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11
,
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.
1
,
Feb
r
u
ar
y
2021
,
p
p
.
27
~
36
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v
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s
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R
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CC B
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C
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A
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Ma
r
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lb
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to
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Dep
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ar
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a
1
No
.
1
8
A
–
1
2
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B
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C
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E
m
ail:
m
r
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s
@
u
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d
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d
u
.
c
o
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
u
s
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o
f
r
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w
ab
le
en
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g
y
in
b
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te
m
s
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c
h
as
w
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d
p
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lan
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s
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g
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n
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s
tr
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th
a
s
it
b
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g
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a
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ta
g
es
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v
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tr
ad
itio
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s
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li
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latter
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ex
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ab
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t
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th
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p
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s
e
g
ases
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tin
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m
is
s
io
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s
.
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w
ev
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as t
h
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s
o
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s
d
ep
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d
en
t o
n
th
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m
atic
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s
o
f
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,
t
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p
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ated
w
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a
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v
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f
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m
an
ce
o
f
b
u
lk
p
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w
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s
y
s
te
m
s
[
1
,
2
]
.
I
n
ad
d
itio
n
,
th
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p
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w
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s
y
s
te
m
av
a
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p
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r
p
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n
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g
p
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w
er
s
y
s
te
m
s
[
3
]
.
H
o
w
ev
er
,
tr
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iti
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al
m
et
h
o
d
o
lo
g
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m
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d
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g
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er
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ts
as
a
co
m
p
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n
t
w
it
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w
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s
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v
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f
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Ne
v
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4
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[
5
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6
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,
an
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p
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ab
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[
4
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;
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v
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k
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w
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s
s
an
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k
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s
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s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
27
-
36
28
Oth
er
au
t
h
o
r
s
p
r
o
p
o
s
e
tim
e
-
v
ar
y
in
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m
o
d
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th
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b
eh
a
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io
r
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o
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to
ev
alu
ate
r
eliab
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in
o
p
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p
h
as
e
[
8
]
.
T
h
u
s
,
[
8
]
p
r
o
p
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s
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an
a
u
to
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eg
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co
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elatio
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b
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w
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n
s
e
v
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al
W
P
P
s
[
9
,
1
0
]
.
Oth
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au
t
h
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s
p
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s
e
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ass
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[
1
1
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.
On
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a
[
1
2
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.
T
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s
to
m
ee
t
th
e
n
ee
d
s
o
f
u
s
er
s
as t
h
e
co
n
ti
n
u
o
u
s
s
u
p
p
l
y
o
f
e
n
er
g
y
i
n
a
s
e
cu
r
e,
r
eliab
le
w
a
y
a
n
d
at
t
h
e
l
o
w
est
p
o
s
s
ib
le
co
s
t.
Fo
r
th
is
r
ea
s
o
n
,
a
r
eliab
ilit
y
an
al
y
s
i
s
is
p
er
f
o
r
m
ed
i
n
o
r
d
er
to
d
eter
m
i
n
e
h
o
w
w
e
ll
th
e
ex
p
ec
ted
f
u
n
ctio
n
s
o
f
th
e
s
y
s
te
m
ar
e
b
ei
n
g
p
er
f
o
r
m
ed
,
lead
in
g
to
an
i
m
p
r
o
v
e
m
en
t
i
n
th
e
lev
el
o
f
ac
ce
p
ta
b
ilit
y
o
f
th
e
s
y
s
te
m
.
So
m
e
au
t
h
o
r
s
m
o
d
el
co
r
r
elatio
n
b
et
w
ee
n
w
i
n
d
s
g
e
n
er
ato
r
s
b
y
a
co
p
u
la
f
u
n
ctio
n
to
s
p
ec
if
y
m
u
lti
-
va
r
iate
cu
m
u
lat
iv
e
d
is
tr
ib
u
tio
n
f
u
n
cti
o
n
s
to
b
e
u
s
ed
in
a
Mo
n
te
C
ar
lo
s
i
m
u
latio
n
[
1
3
]
f
o
r
th
e
ad
e
q
u
ac
y
ass
e
s
s
m
e
n
t
at
g
en
er
atio
n
lev
e
l.
Fo
r
th
e
ass
e
s
s
m
e
n
t
o
f
a
v
aila
b
ilit
y
o
f
b
u
l
k
s
y
s
te
m
s
,
a
m
o
d
el
o
f
t
w
o
s
tates
is
u
s
ed
to
r
ep
r
esen
t
th
e
u
n
ce
r
tai
n
t
y
o
f
ea
ch
s
y
n
ch
r
o
n
o
u
s
g
e
n
er
atio
n
u
n
it,
tak
in
g
th
e
s
tate
s
o
f
i
n
-
s
er
v
ice
o
r
o
u
t
-
of
-
s
er
v
ic
e
[
3
,
1
2
]
.
Nev
er
th
e
less
,
w
i
n
d
p
o
w
er
p
la
n
ts
(
W
P
P
)
ca
n
n
o
t
b
e
m
o
d
elled
in
t
w
o
s
tate
s
as
s
h
o
w
n
in
[
1
2
]
,
as
th
e
y
d
ep
en
d
d
ir
ec
tl
y
o
n
t
h
e
u
n
ce
r
ta
in
t
y
o
f
t
h
e
w
i
n
d
s
p
ee
d
,
th
e
o
p
er
atio
n
o
f
t
h
e
co
m
p
o
n
en
t
s
o
f
t
h
e
n
et
w
o
r
k
a
n
d
th
e
to
p
o
lo
g
y
o
f
th
e
p
ar
k
[
7
]
.
F
o
r
th
at
r
ea
s
o
n
,
d
if
f
er
en
t
m
eth
o
d
o
lo
g
ies h
a
v
e
b
ee
n
i
m
p
le
m
en
t
ed
.
I
n
[
1
2
]
,
a
p
o
in
t
esti
m
ate
m
et
h
o
d
(
P
E
M)
w
i
th
2
m
lo
ca
tio
n
s
is
p
r
o
p
o
s
ed
to
s
im
u
late
u
n
ce
r
tai
n
tie
s
i
n
lo
ad
a
n
d
/o
r
g
en
er
atio
n
f
o
r
s
o
lv
i
n
g
t
h
e
p
o
w
er
f
lo
w
.
I
n
a
d
d
itio
n
,
as
[
1
4
]
s
h
o
w
n
,
th
e
c
o
r
r
elatio
n
b
et
w
ee
n
t
w
o
W
P
P
h
a
s
a
n
i
m
p
ac
t
o
n
th
e
r
esu
lt
in
g
r
eliab
ilit
y
i
n
d
ice
s
b
y
u
s
i
n
g
Mo
n
te
C
ar
lo
’
s
s
i
m
u
latio
n
.
Ho
w
ev
er
,
[
1
5
]
ca
r
r
ies
o
u
t
a
s
tu
d
y
t
h
at
co
n
clu
d
es
th
a
t
u
s
i
n
g
a
p
o
in
t
-
e
s
ti
m
ate
m
et
h
o
d
h
as
h
ig
h
er
co
m
p
u
tat
io
n
al
e
f
f
icie
n
c
y
co
m
p
a
r
ed
to
Mo
n
te
C
ar
lo
to
s
o
lv
e
p
r
o
b
ab
ilis
tic
lo
ad
f
lo
w
tak
in
g
i
n
to
ac
co
u
n
t
w
i
n
d
e
n
er
g
y
s
o
u
r
ce
s
.
A
lt
h
o
u
g
h
m
an
y
P
E
M
s
ch
e
m
es
h
a
v
e
b
ee
n
s
u
g
g
es
ted
,
a
m
o
n
g
t
h
e
m
th
e
2
m
+1
m
et
h
o
d
p
r
o
p
o
s
ed
b
y
Ho
n
g
[
1
6
]
allo
w
s
a
h
ig
h
p
er
f
o
r
m
a
n
ce
w
h
e
n
th
er
e
ar
e
a
lar
g
e
n
u
m
b
er
o
f
i
n
p
u
t
v
ar
iab
le
s
.
P
E
M
h
as
b
ee
n
u
s
ed
,
r
ec
en
tl
y
,
to
in
clu
d
e
win
d
u
n
ce
r
tai
n
tie
s
in
lo
ad
f
lo
w
w
it
h
F
AC
T
S d
ev
ice
s
[
1
7
]
,
an
d
an
aly
s
is
o
f
co
n
g
est
io
n
f
o
r
in
ter
co
n
n
ec
tio
n
o
f
W
P
P
[
1
8
]
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
th
e
ap
p
licatio
n
o
f
t
h
e
m
et
h
o
d
2
m
+1
p
o
in
t
-
e
s
ti
m
ate
m
et
h
o
d
(
P
E
M)
f
o
r
th
e
a
v
ailab
ili
t
y
as
s
ess
m
e
n
t
o
f
a
b
u
l
k
p
o
w
er
s
y
s
te
m
co
n
s
id
er
in
g
m
W
P
P
s
,
w
h
er
e
ea
c
h
W
PP
is
a
r
a
n
d
o
m
v
ar
iab
le.
