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y
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m
s
in
to
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a
n
d
lay
s
t
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g
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t
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term
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a
n
d
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fficie
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c
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o
f
DC m
icro
g
ri
d
s.
K
ey
w
o
r
d
s
:
Fra
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co
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tr
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l
Op
tim
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PV sy
s
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R
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s
tab
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T
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s
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CC B
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Dep
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Prin
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Ab
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Ab
d
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Stre
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Al
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6
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8
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Sau
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.
h
u
s
s
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1.
I
NT
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I
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m
o
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lik
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ativ
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T
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s
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ce
o
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f
in
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atu
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al
r
eso
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s
[
1
]
,
[
2
]
.
As
th
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wo
r
ld
in
cr
ea
s
in
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ly
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[
3
]
.
T
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allen
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v
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tech
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lik
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DC
co
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v
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ter
s
an
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m
ax
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in
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MPP)
T
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ac
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s
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s
tem
s
ar
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cr
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cial.
DC
co
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v
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ter
s
ar
e
ess
en
tial
f
o
r
h
ar
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ess
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2088
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8
6
9
4
I
n
t J Po
w
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lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
519
-
529
520
r
en
ewa
b
le
en
er
g
y
,
as
th
ey
co
n
v
er
t
th
e
v
ar
iab
le
elec
tr
ical
o
u
t
p
u
t
f
r
o
m
th
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s
in
to
a
s
tab
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f
o
r
m
s
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itab
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s
to
r
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d
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s
e.
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wev
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k
in
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s
tem
s
en
h
an
ce
e
f
f
icien
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b
y
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n
tin
u
o
u
s
ly
ad
ju
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tin
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th
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tr
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to
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p
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ate
at
th
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[
4
]
.
A
d
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itio
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ally
,
m
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r
p
o
in
t
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(
MPPT
)
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p
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tin
u
o
u
s
ly
ad
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u
s
tin
g
th
e
elec
tr
ical
lo
ad
.
T
h
is
ad
v
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d
tech
n
iq
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s
ed
to
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p
tim
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e
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wer
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f
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y
s
y
s
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s
,
in
clu
d
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g
f
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ce
lls
,
p
h
o
to
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(
PV)
s
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an
els,
an
d
win
d
tu
r
b
in
es.
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s
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s
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o
u
s
ly
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lo
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s
f
r
o
m
th
e
n
o
n
lin
ea
r
ch
ar
ac
ter
is
tics
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
wh
er
e
p
o
we
r
o
u
tp
u
t
is
h
i
g
h
ly
d
ep
en
d
e
n
t
o
n
en
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
.
B
y
o
p
tim
izin
g
p
o
w
er
ex
tr
ac
tio
n
,
MPPT
s
y
s
tem
s
s
ig
n
if
ican
tly
en
h
an
ce
th
e
ef
f
icien
c
y
an
d
o
u
tp
u
t
o
f
r
en
ewa
b
le
en
e
r
g
y
i
n
s
tallatio
n
s
[
5
]
,
[
6
]
.
Va
r
io
u
s
MPPT
alg
o
r
ith
m
s
h
av
e
b
ee
n
d
ev
elo
p
e
d
to
m
ee
t
d
if
f
er
e
n
t
s
y
s
tem
r
eq
u
ir
em
en
ts
an
d
c
o
m
p
lex
ities
.
T
h
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
an
d
in
c
r
e
m
en
t
al
co
n
d
u
ctan
ce
(
I
n
c
-
C
o
n
)
m
eth
o
d
s
ar
e
wid
ely
u
s
ed
f
o
r
th
eir
s
im
p
licity
an
d
ef
f
ec
tiv
en
ess
in
m
an
y
s
itu
atio
n
s
.
Mo
r
e
ad
v
a
n
ce
d
alg
o
r
ith
m
s
,
s
u
ch
as
n
eu
r
al
n
etwo
r
k
s
,
f
u
z
zy
lo
g
ic
co
n
tr
o
ller
s
,
an
d
th
e
ad
a
p
tiv
e
n
eu
r
o
-
f
u
zz
y
in
f
er
en
ce
s
y
s
tem
(
ANFI
S),
o
f
f
er
ad
ap
tiv
e
ca
p
a
b
ilit
ies
th
at
ef
f
icien
tly
h
an
d
le
v
ar
iab
le
co
n
d
itio
n
s
,
m
ak
i
n
g
t
h
em
id
ea
l
f
o
r
m
o
r
e
co
m
p
lex
o
r
lar
g
e
-
s
ca
le
ap
p
licatio
n
s
[
7
]
.
T
h
ese
ad
v
an
ce
d
MPPT
tech
n
iq
u
es
ar
e
cr
u
cial
f
o
r
m
ain
tain
in
g
h
i
g
h
e
f
f
icien
cy
in
th
e
DC
v
o
ltag
e
lin
k
o
f
h
y
b
r
i
d
s
y
s
tem
s
,
en
s
u
r
in
g
th
at
r
en
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
ar
e
u
s
ed
to
t
h
eir
f
u
lles
t p
o
ten
t
ial.
As
r
en
ewa
b
le
e
n
er
g
y
u
s
ag
e
e
x
p
an
d
s
,
m
icr
o
g
r
id
s
h
av
e
em
e
r
g
ed
as
a
v
er
s
atile
s
o
lu
tio
n
f
o
r
lo
ca
lized
en
er
g
y
d
is
tr
ib
u
tio
n
.
Mic
r
o
g
r
i
d
s
ar
e
d
ec
en
tr
alize
d
n
etwo
r
k
s
th
at
ca
n
o
p
er
ate
in
d
ep
e
n
d
en
tly
f
r
o
m
th
e
tr
ad
itio
n
al
g
r
id
[
8
]
,
o
f
f
e
r
in
g
en
h
a
n
ce
d
r
eliab
ilit
y
,
r
esil
ie
n
ce
,
an
d
th
e
p
o
ten
tial
f
o
r
a
r
ed
u
c
ed
e
n
v
ir
o
n
m
en
tal
f
o
o
tp
r
in
t.
Ho
wev
er
,
th
e
s
tab
ilit
y
o
f
th
es
e
m
icr
o
g
r
id
s
,
p
a
r
ticu
lar
ly
in
t
er
m
s
o
f
v
o
ltag
e
r
e
g
u
latio
n
,
is
p
ar
am
o
u
n
t
to
th
eir
ef
f
ec
tiv
en
ess
an
d
p
r
o
tectio
n
.
Ach
iev
in
g
o
p
tim
al
s
tab
ilit
y
in
th
e
DC
v
o
ltag
e
lin
k
is
p
iv
o
tal
f
o
r
th
e
ef
f
icien
t
o
p
er
atio
n
o
f
h
y
b
r
id
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
.
