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11
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v11
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47
Jo
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gypt
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ghe
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of E
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l
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gypt
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rt
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c
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re
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bb
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ia
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C
a
ir
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151
7,
E
gy
pt
.
E
m
a
il:
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s
m
a
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a
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a
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a
xi
m
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t
h
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be
s
t
us
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of
t
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m
c
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n be
m
a
de
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a
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w
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[
1
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.
T
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acc
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us
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d
m
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f
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[
2]
,
q
ua
dr
a
t
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c
f
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[
3
]
,
c
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[
4]
,
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pl
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[
5]
a
nd
l
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t
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c
f
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c
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s
[
6
]
.
T
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m
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de
l
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f
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cat
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o
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is
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A
ut
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s
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n
[
7]
r
e
a
c
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d t
ha
t
m
o
de
l
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g
wi
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d
t
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p
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m
ode
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pi
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w
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e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
11
,
No
.
1,
F
e
b
r
ua
r
y
2
02
1
:
47
-
56
48
m
o
d
el
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q
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v
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s
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r
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pe
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d p
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n
c
t
i
on
m
ode
l
l
i
n
g
t
o
gi
ve
be
t
t
e
r
m
o
de
l
l
i
ng
a
c
c
ur
a
c
y
t
ha
n
t
he
d
e
f
a
u
l
t
4
-
p
ar
am
e
t
e
r
s
l
ogi
s
t
i
c
f
u
nc
t
i
o
ns
.
A
ut
ho
r
s
i
n
[
8
]
m
a
de
a
c
o
m
p
r
e
he
ns
i
ve
r
e
vi
e
w
a
bo
ut
w
i
nd t
u
r
bi
ne
s
po
we
r
c
ur
ve
s
m
o
de
l
l
i
n
g
t
e
c
hni
q
ue
s
.
P
o
w
e
r
c
ur
ve
s
d
u
r
i
n
g m
ode
l
l
i
n
g
a
r
e
c
a
t
e
g
or
i
z
e
d i
nt
o de
t
e
r
m
i
ni
s
t
i
c
m
ode
l
l
i
ng a
n
d
pr
ob
a
b
i
l
i
s
t
ic
m
o
d
e
l
l
i
n
g
.
M
a
t
h
e
m
a
t
i
c
a
l
c
u
r
v
e
f
i
t
t
i
n
g
a
n
d
a
r
t
i
f
i
c
i
a
l
i
n
t
e
l
l
i
g
e
n
c
e
t
e
c
h
n
i
q
u
e
s
a
r
e
e
x
a
m
p
l
e
s
o
f
d
e
t
e
r
m
i
n
i
s
t
i
c
m
o
de
l
i
ng
[
9,
1
0]
.
C
u
r
ve
f
i
t
t
i
ng
m
o
de
l
s
ha
ve
t
wo
s
ub
s
e
c
t
i
o
ns
o
ne
of
t
he
m
i
s
s
e
gm
e
nt
e
d
c
ur
ve
f
i
t
t
i
ng m
ode
ls
l
i
k
e
l
i
n
e
a
r
f
u
n
c
t
i
o
n
s
,
p
o
l
y
n
o
m
i
a
l
f
u
n
c
t
i
o
n
s
a
n
d
e
x
p
o
n
e
n
t
i
a
l
f
u
n
c
t
i
o
ns
[
11
-
13
]
.
T
he
s
e
c
on
d s
u
bs
e
c
t
i
on i
s
i
n
t
e
g
r
a
t
e
d
c
u
r
v
e
f
i
t
t
i
n
g
m
o
d
e
l
s
l
i
k
e
d
o
u
b
l
e
e
x
p
o
n
e
n
t
i
a
l
-
ba
s
e
d
f
u
nc
t
i
o
ns
a
nd l
ogi
s
t
i
c
f
un
c
tion
s
[
14
,
1
5]
.
T
he
a
c
c
u
r
a
c
y
of
di
f
f
e
r
e
nt
m
ode
l
s
i
s
de
s
c
r
i
be
d
t
h
r
ou
g
h t
h
e
f
ol
l
o
w
i
n
g c
o
m
m
o
nl
y
us
e
d
c
r
i
t
e
r
i
a
:
m
e
a
n
a
bs
ol
ut
e
e
r
ro
r
(
MA
E
)
,
r
oot
m
e
a
n
s
qua
r
e
e
r
r
o
r
(
R
MS
E
)
a
nd
de
t
e
r
m
i
n
a
t
i
on
c
oe
f
f
i
c
i
e
nt
R
2
.
A
ut
ho
r
s
i
n
[
1
6
]
us
e
d
ni
ne
di
f
f
e
r
e
nt
l
ogi
s
t
i
c
f
u
nc
t
i
o
ns
e
q
ua
t
i
ons
t
o
m
o
de
l
s
i
x c
om
m
onl
y
us
e
d
w
i
n
d
t
ur
bi
ne
s
.
I
n
[
1
7]
,
a
ut
ho
r
s
us
e
d
w
e
i
b
ul
l
c
um
ul
a
t
i
ve
p
r
oba
b
i
l
i
t
y de
ns
i
t
y
f
u
nc
t
i
on
m
ode
l
l
i
n
g
a
s
a
ne
w t
ool
t
o
m
o
de
l
di
f
f
e
r
e
n
t
s
i
x
w
i
nd
t
ur
bi
ne
s
w
i
th
g
e
n
e
r
a
tion
pow
e
r
r
a
ng
e
s
(
2
-
7
M
W
)
.
W
e
i
b
u
l
l
c
u
m
u
l
a
t
i
v
e
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
g
i
v
e
s
l
o
w
e
r
RM
S
E
t
h
a
n
a
l
l
t
y
p
e
s
o
f
4
-
p
o
i
n
t
l
o
g
i
s
t
i
c
f
u
n
c
t
i
o
n
s
w
i
t
h
s
i
m
p
l
e
r
m
o
d
e
l
l
i
n
g
e
q
u
a
t
i
o
n
.