A
s
t
h
e
m
W
P
P
h
av
e
a
co
r
r
elate
d
b
eh
av
io
r
,
a
s
et
o
n
in
d
ep
en
d
en
t
r
an
d
o
m
v
ar
iab
l
es
m
u
s
t
b
e
d
ef
in
ed
b
y
a
lin
ea
r
m
o
d
el
th
at
co
r
r
el
ates
th
e
W
P
P
.
Usi
n
g
t
h
ese
m
i
n
d
ep
en
d
en
t
v
ar
iab
les,
t
h
e
m
et
h
o
d
co
n
s
id
er
s
2
co
n
ce
n
tr
atio
n
p
o
in
ts
f
o
r
ea
c
h
r
an
d
o
m
v
ar
iab
le
(
m
v
ar
i
ab
les)
ar
o
u
n
d
th
e
a
v
er
ag
e
v
alu
e
(
+1
,
an
o
th
er
co
n
ce
n
tr
atio
n
p
o
in
t)
;
t
h
at
is
t
h
e
r
ea
s
o
n
o
f
th
e
n
a
m
e
o
f
t
h
e
m
et
h
o
d
[
1
6
]
.
I
n
co
n
s
eq
u
e
n
c
e,
in
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
lo
g
y
,
t
h
e
P
E
M
m
et
h
o
d
d
ev
elo
p
s
2
m
+1
a
v
ailab
il
it
y
ass
es
s
m
en
t
s
o
f
t
h
e
b
u
l
k
p
o
w
e
r
s
y
s
te
m
,
w
h
er
e
f
o
r
ea
ch
ev
a
lu
at
io
n
a
s
e
t
o
f
p
o
w
er
i
n
j
ec
tio
n
o
f
co
r
r
elate
d
W
PP
is
co
m
p
u
ted
.
I
n
co
n
s
e
q
u
en
ce
,
t
h
e
m
eth
o
d
ca
lcu
late
s
t
h
e
p
o
w
er
g
en
er
ate
d
f
r
o
m
th
e
W
P
P
o
f
th
e
s
y
s
te
m
f
o
r
ea
c
h
2
m
+1
co
n
d
itio
n
s
o
r
co
n
ce
n
tr
atio
n
p
o
in
t
s
an
d
th
e
w
e
ig
h
ti
n
g
f
ac
to
r
f
o
r
co
m
p
u
ti
n
g
t
h
e
w
eig
h
ted
av
er
ag
e
o
f
th
e
av
ailab
il
it
y
i
n
d
ice
s
.
I
n
ad
d
it
io
n
,
ea
ch
W
PP
is
m
o
d
eled
th
r
o
u
g
h
t
h
e
f
o
u
r
ce
n
tr
al
m
o
m
en
ts
t
h
at
m
o
d
els
th
e
p
r
o
b
ab
ilit
y
d
i
s
tr
ib
u
t
io
n
f
u
n
ctio
n
o
f
th
e
in
j
ec
ted
p
o
w
er
b
y
a
W
PP
in
to
th
e
p
o
w
er
s
y
s
te
m
an
d
th
e
m
n
u
m
b
er
o
f
W
P
P
p
ar
k
s
i
n
t
h
e
e
l
e
c
t
r
i
c
a
l
s
y
s
t
e
m
.
T
h
e
s
e
c
e
n
t
r
a
l
m
o
m
e
n
t
s
c
a
n
b
e
a
l
s
o
c
o
m
p
u
t
e
d
f
r
o
m
s
t
a
t
i
s
t
i
c
a
l
d
a
t
a
o
b
t
a
i
n
e
d
f
r
o
m
W
P
P
S
.
T
h
e
in
d
ep
en
d
en
t
(
s
ec
tio
n
2
.
1
.
)
an
d
co
r
r
elate
d
W
PP
s
ce
n
tr
al
m
o
m
e
n
ts
(
s
ec
tio
n
2
.
2
)
ar
e
p
r
esen
ted
,
tak
i
n
g
i
n
to
ac
co
u
n
t
[
7
]
.
I
n
s
ec
tio
n
2
.
3
.
,
th
e
m
e
th
o
d
f
o
r
av
ai
l
ab
ilit
y
a
s
s
e
s
s
m
e
n
t
u
s
i
n
g
P
E
M
is
s
h
o
w
n
.
T
h
e
n
,
i
n
s
ec
t
io
n
3
,
th
e
p
r
o
p
o
s
ed
P
E
M
-
b
ased
av
ailab
ili
t
y
a
s
s
es
s
m
en
t
m
et
h
o
d
o
lo
g
y
is
te
s
ted
o
n
t
h
e
I
E
E
E
R
eliab
ilit
y
T
est
S
y
s
te
m
R
T
S
-
24
[
1
9
]
.
T
h
r
ee
s
ce
n
ar
io
s
w
er
e
i
m
p
le
m
en
ted
to
e
v
al
u
ate
t
h
e
i
m
p
ac
t
o
f
th
e
W
P
P
s
in
th
e
s
y
s
te
m
;
tak
in
g
a
d
i
f
f
er
en
t
v
al
u
e
o
f
co
r
r
elatio
n
b
et
w
ee
n
th
e
i
n
j
ec
ted
p
o
w
er
b
y
t
h
e
W
P
P
s
.
A
s
av
a
ilab
ilit
y
in
d
ices,
t
h
e
e
x
p
ec
ted
en
er
g
y
n
o
n
-
s
er
v
ed
(
E
E
NS)
an
d
t
h
e
lo
s
s
o
f
lo
ad
p
r
o
b
ab
ilit
y
(
L
O
L
P
)
ar
e
u
s
ed
.
Fin
all
y
,
s
ec
t
io
n
4
p
r
esen
ts
t
h
e
co
n
clu
s
io
n
s
o
f
th
is
p
ap
er
an
d
f
u
r
th
er
w
o
r
k
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
P
o
w
er
inje
ct
io
n uncer
t
a
inty
in a
s
ing
le
w
ind
po
w
er
p
la
nt
–
s
t
a
t
is
t
ica
l m
o
de
l
Fig
u
r
e
1
s
h
o
w
s
an
e
x
a
m
p
le
o
f
n
et
w
o
r
k
co
n
f
i
g
u
r
atio
n
o
f
a
W
PP
co
n
n
ec
ted
to
a
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
P
C
C
)
.
T
y
p
icall
y
,
a
W
PP
h
as
a
n
u
m
b
er
o
f
m
ed
i
u
m
v
o
ltag
e
(
MV
)
cir
c
u
its
w
h
er
e
th
e
w
i
n
d
t
u
r
b
i
n
es
ar
e
co
n
n
ec
ted
th
r
o
u
g
h
a
tr
an
s
f
o
r
m
er
[
2
0
]
.
A
ll
th
e
s
e
n
et
w
o
r
k
s
co
m
p
o
n
e
n
t
s
ca
n
b
e
o
u
t
o
f
s
er
v
ice
b
y
f
ails
o
r
m
ai
n
ten
a
n
ce
,
a
m
o
n
g
o
th
er
s
.
I
n
ad
d
itio
n
,
it is
w
ell
k
n
o
w
n
t
h
at
th
e
W
in
d
s
p
ee
d
h
as a
r
a
n
d
o
m
b
eh
a
v
io
r
,
u
s
u
all
y
,
m
o
d
eled
b
y
a
W
eib
u
ll p
r
o
b
ab
ilit
y
f
u
n
ctio
n
[
2
1
]
,
g
iv
en
b
y
:
(
)
=
(
)
(
)
−
1
−
(
)
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
B
u
lk
p
o
w
er sys
tem
a
va
ila
b
ilit
y
a
s
s
ess
men
t
w
ith
…
(
A
n
g
ie
C
.
C
ep
ed
a
)
29
W
in
d
s
p
ee
d
(
)
is
an
in
p
u
t
v
alu
e
th
at
allo
w
s
t
h
e
co
m
p
u
ta
tio
n
o
f
th
e
p
o
w
er
g
en
er
atio
n
o
f
ea
ch
in
d
iv
id
u
al
w
i
n
d
tu
r
b
in
e.
Ho
w
e
v
er
,
th
e
w
i
n
d
s
p
ee
d
is
d
if
f
er
en
t
f
o
r
ea
ch
w
in
d
t
u
r
b
in
e.
I
n
(
1
)
,
b
an
d
a
ar
e
th
e
s
h
ap
e
an
d
s
ca
le
p
ar
a
m
eter
s
o
f
t
h
e
W
eib
u
ll d
is
tr
ib
u
tio
n
.
