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o
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(
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n
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),
in
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8
7
),
g
re
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ter
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n
e
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ss
it
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ted
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a
c
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g
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t
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th
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3
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9
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r
,
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n
if
y
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g
a
5
.
0
7
%
in
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re
a
se
re
lativ
e
to
t
h
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re
fe
re
n
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e
c
o
n
d
it
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.
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h
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su
lt
s
v
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li
d
a
te
th
a
t
th
e
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p
ti
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l
ti
lt
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n
g
le
flu
c
t
u
a
tes
with
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ro
u
n
d
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fa
c
e
a
lb
e
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o
,
a
s
su
rfa
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e
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fle
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ti
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it
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ffe
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ts
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a
n
d
e
n
e
rg
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u
tp
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t
.
In
teg
ra
t
in
g
a
c
tu
a
l
a
lb
e
d
o
v
a
lu
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s
in
p
h
o
to
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lt
a
ic
m
o
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e
ls
is
c
ru
c
ial
fo
r
p
re
c
ise
ti
lt
a
d
ju
stm
e
n
t
a
n
d
e
n
h
a
n
c
e
d
s
y
ste
m
e
fficie
n
c
y
.
K
ey
w
o
r
d
s
:
Alb
ed
o
Gr
o
u
n
d
r
ef
lecto
r
Op
tim
u
m
tilt
an
g
le
PVs
y
s
t
PV sy
s
tem
Yea
r
ly
tilt
an
g
le
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
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r th
e
CC B
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-
SA
li
c
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se
.
C
o
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p
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A
uth
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r
:
Ah
m
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Dau
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M
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Dep
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E
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T
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Al
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T
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Un
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Naja
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Ku
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I
r
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ah
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d
a
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iq
1.
I
NT
RO
D
UCT
I
O
N
So
lar
en
er
g
y
is
wid
ely
r
eg
ar
d
e
d
as
a
h
ig
h
ly
p
r
o
m
is
in
g
,
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en
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ab
le
en
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g
y
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o
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r
ce
th
at
is
b
o
th
ab
u
n
d
a
n
t
an
d
en
v
ir
o
n
m
en
tally
f
r
ien
d
ly
.
Fu
r
th
er
m
o
r
e,
it
r
ep
r
esen
ts
a
v
iab
le
en
e
r
g
y
alter
n
ativ
e
s
o
u
r
ce
.
C
u
r
r
e
n
tly
,
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
ar
e
th
e
b
est
an
d
m
o
s
t
ef
f
icien
t
wa
y
to
h
ar
v
est
th
e
s
o
lar
en
er
g
y
.
T
h
ese
s
y
s
tem
s
h
av
e
th
e
ca
p
ab
ilit
y
to
d
ir
ec
tly
co
n
v
er
t
ir
r
ad
iatio
n
in
ten
s
ity
in
to
elec
tr
ical
en
er
g
y
[
1
]
.
T
h
e
m
ax
i
m
u
m
o
u
tp
u
t
o
f
a
PV
s
y
s
tem
p
an
el
is
ac
h
iev
ed
wh
e
n
th
e
in
ci
d
en
t r
a
y
is
p
er
p
en
d
ic
u
lar
to
th
e
p
lan
e
o
f
th
e
p
an
el
[
2
]
.
T
h
e
s
o
lar
e
n
er
g
y
o
u
tp
u
t
o
f
a
PV
s
y
s
tem
d
ep
en
d
s
o
n
th
e
am
o
u
n
t
o
f
s
o
lar
r
ad
ia
tio
n
r
ea
ch
i
n
g
t
h
e
ar
r
ay
s
[
3
]
.
T
h
e
am
o
u
n
t
o
f
s
o
la
r
r
ad
iatio
n
d
e
p
en
d
s
o
n
th
e
tim
e
o
f
th
e
d
a
y
an
d
th
e
p
an
el
p
lace
m
en
t
wh
er
e
it
co
n
ce
r
n
s
th
e
s
u
n
[
4
]
-
[
6
]
.
Als
o
,
th
e
an
g
le
o
f
th
e
PV
ar
r
ay
s
co
n
ce
r
n
in
g
th
e
h
o
r
izo
n
tal
is
o
n
e
o
f
t
h
e
m
o
s
t
cr
itical
f
ac
to
r
s
th
at
af
f
ec
t
th
e
am
o
u
n
t
o
f
r
ad
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n
c
o
llected
b
y
a
f
i
x
ed
PV
ar
r
ay
.
T
h
er
e
f
o
r
e,
PV
m
o
d
u
les
m
u
s
t
b
e
tilt
ed
at
o
p
tim
al
an
g
les
to
c
ap
tu
r
e
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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I
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N:
2088
-
8
6
9
4
Th
e
effec
ts
o
f su
r
fa
ce
a
lb
ed
o
a
n
d
p
h
o
to
vo
lta
ic
s
ystem
tilt
a
n
g
le
o
n
imp
r
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vin
g
…
(
A
h
med
D
a
u
d
Mo
s
h
ee
r
)
741
o
p
tim
u
m
a
m
o
u
n
t
o
f
av
ailab
le
s
o
lar
en
er
g
y
at
a
g
iv
e
n
lo
ca
tio
n
.
I
n
m
o
s
t
ca
s
es,
th
e
b
est
tilt
a
n
g
le
f
o
r
a
f
ix
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PV
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r
ay
d
ep
en
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o
n
t
h
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wea
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,
th
e
lo
ca
tio
n
a
n
d
t
h
e
s
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s
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al
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im
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B
ec
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s
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,
th
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est
t
ilt
an
g
les
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o
r
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ay
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s
ed
all
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r
will b
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d
if
f
er
en
t f
r
o
m
o
n
e
p
lace
to
an
o
th
e
r
.
Un
til n
o
w,
m
an
y
r
esear
ch
es
h
av
e
b
ee
n
d
o
n
e
o
n
th
e
b
est
tilt
a
n
g
le
f
o
r
PV
ar
r
ay
s
,
an
d
m
an
y
e
x
p
er
im
e
n
tal
co
r
r
elatio
n
s
ca
n
b
e
u
s
ed
to
p
r
ed
ict
th
e
b
est
tilt
an
g
le
[
7
]
,
[
8
]
.
T
h
e
g
r
o
u
n
d
r
ef
l
ec
to
r
(
alb
ed
o
)
a
n
d
th
e
m
o
d
u
le
’
s
o
r
ien
t
atio
n
ar
e
an
o
t
h
er
f
ac
t
o
r
s
wo
u
ld
a
f
f
ec
t
th
e
am
o
u
n
t
o
f
s
o
lar
en
e
r
g
y
o
u
tp
u
t
o
f
th
e
PV
ar
r
ay
.
I
n
th
e
ab
s
en
ce
o
f
g
r
o
u
n
d
alb
ed
o
m
ea
s
u
r
e
m
en
ts
,
it
is
co
m
m
o
n
p
r
ac
tice
to
u
tili
ze
th
e
m
ea
n
v
alu
e
o
f
0
.
2
as
a
s
u
b
s
titu
te,
d
e
n
o
tin
g
t
h
e
r
e
f
lectiv
e
ch
a
r
ac
ter
is
tics
o
f
u
n
co
v
e
r
ed
g
r
o
u
n
d
d
e
v
o
id
o
f
s
n
o
w
[
9
]
.
Sig
n
if
ican
t
r
eso
u
r
ce
s
ar
e
s
p
en
t
o
n
d
esig
n
in
g
an
d
m
o
d
ellin
g
s
o
lar
PV
en
er
g
y
s
y
s
tem
s
to
ac
h
iev
e
m
ax
im
u
m
o
u
tp
u
t
p
o
wer
.
I
n
eich
en
et
a
l.
[
1
0
]
m
e
asu
r
ed
g
r
o
u
n
d
r
ef
lecte
d
r
ad
iat
io
n
co
m
p
ar
ed
with
th
e
v
alu
e
o
f
0
.
2
,
wh
ich
is
p
r
o
p
o
s
ed
b
y
L
iu
an
d
J
o
r
d
an
f
o
r
Ge
n
ev
a.
T
h
e
s
tu
d
y
'
s
f
in
d
i
n
g
s
s
u
g
g
est
th
at
th
e
co
n
s
tan
t
v
alu
e
o
f
0
.
2
is
ex
ce
s
s
iv
ely
h
ig
h
f
o
r
a
g
e
o
g
r
ap
h
ical
s
itu
atio
n
s
u
ch
as
in
Ge
n
ev
a.
Fu
r
th
er
m
o
r
e,
as
I
n
eich
en
et
a
l.
[
1
1
]
ass
er
ted
,
th
e
p
er
s
is
ten
t
n
u
m
er
ical
q
u
a
n
tity
is
d
ee
m
ed
i
n
ad
eq
u
ate
an
d
im
p
l
au
s
ib
le.
Nu
m
er
o
u
s
au
t
h
o
r
s
h
av
e
d
eter
m
in
ed
o
p
tim
al
tilt
a
n
g
les
th
eo
r
etica
lly
,
ex
p
er
im
en
tally
,
an
d
in
s
im
u
la
tio
n
b
y
ca
lcu
latin
g
th
e
m
a
x
im
u
m
s
o
lar
ir
r
a
d
iatio
n
r
ea
ch
in
g
th
e
PV
m
o
d
u
les.
T
u
am
a
et
a
l.
[
1
2
]
s
h
o
wed
th
a
t
th
e
tilt
an
g
le
o
f
3
0
°
with
a
0
°
az
im
u
th
an
g
le
is
th
e
b
est
o
f
all
th
e
an
g
les
f
o
r
B
ag
h
d
ad
city
.