I
n t
hi
s
pa
pe
r
a
s
a
n e
xt
e
ns
i
o
n
f
o
r
p
r
e
v
i
o
u
s
l
i
t
e
r
a
t
u
r
e
,
d
i
f
f
e
r
e
n
t
s
i
n
g
l
e
c
u
m
u
l
a
t
i
v
e
p
r
o
b
a
b
i
l
i
t
y
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
s
a
nd
a
ne
w
a
pp
r
oa
c
h
o
f
a
c
o
m
p
os
i
t
e
c
u
m
ul
a
t
i
ve
p
r
o
ba
bi
l
i
t
y d
e
ns
i
t
y
f
u
n
c
t
i
on a
r
e
us
e
d
t
o m
o
de
l
l
ar
g
e
r
s
cal
e
w
i
n
d
s
pe
e
d
a
n
d p
ow
e
r
va
l
ue
s
.
T
o c
he
c
k t
h
e
s
e
m
ode
l
s
va
l
i
di
t
y,
d
i
f
f
er
e
n
t
2
4
c
o
m
m
er
ci
al
w
i
n
d
t
u
r
b
i
n
es
ar
e
m
o
de
l
l
e
d.
T
he
ge
ne
r
a
t
e
d
po
we
r
o
f
t
he
s
e
w
i
nd t
ur
b
i
ne
s
c
o
ve
r
s
t
he
r
a
nge
(
2
0
0 KW
-
7 MW
)
.
T
he
us
e
d s
i
ngl
e
c
u
m
u
l
a
t
i
v
e
p
r
o
b
a
b
i
l
i
t
y
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
s
f
o
r
m
o
d
e
l
l
i
n
g
a
r
e
w
e
i
b
u
l
l
,
g
a
m
m
a
a
n
d
l
o
g
-
n
o
r
m
a
l
d
i
s
t
r
i
b
u
t
i
o
n
f
un
c
tion
s
.
A
l
s
o
a
n
e
w
c
o
m
p
o
s
i
t
e
o
f
w
e
i
b
u
l
l
–
g
a
m
m
a
c
u
m
u
l
a
t
i
v
e
p
r
o
b
a
b
i
l
i
t
y
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
i
s
g
e
n
e
r
a
t
e
d
a
nd c
o
m
pa
r
e
d
wi
t
h s
i
n
gl
e
d
i
s
t
r
i
but
i
o
n f
u
n
c
t
i
ons
us
e
d i
n
t
hi
s
pa
pe
r
t
o
r
e
a
c
h
m
o
r
e
a
c
c
ur
a
t
e
m
o
de
l
l
i
ng
of
t
h
e
d
i
f
f
e
r
e
n
t
w
i
n
d
t
u
r
b
i
n
e
s
.
E
a
c
h
w
i
n
d
t
u
r
b
i
n
e
i
s
m
o
d
e
l
l
e
d
us
i
n
g a
l
l
c
um
ul
a
t
i
ve
de
ns
i
t
y
f
u
nc
t
i
ons
m
e
n
t
i
one
d
in
t
h
is
p
a
pe
r
a
nd
f
i
n
a
ll
y
r
e
s
u
lt
s
a
r
e
c
o
m
pa
r
e
d
t
o
r
e
a
c
h
m
or
e
a
c
c
ur
a
t
e
m
od
e
l
i
n
e
a
c
h
c
a
s
e
u
s
i
ng
R
MS
E
c
om
p
a
r
is
on
.
2.
MA
T
H
E
M
AT
I
C
AL
M
O
DE
L
L
I
NG
W
I
T
H
C
U
MUL
A
T
I
VE
DE
N
S
I
T
Y
F
U
N
C
T
I
O
N
S
M
a
t
h
e
m
a
t
i
c
a
l
m
o
d
e
l
l
i
n
g
i
s
u
s
e
d
i
n
t
hi
s
pa
p
e
r
t
o
de
s
c
r
i
be
w
i
n
d
t
ur
bi
ne
s
out
put
p
o
we
r
a
c
c
or
di
n
g
t
o
va
l
i
d
wi
n
d s
p
e
e
d i
n
p
ut
s
.
T
he
us
e
d
s
i
n
gl
e
c
um
ul
a
t
i
ve
d
e
ns
i
t
y
f
u
nc
t
i
o
n m
o
de
l
s
a
r
e
w
e
i
b
ul
l
,
ga
m
m
a
a
n
d
l
o
g
-
n
or
m
a
l
.
Al
s
o a
c
o
m
pos
i
t
e
c
um
ul
a
t
i
ve
de
ns
i
t
y f
u
nc
t
i
on
m
o
de
l
i
s
us
e
d.
I
t
c
o
ns
i
s
t
s
of
t
wo t
e
r
m
s
,
t
h
e
fi
rs
t
t
e
r
m
i
s
w
e
i
b
u
l
l
t
e
r
m
w
i
t
h
a
w
e
i
g
h
t
i
n
g
c
o
e
f
f
i
c
i
e
n
t
a
n
d
t
h
e
s
e
c
o
n
d
i
s
g
a
m
m
a
t
e
r
m
w
i
t
h
a
n
o
t
h
e
r
w
e
i
g
h
t
i
n
g
c
oe
f
f
i
c
i
e
nt
.
T
h
e
ge
ne
r
a
l
e
q
ua
t
i
on
t
o
de
s
c
r
i
be
t
he
f
i
t
t
e
d
wi
nd
t
ur
bi
ne
o
ut
p
ut
p
ow
e
r
p
i
a
t
i
n
p
u
t
w
i
n
d
s
p
e
e
d
v
i
i
s
d
e
s
c
r
i
b
e
d in (
1)
.