I
n
s
tab
ilit
ies
ca
n
lead
to
in
ef
f
icien
t
p
o
wer
tr
a
n
s
f
er
,
p
o
ten
tial
s
af
ety
r
is
k
s
,
an
d
r
ed
u
ce
d
s
y
s
tem
lo
n
g
ev
ity
[
9
]
.
T
h
er
ef
o
r
e,
s
er
v
al
s
tu
d
y
was
co
n
d
u
cte
d
to
d
e
v
elo
p
a
s
tab
le
c
o
n
tr
o
ll
er
f
o
r
m
ain
tain
in
g
s
tab
le
DC
v
o
ltag
e.
Pro
p
o
r
tio
n
al
in
teg
r
ato
r
(
PI)
h
as
b
ee
n
esta
b
lis
h
ed
as
th
e
s
tan
d
ar
d
an
d
wid
ely
u
s
ed
co
n
tr
o
ller
in
v
ar
i
o
u
s
ap
p
licatio
n
s
[
1
0
]
wh
ile
f
o
c
u
s
in
g
o
n
a
d
o
p
tin
g
th
e
s
lid
in
g
m
o
d
e
co
n
t
r
o
ller
(
SMC
)
as
a
r
o
b
u
s
t
co
n
t
r
o
l
s
tr
ateg
y
was
d
ev
elo
p
ed
in
[
1
1
]
.
Ad
d
itio
n
ally
,
h
ig
h
li
g
h
ts
th
e
d
ev
elo
p
m
en
t
o
f
th
e
s
u
p
e
r
twis
tin
g
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
STSMC
)
co
n
tr
o
ller
to
m
ain
tain
h
ig
h
er
p
e
r
f
o
r
m
an
ce
s
tan
d
ar
d
s
p
r
o
v
id
ed
in
[
1
2
]
.
Me
ta
h
eu
r
is
tic
al
g
o
r
it
h
m
s
a
r
e
k
n
o
w
n
f
o
r
t
h
e
ir
ab
ilit
y
t
o
f
in
d
o
p
t
im
al
s
o
l
u
ti
o
n
s
in
r
e
g
i
o
n
s
wh
er
e
o
p
ti
m
iz
ati
o
n
is
to
o
c
o
m
p
l
ex
,
a
llo
wi
n
g
u
s
to
f
in
d
p
r
o
m
is
in
g
a
p
p
r
o
a
c
h
es
t
o
im
p
r
o
v
e
c
o
n
t
r
o
l
s
tr
a
te
g
ies
i
n
h
y
b
r
i
d
s
y
s
te
m
s
[
1
3
]
.
I
n
o
r
d
er
t
o
d
e
v
el
o
p
a
r
o
b
u
s
t
c
o
n
tr
o
l
m
ec
h
a
n
is
m
th
at
m
ai
n
t
ai
n
s
t
h
e
r
o
b
u
s
tn
ess
a
n
d
f
le
x
i
b
il
it
y
o
f
th
e
DC
v
o
lt
ag
e
li
n
k
,
s
e
r
v
al
s
tr
ate
g
i
es
s
u
ch
as
co
lo
n
y
-
b
ase
d
o
p
ti
m
i
za
ti
o
n
(
C
B
O)
,
p
a
r
ti
cle
s
wa
r
m
o
p
ti
m
i
za
t
io
n
(
PS
O
)
,
an
d
g
e
n
eti
c
al
g
o
r
it
h
m
s
(
GA
)
h
av
e
b
e
e
n
p
r
o
p
o
s
e
d
t
o
d
ev
el
o
p
r
o
b
u
s
t
co
n
t
r
o
l
m
ec
h
a
n
is
m
s
t
h
at
en
s
u
r
e
t
h
e
s
ta
b
i
lit
y
an
d
e
f
f
ici
e
n
c
y
o
f
t
h
e
DC
v
o
lta
g
e
l
in
k
u
n
d
e
r
v
a
r
i
o
u
s
o
p
e
r
a
ti
n
g
c
o
n
d
i
ti
o
n
s
[
1
4
]
.
T
o
a
d
d
r
ess
t
h
es
e
c
h
al
le
n
g
es,
t
h
is
s
tu
d
y
h
as
o
p
t
ed
f
o
r
t
h
e
wh
ale
o
p
ti
m
iz
er
al
g
o
r
i
th
m
(
W
O
A)
f
o
r
its
s
t
r
ai
g
h
t
f
o
r
w
ar
d
n
ess
[
1
5
]
,
m
in
im
al
p
a
r
a
m
et
er
r
e
q
u
i
r
e
m
e
n
ts
,
r
a
p
i
d
c
o
n
v
e
r
g
e
n
ce
,
r
o
b
u
s
t
n
ess
,
a
n
d
wi
d
e
ap
p
l
ic
ab
i
lit
y
a
cr
o
s
s
d
i
f
f
er
en
t
wi
d
e
ap
p
li
ca
t
io
n
s
i
n
c
lu
d
i
n
g
en
g
i
n
e
er
in
g
,
cl
u
s
te
r
i
n
g
,
c
lass
i
f
icat
io
n
,
r
o
b
o
t
p
at
h
p
la
n
n
i
n
g
,
i
m
a
g
e
p
r
o
c
ess
i
n
g
,
n
etw
o
r
k
o
p
ti
m
iz
ati
o
n
[
1
6
]
.
T
h
is
s
tu
d
y
ex
p
lo
r
es
th
e
ap
p
lic
atio
n
o
f
th
e
wh
ale
o
p
tim
izer
alg
o
r
ith
m
(
W
OA)
to
f
in
e
-
tu
n
e
a
f
r
ac
tio
n
al
-
o
r
d
er
PID
(
FO
-
PID
)
c
o
n
tr
o
lle
r
,
with
th
e
g
o
al
o
f
im
p
r
o
v
in
g
v
o
ltag
e
s
tab
ilit
y
in
DC
m
icr
o
g
r
id
s
.
B
y
co
m
p
ar
in
g
W
OA
with
o
th
er
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
s
u
c
h
as
g
r
e
y
wo
l
f
o
p
tim
izer
(
GW
O)
,
g
en
etic
al
g
o
r
ith
m
(
GA)
,
an
d
s
in
e
co
s
in
e
alg
o
r
ith
m
(
SC
A)
,
th
e
r
esear
ch
aim
s
to
i
d
en
tify
a
r
o
b
u
s
t
ap
p
r
o
ac
h
f
o
r
en
s
u
r
in
g
r
eliab
le
an
d
s
tab
le
m
icr
o
g
r
id
o
p
er
atio
n
.
T
h
e
p
r
o
p
o
s
ed
s
tr
ateg
y
lev
er
a
g
es
th
ese
ad
v
an
ce
d
al
g
o
r
ith
m
s
to
ef
f
e
ctiv
e
ly
m
an
ag
e
th
e
in
h
er
en
t
f
lu
ctu
atio
n
s
in
r
en
e
wab
le
en
er
g
y
o
u
tp
u
ts
,
en
s
u
r
i
n
g
a
co
n
s
is
ten
t
an
d
r
eliab
le
p
o
wer
s
u
p
p
ly
.