T
h
er
e
is
also
ev
id
en
ce
th
at
s
m
all
ch
an
g
es in
d
ir
ec
tio
n
(
u
p
to
3
0
°)
d
o
n
o
t a
f
f
e
ct
th
e
p
er
f
o
r
m
a
n
ce
o
f
PV
s
y
s
tem
s
.
Hu
s
s
ain
et
a
l.
[
1
3
]
s
h
o
wed
th
at
a
3
0
f
ix
e
d
til
t
an
g
le
is
o
p
tim
al
,
an
d
0°
is
th
e
o
p
tim
al
az
im
u
t
h
an
g
le.
Ob
aid
et
a
l.
[
1
4
]
co
m
p
ar
ed
th
e
esti
m
ated
g
lo
b
al
ef
f
icien
t
s
o
lar
r
ad
iatio
n
an
d
ca
lcu
lated
r
ad
ian
ce
f
o
r
a
3
0
° tilted
s
u
r
f
ac
e
.
B
o
th
wer
e
h
ig
h
est in
J
u
ly
an
d
Au
g
u
s
t a
n
d
lo
west in
Dec
em
b
er
.
Al
-
Kh
az
za
r
[
1
5
]
c
o
n
s
id
er
ed
an
av
er
ag
e
tilt
an
g
le
b
etwe
e
n
3
0
°
an
d
5
0
°
d
u
r
in
g
th
e
s
u
m
m
er
an
d
win
ter
as
th
e
o
p
tim
u
m
tilt
an
g
le.
Kh
ad
im
et
a
l.
[
1
6
]
i
n
d
icate
d
th
at
ea
ch
p
r
o
v
in
ce
'
s
o
p
tim
al
m
o
n
th
ly
tilt
an
g
le
is
b
etwe
en
1
an
d
8
d
eg
r
ee
s
.
T
h
is
in
f
o
r
m
atio
n
was
u
s
ed
in
B
ag
h
d
ad
,
w
h
er
e
th
e
o
p
tim
al
tilt
was
3
1
°
,
to
g
et
th
e
m
ax
im
u
m
e
n
er
g
y
f
r
o
m
s
o
lar
p
an
els
ea
ch
y
ea
r
.
T
h
e
o
p
tim
al
tilt
an
g
le
in
[
1
7
]
was
3
1
°,
ac
co
r
d
in
g
to
th
e
m
ax
im
u
m
y
ea
r
l
y
p
o
wer
in
ten
s
ity
.
Kad
h
im
[
1
8
]
f
o
u
n
d
th
at
o
p
tim
u
m
tilt
an
g
les
f
o
r
win
ter
,
s
p
r
i
n
g
,
s
u
m
m
er
,
au
tu
m
n
,
a
n
d
th
e
y
ea
r
ar
e
as
f
o
llo
ws
:
6
0
.
4
1
°,
3
8
.
8
8
°,
5
.
2
6
°,
3
1
.
3
4
°,
an
d
3
3
.
9
7
°
.
A
h
m
ed
et
a
l.
[
1
9
]
f
o
u
n
d
th
at
th
e
o
p
tim
al
tilt
an
g
l
e
is
th
e
s
am
e
as
th
e
latitu
d
e
o
f
B
ag
h
d
ad
.
Ma
h
d
i
an
d
Ab
d
u
l
-
W
ah
id
[
2
0
]
s
h
o
wed
th
at
th
e
o
p
tim
u
m
tilt
an
g
le
f
o
r
all
d
ay
s
o
f
th
e
y
ea
r
was
3
5
°.
Hu
s
s
ein
[
2
1
]
f
o
u
n
d
t
h
at
s
in
ce
th
e
ev
alu
atio
n
s
wer
e
d
o
n
e
in
win
ter
,
t
h
e
o
p
tim
u
m
tilt
an
g
le
f
o
r
B
ag
h
d
ad
s
h
o
u
ld
b
e
4
9
°.
Al
-
S
h
am
m
ar
i
[
2
2
]
s
h
o
wed
th
at
f
o
r
u
n
-
s
h
ad
ed
p
an
els,
th
e
b
est tilt
an
g
le
to
g
et
th
e
m
o
s
t su
n
lig
h
t
is
6
0
o
in
Dec
em
b
er
,
5°
in
J
u
n
e
,
an
d
s
o
m
ewh
er
e
in
b
etwe
en
in
th
e
o
th
er
m
o
n
th
s
.
Ali
[
2
3
]
u
s
ed
a
m
ir
r
o
r
r
ef
lecto
r
an
d
f
o
u
n
d
th
at
t
h
e
b
est
az
im
u
th
an
g
le
f
o
r
th
e
s
u
r
f
ac
e
was
3
6
°E
an
d
th
e
o
p
tim
u
m
d
eg
r
ee
o
f
tilt
f
o
r
th
e
s
u
r
f
ac
e
was
6
0
°.
Als
o
,
th
e
au
th
o
r
s
f
o
u
n
d
th
at
p
u
ttin
g
a
m
ir
r
o
r
at
th
e
b
o
tto
m
o
f
a
s
o
lar
ce
ll
p
an
el
at
an
an
g
le
o
f
1
2
0
°
will
in
cr
ea
s
e
th
e
o
u
tp
u
t
p
o
wer
.
Salu
m
et
a
l.
[
2
4
]
u
s
ed
a
b
i
f
a
cial
PV
m
o
d
u
le
to
in
v
esti
g
ate
th
e
o
p
tim
u
m
h
eig
h
t
an
d
tilt
an
g
le
o
f
b
if
ac
ial
s
o
lar
ce
lls
in
B
ag
h
d
ad
C
ity
at
d
if
f
er
en
t
h
eig
h
ts
ab
o
v
e
th
e
g
r
o
u
n
d
(
1
0
0
,
1
2
0
,
1
4
0
,
a
n
d
6
0
cm
)
an
d
tilt
an
g
les
(
0
°,
1
2
°,
3
0
°,
4
9
°,
an
d
7
0
°)
f
o
r
ea
ch
h
eig
h
t.
T
h
e
r
esu
lts
s
h
o
wed
th
at,
wh
en
th
e
h
eig
h
t
g
o
es
f
r
o
m
1
0
0
cm
to
1
2
0
cm
,
t
h
e
g
r
o
wth
g
e
n
er
ally
lev
els
o
f
f
at
1
4
0
cm
an
d
1
6
0
cm
.
B
ased
o
n
th
is
f
in
d
in
g
,
th
e
b
est h
eig
h
t f
o
r
a
b
if
ac
ial
PV p
an
el
in
B
ag
h
d
ad
is
1
2
0
cm
.
T
h
e
r
esu
lts
ad
d
itio
n
ally
in
d
icate
d
th
at
p
h
o
to
v
o
ltaics
p
er
f
o
r
m
b
est at
a
tilt
o
f
4
9
°.
T
h
e
o
p
tim
al
tilt
an
g
le
f
o
r
m
a
x
im
izin
g
in
cid
en
t
ir
r
ad
iatio
n
o
n
th
e
PV
ar
r
ay
s
d
e
p
en
d
s
o
n
th
e
g
r
o
u
n
d
alb
ed
o
,
esp
ec
ially
wh
en
alb
e
d
o
v
ar
ies
r
ath
er
th
an
r
e
m
ain
in
g
co
n
s
tan
t
[
2
5
]
,
[
2
6
]
.
Prio
r
r
esea
r
ch
o
n
p
h
o
to
v
o
ltaic
PV
s
y
s
tem
p
er
f
o
r
m
an
ce
h
as
p
r
ed
o
m
in
an
tly
co
n
ce
n
tr
ated
o
n
s
o
lar
co
n
f
ig
u
r
atio
n
,
clim
atic
co
n
d
itio
n
s
,
an
d
ar
r
a
y
o
r
ien
tatio
n
,
wh
ile
m
in
im
ally
a
d
d
r
ess
in
g
th
e
s
u
r
f
ac
e
ty
p
e
o
n
wh
ich
PV m
o
d
u
les ar
e
in
s
talle
d
an
d
its
im
p
ac
t o
n
r
ef
lecte
d
r
ad
iatio
n
a
n
d
tilt
-
an
g
le
o
p
tim
izatio
n
.
Mo
s
t
cu
r
r
en
t
m
o
d
els
u
s
e
a
co
n
s
tan
t
a
lb
ed
o
v
alu
e
o
f
0
.
2
,
h
e
n
ce
o
v
er
s
im
p
lify
in
g
th
e
v
ar
iab
ilit
y
o
f
g
r
o
u
n
d
-
s
u
r
f
ac
e
r
ef
lectio
n
o
b
s
er
v
ed
in
ac
tu
al
o
p
er
atio
n
al
c
o
n
tex
ts
.
T
h
u
s
,
th
e
tr
u
e
ef
f
ec
t o
f
alb
ed
o
ch
a
n
g
e
o
n
th
e
o
p
tim
al
tilt
an
g
le
an
d
e
n
er
g
y
o
u
tp
u
t
r
em
ain
s
in
ad
eq
u
at
ely
in
v
esti
g
ated
.
T
h
is
r
esear
ch
m
eth
o
d
ically
in
v
esti
g
ates
th
e
co
r
r
elatio
n
b
et
wee
n
g
r
o
u
n
d
-
s
u
r
f
ac
e
alb
e
d
o
a
n
d
th
e
b
est
tilt
an
g
le
th
at
m
a
x
im
izes
th
e
y
ea
r
ly
p
r
o
d
u
ctio
n
o
f
en
er
g
y
o
f
a
f
ix
ed
o
n
-
g
r
id
p
h
o
to
v
o
ltaic
s
y
s
tem
.
T
h
e
a
n
aly
s
is
co
m
m
en
ce
s
a
r
ef
e
r
en
ce
alb
e
d
o
v
alu
e
o
f
0
.