(
θ
1
,
θ
2
,
…
,
θ
n
)
a
r
e
t
h
e
c
u
m
u
l
a
t
i
v
e
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
d
e
s
i
g
n
i
n
g
v
a
r
i
a
b
l
e
s
w
h
i
c
h
a
r
e
o
p
t
i
m
a
l
l
y
s
e
l
e
c
t
e
d
f
o
r
o
p
t
i
m
a
l
p
o
w
e
r
c
u
r
v
e
m
o
d
e
l
l
i
n
g
.
I
f
(
1
)
i
s
m
u
l
t
i
p
l
i
e
d
b
y
t
h
e
w
i
n
d
t
u
r
b
i
n
e
r
a
t
e
d
o
u
t
p
u
t
p
o
w
e
r
(
P
r
)
i
t
w
i
l
l
t
ra
n
s
fe
r
re
d
t
o
(2
)
wh
e
re
o
u
t
p
u
t
p
o
w
e
r
P
i
u
n
i
t
w
i
l
l
b
e
i
n
(
K
W
).
A
s
i
n
di
c
a
t
e
d i
n
T
a
bl
e
1,
we
i
b
ul
l
c
um
ul
a
t
i
ve
de
n
s
i
t
y f
u
nc
t
i
o
n
ha
s
t
w
o
de
s
i
gni
ng
va
r
i
a
bl
e
s
w
hi
c
h a
r
e
t
he
s
ha
pi
ng
pa
r
a
m
e
t
e
r
(
k
)
a
nd
t
he
s
c
a
l
i
n
g
pa
r
a
m
e
t
e
r
(
c
)
.
B
ut
t
he
s
t
a
nda
r
d
c
um
ul
a
t
i
ve
ga
m
m
a
de
ns
i
t
y
f
u
n
c
t
i
on
ha
s
o
n
l
y
a
s
h
ap
i
n
g
p
a
r
am
et
er
(
a)
.
T
h
e l
o
g
-
n
or
m
a
l
c
u
m
ul
a
t
i
ve
di
s
t
r
i
b
ut
i
on
f
u
nc
t
i
o
n
ha
s
t
w
o
de
s
i
gni
ng
v
ar
i
a
b
l
es
w
h
i
ch
a
r
e
t
h
e
d
i
s
t
r
i
b
u
t
i
o
n
m
ea
n
(
µ)
a
n
d
s
t
an
d
ar
d
d
e
v
i
at
i
o
n
(
σ
)
.
A
s
a
w
a
y
t
o
r
each
a
m
o
r
e
ac
cu
r
at
e
f
i
t
t
i
n
g
c
u
r
v
e
t
h
e
w
e
i
b
u
l
l
–
g
a
m
m
a
c
o
m
p
o
s
i
t
e
d
i
s
t
r
i
b
ut
i
o
n
f
unc
t
i
o
n i
s
ge
n
e
r
a
t
e
d
w
i
t
h
f
i
v
e
de
s
i
gni
ng
va
r
i
a
bl
e
s
as
i
n
d
i
cat
ed
i
n
T
a
b
l
e
1
,
w
h
er
e
w
1
i
s
t
h
e
w
e
i
b
u
l
l
c
u
m
u
l
a
t
i
v
e
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
w
e
i
g
h
t
i
n
t
h
e
c
o
m
p
o
s
i
t
e
.
T
he
de
s
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s
q
u
a
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eg
r
es
s
i
o
n
[
1
8
,
1
9]
or
us
i
ng
f
u
nc
t
i
on
opt
i
m
i
z
a
t
i
o
n t
e
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hni
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[
2
0]
.
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n t
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pa
pe
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a
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opt
i
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l
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[
2
1
]
i
s
us
e
d
f
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o
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ect
i
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h
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ect
i
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ct
i
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as
s
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MS
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w
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c
h s
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n i
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ur
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In
(
3)
s
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on
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h
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N
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n i
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be
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gni
ng va
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[
2
2]
.
p
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v
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n
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K
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M
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m
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:
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M
SE
=
1
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2
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(3)
S
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≤
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,
n
(4)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
E
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e
c
&
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:
208
8
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87
08
C
om
me
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w
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s
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(
O
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n
A
.
M.
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)
49
T
a
bl
e
1.
C
um
u
l
a
t
i
ve
pr
o
ba
bi
l
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t
y
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ns
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i
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m
o
de
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u
m
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lativ
e d
en
s
ity
f
unc
t
i
on m
ode
l
E
q
u
atio
n
θ
1
θ
2
θ
3
θ
4
θ
5
W
eib
u
ll
P
i
=
P
r
(
1
−
e
−
v
i
c
k
)
k
c
−
−
−
Gam
m
a
P
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=
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r
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t
a
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t
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0
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(
a
)
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−
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a
l
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=
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(
l
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(
v
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µ
σ
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σ
−
−
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W
eib
u
ll &
Gam
m
a
C
om
pos
i
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e
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r
(
w
1
1
−
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c
k
+
(
1
−
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1
)
∫
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t
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d
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(
a
)
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c
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σ
w
1
3.
I
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D O
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T
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(I
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h c
um
ul
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t
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t
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o
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e
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o
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d o
pt
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m
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z
a
t
i
on
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ech
n
i
q
u
e
ar
e
[
2
3
]
:
−
P
o
p
u
l
a
t
i
o
n
s
I
n
i
t
i
a
l
i
z
a
t
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:
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p
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t
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s
(
s
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t
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m
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s
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w
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t
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.
W
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e
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s
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um
be
r
o
f
t
h
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de
s
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va
r
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bl
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s
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−
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ds
R
e
pr
od
uc
t
i
on:
e
ve
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s
e
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d g
r
ows
t
o
f
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m
a
ne
w
pl
a
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n
d
pr
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s
ne
w
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nu
m
be
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−
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p
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t
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D
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p
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on
f
u
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t
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on
s
un
de
r
va
r
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a
nc
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va
r
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t
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ons
.