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
ese
o
p
tim
izatio
n
tech
n
i
q
u
es
will
b
e
ass
ess
ed
b
ased
o
n
s
ev
er
al
m
etr
i
cs,
in
clu
d
in
g
m
ea
n
o
p
tim
izatio
n
r
esu
lts
,
s
tan
d
ar
d
d
e
v
iatio
n
o
f
o
u
tco
m
es,
co
n
v
er
g
e
n
ce
an
aly
s
is
,
an
d
s
en
s
itiv
ity
an
aly
s
is
f
o
r
d
eter
m
in
in
g
o
p
tim
al
p
ar
a
m
eter
s
s
u
ch
as
,
,
a
n
d
lam
b
d
a
(
λ
)
th
r
o
u
g
h
a
s
er
ies
o
f
s
im
u
latio
n
test
s
.
T
h
is
an
aly
s
is
d
em
o
n
s
tr
ates
th
e
p
o
ten
tial
o
f
th
ese
m
eth
o
d
s
in
en
h
an
cin
g
th
e
ad
ap
tab
ilit
y
an
d
ef
f
i
cien
cy
o
f
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
.
T
h
r
o
u
g
h
th
is
ap
p
r
o
ac
h
,
th
e
p
ap
er
co
n
t
r
ib
u
t
es
to
th
e
b
r
o
a
d
er
d
is
co
u
r
s
e
o
n
r
en
ewa
b
le
en
er
g
y
ad
o
p
tio
n
,
o
f
f
er
in
g
i
n
s
ig
h
ts
in
t
o
ad
v
an
ce
d
co
n
tr
o
l
s
tr
ateg
ies
th
at
ca
n
f
ac
ilit
ate
a
s
m
o
o
th
er
tr
an
s
f
o
r
m
atio
n
to
a
s
u
s
tain
ab
le
en
er
g
y
f
u
tu
r
e.
T
h
e
p
a
p
er
o
u
tco
m
e
is
s
tr
u
ctu
r
ed
ac
r
o
s
s
f
iv
e
k
ey
s
ec
tio
n
s
.
T
h
e
f
ir
s
t
s
ec
tio
n
in
tr
o
d
u
ce
s
t
h
e
r
esear
ch
to
p
ic,
o
u
tlin
in
g
its
b
ac
k
g
r
o
u
n
d
,
o
b
jectiv
es,
an
d
s
ig
n
if
ican
ce
with
in
th
e
f
ield
.
s
y
s
tem
m
o
d
e
lin
g
f
o
llo
ws
with
a
co
m
p
r
eh
e
n
s
iv
e
o
v
e
r
v
iew
o
f
th
e
s
tr
u
ctu
r
al
an
d
f
u
n
ctio
n
al
co
m
p
o
n
e
n
ts
o
f
th
e
s
y
s
tem
.
W
h
ile,
th
e
co
n
tr
o
l
s
tr
ateg
y
an
d
o
p
tim
izatio
n
tech
n
iq
u
es
s
ec
tio
n
d
etail
th
e
m
eth
o
d
o
lo
g
ies,
m
o
d
els,
an
d
ap
p
r
o
ac
h
es
u
s
ed
t
o
o
p
tim
ize
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
s
ec
tio
n
th
en
p
r
esen
ts
th
e
f
in
d
in
g
s
,
s
h
o
wca
s
in
g
d
at
a,
an
aly
s
es,
an
d
k
e
y
in
s
ig
h
ts
th
at
s
u
p
p
o
r
t
t
h
e
s
tu
d
y
'
s
h
y
p
o
th
eses
.
Fin
ally
,
t
h
e
c
o
n
clu
s
io
n
s
u
m
m
ar
izes
th
e
r
es
ea
r
ch
o
u
tco
m
es
a
n
d
th
eir
im
p
licatio
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
Op
tima
l p
a
r
a
mete
r
id
en
tifi
ca
tio
n
o
f fra
ctio
n
a
l
-
o
r
d
er p
r
o
p
o
r
tio
n
a
l in
teg
r
a
l c
o
n
tr
o
ller
…
(
Ta
ib
i A
b
d
elh
a
lim
)
521
2.
SYST
E
M
M
O
D
E
L
I
NG
T
h
e
s
tu
d
y
h
y
b
r
id
s
y
s
tem
a
r
ch
itectu
r
e
in
teg
r
ates
v
a
r
io
u
s
co
m
p
o
n
e
n
ts
to
o
p
tim
ize
en
er
g
y
g
en
er
atio
n
,
s
to
r
ag
e,
an
d
d
is
tr
ib
u
tio
n
w
h
ile
en
h
an
cin
g
p
o
wer
q
u
ality
.
At
th
e
co
r
e
o
f
th
is
s
etu
p
is
an
8
k
W
p
h
o
to
v
o
ltaic
(
PV
)
ar
r
ay
th
at
h
ar
n
ess
es
s
o
lar
en
er
g
y
.
C
o
m
p
lem
en
tin
g
th
e
PV
ar
r
ay
is
a
6
k
W
li
th
iu
m
-
io
n
b
att
er
y
s
y
s
tem
,
wh
ich
p
r
o
v
id
es
s
to
r
a
g
e
to
b
alan
ce
s
u
p
p
ly
a
n
d
d
em
an
d
f
lu
ct
u
atio
n
s
b
y
ch
a
r
g
in
g
d
u
r
in
g
p
er
i
o
d
s
o
f
s
u
r
p
lu
s
p
o
wer
an
d
d
is
ch
ar
g
in
g
wh
en
th
er
e
is
a
p
o
wer
d
ef
icit.
T
o
m
ax
im
ize
th
e
ef
f
icien
cy
o
f
th
e
PV a
r
r
ay
,
a
DC
-
to
-
DC
co
n
v
er
ter
with
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
is
em
p
lo
y
e
d
,
e
n
s
u
r
in
g
th
e
PV
s
y
s
tem
co
n
s
is
ten
tly
wo
r
k
s
at
p
ea
k
p
o
wer
o
u
tp
u
t.
Ad
d
itio
n
ally
,
a
b
id
ir
ec
tio
n
al
DC
-
DC
co
n
v
er
te
r
is
cr
u
cial
in
m
ain
tain
in
g
th
e
DC
lo
ad
f
o
r
is
o
lated
ar
ea
s
,
en
s
u
r
in
g
s
ea
m
less
p
o
w
er
d
is
tr
ib
u
tio
n
,
u
tili
za
tio
n
,
an
d
en
h
an
ce
d
p
o
we
r
q
u
ality
.