2
a
n
d
its
co
r
r
esp
o
n
d
in
g
o
p
tim
al
tilt
o
f
3
1
°
f
o
r
th
e
clim
atic
co
n
d
itio
n
s
o
f
B
ag
h
d
a
d
,
I
r
aq
,
s
u
b
s
eq
u
en
tly
f
o
llo
wed
b
y
s
im
u
latio
n
s
ac
r
o
s
s
v
ar
io
u
s
alb
e
d
o
v
alu
es
to
ascer
tain
h
o
w
f
lu
ctu
atio
n
s
in
s
u
r
f
ac
e
r
ef
lecti
v
ity
alter
th
e
in
cid
e
n
t ir
r
ad
iati
o
n
an
d
p
o
wer
g
en
er
at
i
o
n
.
T
h
is
s
tu
d
y
'
s
o
r
ig
in
ality
is
i
n
q
u
an
tify
in
g
t
h
e
r
elatio
n
s
h
ip
b
etwe
en
alb
ed
o
v
a
r
iatio
n
s
an
d
tilt
-
an
g
le
o
p
tim
izatio
n
th
r
o
u
g
h
PVs
y
s
t
s
im
u
latio
n
s
.
T
h
is
m
eth
o
d
o
lo
g
y
p
r
esen
ts
a
m
o
r
e
r
ea
lis
tic
an
d
s
ite
-
s
p
ec
if
ic
s
tr
u
ctu
r
e
f
o
r
p
h
o
to
v
o
ltaic
d
esig
n
,
p
r
o
v
i
d
in
g
c
r
itical
in
s
ig
h
ts
f
o
r
en
h
an
cin
g
th
e
p
r
ec
is
io
n
o
f
p
er
f
o
r
m
a
n
ce
f
o
r
ec
asti
n
g
an
d
s
y
s
tem
o
p
tim
izatio
n
ac
r
o
s
s
v
a
r
y
in
g
s
u
r
f
ac
e
co
n
d
itio
n
s
.
T
h
e
s
u
b
s
eq
u
en
t
s
ec
tio
n
s
o
f
th
is
wo
r
k
ar
e
s
tr
u
ct
u
r
ed
as
f
o
llo
ws
:
i)
Sectio
n
2
d
elin
ea
tes
th
e
r
esear
ch
m
eth
o
d
o
lo
g
y
,
e
n
c
o
m
p
ass
in
g
th
e
c
h
ar
ac
te
r
izatio
n
o
f
th
e
PV
s
y
s
tem
,
s
im
u
latio
n
co
n
f
ig
u
r
atio
n
,
a
n
d
an
aly
tical
p
r
o
ce
d
u
r
e
;
ii)
Sectio
n
3
d
is
cu
s
s
es
th
e
r
esu
lts
an
d
a
n
aly
s
is
,
em
p
h
asizin
g
th
e
co
r
r
elatio
n
am
o
n
g
alb
ed
o
,
tilt
an
g
le,
an
d
e
n
er
g
y
y
ield
; a
n
d
iii)
Fin
ally
,
s
ec
tio
n
4
p
r
esen
t
s
th
e
co
n
clu
s
io
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
740
-
7
51
742
2.
RE
S
E
ARCH
M
E
T
H
O
DO
L
O
G
Y
So
lar
en
er
g
y
p
o
wer
is
ty
p
ically
ca
lcu
lated
b
ased
o
n
th
e
ir
r
a
d
iatio
n
r
ec
ei
v
ed
b
y
th
e
PV
ar
r
ay
'
s
tilt
ed
p
lan
e.
T
h
e
th
eo
r
etica
l
m
o
d
el
s
h
o
ws
th
e
r
elatio
n
s
h
ip
b
etwe
en
alb
ed
o
an
d
tilt
an
g
les
,
as
well
as
th
e
ef
f
ec
t
o
f
th
ese
an
g
les
o
n
ir
r
a
d
iatio
n
r
ec
eiv
ed
b
y
PV
m
o
d
u
les.
T
h
e
Per
ez
m
o
d
el
in
PVs
y
s
t
s
o
f
twar
e
is
u
s
ed
to
s
im
u
late
th
e
am
o
u
n
t
o
f
ir
r
ad
iatio
n
th
at
r
ea
ch
es
th
e
PV
ar
r
ay
s
.
Sy
s
te
m
d
esig
n
er
s
r
eq
u
ir
e
v
alu
es
f
o
r
s
o
lar
ir
r
ad
iatio
n
o
n
s
u
ch
tilt
ed
p
an
els
;
h
o
wev
er
,
m
ea
s
u
r
ed
o
r
ap
p
r
o
x
im
ated
ir
r
ad
iatio
n
d
ata
ar
e
p
r
im
a
r
il
y
av
ailab
le
f
o
r
s
u
r
f
ac
es
with
n
o
r
m
al
in
cid
en
ce
o
r
h
o
r
iz
o
n
tal
o
r
ie
n
tatio
n
.
T
h
er
ef
o
r
e,
it
is
n
ec
ess
ar
y
to
co
n
v
er
t
th
ese
d
ata
in
to
ir
r
ad
iatio
n
o
n
in
clin
ed
s
u
r
f
ac
es.
2
.
1
.
T
ilt
a
ng
le
a
nd
a
lbedo
A
f
lat
s
u
r
f
ac
e
ab
s
o
r
b
s
s
o
lar
ir
r
ad
iatio
n
in
th
r
ee
way
s
,
as sh
o
wn
in
(
1
)
[
2
7
]
,
[
28]
.
=
+
+
(
1
)
W
h
er
e:
G
B
is
th
e
b
ea
m
ir
r
ad
i
atio
n
,
G
D
is
th
e
d
if
f
u
s
e
ir
r
ad
i
atio
n
,
an
d
G
G
is
th
e
g
r
o
u
n
d
-
r
ef
lecte
d
ir
r
ad
iatio
n
.
Fro
m
Fig
u
r
e
1
,
th
e
tilt
ed
s
u
r
f
a
ce
b
ea
m
ir
r
a
d
iatio
n
(
G
Bt
)
is
(
2
)
.
=
(
)
(
2
)
I
n
ad
d
itio
n
,
th
e
h
o
r
izo
n
tal
s
u
r
f
ac
e
b
ea
m
ir
r
a
d
iatio
n
(
G
Bh
)
is
(
3
)
.
ℎ
=
(
)
(
3
)
Fig
u
r
e
1
.
B
ea
m
ir
r
a
d
iatio
n
o
n
th
e
h
o
r
izo
n
tal
an
d
tilt
ed
s
u
r
f
ac
es
T
h
e
ex
p
r
ess
io
n
u
s
ed
in
g
e
n
er
a
l to
in
cid
en
ce
a
n
g
le
is
(
4
)
.
=
−
+
ℎ
+
ℎ
+
ℎ
(
4
)
W
h
er
e
: I
n
cid
en
ce
a
n
g
le,
ϕ
: z
en
ith
an
g
le,
: tilt a
n
g
le,
az
im
u
th
an
g
le,
ℎ
:
Ho
u
r
a
n
g
le,
: D
ec
lin
atio
n
,
an
d
: So
lar
altitu
d
e
an
g
le
.
Fo
r
th
e
h
o
r
izo
n
tal
s
u
r
f
ac
es,
=
,
=
0
,
s
u
b
s
titu
te
in
(
4
).
(
)
=
s
in
s
in
+
c
os
c
os
c
os
ℎ
(
5
)
T
h
e
b
ea
m
ir
r
ad
iatio
n
tilt
f
ac
to
r
is
(
6
)
.
=
ℎ
=
(
)
(
)
(
6
)
Fo
r
an
y
s
u
r
f
ac
e
b
ea
m
ir
r
ad
iati
o
n
is
(
7
)
.
=
ℎ
(
7
)
Acc
o
r
d
in
g
t
o
th
e
is
o
tr
o
p
ic
s
k
y
m
o
d
el,
d
if
f
u
s
e
ir
r
a
d
iatio
n
o
n
t
h
e
h
o
r
iz
o
n
tal
s
u
r
f
ac
e
is
ca
lcu
l
ated
as
(
8
)
an
d
(
9
)
.
=
2
∫
(
)
2
⁄
0
=
2
(
8
)
=
2
(
9
)
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
Th
e
effec
ts
o
f su
r
fa
ce
a
lb
ed
o
a
n
d
p
h
o
to
vo
lta
ic
s
ystem
tilt
a
n
g
le
o
n
imp
r
o
vin
g
…
(
A
h
med
D
a
u
d
Mo
s
h
ee
r
)
743
W
h
er
e
:
d
if
f
u
s
e
s
k
y
ir
r
ad
ian
ce
(
W/m
2
r
a
d
)
.
Dif
f
u
s
e
ir
r
ad
iatio
n
o
n
tilt
ed
is
(
1
0
)
.
=
∫
c
os
Φ
2
−
0
Φ
+
∫
c
os
Φ
2
0
Φ
(
1
0
)
Su
b
s
titu
te
in
(
9
)
an
d
(
1
0
)
:
=
[
1
+
(
)
2
]
(
1
1
)
Similar
ly
,
th
e
g
r
o
u
n
d
-
r
e
f
lecte
d
ir
r
ad
iatio
n
is
ex
p
r
ess
ed
as
is
(
+
)
,
wh
ich
p
er
tain
s
to
th
e
r
ef
lectiv
ity
o
f
th
e
g
r
o
u
n
d
with
r
esp
ec
t t
o
i
s
o
tr
o
p
ic
g
r
o
u
n
d
r
ef
lecte
d
r
ad
i
atio
n
(
)
[
2
7
]
,
[
29
]
,
[
3
0
]
.
(
+
)
=
2
∫
c
os
(
)
2
0
=
2
(
1
2
)
On
a
tilt
ed
s
u
r
f
ac
e
(
1
3
)
.