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s
t
a
nda
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de
vi
a
t
i
on
(
σ
)
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f
t
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a
nda
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(
σ
in
it
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l
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d
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f
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σ
f
i
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l
)
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n e
ve
r
y
s
t
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p.
D
u
r
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n
g
s
i
m
u
l
a
t
i
o
n
,
a
n
o
n
l
i
n
e
a
r
a
l
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a
t
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o
n
-
m
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ul
a
t
i
on i
nde
x
(
)
i
s
s
el
ect
ed
t
o
r
each
ce
r
t
ai
n
s
at
i
s
f
act
o
r
y
p
er
f
o
r
m
a
n
ce.
In
(
5)
s
h
ows
h
o
w
t
he
s
t
a
n
da
r
d
de
vi
a
t
i
o
n (
σ
it
e
r
)
at
each
i
t
er
at
i
o
n
(
it
er
)
i
s
cal
cu
l
at
ed
,
wh
e
re
it
er
ma
x
i
s
t
h
e
m
a
x
i
m
um
nu
m
be
r
of
i
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e
r
a
t
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ons
.
σ
it
e
r
=
(
i
t
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m
ax
−
i
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)
n
it
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r
m
ax
n
(
σ
in
it
ia
l
−
σ
f
i
n
a
l
)
+
σ
f
i
n
a
l
(
5)
−
C
om
pe
t
i
t
i
ve
E
xc
l
us
i
on:
i
n
t
h
i
s
p
r
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c
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s
s
a
n
d
a
f
t
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r
m
a
xi
m
u
m
n
um
be
r
of
pl
a
nt
s
i
s
r
e
a
c
h
e
d,
onl
y t
he
pl
a
nt
s
w
i
t
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l
ow
e
r
f
i
t
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s
s
c
a
n pul
l
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ut
a
nd
p
r
od
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e
s
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d
s
,
ot
he
r
s
a
r
e
be
i
n
g
di
s
c
a
r
de
d.
T
he
pr
o
c
e
s
s
c
ont
i
n
ue
s
i
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e
a
c
h
i
t
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r
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t
i
o
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t
i
l
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m
a
x
i
m
u
m
i
t
e
r
a
t
i
o
n
s
a
r
e
r
e
a
c
h
e
d
a
n
d
s
i
m
p
l
y
t
h
e
p
l
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n
t
w
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t
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b
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s
t
f
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s
s
i
s
t
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c
l
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s
t
t
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t
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o
p
t
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m
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o
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u
t
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n
.
I
W
O
a
l
g
o
r
i
t
h
m
f
l
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w
c
h
a
r
t
i
s
a
s
i
n
d
i
c
a
t
e
d
i
n
F
i
g
u
r
e
1
.
F
i
gure
1.
IW
O
a
l
gori
t
hm
fl
ow
c
h
a
rt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
11
,
No
.
1,
F
e
b
r
ua
r
y
2
02
1
:
47
-
56
50
4.
R
E
S
U
L
T
S
A
ND
DI
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C
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x
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t
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c
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2
M
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n
d c
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s
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c
um
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a
t
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ve
de
ns
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t
y
f
unc
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i
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ns
(
C
D
F
s
)
[
2
4
,
25
]
.
D
i
f
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n
t
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d.
T
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um
be
r
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t
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a
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W
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i
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i
m
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t
he
R
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m
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t
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n R
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r
e
d a
s
t
he
o
pt
i
m
a
l
o
ne
.
T
he
n,
t
he
c
u
m
ul
a
t
i
ve
d
e
ns
i
t
y f
unc
t
i
o
n
s
m
ode
l
s
ar
e
e
xt
e
nde
d t
o
m
o
de
l
w
i
de
r
r
a
n
g
e
o
f
c
o
m
m
e
r
c
i
a
l
w
i
n
d
t
u
r
b
i
n
e
s
t
o
c
h
e
c
k
t
h
e
i
r
v
a
l
i
d
i
t
y
o
f
m
o
d
e
l
l
i
n
g
.
T
h
e
o
t
h
e
r
c
o
m
m
e
r
c
i
a
l
w
i
n
d
t
u
r
b
i
n
e
s
ar
e
c
a
t
e
g
o
r
i
z
e
d
i
nt
o
t
he
f
ol
l
o
w
i
ng
r
a
nge
s
i
n
a
de
s
c
e
ndi
ng
o
r
d
e
r
:
-
W
i
n
d
t
u
r
bi
ne
s
wi
t
h
ge
ne
r
a
t
i
o
n
r
a
n
ge
f
r
om
6
00
K
W
t
o
10
0
0
K
W
.
-
W
i
n
d
t
u
r
bi
ne
s
wi
t
h
ge
ne
r
a
t
i
o
n
r
a
n
ge
f
r
om
4
00
K
W
t
o
50
0
K
W
.
-
W
ind
t
u
r
bi
ne
s
wi
t
h ge
ne
r
a
t
i
o
n
r
a
n
ge
f
r
om
2
00
K
W
t
o
30
0
KW
.
4.
1.
W
i
nd
t
u
r
bi
ne
s
wi
t
h
ge
n
e
r
at
i
on
r
an
ge
[
2
M
W
-
7
M
W]
W
i
n
d t
u
r
bi
ne
s
m
o
de
l
l
e
d i
n
t
hi
s
s
e
c
t
i
on a
r
e
:
Ve
s
t
a
s
(
V
80
)
,
S
i
e
m
e
ns
(
S
8
2)
,
R
e
p
ow
e
r
(
R
E
82
)
,
N
or
de
x
(
N9
0)
,
S
ie
m
e
ns
(
S
10
7)
a
nd
Ve
s
ta
s
(
V
164
)
.
T
h
e
r
a
ting
of
e
a
c
h
wi
n
d t
ur
bi
ne
i
s
a
s
i
n
di
c
a
t
e
d i
n
T
a
bl
e
2.
