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2
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1
7
I
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titu
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Adv
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Eng
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Sc
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All
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t
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re
s
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rve
d.
1.
Int
r
o
d
u
ctio
n
Rene
wab
l
e
en
erg
y
s
ou
r
c
es
i
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op
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tr
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pros
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am
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t
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s
organ
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d
as
f
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w
s
:
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I
I
an
a
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s
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t
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ex
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m
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m
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pres
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s
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t
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on
II
I
.
S
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t
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on
IV
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t
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ath
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s
the
di
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us
s
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on
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e
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ts
of
thi
s
w
ork
an
d
draw
s
the
o
pti
m
al
pe
r
f
or
m
an
c
es
. T
he
c
on
c
l
us
i
on
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s
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ep
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S
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t
i
on
V
I.
T
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l
i
terature
o
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the
op
t
i
m
i
z
ati
on
of
the
ti
l
t
an
gl
e
of
a
P
V
m
od
ul
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s
ho
w
s
a
v
ari
et
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of
ap
pro
ac
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s
:
pre
v
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tud
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ate
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ha
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th
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no
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t
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r
n
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m
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s
ph
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t
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m
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m
ti
l
t
an
g
l
e
de
pe
nd
s
on
l
y
on
th
e
l
a
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de
.
O
the
r
s
arti
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es
ap
pr
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h
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i
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th
at
th
ere
i
s
a
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um
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gl
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pe
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a
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l
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ate
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e
v
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e s
tu
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v
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t
o t
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S
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v
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b
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[1
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a
l
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w
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ha
t
P
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to
war
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y
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of
thi
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an
gl
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[2
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[3]
.
In
f
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f
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Chha
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Ind
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de
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2
3.5
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[
5]
A
l
s
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tha
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wi
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J
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Ho
we
v
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[6
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Evaluation Warning : The document was created with Spire.PDF for Python.
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i
n
35
s
i
t
es
i
n
d
i
f
f
erent
c
ou
ntri
es
of
the
M
ed
i
terr
an
ea
n
r
eg
i
on
.
[7]
Ha
v
e
d
em
on
s
tr
ate
d
thre
e
m
ath
em
ati
c
al
m
od
el
s
:
the
i
s
otrop
i
c
,
the
K
l
uc
he
r
an
d
the
P
ere
z
m
od
el
f
or
the
po
i
nt
s
ou
r
c
e
w
i
th
pa
r
am
ete
r
s
op
ti
m
i
z
e
d
f
or
a
v
ari
et
y
of
c
l
i
m
ate
c
on
d
i
ti
on
s
i
n
B
a
ng
l
ad
es
h.
A
l
tho
ug
h
i
n
Ma
l
a
y
s
i
a
[8]
th
e
L
i
w
an
d
J
ordan
m
od
el
was
ap
p
l
i
ed
to
f
ou
n
d
th
e
m
on
th
l
y
op
t
i
m
al
ti
l
t
a
ng
l
e.
T
h
e
l
i
terat
ure
o
n
T
ai
w
a
n
s
ho
w
s
a
v
arie
t
y
of
ap
pro
ac
he
s
:
i
n
[9]
the
P
S
O
-
NT
V
E
m
eth
od
was
ad
op
te
d
f
or
f
i
x
ed
P
V
m
od
ul
es
f
ac
i
ng
s
ou
t
h
a
nd
f
or
[10
]
an
an
t
di
r
ec
t
i
on
di
f
ferenti
al
ev
ol
u
ti
o
n
a
l
go
r
i
thm
(
A
DHDE
A
)
w
as
prop
os
ed
.
[11
]
ha
s
a
l
s
o
c
o
m
bi
ne
d
an
art
i
f
i
c
i
al
ne
ural
ne
t
wor
k
an
d
a
ge
ne
t
i
c
a
l
go
r
i
thm
(
A
NNG
A
)
t
o
f
ou
nd
the
s
ea
s
on
a
l
op
ti
m
um
an
gl
e.
2.
E
xper
i
men
t
al
o
u
t
line
T
he
ex
pe
r
i
m
en
t
w
as
c
on
du
c
ted
i
n
the
Hi
gh
er
In
s
ti
tut
e
of
A
pp
l
i
ed
S
c
i
e
nc
e
s
an
d
T
ec
hn
ol
og
y
of
G
af
s
a
s
i
tua
t
ed
at
t
he
N
34
°
26
’
14
.