=
∫
(
)
2
2
−
(
1
3
)
Fro
m
(
1
2
)
an
d
(
1
3
)
th
e
g
r
o
u
n
d
r
ef
lecte
d
will b
e:
=
(
+
)
[
1
−
(
)
2
]
(
1
4
)
W
h
er
e
: r
ep
r
esen
ts
th
e
g
r
o
u
n
d
alb
ed
o
.
Su
b
s
titu
te
(
1
0
)
a
n
d
(
1
3
)
in
(
6
)
,
th
e
n
(
1
6
)
.
=
+
[
1
+
(
)
2
]
+
(
+
)
[
1
−
(
)
2
]
(
1
5
)
T
h
e
g
lo
b
al
h
o
r
iz
o
n
tal
ir
r
ad
iati
o
n
(
)
is
th
e
to
tal
o
f
th
e
d
ir
ec
t r
ad
iatio
n
an
d
th
e
d
if
f
u
s
e
ir
r
ad
ia
tio
n
in
cid
en
t
o
n
th
e
h
o
r
izo
n
tal
p
lan
e.
=
+
(
1
6
)
T
h
e
(
1
5
)
m
ay
b
e
wr
itten
as
(
1
7
)
.
=
=
+
[
1
+
(
)
2
]
+
[
1
−
(
)
2
]
(
1
7
)
W
h
er
e
is
tilt
f
ac
to
r
to
tal
r
ad
ia
tio
n
.
Fro
m
,
(
1
7
)
th
e
tilt
f
ac
to
r
o
f
g
r
o
u
n
d
r
ef
lecte
d
is
(
1
8
)
.
=
[
1
−
(
)
2
]
(
1
8
)
T
h
e
tilt
f
ac
to
r
f
o
r
d
if
f
u
s
e
ir
r
ad
iatio
n
is
(
1
9
)
.
=
[
1
+
(
)
2
]
(
1
9
)
2.
2
.
T
ilte
d a
ng
le
a
nd
P
V
mo
du
le
Mo
s
t
s
o
lar
en
er
g
y
m
a
y
b
e
co
l
lecte
d
f
r
o
m
tilt
ed
s
u
r
f
ac
es.
T
h
e
tilt
is
also
af
f
ec
ted
b
y
th
e
tim
e
o
f
y
ea
r
an
d
latitu
d
e.
At
m
id
d
ay
in
Sep
tem
b
er
an
d
Ma
r
ch
,
th
e
r
a
d
iatio
n
f
r
o
m
th
e
s
u
n
is
g
o
in
g
to
b
e
p
er
p
en
d
icu
lar
to
th
e
s
u
r
f
ac
e
o
f
th
e
co
llecto
r
if
t
h
e
an
g
le
at
wh
ich
it
tilt
s
i
s
eq
u
al
to
th
e
latitu
d
e.
I
n
th
e
s
u
m
m
er
,
wh
en
s
u
n
r
ad
iatio
n
is
at
its
s
tr
o
n
g
est,
it is
h
elp
f
u
l to
an
g
le
th
e
s
u
r
f
ac
e
s
lig
h
tly
a
way
f
r
o
m
v
e
r
tical.
Ho
wev
er
,
f
o
r
th
e
m
ax
im
izatio
n
in
th
e
win
ter
,
th
e
s
u
r
f
ac
e
m
u
s
t
tilt
f
u
r
th
er
to
th
e
v
er
tical.
T
ilt
an
d
o
r
ien
tatio
n
d
o
n
'
t
h
av
e
a
h
u
g
e
im
p
ac
t.
I
n
t
h
is
r
esear
ch
,
it
was
tak
en
in
to
ac
c
o
u
n
t
th
at
th
e
an
g
le
is
f
ix
e
d
th
r
o
u
g
h
o
u
t
th
e
y
ea
r
,
a
n
d
f
o
r
th
e
p
u
r
p
o
s
e
o
f
in
cr
ea
s
in
g
s
o
lar
r
ad
iatio
n
an
d
th
e
en
e
r
g
y
o
u
tp
u
t
f
r
o
m
t
h
e
s
y
s
tem
,
th
e
e
f
f
ec
t
o
f
th
e
g
r
o
u
n
d
r
ef
lecto
r
o
n
th
e
o
p
tim
u
m
tilt
an
g
le
th
at
ac
h
iev
es
th
e
m
a
x
im
u
m
o
u
tp
u
t
p
o
wer
was
s
tu
d
ied
.
T
h
is
will
b
e
ch
ea
p
er
th
an
u
s
in
g
a
s
o
lar
tr
ac
k
e
r
f
o
r
th
e
p
u
r
p
o
s
e
o
f
c
h
an
g
in
g
th
e
a
n
g
le
ev
e
r
y
m
o
n
th
.
W
ith
th
e
h
elp
o
f
Fig
u
r
e
2
,
it
ca
n
ea
s
ily
ca
lcu
late
th
e
s
o
lar
altitu
d
e
an
g
le
N
at
s
o
l
ar
n
o
o
n
,
wh
ich
is
a
cr
u
cial
s
o
lar
p
ar
a
m
eter
[
2
8
]
.
T
h
e
altitu
d
e
an
g
le
r
ef
er
s
to
th
e
an
g
u
lar
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
740
-
7
51
744
d
is
tan
ce
b
etwe
en
th
e
s
u
n
a
n
d
th
e
h
o
r
izo
n
lo
ca
ted
d
ir
ec
tly
b
en
ea
th
it
at
a
g
iv
en
lo
ca
tio
n
.
T
h
e
r
elatio
n
s
h
ip
d
ep
icted
in
Fig
u
r
e
3
ca
n
b
e
e
x
p
r
ess
ed
as (
2
0
)
.
=
(
90
0
)
−
+
(
2
0
)
Fig
u
r
e
2
.
Dif
f
e
r
en
t v
iew
f
o
r
th
e
ea
r
th
an
d
s
u
n
Fig
u
r
e
3
.
T
h
e
s
o
lar
n
o
o
n
altitu
d
e
an
g
le
a
b
o
u
t th
e
s
u
n
2.
3
.
Sim
ula
t
i
o
n m
o
del
m
et
h
o
d
PVs
y
s
t
o
f
f
er
s
Hay
'
s
an
d
Per
ez
tr
an
s
p
o
s
itio
n
m
o
d
els
th
at
ca
n
b
e
u
s
ed
to
f
in
d
th
e
w
o
r
ld
in
cid
en
ce
o
f
r
ad
iatio
n
o
n
a
tilt
ed
p
lan
e.
[
2
9
]
.
T
h
e
two
m
o
d
els
co
m
e
u
p
wi
th
d
if
f
er
en
t
wa
y
s
to
f
ig
u
r
e
o
u
t
th
e
s
ca
tter
ed
p
ar
ts
o
f
th
e
r
a
d
iatio
n
th
at
h
its
th
e
tilt
in
g
p
lan
e.
Acc
o
r
d
in
g
to
th
e
Hay
m
o
d
el,
d
if
f
u
s
e
ir
r
ad
ian
c
e
is
m
ad
e
u
p
o
f
an
is
o
tr
o
p
ic
in
p
u
t a
n
d
a
"c
ir
cu
m
s
o
lar
"
co
m
p
o
n
en
t th
at
is
eq
u
al
t
o
th
e
b
ea
m
co
m
p
o
n
e
n
t.
[
3
0
]
.
T
h
e
"h
o
r
izo
n
b
an
d
"
th
at
th
e
Per
ez
-
I
n
eich
en
m
o
d
el
ad
d
s
is
an
o
th
e
r
s
ca
tter
ed
p
a
r
t.
[
3
1
]
.
I
t
d
iv
id
es
th
e
s
k
y
in
to
s
ec
tio
n
s
an
d
f
i
g
u
r
es
o
u
t
h
o
w
th
e
cir
c
u
m
s
o
lar
an
d
h
o
r
izo
n
b
a
n
d
s
ch
an
g
e
b
y
c
o
m
p
a
r
in
g
d
ata
f
r
o
m
m
o
r
e
th
an
two
d
o
ze
n
m
ea
s
u
r
e
m
en
t
s
ites
ar
o
u
n
d
th
e
wo
r
ld
.
B
ec
au
s
e
o
f
th
at
a
n
d
b
ased
o
n
[
3
2
]
,
P
er
ez
m
o
d
el
is
m
o
r
e
ac
cu
r
ate
t
h
an
th
e
Hay
m
o
d
el.
T
h
er
ef
o
r
e,
th
is
s
tu
d
y
u
s
es
th
e
Per
ez
tr
an
s
p
o
s
itio
n
m
o
d
el.
T
r
a
n
s
p
o
s
itio
n
r
ef
er
s
to
th
e
m
eth
o
d
o
f
d
eter
m
in
in
g
th
e
in
cid
en
t
ir
r
ad
ian
ce
o
n
a
tilt
ed
p
lan
e
b
ased
o
n
a
v
ailab
le
h
o
r
iz
o
n
tal
ir
r
a
d
ian
ce
d
ata
[
2
9
]
.
T
h
e
PV
s
y
s
t
is
u
tili
ze
d
to
co
n
v
e
r
t
th
e
g
lo
b
al
h
o
r
izo
n
tal
ir
r
ad
iatio
n
(
Glo
b
Ho
r
)
to
th
e
g
lo
b
al
in
ci
d
en
t
ir
r
a
d
iatio
n
i
n
th
e
co
llecto
r
p
lan
e
(
Glo
b
I
n
c)
f
o
r
an
y
g
iv
en
tilt
an
g
le.