T
h
is
co
m
p
r
eh
en
s
iv
e
ar
ch
itectu
r
e
ef
f
icien
tly
m
a
n
a
g
es
r
en
ewa
b
le
en
er
g
y
r
eso
u
r
ce
s
,
s
to
r
ag
e,
an
d
d
is
tr
ib
u
tio
n
,
co
n
tr
ib
u
tin
g
to
s
u
s
tain
ab
le
p
o
wer
s
o
lu
tio
n
s
f
o
r
b
o
th
o
n
-
g
r
id
an
d
o
f
f
-
g
r
id
ap
p
licatio
n
s
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
g
lo
b
al
s
tr
u
ct
u
r
e
o
f
th
e
s
tu
d
ied
s
y
s
tem
.
DC
DC
DC
B
i
d
i
r
e
c
ti
o
n
a
l
D
C
-
D
C
c
o
n
v
e
r
te
r
DC
L
o
a
d
DC
-
D
C
c
o
n
v
e
r
te
r
DC
B
a
t
t
e
r
y
PV
E
M
S
Fig
u
r
e
1.
Stru
ctu
r
e
d
iag
r
am
o
f
th
e
s
tu
d
ied
s
y
s
tem
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
a
rr
a
y
T
h
e
PV
ar
r
ay
in
o
u
r
s
y
s
tem
is
co
n
s
tr
u
cted
u
tili
zin
g
th
e
s
in
g
l
e
-
d
io
d
e
m
o
d
el,
wh
ich
is
o
n
e
o
f
th
e
m
o
s
t
co
m
m
o
n
tech
n
iq
u
es
f
o
r
d
ep
ic
tin
g
th
e
elec
tr
ical
c
h
ar
ac
ter
is
tics
o
f
PV
ce
lls
[
1
7
]
.
T
h
is
m
o
d
el
in
co
r
p
o
r
ates
a
s
in
g
le
d
io
d
e
to
s
im
u
late
th
e
n
o
n
lin
ea
r
r
elatio
n
s
h
ip
b
etwe
en
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
o
f
th
e
ce
ll
an
d
in
clu
d
es
m
u
ltip
le
p
ar
a
m
eter
s
,
th
e
p
h
o
to
c
u
r
r
e
n
t
(
ℎ
)
,
wh
ich
r
ep
r
esen
ts
th
e
cu
r
r
en
t
g
en
er
ate
d
b
y
th
e
in
cid
en
t
lig
h
t
th
e
d
io
d
e
s
atu
r
atio
n
c
u
r
r
e
n
t
(
)
,
wh
ich
in
cr
ea
s
es
with
tem
p
er
atu
r
e
,
th
e
s
er
ies
r
esis
tan
ce
(
)
,
wh
ic
h
ac
co
u
n
ts
f
o
r
lo
s
s
es
d
u
e
to
th
e
r
esis
tan
ce
o
f
th
e
m
ater
ial
in
t
h
e
ce
ll,
t
h
e
s
h
u
n
t
r
esis
tan
ce
(
ℎ
)
,
r
ep
r
esen
tin
g
le
ak
ag
e
cu
r
r
en
ts
v
ia
th
e
ce
ll
an
d
th
e
i
d
ea
lity
co
ef
f
icien
t
o
f
th
e
d
io
d
e
,
wh
ich
i
n
d
icate
s
th
e
ce
ll'
s
d
ev
iatio
n
f
r
o
m
id
ea
l
b
eh
a
v
io
r
.
B
y
ac
cu
r
ately
r
e
f
lectin
g
th
e
p
er
f
o
r
m
a
n
ce
u
n
d
er
d
if
f
e
r
en
t
ir
r
ad
ian
ce
a
n
d
tem
p
er
atu
r
e
co
n
d
itio
n
s
,
th
is
m
o
d
e
l
se
r
v
es a
s
a
cr
itical
t
o
o
l
f
o
r
p
r
e
d
ictin
g
th
e
en
e
r
g
y
o
u
t
p
u
t a
n
d
ef
f
icien
cy
o
f
th
e
PV
ar
r
ay
.
Fig
u
r
e
2
r
e
p
r
esen
ts
th
e
PV a
r
r
ay
o
f
a
s
in
g
le
-
d
io
d
e
m
o
d
el.
I
ph
Ir
Id
V
p
v
I
R
s
h
Rs
Fig
u
r
e
2.
PV c
ell
o
f
SDM
m
o
d
el
T
h
e
co
n
n
ec
tio
n
b
etwe
en
th
e
o
u
tp
u
t c
u
r
r
en
t a
n
d
v
o
ltag
e
is
r
e
p
r
esen
ted
b
y
th
e
(
1
)
.
=
−
−
+
ℎ
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
519
-
529
522
T
h
e
cu
r
r
en
t
g
e
n
er
ated
b
y
th
e
PV
ar
r
ay
,
d
en
o
te
d
as
,
r
esu
lts
f
r
o
m
th
e
g
en
er
atio
n
o
f
elec
tr
o
n
-
h
o
le
p
air
s
with
in
a
s
o
lar
ce
ll.
Me
an
wh
ile,
th
e
c
u
r
r
en
t
f
lo
win
g
ac
r
o
s
s
th
e
Sh
o
ck
ley
d
i
o
d
e,
r
ef
e
r
r
ed
to
as
,
is
d
ef
in
ed
b
y
(
2
)
.
I
n
th
is
eq
u
atio
n
,
r
ep
r
esen
ts
th
e
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t,
wh
ich
ass
ess
e
s
th
e
leak
ag
e
o
r
r
e
co
m
b
in
atio
n
o
f
m
in
o
r
ity
ca
r
r
ier
s
th
r
o
u
g
h
th
e
−
ju
n
ctio
n
wh
e
n
u
n
d
er
r
e
v
er
s
e
b
ias,
as
d
etailed
in
(
3
)
.
Acc
o
r
d
in
g
to
th
e
s
in
g
le
-
d
io
d
e
(
SDM)
m
o
d
el
,
t
h
e
Sh
o
ck
ley
c
u
r
r
en
t
f
o
llo
ws
a
s
in
g
le
ex
p
o
n
en
tial
d
e
p
en
d
e
n
ce
,
wh
ich
is
im
p
ac
ted
b
y
th
e
d
i
o
d
e
id
ea
lity
c
o
ef
f
icie
n
t,
a.
T
h
e
b
an
d
g
ap
en
e
r
g
y
(
)
o
f
th
e
s
em
ico
n
d
u
ct
o
r
m
ater
ial
p
lay
s
a
v
ital
r
o
le
in
th
is
co
n
d
u
ct
f
o
r
cr
y
s
tallin
e
s
ilico
n
at
2
5
°C
,
is
1
.
1
2
e
V.