As
[
7
]
s
h
o
w
n
,
a
Mo
n
te
C
ar
lo
s
i
m
u
lat
io
n
t
h
at
ta
k
es
in
to
ac
co
u
n
t
th
e
r
an
d
o
m
s
tate
o
f
o
p
er
atio
n
o
f
t
h
e
n
et
w
o
r
k
co
m
p
o
n
en
ts
(
in
-
s
er
v
ice
o
r
o
u
t
-
of
-
s
er
v
ice)
,
t
h
e
s
tate
o
f
o
p
er
atio
n
o
f
th
e
t
u
r
b
in
e
(
i
n
o
r
o
u
t
o
f
s
er
v
ice)
,
an
d
th
e
r
an
d
o
m
ch
ar
ac
ter
is
t
ics
o
f
t
h
e
w
i
n
d
s
p
ee
d
an
d
th
e
w
i
n
d
d
ir
ec
tio
n
[
2
2
]
; su
c
h
a
s
,
th
e
p
o
w
er
i
n
j
ec
ted
at
th
e
P
C
C
ca
n
b
e
co
m
p
u
ted
f
o
r
a
n
u
m
b
er
o
f
p
r
o
b
a
b
ilis
tic
r
ea
lizatio
n
s
.
W
it
h
t
h
ese
s
i
m
u
l
atio
n
s
a
p
r
o
b
ab
ilis
tic
d
is
tr
ib
u
t
io
n
f
u
n
ctio
n
(
p
d
f
)
ca
n
b
e
ad
j
u
s
ted
,
o
r
a
d
is
cr
ete
p
d
f
ca
n
b
e
co
m
p
u
ted
; f
o
llo
w
i
n
g
th
e
s
e
s
tep
s
:
Gen
er
ate
th
e
r
a
n
d
o
m
v
ar
iab
les
f
o
r
w
i
n
d
d
ir
ec
tio
n
an
d
w
i
n
d
s
p
ee
d
.
R
an
d
o
m
l
y
,
d
eter
m
i
n
e
t
h
e
o
p
er
atin
g
s
tat
u
s
o
f
ea
ch
t
u
r
b
in
e
(
in
o
r
o
u
t
-
of
-
s
er
v
ice)
.
C
alcu
late
th
e
p
o
w
er
g
e
n
er
atio
n
o
f
ea
ch
w
i
n
d
t
u
r
b
in
e.
Gen
er
ate
r
an
d
o
m
v
ar
iab
les
f
o
r
ea
ch
cir
cu
i
t
co
m
p
o
n
e
n
t
a
n
d
d
eter
m
i
n
e
it
s
o
p
er
atin
g
s
tat
e
(
in
o
r
o
u
t
-
of
-
s
er
v
ice)
.
C
alcu
late
p
o
w
er
g
e
n
er
ated
f
o
r
ea
ch
cir
cu
it a
n
d
b
y
th
e
w
i
n
d
p
ar
k
b
y
lo
ad
f
lo
w
.
C
alcu
late
th
e
2
ce
n
tr
al
m
o
m
en
ts
m
ea
n
an
d
v
ar
ian
ce
o
f
t
h
e
to
t
al
in
j
ec
ted
p
o
w
er
at
th
e
P
C
C
.
I
f
th
e
co
n
v
er
g
en
ce
cr
iter
io
n
o
f
th
e
Mo
n
te
C
ar
lo
s
i
m
u
latio
n
is
s
a
tis
f
ied
co
n
ti
n
u
e
to
8
.
Oth
er
w
i
s
e
r
ep
ea
t
s
tep
s
1
-
6.
Ob
tain
th
e
h
i
s
to
g
r
a
m
s
o
f
t
h
e
d
en
s
it
y
a
n
d
d
is
tr
ib
u
tio
n
f
u
n
ct
io
n
s
o
f
t
h
e
p
o
w
er
g
en
er
atio
n
o
f
t
h
e
w
i
n
d
f
ar
m
P
er
f
o
r
m
s
tatis
t
ical
an
al
y
s
is
C
o
n
s
id
er
in
g
t
h
e
p
r
ev
io
u
s
s
tep
s
,
in
[
7
]
th
e
s
i
m
u
latio
n
w
as c
a
r
r
ied
o
u
t f
o
r
a
W
PP
o
f
2
0
0
M
W
,
8
0
w
i
n
d
tu
r
b
in
es
ar
r
an
g
ed
in
1
0
MV
cir
cu
its
co
n
n
ec
ted
li
k
e
F
i
g
u
r
e
1
s
h
o
w
s
,
an
d
co
n
v
er
g
ed
af
ter
1
5
6
9
r
ea
lizatio
n
s
.
As
a
r
esu
l
t,
th
e
p
o
w
er
ch
ar
ac
ter
is
tics
o
f
th
e
p
o
w
er
in
j
ec
tio
n
W
P
P
m
o
d
el
w
er
e
o
b
tain
ed
.
Alter
n
ati
v
el
y
,
in
o
p
er
atin
g
W
P
P
,
a
h
is
to
r
ic
d
ata
ca
n
b
e
e
m
p
lo
y
ed
in
o
r
d
er
to
co
u
n
t
w
it
h
a
r
ep
r
ese
n
tati
v
e
s
a
m
p
le
th
a
t
allo
w
s
th
e
s
tat
is
tical
m
o
d
elli
n
g
o
f
t
h
e
in
j
ec
ted
p
o
w
er
o
f
t
h
e
W
P
P
.
Fig
u
r
e
1
.
E
x
a
m
p
le
o
f
a
W
P
P
n
et
w
o
r
k
So
,
f
r
o
m
s
tati
s
tical
d
ata
o
r
f
r
o
m
a
Mo
n
te
C
ar
lo
s
i
m
u
latio
n
;
a
s
tati
s
tical
m
o
d
el
o
f
th
e
in
j
ec
ted
p
o
w
er
(P
i
)
b
y
th
e
W
P
P
is
f
i
x
ed
co
m
p
u
ti
n
g
it
s
f
o
u
r
ce
n
tr
al
m
o
m
en
ts
w
h
ic
h
ar
e:
m
ea
n
o
r
av
er
ag
e
i
n
j
ec
ted
p
o
w
er
(
)
,
its
s
tan
d
ar
d
d
ev
iatio
n
(
)
,
an
d
it
s
s
k
e
w
n
ess
(
,
3
)
an
d
k
u
r
to
s
is
(
,
4
)
.
T
h
e
s
e
f
o
u
r
s
tat
is
tic
s
ar
e
u
s
ed
b
y
th
e
P
E
M
m
eth
o
d
o
lo
g
y
(
a
s
s
ec
t
io
n
2
.
3
ex
p
lain
s
)
,
an
d
ar
e
d
ef
i
n
ed
as f
o
llo
w
:
=
∑
=
1
=
̅
(
2
)
=
√
∑
(
−
̅
)
2
=
1
−
1
(
3
)
,
3
=
3
2
3
/
2
(
4
)
,
4
=
4
2
2
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
27
-
36
30
w
h
er
e,
N
is
t
h
e
n
u
m
b
er
o
f
d
at
a
s
a
m
p
les,
a
n
d
2
=
∑
(
−
̅
)
2
=
1
(
6
)
3
=
∑
(
−
̅
)
3
=
1
(
7
)
4
=
∑
(
−
̅
)
4
=
1
(
8
)
2
.
2
.
Co
rr
el
a
t
ed
w
ind
po
w
er
pla
nts uncer
t
a
inties
m
o
del
Fro
m
s
ec
tio
n
2
.
1
,
ea
ch
W
P
P
is
r
ep
r
esen
ted
b
y
a
s
tatis
tical
m
o
d
el
o
f
f
o
u
r
s
tatis
t
ics
co
m
p
u
ted
f
r
o
m
th
e
in
j
ec
ted
p
o
w
er
at
th
e
P
C
C
:
m
ea
n
o
r
av
er
ag
e
in
j
ec
ted
p
o
w
er
(
)
,
its
s
tan
d
ar
d
d
ev
ia
tio
n
(
)
,
s
k
e
w
n
e
s
s
(
,
3
)
,
an
d
k
u
r
to
s
is
(
,
4
)
.
Nev
er
th
eles
s
,
if
a
p
o
w
er
s
y
s
te
m
h
as
m
W
P
P
,
th
e
w
in
d
b
eh
a
v
io
r
o
f
th
ese
W
W
P
ca
n
b
e
co
r
r
elate
d
ta
k
in
g
in
to
ac
co
u
n
t
w
ea
t
h
er
s
ea
s
o
n
s
,
W
W
P
s
lo
ca
tio
n
s
,
a
m
o
n
g
o
th
er
f
ac
to
r
s
[
2
3
]
.
So
,
th
e
s
tati
s
tical
b
e
h
av
io
r
o
f
a
s
et
o
f
W
W
P
s
is
g
i
v
en
n
o
t
o
n
l
y
f
o
r
th
e
ir
i
n
d
iv
id
u
al
s
tatis
t
ic
s
(
,
,
,
3
,
,
4
)
b
u
t
also
b
y
t
h
e
co
v
ar
ian
ce
b
etw
ee
n
t
h
e
in
j
ec
ted
p
o
w
er
o
f
t
h
ese
W
W
P
.
