I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
(
I
J
P
E
DS)
Vo
l.
1
6
,
No
.
3
,
Sep
tem
b
er
2
0
2
5
,
p
p
.
1
9
1
4
~
1
9
2
5
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
6
.
i3
.
p
p
1
9
1
4
-
1
9
2
5
1914
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Inv
estig
a
tion o
f
o
ptima
l t
il
t,
orie
nt
a
tion
,
a
nd t
ra
ckin
g
of a so
la
r
PV
sy
stem
in
Ira
q
Ahm
ed
Z
urf
i
1,
2
,
Ali A
b
du
l R
a
zz
a
q Alt
a
hir
3
,
Ali Ib
ra
him
4
1
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
Te
c
h
n
i
q
u
e
s
,
U
n
i
v
e
r
si
t
y
o
f
K
e
r
b
a
l
a
,
K
a
r
b
a
l
a
,
I
r
a
q
2
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
Te
c
h
n
i
q
u
e
s,
A
l
-
H
u
ss
a
i
n
U
n
i
v
e
r
s
i
t
y
C
o
l
l
e
g
e
,
K
a
r
b
a
l
a
,
I
r
a
q
3
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
a
n
d
El
e
c
t
r
o
n
i
c
E
n
g
i
n
e
e
r
i
n
g
,
C
o
l
l
e
g
e
o
f
En
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
si
t
y
o
f
K
e
r
b
a
l
a
,
K
a
r
b
a
l
a
,
I
r
a
q
4
C
o
l
l
e
g
e
o
f
E
n
g
i
n
e
e
r
i
n
g
a
n
d
C
o
mp
u
t
e
r
S
c
i
e
n
c
e
,
F
l
o
r
i
d
a
A
t
l
a
n
t
i
c
U
n
i
v
e
r
si
t
y
,
B
o
c
a
R
a
t
o
n
,
U
n
i
t
e
d
S
t
a
t
e
s
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
1
0
,
2
0
2
4
R
ev
is
ed
Ap
r
2
1
,
2
0
2
5
Acc
ep
ted
Ma
y
2
5
,
2
0
2
5
Th
is
p
a
p
e
r
e
x
a
m
in
e
s
th
e
e
ffe
c
t
o
f
ti
lt
a
n
g
le
a
n
d
trac
k
in
g
m
o
d
e
s
o
n
e
n
e
r
g
y
p
e
rfo
rm
a
n
c
e
o
f
a
P
V
sy
ste
m
u
n
d
e
r
Ira
q
i
we
a
th
e
r
c
o
n
d
it
i
o
n
s.
A
5
-
k
Wd
c
ro
o
ft
o
p
re
sid
e
n
ti
a
l
P
V
s
y
ste
m
is
m
o
d
e
led
a
n
d
sim
u
late
d
u
si
n
g
sy
ste
m
a
d
v
iso
r
m
o
d
e
l
(S
AM)
t
o
in
v
e
sti
g
a
te
it
s
o
p
ti
m
a
l
c
o
n
fig
u
ra
ti
o
n
o
f
ti
lt
a
n
g
le
a
n
d
trac
k
i
n
g
a
x
e
s
f
o
r
m
a
x
imu
m
e
n
e
rg
y
e
x
trac
ti
o
n
.
Th
e
sy
ste
m
is
sim
u
late
d
with
m
e
teo
ro
l
o
g
ica
l
d
a
tas
e
ts
fo
r
a
ll
1
8
Ira
q
i
p
ro
v
i
n
c
e
s.
Th
e
e
ffe
c
t
o
f
so
il
i
n
g
lo
ss
e
s
d
u
e
t
o
d
u
st
a
c
c
u
m
u
lati
o
n
o
n
in
c
i
d
e
n
t
irrad
ian
c
e
a
n
d
e
n
e
r
g
y
g
e
n
e
ra
ti
o
n
is
c
o
n
si
d
e
re
d
a
s
m
o
st
Ira
q
i
ter
rit
o
ries
su
ffe
r
fro
m
fre
q
u
e
n
t
d
u
st
sto
rm
s
y
e
a
rly
.
T
h
e
sy
ste
m
a
n
n
u
a
l
AC
e
n
e
rg
y
a
n
d
o
p
ti
m
a
l
ti
lt
a
n
g
les
a
re
e
v
a
lu
a
ted
a
n
d
c
o
m
p
a
re
d
in
fiv
e
d
iffere
n
t
sc
e
n
a
rio
s
in
c
lu
d
in
g
fi
x
e
d
-
a
x
is
w
it
h
ti
lt
a
t
latit
u
d
e
,
fi
x
e
d
-
a
x
is
wit
h
ti
lt
a
t
a
n
n
u
a
l
o
p
ti
m
a
l
a
n
g
le,
fix
e
d
-
a
x
is
with
ti
lt
a
t
m
o
n
th
l
y
a
n
n
u
a
l
a
n
g
le,
o
n
e
-
a
x
is
t
ra
c
k
in
g
a
n
d
d
u
a
l
-
a
x
is
trac
k
in
g
.
T
h
e
re
su
lt
s
sh
o
we
d
t
h
a
t
c
o
n
sid
e
ra
b
le
a
m
o
u
n
t
o
f
e
n
e
rg
y
is
left
u
n
h
a
rn
e
ss
e
d
i
n
fix
e
d
-
a
x
is
sc
e
n
a
rio
s
wh
e
n
ti
lt
a
n
g
les
a
re
a
d
ju
ste
d
a
t
latit
u
d
e
a
n
d
o
p
ti
m
a
l
a
n
n
u
a
l
v
a
lu
e
s.
Us
in
g
o
p
t
ima
l
m
o
n
t
h
ly
ti
lt
with
fix
e
d
-
a
x
is
imp
r
o
v
e
d
e
n
e
rg
y
e
x
t
ra
c
ti
o
n
b
y
5
-
6
%
fo
r
a
ll
lo
c
a
ti
o
n
s.
E
n
e
rg
y
p
e
rfo
rm
a
n
c
e
is
fu
rth
e
r
imp
r
o
v
e
d
with
o
n
e
-
a
x
is
trac
k
in
g
.
Du
a
l
-
a
x
is
trac
k
in
g
a
c
h
iev
e
d
h
ig
h
e
st
e
n
e
rg
y
y
ield
c
o
m
p
a
re
d
to
o
th
e
r
sc
e
n
a
rio
s.
O
v
e
ra
ll
,
m
id
-
s
o
u
t
h
p
ro
v
i
n
c
e
s
p
ro
v
i
d
e
d
h
i
g
h
e
st
e
n
e
rg
y
o
p
p
o
rt
u
n
it
ies
a
m
o
n
g
o
t
h
e
rs.
K
ey
w
o
r
d
s
:
I
r
aq
s
o
lar
Op
tim
al
tilt
PV sy
s
tem
s
PV tr
ac
k
in
g
So
lar
en
er
g
y
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ah
m
ed
Z
u
r
f
i
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
T
ec
h
n
iq
u
es,
Al
-
Hu
s
s
ain
Un
iv
er
s
ity
C
o
lleg
e
Kar
b
ala
-
Naja
f
R
o
ad
,
Kar
b
ala
5
6
0
0
1
,
I
r
a
q
E
m
ail:
ah
m
ed
.
jab
b
ar
@
u
o
k
er
b
ala.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
I
r
a
q
i
p
o
w
e
r
s
y
s
t
e
m
h
as
b
e
e
n
s
u
f
f
e
r
i
n
g
f
r
o
m
d
a
i
l
y
p
o
w
e
r
o
u
t
a
g
e
s
f
o
r
m
o
r
e
t
h
a
n
t
h
r
e
e
d
e
c
a
d
e
s
.
S
u
c
h
p
o
w
e
r
o
u
t
a
g
e
s
c
a
n
r
e
a
ch
u
p
t
o
t
w
e
l
v
e
h
o
u
r
s
p
e
r
d
a
y
,
a
n
d
t
h
e
s
i
t
u
a
ti
o
n
g
e
t
s
w
o
r
s
e
a
s
t
e
m
p
e
r
a
t
u
r
es
h
i
t
5
0
°
C
d
u
r
i
n
g
s
c
o
r
c
h
i
n
g
s
u
m
m
e
r
s
.
T
h
e
r
ea
s
o
n
b
e
h
i
n
d
t
h
i
s
p
o
w
e
r
s
h
o
r
t
a
g
e
is
a
tt
r
i
b
u
t
e
d
to
d
i
f
f
e
r
e
n
t
t
e
c
h
n
ic
al
r
e
a
s
o
n
s
i
n
c
l
u
d
i
n
g
d
e
t
e
r
i
o
r
at
i
o
n
o
f
t
h
e
p
o
w
e
r
n
e
t
w
o
r
k
i
n
f
r
a
s
t
r
u
c
t
u
r
e
,
i
n
c
r
e
a
s
i
n
g
d
e
m
a
n
d
,
l
a
c
k
o
f
p
o
w
e
r
p
l
a
n
t
s
f
u
e
l
a
s
w
e
l
l
as
o
t
h
e
r
p
o
l
i
t
i
c
a
l
an
d
f
i
n
a
n
c
i
a
l
c
h
a
l
l
e
n
g
e
s
[
1
]
.
C
u
r
r
e
n
t
l
y
,
t
h
e
t
o
t
a
l
p
o
w
e
r
g
e
n
e
r
a
t
i
o
n
i
n
I
r
a
q
i
s
a
r
o
u
n
d
2
8
,
0
0
0
M
W
,
a
n
d
t
h
i
s
a
m
o
u
n
t
c
o
v
e
r
s
o
n
l
y
a
b
o
u
t
6
0
%
o
f
t
h
e
c
o
u
n
t
r
y
’
s
t
o
t
a
l
d
e
m
a
n
d
w
h
i
c
h
i
s
e
s
t
i
m
a
t
e
d
t
o
b
e
4
0
,
0
0
0
M
W
[
2
]
.
U
t
il
i
z
i
n
g
s
u
s
ta
i
n
a
b
l
e
e
n
e
r
g
y
s
o
u
r
c
e
s
,
es
p
e
c
ia
l
l
y
s
o
l
a
r
e
n
e
r
g
y
,
i
s
o
n
e
o
f
t
h
e
k
e
y
t
o
o
l
s
t
h
a
t c
a
n
b
e
a
d
o
p
t
e
d
t
o
c
o
m
b
a
t
t
h
e
e
l
e
ct
r
i
c
p
o
w
e
r
c
r
is
i
s
i
n
I
r
a
q
a
n
d
b
r
i
d
g
e
t
h
e
g
a
p
b
e
tw
e
e
n
d
e
m
a
n
d
a
n
d
s
u
p
p
l
y
.
H
o
w
e
v
e
r
,
d
e
s
p
i
t
e
t
h
e
a
b
u
n
d
a
n
t
a
m
o
u
n
t
o
f
s
o
l
a
r
e
n
e
r
g
y
t
h
at
I
r
a
q
r
ec
e
i
v
es
t
h
r
o
u
g
h
o
u
t
t
h
e
y
e
a
r
,
s
o
l
a
r
e
n
e
r
g
y
i
s
u
n
d
e
r
u
t
i
l
i
ze
d
a
n
d
t
h
e
g
o
v
e
r
n
m
e
n
t
’
s
s
t
e
p
s
t
o
w
a
r
d
s
i
n
v
e
s
t
i
n
g
i
n
s
o
la
r
e
n
e
r
g
y
p
r
o
j
e
c
t
s
r
e
m
a
i
n
li
m
i
t
e
d
[
3
]
.
O
n
e
o
f
t
h
e
p
r
i
m
a
r
y
s
t
u
m
b
l
i
n
g
b
l
o
c
k
s
t
h
a
t
h
i
n
d
e
r
s
w
i
d
e
r
a
d
o
p
t
i
o
n
o
f
s
o
l
a
r
e
n
e
r
g
y
i
n
I
r
a
q
i
s
r
e
l
at
e
d
t
o
f
i
n
a
n
c
ia
l
lim
i
t
a
t
i
o
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
I
n
ve
s
tig
a
tio
n
o
f
o
p
tima
l tilt,
o
r
ien
ta
tio
n
a
n
d
tr
a
ck
in
g
o
f
a
s
o
la
r
P
V
s
ystem
in
I
r
a
q
(
A
h
med
Zu
r
fi
)
1915
I
n
s
t
a
l
li
n
g
p
h
o
t
o
v
o
l
t
a
i
c
(
P
V
)
s
y
s
t
e
m
s
,
w
h
e
t
h
e
r
a
s
g
r
i
d
-
s
c
a
l
e
o
r
d
i
s
t
r
i
b
u
t
e
d
,
is
c
o
n
s
i
d
e
r
e
d
a
c
a
p
i
t
a
l
-
i
n
t
e
n
s
i
v
e
p
r
o
j
e
c
t
[
4
]
.
F
o
r
i
n
s
t
an
c
e
,
h
o
m
e
o
w
n
e
r
s
f
i
n
d
i
t
u
n
a
f
f
o
r
d
a
b
l
e
a
n
d
o
u
t
o
f
t
h
e
i
r
r
e
a
c
h
t
o
i
n
s
t
a
l
l
r
o
o
f
t
o
p
P
V
s
y
s
te
m
s
.
T
h
e
r
e
f
o
r
e
,
t
h
e
e
c
o
n
o
m
i
c
f
e
a
s
i
b
i
li
t
y
o
f
s
o
la
r
e
n
e
r
g
y
s
y
s
t
e
m
s
is
a
c
r
u
c
i
a
l
f
ac
t
o
r
t
h
a
t
i
n
f
l
u
e
n
c
es
t
h
e
a
c
c
e
p
t
a
n
c
e
a
n
d
p
r
o
m
o
t
i
o
n
o
f
s
o
l
a
r
s
y
s
t
e
m
s
.
T
h
e
e
c
o
n
o
m
i
c
v
a
l
u
e
a
n
d
r
e
t
u
r
n
o
f
a
P
V
s
y
s
t
e
m
a
r
e
p
r
i
m
a
r
i
l
y
r
e
l
i
a
n
t
o
n
t
h
e
a
m
o
u
n
t
o
f
p
o
w
e
r
a
PV
s
y
s
t
e
m
g
e
n
e
r
at
e
s
a
n
n
u
a
l
l
y
.
P
u
t
d
i
f
f
e
r
e
n
t
l
y
,
t
h
e
m
o
r
e
p
o
w
e
r
t
h
e
P
V
s
y
s
t
e
m
p
r
o
v
i
d
e
s
,
t
h
e
m
o
r
e
e
c
o
n
o
m
i
c
a
ll
y
a
c
c
e
p
t
a
b
l
e
i
t
wi
l
l
b
e
.
T
h
e
am
o
u
n
t
o
f
s
o
l
a
r
r
a
d
i
a
t
i
o
n
a
PV
m
o
d
u
l
e
c
a
n
h
a
r
v
e
s
t
a
n
d
c
o
n
v
e
r
t
i
n
t
o
e
l
e
c
t
r
i
c
al
e
n
er
g
y
d
e
p
e
n
d
s
s
i
g
n
i
f
i
c
a
n
tl
y
o
n
th
e
l
o
c
a
ti
o
n
,
o
r
i
e
n
t
at
i
o
n
,
a
n
d
d
ir
e
c
t
i
o
n
o
f
t
h
e
p
a
n
e
l
w
i
t
h
r
e
f
e
r
e
n
c
e
t
o
t
h
e
s
u
n
'
s
r
a
y
s
[
5
]
,
[
6
]
.