I
n
t
hi
s
s
e
c
t
i
o
n
r
e
s
u
l
t
s
s
h
o
w
e
d
t
h
a
t
s
i
n
g
l
e
w
e
i
b
u
l
l
c
u
m
u
l
a
t
i
v
e
p
r
o
b
a
b
i
l
i
t
y
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
g
i
v
e
s
t
h
e
m
i
n
i
m
u
m
RM
S
E
f
o
r
a
l
l
t
h
e
s
i
x
w
i
n
d
t
u
r
b
i
n
e
s
,
s
o
i
t
c
o
n
s
i
d
e
r
e
d
t
h
e
o
p
t
i
m
a
l
m
o
d
e
l
i
n
t
h
i
s
g
e
ne
r
a
t
i
on p
ow
e
r
r
a
nge
.
W
e
i
b
u
l
l
-
ga
m
m
a
c
o
m
p
os
i
t
e
gi
ve
s
l
ow
e
r
a
c
c
ur
a
c
y t
ha
n s
i
n
gl
e
we
i
bul
l
m
o
de
l
s
b
ut
i
t
ha
s
hi
g
he
r
a
c
c
u
r
a
c
y t
ha
n
bot
h s
i
n
gl
e
ga
m
m
a
a
n
d s
i
n
gl
e
l
og
-
n
o
r
m
a
l
c
u
m
u
l
a
t
i
v
e
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
(
CD
F
)
m
o
d
e
l
s
.
L
o
g
-
n
or
m
a
l de
n
s
ity
f
u
n
ct
i
o
n
m
o
d
el
g
i
v
e
s
t
h
e
l
o
w
e
s
t
accu
r
acy
.
T
h
e
cu
m
u
l
at
i
v
e
d
e
ns
i
t
y
f
u
nc
t
i
o
n
s
m
ode
l
s
o
f
e
a
c
h
w
i
n
d
t
ur
bi
n
e
a
n
d
a
c
t
ua
l
p
ow
e
r
c
ur
ve
by m
a
nu
f
a
c
t
ur
e
r
s
r
eac
h
ed
t
h
r
o
u
g
h
m
e
as
u
r
e
d
d
at
a p
o
i
n
t
s
ar
e s
k
et
ch
ed
o
n
s
a
m
e a
x
es
as
s
ho
w
n i
n F
i
gu
r
e
2.
W
e
i
b
ul
l
p
ow
e
r
c
ur
ve
s
gi
ve
a
ve
r
y
a
c
c
u
r
a
t
e
a
p
p
r
o
xi
m
a
t
i
ons
f
o
r
t
he
a
c
t
ua
l
p
ow
e
r
c
u
r
ve
s
a
s
i
ndi
c
a
t
e
d
i
n F
i
gu
r
e
2,
w
he
r
e
a
c
t
ua
l
c
ur
ve
s
a
n
d
w
e
i
b
ul
l
c
ur
ve
s
a
r
e
ve
r
y
ne
a
r
t
o c
oi
n
c
i
de
.
E
rr
o
r b
e
t
w
e
e
n
a
c
t
ua
l
po
w
e
r
c
ur
ve
s
a
nd a
l
l
m
o
de
l
s
ha
s
hi
g
he
r
va
l
ue
s
a
r
o
un
d t
he
r
a
t
e
d
s
pe
e
d
p
oi
nt
o
f
e
a
c
h w
i
nd t
ur
bi
ne
a
n
d
s
l
i
g
h
t
l
y
a
f
t
e
r
c
u
t
-
i
n
s
p
e
e
d
p
o
i
n
t
o
f
a
l
l
w
i
nd
t
u
r
bi
ne
s
.
I
n c
a
s
e
of
a
l
l
w
i
n
d t
ur
bi
ne
s
und
e
r
u
s
ing
w
i
e
b
u
l
l
m
o
de
l
l
i
ng
c
ur
ve
s
,
e
r
r
or
t
a
ke
s
ve
r
y
s
m
a
l
l
va
l
ue
s
f
o
r
wi
nd
s
pe
e
d
va
l
u
e
s
hi
g
he
r
t
ha
n
w
i
n
d t
ur
bi
ne
s
r
a
t
e
d
w
i
n
d
s
pe
e
ds
.
4.
2.
W
i
nd
t
u
r
bi
ne
s
w
i
t
h
ge
n
e
r
at
i
on
r
an
ge
[
6
0
0
K
W
-
1
000
K
W
]
W
i
n
d t
ur
bi
ne
s
m
ode
l
l
e
d
i
n
t
hi
s
pa
r
t
a
r
e
A
n
-
B
onus
100
0
/
5
4,
E
n
e
rc
o
n
(E
5
3
),
L
e
i
t
w
i
n
d
(L
T
W7
7
-
10
00)
,
L
e
itw
i
n
d
(
LT
W
8
0
-
8
5
0
)
,
L
e
i
t
w
i
n
d
(
L
T
W
9
-
10
00
)
a
nd
V
e
s
ta
s
(
V47
)
w
i
th
r
a
te
d
p
ow
e
r
s
s
how
n
i
n
T
a
b
l
e
3
.
T
h
r
o
u
g
h
r
e
s
u
l
t
s
,
w
e
i
b
u
l
l
c
u
m
u
l
a
t
i
v
e
p
r
o
b
a
b
i
l
i
t
y
d
e
n
s
i
t
y
(
C
D
F
)
g
i
v
e
s
l
o
w
e
s
t
R
M
S
E
a
nd hig
h
e
r
a
c
c
ur
a
c
y i
n
f
o
ur
o
ut
of
s
i
x
o
f
t
he
w
i
n
d t
u
r
bi
ne
s
i
n t
hi
s
g
e
ne
r
a
t
i
o
n
r
a
n
g
e
.
