
)
[
2
4
]
.
=
ℎ
−
−
ℎ
(
1
)
W
h
er
e
ℎ
r
ep
r
esen
ts
th
e
p
h
o
to
cu
r
r
en
t
g
en
e
r
ated
b
y
t
h
e
p
h
o
to
v
o
ltaic
ce
ll,
d
e
n
o
tes
th
e
c
u
r
r
en
t
f
lo
win
g
th
r
o
u
g
h
th
e
d
io
d
e,
an
d
ℎ
co
r
r
esp
o
n
d
s
to
th
e
cu
r
r
e
n
t
f
lo
wi
n
g
th
r
o
u
g
h
th
e
s
h
u
n
t
r
esis
tan
ce
(
s
h
u
n
t
)
.
B
y
s
u
b
s
titu
t
in
g
th
e
cu
r
r
e
n
ts
an
d
ℎ
with
th
eir
r
esp
ec
tiv
e
ex
p
r
es
s
io
n
s
in
(
1
)
,
th
e
ex
p
r
ess
io
n
o
f
th
e
o
u
t
p
u
t
cu
r
r
en
t
o
f
th
e
p
h
o
to
v
o
ltaic
ce
l
l is o
b
tain
ed
,
g
iv
e
n
b
y
(
2
)
.
=
ℎ
−
0
⋅
[
(
⋅
(
+
⋅
)
⋅
⋅
⋅
)
−
1
]
−
+
⋅
ℎ
(
2)
T
h
e
ch
ar
ac
ter
is
tic
p
ar
am
eter
s
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
a
r
e
s
u
m
m
ar
ized
in
T
ab
le
2
.
T
h
e
(
1
)
an
d
(
2
)
co
n
s
titu
te
th
e
m
ath
em
atica
l
m
o
d
el
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el,
m
a
k
in
g
it
p
o
s
s
ib
le
to
r
ep
r
o
d
u
ce
its
elec
tr
ical
b
eh
av
io
r
in
th
e
Simu
lin
k
s
im
u
latio
n
en
v
ir
o
n
m
e
n
t.
T
o
ev
alu
ate
th
e
m
o
d
el'
s
p
er
f
o
r
m
an
ce
,
s
ev
er
al
s
im
u
lati
o
n
s
wer
e
ca
r
r
ied
o
u
t
u
n
d
e
r
d
if
f
er
en
t
s
o
lar
ir
r
ad
ian
ce
lev
els.
Fig
u
r
e
4
s
h
o
ws
th
e
ch
ar
ac
ter
is
tics
o
b
tain
ed
f
o
r
ir
r
ad
ian
ce
v
alu
es
r
a
n
g
in
g
f
r
o
m
2
0
0
to
1
0
0
0
W
/m
²,
in
s
tep
s
o
f
2
0
0
W
/m
².
T
h
e
MPP a
r
e
m
ar
k
ed
with
r
e
d
aster
is
k
s
(
*
)
.
T
ab
le
2
p
r
esen
ts
th
e
p
h
o
to
v
o
ltaic
p
an
el
p
ar
am
eter
s
.
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:
2088
-
8
6
9
4
E
n
erg
y
o
p
timiz
a
tio
n
o
f
a
n
elec
tr
ic
ve
h
icle
ch
a
r
g
in
g
s
ta
tio
n
u
s
in
g
a
h
yb
r
id
S
TA
-
GWO
…
(
S
a
mia
A
mro
u
n
i
)
2187
Fig
u
r
e
3.
E
q
u
iv
alen
t c
ir
c
u
it o
f
s
o
lar
ce
ll
T
ab
le
2
.
P
h
o
t
o
v
o
ltaic
p
a
n
el
p
a
r
am
eter
s
S
y
mb
o
l
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
P
pv
P
h
o
t
o
v
o
l
t
a
i
c
p
o
w
e
r
8
0
W
p
I
m
ppt
M
a
x
i
m
u
m
c
u
r
r
e
n
t
a
t
M
P
P
4
.
6
5
A
V
m
ppt
M
a
x
i
m
u
m
v
o
l
t
a
g
e
a
t
M
P
P
1
7
.
5
V
I
sc
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
4
.
9
5
A
V
oc
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
2
1
.
9
V
α
sc
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
a
t
s
h
o
r
t
-
c
u
r
r
e
n
t
3
mA
/
°
C
ᵝ
oc
V
o
l
t
a
g
e
t
e
m
p
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
s
h
o
r
t
-
c
u
r
r
e
n
t
1
5
0
mV
/
°
C
Fig
u
r
e
4
.
Ph
o
to
v
o
ltaic
STP8
0
I
V
an
d
PV
c
u
r
v
es
2
.
2
.
DC
-
DC
c
o
nv
er
t
er
DC
–
DC
co
n
v
er
ter
s
m
a
k
e
it
p
o
s
s
ib
le
to
r
e
g
u
late
DC
q
u
an
titi
es
b
y
ac
tin
g
o
n
th
e
d
u
ty
cy
cle
o
f
th
e
s
em
ico
n
d
u
cto
r
s
witch
.
I
n
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
,
th
ey
ac
t
as
an
ad
ap
tatio
n
i
n
ter
f
ac
e
b
etwe
en
th
e
PV
g
en
er
ato
r
an
d
th
e
lo
ad
,
ad
ju
s
tin
g
v
o
ltag
e
an
d
cu
r
r
e
n
t
to
en
s
u
r
e
o
p
er
atio
n
at
th
e
MPP
wh
i
le
av
o
id
in
g
s
h
o
r
t
-
cir
c
u
it
co
n
d
itio
n
s
.
Fig
u
r
e
5
s
h
o
ws
th
e
s
tr
u
ctu
r
e
o
f
a
B
o
o
s
t
co
n
v
er
ter
,
co
m
m
o
n
l
y
u
s
ed
in
p
h
o
to
v
o
ltaic
in
s
tallatio
n
s
.
