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I
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ased
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1
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o
p
tim
izatio
n
alg
o
r
ith
m
(
GOA)
[
1
8
]
,
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
[
1
9
]
.
T
h
ese
m
eth
o
d
s
p
r
im
ar
il
y
f
o
c
u
s
o
n
m
ax
im
izin
g
p
o
w
er
o
u
tp
u
t,
b
u
t
o
f
te
n
n
eg
lect
th
e
im
p
ac
t
o
f
f
r
eq
u
en
t
s
witch
in
g
,
wh
ich
ca
n
in
cr
ea
s
e
co
n
tr
o
l
co
m
p
le
x
ity
an
d
r
e
d
u
ce
th
e
life
s
p
an
o
f
s
witch
in
g
co
m
p
o
n
en
ts
.
R
ec
en
t
r
esear
ch
h
as
p
r
o
p
o
s
ed
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
f
r
am
e
wo
r
k
s
th
at
co
n
s
id
er
b
o
th
p
o
wer
o
u
tp
u
t
an
d
s
witch
in
g
ac
tio
n
m
in
im
izatio
n
[
2
0
]
,
[
2
1
]
.
Ho
we
v
er
,
a
d
d
in
g
m
o
r
e
o
p
tim
izatio
n
p
ar
am
eter
s
ty
p
ically
in
c
r
ea
s
es c
o
m
p
u
tatio
n
al
tim
e
an
d
al
g
o
r
i
th
m
ic
co
m
p
lex
ity
.
T
o
ad
d
r
ess
th
is
ch
allen
g
e,
th
e
p
r
esen
t
s
tu
d
y
in
t
r
o
d
u
ce
s
a
n
o
v
el
weig
h
te
d
o
b
jectiv
e
f
u
n
ctio
n
th
at
co
m
b
in
es
th
e
g
o
als
o
f
m
ax
im
izin
g
p
o
wer
o
u
tp
u
t
an
d
m
in
i
m
izin
g
th
e
n
u
m
b
e
r
o
f
s
witch
in
g
o
p
er
atio
n
s
.
T
h
e
ap
p
r
o
ac
h
p
r
io
r
itizes r
ec
o
n
f
i
g
u
r
in
g
PV c
ells
w
ith
h
ig
h
er
s
h
ad
in
g
v
alu
es,
th
er
eb
y
im
p
r
o
v
i
n
g
en
er
g
y
y
ield
wh
ile
r
ed
u
cin
g
s
witch
in
g
s
tr
ess
.
T
o
o
p
tim
ize
th
is
o
b
jectiv
e
f
u
n
ctio
n
,
an
en
h
an
ce
d
f
ir
eb
u
g
s
war
m
o
p
tim
izatio
n
(
FS
O)
alg
o
r
ith
m
is
em
p
lo
y
ed
.
T
h
is
im
p
r
o
v
e
d
FS
O
r
e
d
u
ce
s
d
is
cr
etiza
tio
n
co
m
p
lex
ity
,
o
p
er
ates
with
f
ewe
r
p
ar
am
eter
s
,
an
d
f
ac
ilit
ates
ef
f
icien
t
co
n
v
er
g
en
ce
—
o
f
f
er
in
g
an
ad
v
an
ta
g
e
o
v
er
ex
is
tin
g
tech
n
iq
u
es
s
u
ch
as
th
o
s
e
d
escr
ib
ed
in
[
2
2
]
-
[
2
4
]
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
is
ev
alu
ated
u
n
d
er
f
i
v
e
r
ep
r
esen
tativ
e
s
h
ad
in
g
p
atter
n
s
—
lef
t
-
d
o
w
n
,
lef
t
-
to
p
,
r
ig
h
t
-
to
p
,
r
ig
h
t
-
d
o
wn
,
an
d
ce
n
ter
s
h
ad
in
g
—
to
v
alid
ate
its
r
o
b
u
s
tn
ess
[
2
5
]
.
Simu
latio
n
r
esu
lts
d
em
o
n
s
tr
ate
n
o
tab
le
im
p
r
o
v
e
m
en
ts
in
p
o
wer
o
u
tp
u
t,
f
ill
f
ac
to
r
,
an
d
r
ed
u
ce
d
m
is
m
atch
lo
s
s
es,
wh
ile
also
ac
h
iev
in
g
a
r
ed
u
ctio
n
in
s
witch
in
g
ac
tio
n
s
.
T
h
ese
f
i
n
d
in
g
s
co
n
f
i
r
m
th
e
p
o
ten
tial
o
f
th
e
p
r
o
p
o
s
ed
s
tr
ateg
y
to
im
p
r
o
v
e
PV
s
y
s
tem
ef
f
icien
cy
an
d
p
r
o
l
o
n
g
d
ev
ice
life
s
p
an
u
n
d
er
p
ar
tial sh
ad
in
g
c
o
n
d
itio
n
s
.
2.
M
O
DE
L
L
I
NG
O
F
P
V
ARR
AY
M
E
T
H
O
D
T
h
e
to
tal
cr
o
s
s
-
tied
(
T
C
T
)
c
o
n
f
ig
u
r
atio
n
is
a
wid
ely
a
d
o
p
t
ed
ap
p
r
o
ac
h
f
o
r
a
r
r
an
g
in
g
p
h
o
to
v
o
ltaic
(
PV)
ar
r
ay
s
to
m
itig
ate
m
is
m
a
tch
lo
s
s
es c
au
s
ed
b
y
p
ar
tial sh
ad
in
g
.