=
(
−
1
)
(
2
)
=
3
e
xp
(
−
)
(
3
)
PV
g
en
er
ato
r
s
,
i
n
p
r
ac
tice,
c
o
m
p
r
is
e
n
u
m
er
o
u
s
ce
lls
ar
r
an
g
ed
in
s
er
ies
an
d
p
ar
allel
r
at
h
er
th
a
n
as
s
in
g
le
u
n
its
.
E
ac
h
ce
ll
o
p
er
ates
at
a
v
o
ltag
e
o
f
a
f
ew
h
u
n
d
r
ed
m
illi
v
o
lts
,
wh
ile
at
h
ig
h
ir
r
ad
ia
n
ce
,
it
ca
n
g
en
er
ate
cu
r
r
en
t in
th
e
r
an
g
e
o
f
s
ev
er
al
am
p
er
es.
T
h
e
(
4
)
is
ex
p
an
d
e
d
u
s
in
g
(
1
)
an
d
(
2
)
:
=
−
(
−
1
)
−
+
ℎ
(
4
)
is
d
ef
in
ed
as th
e
th
e
r
m
al
v
o
lta
g
e
o
f
th
e
ce
ll
in
(
5
)
:
=
(
5
)
2
.
2
.
B
o
o
s
t
co
nv
er
t
er
I
n
h
y
b
r
id
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
f
ea
tu
r
in
g
b
o
th
PV
ar
r
ay
s
an
d
win
d
tu
r
b
in
es,
th
e
b
o
o
s
t
co
n
v
er
te
r
is
ess
en
tial
f
o
r
en
h
an
cin
g
s
y
s
tem
ef
f
icien
c
y
[
1
8
]
.
I
t
s
tep
s
u
p
th
e
lo
w
v
o
ltag
e
f
r
o
m
th
e
PV
a
r
r
ay
t
o
h
ig
h
er
lev
els
r
eq
u
ir
ed
f
o
r
s
to
r
a
g
e
ch
ar
g
i
n
g
o
r
d
ir
ec
t
u
s
e
.
T
h
e
c
o
n
v
e
r
ter
o
p
er
ates
b
y
s
av
in
g
en
e
r
g
y
i
n
an
in
d
u
cto
r
d
u
r
in
g
th
e
on
-
m
o
d
e
p
h
ase
an
d
r
elea
s
in
g
it
at
a
h
ig
h
er
v
o
ltag
e
in
th
e
Of
f
-
m
o
d
e
p
h
ase,
m
ain
tain
i
n
g
th
a
t
p
o
wer
tr
an
s
f
er
is
m
ax
im
ized
wh
ile
m
ain
tain
in
g
v
o
ltag
e
s
tab
ilit
y
.
T
h
is
co
n
v
er
te
r
is
co
n
n
ec
ted
with
a
P&
O
m
a
x
im
u
m
p
o
wer
p
o
i
n
t
(
MPP)
tr
ac
k
in
g
co
n
t
r
o
ller
as
d
ep
icted
in
Fig
u
r
e
3
,
wh
ich
is
c
r
u
cial
f
o
r
m
a
n
ag
in
g
th
e
s
witch
in
g
o
p
er
atio
n
s
.
T
h
e
P&
O
MPPT
co
n
tr
o
ller
o
p
tim
izes
th
e
d
u
ty
cy
cle
o
f
th
e
b
o
o
s
t
co
n
v
e
r
ter
'
s
s
witch
b
ased
o
n
r
ea
l
-
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y
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t d
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ilit
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[
1
9
]
.
PV
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L
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P
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T
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r
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e
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u
r
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3.
DC
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t c
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ter
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P&
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ith
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u
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4
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
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4
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T
h
e
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i
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to
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ter
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y
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e
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etwe
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atter
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d
th
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m
icr
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r
id
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h
is
co
n
v
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ter
ca
n
s
witch
th
e
d
ir
ec
tio
n
o
f
p
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lo
w
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eith
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ch
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g
e
th
e
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atter
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with
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atter
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g
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h
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ilizin
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g
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Fig
u
r
e
5
r
e
p
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e
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id
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DC
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ated
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o
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.
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h
is
d
y
n
am
ic
ab
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to
ad
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s
t
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o
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n
d
co
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s
u
m
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th
e
m
icr
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g
r
id
[
2
0
]
.
2
.
4
.
L
it
hiu
m
ba
t
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y
T
h
e
lith
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b
atter
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ch
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s
en
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o
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u
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ch
ar
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ter
is
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ter
m
s
o
f
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aster
ch
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p
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ig
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y
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life
cy
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co
m
p
ar
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to
o
th
er
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atter
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tech
n
o
lo
g
ies
[
2
1
]
.
I
n
th
e
co
n
tex
t
o
f
a
m
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th
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atter
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y
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eser
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ir
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s
tab
ilize
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e
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wer
s
u
p
p
ly
b
y
s
m
o
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th
in
g
o
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th
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n
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h
u
s
m
ain
tain
in
g
co
n
s
is
ten
t
av
ailab
ilit
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o
f
elec
tr
icity
.
T
h
e
m
o
d
elin
g
o
f
th
e
lith
iu
m
b
atter
y
as
d
e
p
icted
in
Fig
u
r
e
6
i
n
clu
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es
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e
c
h
ar
g
e
an
d
d
is
ch
ar
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cy
cles,
ef
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icien
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d
th
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im
p
ac
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f
tem
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ag
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o
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its
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er
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o
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ce
[
2
2
]
.
T
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d
etailed
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ip
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ilit
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2
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]
.
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ase,
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o
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atter
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(
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.
=
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n
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ase,
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th
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atter
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=
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(
7
)
I
n
th
e
s
tu
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ied
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o
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el,
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e
p
r
esen
ts
th
e
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ile
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er
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ip
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l
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en
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atter
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.
T
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e
ter
m
I
b
att
r
ef
er
s
t
o
th
e
cu
r
r
e
n
t
in
v
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l
v
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in
th
e
ch
ar
g
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o
r
d
is
ch
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g
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n
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p
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s
s
es.
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tili
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d
to
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d
icate
th
e
v
o
ltag
e
th
at
is
ass
o
ciate
d
with
th
e
p
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lar
izatio
n
.
Ad
d
itio
n
ally
,
d
escr
ib
es
th
e
b
atter
y
’
s
u
tili
ze
d
ca
p
ac
ity
,
s
p
ec
if
y
in
g
th
e
t
o
tal
ca
p
ac
ity
th
at
h
as
b
ee
n
u
s
ed
.
Fin
ally
,
_
is
th
e
v
o
ltag
e
n
o
tic
ed
at
th
e
elec
tr
ical
co
n
tact
p
o
in
ts
o
f
th
e
b
atter
ies.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
519
-
529
524
L
C
B
A
T
T
E
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S1
S2
D1
D2
+
(
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(
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+
1
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+
-
C
on
tr
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Vo
l
tag
e
S
o
ur
ce
S
E
L
I
n
te
r
n
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R
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ce
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P
F
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r
s
t
O
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l
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2
Fig
u
r
e
5
.