T
he
wi
n
d t
u
r
bi
ne
s
be
s
t
m
o
de
l
l
e
d
us
i
n
g w
e
i
b
u
l
l
CD
F
a
r
e
L
e
i
t
w
i
n
d
(
L
T
W
7
7
-
100
0)
,
L
e
itw
in
d
(
L
T
W
80
-
85
0)
,
(
L
e
itw
i
n
d L
T
W
90
-
10
00)
a
n
d
V
e
s
t
a
s
(V
4
7
).
W
e
i
b
u
l
l
–
g
a
m
m
a
c
o
m
p
o
s
i
t
e
CD
F
gi
ve
s
l
o
w
e
s
t
R
M
S
E
a
n
d
hi
g
he
r
a
c
c
ur
a
c
y i
n
t
w
o
o
ut
of
s
i
x
of
t
he
w
i
n
d t
u
r
b
i
ne
s
i
n t
hi
s
r
a
nge
.
T
he
wi
nd t
ur
bi
ne
s
b
e
s
t
m
o
d
e
l
l
e
d
u
s
i
n
g
w
e
i
b
u
l
l
–
ga
m
m
a
c
om
pos
i
t
e
i
s
A
n
-
B
o
n
us
1
00
0/
5
4
a
n
d
E
ne
r
c
on
(
E
5
3)
.
A
l
s
o
f
r
o
m
r
e
s
ul
t
s
,
t
he
s
i
ngl
e
l
o
g
-
n
o
r
m
a
l
CD
F
i
s
t
h
e
w
o
r
s
t
m
o
d
e
l
w
i
t
h
hi
g
he
s
t
R
MS
E
va
l
ue
s
.
E
a
c
h
wi
n
d
t
u
r
b
i
n
e
a
c
t
u
a
l
p
o
w
e
r
c
u
r
v
e
a
n
d
m
o
s
t
a
c
c
u
r
a
t
e
CD
F
m
o
d
e
l
d
e
s
c
r
i
b
i
n
g
i
t
a
r
e
s
ke
t
c
he
d
o
n
s
a
m
e
g
r
a
ph
a
s
s
h
ow
n
i
n
F
i
gu
r
e
3.
4.
3.
W
i
nd
t
u
r
bi
ne
s
w
i
t
h
ge
n
e
r
at
i
on
r
an
ge
[
4
0
0
K
W
-
50
0
K
W
]
D
a
ni
s
h W
i
nd
T
e
c
h
W
i
n
da
ne
(
D
W
T
34
)
,
E
ne
r
c
on
(
E
40
)
/
5.
4,
T
ur
b
ow
i
n
ds
T
40
0
-
3
4
,
V
e
s
t
a
s
(
V
3
9
),
W
e
s
p
a
500
/47 a
nd
W
i
n
df
low
45
-
5
0
0 a
r
e
t
he
s
i
x
wi
n
d t
ur
bi
ne
s
m
ode
l
l
e
d i
n t
hi
s
pa
r
t
us
i
n
g
di
f
f
e
r
e
n
t
C
D
F
m
od
e
ls
.
A
s
s
h
ow
n
i
n
T
a
bl
e
4
,
w
e
i
b
ul
l
–
g
am
m
a
C
D
F
g
i
v
es
m
o
r
e
accu
r
at
e
r
es
u
l
t
s
w
i
t
h
l
o
w
er
R
M
S
E
i
n
f
o
u
r
o
u
t
o
f
s
i
x
o
f
wi
n
d t
u
r
bi
ne
s
i
n
t
hi
s
p
o
we
r
r
a
nge
.
T
he
wi
n
d t
u
r
bi
ne
s
be
s
t
m
o
de
l
l
e
d us
i
ng w
e
i
b
ul
l
–
ga
m
m
a
c
o
m
p
os
ite
a
r
e
E
n
e
r
c
on
(
E
4
0)
/5
.
4,
T
ur
bow
ind
s
T
400
–
34
,
V
e
s
ta
s
(
V
39)
a
nd
W
indf
low
45
-
5
0
0
.
S
i
n
g
l
e
w
e
i
b
u
l
l
C
D
F
gi
ve
s
l
o
we
s
t
R
M
S
E
a
nd
hi
g
he
r
a
c
c
u
r
a
c
y i
n t
w
o
wi
nd t
ur
bi
n
e
s
w
h
i
ch
ar
e D
W
T
3
4
an
d
W
es
p
a 5
0
0
/
4
7
.
T
h
e
w
i
n
d
t
u
r
b
i
n
e (
D
W
T
3
4
)
h
as
act
u
al
p
o
w
er
cu
r
v
e
d
i
f
f
er
t
h
a
n
u
s
u
al
act
u
al
p
o
w
er
c
u
r
v
es
w
h
er
e
t
h
e
d
at
a
poi
nt
s
w
i
t
h
wi
nd
s
pe
e
d
s
l
ow
e
r
t
ha
n
r
a
t
e
d
wi
n
d
s
pe
e
d a
r
e
i
nt
e
r
m
i
t
t
e
nt
a
nd
not
s
m
oot
h.
W
e
i
bul
l
C
DF
i
s
t
h
e b
es
t
m
o
d
el
f
o
r
t
hi
s
w
i
n
d t
ur
bi
ne
a
c
t
ua
l
c
ur
ve
s
ha
pe
.
Ac
t
ua
l
p
owe
r
c
u
r
ve
s
a
nd
m
o
s
t
a
c
c
ur
a
t
e
C
D
F
m
o
de
l
de
s
c
r
i
bi
n
g
e
a
c
h
t
u
r
bi
ne
i
s
s
ke
t
c
he
d
o
n
s
a
m
e
gr
a
p
h
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
4.
4.
4.
W
i
n
d
t
u
r
b
i
n
e
s
w
i
t
h
ge
n
e
r
at
i
on
r
an
ge
[
2
0
0
K
W
-
30
0
K
W
]
W
i
n
d
t
u
r
b
i
n
e
s
m
o
d
e
l
l
e
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4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
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om
p
E
n
g,
V
o
l
.
