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
.
2
,
J
u
n
e
20
2
6
,
p
p
.
1475
~
1
4
8
5
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
2
.
p
p
1
4
7
5
-
1
4
8
5
1475
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Super
-
twisti
ng
MPPT e
nha
nced vi
a
grey
wolf optim
iza
tion for
dy
na
mic PV
o
pe
r
a
tion
Sli
m
a
ne
H
a
dji
1
,
Sa
id Ais
s
o
u
2
,
Abdelh
a
k
im
B
elk
a
id
1
1
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
,
B
e
j
a
i
a
,
A
l
g
é
r
i
e
2
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
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
7
,
2
0
2
5
R
ev
is
ed
Ap
r
1
9
,
2
0
2
6
Acc
ep
ted
Ma
y
5
,
2
0
2
6
Th
is
p
a
p
e
r
i
n
tro
d
u
c
e
s
a
h
y
b
ri
d
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
(M
P
P
T)
stra
teg
y
fo
r
p
h
o
t
o
v
o
lt
a
ic
(P
V)
sy
ste
m
s
u
n
d
e
r
ra
p
id
l
y
v
a
r
y
in
g
irrad
ian
c
e
c
o
n
d
i
ti
o
n
s.
Th
e
a
p
p
r
o
a
c
h
c
o
m
b
i
n
e
s
th
e
su
p
e
r
-
twisti
n
g
a
l
g
o
ri
th
m
(S
TA),
a
se
c
o
n
d
-
o
r
d
e
r
sli
d
in
g
m
o
d
e
c
o
n
tr
o
l
tec
h
n
iq
u
e
,
wit
h
t
h
e
g
re
y
w
o
lf
o
p
ti
m
ize
r
(G
WO)
in
a
c
o
o
rd
i
n
a
ted
fra
m
e
wo
rk
wh
e
re
c
o
n
tr
o
l
a
c
ti
o
n
a
n
d
p
a
ra
m
e
ter
a
d
a
p
tatio
n
a
re
jo
in
tl
y
a
d
d
re
ss
e
d
.
Un
li
k
e
c
o
n
v
e
n
t
io
n
a
l
M
P
P
T
m
e
th
o
d
s
th
a
t
trea
t
c
o
n
tro
l
a
n
d
o
p
t
imiz
a
ti
o
n
s
e
p
a
ra
tely
,
th
e
p
ro
p
o
se
d
sc
h
e
m
e
imp
ro
v
e
s
tran
sie
n
t
re
sp
o
n
se
wh
i
le
li
m
it
i
n
g
ste
a
d
y
-
sta
te
o
sc
il
latio
n
s.
T
h
e
m
e
th
o
d
is
e
v
a
lu
a
ted
t
h
ro
u
g
h
M
ATLAB/S
i
m
u
li
n
k
sim
u
lati
o
n
s
u
n
d
e
r
m
u
lt
i
p
le
d
y
n
a
m
ic
irrad
ian
c
e
p
r
o
fil
e
s,
i
n
c
lu
d
in
g
fa
st
-
c
h
a
n
g
in
g
e
n
v
ir
o
n
m
e
n
tal
c
o
n
d
it
io
n
s
.
P
e
rfo
rm
a
n
c
e
is
a
ss
e
s
se
d
u
sin
g
c
o
m
p
lem
e
n
tary
m
e
tri
c
s,
n
a
m
e
ly
trac
k
in
g
e
fficie
n
c
y
,
c
o
n
v
e
rg
e
n
c
e
d
y
n
a
m
ics
,
a
n
d
ro
o
t
m
e
a
n
sq
u
a
re
e
rro
r
(R
M
S
E),
t
o
p
ro
v
id
e
a
n
o
b
jec
ti
v
e
a
n
a
ly
sis.
Re
su
lt
s
sh
o
w
th
a
t
th
e
S
TA
-
G
WO
stra
teg
y
a
c
h
iev
e
s
fa
ste
r
c
o
n
v
e
rg
e
n
c
e
a
n
d
imp
r
o
v
e
d
sta
b
il
it
y
c
o
m
p
a
re
d
to
c
o
n
v
e
n
ti
o
n
a
l
S
M
C
-
G
WO.
It
re
a
c
h
e
s
a
n
a
v
e
ra
g
e
trac
k
in
g
e
ffi
c
ien
c
y
o
f
9
9
.
3
4
%
,
c
o
m
p
a
re
d
to
9
9
.
1
9
%
fo
r
S
M
C
-
G
WO,
with
re
d
u
c
e
d
p
o
we
r
flu
c
tu
a
ti
o
n
s
re
flec
ted
b
y
a
lo
we
r
RM
S
E
.
T
h
e
se
imp
ro
v
e
m
e
n
ts
i
n
d
ica
te
a
b
e
tt
e
r
trad
e
-
o
ff
b
e
twe
e
n
d
y
n
a
m
ic
p
e
rfo
rm
a
n
c
e
a
n
d
ste
a
dy
-
sta
te
a
c
c
u
ra
c
y
.
Wh
il
e
th
is
st
u
d
y
is
b
a
se
d
o
n
si
m
u
latio
n
s,
i
ts
fin
d
in
g
s
re
q
u
ire
e
x
p
e
rime
n
tal
v
a
li
d
a
ti
o
n
.
F
u
t
u
re
wo
rk
wi
ll
th
e
r
e
fo
re
in
c
lu
d
e
re
a
l
-
ti
m
e
imp
lem
e
n
tatio
n
to
c
o
n
firm t
h
e
p
ra
c
ti
c
a
l
a
p
p
l
ica
b
il
it
y
o
f
t
h
e
p
r
o
p
o
se
d
a
p
p
ro
a
c
h
.
K
ey
w
o
r
d
s
:
E
n
er
g
y
ef
f
icien
cy
Gr
ey
wo
lf
o
p
tim
izer
Ma
x
im
u
m
p
o
wer
p
o
i
n
t
Ph
o
to
v
o
ltaic
s
y
s
tem
s
Su
p
er
twis
tin
g
alg
o
r
ith
m
T
r
ac
k
in
g
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
a
b
o
r
at
o
ir
e
d
e
Ma
it
r
is
e
d
es
E
n
er
g
i
es R
e
n
o
u
v
ela
b
l
es
(
L
ME
R
)
,
F
ac
u
lt
é
d
e
T
ec
h
n
o
l
o
g
ie
,
Un
iv
er
s
i
té
d
e
B
eja
ia
B
ejaia
,
Alg
ér
ie
E
m
ail: said
.
aiss
o
u
@
u
n
iv
-
b
ejaia
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
So
lar
en
er
g
y
,
with
its
ab
u
n
d
an
ce
an
d
lo
w
ca
r
b
o
n
f
o
o
t
p
r
in
t,
is
ce
n
tr
al
to
th
e
g
lo
b
al
en
er
g
y
tr
an
s
itio
n
[
1
]
-
[
3
]
.
Ph
o
to
v
o
lt
aic
(
PV)
s
y
s
tem
s
ar
e
s
tr
o
n
g
ly
in
f
lu
en
ce
d
b
y
ir
r
a
d
ian
c
e
an
d
tem
p
er
atu
r
e
v
ar
iatio
n
s
,
wh
ich
ca
u
s
e
f
lu
ctu
atio
n
s
in
p
o
wer
o
u
tp
u
t.
T
o
ad
d
r
ess
th
is
,
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
alg
o
r
ith
m
s
ar
e
e
m
p
lo
y
ed
t
o
c
o
n
tin
u
o
u
s
ly
o
p
tim
ize
o
p
er
atin
g
c
o
n
d
itio
n
s
an
d
m
ax
im
ize
en
er
g
y
ex
tr
ac
tio
n
[
4
]
,
[
5
]
.
C
o
n
v
en
tio
n
al
m
eth
o
d
s
s
u
ch
as
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P&
O)
an
d
in
cr
e
m
en
tal
co
n
d
u
ctan
ce
(
I
NC
)
h
av
e
b
ee
n
wid
ely
u
s
ed
d
u
e
to
th
eir
s
im
p
licity
a
n
d
l
o
w
co
s
t,
th
o
u
g
h
t
h
ey
f
ac
e
lim
it
atio
n
s
u
n
d
e
r
r
a
p
id
ly
ch
an
g
in
g
wea
th
er
co
n
d
itio
n
s
.
T
h
e
P&
O
alg
o
r
ith
m
p
er
tu
r
b
s
t
h
e
o
p
er
atin
g
p
o
i
n
t
to
d
etec
t
p
o
wer
v
a
r
iatio
n
s
an
d
ad
j
u
s
t
v
o
l
tag
e,
b
u
t
it
s
u
f
f
er
s
f
r
o
m
o
s
cillatio
n
s
ar
o
u
n
d
th
e
m
ax
im
u
m
p
o
we
r
p
o
in
t
(
MPP)
an
d
s
lo
w
co
n
v
e
r
g
en
ce
u
n
d
er
r
a
p
id
ir
r
ad
ian
ce
c
h
an
g
es
[
6
]
,
[
7
]
.
T
h
e
in
cr
em
e
n
tal
co
n
d
u
ctan
ce
(
I
NC
)
m
eth
o
d
im
p
r
o
v
es
ac
cu
r
a
cy
b
y
ex
p
l
o
itin
g
th
e
p
o
wer
–
v
o
ltag
e
d
e
r
iv
ativ
e,
y
et
r
em
ain
s
s
en
s
itiv
e
to
n
o
is
e.
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
.
2
,
J
u
n
e
20
2
6
:
1
4
7
5
-
1485
1476
T
h
ese
lim
itatio
n
s
h
av
e
d
r
iv
e
n
th
e
d
ev
elo
p
m
en
t
o
f
ad
v
a
n
c
ed
MPPT
s
tr
ateg
ies
b
ased
o
n
ar
tific
ial
in
tellig
en
ce
an
d
m
etah
eu
r
is
tic
o
p
tim
izatio
n
,
o
f
f
er
i
n
g
en
h
an
ce
d
tr
ac
k
in
g
s
p
ee
d
,
s
tab
ili
ty
,
an
d
r
o
b
u
s
tn
ess
.
Fu
zz
y
lo
g
ic
h
as
b
ee
n
wid
el
y
ap
p
lied
i
n
MPPT
d
u
e
to
its
ab
ilit
y
to
m
an
ag
e
u
n
ce
r
t
ain
ty
an
d
a
d
ap
t
to
en
v
ir
o
n
m
en
tal
ch
a
n
g
es.