T
h
is
s
ec
tio
n
o
u
tlin
es th
e
m
ath
em
atica
l a
n
d
co
m
p
u
tatio
n
al
m
o
d
elin
g
o
f
a
PV
ar
r
ay
in
th
e
T
C
T
co
n
f
ig
u
r
atio
n
,
wh
ich
en
s
u
r
es
u
n
if
o
r
m
cu
r
r
en
t
s
h
ar
in
g
am
o
n
g
p
ar
allel
r
o
ws
an
d
e
n
h
an
ce
s
th
e
o
v
er
all
p
e
r
f
o
r
m
a
n
ce
o
f
th
e
s
y
s
tem
u
n
d
er
d
iv
er
s
e
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
A
PV
ce
ll
is
r
ep
r
esen
ted
u
s
in
g
th
e
o
n
e
-
d
io
d
e
m
o
d
el,
wh
ich
p
r
o
v
id
es
a
d
etailed
ch
ar
ac
ter
izatio
n
o
f
its
elec
tr
ical
b
eh
av
io
r
,
as in
(
1
)
.
=
ℎ
−
0
(
(
+
)
−
1
)
−
+
ℎ
(
1
)
W
h
er
e:
−
is
th
e
o
u
tp
u
t
cu
r
r
en
t,
is
th
e
o
u
tp
u
t
v
o
ltag
e,
ℎ
is
th
e
p
h
o
to
g
en
er
ated
cu
r
r
en
t,
an
d
0
is
th
e
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
e
n
t.
−
an
d
ℎ
r
ep
r
esen
t th
e
s
er
ies an
d
s
h
u
n
t r
esis
tan
ce
s
,
r
esp
ec
tiv
ely
.
−
is
the
te
mpe
r
a
tur
e
in
Ke
l
vin
,
is
the
B
ol
tzma
n
n
c
on
s
ta
n
t
(
1
.
38
×
10
−
23
J
/
K
)
,
is
th
e
elec
tr
o
n
ch
ar
g
e
(
1
.
6
×
1
0
−1
9
C
)
,
an
d
is
th
e
id
ea
lity
f
ac
to
r
.
T
h
is
eq
u
atio
n
f
o
r
m
s
th
e
f
o
u
n
d
atio
n
f
o
r
m
o
d
elin
g
th
e
elec
tr
ic
al
ch
ar
ac
ter
is
tics
o
f
in
d
iv
id
u
al
PV c
ells
.
T
o
attain
th
e
r
eq
u
ir
ed
v
o
ltag
e
an
d
cu
r
r
e
n
t
lev
els,
a
PV
m
o
d
u
le
co
n
s
is
ts
o
f
m
a
n
y
ce
lls
co
n
n
ec
ted
in
p
ar
allel
o
r
s
er
ies.
Fo
r
a
m
o
d
u
l
e,
th
e
r
elatio
n
s
h
ip
s
ar
e
e
x
p
r
ess
ed
as
(
2
)
.
=
.
,
=
(
2
)
W
h
er
e
is
th
e
n
u
m
b
e
r
o
f
ce
lls
co
n
n
ec
ted
i
n
s
er
ies with
in
th
e
m
o
d
u
le.
PV
m
o
d
u
les
ar
e
s
et
u
p
in
a
m
atr
ix
lay
o
u
t
with
m
r
o
ws
a
n
d
n
co
lu
m
n
s
in
th
e
T
C
T
c
o
n
f
ig
u
r
atio
n
.
I
n
o
r
d
er
to
b
alan
ce
th
e
d
is
tr
ib
u
t
io
n
o
f
c
u
r
r
e
n
t
th
r
o
u
g
h
o
u
t
th
e
ar
r
a
y
,
m
o
d
u
les
with
in
a
r
o
w
ar
e
c
o
n
n
ec
te
d
in
p
ar
allel,
an
d
r
o
ws
ar
e
co
n
n
ec
t
ed
b
y
h
o
r
izo
n
tal
cr
o
s
s
-
ties
.
R
ed
u
ce
d
m
is
m
atch
lo
s
s
es
an
d
i
m
p
r
o
v
e
d
r
esis
tan
ce
to
s
h
ad
in
g
ef
f
ec
ts
ar
e
g
u
ar
an
t
ee
d
b
y
th
is
ar
r
an
g
em
e
n
t.
T
h
e
o
v
er
all
cu
r
r
en
t
an
d
v
o
ltag
e
o
f
th
e
ar
r
ay
in
T
C
T
co
n
f
ig
u
r
atio
n
ar
e
g
iv
en
b
y
(
3
)
.
=
.
,
=
∑
=
1
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
n
h
a
n
ce
d
a
d
a
p
tive
r
ec
o
n
fig
u
r
a
tio
n
fo
r
o
p
timiz
in
g
p
o
w
er g
en
era
tio
n
a
n
d
…
(
D.
Ma
n
imeg
a
la
i
)
779
Par
tial
s
h
ad
in
g
i
n
tr
o
d
u
ce
s
v
a
r
iab
ilit
y
in
t
h
e
c
u
r
r
en
t
g
e
n
er
a
ted
b
y
in
d
iv
id
u
al
m
o
d
u
les.