11
,
No
.
1,
F
e
b
r
ua
r
y
2
02
1
:
47
-
56
52
V
80
–
A
c
t
ua
l
p
owe
r
c
ur
ve
a
n
d
C
D
F
po
we
r
m
o
de
l
s
S
82
–
A
c
t
ua
l
p
owe
r
c
ur
ve
a
n
d
C
D
F
po
we
r
m
o
de
l
s
RE
8
2
–
A
c
t
ua
l
p
owe
r
c
ur
ve
a
nd
C
DF
p
o
w
e
r
m
o
de
l
s
F
i
gure
2.
W
i
nd t
urbi
ne
s
a
c
t
u
a
l
p
ow
e
r c
urv
e
s
a
nd
CD
F
pow
e
r m
od
e
l
s
w
i
t
h
out
put
p
ow
e
r ra
ng
e
[2
M
W
-
7
MW
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
l
e
c
&
C
om
p
E
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g
IS
S
N
:
208
8
-
87
08
C
om
me
r
c
i
al
w
i
nd
t
ur
bi
ne
s
m
o
de
l
i
ng
u
s
i
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g
s
i
ngl
e
a
nd
…
(
O
t
hm
a
n
A
.
M.
O
m
a
r
)
53
N
90
–
A
c
t
ua
l
p
owe
r
c
ur
ve
a
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d
C
D
F
po
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10
7
–
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c
t
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l
po
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r
c
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ve
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DF
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e
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s
V
164
–
A
c
t
ua
l
po
we
r
c
ur
ve
a
nd
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DF
p
o
w
e
r
m
o
de
l
s
F
i
gure
2.
W
i
nd t
urbi
ne
s
a
c
t
u
a
l
p
ow
e
r c
urv
e
s
a
nd
CD
F
pow
e
r m
od
e
l
s
w
i
t
h
out
put
p
ow
e
r ra
ng
e
[2
M
W
-
7
MW
]
(
c
ont
i
nue
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
11
,
No
.
1,
F
e
b
r
ua
r
y
2
02
1
:
47
-
56
54
F
i
gu
r
e
3.
W
i
nd
t
ur
bi
ne
s
a
c
t
ua
l
p
ow
e
r
c
ur
ve
s
a
nd
t
he
i
r
o
pt
i
m
a
l
C
D
F
m
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l
s
f
or
p
ow
e
r
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a
n
ge
[
600
K
W
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100
0
KW
]
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ab
l
e
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.
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n
g
l
e
an
d
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om
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o
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e
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ul
t
s
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owe
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500
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W
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ode
l
Par
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eter
s
D
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34
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40
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39
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500
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5
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s
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r
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[
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l
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eter
s
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z
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27
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4.
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ua
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p
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c
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s
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400
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5.
W
i
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t
ur
bi
ne
s
a
c
t
ua
l
p
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r
c
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s
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ge
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200
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300
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W
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R
EF
ER
E
N
C
ES
[1]
D
an
Z
h
ao
,
N
uom
i
n H
a
n,
E
rn
e
s
t
G
oh,
J
ohn Ca
t
e
r,
"
A
rne
Re
i
n
e
c
ke
,
W
i
nd T
ur
bi
ne
s
a
nd A
e
ro
dyna
m
i
cs
E
n
er
g
y
Ha
r
v
e
st
e
r
s,
"
Ch
apt
e
r
1: G
e
ne
r
al
i
nt
r
oduc
t
i
on
t
o
wi
nd t
ur
bi
n
es
, A
ca
d
em
i
c
P
r
es
s
,
pp
.
1
-
20
,
2019
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o
h
am
m
ed
G
. K
h
al
f
al
l
ah
,
a
n
d
A
boe
l
ya
z
i
e
d M
.
K
ol
i
ub,
"
S
ugge
s
t
i
ons
for i
m
p
rov
i
ng w
i
nd t
u
rbi
ne
s
pow
e
r c
urve
s
,
"
D
e
s
al
i
nat
i
on
,
vo
l
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3
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M.
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l
b
a
d
i
, E
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F. E
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S
a
a
da
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,
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W
i
nd t
u
rbi
ne
s
c
a
pa
c
i
t
y
f
a
c
t
or
m
ode
l
i
ng
-
a
nove
l
a
pproa
c
h,
"
IE
E
E
T
r
ans
ac
t
i
ons
on
P
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w
e
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st
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a
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a
u
,
"
S
i
t
e
m
a
t
c
hi
ng
of w
i
nd t
urbi
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e
ge
ne
ra
t
ors
:
a
c
a
s
e
s
t
udy,
"
IE
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ul
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on
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l
a
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e
d
w
i
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s
pe
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da
t
a
for
e
c
onom
i
c
di
s
pa
t
c
h
ev
al
u
at
i
o
n
,"
IE
E
E
T
r
ans
ac
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i
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nabl
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nc
e
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c
u
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IE
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T
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e
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j
óo,
"
R
e
form
ul
a
t
i
on of p
a
ra
m
e
t
e
rs
of t
he
l
ogi
s
t
i
c
func
t
i
on a
ppl
i
e
d t
o
pow
e
r
c
urv
e
s
of w
i
nd t
urb
i
ne
s
,
"
E
l
e
ct
r
i
c P
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I
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SN
:
2
088
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E
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No
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ua
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Y
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urve
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i
ng:
A
re
vi
e
w
a
nd di
s
c
us
s
i
on,
"
R
e
ne
wab
l
e
a
nd
Sus
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ai
nabl
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E
ne
r
gy
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ve
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ri
c
a
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M
e
t
hods
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or E
ngi
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rs
,
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H
ill Ed
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P
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l
et
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as
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n
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,
"
W
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nd
t
u
rbi
ne
pow
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r
c
ur
ve
m
od
e
l
l
i
ng u
s
i
ng a
rt
i
fi
c
i
a
l
n
e
ura
l
ne
t
w
ork
,
"
R
en
ew
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n
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u
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ar
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,
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e
l
va
k
um
a
r
A
I,
K
um
a
r G
E
P
,
"
A
c
o
m
pre
he
ns
i
ve
r
e
vi
e
w
on w
i
nd
t
urb
i
ne
pow
e
r
c
urve
m
ode
l
i
ng
t
e
c
hni
que
s
,
"
R
e
ne
wabl
e
and Sus
t
a
i
nabl
e
E
n
e
r
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e
v
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g
Y
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v
i
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on
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e
l
i
a
bi
l
i
t
y
a
s
s
e
s
s
m
e
nt
for w
i
nd
p
ow
e
r,
”
R
e
n
e
wab
l
e
and
s
us
t
ai
nab
l
e
en
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g
y r
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vi
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Ya
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Osa
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a
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W
hi
t
e
E
.