T
h
e
r
e
f
o
r
e
,
i
m
p
r
o
p
e
r
i
n
s
t
a
ll
a
t
i
o
n
a
n
d
o
r
i
e
n
t
a
ti
o
n
o
f
P
V
s
u
b
a
r
r
a
y
s
c
a
n
a
f
f
e
c
t
t
h
ei
r
p
e
r
f
o
r
m
a
n
c
e
a
n
d
an
n
u
a
l
e
n
e
r
g
y
y
i
e
l
d
.
T
h
u
s
,
t
o
m
a
x
i
m
i
z
e
p
o
we
r
g
e
n
e
r
a
ti
o
n
f
r
o
m
a
PV
s
y
s
t
e
m
,
i
t
s
s
u
b
a
r
r
a
y
(
s
)
o
r
i
e
n
t
a
ti
o
n
m
u
s
t
b
e
o
p
t
i
m
i
z
e
d
t
o
i
n
c
r
e
as
e
t
h
e
s
u
r
f
a
c
e
a
r
e
a
e
x
p
o
s
e
d
t
o
s
o
l
a
r
i
r
r
a
d
ia
n
c
e
o
n
a
d
a
i
l
y
a
n
d
s
e
as
o
n
a
l
b
a
s
i
s
[
7
]
.
A
c
c
o
r
d
i
n
g
t
o
t
h
e
c
o
s
i
n
e
e
f
f
ec
t
[
8
]
,
m
a
x
im
u
m
i
r
r
a
d
i
a
n
c
e
h
a
r
v
e
s
t
c
a
n
b
e
a
t
t
a
i
n
e
d
w
h
e
n
t
h
e
s
u
r
f
a
c
e
o
f
a
P
V
p
a
n
e
l
is
o
r
i
e
n
te
d
s
u
c
h
t
h
at
i
t
m
a
k
e
s
a
r
i
g
h
t
an
g
l
e
w
i
t
h
t
h
e
d
i
r
e
ct
i
o
n
o
f
t
h
e
in
c
i
d
e
n
t
s
u
n
r
a
y
s
.
I
n
o
t
h
e
r
w
o
r
d
s
,
w
h
e
n
t
h
e
a
n
g
l
e
o
f
i
n
c
i
d
e
n
c
e
e
q
u
a
l
s
ze
r
o
r
e
l
a
t
i
v
e
t
o
t
h
e
n
o
r
m
a
l
p
l
a
n
e
t
o
t
h
e
P
V
m
o
d
u
l
e
s
u
r
f
a
c
e
,
a
ll
i
n
c
i
d
e
n
t
r
a
y
s
wi
l
l
p
e
n
et
r
a
t
e
t
h
e
P
V
g
l
as
s
la
y
e
r
.
O
t
h
e
r
wi
s
e
,
w
h
e
n
t
h
e
P
V
s
u
r
f
a
c
e
i
s
n
o
t
p
e
r
p
en
d
i
c
u
l
a
r
t
o
t
h
e
p
a
t
h
o
f
i
r
r
a
d
i
a
n
c
e
r
a
y
s
,
a
p
r
o
p
o
r
t
i
o
n
o
f
t
h
e
r
a
y
s
w
il
l
b
e
r
e
f
l
ec
t
e
d
aw
a
y
f
r
o
m
t
h
e
P
V
s
u
r
f
a
c
e
,
a
f
f
e
ct
i
n
g
i
ts
e
f
f
i
c
i
e
n
c
y
.
T
h
e
PV
ar
r
ay
s
u
r
f
ac
e
o
r
ien
tati
o
n
is
d
ef
in
e
d
in
ter
m
s
o
f
two
m
ain
p
ar
am
ete
r
s
,
i.e
.
,
a
n
g
les
th
at
ar
e
th
e
an
g
le
o
f
tilt
an
d
th
e
az
im
u
th
a
n
g
le.
T
h
ese
an
g
les
d
ep
en
d
o
n
th
e
tr
ac
k
in
g
a
x
es
o
f
th
e
s
u
b
ar
r
ay
.
T
h
e
r
e
ar
e
th
r
ee
d
if
f
er
en
t
co
n
f
ig
u
r
atio
n
s
o
f
PV
s
u
b
ar
r
ay
tr
ac
k
in
g
,
in
clu
d
i
n
g
f
ix
ed
,
az
im
u
t
h
,
an
d
two
-
ax
is
tr
ac
k
in
g
.
Mo
r
e
d
etails
ab
o
u
t
ea
ch
tr
ac
k
in
g
s
ch
em
e
ar
e
d
is
cu
s
s
ed
in
s
ec
t
i
o
n
3
.
Op
tim
al
s
elec
tio
n
o
f
th
e
m
o
s
t
ef
f
ec
tiv
e
co
m
b
in
atio
n
o
f
th
ese
o
r
ien
tati
o
n
p
a
r
am
eter
s
an
d
tr
ac
k
in
g
m
eth
o
d
s
,
an
d
th
ei
r
ef
f
ec
t
o
n
PV sy
s
tem
p
o
wer
y
ield
h
as
b
ee
n
a
to
p
ic
o
f
in
ter
est
o
f
a
lar
g
e
co
r
p
u
s
o
f
r
esear
ch
o
v
er
a
wid
e
r
an
g
e
o
f
g
eo
g
r
ap
h
ic
al
r
eg
io
n
s
[
9
]
,
[
1
0
]
.
E
v
alu
atio
n
o
f
o
p
tim
al
tilt
an
g
le
th
at
ac
h
iev
es
m
ax
im
u
m
p
o
wer
g
en
er
ati
o
n
b
y
a
PV
s
y
s
tem
in
th
r
ee
I
r
aq
i
g
o
v
er
n
o
r
ates
was
d
is
cu
s
s
ed
in
[
1
1
]
.
Ma
th
em
atica
l
m
o
d
els
wer
e
u
s
ed
to
esti
m
ate
p
o
wer
in
ten
s
ity
ex
tr
ac
ted
f
r
o
m
s
o
lar
r
ad
iatio
n
d
ata
in
B
ag
h
d
ad
,
Diy
ala
,
an
d
T
ik
r
it
,
wh
ich
ar
e
lo
ca
ted
o
n
th
e
s
a
m
e
latitu
d
e
th
at
i
s
b
etwe
en
3
3
°
an
d
3
4
°
.
T
h
e
r
esu
lts
s
h
o
wed
th
at
th
e
o
p
tim
al
a
n
n
u
al
an
g
le
f
o
r
th
e
th
r
ee
lo
ca
t
io
n
s
is
3
1
°
,
as
th
e
th
r
ee
cities
s
h
ar
e
th
e
s
am
e
lat
itu
d
e.
T
h
e
o
p
tim
al
m
o
n
th
l
y
tilt
an
g
le
is
d
if
f
er
en
t
f
o
r
ea
ch
city
.
H
o
wev
er
,
th
e
d
if
f
er
en
ce
is
v
er
y
s
lig
h
t
,
an
d
t
h
at
is
also
attr
ib
u
te
d
to
th
e
f
a
ct
th
at
th
e
s
tu
d
ied
l
o
ca
tio
n
s
f
all
with
in
th
e
s
am
e
latitu
d
e.
T
h
e
lim
itatio
n
o
f
th
is
s
tu
d
y
is
th
at
it
d
id
n
o
t
co
v
er
a
d
iv
er
s
e
r
an
g
e
o
f
g
eo
g
r
a
p
h
ic
al
lo
ca
tio
n
s
in
I
r
aq
.
B
esid
es,
th
e
s
im
u
lated
s
y
s
te
m
o
p
er
ates
in
a
f
ix
ed
-
tr
ac
k
i
n
g
m
o
d
e
an
d
d
o
es
n
o
t
co
n
s
id
er
th
e
ef
f
ec
t
o
f
th
e
az
im
u
th
an
g
le.
A
s
im
ilar
ef
f
o
r
t
was
m
ad
e
in
[
1
2
]
f
o
r
a
f
ix
e
d
-
ax
es
s
y
s
tem
in
Du
h
o
k
g
o
v
e
r
n
o
r
ate
,
tak
i
n
g
in
to
ac
co
u
n
t
to
p
o
g
r
ap
h
y
r
estrictio
n
s
im
p
o
s
ed
b
y
m
o
u
n
tain
s
.
T
h
e
o
p
tim
al
an
n
u
al
tilt
an
g
le
w
as
q
u
an
tifie
d
t
o
b
e
25
°
f
o
r
Du
h
o
k
.
Ho
we
v
er
,
th
e
m
o
n
th
ly
an
al
y
s
is
o
f
th
e
o
p
ti
m
al
tilt
an
g
le
was
n
o
t
d
is
cu
s
s
ed
.
T
h
is
m
atter
was
in
v
esti
g
ated
in
[
1
3
]
,
wh
ich
a
n
aly
ze
d
th
e
o
p
tim
al
an
n
u
al
an
d
m
o
n
th
l
y
tilt
an
g
le
o
f
a
s
i
m
u
lated
PV
s
y
s
tem
lo
ca
ted
in
Du
h
o
k
.
C
o
m
p
a
r
ed
to
[
1
2
]
,
th
e
o
p
tim
al
an
n
u
al
tilt
an
g
le
was
ev
alu
ated
to
b
e
3
2
.
7
°
wh
ile
th
e
o
p
tim
al
m
o
n
t
h
ly
tilt
an
g
le
r
a
n
g
ed
f
r
o
m
1
.
5
°
to
6
4
°
d
ep
en
d
in
g
o
n
th
e
m
o
n
t
h
s
o
f
th
e
y
ea
r
.
Ho
wev
er
,
th
e
an
aly
s
is
d
id
n
o
t
tak
e
in
to
ac
co
u
n
t
th
e
az
im
u
th
tr
ac
k
in
g
ef
f
ec
t.
T
h
e
o
p
tim
u
m
tilt
o
f
Du
h
o
k
was
al
s
o
ev
alu
ated
in
[
1
4
]
a
n
d
p
r
o
v
i
d
ed
d
if
f
er
en
t
o
p
tim
al
an
n
u
al
an
d
m
o
n
th
ly
tilt
an
g
les
co
m
p
ar
ed
to
[
1
3
]
.
T
h
e
o
p
tim
al
an
n
u
al
tilt
an
g
le
was
3
6
.
8
8
°
,
wh
ich
is
h
ig
h
er
th
an
th
e
v
alu
e
o
b
tain
ed
in
[
1
3
]
.
No
ticea
b
le
d
if
f
er
en
ce
s
wer
e
also
o
b
s
er
v
ed
in
th
e
o
p
tim
al
m
o
n
th
ly
tilt
s
in
all
m
o
n
th
s
,
b
u
t
th
e
v
ar
ian
ce
was
m
o
r
e
s
ig
n
if
ican
t
in
s
u
m
m
er
,
p
ar
ticu
lar
ly
th
e
m
o
n
th
s
o
f
M
ay
,
J
u
n
e,
J
u
ly
,
an
d
Au
g
u
s
t.
T
h
e
o
p
tim
al
tilt
o
f
a
s
o
lar
s
y
s
tem
in
B
ag
h
d
ad
was
d
is
cu
s
s
ed
in
[
1
5
]
an
d
[
1
6
]
f
o
r
a
f
ix
ed
-
an
g
le
s
y
s
tem
,
an
d
in
[
1
7
]
f
o
r
a
o
n
e
-
ax
is
tr
ac
k
in
g
s
y
s
tem
,
an
d
in
[
1
8
]
f
o
r
a
two
-
ax
is
tr
ac
k
in
g
s
y
s
tem
.
Du
h
is
et
a
l.
[
1
9
]
d
is
cu
s
s
ed
th
e
ef
f
ec
t
o
f
alb
e
d
o
o
n
th
e
a
m
o
u
n
t
o
f
in
cid
en
t
r
ad
iatio
n
an
d
p
o
wer
g
en
e
r
ated
b
y
a
6
9
0
W
,
o
f
f
-
g
r
id
PV
s
y
s
t
em
in
s
talled
in
Kar
b
ala.
T
h
e
co
r
r
elatio
n
b
etwe
en
alb
ed
o
v
alu
e
a
n
d
o
p
tim
al
tilt
an
g
le
was
s
tu
d
ied
b
y
ev
al
u
atin
g
a
n
d
c
o
m
p
a
r
in
g
th
e
g
ain
i
n
s
y
s
tem
en
er
g
y
y
ield
at
d
if
f
er
en
t
s
ettin
g
s
o
f
alb
ed
o
v
alu
e
an
d
tilt
o
r
ien
tatio
n
s
.
Ho
wev
er
,
a
m
o
n
th
ly
a
n
aly
s
is
was
n
o
t
p
r
o
v
id
ed
.
I
n
s
ig
h
ts
o
n
th
e
o
p
tim
al
tilt
an
g
les
o
f
PV
p
an
els
in
f
o
u
r
d
if
f
er
en
t
I
r
a
q
i
cities
wer
e
o
f
f
er
e
d
in
[
2
0
]
.
T
h
e
r
esu
lts
co
n
f
ir
m
e
d
th
at
ad
ju
s
tin
g
t
h
e
a
n
n
u
al
tilt
an
g
le
to
b
e
eq
u
al
to
th
e
lo
ca
tio
n
latitu
d
e
ca
n
b
e
a
f
ea
s
ib
le
ch
o
ice
to
ex
tr
ac
t
m
ax
im
u
m
p
o
wer
b
y
a
PV
s
y
s
tem
.
Ab
d
u
llah
an
d
A
b
d
u
lk
ar
im
[
2
1
]
s
h
ed
lig
h
t
o
n
th
e
f
ea
s
ib
ilit
y
o
f
a
s
im
u
lated
h
o
m
e
PV
s
y
s
tem
in
E
r
b
il
th
at
u
tili
ze
d
a
tr
ac
k
in
g
m
ec
h
an
is
m
an
d
co
m
p
a
r
ed
th
e
s
y
s
tem
en
er
g
y
p
er
f
o
r
m
an
ce
u
n
d
er
o
n
e
-
a
x
is
an
d
two
-
ax
is
m
o
d
es.
T
h
e
in
v
esti
g
atio
n
s
p
r
esen
ted
i
n
th
e
af
o
r
em
en
tio
n
e
d
liter
atu
r
e
wer
e
ea
c
h
lim
ited
to
ce
r
tain
lo
ca
tio
n
s
an
d
cities,
an
d
t
h
ey
d
id
n
o
t
lo
o
k
at
all
g
o
v
er
n
o
r
ates
at
th
e
s
am
e
tim
e
,
w
h
ich
m
a
k
es
it
h
ar
d
to
g
ain
co
m
p
ar
ativ
e
in
s
ig
h
ts
b
etwe
en
s
o
lar
p
o
ten
tial
o
f
d
if
f
er
e
n
t
I
r
a
q
i
lo
ca
tio
n
s
.
B
esid
es,
th
e
r
ev
i
ewe
d
wo
r
k
s
d
id
n
o
t
co
n
s
id
er
d
i
f
f
er
en
t
o
r
ien
tatio
n
tr
ac
k
in
g
s
ch
em
es
,
in
cl
u
d
in
g
o
n
e
-
a
x
is
an
d
two
-
ax
is
tr
ac
k
in
g
to
g
et
h
er
with
o
p
tim
al
tilt
an
aly
s
is
.
T
h
e
f
o
r
m
er
s
h
o
r
tco
m
in
g
was
ad
d
r
ess
ed
in
[
2
2
]
,
wh
ich
s
tu
d
ied
th
e
ef
f
ec
t
o
f
o
p
tim
al
tilt
an
g
le
o
n
e
n
er
g
y
p
e
r
f
o
r
m
an
ce
o
f
PV
p
an
els
in
1
5
I
r
aq
i
g
o
v
er
n
o
r
ates,
ex
clu
d
in
g
Ku
r
d
is
tan
r
eg
io
n
g
o
v
er
n
o
r
ates.