I
n
o
r
d
er
to
av
o
id
s
h
ad
e
d
m
o
d
u
les
f
r
o
m
n
eg
ativ
ely
im
p
ac
tin
g
th
e
s
tr
in
g
'
s
o
v
er
all
p
er
f
o
r
m
an
ce
,
b
y
p
ass
d
io
d
es
ar
e
in
teg
r
ated
in
to
th
e
ar
r
a
y
ar
c
h
itectu
r
e.
T
h
e
p
o
wer
o
u
tp
u
t
o
f
in
d
iv
id
u
al
m
o
d
u
les
an
d
th
e
en
tire
ar
r
ay
is
ca
lcu
lated
as
(
4
)
.
=
.
,
=
∑
∑
(
,
)
=
1
=
1
(
4
)
I
n
r
esp
o
n
s
e
to
s
h
ad
in
g
cir
c
u
m
s
tan
ce
s
,
d
y
n
am
ic
r
ec
o
n
f
i
g
u
r
at
io
n
u
s
es
a
s
witch
m
atr
ix
t
o
ch
an
g
e
th
e
elec
tr
ical
co
n
n
ec
tio
n
s
in
s
id
e
th
e
PV
ar
r
ay
.
T
h
e
s
witch
in
g
s
tate
o
f
ea
ch
m
o
d
u
le
is
r
ep
r
esen
ted
b
y
a
b
in
ar
y
m
atr
ix
,
wh
er
ea
s
ca
lcu
lated
in
(
5
)
.
=
{
1
,
0
,
(
5
)
T
h
e
to
tal
p
o
wer
o
u
tp
u
t a
n
d
cu
r
r
en
t o
f
th
e
ar
r
a
y
ar
e
d
y
n
a
m
ically
u
p
d
ated
b
ased
o
n
th
e
s
witch
m
atr
ix
,
as (
6
)
.
=
∑
∑
.
(
,
)
=
1
=
1
(
6
)
3.
DYNA
M
I
C
RE
CO
NF
I
G
U
RATI
O
N
O
F
P
V
ARRA
YS
USI
NG
F
I
RE
B
U
G
SWARM
O
P
T
I
M
I
Z
AT
I
O
N
WI
T
H
A
NO
VE
L
O
B
J
E
C
T
I
V
E
F
UN
CT
I
O
N
Par
tial
s
h
ad
in
g
s
ig
n
if
ican
tly
r
ed
u
ce
s
th
e
en
er
g
y
o
u
t
p
u
t
o
f
P
V
s
y
s
tem
s
b
y
ca
u
s
in
g
m
is
m
atch
lo
s
s
es.
T
h
ese
ef
f
ec
ts
—
ca
u
s
ed
b
y
clo
u
d
s
,
n
ea
r
b
y
o
b
s
tr
u
ctio
n
s
,
o
r
d
ir
t
—
lim
it
ar
r
ay
p
er
f
o
r
m
a
n
ce
,
as
s
h
ad
ed
m
o
d
u
les
r
estrict
th
e
o
v
er
all
cu
r
r
en
t
f
lo
w.
T
r
ad
itio
n
al
m
eth
o
d
s
,
s
u
ch
as b
y
p
ass
d
io
d
es a
n
d
T
C
T
co
n
f
ig
u
r
atio
n
s
,
m
itig
ate
th
ese
ef
f
ec
ts
b
u
t la
ck
ad
a
p
tab
i
lity
to
r
ea
l
-
tim
e
s
h
ad
in
g
v
ar
iat
io
n
s
.
Dy
n
am
ic
r
ec
o
n
f
ig
u
r
atio
n
a
d
d
r
ess
es
th
is
lim
itat
io
n
b
y
a
d
ju
s
tin
g
th
e
elec
tr
ical
co
n
n
ec
tio
n
s
b
etwe
en
PV
m
o
d
u
les
th
r
o
u
g
h
a
s
witch
m
atr
ix
.
Ho
wev
er
,
m
an
y
e
x
is
tin
g
tech
n
iq
u
es
f
o
cu
s
o
n
ly
o
n
m
ax
im
izin
g
p
o
wer
o
u
tp
u
t,
o
v
er
lo
o
k
in
g
th
e
o
p
er
atio
n
al
co
m
p
lex
ity
an
d
h
ar
d
war
e
d
eg
r
ad
atio
n
ca
u
s
ed
b
y
f
r
eq
u
e
n
t
s
witch
in
g
ac
tio
n
s
.
T
o
o
v
e
r
co
m
e
t
h
ese
is
s
u
es,
th
is
s
tu
d
y
p
r
o
p
o
s
es
a
weig
h
ted
o
b
jectiv
e
f
u
n
ctio
n
t
h
at
s
im
u
ltan
eo
u
s
ly
o
p
tim
izes
p
o
wer
o
u
tp
u
t
an
d
m
in
im
izes
s
witch
in
g
o
p
er
atio
n
s
.
An
en
h
an
ce
d
FS
O
alg
o
r
it
h
m
is
u
s
ed
t
o
s
o
lv
e
th
is
d
u
al
-
o
b
jectiv
e
p
r
o
b
lem
,
im
p
r
o
v
in
g
b
o
th
en
e
r
g
y
y
ield
an
d
s
y
s
tem
r
eliab
ilit
y
u
n
d
er
d
y
n
am
ic
s
h
a
d
in
g
co
n
d
itio
n
s
.