Ho
wev
er
,
d
esp
ite
th
is
p
er
f
o
r
m
an
ce
,
it
r
eq
u
ir
es
o
p
tim
iz
atio
n
to
im
p
r
o
v
e
r
o
b
u
s
tn
ess
[
5
]
.
Ar
tific
ial
n
eu
r
al
n
etwo
r
k
s
(
ANNs)
o
f
f
er
an
o
th
er
p
r
o
m
is
in
g
s
o
lu
tio
n
b
y
l
ev
er
ag
in
g
lear
n
i
n
g
ca
p
ab
ilit
ies
to
p
r
ed
ict
th
e
M
PP
[
1
]
.
Ho
wev
er
,
ANN
d
e
p
lo
y
m
en
t
d
e
m
an
d
s
h
i
g
h
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
,
wh
ich
lim
its
th
eir
u
s
e
in
lo
w
-
p
o
wer
em
b
ed
d
e
d
s
y
s
tem
s
.
Me
an
wh
ile,
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
h
av
e
g
ain
ed
p
o
p
u
lar
ity
d
u
e
to
th
eir
ef
f
ici
en
cy
.
Am
o
n
g
th
ese
tech
n
iq
u
es,
p
ar
ticle
s
war
m
o
p
tim
izati
o
n
(
PS
O)
h
as
b
ee
n
wid
ely
ap
p
lied
t
o
MPPT
b
ec
a
u
s
e
o
f
its
f
ast
co
n
v
e
r
g
en
ce
an
d
r
o
b
u
s
tn
ess
ag
ain
s
t
en
v
ir
o
n
m
en
tal
d
is
tu
r
b
an
ce
s
[
8
]
,
[
9
]
.
Hy
b
r
id
a
p
p
r
o
ac
h
es,
s
u
ch
as
PS
O
-
P&
O,
im
p
r
o
v
e
b
o
th
s
tab
ilit
y
an
d
tr
ac
k
i
n
g
ac
cu
r
ac
y
.
Oth
e
r
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
,
in
clu
d
in
g
an
t
co
lo
n
y
o
p
tim
izati
o
n
(
AC
O)
[
1
0
]
,
[
1
1
]
,
g
r
e
y
wo
lf
o
p
tim
izatio
n
(
GW
O)
[
1
2
]
,
[
1
3
]
,
an
d
d
if
f
e
r
en
tial
ev
o
lu
tio
n
(
DE
)
,
h
av
e
also
b
ee
n
in
v
esti
g
ated
,
ea
c
h
o
f
f
e
r
in
g
d
is
tin
ct
ad
v
an
tag
es in
ter
m
s
o
f
r
o
b
u
s
tn
ess
,
co
n
v
er
g
en
ce
s
p
ee
d
,
a
n
d
c
o
m
p
u
tatio
n
al
e
f
f
icien
cy
.
R
ec
en
t stu
d
ies p
r
o
p
o
s
e
h
y
b
r
id
m
eth
o
d
s
to
f
u
r
th
e
r
en
h
a
n
ce
MPPT
p
er
f
o
r
m
an
ce
,
s
u
ch
as
ANFI
S
–
PS
O
an
d
f
u
zz
y
l
o
g
ic
–
GW
O
[
1
4
]
,
wh
ich
im
p
r
o
v
e
a
d
ap
tab
ilit
y
a
n
d
p
o
wer
e
x
tr
ac
tio
n
u
n
d
er
v
ar
iab
le
co
n
d
itio
n
s
.
Sli
d
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
h
as
also
b
ee
n
ex
p
lo
r
ed
f
o
r
its
d
is
tu
r
b
an
ce
r
ejec
tio
n
,
t
h
o
u
g
h
its
ch
atter
in
g
ef
f
ec
t
in
d
u
ce
s
o
s
cillatio
n
s
an
d
e
n
e
r
g
y
lo
s
s
es.
T
h
e
s
u
p
er
-
twis
tin
g
alg
o
r
ith
m
(
STA)
m
itig
ates
th
is
d
r
awb
ac
k
,
im
p
r
o
v
in
g
s
tab
ilit
y
an
d
ef
f
ic
ien
cy
in
SMC
-
b
ased
MPPT
[
1
5
]
,
[
1
6
]
.
Desp
ite
th
ese
ad
v
an
ce
s
,
ex
ten
s
iv
e
v
alid
atio
n
u
n
d
er
r
ea
l
-
wo
r
ld
c
o
n
d
itio
n
s
r
em
ain
s
n
ec
ess
ar
y
.
T
h
is
s
tu
d
y
p
r
esen
ts
a
co
m
p
r
eh
en
s
iv
e
ass
ess
m
en
t
o
f
two
M
PP
T
tech
n
iq
u
es,
SMC
-
G
W
O
an
d
STA
-
GW
O,
with
a
p
ar
ticu
lar
e
m
p
h
asis
o
n
th
eir
p
er
f
o
r
m
a
n
ce
u
n
d
er
d
y
n
am
ically
v
ar
y
i
n
g
ir
r
ad
ian
ce
a
n
d
tem
p
er
atu
r
e
co
n
d
itio
n
s
.
Usi
n
g
MA
T
L
AB
/S
im
u
lin
k
s
im
u
latio
n
s
,
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
s
,
th
is
s
tu
d
y
p
r
o
v
id
es
v
alu
ab
le
in
s
i
g
h
ts
in
to
th
e
ef
f
icien
cy
o
f
t
h
e
p
r
o
p
o
s
ed
MPPT
alg
o
r
ith
m
s
,
h
ig
h
lig
h
tin
g
t
h
e
s
tr
en
g
th
s
o
f
th
e
c
o
m
b
in
ed
a
p
p
r
o
ac
h
u
n
d
er
v
ar
io
u
s
o
p
e
r
atin
g
c
o
n
d
itio
n
s
.
Ho
wev
er
,
a
k
e
y
lim
itatio
n
o
f
t
h
is
wo
r
k
lies
in
th
e
ab
s
en
ce
o
f
a
h
ar
d
war
e
-
in
-
t
h
e
-
lo
o
p
(
HI
L
)
im
p
lem
en
tatio
n
,
wh
ich
r
em
a
in
s
a
d
ir
ec
tio
n
f
o
r
f
u
tu
r
e
wo
r
k
.
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
A
ND
M
O
DE
L
L
I
NG
Ph
o
to
v
o
ltaic
p
o
wer
g
e
n
er
ati
o
n
is
s
tr
o
n
g
ly
af
f
ec
ted
b
y
m
eteo
r
o
lo
g
ical
co
n
d
itio
n
s
,
with
s
o
lar
ir
r
ad
ian
ce
b
ein
g
th
e
d
o
m
in
an
t
f
ac
to
r
.
W
h
ile
m
an
u
f
ac
tu
r
er
s
s
p
ec
if
y
m
o
d
u
le
p
ar
am
eter
s
u
n
d
er
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC),
r
ea
l
-
wo
r
ld
o
p
er
atio
n
r
a
r
ely
m
atc
h
es
th
ese
id
ea
l
v
alu
es.
L
o
w
ir
r
ad
i
an
ce
ca
n
f
o
r
ce
th
e
s
y
s
tem
to
it
s
h
o
r
t
-
cir
cu
it
cu
r
r
en
t
wh
en
lo
a
d
d
em
a
n
d
e
x
ce
e
d
s
m
o
d
u
le
ca
p
ac
ity
,
ca
u
s
in
g
f
ailu
r
e.
T
o
en
s
u
r
e
s
tab
le
o
p
er
atio
n
,
lo
ad
–
g
en
er
ato
r
d
ec
o
u
p
lin
g
is
r
eq
u
ir
e
d
,
ac
h
iev
ed
t
h
r
o
u
g
h
p
o
wer
e
lectr
o
n
ics.
DC
/DC
co
n
v
er
ter
s
with
MPPT
en
ab
le
ef
f
icien
t
ad
ap
tatio
n
,
with
B
o
o
s
t
-
ty
p
e
co
n
v
er
ter
s
(
n
o
n
-
is
o
la
ted
s
tep
-
u
p
)
wid
ely
u
s
ed
in
r
esear
c
h
f
o
r
r
aisi
n
g
th
e
lo
w
v
o
ltag
e
o
f
PV
p
a
n
els.
Fig
u
r
e
1
s
h
o
ws
a
PV
s
y
s
tem
ar
ch
itectu
r
e
em
p
lo
y
in
g
a
b
o
o
s
t c
o
n
v
e
r
ter
f
o
r
d
ec
o
u
p
lin
g
.
Fig
u
r
e
1
.
I
ll
u
s
tr
atio
n
o
f
t
h
e
PV sy
s
tem
u
n
d
er
s
tu
d
y
2
.
1
.
P
V
m
o
del
m
o
delin
g
T
h
e
p
h
o
to
v
o
ltaic
s
in
g
le
-
d
io
d
e
eq
u
iv
alen
t
cir
cu
it
m
o
d
el,
as
s
h
o
wn
in
Fig
u
r
e
2
,
is
wid
ely
ad
o
p
ted
f
o
r
PV
ce
ll
m
o
d
ellin
g
b
ec
au
s
e
o
f
its
s
im
p
licity
an
d
s
atis
f
ac
to
r
y
ac
cu
r
ac
y
.
T
h
e
m
o
d
el
u
tili
ze
d
in
th
is
s
tu
d
y
is
th
e
s
am
e
as th
e
o
n
e
u
s
ed
in
p
r
e
v
io
u
s
r
esear
ch
[
9
]
,
[
1
0
]
,
[
1
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:
2088
-
8
6
9
4
S
u
p
er
-
tw
is
tin
g
MPP
T e
n
h
a
n
ce
d
via
g
r
ey
w
o
lf o
p
timiz
a
tio
n
fo
r
d
yn
a
mic
P
V
o
p
era
tio
n
(
S
lima
n
e
Ha
d
ji)
1477
I
n
ac
co
r
d
an
ce
with
Kir
ch
h
o
f
f
'
s
th
eo
r
em
ap
p
lied
to
t
h
e
p
r
esen
ted
m
o
d
el,
th
e
cu
r
r
e
n
ts
with
in
th
e
p
h
o
to
v
o
ltaic
ce
ll c
an
b
e
e
x
p
r
e
s
s
ed
as (
1
)
[
5
]
,
[
1
1
]
.
