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m
o
d
elin
g
s
o
f
t
w
ar
e,
an
d
a
d
em
o
n
s
tr
ati
v
e
class
d
is
p
atch
er
o
f
f
r
ee
-
h
a
n
d
d
r
a
w
n
s
k
etc
h
es
[
6
]
in
o
r
d
er
t
o
i
m
p
r
o
v
e
th
e
r
eg
ar
d
o
f
th
e
in
ter
ac
ti
v
it
y
s
y
s
te
m
(
s
o
lar
ir
r
ad
iatio
n
an
d
P
ar
ab
o
lic
co
n
ce
n
tr
ato
r
)
,
b
ased
o
n
an
ef
f
icien
t
al
g
o
r
ith
m
:
Gr
av
itatio
n
al
Sear
c
h
A
l
g
o
r
ith
m
,
t
h
is
latter
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
o
r
d
er
to
tak
e
i
n
to
ac
c
o
u
n
t
th
e
n
o
n
-
li
n
ea
r
co
n
s
tr
ain
ts
,
t
h
e
Vir
t
u
al
R
ea
l
it
y
m
an
u
f
ac
t
u
r
in
g
to
o
l
h
a
s
b
ee
n
d
ev
elo
p
ed
.
T
h
en
a
d
ev
elo
p
m
e
n
t,
te
s
t
an
d
m
an
u
f
ac
t
u
r
in
g
o
f
a
n
elec
tr
o
n
ic
b
o
ar
d
f
o
r
p
ar
ab
o
lic
co
n
ce
n
tr
ato
r
,
ai
m
ed
to
en
s
u
r
e
t
h
e
f
ea
s
ib
ilit
y
a
n
d
th
e
r
o
b
u
s
tn
e
s
s
o
f
t
h
e
o
p
ti
m
al
s
o
lu
tio
n
o
b
tain
ed
an
d
th
e
o
p
tim
al
s
o
lar
tr
ac
k
.
Fin
a
ll
y
a
b
u
il
d
o
f
a
law
co
asted
p
r
o
to
ty
p
e
w
it
h
m
o
d
er
n
m
ate
r
ials
[
7
,
8
]
,
test
in
g
an
d
d
esig
n
r
ef
in
e
m
e
n
t,
th
i
s
p
r
o
ce
s
s
is
estab
lis
h
ed
w
it
h
a
v
ar
io
u
s
e
n
g
i
n
ee
r
i
n
g
p
h
ases
s
ch
e
m
a
tized
in
Fi
g
u
r
e
2
.
(
a)
(
b
)
Fig
u
r
e
1.
(
a)
T
h
e
d
is
tr
ib
u
tio
n
of
r
en
e
w
ab
le
en
er
g
y
o
p
er
atio
n
an
d
(
b
)
t
he
lay
o
u
t
of
li
m
e
p
o
i
n
ts
in
A
l
g
er
ia
Fig
u
r
e
2
.
Si
m
u
latio
n
p
r
o
ce
s
s
es
m
a
n
u
f
ac
to
r
y
2.
O
VE
RVI
E
W
O
F
T
H
E
SO
L
UT
I
O
N
O
P
T
I
O
NS
Ho
w
e
v
er
,
g
i
v
e
n
t
h
e
b
et
to
co
n
tr
ib
u
te
to
s
to
p
p
in
g
ec
o
lo
g
ical
d
eg
r
ad
atio
n
,
a
n
d
to
r
e
m
ed
y
th
e
s
i
g
n
i
f
ica
n
t
d
r
o
p
in
f
o
s
s
il
f
u
e
l
s
o
u
r
ce
s
,
m
a
n
y
s
t
u
d
ies
f
o
cu
s
on
r
en
e
w
ab
le
e
n
er
g
ie
s
,
b
ec
au
s
e
t
h
ese
h
a
v
e
th
e
p
o
ten
tial
to
p
r
o
v
id
e
an
u
n
l
i
m
ited
,
clea
n
a
n
d
s
u
s
tai
n
ab
le
en
er
g
y
[
9
]
,
an
d
ec
o
n
o
m
ica
ll
y
m
i
n
i
m
ize
co
s
ts
,
a
n
d
h
elp
cr
ea
te
j
o
b
s
.
So
lar
an
d
w
i
n
d
en
er
g
y
ar
e
u
n
a
n
i
m
o
u
s
in
t
h
e
f
ield
of
r
en
e
w
ab
le
e
n
er
g
ie
s
.