Ho
wev
e
r
,
tr
ac
k
i
n
g
ax
es
wer
e
n
o
t
in
clu
d
ed
i
n
t
h
e
s
tu
d
y
.
Fr
o
m
th
e
liter
atu
r
e
r
ev
iew
ab
o
v
e,
it
ca
n
b
e
s
aid
th
at
d
if
f
e
r
en
t
ap
p
r
o
a
ch
es
wer
e
u
s
ed
to
ev
al
u
ate
o
p
tim
al
o
r
ien
tatio
n
co
n
d
itio
n
s
o
f
PV
s
y
s
tem
s
to
m
ax
im
ize
th
eir
en
er
g
y
p
r
o
d
u
ctio
n
.
T
h
ese
ap
p
r
o
ac
h
es
wer
e
eith
er
b
ased
o
n
n
u
m
e
r
ical
ev
alu
atio
n
o
f
m
ath
em
atica
l
m
o
d
els
o
r
o
n
u
s
in
g
v
ar
io
u
s
s
o
lar
s
im
u
latio
n
to
o
ls
.
T
h
er
ef
o
r
e,
it
is
ch
allen
g
in
g
to
m
ak
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
191
4
-
1
9
2
5
1916
co
n
s
is
ten
t
d
ec
is
io
n
s
ab
o
u
t
th
e
p
r
ec
is
e
o
p
tim
al
tilt
o
r
ien
tatio
n
f
o
r
a
ce
r
tain
lo
ca
tio
n
b
ased
o
n
th
e
s
cr
u
tin
ized
co
n
tr
ib
u
tio
n
s
b
ec
au
s
e
t
h
e
r
e
s
u
lts
ar
e
d
is
cr
ep
an
t
a
n
d
d
is
ag
r
ee
to
s
o
m
e
e
x
ten
t.
T
h
is
d
is
cr
ep
an
cy
is
also
attr
ib
u
ted
to
th
e
u
s
e
o
f
d
if
f
e
r
en
t
wea
th
er
d
atasets
f
r
o
m
d
if
f
er
en
t
r
eso
u
r
ce
s
.
T
h
e
o
t
h
er
s
h
o
r
tco
m
in
g
th
at
h
as
b
ee
n
id
e
n
tifie
d
in
th
e
r
ev
iewe
d
liter
atu
r
e
is
th
at
ir
r
ad
ia
n
ce
l
o
s
s
es
d
u
e
to
th
e
s
o
ilin
g
e
f
f
ec
t w
er
e
n
o
t
c
o
n
s
id
er
ed
in
th
e
an
aly
s
is
,
wh
ich
ca
n
lead
to
an
in
ac
c
u
r
ate
ev
alu
atio
n
o
f
PV sy
s
tem
p
er
f
o
r
m
an
ce
.
T
h
e
aim
o
f
th
is
wo
r
k
is
to
o
v
er
co
m
e
th
ese
ch
allen
g
es b
y
p
r
o
v
id
in
g
a
co
u
n
tr
y
wid
e
,
co
m
p
lete
an
aly
s
is
o
f
o
p
tim
al
tilt
an
g
le
an
d
o
r
ien
tatio
n
o
f
a
PV
s
y
s
tem
in
I
r
aq
.
Mo
n
th
ly
,
s
ea
s
o
n
al
,
an
d
y
ea
r
l
y
v
alu
es
o
f
o
p
tim
al
tilt
an
g
le
with
o
n
e
-
ax
is
an
d
two
-
ax
is
tr
ac
k
in
g
ar
e
in
v
esti
g
ated
u
s
in
g
th
e
Sy
s
tem
Ad
v
is
o
r
Mo
d
el
(
SAM)
f
r
o
m
th
e
Natio
n
al
R
en
ewa
b
le
E
n
er
g
y
L
a
b
o
r
ato
r
y
(
NR
E
L
)
[
2
3
]
wh
ich
p
r
o
v
id
es
a
s
o
lar
p
e
r
f
o
r
m
an
ce
m
o
d
el
b
ased
o
n
s
o
lar
an
d
m
eteo
r
o
lo
g
ical
d
atasets
f
r
o
m
th
e
Natio
n
al
So
lar
R
ad
iatio
n
Data
b
ase
(
NSR
D
B
)
an
d
o
th
er
s
o
u
r
ce
s
,
tak
in
g
in
to
c
o
n
s
id
er
atio
n
s
y
s
tem
lo
s
s
es
,
in
clu
d
in
g
ir
r
ad
ia
n
ce
an
d
elec
tr
ical
lo
s
s
es.
T
h
e
r
em
ain
in
g
p
ar
t
o
f
th
is
m
an
u
s
cr
ip
t
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws
:
i)
I
n
s
ec
tio
n
2
,
th
e
m
ath
em
atica
l
r
elatio
n
s
h
ip
s
b
etwe
en
th
e
co
m
p
o
n
en
ts
o
f
s
o
lar
ir
r
ad
ia
n
ce
ar
e
p
r
esen
te
d
b
ased
o
n
g
e
o
m
etr
ic
an
aly
s
is
in
th
e
ca
s
e
o
f
s
lo
p
ed
s
u
r
f
ac
es
;
ii)
Sectio
n
3
d
is
cu
s
s
es
th
e
r
es
ea
r
ch
m
eth
o
d
o
lo
g
y
in
clu
d
in
g
th
e
d
esig
n
o
f
th
e
PV
s
y
s
tem
an
d
th
e
s
im
u
latio
n
en
v
ir
o
n
m
en
t
;
iii)
T
h
e
r
esu
lts
a
r
e
d
is
cu
s
s
ed
in
s
ec
tio
n
4
in
f
iv
e
s
ce
n
ar
io
s
; a
n
d
iv
)
Sectio
n
5
is
d
ed
icate
d
f
o
r
th
e
co
n
clu
s
io
n
s
an
d
t
h
o
u
g
h
ts
ab
o
u
t f
u
r
th
e
r
r
esear
ch
b
ased
o
n
th
is
wo
r
k
.
2.
T
H
E
CO
M
P
RE
H
E
NS
I
VE
T
H
E
O
RE
T
I
CA
L
B
ASI
S
2
.
1
.
M
a
t
hema
t
ica
l
des
cr
iptio
n o
f
s
o
la
r
ra
dia
t
io
n a
nd
o
pt
im
a
l t
ilt
T
ilt
an
g
le
an
d
az
im
u
th
o
r
ie
n
tatio
n
p
lay
a
cr
u
cial
r
o
le
in
m
ax
im
izin
g
PV
p
an
el
ex
p
o
s
u
r
e
to
s
o
lar
r
ad
iatio
n
a
n
d
,
co
n
s
eq
u
en
tly
,
m
ax
im
izin
g
en
e
r
g
y
g
en
e
r
at
io
n
[
2
4
]
.
T
o
ev
alu
ate
th
e
o
p
tim
u
m
v
alu
es
an
d
s
ettin
g
s
o
f
th
ese
an
g
les
in
a
n
y
PV
s
y
s
tem
,
it
is
im
p
o
r
ta
n
t
f
ir
s
t
to
u
n
d
e
r
s
tan
d
th
e
b
e
h
av
io
r
an
d
m
ec
h
an
is
m
s
o
f
s
o
lar
r
ad
iatio
n
th
at
is
r
ec
eiv
e
d
b
y
a
h
o
r
izo
n
tal
p
lan
e
m
o
u
n
ted
o
n
E
ar
th
'
s
s
u
r
f
ac
e.
B
ef
o
r
e
s
tr
ik
in
g
E
a
r
th
,
s
o
lar
r
ad
iatio
n
r
ay
s
tr
av
el
th
r
o
u
g
h
th
e
atm
o
s
p
h
er
e,
an
d
p
ar
t
o
f
t
h
at
s
o
lar
r
ad
iatio
n
is
lo
s
t
d
u
e
t
o
ab
s
o
r
p
tio
n
b
y
th
e
p
ar
ticles
an
d
m
o
lecu
les
th
at
f
ill
th
e
atm
o
s
p
h
e
r
e.
An
o
th
er
p
ar
t
o
f
s
o
lar
r
a
d
iatio
n
s
ca
tter
s
d
u
e
to
th
e
s
am
e
ef
f
ec
t
;
h
o
we
v
er
,
it
s
till
r
ea
ch
e
s
th
e
s
u
r
f
ac
e
o
f
th
e
E
ar
th
.
T
h
e
r
ef
o
r
e,
d
ep
e
n
d
in
g
o
n
th
is
b
eh
a
v
io
r
,
t
h
er
e
a
r
e
two
d
if
f
er
en
t
d
e
f
in
itio
n
s
(
co
m
p
o
n
e
n
ts
)
o
f
s
o
lar
ir
r
ad
ian
ce
th
at
f
al
l
o
n
a
h
o
r
izo
n
tal
s
u
r
f
ac
e
s
tatio
n
ed
o
n
E
a
r
th
.
T
h
e
co
m
p
o
n
en
t
o
f
s
o
lar
ir
r
ad
ian
ce
th
at
f
alls
o
n
a
f
lat
s
u
r
f
ac
e
in
a
n
o
r
m
al
d
ir
ec
tio
n
is
d
ef
in
ed
as
th
e
d
ir
ec
t
n
o
r
m
al
ir
r
ad
ian
ce
(
DNI
)
.
I
t
r
ep
r
esen
t
s
th
e
q
u
an
tity
o
f
s
o
lar
f
l
u
x
p
er
s
q
u
a
r
e
m
ete
r
th
at
is
co
ll
ec
ted
b
y
a
s
u
r
f
ac
e
v
er
tical
to
th
e
d
ir
ec
tio
n
o
f
t
h
e
s
u
n
th
r
o
u
g
h
a
n
ar
r
o
w
s
o
lid
a
n
g
le.
T
h
e
DNI
co
m
p
o
n
e
n
t
co
n
s
titu
tes
th
e
h
ig
h
est
am
o
u
n
t
o
f
ir
r
ad
ian
ce
r
ea
ch
in
g
th
e
s
u
r
f
ac
e
,
esp
ec
ially
o
n
cle
ar
d
ay
s
.
DNI
is
cr
u
cial
f
o
r
s
o
l
ar
en
er
g
y
s
y
s
tem
s
th
at
d
ep
en
d
o
n
co
n
ce
n
tr
ated
s
o
lar
ir
r
ad
ian
ce
.
T
h
e
o
th
er
c
o
m
p
o
n
en
t
o
f
s
o
lar
ir
r
ad
ian
ce
th
at
is
s
ca
tter
ed
o
r
d
if
f
u
s
ed
th
r
o
u
g
h
o
u
t
th
e
am
b
i
en
t
b
y
o
b
jects
s
u
ch
as
clo
u
d
s
is
d
ef
in
ed
as
th
e
d
if
f
u
s
e
h
o
r
izo
n
tal
ir
r
ad
ian
ce
(
DHI
)
.
I
t
is
th
e
am
o
u
n
t
o
f
s
o
l
ar
ir
r
ad
ian
ce
th
at
is
r
ec
eiv
ed
b
y
a
h
o
r
izo
n
tal
s
u
r
f
ac
e
p
er
u
n
it
ar
ea
f
r
o
m
s
u
n
r
a
y
s
th
at
ar
e
n
o
t
d
ir
ec
tly
co
m
in
g
f
r
o
m
th
e
s
u
n
[
2
4
]
.
T
h
e
s
u
m
o
f
th
ese
two
co
m
p
o
n
en
ts
is
d
e
f
in
ed
as
th
e
g
lo
b
al
h
o
r
izo
n
tal
ir
r
a
d
ian
ce
(
GHI
)
,
wh
ich
co
n
s
titu
tes
th
e
to
tal
s
o
lar
ir
r
ad
ian
ce
r
ec
ei
v
ed
b
y
a
h
o
r
izo
n
tal
p
lan
e
with
r
esp
ec
t to
th
e
g
r
o
u
n
d
lev
el.
M
ath
em
atica
lly
,
GHI
,
DNI
,
an
d
DHI
ca
n
b
e
r
elate
d
as
(
1
)
[
2
5
]
.
=
+
c
os
(
1
)
W
h
er
e
,
an
d
ar
e
th
e
GHI
,
DNI
,
an
d
DHI
c
o
m
p
o
n
en
ts
,
r
esp
ec
tiv
ely
.
is
th
e
ze
n
ith
a
n
g
le
wh
ich
r
ep
r
esen
ts
th
e
an
g
le
th
at
DNI
r
ay
s
m
ak
e
with
th
e
v
er
tical
d
i
r
ec
tio
n
.
Fig
u
r
e
1
s
h
o
ws
a
d
iag
r
am
th
at
p
r
o
v
id
es
f
u
r
th
er
d
escr
ip
tio
n
o
f
GHI
co
m
p
o
n
e
n
ts
.
Fo
r
a
tilt
ed
s
u
r
f
ac
e
s
lo
p
ed
at
an
an
g
le
with
r
esp
ec
t
to
th
e
g
r
o
u
n
d
lev
el,
it
is
r
eq
u
ir
ed
to
ev
alu
ate
th
e
to
tal
am
o
u
n
t
o
f
r
ad
iatio
n
th
e
tilt
ed
s
u
r
f
ac
e
r
ec
eiv
es
in
t
er
m
s
o
f
g
lo
b
al
r
ad
iatio
n
o
f
a
h
o
r
izo
n
tal
s
u
r
f
ac
e
,
tak
in
g
in
to
ac
co
u
n
t
th
e
i
n
clin
atio
n
ef
f
ec
t
o
n
t
h
e
d
ir
ec
t
a
n
d
d
if
f
u
s
e
co
m
p
o
n
e
n
ts
.
T
h
e
b
eh
av
io
r
o
f
th
e
d
if
f
u
s
e
r
ad
iatio
n
c
o
m
p
o
n
en
t
m
ain
ly
d
ep
en
d
s
o
n
t
h
e
s
k
y
d
o
m
e
co
n
d
itio
n
s
in
ter
m
s
o
f
cl
o
u
d
in
ess
,
r
ef
lectiv
ity
o
f
t
h
e
s
u
r
r
o
u
n
d
in
g
s
,
a
n
d
o
th
er
e
n
v
i
r
o
n
m
en
tal
c
o
n
d
itio
n
s
.
T
h
er
e
f
o
r
e,
th
e
to
tal
d
aily
s
o
lar
r
ad
iatio
n
o
n
a
s
lo
p
ed
s
u
r
f
ac
e,
is
g
iv
en
in
(
2
)
[
2
6
]
,
[
2
7
]
.
=
+
+
(
2
)
W
h
er
e
is
th
e
d
aily
d
ir
ec
t r
ad
iatio
n
co
m
p
o
n
en
t r
ec
eiv
e
d
b
y
t
h
e
tilt
ed
s
u
r
f
ac
e
in
(
W
/m
2
)
,
is
th
e
d
if
f
u
s
e
r
ad
iatio
n
co
m
p
o
n
en
t
o
n
th
e
tilt
ed
s
u
r
f
ac
e
in
(
W
/m
2
)
,
an
d
is
th
e
r
ad
iatio
n
c
o
m
p
o
n
en
t
r
e
f
lecte
d
o
f
f
th
e
g
r
o
u
n
d
an
d
r
ec
eiv
e
d
b
y
th
e
s
u
r
f
ac
e
in
(
W
/m
2
).