=
ℎ
−
−
ℎ
(
1
)
W
h
er
e:
ℎ
,
th
e
p
h
o
t
o
-
cu
r
r
en
t,
th
e
d
io
d
e
-
c
u
r
r
en
t
a
n
d
ℎ
th
e
s
h
u
n
t c
u
r
r
en
t
[
1
8
]
-
[
2
1
]
.
Af
ter
s
u
b
s
titu
tin
g
th
e
c
u
r
r
e
n
t
s
a
n
d
ℎ
w
i
t
h
t
h
e
i
r
e
x
p
r
e
s
s
i
o
n
s
i
n
(
1
)
,
p
h
o
t
o
v
o
l
t
a
i
c
c
u
r
r
e
n
t
i
s
o
b
t
ai
n
e
d
a
s
e
x
p
r
es
s
e
d
i
n
(
2
)
[
1
1
]
,
[
1
3
]
.
=
ℎ
−
0
⋅
[
(
⋅
(
+
⋅
)
⋅
⋅
⋅
)
−
1
]
−
+
⋅
ℎ
(
2
)
T
ab
le
1
p
r
esen
ts
th
e
p
h
o
t
o
v
o
lt
aic
p
an
el
p
ar
am
eter
s
.
T
h
e
(
1
)
a
n
d
(
2
)
r
e
p
r
esen
t
a
m
ath
em
atica
l
m
o
d
el
o
f
a
PV
p
a
n
el,
ab
le
to
d
escr
ib
e
th
e
b
e
h
a
v
io
r
o
f
t
h
e
m
o
d
u
le
in
Simu
lin
k
.
Sev
er
al
s
im
u
latio
n
s
wer
e
ca
r
r
ied
o
u
t.
Fig
u
r
e
3
illu
s
tr
ates
th
e
ch
ar
ac
ter
is
tics
o
b
tain
ed
u
n
d
er
v
ar
y
in
g
lev
els
o
f
s
o
lar
ir
r
ad
ian
ce
,
r
a
n
g
in
g
f
r
o
m
1
0
0
0
W
/m
²
with
an
in
cr
em
e
n
t
o
f
2
0
0
W
/m
².
T
h
e
m
ax
im
u
m
p
o
wer
p
o
in
ts
ar
e
in
d
icate
d
b
y
r
ed
aster
is
k
s
(
*
).
Fig
u
r
e
2
.
E
q
u
iv
alen
t c
ir
c
u
it o
f
s
o
lar
ce
ll
T
ab
le
1
.
Ph
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
3
.
E
lectr
ical
I
V
a
n
d
PV
cu
r
v
es f
o
r
p
h
o
to
v
o
ltaic
p
an
el
STP8
0
2
.
2
.
DC
-
DC
co
nv
er
t
er
I
n
p
o
wer
elec
tr
o
n
ics,
DC
–
DC
co
n
v
er
ter
s
r
eg
u
late
av
e
r
a
g
e
DC
s
ig
n
als
v
ia
d
u
ty
cy
cle
o
f
th
e
s
witch
in
g
d
ev
ice.
W
ith
in
PV
s
y
s
tem
s
,
th
ey
ac
t
as
ad
a
p
tatio
n
in
ter
f
ac
es,
ad
ju
s
tin
g
v
o
ltag
e
a
n
d
c
u
r
r
en
t
to
tr
ac
k
th
e
MPP
an
d
av
o
id
s
h
o
r
t
-
cir
c
u
it
o
p
er
atio
n
.
Fig
u
r
e
4
s
h
o
ws
th
e
b
o
o
s
t
co
n
v
e
r
ter
to
p
o
lo
g
y
co
m
m
o
n
l
y
u
s
ed
f
o
r
PV
p
an
els.
W
h
en
th
e
I
GB
T
/
MO
SF
E
T
is
ON,
th
e
s
o
u
r
ce
ch
ar
g
es
th
e
in
d
u
cto
r
wh
ile
th
e
d
io
d
e
is
r
ev
er
s
e
-
b
iased
.
W
h
en
th
e
s
witch
is
O
FF
,
b
o
th
th
e
i
n
d
u
ct
o
r
an
d
s
o
u
r
ce
d
eliv
er
en
er
g
y
to
th
e
lo
a
d
.
T
h
e
in
p
u
t
–
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t r
elatio
n
s
h
i
p
s
ar
e
d
ef
in
e
d
b
y
(
3
)
[
2
]
,
[
5
]
.
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
.
2
,
J
u
n
e
20
2
6
:
1
4
7
5
-
1485
1478
=
(
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
as
(
4
)
to
(
6
)
[
2
2
]
,
[
2
3
]
.
(
=
−
0
+
0
0
=
(
−
0
+
)
0
)
(
4
)
̇
=
(
)
+
(
)
(
5
)
(
)
=
[
−
0
−
0
+
]
(
)
=
[
0
−
0
]
(
6
)
Fig
u
r
e
4
.
T
h
e
p
o
we
r
cir
cu
it o
f
a
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
2
.
3
.
M
P
P
T
co
ntr
o
ller
2
.
3
.
1
.
Su
per
-
t
wis
t
ing
s
li
din
g
m
o
de
co
ntr
o
l
f
o
r
M
P
P
T
T
h
e
s
u
p
er
-
twis
tin
g
alg
o
r
ith
m
is
an
ad
v
an
ce
d
f
o
r
m
o
f
SMC
d
esig
n
ed
to
s
u
p
p
r
ess
ch
atter
in
g
,
th
er
eb
y
im
p
r
o
v
in
g
th
e
d
u
r
ab
ilit
y
an
d
ef
f
icien
cy
o
f
PV
s
y
s
tem
s
.
Usi
n
g
a
n
o
n
lin
ea
r
co
n
tr
o
l
law,
it
r
ed
u
ce
s
s
witch
in
g
ef
f
o
r
t
an
d
en
h
an
ce
s
d
y
n
am
i
c
r
esp
o
n
s
e.
I
n
en
v
ir
o
n
m
e
n
ts
with
v
ar
iab
le
ir
r
a
d
ian
ce
an
d
tem
p
er
atu
r
e,
th
e
co
n
tr
o
ller
en
s
u
r
es
r
o
b
u
s
t
MPPT.
I
ts
im
p
lem
en
tatio
n
in
v
o
l
v
es
two
s
tag
es:
i)
d
ef
in
in
g
a
s
lid
in
g
s
u
r
f
ac
e
b
ased
o
n
s
y
s
tem
d
y
n
am
ics
to
g
u
ar
a
n
tee
f
ast
an
d
s
tab
le
c
o
n
v
e
r
g
e
n
ce
,
an
d
ii)
d
esig
n
i
n
g
a
co
n
tr
o
l
law
co
m
p
r
is
in
g
eq
u
iv
alen
t
an
d
s
witch
in
g
ac
t
io
n
s
th
at
co
n
s
tr
ain
s
s
y
s
tem
s
tates
to
th
e
s
u
r
f
ac
e.
E
m
b
e
d
d
ed
in
an
ad
ap
tiv
e
f
ee
d
b
ac
k
lo
o
p
,
th
e
m
et
h
o
d
m
in
im
izes
d
is
tu
r
b
an
ce
s
,
r
ed
u
ce
s
o
s
cillatio
n
s
,
an
d
im
p
r
o
v
es
b
o
th
ef
f
icien
cy
a
n
d
r
eliab
ilit
y
o
f
PV sy
s
tem
s
[
2
]
.
−
Sli
d
in
g
s
u
r
f
ac
e
Acc
o
r
d
in
g
to
th
e
liter
atu
r
e,
a
s
elec
tio
n
o
f
s
lid
in
g
s
u
r
f
ac
es h
a
s
b
ee
n
e
m
p
lo
y
e
d
b
y
r
esear
ch
e
r
s
[
1
]
.
T
h
e
s
lid
in
g
s
u
r
f
ac
e
S(x
,
t)
is
ch
o
s
en
ac
co
r
d
in
g
to
(
7
)
.
B
o
th
it
an
d
th
e
f
ir
s
t
d
er
iv
ativ
e
s
h
o
u
ld
b
e
ze
r
o
.
T
h
e
s
lid
in
g
s
u
r
f
ac
e
p
r
o
p
o
s
ed
in
[
7
]
is
ch
o
s
en
to
v
alid
ate
th
at
t
h
e
s
y
s
tem
attain
s
th
e
MPP.
˙
(
,
)
=
0
(
,
)
=
=
(
+
)
=
0
(
7
)
−
C
o
n
tr
o
l la
w
d
esig
n
T
h
e
SMC
s
ig
n
al
i
s
co
m
p
o
s
ed
o
f
two
d
is
tin
ct
co
m
p
o
n
e
n
ts
,
ea
ch
f
u
lf
illi
n
g
a
cr
itical
r
o
le
i
n
en
s
u
r
in
g
r
o
b
u
s
t
an
d
p
r
ec
is
e
MPPT
o
p
er
atio
n
.
T
h
e
f
ir
s
t
co
m
p
o
n
e
n
t,
th
e
eq
u
iv
alen
t
co
n
tr
o
l,
co
n
tin
u
o
u
s
ly
ad
ju
s
ts
s
y
s
tem
d
y
n
am
ics
to
m
ain
tain
ad
h
e
r
en
ce
to
th
e
s
lid
in
g
s
u
r
f
ac
e.
B
y
e
n
s
u
r
in
g
a
s
m
o
o
t
h
a
n
d
s
tab
le
r
e
s
p
o
n
s
e,
it
s
tab
ilizes
th
e
s
y
s
tem
u
n
d
er
n
o
r
m
al
co
n
d
itio
n
s
an
d
o
p
tim
izes
PV
p
er
f
o
r
m
an
ce
b
y
ac
cu
r
ately
tr
ac
k
i
n
g
th
e
MPP
d
esp
ite
v
ar
iatio
n
s
in
ir
r
ad
ia
n
ce
an
d
tem
p
er
atu
r
e.