09
’
’
E
8°
44
’
f
or
tw
o
da
y
s
.
T
he
a
i
m
o
f
thi
s
wor
k
was
to
de
term
i
ne
t
he
am
ou
nt
of
el
ec
tr
i
c
al
en
erg
y
ge
ne
r
ate
d
b
y
t
wo
d
i
f
f
erent
s
ol
ar
pa
n
el
s
to
w
ards
th
e
E
as
t,
S
o
uth
an
d
W
es
t
an
d
po
s
i
t
i
on
ed
f
or
the
an
gl
es
0°
,
3
0°
,
45
°,
60
°
an
d
9
0°
.I
n
th
i
s
po
s
i
t
i
on
s
th
e
v
a
l
u
es
of
ou
tpu
t
v
ol
t
ag
e
wer
e
m
ea
s
ured.
T
w
o
t
y
pe
s
of
m
on
oc
r
y
s
tal
l
i
ne
s
i
l
i
c
o
n
pa
ne
l
s
w
i
th
no
r
m
al
s
ol
ar
r
ad
i
ati
on
i
nt
ak
e
i
nte
ns
i
t
y
of
10
0
0
w
/m
²
at
tem
pe
r
atu
r
e
T
=
25
°c
.
T
he
f
i
r
s
t
pa
ne
l
w
a
s
wi
th
d
i
m
en
s
i
on
s
37
0x
29
5x
1
5
m
m
,
w
i
t
h
m
ax
i
m
u
m
po
w
er
10
W
.
T
h
e
s
ec
on
d
on
e
was
wi
th
di
m
en
s
i
on
s
21
5x
22
5x
18
m
m
,
w
i
th
m
ax
i
m
u
m
po
wer
4
W
.
T
he
s
ol
ar
m
od
ul
es
w
er
e
po
s
i
t
i
on
ed
i
n
t
he
predef
i
n
e
d
an
gl
es
an
d
orie
nta
t
i
o
ns
:
O
n
ea
c
h
t
en
m
i
nu
tes
f
r
om
8.3
0
am
un
ti
l
1
pm
f
or
tw
o
da
y
s
.
T
he
te
m
pe
r
atu
r
e
was
29
°
i
n t
h
e f
i
r
s
t d
a
y
an
d i
nc
r
ea
s
e t
h
e s
ec
on
d d
a
y
t
o 3
2
°.
F
i
gu
r
e
.
1.
P
os
i
t
i
o
n o
f
s
ol
ar
m
od
ul
e f
or c
ho
s
en
an
gl
es
3.
T
h
eore
t
ica
l
anal
ys
is
T
he
i
nc
i
de
nt
tot
al
r
ad
i
at
i
o
n
on
ti
l
ted
s
urf
ac
e
on
a
n
i
nc
l
i
n
ed
a
ng
l
e
f
r
o
m
the
ho
r
i
z
o
nta
l
i
s
gi
v
en
b
y
:
=
+
+
(
1)
T
he
di
r
ec
t s
ol
ar r
ad
i
ati
on
r
e
c
ei
v
ed
o
n a
n i
nc
l
i
ne
d
s
urf
ac
e c
an
be
ex
pres
s
ed
as
:
=
*(
G
H
−
DH
)
(
2)
W
h
ere G
H an
d DH
are t
he
da
i
l
y
gl
ob
a
l
a
nd
di
f
f
us
e radi
ati
o
n o
n h
or
i
z
on
t
al
s
urf
ac
e:
=
(
3)
R
b
i
s
the
r
at
i
o
of
the
a
v
era
g
e
da
i
l
y
i
nc
i
de
nt
r
ad
i
at
i
on
o
n
a
ti
l
te
d
s
urf
ac
e
to
tha
t
o
n
a
ho
r
i
z
on
t
al
s
urf
ac
e.
T
he
i
nc
i
de
nc
e
a
ng
l
e
θ
i
s
p
r
ov
i
de
d
b
y
E
q
.(
4),
w
h
ere
p
aram
ete
r
s
i
nv
o
l
v
ed
a
l
s
o
i
n
c
l
ud
e
the
pa
ne
l
t
i
l
t
a
ng
l
e
β
the
l
a
ti
tu
de
of
the
l
oc
at
i
on
ex
am
i
ne
d
φ,
the
a
z
i
m
uth
an
g
l
e
γ
T
he
s
ol
ar
ho
ur
an
g
l
e
ω
an
d
δ
t
he
s
o
l
ar d
e
c
l
i
na
ti
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N:
25
02
-
4
75
2
IJE
E
CS
V
ol
.