3
.
1
.
P
r
o
po
s
ed
no
v
el
o
bje
ct
iv
e
f
un
ct
io
n
T
h
e
p
r
o
p
o
s
ed
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
m
s
th
e
co
r
e
o
f
th
e
d
y
n
a
m
ic
r
ec
o
n
f
i
g
u
r
atio
n
s
tr
ateg
y
,
o
p
tim
izin
g
th
e
tr
ad
e
-
o
f
f
b
etwe
en
two
co
n
f
lictin
g
o
b
jectiv
es:
−
Ma
x
im
izin
g
p
o
wer
o
u
tp
u
t
:
T
h
e
PV
s
y
s
tem
m
u
s
t
p
r
o
d
u
ce
th
e
h
ig
h
est
p
o
wer
p
o
s
s
ib
le
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
−
Min
im
izin
g
s
witch
in
g
ac
tio
n
s
:
R
ed
u
cin
g
f
r
eq
u
en
t
r
ec
o
n
f
i
g
u
r
atio
n
s
h
elp
s
e
x
ten
d
s
witch
lif
esp
an
,
s
im
p
lify
co
n
tr
o
l,
a
n
d
r
e
d
u
ce
m
ai
n
ten
an
ce
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
ex
p
r
ess
ed
as
(
7
)
.
W
h
er
e,
:
th
e
o
v
er
all
f
itn
ess
v
alu
e
o
f
a
g
iv
en
PV
ar
r
ay
co
n
f
ig
u
r
atio
n
,
:
p
o
wer
o
u
tp
u
t
o
f
th
e
cu
r
r
en
t
c
o
n
f
ig
u
r
atio
n
,
:
m
ax
im
u
m
ac
h
iev
ab
le
p
o
wer
o
u
tp
u
t
f
o
r
a
g
iv
e
n
s
h
ad
in
g
s
ce
n
ar
io
,
:
t
h
e
n
u
m
b
e
r
o
f
s
witch
ch
an
g
es r
eq
u
ir
ed
f
o
r
th
e
c
u
r
r
e
n
t r
ec
o
n
f
ig
u
r
atio
n
,
:
t
h
e
to
tal
p
o
s
s
ib
le
n
u
m
b
e
r
o
f
s
witch
ch
an
g
es
in
th
e
s
y
s
tem
,
1
an
d
2
:
w
eig
h
t
f
ac
to
r
s
r
e
p
r
esen
t
in
g
th
e
r
elativ
e
im
p
o
r
tan
ce
o
f
p
o
wer
o
p
tim
izatio
n
an
d
s
witch
in
g
m
i
n
im
izatio
n
.
=
1
.
−
2
.
(
7
)
T
h
ese
weig
h
ts
ca
n
b
e
d
y
n
am
ically
ad
ju
s
ted
b
ased
o
n
s
y
s
tem
r
eq
u
ir
em
en
ts
—
p
r
io
r
iti
zin
g
1
d
u
r
in
g
h
ig
h
en
er
g
y
d
em
an
d
an
d
2
d
u
r
in
g
m
ain
ten
an
ce
-
s
en
s
itiv
e
co
n
d
itio
n
s
.
3
.
2
.
I
m
pro
v
ed
f
irebug
s
wa
rm
o
ptim
iz
a
t
io
n
a
lg
o
rit
hm
T
h
e
FS
O
alg
o
r
ith
m
is
a
m
etah
eu
r
is
tic
in
s
p
ir
ed
b
y
t
h
e
m
o
v
em
en
t
an
d
co
m
m
u
n
icatio
n
b
e
h
av
io
r
s
o
f
f
ir
eb
u
g
s
.
I
n
th
is
s
tu
d
y
,
it
is
en
h
an
ce
d
to
ef
f
ec
tiv
ely
o
p
tim
ize
th
e
p
r
o
p
o
s
ed
d
u
al
-
o
b
je
ctiv
e
f
u
n
ctio
n
u
n
d
e
r
d
if
f
er
en
t
p
ar
tial sh
ad
in
g
s
ce
n
a
r
io
s
.
T
h
e
k
e
y
im
p
r
o
v
em
e
n
ts
ar
e
as f
o
llo
ws:
−
Dy
n
am
ic
weig
h
t
ad
j
u
s
tm
en
t
:
Ma
in
tain
s
a
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
e
x
p
lo
itatio
n
t
o
en
s
u
r
e
ef
f
icien
t
co
n
v
er
g
en
ce
.
−
Prio
r
ity
-
b
ased
m
o
d
u
le
r
ec
o
n
f
i
g
u
r
atio
n
: Pr
io
r
itizes m
o
d
u
les
with
h
ig
h
er
s
h
ad
i
n
g
lev
els f
o
r
r
ec
o
n
f
ig
u
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
.
1
,
Ma
r
c
h
20
2
6
:
777
-
785
780
−
E
n
h
an
ce
d
f
itn
ess
ev
alu
atio
n
:
Uses
th
e
n
o
v
el
o
b
jectiv
e
f
u
n
c
tio
n
to
ev
alu
ate
c
o
n
f
ig
u
r
atio
n
s
b
ased
o
n
b
o
t
h
p
o
wer
an
d
s
witch
in
g
cr
iter
ia.