T
h
e
s
ec
o
n
d
co
m
p
o
n
en
t,
th
e
s
witch
in
g
c
o
n
tr
o
l,
c
o
u
n
ter
ac
ts
d
is
tu
r
b
an
ce
s
an
d
m
o
d
el
u
n
ce
r
tain
ties
b
y
ap
p
ly
in
g
a
d
is
co
n
tin
u
o
u
s
co
n
t
r
o
l
ac
tio
n
th
at
r
ed
ir
ec
ts
th
e
s
y
s
tem
s
tate
to
war
d
th
e
s
lid
in
g
s
u
r
f
a
ce
wh
en
ev
e
r
d
ev
iatio
n
s
o
cc
u
r
.
T
h
is
m
ec
h
an
is
m
e
n
h
an
ce
s
s
y
s
tem
r
esil
ien
ce
b
y
s
wif
tly
co
r
r
ec
tin
g
o
f
f
-
s
u
r
f
ac
e
ex
cu
r
s
io
n
s
,
en
s
u
r
i
n
g
r
o
b
u
s
tn
e
s
s
ag
ain
s
t e
x
ter
n
al
p
er
tu
r
b
atio
n
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
S
u
p
er
-
tw
is
tin
g
MPP
T e
n
h
a
n
ce
d
via
g
r
ey
w
o
lf o
p
timiz
a
tio
n
fo
r
d
yn
a
mic
P
V
o
p
era
tio
n
(
S
lima
n
e
Ha
d
ji)
1479
T
h
e
s
y
n
er
g
y
b
etwe
en
eq
u
iv
al
en
t
an
d
s
witch
in
g
co
n
tr
o
ls
m
ak
es
SMC
h
ig
h
ly
ef
f
ec
tiv
e
in
d
y
n
am
ic
an
d
u
n
ce
r
tain
en
v
ir
o
n
m
en
ts
.
W
h
ile
th
e
eq
u
iv
alen
t
co
n
tr
o
l
m
ain
tain
s
o
p
er
atio
n
al
s
tab
ilit
y
an
d
ef
f
icien
cy
,
th
e
s
witch
in
g
co
n
tr
o
l
g
u
ar
an
tees
r
ap
id
d
is
tu
r
b
an
ce
r
ejec
tio
n
.
T
h
is
d
u
al
-
co
m
p
o
n
e
n
t
d
esig
n
is
i
n
teg
r
al
to
ad
v
an
ce
d
MPPT
s
tr
ateg
ies,
en
ab
lin
g
c
o
n
s
is
ten
t
MPP
tr
ac
k
in
g
an
d
m
ax
im
izin
g
e
n
er
g
y
h
ar
v
esti
n
g
in
PV
s
y
s
tem
s
.
Fig
u
r
e
5
p
r
o
v
i
d
es
t
h
e
s
t
r
u
ct
u
r
e
o
f
t
h
e
ST
-
SMC
m
et
h
o
d
[
3
]
.
T
h
e
g
l
o
b
al
s
y
s
te
m
eq
u
a
ti
o
n
c
o
n
t
r
o
l
is
g
i
v
e
n
i
n
(
8
)
.
=
+
(
8
)
W
h
er
e,
U
ec
eq
u
iv
alen
t c
o
n
tr
o
l
an
d
U
sc
is
s
witch
in
g
co
n
tr
o
l,
t
h
e
eq
u
atio
n
o
f
s
witch
in
g
co
n
tr
o
l is g
iv
en
in
(
9
)
.
=
1
+
2
(
9
)
T
h
e
eq
u
atio
n
s
o
f
U
1
a
n
d
U
2
is
g
iv
en
in
(
1
0
)
.
̇
1
=
−
.
(
)
2
=
−
.
|
|
1
2
(
)
(
1
0
)
W
h
er
e
γ
an
d
λ
ar
e
d
esig
n
p
a
r
a
m
eter
s
,
th
eir
r
esp
ec
tiv
e
eq
u
atio
n
s
ar
e
g
iv
e
n
b
y
(
1
1
)
.
>
Γ
>
√
2
Γ
2
.
(
Γ
+
)
2
Γ
−
(
11
)
T
h
e
(
1
2
)
p
r
o
v
id
es th
e
e
q
u
iv
ale
n
t c
o
n
tr
o
l
.
=
−
[
]
(
)
[
]
(
)
=
1
−
0
(
1
2
)
T
h
e
n
ex
t
s
tep
i
n
v
o
lv
es
d
er
iv
i
n
g
an
d
d
em
o
n
s
tr
atin
g
th
e
s
tab
ilit
y
co
n
d
itio
n
s
to
en
s
u
r
e
t
h
e
s
y
s
tem
o
p
er
ates
with
in
d
esire
d
p
ar
am
ete
r
s
.
−
Stab
ilit
y
an
aly
s
is
T
h
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
d
ef
in
ed
to
e
n
s
u
r
e
th
e
s
tab
ilit
y
o
f
th
e
s
u
g
g
ested
c
o
n
tr
o
ller
,
as
d
etailed
in
(
1
3
)
a
n
d
(
1
4
)
.
V
(
t
)
=
1
2
S
2
(
t
)
(
13)
˙
=
[
]
˙
=
[
]
(
−
(
1
−
)
+
)
(
1
4
)
A
d
escr
ip
tio
n
o
f
th
e
f
ir
s
t te
r
m
ca
n
b
e
f
o
u
n
d
in
(
1
5
)
.
[
]
=
1
+
−
2
(
1
5
)
T
h
e
f
ir
s
t d
er
iv
ativ
e
o
f
I
PV
is
g
i
v
en
b
y
(
1
6
)
.
=
−
(
e
xp
(
ₛ
ₜ
)
)
·
ₛ
ₜ
·
<
0
(
1
6
)
V
PV
is
d
ef
in
ed
as in
(
1
7
)
.
=
ln
(
ℎ
+
−
)
(
1
7
)
T
h
e
d
er
iv
ativ
e
o
f
(
1
7
)
ca
n
b
e
wr
itten
as (
1
8
)
.
∂
=
−
(
(
ℎ
+
−
)
)
<
0
(
1
8
)
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
.
2
,
J
u
n
e
20
2
6
:
1
4
7
5
-
1485
1480
Acc
o
r
d
in
g
to
(
1
8
)
,
it
is
o
b
v
io
u
s
th
at
th
e
f
ir
s
t
ter
m
(
∂
S
/(
∂
I
p
v
)
)
h
as
a
p
o
s
itiv
e
s
ig
n
,
in
th
e
n
ex
t
s
tep
we
h
av
e
to
in
v
esti
g
ate
th
e
s
ec
o
n
d
ter
m
:
̇
=
−
(
0
)
(
1
−
)
+
(
)
=
−
(
)
(
1
−
−
)
+
(
)
(
1
9
)
=
(
−
|
|
1
2
(
)
−
∫
(
)
(
2
0
)
Acc
o
r
d
in
g
t
o
(
2
0
)
,
we
h
av
e
(
2
1
)
.
̇
=
[
]
(
−
|
|
1
2
(
)
−
∫
(
)
)
(
2
1
)
As
a
r
esu
lt,
we
ca
n
s
tate
th
at
th
e
L
y
ap
u
n
o
v
s
tab
ilit
y
is
g
u
ar
an
teed
b
ec
au
s
e
S
an
d
S˙
h
av
e
alwa
y
s
d
if
f
er
en
t
s
ig
n
s
.
2
.
3
.
2
.
Su
per
-
t
wis
t
ing
pa
ra
m
et
er
s
us
ing
t
he
g
re
y
wo
lf
o
pt
im
izer
T
h
e
GW
O
alg
o
r
ith
m
is
a
s
war
m
in
tellig
en
ce
tech
n
iq
u
e
in
s
p
ir
ed
b
y
th
e
s
o
cial
h
ier
ar
ch
y
an
d
co
o
r
d
in
ate
d
h
u
n
tin
g
b
e
h
av
io
r
o
b
s
er
v
ed
in
g
r
ey
wo
lv
es.
I
n
th
is
m
etah
eu
r
is
tic
ap
p
r
o
ac
h
,
s
o
lu
tio
n
ag
en
ts
ar
e
ca
teg
o
r
ized
in
t
o
f
o
u
r
h
ier
ar
ch
ical
lev
els:
Alp
h
a,
B
eta,
Delta,
an
d
Om
e
g
a,
r
e
p
r
esen
tin
g
th
e
b
est,
s
ec
o
n
d
-
b
est,
th
ir
d
-
b
est,
an
d
r
em
ain
i
n
g
ca
n
d
id
ate
s
o
lu
tio
n
s
.
T
h
e
Alp
h
a
ag
en
ts
lead
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
b
y
s
teer
in
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
id
en
tifie
d
s
o
f
ar
.
B
eta
an
d
Delta
ag
en
ts
r
ein
f
o
r
ce
th
is
p
r
o
g
r
ess
io
n
b
y
r
ef
i
n
in
g
th
e
s
ea
r
ch
tr
ajec
to
r
y
,
wh
ile
Om
eg
a
ag
en
ts
ex
p
lo
r
e
less
f
av
o
r
ab
le
r
eg
io
n
s
o
f
th
e
s
o
lu
tio
n
s
p
ac
e.
T
h
is
ex
p
lo
r
atio
n
en
h
a
n
ce
s
p
o
p
u
latio
n
d
iv
er
s
ity
a
n
d
r
e
d
u
c
es th
e
r
is
k
o
f
p
r
em
atu
r
e
c
o
n
v
e
r
g
en
ce
to
l
o
ca
l o
p
tim
a.
T
h
e
co
r
e
o
p
tim
izatio
n
m
ec
h
a
n
is
m
f
o
llo
ws
th
r
ee
s
eq
u
e
n
tial
p
h
ases
:
tar
g
et
lo
ca
lizatio
n
,
en
cir
clem
en
t,
an
d
f
in
al
attac
k
.
T
h
ese
s
tag
es
ar
e
em
u
lated
b
y
th
e
g
r
ad
u
al
c
o
n
v
er
g
en
ce
o
f
ag
e
n
ts
to
war
d
th
e
g
lo
b
al
o
p
tim
u
m
,
ac
h
iev
ed
th
r
o
u
g
h
th
e
iter
ativ
e
r
ed
u
ctio
n
o
f
th
e
d
is
tan
ce
b
et
wee
n
ca
n
d
id
ate
s
o
lu
tio
n
s
an
d
th
e
b
est
-
p
er
f
o
r
m
i
n
g
in
d
iv
id
u
al.