So
th
ese
co
v
ar
ian
c
e
o
f
i
n
j
ec
ted
p
o
w
er
b
y
t
h
e
W
P
P
s
(
[
]
)
is
g
iv
e
n
b
y
:
[
]
=
[
1
2
1
2
⋯
1
1
2
⋮
p1
2
2
⋮
p2
⋯
2
⋱
⋯
⋮
2
]
(
9
)
w
h
er
e
is
th
e
s
tan
d
ar
d
d
ev
iatio
n
o
f
th
e
in
j
ec
ted
p
o
w
er
b
y
th
e
i
-
th
W
W
P
o
b
tain
ed
in
s
ec
tio
n
2
.
1
;
an
d
i
j
is
th
e
co
v
ar
ia
n
ce
b
et
w
ee
n
t
h
e
p
o
w
er
in
j
ec
tio
n
s
o
f
i
-
t
h
W
W
P a
n
d
th
e
j
-
th
p
ar
k
;
w
h
ic
h
is
g
i
v
en
b
y
:
=
×
×
(
1
0
)
w
h
e
r
e
i
j
i
s
t
h
e
c
o
r
r
e
l
a
t
i
o
n
f
a
c
t
o
r
b
e
t
w
e
e
n
t
h
e
p
o
w
e
r
i
n
j
e
c
t
i
o
n
s
o
f
i
-
t
h
W
W
P
a
n
d
t
h
e
j
-
t
h
p
a
r
k
[
1
5
]
.
T
h
is
co
r
r
elate
d
m
o
d
el
is
u
s
e
f
u
l
to
tak
e
i
n
to
ac
co
u
n
t
th
i
s
s
ta
tis
tical
ch
ar
ac
ter
is
tic
t
h
at
ce
n
b
e
p
r
esen
t
in
a
s
et
o
f
W
W
P
s
.
Ho
w
e
v
er
,
t
h
ese
m
o
d
el
m
u
s
t
b
e
tr
an
s
f
o
r
m
ed
in
a
d
ec
o
u
p
led
(
n
o
n
-
co
r
r
elate
d
)
s
et
o
f
r
an
d
o
m
v
ar
iab
les
t
h
at
al
lo
w
s
p
r
o
b
ab
ilis
tic
tr
ea
t
m
e
n
t
b
y
th
e
P
o
in
t
E
s
t
i
m
ate
Me
th
o
d
(
p
r
o
p
o
s
ed
in
th
e
n
e
x
t
s
ec
tio
n
2
.
3
)
an
d
f
o
r
Mo
n
te
C
ar
lo
s
i
m
u
lati
o
n
,
also
.
T
h
u
s
,
tr
an
s
f
o
r
m
atio
n
o
f
co
r
r
elate
d
v
ar
iab
les
=
[
1
…
]
in
to
a
s
et
o
f
n
o
n
-
co
r
r
elate
d
v
ar
iab
l
es
=
[
1
…
]
is
o
b
tain
ed
b
y
th
e
f
o
llo
w
i
n
g
lin
ea
r
tr
a
n
s
f
o
r
m
a
tio
n
:
[
]
=
[
]
−
[
]
(
1
1
)
Su
c
h
as t
h
e
co
v
ar
ian
ce
o
f
th
e
n
o
n
-
co
r
r
elate
d
v
ar
iab
les
x
([
]
)
b
e
g
iv
e
n
b
y
[
1
5
]
:
[
]
=
[
]
−
[
]
[
[
]
−
]
=
[
]
(
1
2
)
w
h
er
e
[
]
is
co
m
p
u
ted
f
r
o
m
t
h
e
C
h
o
le
s
k
y
d
ec
o
m
p
o
s
itio
n
o
f
th
e
co
v
ar
ian
ce
m
atr
i
x
[
]
,
s
u
ch
a
s
[
3
,
1
5
]
:
[
]
=
[
]
[
]
(
1
3
)
No
w
,
f
o
r
th
e
ap
p
licatio
n
o
f
P
E
M
(
s
ee
s
ec
tio
n
2
.
3
)
is
n
ec
ess
ar
y
to
co
m
p
u
te
th
e
f
o
u
r
ce
n
tr
a
l
m
o
m
e
n
ts
o
f
ea
ch
v
ar
iab
le
x
.
T
h
u
s
,
f
r
o
m
th
e
i
n
itia
l
v
ar
iab
les
p
,
t
h
e
s
tatis
tical
ce
n
tr
al
m
o
m
e
n
ts
f
o
r
th
e
n
e
w
v
ar
iab
les
x
ar
e
ca
lcu
lated
as
[
1
5
]
:
[
]
=
[
−
]
[
]
(
1
4
)
,
3
=
∑
(
−
1
)
3
,
3
3
=
1
(
1
5
)
,
4
=
∑
(
−
1
)
4
,
4
4
=
1
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
B
u
lk
p
o
w
er sys
tem
a
va
ila
b
ilit
y
a
s
s
ess
men
t
w
ith
…
(
A
n
g
ie
C
.
C
ep
ed
a
)
31
w
h
er
e
[
]
=
[
…
]
is
th
e
v
ec
to
r
o
f
th
e
av
er
ag
e
v
al
u
es
o
f
t
h
e
m
v
ar
iab
l
es
x
.
,
3
an
d
,
4
ar
e
th
e
s
k
e
w
n
es
s
a
n
d
th
e
k
u
r
to
s
is
o
f
th
e
l
-
th
v
ar
iab
le
x
.
I
n
ad
d
i
tio
n
,
as
[
]
=
[
]
,
th
e
v
al
u
e
o
f
t
h
e
v
ar
i
an
ce
o
f
ea
ch
is
1
; th
e
n
=
1
.
2
.
3
.
Av
a
ila
bil
it
y
a
s
s
ess
m
ent
us
ing
po
int
esti
m
a
t
e
m
et
ho
d
Mo
n
te
C
ar
lo
s
i
m
u
latio
n
an
d
s
tate
en
u
m
er
atio
n
h
av
e
b
ee
n
th
e
tr
ad
itio
n
al
m
e
th
o
d
o
lo
g
i
es
u
s
ed
to
ass
es
s
th
e
a
v
ailab
ilit
y
o
f
b
u
lk
p
o
w
er
s
y
s
te
m
s
[
3
,
2
4
-
2
7
]
.
So
m
e
co
m
m
er
cial
s
o
f
t
w
ar
e
h
av
e
r
eliab
ilit
y
ass
es
s
m
en
t
to
o
ls
b
ased
o
n
t
h
ese
tech
n
iq
u
e
s
.
T
h
ese
s
o
f
t
w
ar
e,
tr
ad
itio
n
all
y
,
u
s
es
f
o
r
th
e
as
s
ess
m
e
n
t
o
f
av
ailab
ilit
y
/r
eliab
ilit
y
o
f
b
u
lk
s
y
s
te
m
s
a
m
o
d
el
o
f
t
w
o
s
tates
to
r
ep
r
esen
t
th
e
u
n
ce
r
tai
n
t
y
o
f
ea
ch
s
y
n
c
h
r
o
n
o
u
s
g
en
er
atio
n
u
n
it,
ta
k
i
n
g
t
h
e
s
ta
tes
o
f
i
n
-
s
er
v
ice
o
r
o
u
t
-
of
-
s
er
v
ice
[
3
]
.
Nev
er
th
ele
s
s
,
as
it
h
a
s
s
h
o
w
n
i
n
s
ec
tio
n
s
2
.
1
an
d
2
.
2
,
w
in
d
p
o
w
er
p
lan
ts
(
W
P
P
)
ca
n
n
o
t
b
e
m
o
d
elled
in
t
w
o
s
tate
s
,
as
t
h
e
y
d
ep
en
d
d
ir
ec
tly
o
n
th
e
u
n
ce
r
tai
n
t
y
o
f
th
e
w
in
d
s
p
ee
d
,
th
e
o
p
er
atio
n
o
f
t
h
e
c
o
m
p
o
n
en
t
s
o
f
th
e
n
et
w
o
r
k
a
n
d
th
e
to
p
o
lo
g
y
o
f
th
e
p
ar
k
[
7
]
,
an
d
th
e
co
r
r
elatio
n
b
et
w
ee
n
t
h
e
d
if
f
er
en
t W
P
P
s
co
n
n
ec
ted
to
th
e
p
o
w
er
s
y
s
te
m
.
T
h
e
p
r
o
p
o
s
al
o
f
th
is
p
ap
er
is
t
o
ap
p
ly
th
e
co
n
ce
p
ts
o
f
th
e
P
o
in
t
E
s
ti
m
ate
Me
th
o
d
(
P
E
M)
in
o
r
d
er
t
o
tak
e
in
to
ac
co
u
n
t
u
n
ce
r
tai
n
tie
s
m
o
d
el
o
f
W
P
P
an
d
co
r
r
elate
d
b
eh
av
io
r
o
f
a
s
et
o
f
W
PP
.