W
h
en
th
e
p
o
wer
s
witch
(
I
GB
T
o
r
MO
SF
E
T
)
is
co
n
d
u
ctin
g
,
th
e
en
er
g
y
s
u
p
p
lied
b
y
t
h
e
p
h
o
to
v
o
ltaic
g
e
n
er
ato
r
is
s
to
r
ed
in
th
e
i
n
d
u
ct
o
r
,
wh
ile
th
e
d
io
d
e
is
b
lo
c
k
ed
.
W
h
en
th
e
s
witch
o
p
e
n
s
,
th
e
en
e
r
g
y
ac
cu
m
u
lated
in
th
e
in
d
u
cto
r
a
d
d
s
to
th
at
d
eliv
er
e
d
b
y
th
e
s
o
u
r
ce
t
o
s
u
p
p
ly
t
h
e
lo
ad
.
T
h
e
r
elatio
n
s
h
i
p
s
lin
k
in
g
t
h
e
in
p
u
t a
n
d
o
u
t
p
u
t
v
o
ltag
es a
n
d
c
u
r
r
en
ts
o
f
th
e
co
n
v
er
ter
ar
e
g
iv
en
b
y
(
3
)
[
2
3
]
.
=
(
1
−
D
)
=
(
1
−
)
(
3
)
T
h
e
d
y
n
am
ic
eq
u
atio
n
s
of
th
is
co
n
v
er
te
r
ar
e
(
4
)
-
(
6
)
.
(
=
−
0
+
0
0
=
(
−
0
+
)
0
)
(
4
)
̇
=
(
)
+
(
)
(
5
)
(
)
=
[
−
0
−
0
+
]
(
)
=
[
0
−
0
]
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
2183
-
2
1
9
6
2188
Fig
u
r
e
5
.
DC
-
DC
b
o
o
s
t c
o
n
v
e
r
ter
p
o
wer
ci
r
cu
it
2
.
3
.
M
a
x
i
m
um
po
wer
po
int
t
ra
ck
er
a
lg
o
ri
t
hm
2
.
3
.
1
.
ST
A
f
o
r
M
P
P
T
T
h
e
STA
is
a
r
o
b
u
s
t
co
n
tr
o
l
tech
n
iq
u
e
b
elo
n
g
in
g
to
th
e
f
am
ily
o
f
h
ig
h
er
-
o
r
d
er
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
s
.
I
t
was
d
ev
elo
p
ed
to
r
etain
th
e
m
ain
a
d
v
an
ta
g
es
o
f
class
ical
s
l
id
in
g
m
o
d
e
co
n
tr
o
l,
n
am
ely
its
r
o
b
u
s
tn
ess
an
d
tr
ac
k
in
g
ac
cu
r
ac
y
,
wh
ile
r
ed
u
cin
g
th
e
p
h
en
o
m
en
o
n
k
n
o
wn
as
ch
atter
in
g
.
I
n
PV
s
y
s
tem
s
,
th
e
STA
is
u
s
ed
to
ad
ju
s
t
th
e
d
u
ty
cy
cle
o
f
th
e
DC
–
DC
co
n
v
e
r
ter
in
o
r
d
er
to
k
ee
p
t
h
e
g
e
n
er
ato
r
n
ea
r
th
e
MPP,
ev
en
u
n
d
er
r
a
p
id
v
ar
iatio
n
s
i
n
ir
r
ad
ian
ce
a
n
d
tem
p
e
r
atu
r
e.
I
ts
im
p
lem
en
tatio
n
r
elies
o
n
two
ess
en
tial
s
tep
s
:
d
ef
in
in
g
a
s
lid
in
g
s
u
r
f
ac
e
th
a
t
g
u
ar
an
tees
r
ap
id
co
n
v
er
g
e
n
c
e
to
war
d
th
e
MPP,
an
d
th
en
d
esig
n
in
g
th
e
STA
co
n
tr
o
l
law
th
at
k
ee
p
s
th
e
s
y
s
t
em
s
tates
o
n
th
is
s
u
r
f
ac
e.
Owin
g
to
its
f
ast
co
n
v
er
g
e
n
ce
an
d
r
o
b
u
s
tn
ess
ag
ain
s
t
d
is
tu
r
b
an
ce
s
,
th
e
STA
is
a
s
o
lu
tio
n
p
a
r
ticu
lar
ly
well
s
u
ited
to
ad
v
an
ce
d
MPPT
s
tr
ateg
ies
[
1
5
]
,
[
2
5
]
.
I
n
th
is
s
tu
d
y
,
th
e
s
lid
in
g
s
u
r
f
a
ce
ch
o
s
en
f
o
r
th
e
STA
co
n
tr
o
l
is
d
ef
in
ed
f
r
o
m
th
e
MPPT
o
p
tim
ality
cr
iter
io
n
.
At
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
,
th
e
d
er
iv
ativ
e
o
f
th
e
p
h
o
to
v
o
ltaic
p
o
wer
with
r
esp
ec
t
t
o
v
o
ltag
e
is
ze
r
o
.
T
h
is
cr
iter
io
n
is
th
en
u
s
ed
to
d
e
f
in
e
a
s
lid
in
g
s
u
r
f
ac
e
g
u
a
r
an
teein
g
th
e
s
y
s
tem
'
s
co
n
v
er
g
en
ce
to
war
d
th
e
MPP.
T
h
e
s
lid
in
g
co
n
d
itio
n
s
ar
e
g
iv
en
b
y
(
7
)
.
˙
(
,
)
=
0
(
,
)
=
=
(
+
)
=
0
(
7
)
On
ce
th
e
s
lid
in
g
s
u
r
f
ac
e
h
as
b
ee
n
d
e
f
in
ed
,
th
e
n
ex
t
s
tep
c
o
n
s
is
ts
o
f
d
esig
n
in
g
th
e
c
o
n
tr
o
l
law
th
at
d
r
iv
es th
e
s
y
s
tem
to
war
d
th
is
s
u
r
f
ac
e
an
d
k
ee
p
s
it th
er
e
d
esp
ite
m
o
d
el
u
n
ce
r
tain
ties
an
d
ex
t
er
n
al
d
is
tu
r
b
an
ce
s
.