8
,
N
o.
3
,
Dec
em
be
r
2017
:
7
6
2
–
7
6
9
764
c
os
=
(
−
)
∗
s
in
+
(
∗
s
in
+
(
+
)
∗
c
os
)
∗
c
os
(
4)
W
i
th
=
s
in
φ
∗
c
os
β
B
=
s
in
β
∗
c
os
γ
∗
c
os
φ
C
=
s
in
β
∗
s
in
γ
D
=
c
os
φ
∗
c
os
β
E
=
s
in
φ
∗
s
in
β
∗
c
os
γ
γ
=
90
−
β
(
5)
F
urtherm
ore, s
ol
ar ho
ur an
gl
e
ω
i
s
a
f
un
c
t
i
on
of
s
ol
ar t
i
m
e
T
S
an
d
i
s
pro
v
i
de
d
b
y
t
he
f
ol
l
o
wi
ng
eq
u
at
i
on
:
=
0
-
+(
+
4
60
)
(6)
c
orr
es
po
nd
s
to
the
ti
m
e c
orr
ec
ti
on
f
un
c
ti
on
=
229
.
2
∗
(
0
.
000075
+
0
.
001868
∗
c
os
−
0
.
032077
∗
s
in
−
0
.
014615
∗
c
os
2
−
0
.
040089
∗
s
in
2
(
7)
W
i
th
=
360
365
∗
(
−
1
)
(
8)
s
in
ℎ
=
c
os
∗
c
os
+
s
in
∗
s
in
(
9)
T
he
da
i
l
y
groun
d ref
l
ec
te
d r
ad
i
ati
on
c
an
be
w
r
i
tt
en
as
:
=
(
*
s
i
n (δ)
+
DH)
*
ρ
*
(
(
1
+
c
os
(
β
)
)
/ 2
)
(
10
)
W
h
ere
ρ
i
s
the
al
be
d
o
(
r
ad
i
ati
on
r
ef
l
ec
ti
on
r
at
e)
of
the
grou
nd
.
T
he
d
i
f
f
us
ed
s
ol
ar
r
ad
i
at
i
o
n o
f
s
l
op
e i
s
c
a
l
c
ul
a
ted
b
y
t
he
f
ol
l
o
wi
ng
ex
pres
s
i
on
:
=
DH
*
(
(
1
+
c
os
(
β
)
)
/ 2
)
(
1
1)
T
he
v
al
ue
of
the
m
on
th
l
y
a
v
era
ge
d
ai
l
y
di
f
f
us
e
r
ad
i
ati
on
o
n
a
h
ori
z
on
tal
s
urf
ac
e
de
pe
nd
s
on
t
hree
d
i
f
f
erent
r
an
ge
s
of
c
l
ea
r
ne
s
s
i
n
de
x
.
T
he
r
es
ul
ti
ng
c
orr
e
l
at
i
on
s
a
r
e
gi
v
en
i
n
the
T
ab
l
e.
4.
R
es
u
lt
s
and
dis
cussion
s
E
x
pe
r
i
m
en
tal
r
es
ul
ts
of
th
e
pa
ne
l
I
ob
t
ai
ne
d
ap
pe
ars
i
n
f
i
g
ure
2,3
an
d
4.I
n
ot
he
r
s
i
de
f
i
gu
r
e
5,6
a
nd
7
s
h
o
w
th
e
r
es
ul
ts
of
the
s
ec
on
d
pa
n
el
.
It
i
s
c
l
ea
r
f
r
o
m
the
f
i
gu
r
es
,
r
ep
r
es
en
ti
n
g
the
pe
r
f
orm
an
c
e
of
the
f
i
r
s
t
pa
ne
l
,
tha
t
the
E
as
t
a
nd
the
S
o
uth
g
i
v
e
the
m
ax
i
m
u
m
ou
tpu
t
v
o
l
tag
e.
In
order
t
o
de
c
i
de
the
o
pti
m
al
ti
l
t
an
g
l
e,
t
he
m
a
x
i
m
u
m
ou
tpu
t
v
o
l
ta
g
e
g
en
erat
ed
was
38
V
,
whi
c
h
c
orr
es
p
on
ds
t
o
i
nc
l
i
na
t
i
o
n
an
gl
e
of
90
°
E
a
s
t.