A
lth
o
u
g
h
m
an
y
P
E
M
s
ch
e
m
es
h
a
v
e
b
ee
n
s
u
g
g
e
s
te
d
[
1
2
-
16]
an
d
h
av
e
b
ee
n
u
s
ed
to
s
o
lv
e
th
e
p
r
o
b
le
m
o
f
p
r
o
b
a
b
ilis
tic
p
o
w
er
f
lo
w
[
1
5
,
2
6
]
,
th
is
p
ap
er
p
r
o
p
o
s
es
th
e
u
s
e
o
f
t
h
e
2
m
+1
P
E
M
p
r
o
p
o
s
ed
b
y
Ho
n
g
i
n
[
1
6
]
.
T
h
e
p
u
r
p
o
s
e
is
to
co
m
p
u
te
t
h
e
co
m
m
o
n
r
eliab
i
lit
y
(
a
v
ailab
ilit
y
)
i
n
d
ices:
L
o
s
s
o
f
L
o
ad
P
r
o
b
ab
ilit
y
(
L
O
L
P
)
an
d
E
x
p
ec
ted
E
n
er
g
y
No
t Su
p
p
lied
(
E
E
NS)
as a
r
e
d
ef
in
ed
at
[
2
6
,
2
7
]
,
u
s
in
g
th
e
s
tate
en
u
m
er
atio
n
m
et
h
o
d
.
T
h
e
P
E
M
-
b
ased
ad
eq
u
ac
y
a
s
s
ess
m
en
t
h
er
e
p
r
o
p
o
s
ed
s
tar
ts
c
o
m
p
u
ti
n
g
th
e
s
et
o
f
2
m
+1
co
n
ce
n
tr
atio
n
p
o
in
ts
n
a
m
ed
(
[
]
,
,
,
)
,
w
h
er
e
[
]
,
is
t
h
e
i
n
j
ec
ted
p
o
w
er
o
f
th
e
m
W
P
P
s
in
t
h
e
p
o
w
er
s
y
s
te
m
f
o
r
t
h
e
k
-
t
h
co
n
ce
n
tr
atio
n
(
k
=1
,
2
,
an
d
3
)
ass
o
ciate
d
to
th
e
l
-
th
r
an
d
o
m
v
ar
iab
le
(
l
=1
,
2
,
…,
m
)
;
an
d
,
i
s
th
e
w
e
ig
h
ti
n
g
f
ac
to
r
co
m
p
u
ted
f
o
r
th
is
co
n
ce
n
tr
atio
n
p
o
in
t.
As,
th
e
W
P
P
s
ar
e
co
r
r
elate
d
,
a
s
a
g
en
er
al
a
s
s
u
m
p
tio
n
,
th
e
[
]
,
is
co
m
p
u
ted
f
r
o
m
(
1
1
)
as:
[
]
,
=
[
]
[
]
,
(
1
7
)
I
t
m
ea
n
s
,
t
h
at
p
r
ev
io
u
s
l
y
it
m
u
s
t
b
e
co
m
p
u
ted
th
e
co
n
ce
n
tr
atio
n
p
o
in
t
s
an
d
th
e
w
ei
g
h
tin
g
f
ac
to
r
s
u
s
i
n
g
th
e
d
ec
o
u
p
led
v
ar
iab
les,
w
h
ic
h
ar
e
s
tatis
t
icall
y
i
n
d
ep
en
d
en
t.
T
h
u
s
,
th
e
v
ec
to
r
[
]
,
is
g
i
v
en
b
y
:
[
]
,
=
[
1
,
⋯
,
,
,
⋯
,
]
(
1
8
)
w
h
er
e
1
m
ea
n
s
t
h
at
all
r
a
n
d
o
m
v
ar
iab
le
x
i
d
i
f
f
er
e
n
t
to
th
e
l
-
t
h
r
an
d
o
m
v
ar
iab
le
tak
e
s
th
e
f
ir
s
t
ce
n
tr
al
m
o
m
e
n
t;
i.e
.
t
h
e
m
ea
n
v
al
u
e
o
f
x
i.
Fo
r
ea
c
h
l
-
t
h
r
a
n
d
o
m
v
ar
iab
le
ar
e
3
co
n
ce
n
tr
atio
n
p
o
in
ts
;
i.e
.
k
=1
,
2
,
3
.
T
h
e
l
-
th
r
an
d
o
m
v
ar
iab
le
tak
e
s
th
e
v
al
u
e
,
=
+
,
(
1
9
)
w
h
er
e
,
is
th
e
s
ta
n
d
ar
d
lo
ca
tio
n
,
an
d
,
,
,
3
,
,
4
th
e
ce
n
tr
al
m
o
m
e
n
t
s
o
f
th
e
in
p
u
t
r
an
d
o
m
v
ar
iab
l
e
x
l
.
T
h
u
s
,
,
=
,
3
2
+
(
−
1
)
3
−
√
,
4
−
3
4
,
3
2
for
=
1
,
2
(
2
0
)
,
3
=
0
=
3
(
2
1
)
w
h
er
e
th
e
s
k
e
w
n
e
s
s
(
,
3
)
an
d
th
e
k
u
r
to
s
i
s
(
,
4
)
o
f
x
l
ar
e
co
m
p
u
ted
f
r
o
m
(
1
5
)
an
d
(
1
6
)
.
No
te
th
at
f
o
r
all
l
-
t
h
r
an
d
o
m
v
ar
iab
le
[
]
,
3
is
a
co
m
m
o
n
v
ec
to
r
g
i
v
e
n
b
y
:
[
]
,
3
=
[
1
,
⋯
,
,
⋯
,
]
(
2
2
)
On
t
h
e
o
th
er
h
a
n
d
,
th
e
w
ei
g
h
ti
n
g
f
ac
to
r
,
is
co
m
p
u
ted
as:
,
=
(
−
1
)
3
−
,
(
,
1
−
,
2
)
for
=
1
,
2
(
2
3
)
,
3
=
1
−
1
(
,
4
−
,
3
2
)
=
3
(
2
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
27
-
36
32
On
ce
t
h
e
co
n
ce
n
tr
atio
n
p
o
i
n
t
s
[
]
,
is
o
b
tain
ed
f
r
o
m
(
1
7
)
,
an
av
ailab
ilit
y
as
s
es
s
m
en
t
o
f
t
h
e
b
u
lk
p
o
w
er
s
y
s
te
m
is
ca
r
r
ied
o
u
t
u
s
i
n
g
s
ta
te
e
n
u
m
er
atio
n
.
I
n
e
ac
h
as
s
es
s
m
e
n
t,
th
e
r
eliab
ilit
y
i
n
d
ices
E
E
N
S
a
n
d
L
O
L
P
ar
e
co
m
p
u
ted
f
o
r
ev
er
y
lo
ad
p
o
in
t
o
f
th
e
s
y
s
te
m
a
n
d
/
o
r
f
o
r
th
e
s
y
s
te
m
.
L
et
(
,
)
th
e
r
eliab
ilit
y
in
d
e
x
(
E
E
NS
o
r
L
OL
P
)
co
m
p
u
ted
f
o
r
b
u
s
i
(
i.e
.
a
lo
a
d
b
u
s
)
u
s
i
n
g
th
e
p
o
w
er
in
j
ec
tio
n
s
W
P
P
[
]
,
,
th
e
m
ea
n
v
alu
e
an
d
th
e
s
ta
n
d
ar
d
d
ev
iatio
n
o
f
t
h
e
r
eliab
ilit
y
i
n
d
ex
a
t
b
u
s
i
co
n
s
id
er
in
g
al
l
t
h
e
co
n
ce
n
tr
atio
n
p
o
in
ts
i
s
o
b
tain
ed
as th
e
w
ei
g
h
ted
av
er
ag
e,
g
iv
e
n
b
y
:
=
∑
∑
,
(
,
)
3
=
1
=
1
(
2
5
)
[
2
]
=
∑
∑
,
(
(
,
)
)
2
3
=
1
=
1
(
2
6
)
=
√
[
2
]
−
2
(
2
7
)
Fig
u
r
e
2
p
r
esen
ts
t
h
e
g
en
er
al
p
r
o
ce
d
u
r
e
o
f
av
ailab
ilit
y
a
s
s
ess
m
en
t
u
s
in
g
P
E
M.
T
h
e
ca
lcu
latio
n
o
f
co
n
ce
n
tr
atio
n
p
o
in
t
s
i
s
m
ad
e
ap
p
ly
i
n
g
(
1
7
)
to
(
2
3
)
.
T
h
e
ca
l
cu
latio
n
o
f
r
eliab
ilit
y
i
n
d
ex
e
s
m
a
k
es
u
s
e
o
f
(
2
3
)
to
(
2
7
)
.
I
n
Fig
u
r
,
m
i
s
t
h
e
n
u
m
b
er
o
f
W
P
P
s
in
t
h
e
p
o
w
er
s
y
s
t
e
m
.
No
te
th
at
k
=1
,
2
,
3
.