T
h
e
d
a
i
l
y
d
i
r
e
ct
r
a
d
i
at
i
o
n
c
o
m
p
o
n
e
n
t
,
i
n
(
2
)
c
a
n
b
e
e
v
a
l
u
at
ed
i
n
t
e
r
m
s
o
f
t
h
e
m
o
n
t
h
l
y
a
v
e
r
a
g
e
o
f
t
h
e
d
a
i
l
y
g
l
o
b
a
l
,
a
n
d
d
i
f
f
u
s
e
,
r
a
d
i
a
t
i
o
n
c
o
m
p
o
n
e
n
t
s
r
e
c
ei
v
e
d
b
y
a
h
o
r
i
z
o
n
t
a
l
s
u
r
f
a
c
e
as
(
3
)
[
2
6
]
,
[
2
7
]
.
=
(
−
)
×
(
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
I
n
ve
s
tig
a
tio
n
o
f
o
p
tima
l tilt,
o
r
ien
ta
tio
n
a
n
d
tr
a
ck
in
g
o
f
a
s
o
la
r
P
V
s
ystem
in
I
r
a
q
(
A
h
med
Zu
r
fi
)
1917
W
h
er
e
is
th
e
r
atio
o
f
th
e
av
er
ag
e
p
er
-
d
a
y
d
ir
ec
t
r
ad
iatio
n
o
n
a
tilt
ed
s
u
r
f
ac
e
to
th
at
o
n
a
h
o
r
izo
n
tal
s
u
r
f
ac
e
o
v
er
a
p
er
io
d
o
f
a
m
o
n
th
.
T
h
e
v
a
l
u
e
o
f
d
e
p
e
n
d
s
o
n
t
h
e
h
e
m
i
s
p
h
e
r
i
c
l
o
ca
t
i
o
n
o
f
t
h
e
s
u
r
f
a
c
e
t
i
lt
e
d
t
o
w
a
r
d
s
t
h
e
e
q
u
a
t
o
r
.
F
o
r
a
s
y
s
te
m
l
o
c
a
t
e
d
i
n
t
h
e
n
o
r
th
e
r
n
h
e
m
is
p
h
e
r
e
(
i
n
t
h
e
c
a
s
e
o
f
I
r
a
q
)
,
c
a
n
b
e
e
x
p
r
e
s
s
e
d
as
(
4
)
.
=
co
s
(
∅
−
)
co
s
s
i
n
+
(
/
180
)
s
i
n
(
∅
−
)
s
i
n
co
s
∅
co
s
s
i
n
+
(
/
180
)
s
i
n
∅
s
i
n
(
4
)
W
h
er
e
∅
is
th
e
latitu
d
e
;
is
th
e
tilt
an
g
le
o
f
th
e
s
u
r
f
ac
e
with
r
esp
ec
t
to
th
e
h
o
r
izo
n
tal
lev
el
;
is
th
e
s
u
n
an
g
u
lar
lo
ca
tio
n
in
th
e
s
k
y
at
th
e
m
o
m
e
n
t
wh
e
n
it
is
at
its
h
ig
h
est
elev
atio
n
;
an
d
is
th
e
a
zim
u
th
an
g
le
at
astro
n
o
m
ical
s
u
n
s
et
with
r
esp
ec
t
to
th
e
tilt
ed
s
u
r
f
ac
e.
T
h
e
d
aily
g
r
o
u
n
d
-
r
ef
lecte
d
r
a
d
iatio
n
co
m
p
o
n
en
t
ca
n
b
e
ex
p
r
ess
ed
as
(
5
)
.
=
×
(
1
−
co
s
)
2
(
5
)
W
h
er
e
is
g
r
o
u
n
d
r
ef
lectiv
ity
.
Un
l
ik
e,
an
d
w
h
i
c
h
o
b
v
i
o
u
s
ly
ca
n
b
e
m
ea
s
u
r
e
d
wit
h
o
u
t
d
i
f
f
i
cu
l
ties
,
as
ca
n
b
e
s
e
e
n
i
n
(
3
)
a
n
d
(
5
)
,
is
s
tr
o
n
g
l
y
a
f
f
e
cte
d
b
y
its
d
is
t
r
i
b
u
ti
o
n
t
h
r
o
u
g
h
o
u
t
th
e
s
k
y
d
o
m
e
,
a
n
d
m
ea
s
u
r
i
n
g
it
is
n
o
t
a
s
tr
a
ig
h
t
f
o
r
wa
r
d
p
r
o
c
ess
.
T
h
e
r
e
ar
e
t
wo
m
o
d
els
u
s
e
d
t
o
ev
al
u
a
te
t
h
e
d
if
f
u
s
e
c
o
m
p
o
n
e
n
t
:
th
e
i
s
o
t
r
o
p
i
c
m
o
d
el
an
d
th
e
a
n
is
o
t
r
o
p
i
c
m
o
d
e
l.
T
h
e
ch
ief
d
i
f
f
e
r
e
n
c
e
b
et
we
en
th
e
tw
o
m
o
d
e
ls
li
es
i
n
t
h
e
wa
y
t
h
e
y
in
co
r
p
o
r
ate
th
e
s
k
y
ef
f
e
ct
o
n
t
h
e
d
if
f
u
s
e
r
a
d
i
ati
o
n
c
o
m
p
o
n
e
n
t
.
I
n
t
h
e
is
o
t
r
o
p
i
c
m
o
d
el
,
wh
ic
h
is
th
e
f
o
c
u
s
o
f
t
h
is
wo
r
k
,
a
n
ap
p
r
o
x
i
m
a
ti
o
n
is
m
ad
e
b
y
ass
u
m
i
n
g
t
h
a
t
t
h
e
s
k
y
d
i
f
f
u
s
e
c
o
m
p
o
n
e
n
t
is
u
n
i
f
o
r
m
l
y
d
is
t
r
i
b
u
te
d
th
r
o
u
g
h
o
u
t
t
h
e
s
k
y
d
o
m
e
[
2
6
]
.
T
h
er
e
f
o
r
e
,
ac
c
o
r
d
i
n
g
t
o
a
n
is
o
tr
o
p
i
c
m
o
d
el,
t
h
e
d
ail
y
d
i
f
f
u
s
e
c
o
m
p
o
n
e
n
t
ca
n
b
e
ca
l
cu
lat
ed
as
(
6
)
.
=
×
(
1
+
co
s
)
2
(
6
)
T
h
u
s
,
th
e
to
tal
d
aily
s
o
lar
ir
r
a
d
ian
ce
o
n
a
tilt
ed
s
u
r
f
ac
e
is
ex
p
r
ess
ed
as
(
7
)
.
=
(
−
)
×
+
×
(
1
+
co
s
)
2
+
×
(
1
−
co
s
)
2
(
7
)
I
t
is
clea
r
t
h
at
th
e
to
tal
am
o
u
n
t
o
f
s
o
lar
r
a
d
iatio
n
a
tilt
ed
s
u
r
f
ac
e
r
ec
eiv
es
p
er
d
ay
s
tr
o
n
g
ly
d
ep
e
n
d
s
o
n
th
e
tilt
an
g
le,
in
a
n
o
n
lin
ea
r
r
elatio
n
s
h
ip
.
Hen
ce
,
th
e
o
p
tim
al
v
alu
e
o
f
ca
n
b
e
s
elec
ted
as
th
e
v
alu
e
at
wh
ich
is
m
ax
im
ized
at
ce
r
tain
v
alu
es o
f
th
e
o
th
er
p
ar
am
eter
s
in
(
7
)
.
Fig
u
r
e
1
.
R
ad
iatio
n
c
o
m
p
o
n
en
ts
r
ec
eiv
ed
b
y
a
s
u
r
f
ac
e
h
o
r
izo
n
tal
to
g
r
o
u
n
d
lev
el
2
.
2
.
P
V
pa
nel a
ng
les a
nd
s
un
t
ra
ck
ing
T
h
e
o
r
ie
n
tatio
n
o
f
a
PV
p
an
el
s
u
r
f
ac
e
is
s
elec
ted
in
ter
m
s
o
f
two
an
g
les
th
at
ar
e
th
e
tilt
a
n
g
le,
wh
ich
was
d
escr
ib
ed
in
d
etail
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
,
an
d
th
e
az
i
m
u
th
an
g
le
wh
ich
is
b
asically
th
e
p
an
el’
s
s
u
r
f
ac
e
alig
n
m
en
t
with
th
e
s
u
n
p
o
s
itio
n
alo
n
g
t
h
e
n
o
r
th
-
to
-
s
o
u
th
d
ir
ec
tio
n
[
2
8
]
.
Acc
o
r
d
in
g
to
t
h
e
co
n
f
ig
u
r
atio
n
o
f
th
e
PV
p
an
els
m
o
u
n
tin
g
s
tr
u
ctu
r
e
,
th
er
e
ar
e
f
o
u
r
m
o
d
es
o
f
PV
tr
ac
k
in
g
th
at
ar
e
th
e
f
ix
ed
m
o
d
e
,
az
im
u
th
tr
ac
k
in
g
,
one
-
ax
is
tr
ac
k
in
g
a
n
d
th
e
two
-
ax
is
tr
ac
k
in
g
m
o
d
es
[
2
3
]
,
[
2
9
]
.
I
n
th
e
f
ir
s
t
m
o
d
e,
th
e
p
an
els
ar
e
s
tatio
n
ar
y
an
d
in
s
talled
at
a
f
ix
ed
tilt
an
d
az
i
m
u
th
an
g
le,
=
.
I
n
o
n
e
-
a
x
i
s
m
o
d
e
,
th
e
p
a
n
e
ls
a
r
e
ad
ju
s
te
d
a
t
a
f
i
x
e
d
az
i
m
u
t
h
an
g
l
e
,
=
a
n
d
t
i
l
t
a
n
g
l
e
,
=
b
u
t
t
h
e
y
r
o
t
a
t
e
a
l
o
n
g
t
h
e
t
i
l
t
e
d
a
x
i
s
f
r
o
m
e
a
s
t
t
o
w
e
s
t
t
h
r
o
u
g
h
o
u
t
t
h
e
d
a
y
t
i
m
e
.
I
n
az
im
u
th
t
r
ac
k
i
n
g
,
t
h
e
p
a
n
e
l
s
t
r
a
c
k
t
h
e
s
u
n
a
z
i
m
u
t
h
a
n
g
l
e
t
h
r
o
u
g
h
o
u
t
t
h
e
d
a
y
w
h
i
l
e
a
d
j
u
s
t
e
d
a
t
a
f
i
x
ed
t
i
l
t
a
n
g
l
e
,
=
(
)
,
=
.
I
n
t
w
o
-
a
x
i
s
t
r
a
c
k
i
n
g
,
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
191
4
-
1
9
2
5
1918
t
h
e
m
o
d
u
l
e
s
’
t
i
l
t
a
n
d
a
z
i
m
u
t
h
a
n
g
l
e
s
a
r
e
a
d
j
u
s
t
e
d
t
o
f
o
l
lo
w
s
u
n
p
o
s
i
ti
o
n
o
n
s
e
aso
n
al
a
n
d
d
a
i
l
y
b
a
s
i
s
.
T
h
e
r
e
f
o
r
e
,
t
h
e
t
i
l
t
an
d
az
im
u
t
h
a
n
g
les
b
ec
o
m
e
tim
e
r
ela
te
d
an
d
a
r
e
e
x
p
r
e
s
s
ed
as
=
(
)
,
=
(
)
,
r
es
p
e
cti
v
e
ly
.
3.
M
E
T
H
O
DO
L
O
G
Y
A
5
k
W
d
c
r
o
o
f
to
p
PV
s
y
s
te
m
was
d
esig
n
ed
an
d
m
o
d
ele
d
in
s
y
s
tem
ad
v
is
o
r
m
o
d
el
(
SAM)
f
o
r
o
p
tim
al
tilt
an
d
o
r
ien
tatio
n
s
im
u
latio
n
s
with
wea
th
er
d
ata
f
o
r
all
I
r
aq
i
p
r
o
v
i
n
ce
s
.
T
h
e
PV
ar
r
ay
was
d
esig
n
e
d
with
o
n
e
s
tr
in
g
wh
ich
co
n
s
is
ts
o
f
1
0
(
5
0
0
W
d
c,
4
2
Vd
c
,
Mo
n
o
cr
y
s
tallin
e
s
ilico
n
)
m
o
d
u
les
in
s
er
ies.
On
e
P
V
in
v
er
ter
with
ca
p
ac
ity
o
f
4
.
3
7
k
W
d
c,
4
.
2
k
W
ac
was u
s
ed
to
ac
h
iev
e
a
DC
to
AC
r
atio
o
f
1
.
1
9
.
All
o
f
th
e
s
y
s
te
m
AC
p
o
we
r
g
e
n
e
r
a
te
d
is
s
u
p
p
o
s
ed
to
b
e
d
el
iv
e
r
e
d
t
o
t
h
e
AC
li
n
e
,
i
.
e
.
,
n
o
p
o
w
er
cu
r
t
ail
m
e
n
t
li
m
i
t
is
u
s
ed
.
T
h
e
PV
s
y
s
t
em
d
o
es
n
o
t
in
cl
u
d
e
a
n
y
b
atte
r
y
e
n
e
r
g
y
s
to
r
a
g
e
as
t
h
e
m
ai
n
p
u
r
p
o
s
e
o
f
th
e
s
im
u
l
ate
d
s
y
s
t
em
is
to
e
v
al
u
at
e
its
e
n
e
r
g
y
p
e
r
f
o
r
m
a
n
c
e
wi
th
r
es
p
e
ct
t
o
d
i
f
f
er
e
n
t
ti
lt
a
n
d
o
r
ie
n
t
ati
o
n
s
et
ti
n
g
s
.
Sh
a
d
i
n
g
e
f
f
e
ct
is
n
o
t
co
n
s
i
d
er
ed
as
t
h
e
s
y
s
te
m
is
ass
u
m
e
d
t
o
b
e
in
s
tall
e
d
o
n
a
cle
ar
r
o
o
f
t
o
p
wit
h
o
u
t
s
h
a
d
i
n
g
o
b
je
cts.
H
o
w
e
v
e
r
,
i
r
r
a
d
ia
n
ce
l
o
s
s
es
c
au
s
e
d
b
y
s
o
ili
n
g
is
c
o
n
s
i
d
e
r
e
d
a
n
d
in
c
o
r
p
o
r
at
ed
i
n
t
h
e
s
y
s
te
m
a
n
a
ly
s
is
b
e
ca
u
s
e
i
t
is
o
n
e
o
f
t
h
e
m
a
in
c
o
n
t
r
i
b
u
ti
o
n
s
o
f
t
h
is
w
o
r
k
.
S
o
i
li
n
g
is
d
ef
in
e
d
as
t
h
e
e
f
f
e
ct
o
f
p
a
r
ti
cl
es
ac
c
u
m
u
lat
io
n
s
u
ch
as
d
u
s
t
,
b
i
r
d
d
u
n
g
a
n
d
o
t
h
e
r
f
l
y
i
n
g
d
e
b
r
is
o
n
th
e
s
u
r
f
ac
e
o
f
PV
p
a
n
els
c
au
s
i
n
g
r
e
d
u
c
ti
o
n
i
n
th
e
am
o
u
n
t
o
f
s
o
l
ar
i
r
r
a
d
i
an
ce
r
ec
ei
v
e
d
b
y
th
e
p
a
n
els
[
3
0
]
.
C
o
n
s
eq
u
en
tl
y
,
t
h
e
el
ec
t
r
i
c
p
o
wer
g
e
n
er
ate
d
b
y
t
h
e
PV
s
y
s
te
m
wi
ll
b
e
g
r
ea
t
ly
a
f
f
ec
t
ed
r
esu
lti
n
g
r
e
d
u
ce
d
s
y
s
te
m
e
f
f
ic
ie
n
c
y
ec
o
n
o
m
i
c
f
e
asi
b
i
lit
y
.