I
n
th
is
s
tu
d
y
,
th
e
d
u
ty
cy
cle
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
is
th
e
co
n
tr
o
l
v
ar
iab
le.
T
o
th
is
en
d
,
s
u
p
er
-
twis
tin
g
co
n
tr
o
l
is
ad
o
p
ted
.
I
t
r
elies
o
n
two
co
m
p
lem
en
tar
y
co
m
p
o
n
en
ts
:
a
n
eq
u
iv
alen
t
co
n
tr
o
l,
wh
ich
k
ee
p
s
th
e
s
y
s
tem
o
n
th
e
s
lid
in
g
s
u
r
f
ac
e
,
an
d
a
d
is
co
n
tin
u
o
u
s
co
n
tr
o
l,
wh
ich
g
u
ar
a
n
tees
f
ast
co
n
v
e
r
g
en
ce
t
o
war
d
th
is
s
u
r
f
ac
e
as
well
as
ef
f
ec
tiv
e
d
is
tu
r
b
an
ce
r
ejec
t
io
n
.
T
h
is
c
o
m
b
in
atio
n
i
m
p
r
o
v
es
th
e
s
y
s
te
m
'
s
r
o
b
u
s
tn
ess
an
d
en
s
u
r
es a
cc
u
r
ate
tr
ac
k
in
g
o
f
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
T
h
e
STA
co
n
tr
o
l la
w
is
th
en
wr
itte
n
as
(
8
)
.
{
=
+
=
1
+
2
=
−
[
]
(
)
[
]
(
)
=
1
−
0
(
8
)
W
h
er
e
r
ep
r
esen
ts
th
e
eq
u
iv
alen
t
co
n
tr
o
l
en
s
u
r
in
g
th
e
tr
ajec
to
r
y
is
m
ain
tain
ed
o
n
th
e
s
lid
in
g
s
u
r
f
ac
e,
wh
ile
co
r
r
esp
o
n
d
s
to
th
e
s
u
p
er
-
twis
tin
g
ter
m
en
s
u
r
in
g
f
in
i
te
-
tim
e
co
n
v
er
g
e
n
ce
o
f
th
e
tr
ajec
to
r
y
to
war
d
th
is
s
u
r
f
ac
e
wh
ile
r
ed
u
cin
g
th
e
ch
atter
in
g
p
h
en
o
m
en
o
n
.
T
h
e
eq
u
atio
n
s
f
o
r
1
an
d
2
ar
e
g
iv
en
b
y
(
9
)
a
n
d
(
1
0
)
.
{
1
=
−
λ
|
|
1
2
(
)
2
=
−
γ
(
)
(
9
)
a
n
d
a
r
e
ga
in
s
s
uc
h
tha
t
∶
>
>
√
2
2
.
(
+
)
2
−
(
1
0
)
T
h
e
f
in
ite
-
tim
e
c
o
n
v
e
r
g
en
ce
o
f
th
e
s
lid
in
g
s
u
r
f
ac
e
to
z
er
o
is
estab
lis
h
ed
th
r
o
u
g
h
a
L
y
ap
u
n
o
v
s
tab
ilit
y
an
aly
s
is
.
T
o
th
is
en
d
,
a
p
o
s
itiv
e
d
ef
in
ite
ca
n
d
i
d
ate
f
u
n
ctio
n
i
s
in
tr
o
d
u
ce
d
in
th
e
f
o
r
m
:
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:
2088
-
8
6
9
4
E
n
erg
y
o
p
timiz
a
tio
n
o
f
a
n
elec
tr
ic
ve
h
icle
ch
a
r
g
in
g
s
ta
tio
n
u
s
in
g
a
h
yb
r
id
S
TA
-
GWO
…
(
S
a
mia
A
mro
u
n
i
)
2189
(
)
=
1
2
2
(
)
(
1
1
)
I
n
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l,
t
h
e
d
y
n
am
ics
o
f
th
e
s
lid
in
g
s
u
r
f
a
ce
ar
e
d
eter
m
in
ed
b
y
its
d
ep
e
n
d
en
ce
o
n
th
e
s
tate
v
ar
iab
les,
ex
p
r
ess
ed
b
y
(
1
2
)
.
˙
=
[
]
˙
=
[
]
(
−
(
1
−
)
+
)
(
1
2
)
T
h
e
f
ir
s
t te
r
m
will b
e
d
e
v
elo
p
ed
as
(
1
3
)
.
[
]
=
1
+
−
2
(
1
3
)
Su
ch
th
at:
=
−
(
e
xp
(
ₛ
ₜ
)
)
·
ₛ
ₜ
·
<
0
(
1
4
)
V
PV
is
d
ef
in
ed
as in
(
15
).
=
ln
(
ℎ
+
−
)
(
1
5
)
T
h
e
d
er
iv
ativ
e
o
f
(
15
)
ca
n
b
e
wr
itten
as
(
1
6
)
.
∂
=
−
(
(
ℎ
+
−
)
)
<
0
(
1
6
)
T
h
e
s
ec
o
n
d
ter
m
is
as (
1
7
)
a
n
d
(
1
8
)
.
̇
=
−
(
0
)
(
1
−
)
+
(
)
=
−
(
)
(
1
−
−
)
+
(
)
(
1
7
)
=
(
−
|
|
1
2
(
)
−
∫
(
)
(
1
8
)
Acc
o
r
d
in
g
t
o
(
18
)
,
we
h
av
e
(
1
9
)
.
̇
=
[
]
(
−
|
|
1
2
(
)
−
∫
(
)
)
(
1
9
)
C
o
n
s
eq
u
en
tly
,
it
ca
n
b
e
co
n
clu
d
ed
th
at
L
y
a
p
u
n
o
v
s
tab
ilit
y
is
en
s
u
r
ed
,
s
in
ce
an
d
its
d
er
iv
ativ
e
̇
s
y
s
tem
atica
lly
h
av
e
o
p
p
o
s
ite
s
ig
n
s
.