T
h
e
m
i
x
of
t
h
ese
t
w
o
o
p
p
o
s
ite
f
o
r
m
s
is
ab
le
to
p
r
o
v
id
e
th
e
en
er
g
y
we
n
ee
d
th
r
o
u
g
h
o
u
t
t
h
e
y
ea
r
a
n
d
can
to
s
o
m
e
e
x
te
n
t
f
o
llo
w
th
e
s
ea
s
o
n
al
lo
ad
cu
r
v
e
[
1
0
]
.
Sev
er
al
m
et
h
o
d
s
an
d
tec
h
n
o
lo
g
ies
al
lo
w
us
to
u
s
e
th
e
m
o
r
e
i
m
p
o
r
tan
t
of
th
e
s
e
t
w
o
f
o
r
m
s
,
w
h
ic
h
is
s
o
lar
en
e
r
g
y
.
Ma
i
n
l
y
:
p
h
o
to
v
o
ltaic
s
an
d
s
o
lar
th
er
m
al,
in
ad
d
itio
n
t
h
e
co
n
ce
n
tr
atio
n
of
s
o
lar
th
er
m
al
en
er
g
y
co
n
tr
ib
u
tes
s
ig
n
i
f
ica
n
tl
y
to
th
e
s
u
p
p
ly
of
elec
tr
icit
y
,
a
n
d
r
ep
r
esen
t
an
in
ter
ac
ti
v
e
an
d
g
r
o
w
i
n
g
f
ield
.
Am
o
n
g
t
h
ese
m
et
h
o
d
s
we
q
u
o
te:
t
h
e
s
e
m
i
-
p
ar
ab
o
lic
co
llecto
r
,
th
e
lin
ea
r
r
ef
lecto
r
s
Fre
s
n
e
l,
ce
n
tr
al
r
ec
ep
tio
n
s
y
s
te
m
s
(
p
o
w
er
to
w
er
s
)
,
an
d
p
ar
ab
o
lic
c
o
llecto
r
s
[
1
1
]
.
In
th
is
r
eg
ar
d
,
we
h
a
v
e
p
r
o
p
o
s
e
d
a
p
r
ac
tical
co
n
tr
ib
u
tio
n
b
a
s
e
d
on
a
p
ar
ab
o
lic
co
n
f
ig
u
r
ati
o
n
d
esig
n
a
n
d
a
p
o
w
er
f
u
l
a
l
g
o
r
ith
m
f
o
r
d
esig
n
o
p
tim
izatio
n
.
T
h
er
e
ar
e
h
o
wev
er
,
to
s
av
e
th
e
d
i
f
f
er
en
t
s
ettin
g
s
f
o
r
each
of
t
h
e
o
p
tio
n
s
ar
e
i
m
p
o
r
ta
n
t.
T
h
er
ef
o
r
e,
a
n
u
m
b
er
of
d
if
f
er
en
t
d
etec
tio
n
s
y
s
te
m
s
ar
e
ca
p
ab
le
of
d
etec
tin
g
a
n
d
m
ap
p
in
g
th
e
s
e
v
ar
iatio
n
s
.
In
ad
d
itio
n
,
an
ad
v
a
n
ce
d
u
n
it
is
d
ev
elo
p
ed
w
i
th
an
altit
u
d
e
ca
p
ab
ilit
y
,
w
h
e
n
s
e
v
er
al
s
e
n
s
o
r
s
ar
e
co
n
n
ec
ted
s
i
m
u
lta
n
eo
u
s
l
y
.
In
t
h
e
So
f
t
w
a
r
e
s
ec
tio
n
,
a
p
r
o
g
r
a
m
m
i
n
g
co
d
e
is
g
en
er
ated
to
s
im
u
late
v
a
r
iatio
n
s
in
r
ad
iatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
4
4
7
8
-
4489
4480
an
d
s
o
lar
f
lu
x
.
T
h
e
asp
ec
ts
of
r
ea
l
-
ti
m
e
d
ata
ac
q
u
is
itio
n
w
e
r
e
tak
en
in
to
ac
co
u
n
t
in
t
h
is
s
t
u
d
y
.
T
h
e
g
o
al
is
to
d
esig
n
a
n
d
m
a
n
u
f
ac
tu
r
e
an
o
p
ti
m
ized
p
ar
ab
o
la
b
ased
on
t
h
e
r
es
u
lt
s
of
t
h
e
G
S
A
al
g
o
r
it
h
m
,
t
h
is
p
r
o
to
t
y
p
e
is
lin
ed
w
it
h
a
g
las
s
or
p
o
lis
h
ed
m
etal
m
ir
r
o
r
u
s
ed
as
r
ef
lecto
r
,
w
h
ich
s
er
v
e
s
f
o
r
m
a
x
i
m
u
m
co
llectio
n
of
s
o
lar
r
ad
iatio
n
w
h
ile
t
h
r
o
u
g
h
o
u
t
th
e
d
ay
,
a
bi
-
a
x
ial
tr
ac
k
in
g
s
y
s
te
m
is
d
esi
g
n
ed
f
o
r
th
i
s
p
u
r
p
o
s
e
[
1
2
]
.