−
GW
O
m
o
d
ellin
g
T
o
im
p
lem
en
t
th
e
GW
O
alg
o
r
ith
m
an
d
ex
ec
u
te
th
e
o
p
tim
iza
tio
n
p
r
o
ce
s
s
ef
f
ec
tiv
ely
,
it
is
ess
en
tial
to
co
n
s
tr
u
ct
a
m
ath
em
atica
l
r
ep
r
esen
tatio
n
o
f
b
o
th
th
e
g
r
ey
w
o
lv
es'
h
u
n
tin
g
s
tr
ateg
y
an
d
th
eir
s
o
cial
h
ier
ar
ch
y
[
4
]
.
T
h
e
m
o
d
el
d
e
f
in
es
th
e
s
o
c
ial
s
tr
u
ctu
r
e
o
f
th
e
p
ac
k
as
f
o
llo
ws:
i)
T
h
e
Alp
h
a
(
α
)
c
o
r
r
esp
o
n
d
s
to
th
e
cu
r
r
en
t
b
est
s
o
lu
tio
n
in
th
e
p
o
p
u
latio
n
;
ii)
T
h
e
B
eta
(
β)
r
ep
r
ese
n
ts
th
e
s
ec
o
n
d
-
b
est
ca
n
d
id
ate
;
iii)
T
h
e
Delta
(
δ)
d
en
o
tes th
e
th
ir
d
-
r
an
k
ed
s
o
lu
ti
o
n
; a
n
d
iv
)
All r
em
ain
i
n
g
ag
e
n
ts
ar
e
ca
teg
o
r
ized
as Om
e
g
a
(
ω
)
.
T
h
e
co
llectiv
e
b
eh
av
io
r
o
f
th
ese
f
o
u
r
h
ier
ar
ch
ical
g
r
o
u
p
s
α
,
β,
δ,
an
d
ω
g
u
id
es
th
e
o
p
tim
izatio
n
d
y
n
am
ics th
r
o
u
g
h
o
u
t th
e
s
ea
r
c
h
p
r
o
ce
s
s
.
Su
b
s
eq
u
en
tly
,
th
e
e
n
cir
clin
g
b
eh
a
v
io
r
o
b
s
er
v
ed
in
g
r
ey
wo
lf
h
u
n
tin
g
is
m
ath
em
atica
lly
m
o
d
eled
u
s
in
g
a
s
et
o
f
eq
u
atio
n
s
,
wh
ic
h
s
im
u
late
th
e
ad
ap
tiv
e
p
o
s
itio
n
in
g
o
f
s
o
lu
tio
n
ag
en
ts
ar
o
u
n
d
a
p
o
ten
tial o
p
ti
m
u
m
.
⃗
⃗
=
|
⋅
⃗
⃗
⃗
⃗
−
(
)
|
(
2
2
)
(
+
1
)
=
⃗
⃗
⃗
⃗
(
)
−
⃗
⃗
⋅
(
2
3
)
co
ef
f
icien
t
v
ec
to
r
s
,
t
d
en
o
tes
th
e
cu
r
r
en
t
iter
atio
n
,
⃗
⃗
⃗
⃗
r
ep
r
e
s
en
ts
th
e
p
o
s
itio
n
o
f
th
e
p
r
ey
,
an
d
in
d
icate
s
th
e
p
o
s
itio
n
o
f
a
g
r
e
y
wo
lf
.
T
h
e
v
ec
to
r
s
a
n
d
ar
e
d
ef
i
n
e
d
as (
2
4
)
an
d
(
2
5
)
[
1
3
]
,
[
2
4
]
.
=
2
⋅
1
⃗
⃗
⃗
−
(
2
4
)
=
2
2
⃗
⃗
⃗
(
2
5
)
Vec
to
r
s
1
⃗
⃗
⃗
a
n
d
2
⃗
⃗
⃗
ar
e
r
an
d
o
m
ly
g
en
e
r
a
ted
,
wh
ile
th
e
co
ef
f
icien
t
d
ec
r
ea
s
es
lin
ea
r
ly
f
r
o
m
2
to
0
.
Fig
u
r
e
6
d
em
o
n
s
tr
ates
h
o
w
to
ch
a
n
g
e
th
e
p
o
s
itio
n
s
o
f
elem
en
ts
α
,
β
,
an
d
δ
,
ac
co
r
d
in
g
l
y
.
T
o
m
o
d
el
th
e
h
u
n
tin
g
s
tr
ateg
y
with
in
th
e
p
r
o
m
is
in
g
r
eg
io
n
s
o
f
th
e
s
ea
r
ch
s
p
ac
e,
t
h
e
(
2
6
)
-
(
2
8
)
m
ath
em
atica
l e
x
p
r
ess
io
n
s
ar
e
u
s
ed
.
⃗
⃗
⃗
⃗
⃗
=
|
1
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
|
,
⃗
⃗
⃗
⃗
=
|
2
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
|
,
⃗
⃗
⃗
⃗
=
|
3
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
|
(
2
6
)
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
S
u
p
er
-
tw
is
tin
g
MPP
T e
n
h
a
n
ce
d
via
g
r
ey
w
o
lf o
p
timiz
a
tio
n
fo
r
d
yn
a
mic
P
V
o
p
era
tio
n
(
S
lima
n
e
Ha
d
ji)
1481
{
1
⃗
⃗
⃗
⃗
=
α
⃗
⃗
⃗
⃗
−
1
⃗
⃗
⃗
⃗
(
α
⃗
⃗
⃗
⃗
)
2
⃗
⃗
⃗
⃗
=
β
⃗
⃗
⃗
⃗
−
2
⃗
⃗
⃗
⃗
(
β
⃗
⃗
⃗
⃗
)
3
⃗
⃗
⃗
⃗
=
δ
⃗
⃗
⃗
⃗
−
3
⃗
⃗
⃗
⃗
(
δ
⃗
⃗
⃗
⃗
)
(
2
7
)
(
+
1
)
=
1
3
(
1
⃗
⃗
⃗
⃗
+
2
⃗
⃗
⃗
⃗
+
3
⃗
⃗
⃗
⃗
)
(
2
8
)
is
a
r
an
d
o
m
v
ec
to
r
wh
o
s
e
co
m
p
o
n
en
ts
ar
e
in
d
e
p
en
d
e
n
tly
d
r
awn
f
r
o
m
a
u
n
if
o
r
m
d
is
t
r
ib
u
tio
n
o
v
er
th
e
in
ter
v
al
[
−
,
]
.
Fig
u
r
e
5
.
Pro
v
id
es th
e
s
tr
u
ctu
r
e
o
f
th
e
STA
Fig
u
r
e
6
.
Po
s
itio
n
u
p
d
ate
p
r
o
c
ess
in
g
r
ey
wo
lf
o
p
tim
izatio
n
[
2
5
]
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
MPPT
p
er
f
o
r
m
a
n
ce
o
f
th
e
h
y
b
r
id
STA_
GW
O
alg
o
r
ith
m
was
ev
al
u
ated
th
r
o
u
g
h
MA
T
L
AB
/S
im
u
lin
k
s
im
u
latio
n
s
o
n
a
PV
s
y
s
tem
u
s
in
g
S
T
P8
0
m
o
d
u
les.
T
h
e
GW
O
is
co
n
f
i
g
u
r
ed
with
a
p
o
p
u
latio
n
s
ize
o
f
2
0
ag
en
ts
an
d
a
m
ax
im
u
m
o
f
3
0
iter
ati
o
n
s
.
C
u
r
r
en
t
–
v
o
ltag
e
an
d
p
o
wer
–
v
o
ltag
e
c
u
r
v
es
p
r
esen
ted
in
Fig
u
r
e
3
wer
e
g
en
er
ated
to
ass
ess
th
e
alg
o
r
ith
m
’
s
ab
ilit
y
to
tr
ac
k
an
d
s
tab
ilize
th
e
MPP
u
n
d
er
v
ar
y
in
g
co
n
d
itio
n
s
.
T
h
e
s
y
s
tem
em
p
lo
y
s
a
b
o
o
s
t
DC
–
DC
co
n
v
er
ter
with
L
=
2
m
H
an
d
C
=
3
3
0
μ
F,
en
s
u
r
in
g
Δ
I
<2
0
%
at
2
0
k
Hz.
T
h
e
S
T
A_
GW
O
co
n
tr
o
ller
,
im
p
le
m
en
ted
as
an
ex
ter
n
al
s
cr
ip
t
,
ad
ap
tiv
ely
ad
ju
s
ts
p
ar
am
eter
s
in
r
ea
l
tim
e
b
ased
o
n
s
y
s
tem
f
ee
d
b
ac
k
.
T
wo
s
ce
n
ar
io
s
wer
e
test
ed
:
f
ir
s
t,
u
n
d
er
STC,
th
e
PV
s
y
s
tem
’
s
d
y
n
am
ic
r
esp
o
n
s
e
is
s
h
o
wn
in
Fig
u
r
es
7
(
a)
-
7
(
d
)
,
illu
s
tr
atin
g
o
u
tp
u
t
p
o
wer
,
v
o
ltag
e,
an
d
cu
r
r
en
t.
T
h
e
wav
ef
o
r
m
s
co
n
f
ir
m
r
ap
id
s
ettlin
g
ar
o
u
n
d
th
e
MPP
with
s
tab
le
an
d
r
o
b
u
s
t
tr
ac
k
in
g
.
R
esu
lts
d
em
o
n
s
tr
ate
th
at
th
e
STA_
GW
O
-
b
ased
MP
PT
ac
h
iev
es
f
ast
co
n
v
er
g
en
ce
,
n
e
g
lig
ib
le
s
tead
y
-
s
tate
o
s
cillatio
n
s
,
an
d
h
ig
h
en
e
r
g
y
co
n
v
er
s
io
n
ef
f
icien
c
y
,
u
n
d
er
s
co
r
in
g
its
ef
f
ec
tiv
en
ess
an
d
r
e
liab
ilit
y
f
o
r
PV
s
y
s
tem
s
.
I
n
th
e
s
ec
o
n
d
s
ce
n
ar
i
o
,
th
e
s
y
s
tem
was
s
u
b
jecte
d
to
v
ar
y
in
g
i
r
r
ad
ian
ce
le
v
els
(
5
0
0
,
7
0
0
,
1
0
0
0
,
4
0
0
,
6
0
0
W
/m
²
at
T
=
2
5
°C
)
to
em
u
late
r
ea
lis
tic
en
v
ir
o
n
m
en
t
al
ch
an
g
es
.