B
id
ir
ec
tio
n
al
DC
-
DC
co
n
v
er
ter
Fig
u
r
e
6
.
L
ith
i
u
m
b
atter
ies eq
u
iv
alen
t c
ir
cu
it
3.
CO
NT
RO
L
L
E
R
AND
O
P
T
I
M
I
Z
AT
I
O
N
S
T
RA
T
E
G
Y
A
f
r
ac
tio
n
al
o
r
d
e
r
PI
c
o
n
tr
o
ller
s
er
v
es
as
a
p
iv
o
tal
c
o
m
p
o
n
en
t
in
en
s
u
r
in
g
v
o
ltag
e
s
tab
i
lity
with
in
elec
tr
ical
s
y
s
tem
s
[
2
3
]
.
B
y
ev
alu
atin
g
th
e
r
ef
er
en
ce
v
o
ltag
e
(
_
)
with
th
e
m
ea
s
u
r
ed
v
o
ltag
e
(
_
)
,
th
e
PI
co
n
tr
o
ller
ef
f
ec
tiv
ely
r
e
g
u
late
s
th
e
o
u
tp
u
t
cu
r
r
en
t
t
o
m
ai
n
tain
d
esire
d
v
o
ltag
e
lev
els.
Actin
g
as
th
e
i
n
ter
f
ac
e
b
etwe
en
th
ese
in
p
u
ts
,
th
e
co
n
tr
o
ller
co
n
tin
u
o
u
s
ly
ad
ju
s
ts
th
e
s
y
s
tem
's
p
ar
am
eter
s
to
m
in
im
ize
th
e
d
ev
iatio
n
b
etwe
en
th
e
r
ef
er
e
n
ce
an
d
m
e
asu
r
ed
v
o
ltag
es.
Fig
u
r
e
7
illu
s
tr
ates
th
e
s
ch
em
atic
b
lo
c
o
f
h
is
co
n
tr
o
ller
.
T
h
is
p
r
o
ac
tiv
e
co
n
t
r
o
l
m
ec
h
an
is
m
en
s
u
r
es
th
at
th
e
s
y
s
tem
r
e
m
ain
s
with
in
ac
ce
p
tab
le
v
o
ltag
e
lim
its
,
th
er
eb
y
en
h
an
cin
g
s
tab
ilit
y
an
d
r
eliab
i
lity
.
F
O
P
I
(
s
)
V
D
C_
r
e
f
V
D
C
+
-
I
r
e
f
Fig
u
r
e
7.
FOPI
b
lo
c
o
f
vol
tag
e
co
n
tr
o
l
s
tr
u
ctu
r
e
T
h
e
(
8
)
an
d
(
9
)
i
n
d
icate
s
th
e
tr
an
s
f
er
f
u
n
cti
o
n
o
f
th
e
FO
-
PI
c
o
n
tr
o
ller
.
(
)
=
(
)
E
(
S
)
=
+
−
(
8
)
(
)
=
(
)
(
)
=
+
1
,
(
>
0
)
(
9
)
T
h
e
(
10
)
is
ex
p
a
n
d
ed
f
r
o
m
(
7
)
an
d
(
8
)
r
esp
ec
tiv
ely
.
(
)
=
.
(
)
+
−
(
)
(
1
0
)
W
ith
in
a
f
r
ac
tio
n
al
o
r
d
er
-
PI,
d
en
o
tes
a
p
o
s
itiv
e
r
ea
l
n
u
m
b
e
r
,
in
d
icatin
g
th
e
FO
-
PI
co
n
tr
o
l
ter
m
.
C
o
r
r
esp
o
n
d
in
g
ly
,
an
d
,
r
ep
r
esen
t
p
r
o
p
o
r
tio
n
al
an
d
in
teg
r
al
g
ain
r
esp
ec
tiv
ely
.
I
n
th
is
wo
r
k
,
v
a
r
io
u
s
o
p
tim
izatio
n
alg
o
r
ith
m
s
in
clu
d
in
g
g
en
etic
alg
o
r
ith
m
(
GA)
,
s
in
e
co
s
in
e
alg
o
r
ith
m
(
SC
A)
,
g
r
ey
wo
lf
o
p
tim
izer
(
GW
O)
an
d
wh
ale
o
p
tim
izati
o
n
alg
o
r
ith
m
(
W
OA)
wer
e
ex
p
lo
r
ed
.
E
ac
h
o
f
th
ese
alg
o
r
ith
m
s
h
as
b
ee
n
u
s
ed
to
o
p
tim
ize
a
co
m
m
o
n
o
b
jectiv
e
f
u
n
ctio
n
w
h
ich
is
th
e
in
teg
r
al
ab
s
o
lu
te
er
r
o
r
o
v
e
r
tim
e
th
at
is
d
ef
in
ed
as
in
(
1
1
)
:
=
∫
|
Δ
|
=
|
0
∗
−
|
(
1
1
)
wh
er
e
th
e
g
o
al
is
to
f
in
d
t
h
e
m
in
im
u
m
co
s
t o
f
J
.
3
.
1
.
G
enet
ic
a
lg
o
rit
hm
GA
em
u
lates
th
e
p
r
o
ce
d
u
r
e
o
f
n
atu
r
al
s
elec
tio
n
wh
er
e
t
h
e
f
ittes
t
in
d
iv
id
u
als
ar
e
ap
p
o
in
ted
f
o
r
r
ep
r
o
d
u
ctio
n
in
o
r
d
er
to
p
r
o
d
u
ce
o
f
f
s
p
r
in
g
o
f
th
e
n
e
x
t
g
en
er
atio
n
[
2
4
]
.
I
t
s
tar
ts
b
y
in
itializ
in
g
a
p
o
p
u
latio
n
o
f
p
o
ten
tial
s
o
lu
tio
n
s
an
d
ev
o
lv
es
th
ese
s
o
lu
tio
n
s
o
v
er
s
ev
er
al
g
en
er
atio
n
s
.
Acr
o
s
s
o
p
er
at
io
n
s
lik
e
s
elec
tio
n
,
cr
o
s
s
o
v
er
,
an
d
m
u
tatio
n
,
GA
iter
ativ
ely
im
p
r
o
v
es th
e
s
o
lu
tio
n
s
to
f
in
d
th
e
o
p
tim
u
m
v
alu
e
.
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
Op
tima
l p
a
r
a
mete
r
id
en
tifi
ca
tio
n
o
f fra
ctio
n
a
l
-
o
r
d
er p
r
o
p
o
r
tio
n
a
l in
teg
r
a
l c
o
n
tr
o
ller
…
(
Ta
ib
i A
b
d
elh
a
lim
)
525
3
.
2
.