3.
RE
S
E
ARCH
M
E
T
H
O
DO
L
G
Y
3
.
1
.
Virt
ua
l
re
a
lity
des
ig
n
T
h
e
d
esig
n
of
s
y
s
te
m
s
in
m
ec
h
an
ica
l
en
g
in
ee
r
i
n
g
s
u
c
h
as
g
ea
r
ed
m
o
to
r
s
,
p
ar
ab
o
lic
c
o
n
ce
n
tr
ato
r
s
is
a
v
er
y
co
m
p
licated
o
p
er
atio
n
t
h
at
r
eq
u
ir
es
h
i
g
h
l
y
i
n
ter
ac
ti
v
e
s
o
f
t
w
ar
e
to
o
ls
so
it
is
i
m
p
o
r
ta
n
t
to
d
iv
er
s
i
f
y
th
is
in
ter
ac
ti
v
e
s
i
m
u
latio
n
to
r
ea
ch
s
o
lar
s
y
s
te
m
s
d
esi
g
n
er
s
,
an
d
th
is
m
a
k
es
it
p
o
s
s
ib
le
to
u
n
d
er
s
tan
d
t
h
e
r
ea
l
asp
ec
t
of
t
h
e
s
y
s
te
m
.
In
o
r
d
er
to
h
av
e
o
p
ti
m
al
r
es
u
lt
s
th
e
u
s
e
of
v
ir
t
u
al
r
ea
lit
y
is
a
cr
u
cia
l
ass
et.
It
d
ef
in
ed
as
th
e
u
s
e
of
co
m
p
u
ter
s
y
s
te
m
s
to
s
u
p
p
o
r
t
s
e
v
er
al
ap
p
r
o
ac
h
es
in
d
esi
g
n
l
ik
e
cr
ea
tio
n
,
m
o
d
if
ic
atio
n
,
a
n
al
y
s
is
,
an
d
o
p
tim
izatio
n
[
1
3
–
1
5
]
,
th
e
im
p
le
m
e
n
ted
p
r
o
ce
s
s
is
th
e
r
esu
lt
of
i
n
ter
ac
ti
v
it
y
b
et
w
ee
n
th
e
C
AD
n
a
m
el
y
(
So
lid
W
o
r
k
s
,
Ma
tlab
,
an
d
L
ab
Vie
w
)
.
3
.
2
.
P
ro
po
s
ed
m
a
t
he
m
a
t
ic
m
o
del
T
h
e
m
at
h
e
m
a
tical
m
o
d
el
u
s
e
d
in
t
h
i
s
r
esear
c
h
b
ased
on
of
P
er
r
in
B
r
ich
a
m
b
a
u
t
[
1
6
]
m
o
d
el,
w
h
ic
h
tak
es
i
n
to
co
n
s
id
er
atio
n
ce
r
ta
in
n
u
m
b
er
of
p
h
y
s
ical
p
h
e
n
o
m
en
a
s
u
c
h
as
t
h
er
m
a
l
lo
s
s
e
s
,
o
p
tical
y
ield
s
[
1
7
]
.
T
h
e
m
ai
n
o
b
j
ec
tiv
es
is
th
e
ev
alu
atio
n
of
t
h
e
p
er
f
o
r
m
a
n
ce
of
s
o
lar
en
er
g
y
co
n
v
er
s
io
n
s
y
s
te
m
s
.
A
n
u
m
er
ical
s
i
m
u
lat
io
n
d
ev
elo
p
ed
in
th
i
s
ar
ea
to
p
e
r
f
o
r
m
t
h
e
ir
r
ad
ian
ce
an
d
th
e
s
o
lar
f
lu
x
,
th
e
m
o
d
el
is
d
escr
ib
ed
u
s
in
g
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
.
T
h
e
s
o
lar
f
lu
x
is
ca
lc
u
lated
b
y
:
=
×
(
×
×
)
+
(
×
×
(
−
)
(
1
)
W
ith
F
r
is
t
h
e
h
ea
t
d
is
s
ip
atio
n
f
ac
to
r
ca
lcu
lated
b
y
:
=
×
×
×
(
1
−
×
×
′
×
)
(
2
)
is
o
p
tical
ef
f
icien
c
y
w
h
ic
h
is
g
i
v
en
b
y
:
=
×
×
(
3
)
DNI
is
th
e
s
o
lar
ir
r
ad
iatio
n
w
h
ich
is
g
i
v
en
b
y
:
=
1367
×
ℎ
×
(
1
+
0
.