I
n
f
a
ct
,
s
o
ili
n
g
ef
f
e
ct
b
ec
o
m
es
a
s
er
io
u
s
is
s
u
e
i
n
a
r
i
d
a
n
d
d
ese
r
t
a
r
e
as
w
h
e
r
e
ai
r
b
o
r
n
e
d
u
s
t
is
t
h
ic
k
a
n
d
s
a
n
d
a
n
d
d
u
s
t
s
t
o
r
m
s
ar
e
m
o
r
e
f
r
eq
u
en
t.
B
esi
d
es
,
in
d
es
er
t
a
r
e
as th
at
a
r
e
n
ea
r
t
h
e
e
q
u
at
o
r
,
PV p
an
els a
r
e
ty
p
i
ca
ll
y
o
r
i
en
te
d
at
lo
w
t
ilt
an
g
l
es
an
d
t
h
at
m
a
k
es
t
h
e
p
a
n
els
m
o
r
e
p
r
o
n
e
t
o
d
u
s
t
a
cc
u
m
u
lat
io
n
.
I
n
f
a
ct
,
s
o
il
in
g
e
f
f
e
ct
is
n
o
t
lim
ite
d
t
o
d
es
er
t
an
d
d
r
y
a
r
e
as
o
n
l
y
,
it
c
an
a
ls
o
af
f
e
ct
PV
s
y
s
te
m
s
i
n
s
tall
ed
i
n
c
iti
es
a
n
d
f
a
r
m
s
d
u
e
to
a
cc
u
m
u
l
ati
o
n
o
f
f
u
el
e
m
is
s
i
o
n
s
a
n
d
a
g
r
ic
u
lt
u
r
al
d
eb
r
is
[
3
0
]
.
T
h
e
r
e
f
o
r
e,
f
o
r
PV
s
y
s
te
m
s
i
n
s
t
all
ed
i
n
I
r
a
q
,
i
n
w
h
i
c
h
d
ese
r
t
co
n
s
ti
tu
tes
ab
o
u
t
3
0
%
o
f
its
t
er
r
it
o
r
y
,
PV
s
o
ili
n
g
m
u
s
t
b
e
t
ak
en
i
n
t
o
a
cc
o
u
n
t
w
h
e
n
s
t
u
d
y
in
g
t
h
e
p
er
f
o
r
m
a
n
ce
an
d
f
ea
s
i
b
il
it
y
o
f
an
y
PV
s
y
s
t
e
m
.
So
ili
n
g
lo
s
s
es r
a
n
g
e
f
r
o
m
3
%
t
o
4
0
% o
f
t
h
e
s
y
s
te
m
a
n
n
u
a
l p
o
w
e
r
p
r
o
d
u
ct
io
n
d
e
p
e
n
d
i
n
g
o
n
t
h
e
lo
ca
t
io
n
a
n
d
its
d
u
s
t
s
t
o
r
m
p
r
o
f
iles
as
w
ell
as
w
h
et
h
e
r
p
er
i
o
d
i
c
c
lea
n
i
n
g
i
s
b
e
in
g
p
r
o
v
id
ed
t
o
th
e
PV
s
y
s
te
m
o
r
n
o
t
.
A
cc
o
r
d
i
n
g
t
o
r
ep
o
r
t
ed
e
x
p
e
r
i
m
e
n
t
al
d
a
ta
ab
o
u
t
s
o
ili
n
g
ef
f
e
ct
o
n
p
o
w
e
r
p
r
o
d
u
c
ti
o
n
o
f
PV
s
y
s
te
m
s
in
I
r
a
q
an
d
n
ei
g
h
b
o
r
i
n
g
c
o
u
n
tr
ies
[
3
1
]
,
t
h
e
m
o
n
t
h
l
y
s
o
i
li
n
g
l
o
s
s
es
o
f
t
h
e
d
esi
g
n
e
d
s
y
s
t
em
d
u
e
t
o
d
u
s
t
ac
c
u
m
u
lat
io
n
o
v
er
a
p
e
r
i
o
d
o
f
o
n
e
y
ea
r
is
s
ele
cte
d
t
o
b
e
i
n
cr
e
m
e
n
ts
o
f
2
.
5
% e
a
ch
m
o
n
t
h
w
h
ich
is
e
q
u
i
v
a
le
n
t
t
o
an
a
v
e
r
a
g
e
a
n
n
u
al
s
o
il
in
g
lo
s
s
es
o
f
1
6
.
2
5
%
w
it
h
m
a
x
im
u
m
o
f
3
0
%
in
De
ce
m
b
er
g
iv
e
n
t
h
at
t
h
e
s
y
s
te
m
is
n
o
t
cle
an
ed
o
v
er
th
e
o
n
e
-
y
ea
r
a
n
aly
s
is
p
e
r
i
o
d
.
T
h
e
t
o
t
al
ar
ea
o
f
m
o
d
u
les
i
n
th
e
a
r
r
a
y
is
2
4
m
2
w
h
i
c
h
r
e
q
u
ir
es
g
r
o
u
n
d
a
r
ea
o
f
a
b
o
u
t
7
5
m
2
.
A
b
l
o
c
k
d
ia
g
r
am
o
f
t
h
e
s
t
u
d
ie
d
P
V
s
y
s
te
m
is
s
h
o
w
n
in
Fi
g
u
r
e
2
.
Af
ter
th
e
s
y
s
tem
was
d
esig
n
ed
in
SAM,
wea
th
er
d
ata
f
o
r
ea
ch
o
f
th
e
s
tu
d
ie
d
lo
ca
tio
n
s
(
1
8
I
r
aq
i
p
r
o
v
in
ce
s
)
wer
e
ad
d
e
d
,
an
d
d
if
f
er
en
t
s
ets
o
f
s
im
u
latio
n
s
w
er
e
co
n
d
u
cted
to
in
v
esti
g
ate
th
e
s
y
s
tem
’
s
p
o
wer
an
d
e
n
er
g
y
p
e
r
f
o
r
m
an
ce
u
n
d
e
r
d
if
f
e
r
en
t
o
p
er
atio
n
al
co
n
d
iti
o
n
s
in
ter
m
s
o
f
o
r
ien
tatio
n
an
d
tr
ac
k
in
g
m
o
d
es.
Acc
o
r
d
in
g
ly
,
d
if
f
er
e
n
t
s
ce
n
ar
i
o
s
wer
e
co
n
s
id
er
ed
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
ea
ch
s
ce
n
ar
io
ar
e
ex
p
lain
ed
an
d
d
is
cu
s
s
ed
in
th
e
n
ex
t
s
ec
tio
n
.
I
t
is
im
p
o
r
tan
t
to
m
en
tio
n
h
er
e
th
at
th
e
az
im
u
th
a
n
g
le
is
s
et
to
1
8
0
o
as
th
e
s
y
s
tem
is
o
r
ien
ted
f
ac
in
g
s
o
u
th
wh
ich
is
th
e
ty
p
ical
d
ir
ec
t
io
n
f
o
r
PV
s
y
s
tem
in
s
talled
i
n
a
lo
ca
tio
n
in
t
h
e
n
o
r
th
er
n
h
em
is
p
h
e
r
e.
Fig
u
r
e
2
.
A
b
lo
ck
d
iag
r
am
o
f
t
h
e
s
tu
d
ied
PV sy
s
tem
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
I
n
f
o
r
m
atio
n
o
f
t
h
e
s
tu
d
ied
1
8
lo
ca
tio
n
s
in
clu
d
in
g
th
eir
g
eo
g
r
ap
h
ical
co
o
r
d
in
ate
s
,
av
er
ag
e
tem
p
er
atu
r
e,
a
n
d
ir
r
ad
ian
ce
c
o
m
p
o
n
en
ts
ar
e
lis
ted
in
T
ab
l
e
1
.
I
t
is
o
b
v
io
u
s
f
r
o
m
th
e
tab
le
th
at
th
e
h
ig
h
est
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
I
n
ve
s
tig
a
tio
n
o
f
o
p
tima
l tilt,
o
r
ien
ta
tio
n
a
n
d
tr
a
ck
in
g
o
f
a
s
o
la
r
P
V
s
ystem
in
I
r
a
q
(
A
h
med
Zu
r
fi
)
1919
av
er
ag
e
d
aily
GHI
ir
r
a
d
ian
ce
ca
n
b
e
o
b
tain
ed
in
B
asra
wh
ile
Du
h
o
k
r
ec
eiv
es
th
e
lo
west
d
aily
ir
r
ad
ia
n
ce
.
I
t
ca
n
also
b
e
s
ee
n
th
at
Mid
d
l
e
E
u
p
h
r
ates
an
d
wester
n
p
r
o
v
in
ce
s
r
ec
eiv
e
a
p
le
n
ty
am
o
u
n
t
o
f
i
r
r
ad
ian
ce
th
r
o
u
g
h
o
u
t
th
e
y
ea
r
.
Fo
r
m
o
r
e
d
etails
ab
o
u
t
th
e
s
o
lar
ir
r
ad
i
an
ce
o
f
t
h
e
co
n
s
id
er
ed
lo
ca
tio
n
s
,
Fig
u
r
e
3
s
h
o
ws
th
e
av
e
r
a
g
e
h
o
u
r
l
y
d
is
t
r
i
b
u
ti
o
n
o
f
GH
I
i
r
r
a
d
ia
n
ce
f
o
r
al
l
p
r
o
v
i
n
ce
s
as
ca
lc
u
la
te
d
b
y
t
h
e
S
AM
m
o
d
el
b
as
ed
o
n
th
e
p
r
o
v
i
d
ed
w
ea
th
er
d
a
ta
o
f
t
h
e
l
o
ca
ti
o
n
s
.
F
ig
u
r
e
3
s
h
o
ws
t
h
a
t
al
l
lo
ca
t
io
n
s
r
e
ce
i
v
e
8
h
o
u
r
s
o
f
a
v
e
r
a
g
e
ir
r
a
d
ia
n
ce
o
f
5
5
0
–
6
5
0
W
/m
2
.
No
w,
wi
th
th
e
g
iv
en
s
o
l
ar
i
r
r
a
d
i
an
ce
d
at
a,
t
h
e
PV
s
y
s
te
m
is
s
i
m
u
la
te
d
u
n
d
e
r
d
i
f
f
er
e
n
t s
ce
n
a
r
i
o
s
.
I
n
th
e
f
o
ll
o
win
g
s
ec
ti
o
n
s
,
t
h
e
r
esu
lts
o
f
ea
ch
s
c
en
ar
io
a
r
e
p
r
ese
n
t
e
d
an
d
d
is
c
u
s
s
ed
.
T
ab
le
1
.
Geo
g
r
ap
h
ical
an
d
ir
r
a
d
ian
ce
in
f
o
r
m
atio
n
o
f
th
e
s
tu
d
ied
lo
ca
tio
n
s
(
ty
p
ical
m
ete
o
r
o
l
o
g
ical
y
ea
r
(
T
MY
)
2
0
0
7
-
2
0
2
1
)
P
r
o
v
i
n
c
e
La
t
i
t
u
d
e
(
o
)
Lo
n
g
i
t
u
d
e
(
o
)
El
e
v
a
t
i
o
n
(
m)
A
v
e
r
a
g
e
t
e
m
p
.
(
C
)
G
H
I
(
k
W
h
/
m
2
/
d
a
y
)
D
N
I
(
k
W
h
/
m
2
/
d
a
y
)
D
H
I
(
k
W
h
/
m
2
/
d
a
y
)
Al
-
A
n
b
a
r
3
3
.
4
5
4
3
.
3
1
48
2
4
.
6
5
.
6
6
6
.
6
3
1
.
4
2
B
a
b
i
l
3
2
.
4
5
4
4
.
4
5
27
2
5
.
3
5
.
6
3
6
.
5
7
1
.
3
8
B
a
g
h
d
a
d
3
3
.
2
6
4
4
.
2
3
3
4
.
7
2
4
.
9
5
.
6
1
6
.
6
4
1
.
3
6
B
a
sr
a
3
0
.
5
1
4
7
.
7
8
2
.
6
2
7
.
1
5
.
8
1
6
.
6
7
1
.
4
3
D
h
i
Q
a
r
3
1
.
0
1
4
6
.
2
3
1
.
4
5
2
7
.
1
5
.
7
4
6
.
5
2
1
.
4
5
Al
-
Q
ā
d
i
si
y
y
a
h
3
1
.
9
5
4
4
.
9
5
20
2
6
.
3
5
.
6
9
6
.
6
1
.
4
1
D
i
y
a
l
a
3
4
.
3
5
4
5
.
3
8
2
0
2
2
4
.
2
5
.
5
6
.
4
8
1
.
3
8
D
u
h
o
k
3
6
.
8
6
43
2
7
6
1
8
.
8
5
.
1
7
6
.
2
4
1
.
3
Er
b
i
l
3
6
.
2
3
4
3
.
9
6
4
0
8
.
7
2
1
.
3
5
.
3
6
.
3
4
1
.
3
3
K
a
r
b
a
l
a
3
2
.
5
6
4
4
.
0
5
29
2
5
.
6
5
.
7
3
6
.
7
5
1
.
3
9
K
i
r
k
u
k
3
5
.
4
6
4
4
.
3
4
3
2
3
.
4
2
3
.
6
5
.
4
5
6
.
5
1
.
3
7
M
a
y
sa
n
3
1
.
8
5
4
7
.
1
6
9
2
6
.
9
5
.
6
5
6
.
4
5
1
.
4
4
M
u
t
h
a
n
n
a
3
1
.
2
6
4
5
.
2
6
6
2
6
.
5
5
.
7
7
6
.
6
3
1
.
4
4
N
a
j
a
f
3
1
.
9
5
4
4
.
3
1
32
2
5
.
9
5
.
7
8
6
.
7
6
1
.
4
1
N
i
n
a
w
a
3
6
.
3
4
3
.
1
4
2
1
6
.
1
2
2
.
1
5
.
3
1
6
.
3
3
1
.
3
6
S
a
l
a
h
A
l
-
D
i
n
3
4
.
5
7
4
3
.
6
7
1
0
7
2
4
.
4
5
.
5
8
6
.
5
9
1
.
4
S
u
l
a
y
m
a
n
i
y
a
h
3
5
.
5
5
4
5
.
4
5
8
5
3
1
8
.
5
5
.
3
5
6
.
3
5
1
.
3
7
W
a
si
t
3
2
.
5
4
5
.
8
1
19
2
5
.
9
5
.
6
5
6
.
5
8
1
.
4
1
Fig
u
r
e
3
.
GHI
ir
r
ad
ian
ce
o
f
th
e
1
8
I
r
aq
i p
r
o
v
in
ce
s
ac
co
r
d
in
g
to
t
y
p
ica
l
m
e
te
o
r
o
l
o
g
i
ca
l
y
ea
r
(
T
MY
)
2
0
0
7
-
2
0
2
1
d
at
ase
t
o
f
I
r
a
q
i
r
eg
io
n
d
o
w
n
l
o
ad
ed
f
r
o
m
NSR
DB
4
.
1
.
Scena
rio
1
:
f
ix
ed
-
a
x
is
,
t
i
lt
=
la
t
it
ud
e
I
n
t
h
i
s
s
c
e
n
a
r
i
o
,
t
h
e
s
y
s
t
e
m
i
s
s
i
m
u
l
a
t
e
d
w
i
t
h
a
f
i
x
e
d
t
i
l
t
a
n
g
l
e
.
A
s
a
c
o
m
m
o
n
p
r
a
c
t
i
c
e
,
t
h
e
v
a
l
u
e
o
f
t
i
l
t
a
n
g
l
e
i
s
a
d
j
u
s
t
e
d
t
o
t
h
e
l
o
c
a
t
i
o
n
l
a
t
i
t
u
d
e
f
o
r
t
h
e
b
e
s
t
p
e
r
f
o
r
m
a
n
c
e
o
f
a
P
V
s
y
s
t
e
m
.