Fro
m
(
6
)
,
th
e
b
ea
m
r
ad
iat
io
n
tilt
f
ac
to
r
,
wh
ic
h
is
eq
u
al
t
o
th
e
tilt
ed
s
u
r
f
ac
e
b
ea
m
ir
r
a
d
iatio
n
o
v
er
t
h
e
h
o
r
izo
n
tal
s
u
r
f
ac
e
b
ea
m
ir
r
ad
iatio
n
,
a
n
d
th
e
d
ef
i
n
itio
n
o
f
tr
an
s
p
o
s
itio
n
m
o
d
els
o
r
tr
an
s
p
o
s
itio
n
f
ac
to
r
(
T
F)
in
s
i
m
u
latio
n
,
wh
ich
is
eq
u
al
to
(
2
1
)
.
TF
=
(
2
1
)
T
h
e
tilt
f
ac
to
r
s
an
d
tr
a
n
s
p
o
s
itio
n
f
ac
to
r
d
eter
m
in
e
th
e
b
est
tilt
o
r
ien
tatio
n
.
T
h
e
im
p
o
r
tan
t
p
ar
am
eter
s
o
f
th
e
s
im
u
latio
n
d
ep
en
d
o
n
g
lo
b
al
i
n
cid
en
t
ir
r
ad
iatio
n
in
th
e
co
lle
cto
r
p
lan
e
(
Glo
b
I
n
c)
b
ec
au
s
e
t
h
e
g
lo
b
al
h
o
r
iz
o
n
tal
ir
r
ad
iatio
n
(
Glo
b
Ho
r
)
is
co
n
s
tan
t in
th
e
s
am
e
lo
ca
tio
n
.
2
.
4
.
Sim
ula
t
io
n m
e
t
ho
do
lo
g
y
2
.
4
.
1
.
Set
g
eo
g
ra
ph
ica
l c
o
o
rd
ina
t
es
T
h
is
r
esear
ch
d
esig
n
s
an
d
s
im
u
lates
an
o
n
-
g
r
i
d
PV
s
y
s
te
m
lo
ca
tio
n
in
B
ag
h
d
ad
,
I
r
aq
,
with
th
e
co
o
r
d
in
ates a
t
3
3
.
3
1
N
o
,
4
4
.
3
8
E
o
an
d
3
0
m
ab
o
v
e
s
ea
le
v
el.
Geo
g
r
ap
h
ic
co
o
r
d
in
ates f
r
o
m
PV
s
y
s
t so
f
twar
e
,
as
s
h
o
wn
in
Fig
u
r
e
4
,
p
r
o
v
id
e
m
eteo
r
o
lo
g
ical
d
ata.
Yea
r
l
y
h
o
r
izo
n
tal
g
lo
b
al
s
u
n
ir
r
ad
ian
ce
(
Glo
b
H)
an
d
d
if
f
u
s
e
co
m
p
o
n
en
t (
Dif
f
H)
a
r
e
s
h
o
wn
in
T
ab
le
1
.
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
Th
e
effec
ts
o
f su
r
fa
ce
a
lb
ed
o
a
n
d
p
h
o
to
vo
lta
ic
s
ystem
tilt
a
n
g
le
o
n
imp
r
o
vin
g
…
(
A
h
med
D
a
u
d
Mo
s
h
ee
r
)
745
T
ab
le
1
.
Yea
r
ly
h
o
r
iz
o
n
tal
g
lo
b
al
an
d
d
if
f
u
s
e
ir
r
a
d
ian
ce
in
B
ag
h
d
ad
P
a
r
a
me
t
e
r
G
l
o
b
H
D
i
f
f
H
V
a
l
u
e
s
k
W
h
/
m²
k
W
h
/
m²
Y
e
a
r
l
y
v
a
l
u
e
1
8
3
3
.
9
5
5
4
.
7
Fig
u
r
e
4
.
Geo
g
r
ap
h
ical
co
o
r
d
i
n
ates in
PVs
y
s
t f
o
r
B
ag
h
d
ad
c
ity
2
.
4
.
2
.
T
he
o
rient
a
t
io
n o
f
t
he
P
V
pa
nel
PV
s
y
s
t c
alcu
lates th
e
an
n
u
al
o
p
tim
al
tilt
an
g
le
f
o
r
f
ix
ed
tilt
e
d
p
lan
e
in
th
e
o
r
ien
tatio
n
s
tag
e.
B
ag
h
d
ad
s
h
o
u
ld
tilt
at
3
0
°
an
d
0
o
Azim
u
th
as
s
h
o
wn
in
F
ig
u
r
e
5
w
ith
alb
ed
o
(
0
.
2
)
,
an
d
PV
p
an
e
ls
f
ac
e
s
o
u
th
.
Up
o
n
co
n
d
u
ctin
g
n
u
m
er
o
u
s
tilt
an
g
le
test
s
,
th
e
s
im
u
latio
n
r
esu
lts
in
d
icate
th
at
th
e
an
g
le
y
ield
in
g
t
h
e
m
ax
im
u
m
o
u
t
p
u
t
p
o
wer
d
if
f
er
s
f
r
o
m
th
e
an
g
le
p
r
ev
io
u
s
ly
ass
u
m
ed
.
Fig
u
r
e
5
.
Set th
e
tilt
an
g
le
2
.
4
.
3
.
Sy
s
t
em
des
cr
iptio
n
T
h
e
p
h
o
to
v
o
ltaic
s
y
s
tem
co
n
s
id
er
ed
in
th
is
r
esear
ch
is
a
g
r
id
-
co
n
n
ec
ted
s
y
s
tem
with
2
0
.
4
8
k
W
p
p
o
wer
.
I
t
co
n
tain
s
6
4
m
o
d
u
les
(
4
s
tr
in
g
s
×
1
6
in
s
er
ies);
th
e
n
o
r
m
al
p
o
wer
o
f
o
n
e
m
o
d
u
le
is
3
2
0
W
p
,
an
d
th
e
m
o
d
u
le
ar
ea
is
1
2
4
m
2
.
T
h
e
o
t
h
er
PV
s
y
s
tem
ch
ar
ac
ter
is
tics
ar
e
s
h
o
wn
in
T
a
b
le
2
.
2
.
4
.
4
.
E
f
f
ec
t
o
f
g
ro
un
d a
lbedo
o
n t
he
o
ptima
l t
ilt
a
ng
le
o
f
P
V
pa
nels
T
h
e
g
r
o
u
n
d
f
o
r
in
s
tallin
g
s
o
la
r
s
y
s
tem
s
m
ay
b
e
co
n
cr
ete,
s
an
d
,
W
h
ite
Po
r
tlan
d
ce
m
e
n
t,
s
n
o
w
,
an
d
ea
ch
o
f
th
ese
g
r
o
u
n
d
s
h
as
a
s
p
ec
ial
alb
ed
o
v
alu
e.
I
n
th
is
r
ese
ar
ch
,
s
ix
PV
s
y
s
tem
-
m
o
u
n
tin
g
s
u
r
f
ac
es
wer
e
test
ed
in
th
e
s
im
u
latio
n
b
y
s
elec
tin
g
th
e
ap
p
r
o
p
r
iate
alb
e
d
o
v
alu
e
f
o
r
ea
ch
s
u
r
f
ac
e.
T
h
e
v
alu
e
o
f
alb
ed
o
f
o
r
ea
ch
ty
p
e
o
f
g
r
o
u
n
d
is
as
li
s
ted
in
[
3
3
]
,
[
3
4
]
.
I
n
c
r
ea
s
es
in
tilt
an
g
le
will
b
e
m
ad
e
if
th
e
s
u
r
f
ac
e
alb
ed
o
v
alu
e
ex
ce
ed
s
th
e
co
n
s
tan
t
alb
ed
o
v
alu
e
(
0
.
2
)
.
If
th
e
s
u
r
f
ac
e'
s
alb
ed
o
is
less
th
an
th
e
r
ef
er
e
n
ce
lev
el
o
f
0
.
2
.
T
h
en
,
th
e
tilt
an
g
le
will
g
r
ad
u
ally
d
ec
r
ea
s
e
u
n
til
th
e
m
ax
im
u
m
o
f
th
e
g
lo
b
al
in
cid
en
t
in
th
e
co
llecto
r
p
lan
e
(
Glo
b
I
n
c)
an
d
th
e
e
n
er
g
y
in
jecte
d
in
to
th
e
g
r
id
(
E
_
Gr
id
)
ar
e
r
ea
c
h
ed
[
2
5
]
.
T
h
e
t
y
p
e
o
f
m
o
u
n
tin
g
s
u
r
f
ac
es u
s
ed
in
th
is
r
esear
ch
is
s
h
o
wn
in
T
ab
le
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
740
-
7
51
746
T
ab
le
2
.
Gr
id
-
co
n
n
ec
ted
s
y
s
tem
ch
ar
ac
ter
is
tics
I
t
e
m
P
a
r
a
me
t
e
r
s
V
a
l
u
e
/
D
e
scr
i
p
t
i
o
n
P
V
mo
d
u
l
e
M
a
n
u
f
a
c
t
u
r
e
r
P
h
o
n
o
S
o
l
a
r
M
o
d
e
l
P
S
3
2
0
P
-
2
4
/
T
M
a
x
i
m
U
n
i
t
N
o
m
.
P
o
w
e
r
3
2
0
W
p
N
u
mb
e
r
o
f
P
V
m
o
d
u
l
e
s
64
N
o
mi
n
a
l
(
S
T
C
)
2
0
.
4
8
k
W
p
M
o
d
u
l
e
s
4
S
t
r
i
n
g
s
x
1
6
i
n
seri
e
s
N
o
mi
n
a
l
(
S
T
C
)
2
0
k
W
p
To
t
a
l
6
4
M
o
d
u
l
e
s
M
o
d
u
l
e
a
r
e
a
1
2
4
m²
I
n
v
e
r
t
e
r
M
a
n
u
f
a
c
t
u
r
e
Tr
a
n
n
e
r
g
y
M
o
d
e
l
TR
N
0
2
0
K
TL
U
n
i
t
N
o
m
.