Sin
e
co
s
ine a
lg
o
rit
hm
SC
A
u
s
e
s
a
m
ath
em
atica
l
m
o
d
el
th
at
o
s
cillates
b
etwe
en
s
i
n
e
an
d
co
s
in
e
f
u
n
ctio
n
s
to
n
av
ig
ate
th
e
s
ea
r
ch
s
p
ac
e.
T
h
is
alg
o
r
ith
m
ex
p
lo
r
es
p
o
ten
tial
s
o
lu
tio
n
s
b
y
ad
ju
s
tin
g
t
h
e
am
p
litu
d
e
o
f
o
s
cillatio
n
s
,
wh
ich
ef
f
ec
tiv
ely
d
ir
ec
ts
th
e
s
ea
r
ch
t
o
war
d
g
lo
b
al
an
d
l
o
c
al
m
in
im
a
b
ased
o
n
th
e
s
in
e
an
d
c
o
s
in
e
r
u
les.
I
t
d
y
n
a
m
ically
b
alan
ce
s
th
e
ex
p
lo
r
atio
n
a
n
d
e
x
p
lo
itatio
n
p
h
ases
to
en
h
an
ce
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
[
2
5
]
.
3
.
3
.
G
re
y
wo
lf
o
pti
m
izer
GW
O
s
im
u
lates
th
e
lead
er
s
h
i
p
h
ier
ar
ch
y
a
n
d
h
u
n
tin
g
s
tr
ateg
y
o
f
g
r
e
y
wo
lv
es.
I
t
id
en
tifie
s
d
if
f
er
en
t
wo
lv
es
with
th
e
r
o
le’
s
alp
h
a,
b
eta,
an
d
d
elta
th
at
g
u
id
e
th
e
p
ac
k
.
D
u
r
in
g
o
p
tim
izatio
n
,
wo
lv
es
en
cir
cle
th
eir
p
r
ey
,
ad
ju
s
t
th
eir
p
o
s
itio
n
s
,
a
n
d
f
in
ally
p
o
u
n
ce
wh
en
th
e
o
p
p
o
r
tu
n
ity
is
r
ip
e.
T
h
is
h
ier
ar
ch
ical
s
tr
ateg
y
an
d
g
u
id
ed
e
x
p
lo
r
atio
n
h
elp
in
ef
f
i
cien
tly
co
n
v
e
r
g
in
g
to
war
d
t
h
e
b
est s
o
lu
tio
n
[
2
6
]
.
3
.
4
.
Wha
le
o
ptim
iza
t
io
n a
lg
o
rit
hm
W
OA
m
im
ics
th
e
b
u
b
b
le
-
n
e
t
-
ch
asin
g
tech
n
iq
u
e
o
f
h
u
m
p
b
ac
k
wh
ales.
T
h
is
alg
o
r
ith
m
in
clu
d
es
en
cir
clin
g
p
r
e
y
,
cr
ea
tin
g
b
u
b
b
le
n
ets
f
o
r
tr
ap
p
in
g
,
an
d
th
en
f
in
ally
attac
k
in
g
th
e
p
r
ey
.
T
h
e
alg
o
r
ith
m
'
s
ab
ilit
y
to
s
witch
b
etwe
en
en
ci
r
clin
g
b
eh
av
io
r
an
d
th
e
s
p
ir
al
-
sh
ap
e
d
p
ath
to
war
d
th
e
p
r
ey
m
ak
es
it
r
o
b
u
s
t
in
h
an
d
lin
g
d
if
f
er
en
t
k
in
d
s
o
f
o
p
tim
izatio
n
is
s
u
es
[
2
7
]
,
[
2
8
]
.
Fig
u
r
e
8
d
e
p
icts
a
f
lo
wch
ar
t
illu
s
tr
atin
g
th
e
f
u
n
ctio
n
in
g
o
f
th
e
W
OA
alg
o
r
ith
m
.
I
t o
u
tlin
es th
e
s
tep
-
by
-
s
tep
p
r
o
ce
s
s
.
In
p
ut
N
&
M
a
x
im
um
It
e
r
a
t
io
n
I
nit
i
a
l
i
z
a
t
i
on of
I
nti
a
l
P
os
t
i
t
i
on
I
s
t
he
ma
xi
mum
i
te
r
a
ti
on a
c
hi
e
ve
d ?
E
N
D
S
T
A
R
T
P
e
r
f
or
m the
C
ons
tr
a
int
C
he
c
k
C
a
l
c
ulate
t
he
T
otal P
r
of
i
t
T
he
mos
t
O
pt
im
a
l
A
dva
nt
a
ge
S
e
t
a
s
X
U
pda
te
t
he
pos
it
io
n us
in
g t
he
s
pe
c
i
f
i
e
d e
qua
t
i
on
E
va
lua
te
T
he
mos
t opti
ma
l be
ne
f
it
s
X
Fig
u
r
e
8.
W
OA
f
lo
wch
ar
t
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
e
r
esu
lts
s
ec
t
io
n
,
th
is
s
t
u
d
y
p
r
esen
ts
th
e
f
in
d
in
g
s
an
d
p
er
f
o
r
m
an
ce
m
etr
ics
o
b
tain
ed
f
r
o
m
a
co
m
p
ar
ativ
e
a
n
aly
s
is
o
f
f
o
u
r
t
ec
h
n
iq
u
es,
GW
O,
W
OA,
GA
,
an
d
SC
A.
T
h
e
s
im
u
latio
n
s
wer
e
co
n
d
u
cted
a
n
d
ev
alu
ated
with
in
th
e
MA
T
L
A
B
en
v
ir
o
n
m
en
t
,
th
e
s
im
u
latio
n
was
test
ed
u
n
d
er
1
5
iter
atio
n
s
an
d
3
r
u
n
s
f
o
r
ea
ch
alg
o
r
ith
m
.
T
a
b
le
1
p
r
o
v
i
d
es a
co
m
p
r
eh
e
n
s
iv
e
o
v
e
r
v
iew.
As
illu
s
tr
ated
in
T
ab
le
1
,
th
e
r
esu
lts
f
o
r
th
e
f
o
u
r
o
p
tim
izer
tech
n
iq
u
es
GW
O,
W
OA,
G
A,
an
d
SC
A,
s
h
o
w
th
eir
av
er
a
g
e
v
alu
es
ac
r
o
s
s
th
r
ee
r
u
n
s
as
1
.
3
3
2
,
0
.
1
4
8
,
1
.
0
7
2
,
an
d
0
.
3
1
7
r
esp
ec
tiv
ely
.
T
h
e
GW
O
o
p
tim
izer
ex
ce
ls
in
th
e
f
ir
s
t
r
u
n
b
u
t
p
er
f
o
r
m
s
p
o
o
r
l
y
in
th
e
s
ec
o
n
d
an
d
th
ir
d
r
u
n
s
.
I
n
co
n
tr
ast.