03344
×
c
os
(
0
.
98
×
)
−
2
.
8
)
)
(
4
)
We
can
ex
p
r
ess
t
h
e
h
ei
g
h
t
of
t
h
e
s
u
n
b
y
:
ℎ
=
a
r
c
s
in
(
s
in
(
)
×
s
in
(
)
+
c
os
(
)
×
c
os
(
)
×
c
os
(
Ω
)
)
(
5
)
is
th
e
s
o
lar
d
ec
lin
atio
n
w
h
ic
h
is
g
i
v
en
b
y
:
=
a
r
c
s
in
(
0
.
398
×
s
in
(
360
365
×
(
−
82
)
+
2
×
s
in
360
365
×
(
−
2
)
)
(
6
)
An
d
Ω
is
th
e
h
o
u
r
a
n
g
le
t
h
at
c
an
be
ca
lcu
lated
w
it
h
:
Ω
=
15
×
(
−
12
)
(
7
)
T
SV
is
th
e
tr
u
e
s
o
lar
ti
m
e
g
i
v
e
n
b
y
:
=
+
+
4
×
60
−
(
8
)
an
d
E
t
is
th
e
co
r
r
ec
tio
n
of
t
h
e
eq
u
atio
n
of
ti
m
e
g
i
v
en
b
y
:
=
9
.
87
×
s
in
(
2
×
′
)
−
7
.
53
×
c
os
′
−
s
in
′
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
in
tera
ctive
a
p
p
r
o
a
ch
fo
r
s
o
la
r
en
erg
y
s
ystem:
d
esig
n
…
(
B
en
b
a
z
iz
Dja
lla
l
E
d
d
in
e
Ma
h
d
i
)
4481
W
ith
N’
g
i
v
en
b
y
:
′
=
360
×
(
−
81
)
365
(1
0
)
A
a
is
T
h
e
o
p
en
in
g
s
u
r
f
ac
e
of
t
h
e
co
llecto
r
g
iv
e
n
b
y
:
=
×
2
4
(1
1
)
A
r
is
th
e
s
u
r
f
ac
e
of
t
h
e
r
ec
eiv
e
r
ca
lcu
lated
b
y
:
=
2
×
×
ℎ
(1
2
)
U
l
is
th
e
t
h
er
m
al
lo
s
s
co
ef
f
icie
n
t,
we
can
ca
lc
u
late
it
w
i
th
:
=
1
(
ℎ
+
ℎ
)
×
(
1
ℎ
)
(1
3
)
A
C
T
h
e
s
u
r
f
ac
e
of
t
h
e
m
ir
r
o
r
s
g
iv
e
n
b
y
:
=
2
×
×
ℎ
(1
4
)
h
w
is
t
h
e
co
ef
f
icie
n
t
of
co
n
v
ec
tio
n
ex
c
h
an
g
e
b
et
w
ee
n
th
e
g
la
s
s
an
d
t
h
e
at
m
o
s
p
h
er
e
g
i
v
e
n
b
y
:
ℎ
=
0
.
3
×
0
.
6
×
(1
5
)
W
ith
h
rca
is
th
e
r
ad
iati
v
e
ex
c
h
a
n
g
e
co
e
f
f
ic
ien
t
b
et
w
ee
n
t
h
e
g
l
ass
an
d
t
h
e
at
m
o
s
p
h
er
e
g
i
v
e
n
b
y
:
ℎ
=
×
×
(
+
)
×
(
2
+
2
)
(1
6
)
h
rra
is
th
e
r
ad
iativ
e
e
x
ch
a
n
g
e
co
ef
f
icien
t
b
et
w
ee
n
t
h
e
ab
s
o
r
b
er
an
d
th
e
g
la
s
s
w
h
ic
h
is
g
i
v
en
b
y
:
ℎ
=
×
(
+
)
×
(
2
+
2
)
(
1
+
)
×
(
1
−
1
)
(1
7
)
F’
is
th
e
e
f
f
icien
c
y
f
ac
to
r
of
th
e
m
ir
r
o
r
g
iv
e
n
b
y
:
′
=
1
1
+
ℎ
×
+
2
×
ln
(
)
(1
8
)
3
.
3
.