W
h
en
k=
3
,
f
o
r
a
n
y
l
,
t
h
e
co
n
ce
n
tr
atio
n
p
o
in
t is t
h
e
s
a
m
e,
g
iv
e
n
b
y
(
2
2
)
.
Fig
u
r
e
2
.
A
l
g
o
r
ith
m
o
f
a
v
ailab
ilit
y
a
s
s
es
s
m
en
t
u
s
in
g
P
E
M
3.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
3
.
1
.
Study
sy
s
t
e
m
Fig
u
r
e
3
s
h
o
w
s
th
e
test
s
y
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te
m
,
w
h
ich
co
r
r
esp
o
n
d
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t
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e
I
E
E
E
R
eliab
ilit
y
T
est
S
y
s
te
m
2
4
n
o
d
es
[
1
9
]
,
m
o
d
if
ied
.
I
n
o
r
d
er
to
ap
p
ly
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
,
t
w
o
W
P
P
s
ar
e
p
lace
d
at
n
o
d
es
7
an
d
1
6
;
r
ep
lacin
g
th
e
o
r
ig
i
n
al
s
y
n
ch
r
o
n
o
u
s
g
e
n
er
atio
n
g
iv
e
n
at
[
1
9
]
.
E
ac
h
W
PP
co
n
s
is
t
o
f
1
0
MV
cir
cu
its
w
it
h
8
tu
r
b
in
es
ea
c
h
o
n
e,
f
o
r
a
to
t
al
o
f
8
0
w
i
n
d
t
u
r
b
in
e
s
o
f
2
.
5
MW
,
b
ased
o
n
[
5
]
.
I
n
ad
d
itio
n
,
a
s
tatic
v
ar
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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m
p
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g
I
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N:
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8
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B
u
lk
p
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er sys
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a
va
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a
s
s
ess
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t
w
ith
…
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A
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C
.
C
ep
ed
a
)
33
co
m
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n
s
ato
r
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ev
ice
(
SV
C
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i
s
p
lace
d
in
b
o
th
n
o
d
es
f
o
r
v
o
ltag
e
r
eg
u
lat
io
n
o
f
t
h
e
s
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s
t
e
m
.
As
[
7
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s
h
o
w
s
,
a
Mo
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ar
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i
m
u
lat
io
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s
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t a
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tat
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l c
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ar
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ter
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er
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y
t
h
e
W
P
P
.
T
ab
le
1
s
h
o
w
s
th
i
s
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h
ar
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izatio
n
b
a
s
ed
o
n
a
Mo
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te
C
ar
lo
s
i
m
u
lati
o
n
o
f
1
5
6
9
r
ea
lizatio
n
s
,
s
h
o
w
i
n
g
t
h
e
f
o
u
r
ce
n
tr
al
m
o
m
e
n
t
s
(
,
,
,
3
,
,
4
).
Fig
u
r
e
3
.
T
est
s
y
s
te
m
–
IEEE
r
eliab
ilit
y
tes
t s
y
s
te
m
m
o
d
i
f
ie
d
T
ab
le
1
.
C
en
tr
al
m
o
m
e
n
t
s
o
f
t
h
e
W
P
P
C
e
n
t
r
a
l
M
o
me
n
t
s
V
a
l
u
e
M
e
a
n
(
)
[
M
W
]
6
0
.
3
6
S
t
a
n
d
a
r
d
D
e
v
i
a
t
i
o
n
(
)
[
M
W
]
6
0
.
9
4
S
k
e
w
n
e
ss (
,
3
)
0
.
8
4
9
K
u
r
t
o
si
s (
,
4
)
2
.
4
2
7
3
.
2
.
Study
ca
s
es
T
h
r
ee
s
ce
n
ar
io
s
b
ased
o
n
th
e
co
r
r
elatio
n
b
et
w
ee
n
th
e
b
e
h
av
io
r
s
o
f
p
o
w
er
i
n
j
ec
tio
n
s
o
f
W
P
P
1
(
p
lace
d
at
n
o
d
e
1
6
)
an
d
W
PP
2
(
p
lace
d
at
n
o
d
e
7
)
ar
e
an
aly
ze
d
.
T
h
ese
s
ce
n
ar
io
s
ar
e:
Scen
a
r
i
o
1
:
T
h
e
in
jecti
o
n
o
f
b
o
th
W
PP
s
a
r
e
ass
u
m
ed
as
in
d
ep
en
d
en
t
r
an
d
o
m
v
ar
ia
b
l
es;
i
.
e.
th
e
c
o
r
r
ela
ti
o
n
1
2
=
0
.
Scen
a
r
i
o
2
:
T
h
e
in
jec
ti
o
n
o
f
b
o
th
W
PP
s
a
r
e
in
v
e
r
s
e
ly
co
r
r
el
at
ed
;
ass
u
m
in
g
a
co
r
r
el
ati
o
n
1
2
=
−
0
.
5
.
Scen
a
r
i
o
3
:
T
h
e
in
jec
ti
o
n
o
f
b
o
th
W
PP
s
a
r
e
d
i
r
e
ctly
c
o
r
r
e
lat
e
d
;
ass
u
m
in
g
a
c
o
r
r
ela
ti
o
n
1
2
=
0
.
5
.
I
n
th
i
s
ca
s
e,
th
er
e
ar
e
2
W
P
P
s
,
th
en
tak
es
th
e
v
alu
e
o
f
2
.
I
n
co
n
s
eq
u
e
n
ce
,
5
co
n
ce
n
tr
atio
n
p
o
in
t
s
(
,
,
,
)
ar
e
estab
lis
h
ed
(
2
m
+1
)
ac
co
r
d
in
g
to
s
ec
tio
n
2
.
3
.
T
h
ese
co
n
ce
n
tr
atio
n
p
o
in
ts
ar
e
d
e
f
i
n
ed
at
T
ab
le
2
.
I
t is im
p
o
r
tan
t to
ex
p
l
ain
th
e
c
h
ar
ac
ter
is
tic
o
f
th
e
f
ir
s
t c
o
n
ce
n
tr
atio
n
p
o
in
t:
C
o
n
ce
n
t
r
a
ti
o
n
P
o
in
t
1
:
th
is
c
as
e
w
ill
b
e
th
e
c
o
m
m
o
n
co
n
ce
n
t
r
at
io
n
p
o
in
t
d
e
r
iv
e
d
f
r
o
m
(
1
8
)
.
W
h
en
k
=3
f
o
r
ea
ch
r
an
d
o
m
v
ar
ia
b
le
l
,
b
o
th
W
PP
ar
e
g
en
e
r
a
tin
g
th
e
v
a
lu
e
o
f
th
ei
r
m
ea
n
v
alu
e
1
an
d
2
.
I
n
s
u
ch
ca
s
e
[
]
1
,
3
=
[
]
2
,
3
,
th
en
f
r
o
m
(
1
7
)
[
]
1
,
3
=
[
]
2
,
3
.
I
n
ad
d
i
tio
n
,
th
e
w
eig
h
tin
g
f
ac
to
r
o
f
th
e
c
o
m
m
o
n
co
n
c
en
tr
ati
o
n
p
o
in
t
is
th
e
s
u
m
o
f
th
e
w
eig
h
ts
1
,
3
+
2
,
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
27
-
36
34
On
th
e
o
th
er
h
an
d
,
th
e
o
th
er
co
n
ce
n
tr
atio
n
p
o
in
t
s
[
]
,
ar
e
d
e
f
i
n
ed
b
ased
o
n
(
1
8
)
,
w
h
en
l
tak
es
th
e
v
al
u
es o
f
1
an
d
2
; a
n
d
k
=
1
an
d
2
(
k
=3
is
th
e
co
m
m
o
n
c
o
n
ce
n
tr
atio
n
p
o
in
t)
.
T
h
en
,
[
]
,
is
t
r
an
s
f
o
r
m
ed
to
[
p
]
,
u
s
i
n
g
(
1
7
)
.
T
ab
le
2
s
h
o
w
s
t
h
e
g
e
n
er
al
d
ef
i
n
it
io
n
o
f
t
h
e
c
o
n
ce
n
tr
atio
n
p
o
in
ts
.
T
h
e
v
al
u
es
d
ep
en
d
o
n
th
e
s
ce
n
ar
io
u
n
d
er
an
al
y
s
i
s
.
T
ab
le
3
s
h
o
w
s
f
o
r
th
e
t
h
r
ee
s
ce
n
ar
io
s
t
h
e
p
o
w
er
g
en
er
ated
i
n
MW
f
o
r
ea
ch
W
P
P
ac
co
r
d
in
g
to
t
h
e
5
co
n
ce
n
tr
at
io
n
p
o
in
t
s
.
T
ab
le
4
p
r
esen
ts
t
h
e
w
ei
g
h
ti
n
g
f
ac
to
r
f
o
r
t
h
e
c
o
n
ce
n
tr
atio
n
p
o
in
t
s
ac
co
r
d
in
g
to
T
ab
le
2
.
T
ab
le
2
.