T
h
e
GA
o
p
tim
izer
s
tar
ts
s
tr
o
n
g
b
u
t
s
tr
u
g
g
les
in
s
u
b
s
eq
u
en
t
r
u
n
s
.
T
h
e
SC
A
o
p
tim
izer
p
r
o
d
u
ce
s
co
n
s
is
ten
t
r
esu
lts
i
n
two
o
u
t
o
f
th
r
ee
r
u
n
s
.
No
tab
ly
,
GW
O
ac
h
iev
es
th
e
b
est
s
in
g
le
iter
atio
n
v
alu
e
o
f
1
.
3
2
7
9
,
wh
ile
W
OA
d
em
o
n
s
t
r
ates
r
o
b
u
s
tn
ess
th
r
o
u
g
h
o
u
t
all
s
im
u
latio
n
s
,
th
e
W
OA
o
p
tim
izer
is
r
o
b
u
s
t,
co
n
s
is
ten
tly
d
eliv
er
in
g
s
im
ilar
v
alu
es
ac
r
o
s
s
all
th
r
ee
r
u
n
s
an
d
ac
h
ie
v
in
g
th
e
b
est
s
tan
d
ar
d
d
ev
iatio
n
s
co
r
e
with
0
.
0
0
0
4
co
m
p
ar
ed
with
GW
O,
GA
,
an
d
SC
A
with
0
.
8
9
2
,
0
.
6
5
9
,
an
d
0
.
0
9
6
r
esp
ec
tiv
ely
.
Fig
u
r
e
9
d
e
p
icts
th
e
co
n
v
er
g
en
ce
c
u
r
v
es
o
f
th
e
f
o
u
r
alg
o
r
ith
m
s
.
I
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
519
-
529
526
co
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clu
s
io
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is
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p
er
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r
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er
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o
r
m
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y
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ti
v
ely
co
m
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in
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ch
ar
ac
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ch
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tan
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n
,
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d
b
est o
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r
all
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test
s
.
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u
r
e
1
0
s
h
o
ws th
e
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o
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r
esp
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n
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e
f
o
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th
e
q
u
ad
al
g
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ith
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s
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h
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th
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r
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ig
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c
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m
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an
aly
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is
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etwe
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ad
al
g
o
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s
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h
e
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r
v
e
d
em
o
n
s
tr
ates
th
e
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p
er
io
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ed
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ith
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to
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ith
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t
r
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e
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s
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tr
ac
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ich
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o
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1
V.
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ely
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u
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C
o
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r
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u
r
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ltag
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am
iq
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e
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esp
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h
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p
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wer
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l te
ch
n
iq
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o
n
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y
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etwe
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atter
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le
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o
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As
illu
s
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ated
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Fig
u
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e
1
1
,
th
e
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er
g
y
m
an
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em
en
t
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
Op
tima
l p
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mete
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atter
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r
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atter
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o
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Fig
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atter
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ic
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atter
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ile
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Fig
u
r
e
11.
T
h
e
p
o
wer
b
ala
n
ce
p
r
o
f
ile
PV,
b
at
t
er
y
,
an
d
DC
lo
ad
Fig
u
r
e
12.
B
atter
y
SOC
s
tate
o
f
ch
ar
g
e
u
n
d
er
v
ar
iab
le
s
ce
n
a
r
io
s
5.
CO
NCLU
SI
O
N
I
n
co
n
clu
s
io
n
,
th
is
p
ap
e
r
in
v
e
s
tig
ated
th
e
o
p
tim
izatio
n
o
f
a
f
r
ac
tio
n
al
o
r
d
er
p
r
o
p
o
r
tio
n
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in
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r
ato
r
(
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co
n
tr
o
ller
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o
r
s
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ilizin
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DC
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o
ltag
e
in
h
y
b
r
id
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d
DC
m
icr
o
g
r
id
ap
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licatio
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s
u
s
in
g
f
o
u
r
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o
r
ith
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s
a
s
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e
co
s
in
e
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o
r
ith
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,
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e
n
etic
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o
r
ith
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,
g
r
e
y
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lf
o
p
tim
izer
,
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d
wh
ale
o
p
tim
izatio
n
alg
o
r
ith
m
(
W
OA)
.
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e
d
e
v
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m
e
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t
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d
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o
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s
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er
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m
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r
r
ied
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t
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s
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MA
T
L
AB
s
o
f
twar
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an
d
th
e
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f
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m
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ce
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ated
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n
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er
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o
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itio
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s
Af
te
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th
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n
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ly
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o
f
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s
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ess
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s
e
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d
ac
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r
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y
,
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p
r
o
v
ed
t
o
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e
th
e
m
o
s
t
ef
f
icien
t
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d
e
f
f
icien
t
am
o
n
g
th
e
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o
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ith
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s
s
tu
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ied
.
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h
e
lo
west
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er
ag
e
c
o
s
t
f
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n
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n
o
f
0
.
1
4
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is
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h
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d
b
y
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o
llo
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y
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A
(
0
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3
1
7
)
.
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n
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itio
n
,
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e
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est
s
tan
d
ar
d
d
e
v
iatio
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o
r
e
with
0
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0
0
0
4
(
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OA)
co
m
p
ar
ed
t
o
GW
O,
GA
,
an
d
SC
A
with
0
.
8
9
2
,
0
.
6
5
9
,
an
d
0
.
0
9
6
r
esp
ec
tiv
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
519
-
529
528
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
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y
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s
u
p
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m
Prin
ce
Sattam
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in
Ab
d
u
laziz
Un
iv
e
r
s
ity
p
r
o
je
ct
n
u
m
b
er
(
PS
AU/2
0
2
4
/R
/1
4
4
6
)
.
RE
F
E
R
E
NC
E
S
[
1
]
M
.
H
.
R
e
h
m
a
n
i
,
M
.
R
e
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ss
l
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,
A
.
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a
c
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i
,
M
.
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o
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a
r
c
i
,
a
n
d
M
.
R
a
d
e
n
k
o
v
i
c
,
“
I
n
t
e
g
r
a
t
i
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g
r
e
n
e
w
a
b
l
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e
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e
r
g
y
r
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so
u
r
c
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s
i
n
t
o
t
h
e
smar
t
g
r
i
d
:
r
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e
n
t
d
e
v
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l
o
p
me
n
t
s
i
n
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n
f
o
r
mat
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o
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m
mu
n
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c
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c
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s,”
I
EEE
T
ra
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s
a
c
t
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o
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d
u
st
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/
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.
[
2
]
A
.
R
a
i
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n
,
“
A
n
e
c
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o
me
t
r
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a
ssessm
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t
h
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t
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ssi
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U
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d
S
t
a
t
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s,”
E
n
v
i
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a
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Pr
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sses
,
v
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.
1
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[
3
]
M
.
M
.
H
a
q
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t
a
l
.
,
“
Th
r
e
e
-
p
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r
t
c
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t
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r
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r
a
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sy
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,
”
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