G
ra
v
it
a
t
io
na
l
s
ea
rc
h
a
lg
o
rit
h
m
(
G
SA)
GS
A
[
1
8
]
is
a
p
o
w
er
f
u
l
m
e
ta
-
h
eu
r
i
s
tic
al
g
o
r
ith
m
b
ased
m
a
i
n
l
y
on
t
h
e
la
w
of
Ne
w
to
n
ia
n
g
r
av
it
y
a
n
d
m
o
tio
n
[
1
9
–
2
2
]
,
p
r
in
cip
ally
t
h
e
in
f
l
u
en
ce
of
g
r
av
it
y
lead
s
to
a
m
o
v
e
m
e
n
t
of
attr
ac
tio
n
b
et
w
ee
n
ag
e
n
t
s
.
In
GS
A
,
each
m
ass
h
as
f
o
u
r
ch
ar
ac
ter
is
tics
:
i
n
er
tial
m
as
s
,
ac
tiv
e
g
r
av
i
tatio
n
al
m
as
s
,
p
ass
i
v
e
g
r
av
itatio
n
a
l
m
as
s
,
[
2
3
]
.
T
h
e
p
er
f
o
r
m
a
n
ce
in
d
ex
of
each
a
g
en
t
is
m
ea
s
u
r
ed
by
it
s
m
a
s
s
[
2
4
]
,
in
an
o
t
h
e
r
w
a
y
th
e
h
ea
v
iest
ag
en
t
s
m
a
tch
to
th
e
g
o
o
d
co
n
v
er
g
e
n
ce
s
o
lu
tio
n
of
t
h
e
p
r
o
b
le
m
[
2
5
]
,
d
u
e
to
th
e
g
r
av
it
y
f
o
r
ce
s
,
ag
en
ts
w
i
th
th
e
h
ea
v
ier
m
ass
e
s
w
ill
d
r
iv
e
all
ag
en
ts
to
m
o
v
e
to
w
ar
d
s
it.
T
h
e
p
o
s
itio
n
of
an
ag
e
n
t
(
o
b
j
e
ct)
is
:
=
1
,
2
,
…
…
,
(1
9
)
T
h
e
m
a
s
s
v
alu
e
of
each
o
b
j
ec
t
is
d
eter
m
in
ed
ac
co
r
d
in
g
to
its
f
it
n
ess
v
al
u
e:
=
(
)
−
(
)
∑
(
)
−
(
)
=
1
(2
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
4
4
7
8
-
4489
4482
By
t
h
e
ca
lc
u
lati
n
g
t
h
e
m
ass
of
o
b
j
ec
ts
,
th
e
y
ca
n
in
ter
ac
t
by
e
ac
h
o
th
er
b
y
:
(
)
=
∑
(
)
(
)
×
(
)
(
)
+
(
(
)
−
(
)
)
≠
(2
1
)
T
h
e
ac
ce
ler
atio
n
of
th
e
ag
e
n
t
is
ca
lcu
lated
by
t
h
e
s
ec
o
n
d
la
w
of
m
o
tio
n
:
(
)
=
(
)
(
)
(
2
2)
Af
ter
w
ar
d
,
(
23
)
an
d
(
24
)
a
r
e
u
s
ed
to
u
p
d
ate
t
h
e
p
o
s
itio
n
of
each
a
g
en
t.
A
cc
o
r
d
in
g
to
(
23
)
,
th
e
n
e
x
t
v
elo
cit
y
of
th
e
a
g
e
n
t
is
ca
lc
u
la
ted
as
a
f
r
ac
tio
n
of
it
s
cu
r
r
en
t
v
elo
cit
y
ad
d
ed
to
its
ac
ce
ler
ati
o
n
.
(
+
1
)
=
×
(
)
+
(
)
(2
3
)
(
+
1
)
=
(
)
+
(
+
1
)
(2
4
)
w
h
er
e
r
i
an
d
r
j
ar
e
t
w
o
u
n
i
f
o
r
m
d
i
s
tr
ib
u
ted
r
a
n
d
o
m
n
u
m
b
er
s
in
t
h
e
i
n
ter
v
al
[
0
,
1
]
.
Ho
w
e
v
er
,
g
e
n
er
atin
g
th
e
p
s
eu
d
o
co
d
e
r
eq
u
ir
es
th
e
f
o
llo
w
i
n
g
of
s
e
v
er
al
s
tep
s
r
ep
o
r
ted
in
th
e
f
o
llo
w
i
n
g
T
ab
le
1
.
T
ab
le
1
.
P
s
eu
d
o
co
d
e
1.
Search space identification, t=0
2.
Random initialization,
(
)
for i=1,…….N
3.
Fitness evaluation of objects
4.
Update the parameters of G, worst and M
i
for i=1,…….,N
5.
Calculation of the force applied to each object
6.
Calculation of the acceleration and the velocity of each object;
7.