H
o
w
e
v
e
r
,
t
h
i
s
c
o
n
f
i
g
u
r
a
t
i
o
n
d
o
e
s
n
o
t
n
e
c
e
s
s
a
r
i
l
y
a
c
h
i
e
v
e
m
a
x
i
m
u
m
p
o
w
e
r
e
x
t
r
a
c
t
i
o
n
f
r
o
m
a
P
V
s
y
s
t
e
m
a
t
a
l
l
l
o
c
a
t
i
o
n
s
a
n
d
t
i
m
e
s
.
T
h
u
s
,
i
t
i
s
s
i
g
n
i
f
i
c
a
n
t
t
o
i
n
v
e
s
t
i
g
a
t
e
t
h
e
e
f
f
e
c
t
i
v
e
n
e
s
s
o
f
s
u
c
h
a
t
i
l
t
a
n
g
l
e
i
n
a
l
l
o
f
t
h
e
s
t
u
d
i
e
d
l
o
c
a
t
i
o
n
s
a
n
d
t
h
e
n
c
o
m
p
a
r
e
t
h
e
r
e
s
u
l
t
s
t
o
t
h
e
o
p
t
i
m
a
l
t
i
l
t
a
n
g
l
e
s
c
e
n
a
r
i
o
.
T
h
e
s
y
s
t
e
m
p
e
r
f
o
r
m
a
n
c
e
i
n
e
a
c
h
s
c
e
n
a
r
i
o
i
s
a
s
s
e
s
s
e
d
i
n
t
e
r
m
o
f
f
i
v
e
e
n
e
r
g
y
p
a
r
a
m
e
t
e
r
s
i
n
c
l
u
d
i
n
g
t
h
e
p
l
a
n
e
o
f
t
h
e
a
r
r
a
y
(
P
O
A
)
i
r
r
a
d
i
a
n
c
e
w
h
i
c
h
i
s
o
n
e
o
f
t
h
e
e
s
s
e
n
t
i
a
l
i
n
d
i
c
a
t
o
r
s
o
f
P
V
s
y
s
t
e
m
p
e
r
f
o
r
m
a
n
c
e
.
I
t
i
s
a
m
e
a
s
u
r
e
o
f
h
o
w
m
u
c
h
i
n
c
i
d
e
n
t
i
r
r
a
d
i
a
n
c
e
t
h
e
f
r
o
n
t
s
i
d
e
o
f
P
V
p
a
n
e
l
s
r
e
c
e
i
v
e
o
v
e
r
t
i
m
e
.
A
n
n
u
a
l
t
o
t
a
l
P
O
A
r
e
s
u
l
t
s
i
n
k
W
h
w
e
r
e
o
b
t
a
i
n
e
d
w
i
t
h
a
n
d
w
i
t
h
o
u
t
t
h
e
e
f
f
e
c
t
o
f
s
o
i
l
i
n
g
l
o
s
s
e
s
.
T
h
e
o
t
h
e
r
t
h
r
e
e
p
a
r
a
m
e
t
e
r
s
a
r
e
t
h
e
a
n
n
u
a
l
n
o
m
i
n
a
l
D
C
e
n
e
r
g
y
p
r
o
d
u
c
e
d
b
y
t
h
e
s
y
s
t
e
m
,
t
h
e
a
n
n
u
a
l
g
r
o
s
s
D
C
e
n
e
r
g
y
g
e
n
e
r
a
t
e
d
a
n
d
t
h
e
a
n
n
u
a
l
A
C
e
n
e
r
g
y
d
e
l
i
v
e
r
e
d
t
o
t
h
e
l
o
a
d
.
T
h
e
r
e
s
u
l
t
s
o
f
t
h
i
s
s
c
e
n
a
r
i
o
a
r
e
l
i
s
t
e
d
i
n
T
a
b
l
e
2
f
o
r
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
191
4
-
1
9
2
5
1920
1
8
l
o
c
a
t
i
o
n
s
.
T
h
e
a
n
n
u
a
l
D
C
a
n
d
A
C
e
n
e
r
g
y
a
r
e
e
v
a
l
u
a
t
e
d
b
a
s
e
d
o
n
t
h
e
P
O
A
i
r
r
a
d
i
a
n
c
e
a
f
t
e
r
i
n
c
l
u
d
i
n
g
s
o
i
l
i
n
g
l
o
s
s
e
s
.
T
h
e
t
i
l
t
a
n
g
l
e
i
s
f
i
x
e
d
t
h
r
o
u
g
h
o
u
t
t
h
e
y
e
a
r
a
t
t
h
e
l
o
c
a
t
i
o
n
l
a
t
i
t
u
d
e
p
r
e
s
e
n
t
e
d
i
n
T
a
b
l
e
1
.
F
i
r
s
t
t
h
e
o
v
e
r
a
l
l
r
e
s
u
l
t
s
a
r
e
c
o
m
p
a
r
e
d
f
o
r
a
l
l
l
o
c
a
t
i
o
n
s
.
T
h
e
e
f
f
e
c
t
o
f
s
o
i
l
i
n
g
l
o
s
s
c
a
n
b
e
n
o
t
i
c
e
d
b
y
c
o
m
p
a
r
i
n
g
t
h
e
v
a
l
u
e
s
o
f
t
o
t
a
l
P
O
A
i
r
r
a
d
i
a
n
c
e
b
e
f
o
r
e
a
n
d
a
f
t
e
r
s
o
i
l
i
n
g
e
f
f
e
c
t
,
w
h
i
c
h
i
s
s
e
l
e
c
t
e
d
t
o
b
e
1
6
.
2
5
%
a
s
a
n
a
n
n
u
a
l
a
v
e
r
a
g
e
.
I
t
c
a
n
a
l
s
o
b
e
o
b
s
e
r
v
e
d
t
h
a
t
o
n
l
y
2
1
%
o
f
t
h
e
t
o
t
a
l
i
r
r
a
d
i
a
n
c
e
r
e
c
e
i
v
e
d
b
y
t
h
e
p
a
n
e
l
s
i
s
c
o
n
v
e
r
t
e
d
i
n
t
o
D
C
e
n
e
r
g
y
,
w
h
i
c
h
c
a
n
b
e
i
n
t
e
r
p
r
e
t
e
d
a
s
t
h
e
e
f
f
e
c
t
o
f
t
h
e
P
V
p
a
n
e
l
s
i
n
e
f
f
i
c
i
e
n
c
i
e
s
,
f
o
r
t
h
e
e
f
f
i
c
i
e
n
c
y
o
f
t
h
e
s
e
l
e
c
t
e
d
P
V
p
a
n
e
l
s
i
s
2
1
%
.
B
y
c
o
m
p
a
r
i
n
g
t
h
e
n
o
m
i
n
a
l
a
n
d
g
r
o
s
s
D
C
e
n
e
r
g
y
v
a
l
u
e
s
a
s
w
e
l
l
a
s
t
h
e
A
C
e
n
e
r
g
y
v
a
l
u
e
s
,
o
n
e
c
a
n
r
e
l
a
t
e
t
o
t
h
e
e
f
f
e
c
t
o
f
D
C
l
o
s
s
e
s
d
u
e
t
o
D
C
w
i
r
i
n
g
,
d
i
o
d
e
s
,
a
n
d
D
C
p
o
w
e
r
o
p
t
i
m
i
z
e
r
o
n
o
n
e
h
a
n
d
,
a
n
d
t
h
e
A
C
l
o
s
s
e
s
c
a
u
s
e
d
b
y
t
h
e
i
n
v
e
r
t
e
r
i
n
e
f
f
i
c
i
e
n
c
y
a
n
d
A
C
w
i
r
e
s
o
n
t
h
e
o
t
h
e
r
h
a
n
d
.
N
o
w
,
b
y
l
o
o
k
i
n
g
a
t
t
h
e
r
e
s
u
l
t
s
o
f
e
a
c
h
l
o
c
a
t
i
o
n
,
i
t
i
s
c
l
e
a
r
t
h
a
t
N
a
j
a
f
h
a
d
t
h
e
h
i
g
h
e
s
t
a
n
n
u
a
l
A
C
e
n
e
r
g
y
w
h
i
c
h
a
m
o
u
n
t
e
d
t
o
8
6
2
6
.
8
k
W
h
f
o
l
l
o
w
e
d
b
y
K
a
r
b
a
l
a
w
i
t
h
a
n
n
u
a
l
A
C
e
n
e
r
g
y
o
f
8
5
9
7
.
8
6
k
W
h
.
M
u
t
h
a
n
n
a
a
n
d
B
a
s
r
a
h
a
d
n
e
a
r
l
y
e
q
u
a
l
a
n
n
u
a
l
A
C
e
n
e
r
g
y
p
r
o
d
u
c
t
i
o
n
a
n
d
b
o
t
h
c
a
m
e
a
s
t
h
e
t
h
i
r
d
h
i
g
h
e
s
t
.
A
c
c
o
r
d
i
n
g
t
o
T
a
b
l
e
1
,
t
h
e
s
e
f
o
u
r
p
r
o
v
i
n
c
e
s
h
a
v
e
t
h
e
h
i
g
h
e
s
t
G
H
I
a
n
d
D
N
I
v
a
l
u
e
s
t
h
a
t
b
o
t
h
h
a
v
e
s
i
g
n
i
f
i
c
a
n
t
e
f
f
e
c
t
i
n
t
h
e
a
m
o
u
n
t
o
f
e
l
e
c
t
r
i
c
e
n
e
r
g
y
g
e
n
e
r
a
t
e
d
b
y
t
h
e
P
V
s
y
s
t
e
m
.
I
t
c
a
n
a
l
s
o
b
e
i
n
f
e
r
r
e
d
f
r
o
m
t
h
i
s
s
c
e
n
a
r
i
o
t
h
a
t
a
P
V
s
y
s
t
e
m
i
n
s
t
a
l
l
e
d
i
n
D
u
h
o
k
w
i
l
l
p
r
o
d
u
c
e
t
h
e
l
o
w
e
s
t
a
m
o
u
n
t
o
f
e
n
e
r
g
y
c
o
m
p
a
r
e
d
t
o
t
h
e
o
t
h
e
r
s
t
u
d
i
e
d
l
o
c
a
t
i
o
n
s
.
I
n
g
e
n
e
r
a
l
,
n
o
r
t
h
e
r
n
p
r
o
v
i
n
c
e
s
h
a
d
t
h
e
l
e
a
s
t
a
m
o
u
n
t
o
f
g
e
n
e
r
a
t
e
d
e
n
e
r
g
y
c
o
m
p
a
r
e
d
t
o
m
i
d
a
n
d
s
o
u
t
h
e
r
n
p
r
o
v
i
n
c
e
s
.
T
h
e
s
e
d
i
s
p
a
r
i
t
i
e
s
i
n
t
h
e
s
y
s
t
e
m
p
e
r
f
o
r
m
a
n
c
e
c
a
n
a
l
s
o
b
e
a
t
t
r
i
b
u
t
e
d
t
o
v
a
r
i
a
t
i
o
n
s
i
n
t
h
e
D
H
I
r
e
c
e
i
v
e
d
b
y
t
h
e
m
o
d
u
l
e
s
p
e
r
u
n
i
t
a
r
e
a
f
r
o
m
o
n
e
l
o
c
a
t
i
o
n
t
o
a
n
o
t
h
e
r
.
T
h
e
D
H
I
c
o
m
p
o
n
e
n
t
o
f
s
o
l
a
r
r
a
d
i
a
t
i
o
n
i
s
t
h
e
a
m
o
u
n
t
o
f
r
a
d
i
a
t
i
o
n
t
h
a
t
r
e
a
c
h
e
s
t
h
e
m
o
d
u
l
e
s
f
r
o
m
t
h
e
s
u
n
i
n
d
i
r
e
c
t
l
y
a
f
t
e
r
b
e
i
n
g
r
e
f
l
e
c
t
e
d
b
y
c
l
o
u
d
s
a
n
d
p
a
r
t
i
c
l
e
s
i
n
t
h
e
a
t
m
o
s
p
h
e
r
e
.
H
o
w
e
v
e
r
,
t
h
i
s
s
c
e
n
a
r
i
o
d
o
e
s
n
o
t
p
r
o
v
i
d
e
a
c
l
e
a
r
p
i
c
t
u
r
e
a
b
o
u
t
s
e
l
e
c
t
i
n
g
t
h
e
o
p
t
i
m
a
l
t
i
l
t
.
T
h
e
n
e
x
t
s
c
e
n
a
r
i
o
s
a
t
t
e
m
p
t
t
o
i
d
e
n
t
i
f
y
t
h
e
b
e
s
t
t
i
l
t
t
h
a
t
a
c
h
i
e
v
e
s
m
a
x
i
m
u
m
e
n
e
r
g
y
e
x
t
r
a
c
t
i
o
n
.
4
.
2
.
Scena
rio
2
:
f
ix
ed
-
a
x
is
,
t
i
lt
=
o
ptim
a
l a
nn
ua
l v
a
lue
I
n
th
is
s
ce
n
ar
io
,
i
n
s
tead
o
f
s
ettin
g
th
e
p
an
els
tilt
to
th
e
lo
ca
tio
n
’
s
latitu
d
e,
t
h
e
tilt
an
g
le
was
o
p
tim
ized
f
o
r
ea
ch
l
o
ca
tio
n
b
ased
on
th
e
h
ig
h
est
a
n
n
u
al
AC
en
er
g
y
g
e
n
er
ated
b
y
th
e
s
y
s
tem
.
Fo
r
ea
c
h
p
r
o
v
in
ce
,
a
s
et
o
f
s
im
u
latio
n
s
o
f
th
e
PV
s
y
s
tem
wer
e
co
n
d
u
cted
in
SAM
f
o
r
a
r
an
g
e
o
f
i
n
p
u
t
tilt
an
g
les
an
d
co
m
p
u
te
t
h
e
an
n
u
al
AC
en
er
g
y
at
ea
ch
in
p
u
t
tilt
.
T
h
e
o
p
tim
al
tilt
an
g
le
is
s
elec
ted
as
th
e
v
alu
e
at
wh
ich
th
e
an
n
u
al
AC
en
er
g
y
is
m
ax
im
iz
ed
.
Fig
u
r
e
4
s
h
o
ws
a
s
am
p
le
o
f
th
e
o
p
tim
al
tilt
id
en
tific
atio
n
cu
r
v
e
f
o
r
Kar
b
ala
lo
ca
tio
n
wh
ic
h
in
d
icate
s
th
at
o
p
tim
al
tilt
is
3
1
°.
T
a
b
le
3
lis
ts
th
e
o
p
tim
al
an
n
u
al
tilt
a
n
g
l
e
f
o
r
ea
ch
lo
ca
tio
n
co
m
p
ar
ed
to
th
e
lo
ca
ti
o
n
'
s
lati
tu
d
e.
I
t
c
a
n
b
e
n
o
t
i
c
e
d
t
h
a
t
t
h
e
v
a
l
u
e
o
f
o
p
t
i
m
a
l
a
n
n
u
a
l
t
i
l
t
i
s
c
l
o
s
e
t
o
l
a
t
i
t
u
d
e
a
n
g
l
e
f
o
r
m
o
s
t
o
f
t
h
e
l
o
c
a
t
i
o
n
w
i
t
h
a
s
l
i
g
h
t
d
e
v
i
a
t
i
o
n
.