−
I
m
p
r
o
v
ed
lo
ca
l se
ar
c
h
: Pr
ev
en
ts
th
e
alg
o
r
ith
m
f
r
o
m
b
ein
g
tr
a
p
p
ed
in
lo
ca
l o
p
tim
a.
−
Velo
city
-
b
ased
u
p
d
ate
m
ec
h
a
n
is
m
: E
n
h
an
ce
s
s
o
lu
tio
n
d
iv
er
s
ity
an
d
ac
ce
ler
ates c
o
n
v
e
r
g
en
ce
.
3
.
2
.
1
.
F
it
nes
s
e
v
a
lua
t
io
n
E
ac
h
f
ir
eb
u
g
(
ca
n
d
id
ate
s
o
lu
ti
o
n
)
is
ev
alu
ated
u
s
in
g
th
e
wei
g
h
ted
o
b
jectiv
e
f
u
n
ctio
n
as (
8
)
.
=
1
.
(
)
−
2
.
(
)
(
8
)
W
h
er
e
is
th
e
f
itn
ess
o
f
th
e
ℎ
f
ir
eb
u
g
,
a
n
d
o
t
h
er
ter
m
s
ar
e
as d
ef
in
ed
p
r
ev
io
u
s
ly
.
3
.
2
.
2
.
M
o
v
em
ent
a
nd
up
da
t
e
m
ec
ha
nis
m
Fire
b
u
g
s
u
p
d
ate
t
h
eir
p
o
s
itio
n
s
b
ased
o
n
th
e
b
est lo
ca
l a
n
d
g
lo
b
al
s
o
lu
tio
n
s
as (
9
)
.
(
+
1
)
=
(
)
+
.
(
−
(
)
)
+
.
(
−
(
)
)
(
9
)
W
h
er
e
(
)
is
th
e
p
o
s
itio
n
o
f
t
h
e
ℎ
f
ir
eb
u
g
at
tim
e
,
an
d
,
co
n
tr
o
l
th
e
in
f
lu
e
n
ce
o
f
l
o
ca
l
an
d
g
lo
b
al
s
o
lu
tio
n
s
.
3
.
2
.
3
.
Ada
ptiv
e
weig
ht
a
djustm
ent
T
o
im
p
r
o
v
e
co
n
v
er
g
en
ce
b
e
h
a
v
io
r
,
weig
h
t
v
alu
es c
h
an
g
e
d
y
n
am
ically
in
(
1
0
)
a
n
d
(
1
1
)
.
1
(
)
=
1
(
0
)
.
(
1
−
)
(
1
0
)
2
(
)
=
2
(
0
)
.
(
)
(
1
1
)
T
h
is
m
ec
h
an
is
m
p
r
io
r
itizes
p
o
wer
o
p
tim
izatio
n
in
ea
r
ly
iter
atio
n
s
an
d
s
witch
in
g
m
i
n
im
izatio
n
in
later
s
tag
es.
3
.
2
.
4
.
F
irebug
up
da
t
e
rule
wit
h v
elo
cit
y
T
o
en
h
a
n
ce
ex
p
l
o
r
atio
n
,
f
ir
eb
u
g
m
o
v
em
en
t is also
g
o
v
er
n
e
d
b
y
a
v
elo
city
u
p
d
ate
(
1
2
)
a
n
d
(
1
3
)
.
(
+
1
)
=
.
(
)
+
.
(
−
(
)
)
+
.
(
−
(
)
)
(
1
2
)
(
+
1
)
=
(
)
+
(
+
1
)
(
1
3
)
W
h
er
e
is
th
e
in
er
tia
weig
h
t,
c
o
n
tr
o
llin
g
m
o
m
en
t
u
m
an
d
h
el
p
in
g
f
ir
e
b
u
g
s
escap
e
lo
ca
l
m
in
im
a.
3
.
2
.
5
.
Co
nv
er
g
ence
c
rit
er
ia
T
h
e
alg
o
r
ith
m
te
r
m
in
ates
w
h
en
o
n
e
o
f
th
e
f
o
llo
win
g
c
o
n
d
itio
n
s
is
m
et:
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
is
r
ea
ch
ed
,
an
d
t
h
e
ch
an
g
e
in
f
itn
ess
b
etwe
en
co
n
s
ec
u
tiv
e
iter
atio
n
s
is
n
eg
lig
ib
le
,
as in
(
1
4
)
.
:
|
(
+
1
)
−
(
)
|
<
∈
(
1
4
)
W
h
er
e
∈
is
a
s
m
all
th
r
esh
o
ld
in
d
icatin
g
co
n
v
e
r
g
en
ce
.
T
h
e
en
h
a
n
ce
d
FS
O
alg
o
r
ith
m
in
teg
r
ates
a
n
o
v
el
o
b
jectiv
e
f
u
n
ctio
n
with
a
d
ap
ti
v
e
co
n
tr
o
l
m
ec
h
an
is
m
s
to
p
r
o
v
i
d
e
a
r
o
b
u
s
t
an
d
e
f
f
icien
t
d
y
n
a
m
ic
r
ec
o
n
f
ig
u
r
atio
n
s
tr
ateg
y
f
o
r
PV
ar
r
ay
s
u
n
d
er
p
ar
tial
s
h
ad
in
g
.