P
o
w
e
r
2
0
.
0
k
W
a
c
N
u
mb
e
r
o
f
i
n
v
e
r
t
e
r
s
2
*
M
P
P
T
5
0
%
1
u
n
i
t
P
V
sy
st
d
a
t
a
b
a
s
e
To
t
a
l
p
o
w
e
r
2
0
.
0
k
W
a
c
O
p
e
r
a
t
i
n
g
v
o
l
t
a
g
e
2
5
0
-
8
0
0
V
P
n
o
m
r
a
t
i
o
(
D
C
:
A
C
)
1
.
0
2
T
ab
le
3
.
Su
r
f
ac
e
alb
ed
o
u
s
ed
i
n
th
e
s
tu
d
y
[
3
3
]
,
[
3
4
]
S
u
r
f
a
c
e
A
v
e
r
a
g
e
A
l
b
e
d
o
S
a
n
d
,
d
r
y
0
.
1
8
0
S
a
n
d
,
w
e
t
0
.
0
9
0
C
o
n
c
r
e
t
e
0
.
2
5
0
C
o
a
l
fl
y
a
sh
0
.
6
2
0
W
h
i
t
e
p
a
i
n
t
0
.
7
0
0
W
h
i
t
e
P
o
r
t
l
a
n
d
c
e
me
n
t
0
.
8
7
0
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
is
r
esear
c
h
,
th
e
in
f
l
u
en
ce
o
f
s
ev
er
al
f
ac
to
r
s
o
n
th
e
p
er
f
o
r
m
an
ce
o
f
p
h
o
t
o
v
o
ltaic
PV
m
o
d
u
les
h
a
s
b
ee
n
co
n
s
id
er
ed
,
s
u
ch
as
g
lo
b
al
in
cid
en
t
ir
r
ad
iatio
n
in
th
e
co
llecto
r
p
lan
e
(
Glo
b
I
n
c)
,
ef
f
e
ctiv
e
en
er
g
y
at
th
e
o
u
tp
u
t
o
f
th
e
a
r
r
ay
(
E
Ar
r
ay
)
an
d
en
er
g
y
in
jecte
d
in
to
th
e
g
r
id
(
E
_
Gr
i
d
)
.
T
h
e
g
lo
b
al
h
o
r
i
zo
n
tal
ir
r
ad
iatio
n
is
co
n
s
id
er
ed
c
o
n
s
tan
t in
th
is
lo
c
atio
n
.
Fo
r
o
b
tain
in
g
r
esear
ch
r
esu
lts
,
th
e
f
o
llo
win
g
s
tep
s
wer
e
ap
p
lied
:
i)
Step
1
: O
b
tain
th
e
y
ea
r
ly
f
ix
e
d
o
p
tim
al
tilt
an
g
le
PV
Sy
s
t
s
o
f
twar
e
s
u
g
g
ests
3
0
°
as
th
e
an
n
u
al
o
p
tim
u
m
tilt
an
g
le
with
co
n
s
tan
t
alb
ed
o
(
0
.
2
)
.
I
n
th
is
an
g
le,
th
e
y
ea
r
ly
r
esu
lts
s
h
o
wed
th
at
(
Glo
b
I
n
c)
is
2
0
5
4
.
2
k
W
h
/m
²,
E
f
f
ec
tiv
e
en
er
g
y
at
th
e
o
u
tp
u
t
o
f
th
e
ar
r
a
y
(
E
_
Ar
r
ay
)
an
d
th
e
(
E
_
Gr
id
)
i
s
3
5
.
9
1
3
MWh
,
3
5
.
2
0
9
MWh
,
r
esp
ec
tiv
ely
.
T
h
e
3
0
°
an
g
le
th
en
d
ec
r
ea
s
ed
o
r
in
cr
ea
s
ed
to
in
c
r
ea
s
e
th
ese
v
al
u
es.
T
ab
le
4
s
h
o
ws
a
co
m
p
ar
i
s
o
n
b
etwe
en
two
tilt
an
g
les
,
a
3
0
°
an
d
a
3
1
°
.
At
a
31
°
tilt
an
g
le
,
th
e
Glo
b
I
n
c
is
lo
wer
th
an
th
at
wh
en
th
e
tilt
an
g
le
was 3
0
°
,
but
th
e
v
alu
e
o
f
E
_
Ar
r
ay
an
d
E
_
G
r
id
is
s
till
a
h
ig
h
er
v
alu
e
th
at
is
,
b
ec
au
s
e
th
e
PV
lo
s
s
es
d
u
e
to
tem
p
er
atu
r
e
at
tilt
an
g
le
3
0
°
is
1
1
.
8
1
1
%
,
wh
ich
is
m
o
r
e
th
an
th
e
lo
s
s
es a
t
a
tilt
an
g
le
o
f
3
1
°
wh
ich
is
eq
u
al
to
1
1
.
7
9
6
%.
T
ab
le
4
.
Yea
r
ly
h
o
r
iz
o
n
tal
g
lo
b
al,
in
cid
en
ce
ir
r
ad
ian
ce
a
n
d
t
h
e
en
er
g
y
o
u
tp
u
t o
f
th
e
s
y
s
te
m
Ti
l
t
a
n
g
l
e
G
l
o
b
H
o
r
G
l
o
b
I
n
c
EA
r
r
a
y
E_
G
r
i
d
k
W
h
/
m²
k
W
h
/
m²
M
W
h
M
W
h
29
1
8
3
3
.
9
2
0
5
3
.
9
3
5
.
9
0
2
3
5
.
1
9
9
30
1
8
3
3
.
9
2
0
5
4
.
2
3
5
.
9
1
3
3
5
.
2
0
9
31
1
8
3
3
.
9
2
0
5
4
.
0
3
5
.
9
1
6
3
5
.
2
1
2
32
1
8
3
3
.
9
2
0
5
3
.
2
3
5
.
9
1
0
3
5
.
2
0
5
33
1
8
3
3
.
9
2
0
5
2
.
0
3
5
.
8
9
5
3
5
.
1
9
0
ii)
Step
2
:
d
if
f
er
e
n
t su
r
f
ac
e
alb
e
d
o
with
y
ea
r
ly
v
ar
iab
les f
ix
e
d
tilt
an
g
le
Dif
f
er
en
t
s
u
r
f
ac
e
alb
ed
o
,
as
in
T
ab
le
3
,
will
b
e
tak
en
,
an
d
t
h
e
r
esu
lt
f
o
r
ea
ch
ca
s
e.
Fo
r
ea
ch
ca
s
e
in
th
is
s
tu
d
y
,
as
in
s
tep
1
,
th
e
r
e
f
er
en
ce
an
n
u
al
o
p
tim
u
m
tilt
a
n
g
le
is
at
30°
with
co
n
s
tan
t
al
b
ed
o
(
0
.
2
)
,
an
d
t
h
e
co
m
p
ar
is
o
n
will
b
e
ac
co
r
d
in
g
to
r
ef
er
en
ce
a
n
n
u
al
o
p
tim
u
m
ti
lt
an
g
le
r
esu
lts
as
in
T
ab
le
4
.
I
f
th
e
s
u
r
f
ac
e
alb
ed
o
v
alu
e
less
th
an
c
o
n
s
tan
t a
lb
ed
o
(
0
.
2
)
t
h
e
p
r
o
ce
d
u
r
e
will b
e
s
tar
tin
g
at
r
e
f
er
en
ce
an
n
u
al
o
p
ti
m
u
m
tilt
an
g
l
e
th
e
n
d
ec
r
ea
s
ed
o
r
in
cr
ea
s
ed
r
ef
er
e
n
ce
an
n
u
al
o
p
tim
u
m
tilt
an
g
le
u
n
til
r
ea
ch
i
n
g
m
ax
im
u
m
r
esu
lts
o
f
(
E
Ar
r
ay
,
E
_
Gr
id
)
.
T
h
e
p
r
o
ce
d
u
r
es
ar
e
s
u
m
m
ar
ized
in
th
e
f
l
o
w
ch
ar
t
s
h
o
wn
in
Fig
u
r
e
5
.
As
in
T
ab
le
3
,
th
er
e
ar
e
two
v
alu
es
(
0
.
0
9
,
0
.
1
8
)
less
th
an
(
0
.
2
)
.
T
h
e
r
esu
lts
ar
e
s
h
o
wn
in
T
ab
le
6
an
d
T
ab
le
6
f
o
r
alb
e
d
o
v
alu
es
0
.
1
8
an
d
0
.
0
9
.
As
s
h
o
wn
in
T
a
b
le
5
t
h
e
m
ax
im
u
m
r
esu
lts
o
f
(
E
Ar
r
a
y
,
E
_
Gr
id
)
ac
h
iev
ed
at
tilt
an
g
le
3
0
.
5
o
,
w
h
ich
m
ea
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
Th
e
effec
ts
o
f su
r
fa
ce
a
lb
ed
o
a
n
d
p
h
o
to
vo
lta
ic
s
ystem
tilt
a
n
g
le
o
n
imp
r
o
vin
g
…
(
A
h
med
D
a
u
d
Mo
s
h
ee
r
)
747
th
at
at
an
alb
ed
o
v
alu
e
o
f
0
.
1
8
,
th
e
o
p
tim
u
m
tilt
an
g
le
is
at
a
3
0
.
5
°.
Similar
ly
,
f
o
r
s
u
r
f
ac
e
alb
ed
o
o
f
0
.