Update the po
sition of the objects by Eq. 2 to yield
(
+
1
)
;
=
+
1
;
8.
Repeat steps 3 to 7 until the stopping criterion is reached;
9.
Optimal vector return
3
.
4
.
T
ra
c
k
ing
s
y
s
t
e
m
T
h
e
ch
allen
g
e
is
to
co
llect
as
m
u
ch
s
o
lar
en
er
g
y
as
p
o
s
s
i
b
le
u
s
in
g
co
n
ce
n
tr
ato
r
s
y
s
te
m
s
.
Ha
v
in
g
f
o
u
n
d
th
at
en
er
g
y
p
r
o
d
u
ctio
n
is
af
f
ec
ted
by
t
h
e
f
o
llo
w
i
n
g
f
ac
to
r
s
:
th
e
g
eo
g
r
ap
h
ic
lo
ca
tio
n
of
s
o
lar
r
ad
iatio
n
,
th
e
a
m
b
ien
t
te
m
p
er
atu
r
e
a
n
d
w
ea
t
h
er
in
t
h
e
r
e
g
io
n
an
d
t
h
e
an
g
le
of
i
n
cid
en
ce
of
t
h
e
s
u
n
[
2
6
]
.
To
th
is
en
d
,
a
s
y
s
te
m
is
d
esi
g
n
ed
to
k
ee
p
t
h
e
s
u
r
f
ac
e
of
t
h
e
s
e
n
s
o
r
p
er
p
en
d
icu
lar
to
th
e
s
u
n
[
2
7
,
2
8
]
.
T
h
e
s
y
s
te
m
in
p
lace
m
ak
e
s
it
p
o
s
s
ib
le
to
f
o
llo
w
th
e
tr
aj
ec
to
r
y
of
t
h
e
s
u
n
t
h
r
o
u
g
h
o
u
t
t
h
e
d
a
y
in
o
r
d
er
to
be
ab
le
to
ca
p
tu
r
e
th
e
m
a
x
i
m
u
m
of
av
ai
lab
le
en
er
g
y
.
Fo
r
th
i
s
we
d
is
ti
n
g
u
i
s
h
t
w
o
d
if
f
er
e
n
t
m
et
h
o
d
s
:
a
p
ass
iv
e
o
n
e
w
h
ich
d
o
es
n
o
t
r
eq
u
ir
e
co
n
tr
o
ller
s
,
m
o
to
r
s
or
g
ea
r
s
.
An
ac
tiv
e
m
eth
o
d
th
at
we
r
ec
o
m
m
e
n
d
co
n
tr
o
ll
ed
by
co
n
tr
o
ller
s
,
u
s
i
n
g
m
o
to
r
s
a
n
d
g
ea
r
s
[
2
9
]
.
T
h
e
p
r
in
cip
le
of
tr
ac
k
i
n
g
is
to
r
ed
u
ce
th
e
an
g
le
f
o
r
m
ed
by
th
e
s
u
n
'
s
r
a
y
s
a
n
d
th
e
s
u
r
f
ac
e
of
t
h
e
co
llecto
r
,
in
o
r
d
er
to
m
a
x
i
m
ize
t
h
e
a
m
o
u
n
t
of
e
n
er
g
y
ca
p
tu
r
ed
.
T
h
u
s
a
bi
-
a
x
ial
tr
ac
k
i
n
g
s
y
s
te
m
h
a
s
b
ee
n
d
esi
g
n
ed
an
d
p
r
o
d
u
ce
d
[
3
0
,
3
1
]
,
p
r
o
v
id
ed
w
it
h
a
d
u
al
a
x
i
s
tr
ac
k
i
n
g
(
az
im
u
th
a
n
d
altit
u
d
e
)
is
m
o
r
e
e
f
f
ec
ti
v
e.
In
Fi
g
u
r
e
3,
we
p
r
o
v
id
e
o
u
r
b
est
esti
m
ates
of
th
e
co
s
t
p
ar
a
m
eter
s
of
t
h
e
tr
ac
k
in
g
s
y
s
te
m
.
Fig
u
r
e
3.
T
r
ac
k
in
g
p
ar
a
m
eter
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
in
tera
ctive
a
p
p
r
o
a
ch
fo
r
s
o
la
r
en
erg
y
s
ystem:
d
esig
n
…
(
B
en
b
a
z
iz
Dja
lla
l
E
d
d
in
e
Ma
h
d
i
)
4483
4.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
NS
In
th
i
s
ch
al
len
g
i
n
g
ec
o
n
o
m
ic
an
d
s
cien
ti
f
ics
co
n
tex
t,
in
f
ac
t
,
we
h
a
v
e
ap
p
lied
a
n
o
v
el
m
et
h
o
d
o
lo
g
y
w
it
h
h
ei
g
h
t
i
n
ter
ac
ti
v
it
y
in
t
h
e
d
esig
n
of
th
e
s
y
s
te
m
as
d
e
s
cr
ib
ed
in
F
i
g
u
r
e
4.