T
h
e
STA
g
ai
n
s
an
d
wer
e
s
elec
ted
b
ased
o
n
th
e
tu
n
in
g
p
r
o
ce
d
u
r
e
r
e
p
o
r
ted
in
[
2
0
]
.
Acc
o
r
d
in
g
l
y
,
=
0
.
051631
an
d
=
0
.
006629
wer
e
ad
o
p
te
d
in
t
h
e
p
r
esen
t
s
tu
d
y
an
d
k
ep
t
f
ix
ed
th
r
o
u
g
h
o
u
t t
h
e
s
im
u
latio
n
s
.
2
.
3
.
2
.
G
WO
-
ba
s
ed
o
ptim
a
l d
uty
-
cy
cle
s
ea
rc
h
T
h
e
GW
O
is
a
b
io
-
in
s
p
ir
ed
m
etah
eu
r
is
tic
tech
n
iq
u
e
b
ased
o
n
th
e
s
o
cial
b
eh
av
io
r
an
d
h
ier
ar
ch
ical
h
u
n
tin
g
s
tr
ateg
y
o
f
g
r
e
y
wo
lv
es
in
a
p
ac
k
[
1
3
]
.
T
h
is
a
p
p
r
o
ac
h
d
is
tr
ib
u
tes
s
o
lu
tio
n
ag
en
ts
ac
r
o
s
s
f
o
u
r
h
ier
ar
ch
ical
lev
els:
α
,
β
,
δ
,
an
d
ω
,
c
o
r
r
esp
o
n
d
in
g
r
esp
ec
tiv
e
ly
to
th
e
b
est
s
o
lu
tio
n
,
th
e
s
ec
o
n
d
-
b
est,
th
e
th
ir
d
-
b
est,
an
d
th
e
r
em
ain
i
n
g
s
et
o
f
s
o
lu
tio
n
s
.
T
h
e
α
ag
e
n
t
g
u
id
es
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
b
y
d
ir
ec
tin
g
th
e
s
ea
r
ch
to
war
d
th
e
m
o
s
t
p
r
o
m
is
in
g
s
o
lu
tio
n
,
wh
ile
th
e
β
a
n
d
δ
ag
e
n
t
s
r
ef
in
e
th
is
tr
ajec
to
r
y
.
T
h
e
ω
ag
en
ts
ex
p
lo
r
e
less
f
av
o
r
a
b
le
r
eg
io
n
s
o
f
th
e
s
ea
r
c
h
s
p
ac
e,
th
er
eb
y
h
elp
in
g
to
m
ain
tain
p
o
p
u
latio
n
d
iv
er
s
ity
a
n
d
lim
it
th
e
r
is
k
o
f
p
r
em
atu
r
e
c
o
n
v
e
r
g
en
ce
t
o
war
d
a
lo
ca
l o
p
tim
u
m
.
I
n
s
p
ir
ed
b
y
th
is
h
u
n
tin
g
b
eh
a
v
io
r
,
t
h
e
GW
O
o
p
tim
izatio
n
p
r
o
ce
s
s
r
elies
o
n
t
h
r
ee
s
u
cc
ess
iv
e
p
h
ases
:
tar
g
et
lo
ca
tio
n
,
en
cir
clin
g
,
a
n
d
th
e
f
in
al
attac
k
.
I
n
th
e
c
o
n
tex
t
o
f
MPPT,
ea
ch
GW
O
ag
en
t
r
e
p
r
esen
ts
a
ca
n
d
id
ate
v
alu
e
o
f
t
h
e
b
o
o
s
t
co
n
v
er
ter
'
s
d
u
ty
cy
cle.
T
h
e
a
g
e
n
ts
co
o
p
er
ate
to
s
ea
r
ch
f
o
r
th
e
d
u
ty
c
y
cle
v
alu
e
th
at
ex
tr
ac
ts
th
e
m
ax
im
u
m
p
o
wer
f
r
o
m
t
h
e
p
h
o
t
o
v
o
ltaic
g
en
er
ato
r
.
As
th
e
iter
atio
n
s
p
r
o
g
r
ess
,
th
e
ag
en
ts
'
p
o
s
itio
n
s
ar
e
ad
ju
s
ted
,
g
r
a
d
u
a
lly
lead
in
g
t
o
co
n
v
er
g
e
n
ce
to
war
d
th
e
o
p
tim
al
d
u
ty
cy
cle
c
o
r
r
esp
o
n
d
in
g
to
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
2183
-
2
1
9
6
2190
T
h
e
en
cir
clin
g
b
eh
av
i
o
r
ch
a
r
ac
ter
is
tic
o
f
p
ac
k
h
u
n
tin
g
is
th
en
tr
an
s
lated
m
ath
em
atica
lly
in
to
a
s
y
s
tem
o
f
eq
u
atio
n
s
,
m
ak
in
g
it
p
o
s
s
ib
le
to
m
o
d
el
th
e
ad
ap
ti
v
e
p
o
s
itio
n
in
g
o
f
th
e
s
o
lu
tio
n
ag
en
ts
ar
o
u
n
d
th
e
s
o
u
g
h
t o
p
tim
u
m
,
as d
etailed
i
n
(
2
0
)
-
(
2
3
)
.
⃗
⃗
=
|
⋅
⃗
⃗
⃗
⃗
−
(
)
|
(
2
0
)
(
+
1
)
=
⃗
⃗
⃗
⃗
(
)
−
⃗
⃗
⋅
(
2
1
)
D:
th
e
d
is
tan
ce
b
etwe
en
wo
lf
ω
an
d
th
e
p
r
ey
; t:
c
u
r
r
en
t iter
a
tio
n
;
⃗
⃗
⃗
⃗
:
p
o
s
itio
n
o
f
th
e
p
r
ey
; a
n
d
: p
o
s
itio
n
o
f
th
e
wo
lf
.