T
h
e
alg
o
r
ith
m
b
ala
n
ce
s
en
er
g
y
o
p
tim
izatio
n
with
o
p
e
r
atio
n
al
e
f
f
icien
cy
b
y
m
i
n
im
izin
g
s
witch
in
g
ac
tio
n
s
,
m
ak
in
g
it su
itab
le
f
o
r
b
o
th
r
ea
l
-
tim
e
a
p
p
licatio
n
s
an
d
lo
n
g
-
ter
m
d
e
p
lo
y
m
e
n
t.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
P
o
wer
o
ptim
iz
a
t
io
n und
er
v
a
rio
us
s
ha
din
g
co
nd
it
io
n
s
T
h
is
s
ec
tio
n
ev
alu
ates
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
FS
O
alg
o
r
ith
m
co
m
b
in
ed
with
th
e
n
o
v
el
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
o
p
tim
izin
g
PV a
r
r
ay
p
er
f
o
r
m
an
ce
u
n
d
er
p
ar
tial sh
ad
in
g
.
Simu
latio
n
s
wer
e
co
n
d
u
cted
i
n
MA
T
L
AB
(
Ver
s
io
n
9
.
1
3
)
ac
r
o
s
s
f
iv
e
s
h
ad
in
g
s
ce
n
ar
i
o
s
:
r
i
g
h
t
-
d
o
w
n
,
lef
t
-
d
o
wn
,
r
ig
h
t
-
to
p
,
lef
t
-
to
p
d
iag
o
n
al,
an
d
ce
n
ter
s
h
a
d
in
g
.
T
h
ese
p
atter
n
s
r
ef
lect
r
ea
l
-
wo
r
ld
c
o
n
d
itio
n
s
u
s
ed
to
ass
ess
th
e
b
en
ef
its
o
f
d
y
n
am
ic
r
ec
o
n
f
ig
u
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
n
h
a
n
ce
d
a
d
a
p
tive
r
ec
o
n
fig
u
r
a
tio
n
fo
r
o
p
timiz
in
g
p
o
w
er g
en
era
tio
n
a
n
d
…
(
D.
Ma
n
imeg
a
la
i
)
781
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
was
co
m
p
ar
ed
with
co
n
v
en
tio
n
al
o
p
t
im
izatio
n
tech
n
iq
u
es,
f
o
cu
s
in
g
o
n
p
o
wer
o
u
tp
u
t,
f
ill
f
ac
to
r
,
a
n
d
m
is
m
atch
lo
s
s
.
R
esu
lts
co
n
s
is
ten
tl
y
s
h
o
wed
im
p
r
o
v
ed
p
er
f
o
r
m
an
ce
,
v
alid
atin
g
th
e
r
o
b
u
s
tn
ess
o
f
th
e
n
ew
ap
p
r
o
a
ch
.
Fo
r
s
im
u
latio
n
,
th
e
FS
O
alg
o
r
ith
m
u
s
ed
a
p
o
p
u
latio
n
s
ize
o
f
2
5
an
d
1
0
0
iter
atio
n
s
to
b
alan
ce
ac
cu
r
ac
y
an
d
ef
f
icien
c
y
.
T
h
e
PV
ar
r
a
y
was
ass
u
m
ed
to
o
p
er
ate
at
a
s
tan
d
ar
d
tem
p
er
atu
r
e
o
f
2
5
°C
.
I
n
itially
,
th
e
weig
h
t
p
ar
am
eter
α
in
(
6
)
was
s
et
to
0
,
p
r
io
r
itizin
g
o
n
ly
p
o
wer
o
p
tim
izatio
n
.
T
h
ese
f
in
d
in
g
s
h
ig
h
lig
h
t
th
e
p
o
ten
tial
o
f
th
e
p
r
o
p
o
s
ed
d
y
n
am
ic
r
ec
o
n
f
ig
u
r
atio
n
m
eth
o
d
to
en
h
an
ce
p
o
wer
o
u
tp
u
t
an
d
s
y
s
tem
ef
f
icien
cy
in
v
ar
y
i
n
g
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
is
ev
alu
ated
u
s
in
g
th
r
ee
k
ey
p
er
f
o
r
m
an
c
e
m
etr
ics:
m
is
m
atch
lo
s
s
(
ML
)
,
f
ill
f
ac
t
o
r
(
FF
)
,
an
d
ef
f
ic
ien
c
y
(
η
)
.
Mism
atch
lo
s
s
q
u
an
tifie
s
th
e
p
o
wer
lo
s
s
d
u
e
to
u
n
ev
en
s
h
ad
i
n
g
an
d
is
ca
lcu
lated
as
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
GM
PP
)
u
n
d
er
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC
)
an
d
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
(
PS
C
)
,
with
GM
PP
ST
C
f
ix
ed
at
9
8
0
0
W
(
i.e
.
,
2
8
0
W
×
5
×
7
)
.
T
h
e
f
ill
f
ac
to
r
,
wh
ich
r
ef
lects
th
e
q
u
a
lity
o
f
t
h
e
PV
ar
r
ay
,
is
d
ef
in
e
d
as
th
e
r
atio
o
f
th
e
m
ax
im
u
m
p
o
wer
o
u
tp
u
t
u
n
d
e
r
PS
C
to
th
e
r
ated
p
o
wer
o
f
th
e
ar
r
ay
.