In
t
h
is
r
eg
ar
d
,
a
p
o
w
er
f
u
ll
in
ter
ac
ti
v
e
m
o
d
eli
n
g
d
e
s
ig
n
f
o
r
s
o
lar
s
tatio
n
b
ased
on
v
ar
io
u
s
C
A
D
h
as
b
ee
n
d
e
v
o
lo
p
ed
.
A
ca
lc
u
latio
n
an
d
p
r
o
g
r
am
m
i
n
g
p
r
o
ce
d
u
r
e
is
d
ev
elo
p
ed
to
s
i
m
u
la
te
s
o
lar
r
ad
iatio
n
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o
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u
an
ti
f
y
it.
In
th
i
s
r
esp
ec
t,
eq
u
atio
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s
allo
w
us
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o
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o
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ti
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t
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e
p
o
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itio
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u
n
at
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m
o
m
e
n
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e
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a
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.
Fig
u
r
e
5
s
h
o
w
s
th
e
c
h
an
g
e
in
d
ir
ec
t
r
ad
iatio
n
d
u
r
in
g
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e
s
o
ls
tice
s
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o
u
r
s
ea
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o
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(
Ma
r
ch
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J
u
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21
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d
Dec
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er
21)
f
r
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Fig
u
r
e
4
.
I
n
ter
ac
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m
o
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o
ls
Fig
u
r
e
5
.
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h
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o
lu
tio
n
o
f
t
h
e
s
o
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u
s
e
f
u
l f
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T
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e
of
th
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g
r
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r
ch
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o
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a
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ize
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n
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ated
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o
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ti
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n
g
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eo
m
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ical
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d
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eter
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th
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o
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g
u
r
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e
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cr
ib
e
th
e
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o
lu
tio
n
of
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u
r
i
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g
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h
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al
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p
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e
p
r
o
p
o
s
ed
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o
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e,
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les
s
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o
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ar
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i
n
q
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est
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.
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i
n
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icate
d
in
th
e
T
ab
le
2
,
each
s
i
m
u
lat
io
n
is
r
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n
n
i
g
w
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if
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er
en
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iter
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m
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er
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T
ab
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2
illu
s
tr
at
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th
e
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r
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o
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est
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s
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lt
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e.
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e
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at
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i
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atel
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e
s
a
m
e
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lts
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ea
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h
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tr
o
l p
ar
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eter
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er
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to
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ar
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o
m
e
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ar
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eter
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s
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o
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ti
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ized
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x
ec
u
ti
n
g
t
h
r
ee
tes
ts
.
T
ab
le
3
s
u
m
m
ar
ize
s
t
h
e
o
b
tain
ed
r
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lt
s
f
o
r
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ch
p
ar
a
m
eter
.
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th
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e
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u
lts
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t
w
a
s
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th
at
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est
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o
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4
0
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o
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m
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le
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e
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lts
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u
r
p
r
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s
s
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i
n
Fi
g
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6
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n
d
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,
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lt
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w
p
ar
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eter
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m
p
ar
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w
i
th
t
h
at
o
f
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h
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s
ta
n
d
ar
d
r
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lts
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T
ab
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2
.
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p
ar
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N
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masse
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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T
ab
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3
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en
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ar
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t
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d
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W
e
n
o
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a
s
ig
n
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f
ica
n
t
i
n
c
r
ea
s
e
o
f
th
e
s
o
lar
f
l
u
x
w
h
ic
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ca
n
b
e
ex
p
lai
n
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b
y
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ca
n
b
e
ex
p
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b
y
t
h
e
c
h
an
g
e
i
n
v
a
lu
es
o
f
th
e
d
ia
m
eter
o
f
t
h
e
d
is
h
an
d
also
t
h
e
h
eig
h
t
o
f
th
e
a
b
s
o
r
b
er
(
th
e
f
lu
x
i
s
p
r
o
p
o
r
tio
n
al
to
th
e
d
ia
m
e
ter
wh
ile
th
e
h
ei
g
h
t o
f
t
h
e
a
b
s
o
r
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is
d
is
p
r
o
p
o
r
tio
n
al
to
t
h
e
f
l
u
x
)
.