0
9
,
th
e
m
ain
r
esu
lts
,
as sh
o
wn
in
T
ab
l
e
6
,
th
e
m
a
x
im
u
m
r
esu
lts
o
f
(
E
Ar
r
ay
,
E
_
G
r
id
)
ar
e
ac
h
iev
ed
at
tilt
an
g
le
29°
.
Acc
o
r
d
in
g
to
T
ab
le
3
,
t
h
er
e
a
r
e
f
o
u
r
v
alu
es
m
o
r
e
t
h
an
th
e
co
n
s
tan
t
alb
ed
o
v
alu
e
o
f
0
.
2
.
Firstl
y
,
th
e
v
alu
es
o
f
Glo
b
I
n
c,
E
Ar
r
ay
,
E
_
Gr
id
ar
e
m
ea
s
u
r
e
d
f
o
r
ea
ch
alb
ed
o
v
alu
e
an
d
ac
co
r
d
in
g
t
o
f
ix
ed
r
ef
er
e
n
ce
an
n
u
al
o
p
tim
u
m
tilt
an
g
le
wh
ich
is
3
1
°
f
o
r
th
is
ca
s
e,
as
s
h
o
wn
T
ab
le
7
.
Seco
n
d
ly
,
th
e
p
r
o
ce
d
u
r
e
will
s
tar
t
at
th
e
r
ef
er
en
ce
an
n
u
al
tilt
an
g
le
(
3
1
°),
th
en
in
cr
ea
s
e
o
r
d
ec
r
ea
s
e
th
is
r
ef
er
e
n
ce
an
n
u
al
tilt
a
n
g
le.
T
h
e
f
in
al
a
n
n
u
al
o
p
tim
u
m
tilt
an
g
le
with
d
if
f
er
en
t
s
u
r
f
ac
e
alb
ed
o
will
b
e
th
e
o
n
e
th
at
ac
h
iev
es
m
ax
im
u
m
r
esu
lts
o
f
(
Glo
b
I
n
c,
E
Ar
r
ay
,
E
_
G
r
id
)
.
T
h
e
o
p
tim
u
m
tilt
an
g
les
f
o
r
ea
ch
alb
ed
o
v
alu
e
ab
o
v
e
0
.
2
ar
e
as
s
h
o
wn
in
T
ab
le
8
.
Fin
ally
,
th
e
o
p
tim
u
m
tilt
an
g
le,
wh
ich
g
iv
es
m
ax
im
u
m
en
er
g
y
in
jecti
o
n
in
to
th
e
g
r
id
f
o
r
ea
ch
ty
p
e
o
f
g
r
o
u
n
d
alb
ed
o
f
o
r
th
is
s
tu
d
y
ar
e
s
u
m
m
ar
ized
in
Fig
u
r
e
7
.
Fig
u
r
e
6
.
Op
tim
al
tilt
an
g
le
s
elec
tin
g
p
r
o
ce
d
u
r
es
T
ab
le
5
.
E
n
er
g
y
v
alu
es a
n
d
in
cid
en
ce
r
ad
iatio
n
alb
ed
o
v
alu
e
(
0
.
1
8
)
with
r
esp
ec
t to
alb
ed
o
v
alu
e
(
0
.
2
)
Ti
l
t
a
n
g
l
e
D
e
g
r
e
e
A
l
b
e
d
o
V
a
l
u
e
G
l
o
b
I
n
c
EA
r
r
a
y
E_
G
r
i
d
k
W
h
/
m²
M
W
h
M
W
h
33
0
.
1
8
2
0
4
9
.
0
3
5
.
8
5
2
3
5
.
1
4
8
32
0
.
1
8
2
0
5
0
.
4
3
5
.
8
6
9
3
5
.
1
6
6
31
0
.
1
8
2
0
5
1
.
3
3
5
.
8
7
8
3
5
.
1
7
5
3
0
.
5
0
.
1
8
2
0
5
1
.
6
3
5
.
8
7
9
3
5
.
1
7
6
30
0
.
1
8
2
0
5
1
.
7
3
5
.
8
7
8
3
5
.
1
7
5
29
0
.
1
8
2
0
5
1
.
6
3
5
.
8
7
0
3
5
.
1
6
7
T
ab
le
6
.
E
n
er
g
y
v
alu
es a
n
d
in
cid
en
ce
r
ad
iatio
n
f
o
r
s
u
r
f
ac
e
a
lb
ed
o
(
0
.
0
9
)
with
r
esp
ec
t to
al
b
ed
o
v
alu
e
(
0
.
2
)
Ti
l
t
a
n
g
l
e
D
e
g
r
e
e
A
l
b
e
d
o
V
a
l
u
e
G
l
o
b
I
n
c
EA
r
r
a
y
E_
G
r
i
d
k
W
h
/
m²
M
W
h
M
W
h
32
0
.
0
9
2
0
3
7
.
9
3
5
.
6
8
8
3
4
.
9
8
7
31
0
.
0
9
2
0
3
9
.
5
3
5
.
7
0
8
3
5
.
0
0
7
30
0
.
0
9
2
0
4
0
.
7
3
5
.
7
1
9
3
5
.
0
1
9
29
0
.
0
9
2
0
4
1
.
2
3
5
.
7
2
1
3
5
.
0
2
1
28
0
.
0
9
2
0
4
1
.
3
3
5
.
7
1
5
3
5
.
0
1
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
740
-
7
51
748
T
ab
le
7
.
E
n
er
g
y
v
alu
es a
n
d
in
cid
en
ce
r
ad
iatio
n
f
o
r
d
if
f
e
r
en
t
alb
ed
o
v
al
u
es with
r
esp
ec
t to
t
ilt an
g
le
(
3
1
o
)
Ti
l
t
a
n
g
l
e
D
e
g
r
e
e
A
l
b
e
d
o
V
a
l
u
e
G
l
o
b
I
n
c
EA
r
r
a
y
E_
G
r
i
d
k
W
h
/
m²
M
W
h
M
W
h
31
0
.
2
5
2
0
6
0
.
5
3
6
.
0
1
0
3
5
.
3
0
4
31
0
.
6
2
0
2
1
0
9
.
0
3
6
.
7
0
5
3
5
.
9
8
6
31
0
.
7
0
0
2
1
1
9
.
4
3
6
.
8
5
4
3
6
.
1
3
3
31
0
.
8
7
0
2
1
4
1
.
7
3
7
.
1
7
1
3
6
.
4
4
4
T
ab
le
8
.
Fin
al
an
n
u
al
o
p
tim
u
m
tilt
an
g
le
f
o
r
d
if
f
er
en
t su
r
f
a
ce
alb
ed
o
Ti
l
t
A
n
g
l
e
D
e
g
r
e
e
A
l
b
e
d
o
R
a
t
i
o
G
l
o
b
I
n
c
EA
r
r
a
y
E_
G
r
i
d
k
W
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/
m²
M
W
h
M
W
h
3
1
.
5
0
.
2
5
0
2
0
6
0
.
4
3
6
.
0
1
1
3
5
.
3
0
5
38
0
.
6
2
0
2
1
1
9
.
7
3
6
.
8
8
9
3
6
.
1
6
6
40
0
.
7
0
0
2
1
3
1
.
7
3
7
.
0
6
9
3
6
.
3
4
1
45
0
.
8
7
0
2
1
7
7
.
4
3
7
.
7
3
9
3
6
.
9
9
9
Fig
u
r
e
7
.
T
h
e
ty
p
es g
r
o
u
n
d
al
b
ed
o
v
er
s
u
s
o
p
tim
u
m
tilt
an
g
l
e
an
d
en
e
r
g
y
i
n
jectio
n
in
to
th
e
g
r
id
4.
DIS
CU
SS
I
O
N
T
h
e
s
im
u
latio
n
r
esu
lts
in
T
ab
l
es
5
–
8
in
d
icate
a
s
ig
n
if
ican
t
c
o
r
r
elatio
n
am
o
n
g
g
r
o
u
n
d
-
s
u
r
f
ac
e
alb
ed
o
,
tilt
an
g
le,
an
d
th
e
en
er
g
y
p
e
r
f
o
r
m
a
n
ce
m
etr
ics
o
f
th
e
PV
s
y
s
tem
,
s
p
ec
if
ically
(
Glo
b
I
n
c)
,
(
E
Ar
r
ay
)
,
an
d
(
E
_
Gr
id
)
.
I
n
th
e
r
ef
er
e
n
ce
s
ce
n
ar
io
(
alb
e
d
o
=
0
.
2
,
tilt
=
3
1
°),
th
e
Glo
b
I
n
c
attain
ed
r
o
u
g
h
ly
2
0
5
4
k
W
h
/m
²,
r
esu
ltin
g
in
E
Ar
r
a
y
=
3
5
.
9
1
6
MWh
an
d
E
_
Gr
id
=
3
5
.
2
1
2
M
W
h
/y
r
.
As
th
e
alb
ed
o
d
im
in
is
h
ed
to
0
.
1
8
(
T
ab
le
5
)
an
d
0
.
0
9
(
T
ab
le
6
)
,
th
e
o
p
ti
m
al
tilt
an
g
les
y
ield
in
g
th
e
m
ax
im
u
m
E
_
G
r
id
ad
ju
s
ted
t
o
3
0
.
5
°
an
d
2
9
°,
r
esp
ec
tiv
ely
.
T
h
e
d
im
i
n
is
h
ed
g
r
o
u
n
d
r
ef
lectiv
it
y
r
esu
lted
in
a
m
ar
g
in
al
d
ec
lin
e
in
t
h
e
d
if
f
u
s
e
-
r
ef
lecte
d
r
ad
iatio
n
co
m
p
o
n
en
t;
y
et,
r
ed
u
cin
g
th
e
tilt
an
g
le
en
h
an
ce
d
th
e
ca
p
tu
r
e
o
f
d
ir
ec
t
s
o
lar
r
ad
iatio
n
,
p
r
e
s
er
v
in
g
an
en
er
g
y
o
u
tp
u
t
o
f
ar
o
u
n
d
3
5
.