T
h
e
d
e
v
i
a
t
i
o
n
o
f
o
p
t
i
m
a
l
t
i
l
t
f
r
o
m
l
a
t
i
t
u
d
e
i
s
l
e
s
s
t
h
a
n
2
°
f
o
r
m
o
s
t
o
f
t
h
e
l
o
c
a
t
i
o
n
s
.
H
o
w
e
v
e
r
,
o
p
t
i
m
a
l
t
i
l
t
i
n
n
o
r
t
h
e
r
n
a
n
d
m
i
d
-
n
o
r
t
h
e
r
n
p
r
o
v
i
n
c
e
s
d
e
v
i
a
t
e
d
f
r
o
m
l
a
t
i
t
u
d
e
f
o
r
m
o
r
e
t
h
a
n
t
w
o
d
e
g
r
e
e
s
,
a
s
h
i
g
h
l
i
g
h
t
e
d
i
n
T
a
b
l
e
3
.
I
n
o
t
h
e
r
w
o
r
d
s
,
m
o
v
i
n
g
t
o
w
a
r
d
s
t
h
e
s
o
u
t
h
,
t
h
e
a
n
n
u
a
l
o
p
t
i
m
a
l
t
i
l
t
m
o
v
e
s
c
l
o
s
e
r
t
o
l
a
t
i
t
u
d
e
.
S
e
t
t
i
n
g
t
h
e
t
i
l
t
a
n
g
l
e
t
o
t
h
e
o
p
t
i
m
a
l
a
n
n
u
a
l
v
a
l
u
e
o
b
t
a
i
n
e
d
i
n
T
a
b
l
e
3
r
e
s
u
l
t
e
d
i
n
m
i
n
o
r
i
n
c
r
e
a
s
e
i
n
t
h
e
a
n
n
u
a
l
e
n
e
r
g
y
c
o
m
p
a
r
e
d
t
o
s
c
e
n
a
r
i
o
1
.
Y
e
t
,
s
e
t
t
i
n
g
a
f
i
x
e
d
t
i
l
t
a
n
g
l
e
o
v
e
r
t
h
e
w
h
o
l
e
y
e
a
r
d
o
e
s
n
o
t
a
l
l
o
w
u
s
e
r
s
t
o
m
a
k
e
t
h
e
m
o
s
t
o
f
t
h
e
P
V
s
y
s
t
e
m
,
a
n
d
a
c
o
n
s
i
d
e
r
a
b
l
e
a
m
o
u
n
t
o
f
P
V
e
n
e
r
g
y
w
i
l
l
r
e
m
a
i
n
u
n
t
a
p
p
e
d
.
T
h
e
r
e
f
o
r
e
,
a
d
j
u
s
t
i
n
g
t
h
e
t
i
l
t
a
n
g
l
e
o
n
m
o
n
t
h
l
y
b
a
s
i
s
c
a
n
e
x
t
r
a
c
t
m
o
r
e
e
n
e
r
g
y
f
r
o
m
t
h
e
s
y
s
t
e
m
.
T
h
i
s
t
e
c
h
n
i
q
u
e
i
s
i
n
v
e
s
t
i
g
a
t
e
d
i
n
t
h
e
n
e
x
t
s
c
e
n
a
r
i
o
.
T
ab
le
2
.
Mo
d
el
r
esu
lts
o
f
s
ce
n
ar
io
1
: f
ix
e
d
-
ax
is
with
tilt
=
latitu
d
e
P
r
o
v
i
n
c
e
To
t
a
l
P
O
A
i
r
r
a
d
i
a
n
c
e
(
k
W
h
/
y
r
)
To
t
a
l
P
O
A
i
r
r
a
d
i
a
n
c
e
a
f
t
e
r
so
i
l
i
n
g
(
k
W
h
/
y
r
)
A
n
n
u
a
l
n
o
mi
n
a
l
D
C
e
n
e
r
g
y
(
k
W
h
/
y
r
)
A
n
n
u
a
l
g
r
o
ss
D
C
e
n
e
r
g
y
(
k
W
h
/
y
r
)
A
n
n
u
a
l
A
C
En
e
r
g
y
(
k
W
h
)
Al
-
A
n
b
a
r
5
4
,
5
6
8
4
5
,
7
9
4
.
8
9
,
6
5
6
.
7
2
9
,
1
5
4
.
6
4
8
,
4
9
5
.
8
9
B
a
b
i
l
5
4
,
0
5
4
.
3
4
5
,
3
6
8
.
2
9
,
5
6
8
.
1
9
9
,
0
4
3
.
6
8
8
,
3
9
3
.
1
1
B
a
g
h
d
a
d
5
4
,
2
1
1
.
1
4
5
,
4
3
5
.
3
9
,
5
8
2
.
2
1
9
,
0
8
7
.
7
9
8
,
4
3
0
.
4
B
a
sr
a
5
5
,
2
3
8
.
9
4
6
,
3
3
3
.
3
9
,
7
7
4
.
4
1
9
,
2
3
8
.
0
9
8
,
5
6
7
.
4
D
h
i
Q
a
r
5
4
,
5
9
4
4
5
,
8
4
4
.
5
9
,
6
6
8
.
9
4
9
,
0
8
7
.
5
1
8
,
4
3
3
.
3
5
Al
-
Q
ā
d
i
si
y
y
a
h
5
4
,
5
7
4
.
5
4
5
,
8
0
4
9
,
6
6
0
.
4
8
9
,
0
8
6
.
8
9
8
,
4
3
2
.
3
1
D
i
y
a
l
a
5
3
,
3
0
9
.
3
4
4
,
6
8
1
.
3
9
,
4
2
0
.
7
4
8
,
8
6
8
.
1
3
8
,
2
2
7
.
5
3
D
u
h
o
k
5
0
,
6
1
5
.
2
4
2
,
3
2
7
.
4
8
,
9
2
2
.
1
3
8
,
5
0
4
.
0
1
7
,
8
9
0
.
6
3
Er
b
i
l
5
1
,
6
9
3
.
3
4
3
,
3
1
8
.
9
9
,
1
3
1
.
0
9
8
,
6
6
4
.
1
9
8
,
0
3
9
.
1
5
K
a
r
b
a
l
a
5
5
,
2
4
2
.
1
4
6
,
4
0
1
.
7
9
,
7
8
7
.
3
8
9
,
2
7
0
.
0
1
8
,
5
9
7
.
8
6
K
i
r
k
u
k
5
3
,
3
5
0
.
9
4
4
,
6
4
3
9
,
4
1
2
.
5
9
8
,
8
5
9
.
7
2
8
,
2
2
1
.
8
3
M
a
y
sa
n
5
3
,
8
4
9
.
8
4
5
,
1
6
0
.
1
9
,
5
2
3
.
4
2
8
,
9
3
9
.
0
6
8
,
2
9
3
.
4
4
M
u
t
h
a
n
n
a
5
5
,
1
4
8
.
3
4
6
,
2
9
4
.
3
9
,
7
6
4
.
1
4
9
,
2
5
8
.
4
8
8
,
5
8
7
.
7
8
N
a
j
a
f
5
5
,
5
1
1
.
6
4
6
,
6
0
1
.
5
9
,
8
2
9
.
3
4
9
,
3
0
0
.
2
7
8
,
6
2
6
.
7
9
N
i
n
a
w
a
5
1
,
8
9
4
.
8
4
3
,
4
3
1
.
1
9
,
1
5
5
.
0
9
8
,
6
4
1
.
4
9
8
,
0
2
0
.
4
S
a
l
a
h
A
l
-
D
i
n
5
4
,
1
5
1
.
8
4
5
,
4
3
4
.
9
9
,
5
8
0
.
5
1
9
,
0
7
7
.
4
8
8
,
4
1
9
.
9
5
S
u
l
a
y
m
a
n
i
y
a
h
5
2
,
3
1
5
.
1
4
3
,
7
4
5
.
8
9
,
2
2
2
.
3
6
8
,
8
1
5
.
0
8
8
,
1
6
8
.
2
5
W
a
si
t
5
4
,
4
3
1
.
2
4
5
,
6
6
9
.
6
9
,
6
3
2
.
0
2
9
,
1
1
8
.
8
3
8
,
4
5
8
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
I
n
ve
s
tig
a
tio
n
o
f
o
p
tima
l tilt,
o
r
ien
ta
tio
n
a
n
d
tr
a
ck
in
g
o
f
a
s
o
la
r
P
V
s
ystem
in
I
r
a
q
(
A
h
med
Zu
r
fi
)
1921
Fig
u
r
e
4
.
An
n
u
al
AC
en
er
g
y
v
s
.
an
n
u
al
tilt
s
h
o
win
g
o
p
tim
al
v
alu
e
f
o
r
Kar
b
ala
T
ab
le
3
.
O
p
t
im
al
a
n
n
u
al
tilt
a
n
g
le
f
o
r
t
h
e
1
8
l
o
c
ati
o
n
s
ac
co
r
d
i
n
g
t
o
s
c
en
ar
io
2
Lo
c
a
t
i
o
n
La
t
i
t
u
d
e
O
p
t
i
mal
a
n
n
u
a
l
t
i
l
t
D
e
v
i
a
t
i
o
n
Lo
c
a
t
i
o
n
La
t
i
t
u
d
e
O
p
t
i
mal
a
n
n
u
a
l
t
i
l
t
D
e
v
i
a
t
i
o
n
Al
-
A
n
b
a
r
3
3
.
4
5
32
1
.
4
5
K
a
r
b
a
l
a
3
2
.
5
6
7
31
1
.
5
6
7
B
a
b
i
l
3
2
.
4
5
31
1
.
4
5
K
i
r
k
u
k
3
5
.
4
6
9
33
2
.
4
6
9
B
a
g
h
d
a
d
3
3
.
2
6
7
32
1
.
2
6
7
M
a
y
sa
n
3
1
.
8
5
30
1
.
8
5
B
a
sr
a
3
0
.
5
1
7
30
0
.
5
1
7
M
u
t
h
a
n
n
a
3
1
.
2
6
7
30
1
.
2
6
7
D
h
i
Q
a
r
3
1
.
0
1
7
30
1
.
0
1
7
N
a
j
a
f
3
1
.
9
5
31
0
.
9
5
Q
ā
d
i
s
i
y
y
a
h
3
1
.
9
5
31
0
.
9
5
N
i
n
a
w
a
3
6
.
3
0
6
33
3
.
3
0
6
D
i
y
a
l
a
3
4
.
3
5
32
2
.
3
5
S
a
l
a
h
A
l
-
D
i
n
3
4
.
5
7
5
7
32
2
.
5
7
5
7
D
u
h
o
k
3
6
.
8
6
7
33
3
.
8
6
7
S
u
l
a
y
m
a
n
i
y
a
h
3
5
.
5
5
33
2
.
5
5
Er
b
i
l
3
6
.
2
3
3
33
3
.
2
3
3
W
a
si
t
3
2
.
5
31
1
.
5
4
.
3
.
Scena
rio
3
:
f
ix
ed
-
a
x
is
,
t
i
lt
=
o
ptim
a
l
m
o
nthly
v
a
lue
T
o
i
d
e
n
t
i
f
y
t
h
e
m
o
n
t
h
l
y
o
p
ti
m
a
l
ti
l
t
a
n
g
l
e
,
S
A
M
m
o
d
e
l
i
s
s
im
u
l
a
t
e
d
wi
t
h
a
r
a
n
g
e
o
f
i
n
p
u
t
t
i
lt
a
n
g
l
es
a
n
d
t
h
e
AC
e
n
e
r
g
y
f
o
r
e
a
c
h
m
o
n
t
h
i
s
c
o
m
p
u
t
e
d
o
v
e
r
t
h
e
e
n
t
i
r
e
y
e
a
r
.
T
h
e
t
il
t
a
n
g
l
e
v
a
lu
e
t
h
a
t
y
i
el
d
s
t
h
e
m
a
x
i
m
u
m
e
n
e
r
g
y
d
u
r
i
n
g
a
c
e
r
t
a
i
n
m
o
n
t
h
r
e
p
r
e
s
e
n
t
s
t
h
e
o
p
t
i
m
a
l
t
i
lt
a
n
g
l
e
o
f
t
h
e
m
o
n
t
h
.
T
h
e
s
a
m
e
s
e
t
o
f
s
i
m
u
l
at
i
o
n
s
w
a
s
i
m
p
l
e
m
e
n
t
e
d
f
o
r
e
a
c
h
l
o
c
a
t
i
o
n
,
a
n
d
t
h
e
r
es
u
l
ts
a
r
e
s
h
o
w
n
i
n
F
i
g
u
r
e
5
.
I
t
i
s
cle
a
r
t
h
a
t
t
h
e
o
p
ti
m
a
l
t
i
l
t
a
n
g
le
v
a
r
i
e
d
o
v
e
r
a
w
i
d
e
r
a
n
g
e
d
u
r
i
n
g
t
h
e
y
e
a
r
a
c
c
o
r
d
i
n
g
t
o
t
h
e
s
u
n
s
e
as
o
n
a
l
ti
l
t
a
n
d
t
h
a
t
a
l
l
l
o
ca
t
i
o
n
s
f
o
l
l
o
w
e
d
t
h
e
s
a
m
e
t
r
e
n
d
w
i
t
h
in
a
n
a
r
r
o
w
m
a
r
g
i
n
t
h
a
t
d
i
d
n
o
t
e
x
c
e
e
d
6
°
.
I
n
w
i
n
t
e
r
m
o
n
t
h
s
,
h
i
g
h
t
i
l
t
i
s
r
e
q
u
i
r
e
d
f
o
r
m
a
x
i
m
u
m
e
n
e
r
g
y
e
x
t
r
a
c
t
i
o
n
w
h
i
l
e
i
n
s
u
m
m
e
r
m
o
n
t
h
s
,
t
h
e
p
a
n
e
l
s
n
e
e
d
t
o
b
e
t
i
l
t
e
d
a
t
l
o
w
a
n
g
l
e
s
t
o
a
l
i
g
n
w
it
h
t
h
e
s
u
n
s
e
as
o
n
a
l
t
r
a
c
k
f
o
r
m
a
x
im
u
m
e
x
p
o
s
u
r
e
t
o
i
r
r
a
d
i
a
n
c
e
.
Af
t
e
r
t
h
a
t
,
t
h
e
s
y
s
t
e
m
w
a
s
s
i
m
u
la
t
e
d
w
i
t
h
ti
l
t
a
n
g
le
s
e
t
t
o
t
h
e
o
p
t
i
m
a
l
m
o
n
t
h
l
y
v
alu
e
s
o
b
t
a
i
n
e
d
i
n
t
h
e
p
r
e
v
i
o
u
s
s
te
p
.
T
h
e
a
n
n
u
a
l
AC
e
n
e
r
g
y
w
as
t
h
e
n
c
al
c
u
l
at
e
d
f
o
r
e
a
c
h
l
o
c
a
t
i
o
n
.
T
h
e
l
o
c
a
t
i
o
n
s
d
e
m
o
n
s
t
r
a
t
e
d
t
h
e
s
a
m
e
t
r
e
n
d
i
n
t
e
r
m
s
o
f
e
n
e
r
g
y
y
i
e
l
d
w
h
e
r
e
Na
j
a
f
h
a
d
t
h
e
h
i
g
h
e
s
t
v
a
l
u
e
a
n
d
D
u
h
o
k
h
a
d
t
h
e
l
o
w
es
t
.