It
c
an
the
r
ef
ore
be
c
on
c
l
ud
ed
th
at
9
0°
E
as
t i
s
t
he
ex
pe
r
i
m
en
tal
op
ti
m
al
an
g
l
e
of
th
e p
an
e
l
I.
In
f
ac
t,
b
y
o
bs
erv
i
ng
the
r
es
ul
ts
ob
t
ai
ne
d
of
the
s
ec
on
d
pa
ne
l
,
th
ere
i
s
a
m
i
no
r
di
f
f
ere
nc
e
i
n
th
e
pro
du
c
ed
el
ec
tr
i
c
al
v
ol
t
ag
e
be
t
w
e
en
the
thre
e
or
i
en
t
ati
on
s
ev
e
n
be
t
w
ee
n
t
he
di
f
f
erent
prop
os
ed
an
gl
es
.
Ho
w
e
v
er,
i
t
i
nc
r
ea
s
es
up
to
the
po
i
nt
of
90
°
E
as
t.
A
c
k
no
w
l
e
dg
i
ng
th
e
ex
pe
r
i
m
en
tal
pe
r
f
orm
an
c
e
of
the
P
V
p
an
e
l
s
f
or
the
p
erio
d
of
ex
am
i
na
ti
on
,
i
t
be
c
o
m
es
ev
i
de
n
t
tha
t
am
on
g t
he
d
i
f
f
erent d
i
m
en
s
i
on
s
, th
e a
ng
l
e t
ha
t
gi
v
es
th
e m
ax
i
m
u
m
v
ol
ta
ge
i
s
90
°
E
as
t.
A
f
ter
the
ex
p
erim
en
tal
i
n
v
e
s
ti
ga
t
i
on
of
the
o
pti
m
um
ti
l
t
an
g
l
e,
i
t
i
s
ne
c
es
s
ar
y
t
o
i
nte
r
pret
t
ho
s
e
r
es
ul
ts
throu
gh
t
he
t
he
ore
ti
c
al
i
n
v
es
t
i
g
ati
on
.
T
he
oret
i
c
al
d
ete
r
m
i
na
ti
on
of
the
op
t
i
m
u
m
ti
l
t
an
gl
e
i
s
ba
s
ed
on
the
eq
u
ati
on
s
p
r
op
os
ed
on
s
ec
t
i
on
III.
T
he
MA
T
LA
B
r
es
u
l
ts
are
i
l
l
us
tr
ate
d
i
n
F
i
gu
r
e
8,9
,
10
,
1
1,1
2
an
d
13
.
A
s
f
ol
l
o
w
s
f
r
o
m
the
f
i
gu
r
es
s
ho
w
n
ab
o
v
e
,l
e
t u
s
f
i
r
s
t p
r
ov
e t
ha
t t
he
r
e
i
s
no
t
a b
i
g d
i
f
f
erenc
e b
et
w
e
en
t
h
e res
ul
ts
of
th
e
two
pa
ne
l
s
an
d
the
three
orie
nt
ati
on
s
.
B
ut
t
he
i
nc
l
i
na
ti
on
90
_
E
as
t
r
ep
r
es
en
ts
the
o
pti
m
al
ti
l
t
an
g
l
e
tha
t
gi
v
e
th
e
m
ax
i
m
u
m
ou
tpu
t
v
o
l
ta
ge
.
T
he
n
th
i
s
the
oret
i
c
al
m
eth
od
i
s
an
ef
f
ec
ti
v
e
w
a
y
t
o
prov
e
th
e
ex
p
erim
en
tal
r
es
ul
ts
.
A
t
t
hi
s
p
oi
nt,
i
t
i
s
i
m
po
r
tan
t
t
o
no
te
t
ha
t
e
v
en
the
r
e
i
s
a
d
i
f
f
erent
i
n
t
he
di
m
en
s
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Ref
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[1
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T
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M
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m
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En
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ri
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g
.
2016
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).
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u
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AABE
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[4
]
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l
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o
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rg
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Ad
v
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n
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d
E
n
g
i
n
e
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ri
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.
2013
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)
.
[5
]
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n
a
n
S
h
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ri
a
h
.
O
p
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6
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8
7
5
9
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.
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0
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1
[6
]
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n
e
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