Mo
r
e
r
esu
lt
s
w
er
e
p
r
o
v
en
,
th
e
i
m
p
le
m
e
n
tatio
n
t
h
e
C
ar
tesi
a
n
co
o
r
d
in
ates
o
f
o
u
r
s
tu
d
y
ar
ea
(
th
e
cit
y
o
f
Or
an
)
in
o
r
d
er
to
h
av
e
th
e
b
est
p
o
s
s
ib
le
lo
ca
tio
n
f
o
r
a
m
a
x
i
m
u
m
co
n
c
e
n
tr
atio
n
o
f
s
o
lar
f
lu
x
.
T
ab
le
4
illu
s
tr
ates
th
e
o
p
tim
al
lo
n
g
it
u
d
e
an
d
latitu
d
e
p
ar
a
m
eter
s
o
b
tai
n
ed
in
a
d
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in
ed
i
n
ter
v
al.
I
n
ad
d
itio
n
,
Fi
g
u
r
e
8
tr
an
s
lates t
h
e
o
b
tain
ed
r
esu
lt
s
.
(
a)
(
b
)
Fig
u
r
e
6.
T
h
e
ev
o
lu
tio
n
of
s
o
l
ar
u
s
ef
u
l
f
l
u
x
in
(
a)
s
tan
d
ar
d
s
ettin
g
s
a
n
d
(
b
)
o
p
tim
al
s
ett
in
g
s
Fig
u
r
e
7.
T
h
e
co
m
p
ar
is
o
n
b
et
w
ee
n
th
e
d
i
f
f
er
en
t
p
ar
a
m
eter
s
T
ab
le
4
.
B
en
ch
m
ar
k
r
es
u
lts
P
a
r
a
me
t
e
r
s
S
t
a
n
d
a
r
d
v
a
l
u
e
s
M
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e
M
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O
p
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λ
3
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.
6
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6
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3
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3
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3
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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lec
&
C
o
m
p
E
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g
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N:
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4485
Fig
u
r
e
8.
C
o
m
p
ar
is
o
n
b
et
w
ee
n
th
e
d
i
f
f
er
e
n
t
s
et
tin
g
s
Mo
r
eo
v
er
,
th
e
r
esu
l
ts
o
b
tain
e
d
clea
r
ly
s
h
o
w
th
a
t
th
e
i
m
p
le
m
en
tatio
n
of
t
h
e
C
ar
te
s
ia
n
d
ata
can
b
r
in
g
a
p
lu
s
to
t
h
e
p
h
en
o
m
e
n
o
n
of
co
n
ce
n
tr
atio
n
.
I
t
is
n
o
ted
th
a
t
in
t
h
e
f
ir
s
t
h
al
f
of
t
h
e
d
a
y
(
b
ef
o
r
e
s
o
lar
n
o
o
n
)
th
e
s
o
lar
f
lu
x
is
s
li
g
h
tl
y
h
ig
h
e
r
w
h
ile
f
o
r
th
e
s
ec
o
n
d
p
er
io
d
th
er
e
is
a
s
li
g
h
t
d
ec
r
ea
s
e
in
s
o
l
ar
f
l
u
x
.
Desp
ite
t
h
is
d
ec
r
ea
s
e,
th
e
r
esu
l
ts
r
e
m
ain
s
atis
f
ac
to
r
y
b
ec
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s
e
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e
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est
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o
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f
l
u
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ate
is
co
n
ce
n
tr
ate
d
in
th
e
f
ir
s
t
p
er
io
d
of
th
e
d
a
y
.
4
.
1
.
E
x
peri
m
e
nta
l
re
s
ult:
des
ig
n
a
nd
m
a
nu
f
a
ct
uring
In
o
r
d
er
to
r
ed
u
ce
co
s
ts
by
u
s
in
g
m
o
d
er
n
i
n
e
x
p
en
s
iv
e
m
ate
r
ials
,
th
e
p
ar
ab
o
lic
co
llecto
r
tech
n
o
lo
g
y
,
w
h
ic
h
is
s
till
u
n
d
er
d
ev
elo
p
m
en
t,
is
t
h
e
b
est
o
p
tio
n
in
t
h
is
r
e
g
ar
d
.
An
i
n
ter
ac
ti
v
e
ap
p
r
o
ac
h
w
as
tak
e
n
to
r
ea
lize
th
e
co
n
ce
n
tr
ato
r
at
a
lo
w
er
co
s
t
a
n
d
as
s
i
m
p
l
y
as
p
o
s
s
ib
le.
First,
we
h
a
v
e
es
ta
b
lis
h
ed
a
d
esi
g
n
of
th
e
p
ar
ab
le
b
ased
on
th
e
s
o
f
t
war
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