Fig
u
r
es
8
(
a
)
an
d
8
(
b
)
s
h
o
w
th
e
co
r
r
esp
o
n
d
i
n
g
d
y
n
am
ic
r
esp
o
n
s
es
Fig
u
r
es
8
(
b
)
-
8
(
d
)
s
h
o
w
th
at
t
h
e
STA_
GW
O
m
eth
o
d
m
ain
t
ain
s
f
ast
an
d
ac
cu
r
ate
MPPT
with
m
in
im
al
p
o
wer
f
lu
ctu
atio
n
ac
r
o
s
s
all
ir
r
ad
ian
c
e
s
tag
es,
co
n
f
ir
m
in
g
its
r
o
b
u
s
t
n
ess
u
n
d
er
r
a
p
id
ly
ch
an
g
in
g
s
o
lar
co
n
d
itio
n
s
.
T
h
ese
r
esu
lts
h
ig
h
lig
h
t
th
e
al
g
o
r
ith
m
’
s
ex
ce
p
tio
n
al
ca
p
a
b
ilit
y
to
s
wif
tly
ad
ju
s
t
an
d
p
r
ec
i
s
ely
f
o
llo
w
th
e
MPP
u
n
d
er
r
a
p
id
ly
e
v
o
l
v
in
g
o
p
er
atin
g
co
n
d
itio
n
s
.
Fu
r
th
er
m
o
r
e,
th
e
co
n
tr
o
ller
d
em
o
n
s
tr
ates
s
tr
o
n
g
r
o
b
u
s
tn
ess
ag
ain
s
t
s
u
d
d
en
ir
r
ad
ian
ce
an
d
tem
p
e
r
atu
r
e
v
a
r
i
atio
n
s
,
m
ain
tain
in
g
s
tab
le
tr
a
ck
in
g
p
er
f
o
r
m
a
n
ce
with
m
in
im
al
o
s
cillatio
n
s
.
T
h
is
b
eh
av
io
r
co
n
f
ir
m
s
its
s
u
itab
ilit
y
f
o
r
h
ig
h
ly
d
y
n
am
ic
PV
en
v
ir
o
n
m
en
ts
a
n
d
em
p
h
asizes its
p
o
ten
tial f
o
r
im
p
r
o
v
in
g
o
v
er
all
en
er
g
y
h
a
r
v
esti
n
g
ef
f
icien
c
y
.
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
.
2
,
J
u
n
e
20
2
6
:
1
4
7
5
-
1485
1482
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
7
.
Un
d
er
STC,
th
e
PV
s
y
s
tem
’
s
d
y
n
am
ic
r
esp
o
n
s
e
in
(
a)
o
u
t
p
u
t PV
p
o
wer
,
(
b
)
PV c
u
r
v
e,
(
c)
PV v
o
ltag
e,
a
n
d
(
d
)
PV c
u
r
r
en
t
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
8
.
Dy
n
am
ic
r
esp
o
n
s
e
o
f
th
e
PV sy
s
tem
u
n
d
er
v
ar
y
i
n
g
ir
r
ad
ian
ce
c
o
n
d
itio
n
s
in
(
a)
i
r
r
ad
ian
ce
,
(
b
)
PV p
o
wer
,
(
c)
PV v
o
ltag
e,
an
d
(
d
)
PV c
u
r
r
e
n
t u
n
d
er
d
y
n
a
m
ic
ir
r
ad
ian
ce
Fig
u
r
e
9
illu
s
tr
ates
th
e
d
y
n
am
ic
r
esp
o
n
s
e
o
f
SMC
_
GW
O
an
d
STA_
GW
O
MPPT
alg
o
r
it
h
m
s
u
n
d
er
v
ar
iab
le
ir
r
a
d
ian
ce
.
R
esu
lts
s
h
o
w
th
at
STA_
GW
O
s
ig
n
if
ican
tly
r
ed
u
ce
s
o
s
cillatio
n
s
ar
o
u
n
d
t
h
e
MPP,
en
s
u
r
in
g
s
tab
le
o
p
e
r
atio
n
an
d
m
in
im
izin
g
p
o
wer
l
o
s
s
es
d
u
r
in
g
r
ap
i
d
ir
r
ad
ian
ce
c
h
an
g
es
.
T
h
e
m
eth
o
d
also
ac
h
iev
es
f
aster
co
n
v
er
g
e
n
ce
an
d
h
ig
h
er
ef
f
icien
cy
,
co
n
f
ir
m
in
g
its
r
o
b
u
s
tn
ess
in
h
i
g
h
ly
v
a
r
iab
le
s
o
lar
co
n
d
itio
n
s
.
C
o
m
p
ar
e
d
to
S
MC_
GW
O,
STA_
GW
O
d
e
m
o
n
s
tr
ates
s
u
p
er
io
r
r
esp
o
n
s
e
tim
e
an
d
tr
ac
k
in
g
ac
cu
r
ac
y
,
p
o
s
itio
n
in
g
it a
s
a
n
o
tab
le
ad
v
a
n
ce
m
en
t in
MPPT
o
p
tim
izatio
n
f
o
r
m
o
d
er
n
PV s
y
s
tem
s
.
E
f
f
icien
cy
ev
alu
atio
n
o
f
b
o
th
tech
n
iq
u
es
co
n
s
id
er
s
d
eliv
er
e
d
p
o
wer
,
o
v
er
all
ef
f
icien
c
y
,
a
n
d
R
MSE
,
en
ab
lin
g
p
r
ec
is
e
ass
ess
m
en
t
o
f
tr
ac
k
in
g
s
p
ee
d
,
s
tab
ilit
y
,
an
d
ac
cu
r
ac
y
.
T
ab
le
2
p
r
o
v
id
es
av
er
ag
ed
s
tatis
tical
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
S
u
p
er
-
tw
is
tin
g
MPP
T e
n
h
a
n
ce
d
via
g
r
ey
w
o
lf o
p
timiz
a
tio
n
fo
r
d
yn
a
mic
P
V
o
p
era
tio
n
(
S
lima
n
e
Ha
d
ji)
1483
r
esu
lts
ac
r
o
s
s
ir
r
ad
ian
ce
lev
els,
wh
ile
F
ig
u
r
e
1
0
h
ig
h
lig
h
ts
im
p
r
o
v
ed
tr
ac
k
i
n
g
ef
f
icien
c
y
with
STA_
G
W
O.
Ov
er
all,
STA_
GW
O
co
n
s
is
ten
tly
o
u
tp
er
f
o
r
m
s
SMC
_
GW
O
u
n
d
er
f
ast
-
ch
a
n
g
in
g
ir
r
ad
ia
n
ce
p
r
o
f
iles
.
=
(
2
9
)
R
MSE
=
√
∑
(
−
)
2
=
1
(
3
0
)
T
ab
le
2
.
E
f
f
icien
cy
a
n
aly
s
is
f
o
r
MPPT
alg
o
r
ith
m
s
u
n
d
er
v
a
r
io
u
s
ir
r
ad
ian
ce
le
v
els
I
r
r
a
d
i
a
t
i
o
n
(
W
/
m²
)
5
0
0
7
0
0
1
0
0
0
4
0
0
6
0
0
P
e
r
i
o
d
(
S
)
[
0
1
]
[
2
4
]
[
4
6
]
[
6
8
]
[
8
1
0
]
R
e
e
l
P
p
v
(
W
)
(R
PV
)
7
8
.
5
9
1
1
1
.
3
8
1
6
0
6
2
.
2
0
9
4
.
9
8
O
b
t
a
i
n
e
d
P
o
w
e
r
(
W
)
(O
PV
)
S
M
C
7
7
.
9
5
1
1
0
.
4
7
1
5
8
.
7
1
6
1
.
6
7
9
4
.
2
3
S
TA
7
8
.
0
7
1
1
0
.
6
5
1
5
8
.
9
5
6
1
.
7
9
9
4
.
3
7
Ef
f
i
c
i
e
n
c
y
(
η)
S
M
C
9
9
.
1
8
5
6
9
9
.
1
8
2
9
9
9
.
1
9
3
7
9
9
.
1
4
7
9
9
9
.
2
1
0
3
S
TA
9
9
.
3
3
8
3
9
9
.
3
4
4
5
9
9
.
3
4
3
7
9
9
.
3
4
0
8
9
9
.
3
5
7
7
R
M
S
E
S
M
C
0
.
8
6
5
4
7
0
9
7
S
TA
0
.
6
9
9
4
2
8
3
3
Fig
u
r
e
9
.
PV p
o
wer
u
n
d
er
v
ar
y
in
g
ir
r
a
d
ian
ce
Fig
u
r
e
1
0
.
Av
er
ag
e
t
r
ac
k
in
g
e
f
f
icien
cy
o
f
two
MPPT
tech
n
iq
u
es
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
p
r
esen
ts
an
d
ev
al
u
ates
a
n
o
v
el
MPPT
alg
o
r
ith
m
in
teg
r
atin
g
a
s
ec
o
n
d
-
o
r
d
e
r
s
lid
in
g
m
o
d
e
co
n
tr
o
l
-
b
ased
STA
with
th
e
GW
O
m
etah
eu
r
is
tic
to
en
h
an
ce
PV
s
y
s
tem
ef
f
icien
cy
u
n
d
er
v
ar
iab
le
ir
r
ad
ian
ce
co
n
d
itio
n
s
with
in
a
Simu
lin
k
s
im
u
latio
n
f
r
am
ewo
r
k
t
o
i
m
p
r
o
v
e
MPPT
p
er
f
o
r
m
a
n
ce
.
T
h
e
STA
r
ed
u
ce
s
ch
atter
in
g
an
d
im
p
r
o
v
es
ac
c
u
r
ate
tr
ac
k
in
g
o
f
th
e
m
a
x
im
u
m
p
o
we
r
p
o
i
n
t
u
n
d
er
d
y
n
a
m
ic
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
an
d
r
ap
id
ir
r
ad
ian
c
e
v
ar
iatio
n
s
.
T
h
e
GW
O
alg
o
r
i
th
m
f
in
e
-
tu
n
es
co
n
tr
o
ller
p
a
r
a
m
eter
s
,
im
p
r
o
v
in
g
r
o
b
u
s
tn
ess
an
d
s
tab
ilit
y
o
f
t
h
e
PV
s
y
s
tem
co
n
tr
o
l
lo
o
p
.