G
e
n
e
r
a
ll
y
,
c
o
m
p
a
r
e
d
t
o
s
c
en
a
r
i
o
2
w
h
e
r
e
t
h
e
t
il
t
a
n
g
l
e
w
as
f
i
x
e
d
a
t
o
n
e
v
a
l
u
e
t
h
r
o
u
g
h
o
u
t
t
h
e
y
e
a
r
,
A
C
e
n
e
r
g
y
w
a
s
i
n
c
r
e
as
e
d
b
y
5
-
6
%
f
o
r
a
l
l
t
h
e
l
o
ca
t
i
o
n
s
d
u
e
t
o
i
n
cr
e
a
s
e
i
n
i
r
r
a
d
i
a
n
c
e
e
x
p
o
s
u
r
e
b
y
P
V
p
a
n
e
ls
w
h
e
n
t
il
t
a
n
g
l
e
t
r
a
c
k
s
t
h
e
m
o
n
t
h
l
y
s
e
aso
n
a
l
p
a
t
h
o
f
t
h
e
s
u
n
.
4
.
4
.
Scena
rio
4
:
o
ne
-
a
x
is
t
ra
ck
ing
I
n
th
is
co
n
f
ig
u
r
atio
n
,
th
e
PV
p
an
els
ar
e
a
d
ju
s
ted
at
a
f
ix
e
d
az
im
u
th
,
wh
ic
h
is
s
elec
ted
to
b
e
1
8
0
o
f
o
r
I
r
aq
r
eg
io
n
s
,
an
d
allo
w
th
e
p
an
els
to
tr
ac
k
th
e
2
4
-
h
o
u
r
s
u
n
p
o
s
itio
n
with
in
a
r
o
tatio
n
an
g
le
s
et
b
y
“th
e
tr
ac
k
er
r
o
tatio
n
lim
it”
p
ar
am
ete
r
in
SAM
m
o
d
el.
Pra
ctica
lly
,
th
e
r
o
tatio
n
an
g
le
lim
it
d
ep
en
d
s
o
n
t
h
e
tr
ac
k
in
g
m
ec
h
an
is
m
an
d
t
h
e
d
esig
n
o
f
t
h
e
tr
ac
k
er
s
tr
u
ct
u
r
e.
So
m
e
t
r
a
ck
in
g
r
ac
k
s
p
r
o
v
id
e
6
0
°
r
o
tati
o
n
r
an
g
e
an
d
o
th
er
s
ar
e
lim
ited
to
4
5
°.
I
n
th
is
s
ce
n
ar
io
,
th
e
ef
f
ec
t
o
f
th
e
tr
ac
k
er
r
o
tatio
n
lim
it
o
n
th
e
en
er
g
y
p
er
f
o
r
m
an
ce
o
f
th
e
PV
s
y
s
tem
was
f
ir
s
t
in
v
esti
g
a
ted
f
o
r
a
ce
r
tain
lo
ca
tio
n
as
s
h
o
wn
i
n
Fig
u
r
e
6
.
I
t
is
o
b
v
io
u
s
th
at
th
e
wid
er
th
e
r
o
tatio
n
an
g
le
is
th
e
m
o
r
e
s
o
la
r
en
er
g
y
th
e
PV
s
y
s
tem
ca
n
h
ar
n
ess
.
Ho
wev
er
,
f
o
r
p
r
ac
tical
co
n
s
tr
ain
ts
r
elate
d
to
tilt
tr
ac
k
in
g
s
y
s
tem
s
av
aila
b
le
in
th
e
m
ar
k
et,
th
e
an
g
le
o
f
r
o
tatio
n
was
s
et
to
b
e
6
0
°
as
a
r
ea
s
o
n
ab
le
lim
it
in
th
is
s
ce
n
ar
io
.
T
h
e
an
n
u
al
AC
en
er
g
y
was
ev
alu
ate
d
f
o
r
ea
ch
p
r
o
v
in
ce
an
d
co
m
p
ar
e
d
to
th
e
p
r
e
v
io
u
s
s
ce
n
ar
i
o
,
th
e
en
er
g
y
in
cr
ea
s
e
ac
h
ie
v
ed
i
n
th
e
o
n
e
-
ax
is
m
o
d
e
was
b
etw
ee
n
1
6
%
-
1
8
%
f
o
r
all
th
e
lo
ca
t
io
n
s
.
T
h
is
in
cr
ea
s
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
191
4
-
1
9
2
5
1922
is
s
elf
-
ex
p
lan
ato
r
y
as
th
e
PV
p
an
els
ar
e
allo
wed
to
tr
ac
k
th
e
s
u
n
d
aily
ea
s
t
-
west
lo
ca
ti
o
n
m
ax
im
izin
g
th
e
in
cid
en
t ir
r
ad
ia
n
ce
.
Fig
u
r
e
5
.
Mo
n
th
ly
o
p
tim
al
tilt
an
g
le
f
o
r
1
8
p
r
o
v
in
ce
s
Fig
u
r
e
6
.
T
h
e
r
elatio
n
s
h
ip
b
et
wee
n
o
n
e
-
a
x
is
r
o
tatio
n
an
g
le
a
n
d
en
er
g
y
y
ield
f
o
r
Kar
b
ala
4
.
5
.
Scena
rio
5
:
t
wo
-
a
x
is
t
r
a
ck
ing
W
ith
two
-
ax
is
tr
ac
k
in
g
,
t
h
e
P
V
p
an
els
m
o
u
n
t
is
au
to
m
ated
to
r
o
tate
al
o
n
g
th
eir
v
er
tical,
az
im
u
th
,
ax
is
to
tr
ac
k
th
e
s
u
n
s
ea
s
o
n
al
lo
ca
tio
n
f
r
o
m
n
o
r
th
t
o
s
o
u
th
o
v
e
r
th
e
y
ea
r
,
a
n
d
to
r
o
tate
alo
n
g
th
e
tilt
,
h
o
r
izo
n
tal,
ax
is
to
tr
ac
k
t
h
e
s
u
n
d
aily
lo
ca
tio
n
f
r
o
m
s
u
n
r
is
e
to
s
u
n
s
et
in
a
m
ec
h
an
is
m
s
im
ilar
to
o
n
e
-
ax
is
tr
ac
k
in
g
.
W
ith
th
is
tr
ac
k
in
g
m
o
d
e,
th
e
PV
p
an
els
ar
e
ab
le
t
o
co
llect
as
m
u
ch
s
o
lar
ir
r
ad
i
an
ce
as
av
ailab
le
to
th
e
p
an
els.
T
h
is
ir
r
ad
ian
ce
m
ax
im
izatio
n
was c
o
n
f
ir
m
ed
in
th
e
r
esu
lts
wh
ich
s
h
o
wed
th
at
t
h
e
y
ea
r
ly
en
er
g
y
o
f
th
e
s
y
s
tem
in
cr
ea
s
ed
b
y
1
1
-
1
3
%
co
m
p
ar
ed
to
p
r
ev
io
u
s
s
ce
n
ar
io
,
i.e
.
,
th
e
o
n
e
-
a
x
is
tr
ac
k
in
g
.
A
d
etailed
co
m
p
ar
is
o
n
o
f
th
e
en
er
g
y
p
er
f
o
r
m
an
ce
o
f
t
h
e
s
y
s
tem
u
n
d
e
r
s
ce
n
ar
io
s
1
-
4
f
o
r
all
p
r
o
v
in
ce
s
is
ex
p
lain
ed
in
Fig
u
r
e
7
.
I
t
is
clea
r
t
h
at
en
a
b
lin
g
tr
ac
k
i
n
g
m
o
d
e
r
esu
lts
in
co
n
s
id
er
ab
le
e
n
h
an
ce
m
en
t
o
f
th
e
s
y
s
tem
en
er
g
y
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
I
n
ve
s
tig
a
tio
n
o
f
o
p
tima
l tilt,
o
r
ien
ta
tio
n
a
n
d
tr
a
ck
in
g
o
f
a
s
o
la
r
P
V
s
ystem
in
I
r
a
q
(
A
h
med
Zu
r
fi
)
1923
g
en
er
atio
n
.
C
o
n
s
eq
u
en
tly
,
th
e
s
y
s
tem
ec
o
n
o
m
ic
f
ea
s
ib
ilit
y
ca
n
also
b
e
en
h
an
ce
d
.
Ho
we
v
er
,
th
e
a
d
d
itio
n
al
co
s
t
in
cu
r
r
ed
b
y
in
s
tallin
g
tr
a
ck
in
g
m
o
u
n
ts
s
h
o
u
ld
b
e
co
n
s
id
er
ed
wh
ich
is
a
to
p
ic
o
u
t
o
f
th
e
s
co
p
e
o
f
th
is
wo
r
k
.
Fig
u
r
e
7
.
A
c
o
m
p
ar
is
o
n
o
f
s
y
s
tem
an
n
u
al
AC
en
er
g
y
f
o
r
all
l
o
ca
tio
n
s
in
f
o
u
r
d
i
f
f
er
en
t scen
ar
io
s
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
d
elv
e
d
in
to
th
e
e
v
alu
atio
n
o
f
o
p
tim
al
tilt
an
g
l
e
an
d
tr
ac
k
in
g
o
f
a
s
im
u
lated
s
o
lar
PV
s
y
s
tem
in
1
8
p
r
o
v
in
ce
s
in
I
r
a
q
.
T
h
e
in
v
esti
g
atio
n
was
co
n
d
u
cted
th
r
o
u
g
h
a
SAM
m
o
d
el
to
s
tu
d
y
th
e
en
er
g
y
p
er
f
o
r
m
an
ce
o
f
a
5
k
W
d
c
PV
s
y
s
tem
th
at
was
d
esig
n
e
d
an
d
s
im
u
lated
b
ased
o
n
I
r
a
q
i
wea
th
er
c
o
n
d
itio
n
s
in
clu
d
in
g
th
e
ef
f
ec
t
o
f
s
o
ilin
g
lo
s
s
es
a
s
cr
ib
ed
to
d
u
s
t
d
ep
o
s
itio
n
o
n
p
an
els.
T
h
e
o
p
tim
al
tilt
an
g
le
was
co
m
p
u
ted
b
y
r
u
n
n
in
g
s
ets
o
f
s
im
u
latio
n
s
at
a
r
an
g
e
o
f
tilt
an
g
le
in
p
u
ts
an
d
e
v
alu
atin
g
th
e
s
y
s
tem
en
er
g
y
p
er
f
o
r
m
an
ce
as
an
o
u
tp
u
t.
I
t
was
o
b
s
er
v
ed
th
at
th
e
co
m
m
o
n
p
r
ac
tice
o
f
s
ettin
g
th
e
tilt
a
n
g
le
to
th
e
lo
ca
tio
n
latitu
d
e
d
id
n
o
t
ac
h
iev
e
h
i
g
h
est
en
er
g
y
ex
tr
ac
tio
n
f
o
r
all
o
f
th
e
s
tu
d
ied
lo
ca
tio
n
s
an
d
th
at
le
d
to
u
n
d
er
u
tili
za
tio
n
o
f
th
e
s
y
s
tem
.
T
h
er
ef
o
r
e,
with
th
is
“g
o
ld
en
r
u
le”
th
e
s
y
s
tem
n
ee
d
s
to
b
e
o
v
er
s
ized
to
m
ee
t
ce
r
tain
en
er
g
y
d
em
a
n
d
.
Settin
g
th
e
tilt
at
an
n
u
al
o
p
tim
al
v
alu
e
r
esu
lted
in
a
s
lig
h
t
ch
a
n
g
e
f
o
r
all
lo
ca
tio
n
s
b
ec
au
s
e
th
e
o
p
tim
al
an
n
u
al
tilt
was f
o
u
n
d
to
b
e
1
°
-
2
.
5
°
ab
o
v
e
latitu
d
e.
I
t w
as f
o
u
n
d
th
at
th
e
s
y
s
tem
u
tili
za
tio
n
an
d
en
er
g
y
p
er
f
o
r
m
an
ce
ca
n
b
e
im
p
r
o
v
e
d
b
y
s
ettin
g
a
m
o
n
th
ly
tilt
an
d
th
at
r
esu
lted
in
5
-
6
%
in
cr
ea
s
e
in
th
e
y
ea
r
ly
AC
en
er
g
y
d
eliv
er
e
d
t
o
lo
ad
b
y
th
e
s
y
s
tem
.
T
h
e
o
p
tim
al
m
o
n
th
ly
tilt
v
ar
ie
d
f
r
o
m
1
°
-
62
°
th
r
o
u
g
h
o
u
t
th
e
y
ea
r
b
ased
o
n
th
e
s
ea
s
o
n
al
p
o
s
itio
n
o
f
th
e
s
u
n
.
W
ith
o
n
e
-
ax
is
tr
ac
k
in
g
,
th
e
s
y
s
tem
an
n
u
al
en
er
g
y
in
cr
ea
s
ed
b
y
1
6
-
1
8
%
f
o
r
all
th
e
lo
ca
tio
n
s
.
T
h
e
r
esu
lts
also
af
f
ir
m
ed
t
h
at
f
u
r
th
er
u
tili
za
tio
n
ca
n
b
e
ac
h
iev
e
d
b
y
u
s
in
g
two
-
ax
is
tr
ac
k
in
g
with
wh
ich
an
n
u
al
e
n
er
g
y
in
cr
ea
s
e
d
b
y
2
9
%
co
m
p
ar
e
d
to
th
e
o
p
tim
al
m
o
n
th
ly
tilt
s
ce
n
ar
io
.
I
n
all
s
tu
d
ied
s
ce
n
ar
io
s
,
s
o
ilin
g
l
o
s
s
es
ef
f
ec
t
ca
n
n
o
t
b
e
o
v
er
lo
o
k
ed
g
i
v
en
th
at
I
r
aq
i
wea
th
er
is
h
ig
h
ly
-
p
o
llu
ted
d
u
e
to
d
u
s
t
s
to
r
m
s
an
d
p
o
llu
tio
n
f
r
o
m
d
aily
l
if
e
ac
tiv
ities
.
I
g
n
o
r
in
g
s
o
ilin
g
lo
s
s
es
in
as
s
es
s
in
g
PV
s
y
s
tem
p
er
f
o
r
m
an
ce
an
d
th
eir
o
p
tim
al
o
r
ien
tatio
n
ca
u
s
e
s
s
y
s
tem
u
n
d
er
s
izin
g
b
ec
au
s
e
ir
r
ad
ian
ce
lo
s
s
es
d
u
e
to
s
o
ilin
g
ca
n
b
e
as
m
u
ch
as
4
0
%
in
wea
th
er
co
n
d
itio
n
s
lik
e
in
I
r
aq
esp
ec
ial
ly
wh
en
clea
n
in
g
m
ec
h
an
is
m
s
ar
e
n
o
t
ap
p
lied
.
Ov
er
all,
all
I
r
a
q
i
p
r
o
v
in
ce
s
h
av
e
a
s
ig
n
if
ican
t
u
n
tap
p
e
d
p
o
ten
tial
f
o
r
s
o
lar
en
er
g
y
g
e
n
er
atio
n
with
av
er
a
g
e
an
n
u
al
GHI
o
f
2
k
W
h
/m
2
.
T
h
is
wo
r
k
is
co
n
ce
r
n
ed
with
th
e
tech
n
ical
asp
ec
t
o
f
th
e
d
esig
n
o
f
a
PV
s
y
s
tem
in
I
r
aq
,
b
u
t
it
s
till
ca
n
b
e
ex
te
n
d
ed
b
y
c
o
n
s
id
er
in
g
th
e
ec
o
n
o
m
ic
m
o
d
el
o
f
th
e
s
y
s
tem
an
d
th
e
ef
f
ec
t
o
f
ad
d
itio
n
al
co
s
t o
f
tr
ac
k
in
g
s
y
s
tem
o
n
th
e
s
y
s
tem
ec
o
n
o
m
ics.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
e
au
th
o
r
s
r
ec
eiv
ed
n
o
f
u
n
d
i
n
g
f
o
r
th
is
r
esear
ch
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.