E
f
f
icien
cy
is
co
m
p
u
ted
as
th
e
r
atio
o
f
th
e
m
ax
im
u
m
o
u
tp
u
t
p
o
wer
to
th
e
p
r
o
d
u
ct
o
f
ir
r
ad
ian
ce
(
1
0
0
0
W
/m
²)
an
d
th
e
to
tal
PV
ar
r
ay
ar
ea
(
1
.
5
6
m
×
1
.
5
6
m
×
5
×
7
)
,
as
s
p
ec
if
ied
i
n
T
ab
le
1
.
T
h
ese
m
etr
ics
p
r
o
v
id
e
a
c
o
m
p
r
e
h
en
s
iv
e
ass
ess
m
en
t
o
f
s
y
s
tem
p
er
f
o
r
m
an
ce
u
n
d
er
v
ar
y
i
n
g
s
h
ad
in
g
co
n
d
itio
n
s
.
T
ab
le
1
.
PV p
an
el
s
p
ec
if
icatio
n
s
Ty
p
i
c
a
l
t
y
p
e
S
p
e
c
i
f
i
c
a
t
i
o
n
s
M
a
x
i
m
u
m
p
o
w
e
r
(
)
2
8
0
W
M
a
x
i
m
u
m
p
o
w
e
r
v
o
l
t
a
g
e
(
)
3
1
.
7
V
M
a
x
i
m
u
m
p
o
w
e
r
c
u
r
r
e
n
t
(
)
8
.
8
3
A
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
)
9
.
5
4
A
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
)
3
8
.
5
V
D
i
me
n
si
o
n
s
1
5
6
x
1
5
6
mm
N
u
mb
e
r
o
f
c
e
l
l
s
6
0
c
e
l
l
s
i
n
s
e
r
i
e
s
4
.
2
.
P
r
o
po
s
ed
s
wit
ching
-
ba
s
ed
re
co
nfig
ura
t
io
n str
a
t
eg
y
f
o
r
a
5
x
7
P
V
a
rr
a
y
T
o
v
alid
ate
th
e
p
r
o
p
o
s
ed
m
e
th
o
d
,
a
5
×
7
u
n
s
y
m
m
etr
ical
P
V
ar
r
ay
co
n
f
i
g
u
r
atio
n
was
s
e
lecte
d
f
o
r
an
aly
s
is
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
en
h
an
ce
d
FS
O
alg
o
r
ith
m
was
test
ed
u
n
d
e
r
f
iv
e
d
is
tin
ct
p
ar
tial
s
h
ad
in
g
p
atter
n
s
:
lef
t
-
d
o
wn
d
iag
o
n
al
(
Fig
u
r
e
1
(
a)
)
,
r
i
g
h
t
-
d
o
wn
d
iag
o
n
al
(
Fig
u
r
e
1
(
b
)
)
,
lef
t
-
to
p
d
iag
o
n
al
(
Fig
u
r
e
1
(
c)
)
,
r
ig
h
t
-
to
p
d
iag
o
n
al
(
Fig
u
r
e
1
(
d
)
)
,
an
d
ce
n
ter
s
h
ad
in
g
(
Fig
u
r
e
1
(
e
)
)
.
T
h
ese
p
atter
n
s
wer
e
ch
o
s
en
to
r
ep
r
esen
t
co
m
m
o
n
r
ea
l
-
wo
r
l
d
s
h
ad
in
g
co
n
d
itio
n
s
th
at
ca
n
s
ig
n
if
ica
n
tly
af
f
ec
t
th
e
p
er
f
o
r
m
a
n
ce
o
f
PV
ar
r
ay
s
.
T
h
e
co
r
r
esp
o
n
d
in
g
P
–
V
c
h
ar
ac
ter
i
s
tics
f
o
r
ea
ch
o
f
th
ese
s
h
ad
in
g
s
ce
n
ar
io
s
ar
e
illu
s
tr
ated
in
Fig
u
r
e
s
2
(
a)
-
2
(
e
)
.
T
h
ese
p
lo
ts
p
r
o
v
id
e
a
v
is
u
al
co
m
p
ar
is
o
n
o
f
th
e
p
o
wer
o
u
tp
u
t
p
er
f
o
r
m
a
n
ce
o
f
th
e
FS
O
alg
o
r
ith
m
ag
ain
s
t
o
th
er
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
.
T
h
e
s
im
u
latio
n
r
esu
lts
,
s
u
m
m
ar
ized
in
T
ab
le
2
,
d
em
o
n
s
tr
ate
th
e
s
u
p
er
io
r
ity
o
f
th
e
FS
O
alg
o
r
ith
m
in
m
ax
im
izin
g
p
o
wer
o
u
tp
u
t
a
cr
o
s
s
all
test
ed
s
h
ad
in
g
s
ce
n
ar
io
s
wh
en
co
m
p
ar
ed
to
t
h
e
GOA,
g
r
ey
wo
lf
o
p
tim
izatio
n
(
GW
O)
,
an
d
PS
O.
−
Un
d
er
th
e
lef
t
-
d
o
wn
d
iag
o
n
al
s
h
ad
in
g
p
atter
n
(
Fig
u
r
e
1
(
a)
)
,
th
e
FS
O
m
eth
o
d
ac
h
iev
ed
an
o
u
tp
u
t
p
o
wer
o
f
5
1
4
2
.