1
7
–
3
5
.
0
2
MWh
/y
r
.
T
h
is
tr
en
d
in
d
icate
s
t
h
at,
in
lo
w
-
al
b
ed
o
c
o
n
d
itio
n
s
,
a
r
ed
u
ce
d
tilt
an
g
le
is
b
en
ef
icial
f
o
r
o
p
tim
izin
g
d
ir
ec
t so
lar
g
ain
.
C
o
n
v
er
s
ely
,
wh
en
th
e
alb
e
d
o
wen
t
ab
o
v
e
0
.
2
(
T
ab
les
7
–
8
)
,
th
e
g
r
o
u
n
d
ex
h
i
b
ited
h
ig
h
er
r
ef
lectiv
ity
,
co
n
tr
ib
u
tin
g
to
a
g
r
ea
ter
u
p
war
d
r
ad
iatio
n
p
o
r
tio
n
t
h
at
f
av
o
r
ed
s
teep
m
o
d
u
le
o
r
ien
tatio
n
s
.
C
o
n
s
eq
u
en
tly
,
Glo
b
I
n
c
ex
p
er
ien
ce
d
a
g
r
a
d
u
a
l
in
cr
ea
s
e
f
r
o
m
2
0
6
0
.
4
k
W
h
/m
²
at
an
alb
ed
o
o
f
0
.
2
5
to
2
1
7
7
.
4
k
W
h
/m
²
with
a
n
alb
ed
o
o
f
0
.
8
7
.
T
h
e
o
p
tim
al
ti
lt
an
g
le
in
cr
ea
s
ed
f
r
o
m
3
1
.
5
°
to
4
5
°,
wh
ile
E
_
Gr
id
clim
b
e
d
f
r
o
m
3
5
.
3
0
5
MWh
to
3
6
.
9
9
9
MWh
,
r
esu
ltin
g
in
a
to
tal
im
p
r
o
v
e
m
en
t o
f
5
.
0
7
% r
elativ
e
to
th
e
r
ef
e
r
en
ce
s
ce
n
ar
i
o
.
T
h
is
d
is
tin
ct
p
atter
n
d
em
o
n
s
tr
ates
th
e
p
h
y
s
ical
d
ep
e
n
d
en
ce
o
f
p
h
o
to
v
o
ltaic
p
er
f
o
r
m
an
ce
o
n
tilt
an
g
le
an
d
s
u
r
f
ac
e
r
ef
lectiv
ity
.
As
Glo
b
I
n
c
e
x
p
er
ien
ce
s
an
in
cr
ea
s
e
in
alb
ed
o
a
n
d
m
o
d
if
ied
tilt
,
b
o
th
th
e
E
Ar
r
a
y
an
d
E
_
Gr
id
ex
h
ib
it
a
co
r
r
esp
o
n
d
i
n
g
r
is
e,
c
o
n
f
ir
m
i
n
g
th
at
th
e
i
n
cid
en
t
ir
r
ad
iatio
n
o
n
th
e
c
o
llecto
r
p
lan
e
is
th
e
p
r
im
ar
y
d
eter
m
in
an
t
o
f
e
n
er
g
y
g
ain
.
T
h
e
o
p
tim
u
m
tilt
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g
le
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n
o
t
a
co
n
s
tan
t
s
p
ec
if
ic
to
a
lo
ca
tio
n
b
u
t
m
u
s
t
b
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
w
E
lec
&
Dr
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s
t
I
SS
N:
2088
-
8
6
9
4
Th
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effec
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f su
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fa
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a
lb
ed
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p
h
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u
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r
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749
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ased
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n
s
u
r
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g
th
at
th
e
m
o
d
u
les
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ax
im
ize
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e
ca
p
tu
r
e
o
f
b
o
th
d
ir
ec
t
an
d
r
ef
lecte
d
s
o
lar
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ad
iatio
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f
o
r
en
h
an
ce
d
y
ea
r
ly
en
er
g
y
p
r
o
d
u
ctio
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.
Fu
tu
r
e
s
tu
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ies
s
h
o
u
ld
b
e
f
o
cu
s
o
n
d
ev
el
o
p
in
g
l
o
ca
l
d
esig
n
g
u
i
d
elin
es
th
at
lin
k
clim
atic
co
n
d
i
tio
n
s
with
o
p
tim
al
tilt
alb
ed
o
ar
r
a
n
g
em
e
n
t
f
o
r
PV
s
y
s
tem
s
.
Su
b
s
eq
u
en
t
s
tu
d
ies
s
h
o
u
ld
in
clu
d
e
b
i
f
ac
ial
PV
m
o
d
u
les
an
d
in
teg
r
ate
a
c
o
m
p
r
e
h
en
s
iv
e
tec
h
n
o
-
ec
o
n
o
m
ic
an
aly
s
is
in
ac
c
o
r
d
an
ce
with
th
e
I
E
C
6
2
5
4
8
,
I
E
C
6
1
7
3
0
,
a
n
d
I
E
C
6
1
2
1
5
s
tan
d
ar
d
s
.
5.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
ev
al
u
ated
th
e
im
p
ac
t
o
f
g
r
o
u
n
d
-
s
u
r
f
ac
e
r
e
f
lectio
n
(
alb
ed
o
)
o
n
o
p
tim
u
m
tilt
an
g
le
an
d
en
er
g
y
o
u
tp
u
t
o
f
a
s
tatio
n
ar
y
o
n
-
g
r
id
p
h
o
to
v
o
ltaic
PV
s
y
s
tem
s
itu
ated
in
B
ag
h
d
a
d
,
I
r
a
q
.
T
h
e
in
v
esti
g
atio
n
d
em
o
n
s
tr
ated
a
d
ir
ec
t
an
d
co
n
s
tan
t
r
elatio
n
s
h
ip
b
etwe
en
al
b
ed
o
an
d
th
e
tilt
an
g
le
th
at
o
p
ti
m
izes
an
n
u
al
en
er
g
y
o
u
tp
u
t.
T
h
e
r
esu
lts
in
d
icate
d
t
h
at
as
th
e
alb
ed
o
lo
wer
s
b
elo
w
th
e
r
e
f
er
en
ce
v
alu
e
(
0
.
2
)
,
th
e
o
p
tim
al
tilt
an
g
le
m
ar
g
in
ally
r
e
d
u
ce
s
to
s
u
s
tain
m
ax
im
u
m
e
n
er
g
y
ca
p
tu
r
e.
I
n
co
n
tr
ast,
as
th
e
alb
ed
o
r
ea
c
h
es
0
.
2
,
t
h
e
o
p
tim
al
tilt
an
g
le
in
cr
em
en
tally
in
cr
ea
s
es
f
r
o
m
3
1
.
5
°
at
an
alb
ed
o
o
f
0
.
2
5
to
4
5
°
at
0
.
8
7
lead
i
n
g
to
en
h
an
ce
d
r
e
f
lecte
d
ir
r
ad
iatio
n
an
d
a
p
o
ten
tial
an
n
u
al
en
er
g
y
g
ain
o
f
u
p
to
5
.
0
7
%
r
elativ
e
to
th
e
r
ef
er
en
ce
s
itu
atio
n
.
T
h
e
s
tu
d
y
s
u
g
g
ests
th
at
ea
ch
s
u
r
f
ac
e
ty
p
e
with
a
d
if
f
er
e
n
t
alb
ed
o
p
o
s
s
ess
es
a
s
p
ec
if
ic
til
t
co
n
f
ig
u
r
at
io
n
th
at
o
p
tim
izes
s
y
s
tem
ef
f
icien
cy
.
C
o
n
s
eq
u
en
tly
,
ass
u
m
in
g
a
f
ix
ed
tilt
an
g
le
r
eg
ar
d
less
o
f
th
e
s
u
r
r
o
u
n
d
in
g
s
u
r
f
ac
e
r
ef
lectio
n
m
ay
r
esu
lt
in
in
f
er
io
r
p
h
o
to
v
o
ltaic
p
er
f
o
r
m
an
ce
.
I
n
co
r
p
o
r
atin
g
ac
tu
al
alb
ed
o
v
alu
es
in
to
p
h
o
to
v
o
ltaic
d
esig
n
an
d
s
im
u
latio
n
to
o
ls
,
s
u
ch
as
PVs
y
s
t,
is
cr
u
cial
f
o
r
p
r
ec
is
e
tilt
-
an
g
le
ass
ess
m
en
t
an
d
d
ep
en
d
ab
l
e
en
er
g
y
p
r
e
d
ictio
n
.
T
h
is
r
esear
ch
u
n
d
er
s
co
r
es
th
e
n
ec
ess
ity
f
o
r
f
u
tu
r
e
s
tu
d
ies
to
i
n
co
r
p
o
r
ate
th
e
tem
p
o
r
al
v
ar
iat
io
n
o
f
alb
ed
o
(
e
.
g
.
,
r
esu
ltin
g
f
r
o
m
s
ea
s
o
n
al
ch
an
g
es,
d
u
s
t
ac
cu
m
u
latio
n
,
o
r
g
r
o
u
n
d
co
v
er
)
to
im
p
r
o
v
e
f
o
r
ec
ast
ac
cu
r
ac
y
an
d
s
y
s
tem
o
p
tim
izatio
n
in
r
ea
l o
p
er
atin
g
s
ettin
g
s
.
F
UNDING
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NF
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M
A
T
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Au
th
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r
s
s
tate
n
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h
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u
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C
o
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th
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th
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s
h
ip
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an
d
f
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o
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Na
m
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Aut
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Ah
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Hu
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m
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C
:
C
o
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p
t
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a
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