T
h
e
v
ec
to
r
s
a
n
d
ar
e
d
ef
i
n
ed
as
(
2
2
)
an
d
(
2
3
)
.
=
2
⋅
1
⃗
⃗
⃗
−
(
2
2
)
=
2
2
⃗
⃗
⃗
(
2
3
)
A
co
ef
f
icien
t
d
ec
r
ea
s
in
g
lin
ea
r
ly
f
r
o
m
2
to
0
o
v
er
th
e
iter
at
io
n
s
en
s
u
r
in
g
th
e
p
r
o
g
r
ess
iv
e
tr
an
s
itio
n
b
etwe
en
ex
p
lo
r
atio
n
an
d
e
x
p
lo
itatio
n
.
1
2
:
∈
[
0
,
1
]
,
in
tr
o
d
u
cin
g
a
r
an
d
o
m
c
o
m
p
o
n
e
n
t
th
at
d
iv
er
s
if
ies
ex
p
lo
r
atio
n
an
d
t
h
u
s
av
o
id
s
tr
ap
p
in
g
in
a
lo
ca
l
o
p
t
im
u
m
.
S
in
ce
th
e
ex
ac
t
p
o
s
itio
n
o
f
t
h
e
MPPT
is
n
o
t
k
n
o
wn
a
p
r
io
r
i,
th
e
GW
O
r
elies
o
n
th
e
th
r
ee
b
est
ca
n
d
id
ate
s
o
lu
tio
n
s
α
,
β,
a
n
d
δ
to
p
r
o
v
id
e
an
esti
m
ate.
I
n
th
e
co
n
tex
t
o
f
MPPT,
th
ese
th
r
ee
l
ea
d
er
s
co
r
r
es
p
o
n
d
to
th
e
d
u
ty
cy
cle
v
alu
es
ass
o
ciate
d
with
th
e
h
ig
h
est
p
h
o
to
v
o
ltaic
p
o
wer
v
alu
es.
T
h
e
r
e
m
ain
in
g
a
g
en
ts
th
en
u
p
d
ate
th
eir
p
o
s
itio
n
b
ased
o
n
th
ese
th
r
ee
lead
er
s
,
ac
co
r
d
in
g
to
(
2
4
)
.
⃗
⃗
⃗
⃗
⃗
=
|
1
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
|
,
⃗
⃗
⃗
⃗
=
|
2
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
|
,
⃗
⃗
⃗
⃗
=
|
3
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
|
(
2
4
)
E
ac
h
ca
n
d
id
ate
d
u
ty
cy
cle
v
a
lu
e
is
u
p
d
ated
b
ased
o
n
th
e
th
r
ee
lead
e
r
s
α
,
β
,
a
n
d
δ
,
wh
i
ch
jo
in
tly
g
u
id
e
t
h
e
s
ea
r
ch
to
war
d
th
e
d
u
ty
c
y
cle
c
o
r
r
esp
o
n
d
in
g
t
o
th
e
MPPT,
ac
co
r
d
in
g
to
th
e
f
o
llo
win
g
s
y
s
te
m
o
f
eq
u
atio
n
s
:
{
1
⃗
⃗
⃗
⃗
=
α
⃗
⃗
⃗
⃗
−
1
⃗
⃗
⃗
⃗
(
α
⃗
⃗
⃗
⃗
)
2
⃗
⃗
⃗
⃗
=
β
⃗
⃗
⃗
⃗
−
2
⃗
⃗
⃗
⃗
(
β
⃗
⃗
⃗
⃗
)
3
⃗
⃗
⃗
⃗
=
δ
⃗
⃗
⃗
⃗
−
3
⃗
⃗
⃗
⃗
(
δ
⃗
⃗
⃗
⃗
)
(
25)
At
ea
ch
iter
atio
n
,
th
e
p
o
s
itio
n
o
f
ea
ch
ca
n
d
id
ate
s
o
lu
tio
n
is
u
p
d
ated
f
r
o
m
th
e
weig
h
ted
a
v
er
ag
e
o
f
th
e
th
r
ee
p
o
s
itio
n
s
esti
m
ated
b
y
th
e
lea
d
er
s
α
,
β
,
an
d
δ
.
(
+
1
)
=
1
3
(
1
⃗
⃗
⃗
⃗
+
2
⃗
⃗
⃗
⃗
+
3
⃗
⃗
⃗
⃗
)
(
2
6)
T
h
e
GW
O
p
r
o
ce
d
u
r
e
f
o
r
f
in
d
i
n
g
th
e
m
a
x
im
u
m
p
o
we
r
p
o
in
t
is
s
u
m
m
ar
ized
in
Fig
u
r
e
6
,
w
h
ich
illu
s
tr
ates
th
e
m
ain
s
tep
s
o
f
co
m
p
u
tin
g
a
n
d
u
p
d
atin
g
th
e
d
u
ty
cy
cle.
Fig
u
r
e
6
.
E
n
cir
clin
g
m
ec
h
an
is
m
o
f
th
e
GW
O
alg
o
r
ith
m
b
ase
d
o
n
th
e
p
o
s
itio
n
s
o
f
lead
er
s
α
,
β,
an
d
δ
[
1
3
]
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:
2088
-
8
6
9
4
E
n
erg
y
o
p
timiz
a
tio
n
o
f
a
n
elec
tr
ic
ve
h
icle
ch
a
r
g
in
g
s
ta
tio
n
u
s
in
g
a
h
yb
r
id
S
TA
-
GWO
…
(
S
a
mia
A
mro
u
n
i
)
2191
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
ev
alu
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
h
y
b
r
id
STA
-
GW
O
s
t
r
ateg
y
in
tr
ac
k
in
g
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t,
t
h
e
p
h
o
to
v
o
ltaic
s
y
s
te
m
is
s
u
b
jecte
d
to
a
v
a
r
iab
le
i
r
r
ad
ian
ce
p
r
o
f
ile,
s
h
o
w
n
in
Fig
u
r
e
7
.