9
2
W
,
o
u
tp
er
f
o
r
m
in
g
G
OA
(
4
9
5
8
.
4
8
W
)
,
GW
O
(
5
0
1
8
.
3
6
W
)
,
an
d
PS
O
(
4
8
9
8
.
2
4
W
)
.
−
Fo
r
th
e
r
ig
h
t
-
d
o
w
n
d
iag
o
n
al
p
atter
n
(
Fig
u
r
e
1
(
b
)
)
,
FS
O
d
eliv
er
ed
5
0
1
6
.
5
4
W
,
ex
ce
e
d
in
g
th
e
o
u
tp
u
ts
o
f
GOA
(
4
8
3
4
.
8
6
W
)
,
GW
O
(
4
8
8
3
.
1
9
W
)
,
an
d
PS
O
(
4
8
0
4
.
6
8
W
)
.
−
Un
d
er
th
e
lef
t
-
to
p
d
iag
o
n
al
p
atter
n
(
Fig
u
r
e
1
(
c)
)
,
FS
O
ag
ain
led
with
5
2
9
2
.
3
2
W
,
co
m
p
ar
ed
to
GOA
(
5
1
1
5
.
6
4
W
)
,
GW
O
(
5
1
7
8
.
8
8
W
)
,
an
d
PS
O
(
5
0
5
6
.
4
2
W
)
.
−
I
n
th
e
ca
s
e
o
f
th
e
r
ig
h
t
-
to
p
d
i
ag
o
n
al
p
atter
n
(
Fig
u
r
e
1
(
d
)
)
,
FS
O
ac
h
iev
ed
5
2
4
8
.
5
6
W
,
wh
ile
GOA,
GW
O,
an
d
PS
O
p
r
o
d
u
ce
d
5
0
6
7
.
3
8
W
,
5
1
3
6
.
1
4
W
,
an
d
5
0
0
8
.
7
2
W
,
r
esp
ec
tiv
ely
.
−
Fin
ally
,
u
n
d
e
r
th
e
ce
n
ter
s
h
ad
in
g
s
ce
n
ar
i
o
(
Fig
u
r
e
1
(
e)
)
,
FS
O
d
eliv
er
ed
its
h
ig
h
est
p
er
f
o
r
m
an
ce
o
f
5
3
9
5
.
2
6
W
,
s
ig
n
if
ican
tly
o
u
tp
er
f
o
r
m
in
g
GOA
(
5
1
7
2
.
8
6
W
)
,
GW
O
(
5
2
3
8
.
6
4
W
)
,
an
d
PS
O
(
5
0
8
6
.
4
2
W
)
.
I
n
t
e
r
m
s
o
f
m
i
s
m
a
t
c
h
l
o
s
s
es
,
th
e
F
S
O
m
e
t
h
o
d
c
o
n
s
is
t
e
n
tl
y
d
e
m
o
n
s
t
r
a
t
e
d
l
o
w
e
r
v
a
l
u
es
u
n
d
e
r
a
l
l
f
i
v
e
c
o
n
d
i
ti
o
n
s
:
4
6
5
7
.
0
8
W
,
4
7
8
3
.
4
6
W
,
4
5
0
7
.
6
8
W
,
4
5
5
1
.
4
4
W
,
a
n
d
4
4
0
4
.
7
4
W
,
r
e
s
p
e
c
t
i
v
e
l
y
f
o
r
t
h
e
p
a
t
t
e
r
n
s
s
h
o
w
n
i
n
F
i
g
u
r
e
s
1
(
a
)
-
1
(
e
)
.
T
h
es
e
v
a
lu
e
s
w
e
r
e
c
o
n
s
i
d
e
r
a
b
l
y
b
e
tt
e
r
t
h
a
n
t
h
o
s
e
o
b
t
a
i
n
e
d
u
s
i
n
g
G
OA
,
G
W
O
,
a
n
d
P
SO
.
Fu
r
th
er
m
o
r
e
,
th
e
FS
O
-
b
ased
m
eth
o
d
s
h
o
wed
a
co
n
s
is
ten
tly
h
ig
h
er
f
ill
f
ac
to
r
(
FF
)
in
ea
ch
s
h
ad
in
g
s
ce
n
ar
io
,
f
u
r
th
er
u
n
d
er
s
co
r
in
g
its
ab
ilit
y
to
o
p
tim
ize
th
e
ele
ctr
ical
p
er
f
o
r
m
an
ce
o
f
th
e
PV
ar
r
ay
.
Ov
er
all,
th
e
r
esu
lts
—
v
is
u
alize
d
in
Fig
u
r
es
2
(
a)
-
2
(
e)
an
d
q
u
an
tifie
d
in
T
ab
le
2
—
h
ig
h
lig
h
t
th
e
ef
f
icien
cy
,
r
o
b
u
s
tn
ess
,
an
d
r
ea
l
-
wo
r
ld
a
p
p
licab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
FS
O
-
b
ased
d
y
n
am
i
c
r
ec
o
n
f
ig
u
r
atio
n
s
tr
ateg
y
.
I
ts
ab
ilit
y
to
e
n
h
an
c
e
p
o
wer
o
u
tp
u
t,
r
e
d
u
ce
m
is
m
a
tch
lo
s
s
es,
an
d
m
ain
tain
a
h
ig
h
f
ill
f
ac
to
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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6
9
4
I
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