C
o
n
ce
n
tr
atio
n
p
o
in
t
s
–
test
ca
s
e
C
o
n
c
e
n
t
r
a
t
i
o
n
P
o
i
n
t
I
n
j
e
c
t
e
d
P
o
w
e
r
a
t
W
P
P
1
I
n
j
e
c
t
e
d
P
o
w
e
r
a
t
W
P
P
2
W
e
i
g
h
t
F
a
c
t
o
r
1
1
,
3
=
P
1
2
,
3
=
P
2
1
,
3
+
2
,
3
2
P
1
2
,
1
2
,
1
3
P
1
2
,
2
2
,
2
4
1
,
1
P
2
1
,
1
5
1
,
2
P
2
1
,
2
T
ab
le
3
.
P
o
w
er
ge
n
er
ated
(
MW
)
b
y
W
P
P
-
s
ce
n
ar
io
s
d
e
an
al
y
s
i
s
W
P
P
C
o
n
c
e
n
t
r
a
t
i
o
n
P
o
i
n
t
s
C
o
r
r
e
l
a
t
i
o
n
S
c
e
n
a
r
i
o
s
1
2
=
0
1
2
=
−
0
.
5
1
2
=
0
.
5
N
o
d
e
1
6
1
6
0
.
3
6
6
0
.
3
6
6
0
.
3
6
2
6
0
.
3
6
6
0
.
3
6
6
0
.
3
6
3
6
0
.
3
6
6
0
.
3
6
6
0
.
3
6
4
1
6
9
.
9
3
1
6
9
.
9
3
1
6
9
.
9
3
5
2
.
5
3
2
.
5
3
2
.
5
3
N
o
d
e
7
1
6
0
.
3
6
6
0
.
3
6
6
0
.
3
6
2
1
6
9
.
9
3
1
9
0
1
9
0
.
7
2
3
2
.
5
3
8
.
3
2
0
4
6
0
.
3
6
5
.
5
8
1
1
5
.
1
4
5
6
0
.
3
6
8
9
.
2
8
3
1
.
4
4
T
ab
le
4
.
W
eig
h
tin
g
f
ac
to
r
s
b
y
co
n
ce
n
tr
atio
n
p
o
in
t
-
s
ce
n
ar
io
s
d
e
an
al
y
s
is
C
o
n
c
e
n
t
r
a
t
i
o
n
P
o
i
n
t
s
C
o
r
r
e
l
a
t
i
o
n
S
c
e
n
a
r
i
o
s
1
2
=
0
1
2
=
−
0
.
5
1
2
=
0
.
5
1
-
0
.
1
7
2
0
.
0
0
1
0
.
1
0
9
2
0
.
2
0
3
0
.
1
1
8
0
.
1
0
7
3
0
.
3
8
3
0
.
2
9
5
0
.
1
9
9
4
0
.
2
0
3
0
.
2
0
3
0
.
2
0
2
5
0
.
3
8
4
0
.
3
8
4
0
.
3
8
4
On
ce
t
h
e
p
o
w
er
g
e
n
er
atio
n
o
f
W
P
P
s
ar
e
co
m
p
u
ted
f
o
r
ea
ch
s
ce
n
ar
io
an
d
its
co
n
ce
n
tr
ati
o
n
p
o
in
ts
;
th
e
r
eliab
ilit
y
i
n
d
ices
f
o
llo
w
i
n
g
t
h
e
al
g
o
r
ith
m
o
f
Fi
g
u
r
e
2
is
r
u
n
.
T
ab
le
5
p
r
esen
ts
th
e
s
y
s
te
m
E
E
NS
in
d
e
x
a
n
d
T
ab
le
6
s
h
o
w
s
t
h
e
s
y
s
te
m
L
O
L
P
in
d
ex
,
co
m
p
u
ted
f
o
r
ea
ch
co
n
ce
n
tr
atio
n
p
o
in
t
u
n
d
er
ea
c
h
s
ce
n
ar
io
.
A
p
p
l
y
in
g
th
e
w
eig
h
ti
n
g
f
ac
to
r
s
o
f
T
ab
l
e
4
an
d
(
2
5
)
-
(
2
7
)
th
e
m
ea
n
v
alu
e
an
d
th
e
s
ta
n
d
ar
d
d
ev
iatio
n
o
f
th
e
E
E
NS
an
d
th
e
L
OL
P
ar
e
co
m
p
u
ted
.
T
h
e
co
n
ce
n
tr
atio
n
p
o
in
t
1
also
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RE
F
E
R
E
NC
E
S
[1
]
P
.
Bie
,
e
t
a
l.
,
“
P
ro
b
a
b
il
isti
c
d
y
n
a
m
ic
lo
a
d
f
lo
w
w
it
h
c
o
rre
late
d
w
in
d
so
u
rc
e
s,”
IE
EJ
T
ra
n
sa
c
ti
o
n
s
o
n
El
e
c
trica
l
a
n
d
El
e
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tro
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ic E
n
g
i
n
e
e
rin
g
,
v
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l.
1
3
,
n
o
.
1
,
p
p
.
7
6
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3
,
2
0
1
8
.
[2
]
A
.
S
.
A
.
Ba
d
a
w
i,
e
t
a
l.
,
“
Ev
a
lu
a
ti
o
n
o
f
w
in
d
p
o
w
e
r
f
o
r
e
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a
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n
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n
e
ra
ti
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m
e
d
it
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rra
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e
a
n
c
o
st
o
f
P
a
les
ti
n
e
f
o
r
1
4
y
e
a
rs,
”
In
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
E
lec
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
),
v
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l.
9
,
n
o
.
6
,
p
p
.
4
6
1
0
-
4
6
1
6
,
2
0
1
9
.
[3
]
W
.
L
i,
“
Risk
A
s
se
ss
m
e
n
t
o
f
P
o
w
e
r
S
y
ste
m
s
,
”
IEE
E
Pre
ss
,
J
o
h
n
W
il
e
y
&
S
o
n
s.,
2
0
0
5
.
[4
]
A
.
M
o
re
n
o
,
a
n
d
M.
A
.
Río
s,
“
I
m
p
a
c
t
o
f
W
in
d
G
e
n
e
ra
ti
o
n
i
n
t
h
e
G
e
n
e
ra
ti
o
n
Re
li
a
b
il
i
ty
A
ss
e
s
s
m
e
n
t,
”
Ap
p
li
e
d
M
e
c
h
a
n
ics
a
n
d
M
a
ter
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ls (
AM
M
)
J
o
u
rn
a
l,
v
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l.
2
6
7
,
p
p
.
2
9
-
3
2
,
2
0
1
3
.
[5
]
D.
v
a
n
He
rtem
,
O.
G
o
m
is
-
Be
ll
m
u
n
t,
a
n
d
J.
L
ian
g
,
“
Of
f
sh
o
re
W
i
n
d
P
o
w
e
r
P
lan
ts
(OW
P
P
S
),
”
W
il
e
y
-
IEE
E
Pre
ss
,
p
p
.
1
0
9
-
138
,
2
0
1
6
.
[6
]
M
.
d
e
P
ra
d
a
,
L
.
Ig
u
a
lad
a
,
C.
Co
rc
h
e
ro
,
O.
G
o
m
is
-
Be
l
m
u
n
t,
A
.
S
u
m
p
e
r,
“
H
y
b
rid
A
C
-
DC
O
ff
sh
o
re
W
in
d
P
o
w
e
r
P
la
n
t
T
o
p
o
lo
g
y
:
Op
ti
m
a
l
De
si
g
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
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ste
ms
,
v
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3
0
,
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4
,
p
p
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1
8
6
8
-
1
8
7
6
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2
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1
5
.
[7
]
R.
V
e
rg
a
ra
,
“
P
ro
b
a
b
il
isti
c
M
o
d
e
l
o
f
W
in
d
P
o
w
e
r
P
a
rk
s
f
o
r
Re
li
a
b
il
it
y
A
ss
e
ss
m
e
n
t
(
In
S
p
a
n
ish
),
”
M
a
ste
r
De
g
re
e
T
h
e
sis in
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
,
Un
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rs
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d
d
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L
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e
s,
B
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g
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t
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,
2
0
1
8
.
[8
]
Y.
Din
g
,
C.
S
i
n
g
h
,
L
.
G
o
e
l,
J.
Os
terg
a
a
rd
,
P
.
W
a
n
g
,
“
S
h
o
rt
-
T
e
rm
a
n
d
M
e
d
i
u
m
-
T
e
r
m
R
e
li
a
b
il
it
y
Ev
a
lu
a
ti
o
n
f
o
r
P
o
w
e
r
S
y
ste
m
s
w
it
h
Hig
h
P
e
n
e
tr
a
ti
o
n
o
f
W
in
d
P
o
w
e
r,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
u
st
a
i
n
a
b
le
E
n
e
rg
y
,
v
o
l.
5
,
n
o
.
3
,
p
p
.
8
9
6
-
9
0
6
,
2
0
1
4
.
[9
]
X
.
Jia
n
g
,
Z.
Z
h
a
n
g
,
J.