M
AT
L
AB
/Si
m
u
lin
k
r
esu
lts
s
h
o
w
th
at
th
e
p
r
o
p
o
s
ed
STA_
GW
O
o
u
tp
er
f
o
r
m
s
co
n
v
en
tio
n
al
SMC
_
GW
O
MP
PT
i
n
co
m
p
ar
is
o
n
with
th
e
class
ic
al
m
eth
o
d
.
T
r
ac
k
in
g
ef
f
icien
cy
is
i
n
cr
ea
s
ed
(
SMC
_
GW
O:
9
9
.
1
9
%;
STA_
GW
O:
9
9
.
3
4
%)
with
r
ed
u
ce
d
p
o
wer
o
s
cillatio
n
s
,
en
h
an
cin
g
en
er
g
y
ex
tr
ac
tio
n
a
n
d
lead
in
g
to
im
p
r
o
v
ed
e
n
er
g
y
h
ar
v
esti
n
g
p
e
r
f
o
r
m
an
ce
u
n
d
er
h
ig
h
ly
f
l
u
ctu
atin
g
wea
th
er
co
n
d
itio
n
s
in
r
ea
l
o
p
er
atin
g
s
ce
n
ar
io
s
.
Ov
er
all,
t
h
e
h
y
b
r
id
ap
p
r
o
ac
h
im
p
r
o
v
es
tr
ac
k
in
g
ac
cu
r
ac
y
,
r
o
b
u
s
tn
ess
,
an
d
c
h
atter
in
g
r
e
d
u
ctio
n
co
m
p
a
r
ed
with
ex
is
t
in
g
m
eth
o
d
s
f
o
r
p
h
o
to
v
o
ltaic
ap
p
licatio
n
s
with
en
h
an
ce
d
o
v
er
all
s
y
s
tem
p
er
f
o
r
m
an
ce
.
Fu
tu
r
e
wo
r
k
will
f
o
cu
s
o
n
th
e
r
ea
l
-
tim
e
ex
p
er
im
e
n
tal
im
p
lem
en
tatio
n
o
f
th
ese
tech
n
iq
u
es.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
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
.
2
,
J
u
n
e
20
2
6
:
1
4
7
5
-
1485
1484
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
Sli
m
an
e
Had
ji
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Said
Ais
s
o
u
✓
✓
✓
✓
✓
✓
✓
Ab
d
elh
ak
im
B
elk
aid
✓
✓
✓
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
i
z
a
t
i
o
n
Su
:
Su
p
e
r
v
i
s
i
o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
CO
NF
L
I
C
T
O
F
I
N
T
E
R
E
S
T
ST
A
T
E
M
E
NT
Au
th
o
r
s
s
tate
n
o
co
n
f
lict o
f
in
t
er
est.
DATA AV
AI
L
AB
I
L
I
T
Y
All
d
ata
u
n
d
er
p
in
n
in
g
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
ar
e
av
aila
b
le
f
r
o
m
th
e
co
r
r
esp
o
n
d
i
n
g
a
u
th
o
r
,
[
SA]
,
u
p
o
n
r
ea
s
o
n
ab
le
r
eq
u
est.
RE
F
E
R
E
NC
E
S
[
1
]
L.
Z
a
g
h
b
a
e
t
a
l
.
,
“
E
n
h
a
n
c
i
n
g
g
r
i
d
-
c
o
n
n
e
c
t
e
d
p
h
o
t
o
v
o
l
t
a
i
c
s
y
st
e
m
p
e
r
f
o
r
man
c
e
w
i
t
h
n
o
v
e
l
h
y
b
r
i
d
M
P
P
T
t
e
c
h
n
i
q
u
e
i
n
v
a
r
i
a
b
l
e
a
t
m
o
sp
h
e
r
i
c
c
o
n
d
i
t
i
o
n
s,”
S
c
i
e
n
t
i
f
i
c
R
e
p
o
r
t
s
,
v
o
l
.
1
4
,
n
o
.
1
,
p
.
8
2
0
5
,
A
p
r
.
2
0
2
4
,
d
o
i
:
1
0
.
1
0
3
8
/
s
4
1
5
9
8
-
024
-
5
9
0
2
4
-
4.
[
2
]
H
.
D
j
o
u
d
i
e
t
a
l
.
,
“
S
i
m
u
l
a
t
i
o
n
a
n
d
e
x
p
e
r
i
me
n
t
a
l
i
n
v
e
st
i
g
a
t
i
o
n
i
n
t
o
a
p
h
o
t
o
v
o
l
t
a
i
c
a
n
d
f
u
e
l
c
e
l
l
h
y
b
r
i
d
i
n
t
e
g
r
a
t
i
o
n
p
o
w
e
r
s
y
st
e
m
f
o
r
a
t
y
p
i
c
a
l
sma
l
l
h
o
u
s
e
a
p
p
l
i
c
a
t
i
o
n
,
”
E
l
e
c
t
r
i
c
P
o
w
e
r
C
o
m
p
o
n
e
n
t
s
a
n
d
S
y
s
t
e
m
s
,
v
o
l
.
4
8
,
n
o
.
1
4
–
1
5
,
p
p
.
1
5
9
8
–
1
6
1
3
,
S
e
p
.
2
0
2
0
,
d
o
i
:
1
0
.
1
0
8
0
/
1
5
3
2
5
0
0
8
.
2
0
2
0
.
1
8
5
7
4
7
1
.
[
3
]
A
.
B
e
r
b
o
u
c
h
a
,
K
.
D
j
e
r
m
o
u
n
i
,
K
.
G
h
e
d
a
ms
i
,
E.
A
mi
r
o
u
c
h
e
,
S
.
A
i
sso
u
,
a
n
d
D
.
A
o
u
z
e
l
l
a
g
,
“
S
l
i
d
i
n
g
m
o
d
e
c
o
n
t
r
o
l
o
f
a
p
h
o
t
o
v
o
l
t
a
i
c
w
a
t
e
r
p
u
m
p
i
n
g
sy
s
t
e
m
,
”
i
n
Pr
o
c
e
e
d
i
n
g
s
o
f
t
h
e
3
r
d
I
n
t
e
r
n
a
t
i
o
n
a
l
El
e
c
t
ro
n
i
c
C
o
n
f
e
r
e
n
c
e
o
n
Pro
c
e
ss
e
s,
B
a
se
l
,
S
w
i
t
z
e
r
l
a
n
d
,
M
a
y
2
0
2
4
,
p
.
4
8
.
d
o
i
:
1
0
.
3
3
9
0
/
p
r
o
c
e
e
d
i
n
g
s
2
0
2
4
1
0
5
0
4
8
.
[
4
]
R
.
R
o
u
a
s,
M
.
S
i
b
r
a
h
i
m,
S
.
A
i
sso
u
,
a
n
d
S
.
H
a
d
d
a
d
,
“
S
u
st
a
i
n
a
b
l
e
e
n
e
r
g
y
e
mp
o
w
e
r
me
n
t
i
n
r
e
m
o
t
e
r
e
g
i
o
n
s
w
i
n
d
-
so
l
a
r
sy
st
e
m
w
i
t
h
i
n
t
e
l
l
i
g
e
n
t
ma
n
a
g
e
me
n
t
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
w
e
r
El
e
c
t
r
o
n
i
c
s a
n
d
D
ri
v
e
S
y
s
t
e
m
s (I
J
PED
S
)
,
v
o
l
.
1
6
,
n
o
.
1
,
p
p
.
8
6
–
9
5
,
M
a
r
.
2
0
2
5
,
d
o
i
:
1
0
.
1
1
5
9
1
/
i
j
p
e
d
s.
v
1
6
.
i
1
.
p
p
8
6
-
9
5
.
[
5
]
A
.
El
y
a
z
i
d
,
A
.
sa
i
d
,
N
.
B
e
n
y
a
h
i
a
,
A
.
B
e
l
k
a
i
d
,
A
.
B
e
r
b
o
u
c
h
a
,
a
n
d
K
.
G
h
e
d
a
msi,
“
I
n
t
e
l
l
i
g
e
n
t
ma
n
a
g
e
m
e
n
t
a
n
d
o
p
t
i
mi
z
a
t
i
o
n
o
f
r
e
n
e
w
a
b
l
e
s
o
u
r
c
e
s
f
o
r
r
e
mo
t
e
o
f
f
-
g
r
i
d
a
r
e
a
s
,
”
J
o
u
r
n
a
l
El
e
c
t
ri
c
a
l
S
y
st
e
m
s
,
v
o
l
.
2
1
,
n
o
.
1
.
p
p
.
2
4
–
3
7
,
2
0
2
5
.
[
6
]
E.
M
o
h
a
mm
a
d
i
,
M
.
A
l
i
z
a
d
e
h
,
M
.
A
sg
a
r
i
m
o
g
h
a
d
d
a
m,
X
.
W
a
n
g
,
a
n
d
M
.
G
.
S
i
m
o
e
s,
“
A
r
e
v
i
e
w
o
n
a
p
p
l
i
c
a
t
i
o
n
o
f
a
r
t
i
f
i
c
i
a
l
i
n
t
e
l
l
i
g
e
n
c
e
t
e
c
h
n
i
q
u
e
s
i
n
m
i
c
r
o
g
r
i
d
s
,
”
I
E
EE
J
o
u
r
n
a
l
o
f
Em
e
r
g
i
n
g
a
n
d
S
e
l
e
c
t
e
d
T
o
p
i
c
s
i
n
I
n
d
u
st
r
i
a
l
El
e
c
t
ro
n
i
c
s
,
v
o
l
.
3
,
n
o
.
4
,
p
p
.
8
7
8
–
8
9
0
,
O
c
t
.
2
0
2
2
,
d
o
i
:
1
0
.
1
1
0
9
/
JES
TI
E.
2
0
2
2
.
3
1
9
8
5
0
4
.
[
7
]
F
.
F
.
A
h
ma
d
,
C
.
G
h
e
n
a
i
,
A
.
K
.
H
a
mi
d
,
a
n
d
M
.