,
"
Inve
rs
e
da
t
a
t
r
a
ns
form
a
t
i
on for
c
ha
ng
e
d
e
t
e
c
t
i
o
n i
n w
i
nd
t
urb
i
n
e
di
a
gnos
t
i
c
s
,
"
Ca
nadi
an Conf
e
r
e
n
c
e
on
E
l
e
c
t
r
i
c
al
and Com
put
e
r
E
ngi
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Ni
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Ma
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n
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"
R
o
b
u
s
t
e
s
t
i
m
a
t
i
o
n
o
f
t
i
m
e
-
va
r
y
i
n
g c
oe
f
f
i
c
i
e
nt
f
u
nc
t
i
on
s
-
ap
p
l
i
ca
t
i
o
n
t
o
t
h
e
m
od
e
l
i
ng
o
f w
i
n
d
p
ow
e
r
pr
odu
c
t
i
o
n,
"
T
ec
h
n
i
c
a
l
U
n
i
ve
r
s
i
t
y
o
f
D
e
n
m
ar
k
,
I
nf
o
r
m
at
i
c
s
a
nd
M
at
he
m
at
i
c
al
M
o
de
l
l
i
n
g,
20
0
7.
[15]
Ta
s
lim
i
-
Re
n
a
ni
E
.
,
e
t
a
l
.
,
"
D
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ve
l
opm
e
nt
of
a
n
e
n
ha
nc
e
d
pa
r
a
m
e
t
r
i
c
m
ode
l
for
w
i
nd t
urbi
n
e
pow
e
r c
urv
e
,
"
A
p
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d
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D
a
ni
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V
i
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l
a
nue
va
,
a
n
d
A
ndré
s
F
e
i
j
óo,
"
Com
pa
r
i
s
on of
l
ogi
s
t
i
c
f
unc
t
i
ons
for
m
o
de
l
i
ng
w
i
nd
t
urb
i
ne
pow
e
r
c
urve
s
,
"
E
l
e
ct
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i
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D
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,
"
W
i
nd T
urb
i
ne
P
o
w
e
r Curve
s
B
a
s
e
d on t
h
e
W
e
i
bul
l
Cu
m
ul
a
t
i
v
e
D
is
tr
ib
u
tio
n
F
u
n
c
tio
n,
"
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Sc
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i
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G
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e
ri
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a
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M
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t
hods
of Curve
F
i
t
t
i
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a
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ri
d
g
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Un
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P
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n C
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pr
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Ra
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ond
P
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Ca
na
l
e
,
"
N
um
e
ri
c
a
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M
e
t
hods
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or E
ngi
n
e
e
rs
,
"
M
c
Gra
w
-
H
ill Ed
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tio
n
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Z
hi
xi
n F
a
n
,
a
nd
C
ai
ch
ao
Z
h
u
,
"
T
he
opt
i
m
i
z
a
t
i
on
a
nd t
h
e
a
pp
l
i
c
a
t
i
on for t
h
e
w
i
nd
t
urbi
ne
pow
e
r
-
w
i
nd
s
pe
e
d c
u
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,
"
R
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M
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bi
a
n
,
A
l
i
Re
z
a
,
a
nd
C
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ro L
u
c
a
s
,
"
A
nove
l
num
e
ri
c
a
l
op
t
i
m
i
z
a
t
i
on
a
l
gori
t
h
m
i
ns
pi
re
d
from
w
e
e
d
c
ol
oni
z
a
t
i
on,
"
E
c
ol
ogi
c
al
i
nf
o
rma
t
i
c
s
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W
i
nd T
urb
i
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P
ow
e
r Curve
s
,
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[O
nl
i
ne
]
.
A
va
i
l
a
bl
e
:
ht
t
ps
:
/
/
e
n.
w
i
nd
-
t
urbi
ne
-
m
o
de
l
s
.
c
o
m
/
pow
e
r
c
urve
s
,
[
acc
es
s
ed
01.
03.
20
]
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[23]
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.
Ba
s
a
k,
D
.
M
a
ity
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n
d
S
w
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t
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m
D
a
s
,
"
A
d
i
ff
e
re
nt
i
a
l
i
nva
s
i
ve
w
e
e
d
op
t
i
m
i
z
a
t
i
on a
l
gori
t
h
m
f
or
i
m
prove
d
gl
ob
a
l
num
e
ri
c
a
l
opt
i
m
i
z
a
t
i
on,
"
A
ppl
i
e
d
Mat
he
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at
i
c
s
an
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ua
r
da
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C.
Ch
a
rron,
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F
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Che
ba
n
a
,
"
Re
vi
e
w
of c
r
i
t
e
ri
a
for t
h
e
s
e
l
e
c
t
i
on of proba
bi
l
i
t
y
di
s
t
ri
but
i
ons
for
w
i
nd
s
pe
e
d
d
a
t
a
a
nd i
nt
roduc
t
i
on
of
t
he
m
om
e
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124
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2016
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[25]
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.
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1,
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