T
h
is
p
r
o
f
ile
was
d
esig
n
ed
to
r
ep
r
o
d
u
ce
atm
o
s
p
h
er
ic
co
n
d
itio
n
s
r
ep
r
e
s
en
tativ
e
o
f
r
ea
l
o
p
er
atio
n
,
co
m
b
in
in
g
co
n
s
tan
t
ir
r
ad
ian
ce
s
tep
s
,
ab
r
u
p
t tr
an
s
it
io
n
s
,
an
d
p
r
o
g
r
ess
iv
e
r
am
p
s
,
s
o
as to
jo
in
tly
s
tr
ess
th
e
s
tea
dy
-
s
tate
an
d
d
y
n
am
ic
r
eg
im
es
o
f
th
e
s
y
s
tem
.
T
h
e
co
n
s
tan
t
ir
r
ad
ian
ce
s
tep
s
(
1
0
0
0
,
8
5
0
,
8
0
0
,
7
0
0
,
6
0
0
,
5
0
0
,
an
d
4
0
0
W
/m
²)
ar
e
u
s
ed
to
ch
ar
ac
ter
ize
th
e
b
eh
av
io
r
o
f
th
e
STA
co
n
tr
o
ller
in
s
tea
d
y
s
tate.
T
h
e
an
aly
s
is
r
elie
s
o
n
two
q
u
an
titativ
e
in
d
icato
r
s
,
n
am
ely
th
e
s
tab
ilit
y
o
f
th
e
ex
tr
ac
te
d
p
o
wer
a
r
o
u
n
d
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t a
n
d
th
e
am
p
litu
d
e
o
f
th
e
r
esid
u
al
o
s
cillatio
n
s
,
wh
ich
r
esp
ec
tiv
ely
r
ef
lect
th
e
tr
ac
k
in
g
ac
cu
r
ac
y
an
d
th
e
r
o
b
u
s
tn
ess
o
f
th
e
co
n
tr
o
l
in
s
tead
y
-
s
tate
o
p
er
atio
n
.
T
h
e
ab
r
u
p
t
ir
r
ad
ian
ce
v
ar
iatio
n
s
o
b
s
e
r
v
ed
at
t
=
1
.
2
s
,
2
.
5
s
,
4
.
6
s
,
7
s
,
1
2
.
9
s
,
1
6
s
,
an
d
1
8
.
5
s
co
n
s
titu
te
p
er
tu
r
b
atio
n
test
s
d
esig
n
ed
t
o
ev
al
u
ate
t
h
e
d
y
n
am
ic
r
o
b
u
s
tn
ess
o
f
t
h
e
GW
O
alg
o
r
ith
m
.
E
ac
h
o
f
th
ese
s
tep
s
in
s
tan
tan
eo
u
s
ly
s
h
if
ts
th
e
p
o
s
itio
n
o
f
th
e
MPP,
r
eq
u
ir
in
g
th
e
co
n
tr
o
l
ler
to
r
ap
id
l
y
r
elo
ca
t
e
th
e
g
lo
b
al
o
p
tim
u
m
.
T
h
e
p
er
f
o
r
m
an
ce
an
aly
s
is
r
elies
o
n
f
o
u
r
q
u
an
titativ
e
in
d
icato
r
s
:
th
e
co
n
v
e
r
g
en
ce
tim
e,
r
ef
lectin
g
th
e
s
p
ee
d
o
f
r
elo
ca
t
io
n
;
th
e
tr
an
s
ien
t
p
o
wer
lo
s
s
,
co
r
r
esp
o
n
d
in
g
to
th
e
en
e
r
g
y
n
o
t
ex
tr
ac
ted
d
u
r
in
g
th
e
s
ea
r
ch
p
h
a
s
e;
t
h
e
p
o
s
s
ib
le
o
v
er
s
h
o
o
t,
in
d
icativ
e
o
f
o
s
cillato
r
y
b
eh
av
i
o
r
a
r
o
u
n
d
th
e
n
e
w
eq
u
ilib
r
iu
m
p
o
in
t;
an
d
th
e
lo
ca
lizatio
n
ac
c
u
r
ac
y
,
m
ea
s
u
r
ed
b
y
th
e
r
esid
u
al
d
ev
iatio
n
b
etwe
en
th
e
s
tab
iliz
ed
p
o
wer
an
d
th
e
th
eo
r
etica
l
m
ax
im
u
m
p
o
wer
av
ailab
le
at
th
e
n
ew
ir
r
ad
ian
c
e.
I
n
ad
d
itio
n
,
two
in
cr
ea
s
in
g
ir
r
ad
ian
ce
r
am
p
s
ar
e
in
tr
o
d
u
ce
d
,
b
etwe
en
2
.
5
s
an
d
4
.
6
s
(
f
r
o
m
4
0
0
to
7
0
0
W
/m
²)
an
d
b
etwe
en
9
s
an
d
1
2
.
9
s
(
f
r
o
m
6
0
0
to
1
0
0
0
W
/m
²)
,
r
esp
ec
tiv
ely
.
T
h
ese
p
r
o
g
r
ess
iv
e
v
ar
iatio
n
s
ar
e
in
te
n
d
ed
to
ev
alu
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
h
y
b
r
id
STA
-
GW
O
s
tr
ateg
y
in
a
co
n
t
ex
t
wh
er
e
th
e
m
a
x
im
u
m
p
o
w
er
p
o
in
t
e
v
o
lv
es
co
n
tin
u
o
u
s
ly
r
ath
er
th
a
n
th
r
o
u
g
h
d
is
cr
ete
ju
m
p
s
.