B
e
t
t
a
y
e
b
,
“
A
p
p
l
i
c
a
t
i
o
n
o
f
s
l
i
d
i
n
g
m
o
d
e
c
o
n
t
r
o
l
f
o
r
ma
x
i
m
u
m p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
o
f
s
o
l
a
r
p
h
o
t
o
v
o
l
t
a
i
c
s
y
st
e
ms:
a
c
o
mp
r
e
h
e
n
s
i
v
e
r
e
v
i
e
w
,
”
An
n
u
a
l
Re
v
i
e
w
s
i
n
C
o
n
t
r
o
l
,
v
o
l
.
4
9
,
p
p
.
1
7
3
–
1
9
6
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
r
c
o
n
t
r
o
l
.
2
0
2
0
.
0
4
.
0
1
1
.
[
8
]
K
.
H
.
C
h
a
o
a
n
d
M
.
N
.
R
i
z
a
l
,
“
A
h
y
b
r
i
d
M
P
P
T
c
o
n
t
r
o
l
l
e
r
b
a
se
d
o
n
t
h
e
g
e
n
e
t
i
c
a
l
g
o
r
i
t
h
m
a
n
d
a
n
t
c
o
l
o
n
y
o
p
t
i
m
i
z
a
t
i
o
n
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
s
y
st
e
ms
u
n
d
e
r
p
a
r
t
i
a
l
l
y
s
h
a
d
e
d
c
o
n
d
i
t
i
o
n
s
,
”
En
e
rg
i
e
s
,
v
o
l
.
1
4
,
n
o
.
1
0
,
p
.
2
9
0
2
,
M
a
y
2
0
2
1
,
d
o
i
:
1
0
.
3
3
9
0
/
e
n
1
4
1
0
2
9
0
2
.
[
9
]
C
.
B
e
n
R
e
g
a
y
a
,
H
.
H
a
m
d
i
,
F
.
F
a
r
h
a
n
i
,
A
.
M
a
r
a
i
,
A
.
Za
a
f
o
u
r
i
,
a
n
d
A
.
C
h
a
a
r
i
,
“
R
e
a
l
-
t
i
me
i
m
p
l
e
me
n
t
a
t
i
o
n
o
f
a
n
o
v
e
l
M
P
P
T
c
o
n
t
r
o
l
b
a
s
e
d
o
n
t
h
e
i
m
p
r
o
v
e
d
P
S
O
a
l
g
o
r
i
t
h
m
u
s
i
n
g
a
n
a
d
a
p
t
i
v
e
f
a
c
t
o
r
s
e
l
e
c
t
i
o
n
st
r
a
t
e
g
y
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
sy
s
t
e
ms
,
”
I
S
A
T
r
a
n
s
a
c
t
i
o
n
s
,
v
o
l
.
1
4
6
,
p
p
.
4
9
6
–
5
1
0
,
M
a
r
.
2
0
2
4
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
i
sa
t
r
a
.
2
0
2
3
.
1
2
.
0
2
4
.
[
1
0
]
L.
X
u
,
R
.
C
h
e
n
g
,
Z.
X
i
a
,
a
n
d
Z
.
S
h
e
n
,
“
I
mp
r
o
v
e
d
p
a
r
t
i
c
l
e
sw
a
r
m
o
p
t
i
mi
z
a
t
i
o
n
(
P
S
O
)
-
b
a
se
d
M
P
P
T
me
t
h
o
d
f
o
r
PV
st
r
i
n
g
u
n
d
e
r
p
a
r
t
i
a
l
l
y
s
h
a
d
i
n
g
a
n
d
u
n
i
f
o
r
m
i
r
r
a
d
i
a
n
c
e
c
o
n
d
i
t
i
o
n
,
”
i
n
2
0
2
0
As
i
a
E
n
e
r
g
y
a
n
d
El
e
c
t
r
i
c
a
l
E
n
g
i
n
e
e
ri
n
g
S
y
m
p
o
s
i
u
m
,
AEE
ES
2
0
2
0
,
2
0
2
0
,
p
p
.
7
7
1
–
7
7
5
.
d
o
i
:
1
0
.
1
1
0
9
/
A
EE
ES4
8
8
5
0
.
2
0
2
0
.
9
1
2
1
3
7
7
.
[
1
1
]
K
.
X
i
a
,
Y
.
Li
,
a
n
d
B
.
Z
h
u
,
“
I
mp
r
o
v
e
d
p
h
o
t
o
v
o
l
t
a
i
c
M
P
P
T
a
l
g
o
r
i
t
h
m
b
a
s
e
d
o
n
a
n
t
c
o
l
o
n
y
o
p
t
i
mi
z
a
t
i
o
n
a
n
d
f
u
z
z
y
l
o
g
i
c
u
n
d
e
r
c
o
n
d
i
t
i
o
n
s
o
f
p
a
r
t
i
a
l
s
h
a
d
i
n
g
,
”
I
EE
E
Ac
c
e
ss
,
v
o
l
.
1
2
,
p
p
.
4
4
8
1
7
–
4
4
8
2
5
,
2
0
2
4
,
d
o
i
:
1
0
.
1
1
0
9
/
A
C
C
ESS
.
2
0
2
4
.
3
3
8
1
3
4
5
.
[
1
2
]
K
.
G
u
o
,
L
.
C
u
i
,
M
.
M
a
o
,
L.
Z
h
o
u
,
a
n
d
Q
.
Z
h
a
n
g
,
“
A
n
i
m
p
r
o
v
e
d
g
r
a
y
w
o
l
f
o
p
t
i
mi
z
e
r
M
P
P
T
a
l
g
o
r
i
t
h
m
f
o
r
PV
sy
st
e
m
w
i
t
h
b
f
b
i
c
c
o
n
v
e
r
t
e
r
u
n
d
e
r
p
a
r
t
i
a
l
sh
a
d
i
n
g
,
”
I
E
EE
A
c
c
e
ss
,
v
o
l
.
8
,
p
p
.
1
0
3
4
7
6
–
1
0
3
4
9
0
,
2
0
2
0
,
d
o
i
:
1
0
.
1
1
0
9
/
A
C
C
ESS
.
2
0
2
0
.
2
9
9
9
3
1
1
.
[
1
3
]
M
.
W
.
G
u
o
,
J.
S
.
W
a
n
g
,
L
.
F
.
Z
h
u
,
S
.
S
.
G
u
o
,
a
n
d
W
.
X
i
e
,
“
A
n
i
mp
r
o
v
e
d
g
r
e
y
w
o
l
f
o
p
t
i
m
i
z
e
r
b
a
s
e
d
o
n
t
r
a
c
k
i
n
g
a
n
d
s
e
e
k
i
n
g
mo
d
e
s
t
o
so
l
v
e
f
u
n
c
t
i
o
n
o
p
t
i
mi
z
a
t
i
o
n
p
r
o
b
l
e
ms,
”
I
EEE
Ac
c
e
ss
,
v
o
l
.
8
,
p
p
.
6
9
8
6
1
–
6
9
8
9
3
,
2
0
2
0
,
d
o
i
:
1
0
.
1
1
0
9
/
A
C
C
ESS
.
2
0
2
0
.
2
9
8
4
3
2
1
.
[
1
4
]
N
.
P
r
i
y
a
d
a
r
s
h
i
,
S
.
P
a
d
ma
n
a
b
a
n
,
J.
B
.
H
o
l
m
-
N
i
e
l
se
n
,
F
.
B
l
a
a
b
j
e
r
g
,
a
n
d
M
.
S
.
B
h
a
s
k
a
r
,
“
A
n
e
x
p
e
r
i
me
n
t
a
l
e
s
t
i
m
a
t
i
o
n
o
f
h
y
b
r
i
d
A
N
F
I
S
–
PSO
-
b
a
se
d
M
P
P
T
f
o
r
P
V
g
r
i
d
i
n
t
e
g
r
a
t
i
o
n
u
n
d
e
r
f
l
u
c
t
u
a
t
i
n
g
s
u
n
i
r
r
a
d
i
a
n
c
e
,
”
I
E
EE
S
y
s
t
e
m
s
J
o
u
r
n
a
l
,
v
o
l
.
1
4
,
n
o
.
1
,
p
p
.
1
2
1
8
–
1
2
2
9
,
M
a
r
.
2
0
2
0
,
d
o
i
:
1
0
.
1
1
0
9
/
JS
Y
S
T.
2
0
1
9
.
2
9
4
9
0
8
3
.
[
1
5
]
A
.
F
.
S
h
a
l
a
l
,
M
.
A
l
j
a
n
a
b
i
,
a
n
d
A
.
N
.
A
l
-
S
h
a
ma
n
i
,
“
M
o
d
i
f
i
e
d
t
r
a
c
k
i
n
g
me
c
h
a
n
i
sm
o
f
h
o
r
se
o
p
t
i
mi
z
a
t
i
o
n
met
h
o
d
(
H
O
M
)
b
a
s
e
d
M
P
P
T
t
e
c
h
n
i
q
u
e
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
(
P
V
)
sy
s
t
e
ms
,
”
AI
P
C
o
n
f
e
ren
c
e
P
ro
c
e
e
d
i
n
g
s
,
v
o
l
.
3
0
9
2
,
n
o
.
1
,
2
0
2
4
,
d
o
i
:
1
0
.
1
0
6
3
/
5
.
0
2
0
0
0
8
3
.
[
1
6
]
A
.
T.
N
a
ser,
K
.
K
.
M
o
h
a
mm
e
d
,
N
.
F
.
A
.
A
z
i
z
,
K
.
K
a
mi
l
,
a
n
d
S
.
M
e
k
h
i
l
e
f
,
“
I
mp
r
o
v
e
d
c
o
o
t
o
p
t
i
mi
z
e
r
a
l
g
o
r
i
t
h
m
-
b
a
s
e
d
M
P
P
T
f
o
r
P
V
sy
s
t
e
ms
u
n
d
e
r
c
o
m
p
l
e
x
p
a
r
t
i
a
l
s
h
a
d
i
n
g
c
o
n
d
i
t
i
o
n
s
a
n
d
l
o
a
d
v
a
r
i
a
t
i
o
n
,
”
E
n
e
r
g
y
C
o
n
v
e
rsi
o
n
a
n
d
Ma
n
a
g
e
m
e
n
t
:
X
,
v
o
l
.
2
2
,
p
.
1
0
0
5
6
5
,
A
p
r
.
2
0
2
4
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
e
c
mx
.
2
0
2
4
.
1
0
0
5
6
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.