T
h
ey
th
u
s
m
a
k
e
it
p
o
s
s
ib
le
to
v
e
r
if
y
th
e
ab
i
lity
o
f
th
e
STA
co
n
tr
o
l
to
en
s
u
r
e
co
n
ti
n
u
o
u
s
MPP
tr
ac
k
in
g
,
wh
ile
th
e
GW
O
alg
o
r
ith
m
co
n
tin
u
o
u
s
ly
ad
a
p
ts
its
s
ea
r
ch
f
o
r
th
e
n
ew
o
p
tim
al
p
o
s
itio
n
,
illu
s
tr
atin
g
th
e
f
u
n
ctio
n
al
s
y
n
e
r
g
y
b
etwe
en
th
e
two
co
m
p
o
n
en
ts
o
f
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
I
n
th
i
s
s
tu
d
y
,
th
e
GW
O
alg
o
r
ith
m
is
co
n
f
ig
u
r
ed
with
a
p
o
p
u
latio
n
o
f
1
5
wo
lv
es
(
s
ea
r
ch
ag
en
ts
)
an
d
a
m
ax
i
m
u
m
o
f
4
0
iter
atio
n
s
.
T
h
is
co
n
f
ig
u
r
atio
n
r
ep
r
esen
ts
a
tr
ad
e
-
o
f
f
b
etwe
en
co
n
v
er
g
en
ce
s
p
ee
d
,
ac
cu
r
ac
y
in
lo
ca
tin
g
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t,
an
d
c
o
m
p
u
tatio
n
al
lo
ad
,
th
e
latter
h
a
v
in
g
to
r
em
ain
co
m
p
ati
b
le
with
th
e
co
n
s
tr
ain
ts
o
f
a
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
.
T
h
is
test
s
c
en
ar
io
th
u
s
m
a
k
es
it
p
o
s
s
ib
le
to
jo
in
tly
ch
ar
ac
ter
ize
th
e
s
tatic
p
er
f
o
r
m
an
ce
o
f
th
e
STA
co
n
tr
o
l,
r
elate
d
to
MPP
m
ain
ten
an
ce
in
s
tead
y
s
tate,
an
d
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
f
th
e
GW
O
alg
o
r
ith
m
,
r
elate
d
to
th
e
s
ea
r
c
h
f
o
r
an
d
r
a
p
id
lo
ca
lizatio
n
o
f
th
e
n
ew
MPP
f
o
llo
win
g
a
p
er
tu
r
b
atio
n
o
r
d
u
r
i
n
g
a
co
n
tin
u
o
u
s
ir
r
ad
ian
ce
v
ar
ia
tio
n
.
T
h
is
f
u
n
ctio
n
al
s
y
n
er
g
y
h
ig
h
lig
h
ts
th
e
v
alu
e
o
f
th
e
h
y
b
r
id
STA
-
GW
O
ap
p
r
o
ac
h
,
wh
ich
c
o
n
tr
ib
u
tes
to
im
p
r
o
v
in
g
t
h
e
r
o
b
u
s
tn
ess
,
co
n
v
er
g
en
ce
s
p
ee
d
,
an
d
o
v
e
r
all
ef
f
icien
cy
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
u
n
d
er
v
ar
iab
le
ir
r
ad
ian
ce
c
o
n
d
itio
n
s
.
Fig
u
r
e
7
.
Dy
n
am
ic
ir
r
a
d
ian
ce
p
r
o
f
ile
T
h
e
d
y
n
am
ic
r
esp
o
n
s
e
o
f
th
e
PV
s
y
s
tem
is
illu
s
tr
ated
in
Fig
u
r
es
8
-
10
,
r
ep
r
esen
tin
g
th
e
cu
r
r
e
n
t,
v
o
ltag
e,
an
d
o
u
tp
u
t
p
o
wer
,
r
esp
ec
tiv
ely
,
u
n
d
e
r
th
e
d
y
n
a
m
ic
ir
r
ad
ian
ce
p
r
o
f
ile.
T
h
e
o
b
tain
ed
wav
ef
o
r
m
s
r
ev
ea
l
r
ap
i
d
s
tab
ilizatio
n
ar
o
u
n
d
t
h
e
m
ax
im
u
m
p
o
wer
p
o
in
t,
ac
co
m
p
a
n
ied
b
y
s
tab
le
a
n
d
r
o
b
u
s
t
tr
ac
k
in
g
th
r
o
u
g
h
o
u
t
t
h
e
im
p
o
s
ed
ir
r
ad
ian
ce
v
ar
iatio
n
s
.
T
h
ese
r
esu
lt
s
h
ig
h
lig
h
t
th
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
h
y
b
r
id
STA
-
GW
O
MP
PT
s
tr
ateg
y
,
ch
ar
ac
ter
ized
b
y
f
ast
co
n
v
er
g
en
ce
,
n
eg
lig
ib
le
o
s
cillatio
n
s
in
s
tea
d
y
s
tate,
an
d
h
ig
h
en
er
g
y
c
o
n
v
e
r
s
io
n
ef
f
icien
c
y
o
v
er
th
e
e
n
tire
ir
r
a
d
ian
ce
r
a
n
g
e
s
tu
d
ied
.
T
h
is
tr
ac
k
in
g
ac
c
u
r
ac
y
is
o
f
d
i
r
ec
t
r
elev
an
ce
to
th
e
o
p
e
r
atio
n
o
f
th
e
s
tu
d
ied
elec
tr
ic
v
e
h
icle
ch
ar
g
in
g
s
tatio
n
:
b
y
m
in
im
izin
g
tr
an
s
ien
t
lo
s
s
es
an
d
m
ax
im
izin
g
th
e
ef
f
ec
tiv
ely
ex
tr
ac
ted
p
h
o
t
o
v
o
ltaic
p
o
wer
,
th
e
STA
-
GW
O
s
tr
ateg
y
in
cr
ea
s
es
th
e
s
h
ar
e
o
f
s
o
lar
en
er
g
y
d
i
r
ec
tly
av
ailab
le
f
o
r
ch
a
r
g
in
g
th
e
v
eh
icle
(
“PV
to
E
V”
m
o
d
e)
,
th
er
e
b
y
r
e
d
u
cin
g
r
el
ian
ce
o
n
g
r
id
e
n
er
g
y
(
“Gr
i
d
to
E
V”
m
o
d
e)
ac
c
o
r
d
in
g
to
th
e
s
witch
in
g
lo
g
ic
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
2183
-
2
1
9
6
2192
p
r
esen
ted
in
T
ab
le
1
.
T
h
is
ef
f
i
cien
cy
g
ai
n
,
alth
o
u
g
h
lim
ited
t
o
a
f
ew
watts
p
er
tr
a
n
s
itio
n
,
tr
an
s
lates
o
n
a
d
aily
s
ca
le
in
to
a
s
ig
n
if
ican
t
im
p
r
o
v
em
en
t
in
th
e
p
h
o
to
v
o
ltaic
s
elf
-
co
n
s
u
m
p
tio
n
r
ate
an
d
a
co
r
r
e
s
p
o
n
d
in
g
r
ed
u
ctio
n
in
th
e
s
tatio
n
'
s
o
p
er
atin
g
co
s
ts
.
T
h
e
zo
o
m
ed
v
iews
in
Fig
u
r
e
1
0
h
ig
h
lig
h
t
th
e
tr
an
s
ien
t
b
eh
av
io
r
o
f
th
e
PV
p
o
wer
d
u
r
in
g
s
u
cc
ess
iv
e
ir
r
ad
ian
ce
ch
a
n
g
es.
E
ac
h
tr
an
s
itio
n
ca
u
s
es
a
b
r
ief
d
ec
r
e
ase
in
p
o
wer
,
r
esu
ltin
g
f
r
o
m
th
e
MPP
s
h
if
t,
wh
o
s
e
r
elo
ca
tio
n
b
y
th
e
STA
-
GW
O
alg
o
r
ith
m
r
eq
u
ir
es
o
n
l
y
a
v
er
y
s
h
o
r
t
tim
e.
T
h
is
d
r
o
p
n
e
v
er
th
eless
r
em
ain
s
lim
ited
to
a
f
ew
watt
s
ac
r
o
s
s
all
ca
s
e
s
s
tu
d
ied
,
b
ef
o
r
e
th
e
p
o
wer
p
r
o
g
r
ess
iv
ely
r
etu
r
n
s
to
th
e
n
ew
o
p
tim
al
v
alu
e
co
r
r
esp
o
n
d
i
n
g
to
t
h
e
n
e
w
ir
r
ad
ian
ce
lev
el.
T
h
is
f
ast
r
esp
o
n
s
e
r
esu
lts
in
a
co
n
v
er
g
en
ce
tim
e
o
n
th
e
o
r
d
er
o
f
2
to
3
m
s
,
s
ig
n
if
ican
tl
y
r
ed
u
ci
n
g
en
er
g
y
lo
s
s
es
d
u
r
in
g
tr
an
s
ien
t
p
h
ases
an
d
en
s
u
r
in
g
e
f
f
icie
n
t
o
p
er
atio
n
o
f
th
e
p
h
o
to
v
o
lt
aic
s
y
s
tem
.
On
ce
s
tead
y
s
tate
is
r
ea
ch
ed
,
th
e
p
o
wer
s
tab
ilizes
with
r
esid
u
al
o
s
cillatio
n
s
b
elo
w
0
.
1
%
o
f
th
e
n
o
m
in
al
v
alu
e
,
illu
s
tr
atin
g
th
e
ab
ilit
y
o
f
th
e
s
u
p
er
-
twis
tin
g
co
n
tr
o
ller
to
lim
it
th
e
ch
atter
in
g
p
h
e
n
o
m
en
o
n
ty
p
ically
o
b
s
er
v
ed
with
co
n
v
en
tio
n
al
s
lid
in
g
-
m
o
d
e
co
n
tr
o
ls
.
T
h
is
b
eh
av
io
r
is
r
ep
r
o
d
u
cib
le
ac
r
o
s
s
all
te
s
ted
ir
r
ad
ian
ce
lev
els
(
8
0
0
,
7
0
0
,
6
0
0
,
5
0
0
,
a
n
d
4
0
0
W
/m
²)
:
r
eg
ar
d
less
o
f
th
e
v
ar
iatio
n
am
p
litu
d
e,
th
e
STA
-
GW
O
alg
o
r
ith
m
r
a
p
id
ly
co
n
v
er
g
es
to
war
d
th
e
n
e
w
m
ax
im
u
m
p
o
wer
p
o
in
t,
w
ith
o
u
t
s
ig
n
if
ican
t
o
v
er
s
h
o
o
t
an
d
with
ex
ce
llen
t
s
te
a
d
y
-
s
tate
s
tab
ilit
y
.
T
h
ese
q
u
alitativ
e
o
b
s
er
v
atio
n
s
ar
e
co
n
f
ir
m
ed
b
y
th
e
q
u
a
n
titativ
e
r
esu
lts
p
r
esen
ted
in
T
ab
le
3
,
co
m
p
a
r
in
g
th
e
th
eo
r
etica
l
m
ax
im
u
m
p
o
wer
with
th
e
p
o
wer
ex
tr
ac
te
d
b
y
th
e
STA
-
GW
O
co
n
tr
o
l
f
o
r
ea
ch
ir
r
a
d
ian
ce
lev
el
s
tu
d
ied
.
Fig
u
r
e
8.
PV
c
u
r
r
en
t r
esp
o
n
s
e
u
n
d
er
d
y
n
a
m
ic
ir
r
ad
ian
ce
Fig
u
r
e
9
.
PV
v
o
ltag
e
r
esp
o
n
s
e
u
n
d
er
d
y
n
am
ic
ir
r
ad
ian
ce
Fig
u
r
e
1
0.
PV p
o
wer
r
esp
o
n
s
e
u
n
d
er
d
y
n
am
ic
ir
r
ad
ia
n
ce
T
h
e
co
r
r
esp
o
n
d
i
n
g
ca
lcu
latio
n
s
ar
e
d
ef
in
ed
as
(2
7
)
-
(2
9
).
(
W
)
=
(
m
ax
−
G
W
O
)
(2
7
)
E
r
r
o
r
(
%
)
=
(
|
m
ax
−
GWO
|
m
ax
×
100
)
(2
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.