W
a
n
g
,
“
S
t
u
d
ies
o
n
t
h
e
Re
li
a
b
il
it
y
a
n
d
Re
se
rv
e
Ca
p
a
c
it
y
o
f
El
e
c
tri
c
P
o
w
e
r
S
y
st
e
m
w
it
h
W
in
d
P
o
w
e
r
In
teg
ra
ti
o
n
,
”
Po
we
r
E
n
g
i
n
e
e
rin
g
a
n
d
Au
t
o
ma
ti
o
n
Co
n
fer
e
n
c
e
,
2
0
1
2
.
[1
0
]
H.
X
iao
q
i
n
g
,
Y.
Yo
n
g
,
“
W
in
d
P
o
w
e
r
P
e
n
e
trati
o
n
L
im
it
Ca
lc
u
latio
n
b
a
se
d
o
n
P
o
w
e
r
S
y
st
e
m
Re
li
a
b
il
it
y
,
”
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
S
u
st
a
in
a
b
le P
o
we
r Ge
n
e
ra
ti
o
n
a
n
d
S
u
p
p
ly,
p
p
.
1
-
4
,
2
0
0
9
.
[1
1
]
S.
A
.
P
e
ñ
a
,
M
.
A
.
Rio
s,
I
.
Z
u
b
ia
,
“
W
P
P
M
o
d
e
l
i
n
P
o
w
e
r
S
y
ste
m
S
e
c
u
rit
y
As
se
ss
m
e
n
t,
”
In
ter
n
a
ti
o
n
a
l
Rev
iew
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
IRE
E,
v
o
l.
1
5
,
n
o
.
2
,
p
p
.
1
5
5
-
1
6
3
,
2
0
2
0
.
[1
2
]
C.
S
u
,
“
P
ro
b
a
b
il
isti
c
L
o
a
d
-
F
lo
w
Co
m
p
u
tatio
n
Us
in
g
P
o
i
n
t
Es
ti
m
a
te
M
e
th
o
d
,
”
IEE
E
T
ra
n
s
a
c
t
io
n
s
o
n
Po
we
r
S
y
ste
ms
,
vo
l.
2
0
,
n
o
.
4
,
p
p
.
1
8
4
3
-
1
8
5
1
,
2
0
0
5
.
[1
3
]
E.
T
o
m
a
ss
o
n
,
L
.
S
ö
d
e
r,
“
Ge
n
e
ra
ti
o
n
A
d
e
q
u
a
c
y
A
n
a
l
y
sis
o
f
M
u
lt
i
-
A
re
a
P
o
w
e
r
S
y
ste
m
s
w
it
h
a
Hig
h
S
h
a
re
o
f
W
in
d
P
o
w
e
r,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
P
o
we
r S
y
ste
ms
,
v
o
l.
3
3
,
n
o
.
4
,
p
p
.
3
8
5
4
-
3
8
6
2
,
2
0
1
7
.
[1
4
]
W
.
W
a
n
g
d
e
e
a
n
d
R.
Bil
li
n
t
o
n
,
“
Co
n
sid
e
ri
n
g
L
o
a
d
-
Ca
rry
in
g
Ca
p
a
b
il
it
y
a
n
d
W
in
d
S
p
e
e
d
Co
rre
lati
o
n
o
f
W
ECS
in
G
e
n
e
r
a
ti
o
n
A
d
e
q
u
a
c
y
A
ss
e
ss
m
e
n
t,
”
IEE
E
T
r
a
n
s
a
c
ti
o
n
o
n
E
n
e
rg
y
Co
n
v
e
rs
io
n
,
v
o
l.
2
1
,
n
o
.
3
,
p
p
.
7
3
4
-
7
4
1
,
2
0
0
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
27
-
36
36
[1
5
]
J.
M
.
M
o
ra
les
,
L
.
B
a
rin
g
o
,
A
.
J.
Co
n
e
jo
a
n
d
R.
M
ín
g
u
e
z
,
“
P
r
o
b
a
b
il
isti
c
p
o
w
e
r
F
lo
w
w
it
h
c
o
rre
late
d
w
in
d
so
u
rc
e
s,”
IET
Ge
n
e
ra
ti
o
n
T
ra
n
sm
issi
o
n
a
n
d
Distrib
u
ti
o
n
,
v
o
l.
4
,
n
o
.
5
,
p
p
.
6
4
1
-
6
5
1
,
2
0
1
0
.
[1
6
]
H.
P
.
Ho
n
g
,
“
A
n
e
ff
ici
e
n
t
p
o
in
t
e
stim
a
te
m
e
th
o
d
f
o
r
p
ro
b
a
b
il
ist
ic
a
n
a
ly
sis,”
Relia
b
il
it
y
E
n
g
i
n
e
e
rin
g
&
S
y
ste
m
S
a
fety
,
v
o
l
.
5
9
,
n
o
.
3
,
p
p
.
2
61
-
2
6
7
,
1
9
9
8
.
[1
7
]
M.
El
-
A
z
a
b
,
W
.
A
.
O
m
ra
n
,
S
.
F
.
M
e
k
h
a
m
e
r,
H.
E.
A
.
T
a
laa
t,
“
A
p
ro
b
a
b
i
li
stic
m
u
lt
i
-
o
b
jec
ti
v
e
a
p
p
ro
a
c
h
f
o
r
F
A
C
T
S
d
e
v
ice
s
a
ll
o
c
a
ti
o
n
w
it
h
d
if
f
e
re
n
t
lev
e
ls
o
f
w
in
d
p
e
n
e
tratio
n
u
n
d
e
r
u
n
c
e
rtain
ti
e
s
a
n
d
lo
a
d
c
o
rre
latio
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
t
e
r E
n
g
i
n
e
e
rin
g
(
IJ
ECE
),
v
o
l.
1
0
,
n
o
.
4
,
p
p
.
3
8
9
8
-
3
9
1
0
,
2
0
2
0
.
[1
8
]
M
.
A
.
Rio
s,
E.
G
.
G
u
a
m
a
,
“
S
y
ste
m
Co
n
g
e
stio
n
Crit
e
ria
f
o
r
In
terc
o
n
n
e
c
ti
o
n
o
f
W
P
P
th
r
o
u
g
h
V
S
C
-
HV
DC,”
IET
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
a
n
d
Di
strib
u
ti
o
n
,
v
o
l.
1
3
,
n
o
.
1
2
,
p
p
.
2
5
2
6
-
2
5
3
2
,
2
0
1
9
.
[1
9
]
A
lb
re
c
h
t,
P
a
u
l
F
.
,
e
t
a
l.
,
“
IEE
E
re
li
a
b
il
it
y
tes
t
s
y
ste
m
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
Ap
p
a
r
a
tu
s
a
n
d
S
y
ste
ms
,
v
o
l.
9
8
,
n
o
.
6
,
p
p
.
2
0
4
7
-
2
0
5
4
,
1
9
7
9
.
[2
0
]
Q.
Hu
a
n
g
,
X
.
Hu
a
n
g
,
J.
F
a
n
,
X
.
Zh
a
n
g
,
Y.
W
a
n
g
,
“
Re
li
a
b
il
it
y
a
n
d
e
c
o
n
o
m
y
a
ss
e
ss
m
e
n
t
o
f
o
ff
sh
o
re
w
in
d
f
a
r
m
s,”
T
h
e
J
o
u
r
n
a
l
o
f
En
g
in
e
e
rin
g
,
v
o
l
.
2
0
1
9
,
n
o
.
1
6
,
p
p
.
1
5
5
4
-
1
5
5
9
,
2
0
1
9
.
[2
1
]
A.
S.
A
.
Ba
d
a
w
i,
N.
F
.
Ha
sb
u
ll
a
h
,
S
.
Y
u
so
f
f
,
A
.
Ha
sh
a
m
,
M
.
E
lam
a
ss
ie,
“
P
ra
c
ti
c
a
l
e
lec
tri
c
a
l
e
n
e
rg
y
p
ro
d
u
c
t
io
n
t
o
so
lv
e
th
e
sh
o
r
tag
e
in
e
lec
tri
c
it
y
in
P
a
les
ti
n
e
a
n
d
p
a
y
b
a
c
k
p
e
rio
d
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
in
e
e
rin
g
(
IJ
ECE
),
v
o
l.
9
,
n
o
.
6
,
p
p
.
4
6
1
0
-
4
6
1
6
,
2
0
1
9
.
[2
2
]
G
.
Erd
e
m
ir,
A
.
T
.
Zen
g
in
,
T
.
C.
Ak
in
c
i,
“
S
h
o
rt
-
term
w
in
d
sp
e
e
d
f
o
re
c
a
stin
g
s
y
st
e
m
u
sin
g
d
e
e
p
le
a
rn
in
g
f
o
r
w
in
d
tu
rb
i
n
e
a
p
p
li
c
a
ti
o
n
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
in
e
e
rin
g
(
IJ
ECE
),
v
o
l.
1
0
,
n
o
.
6
,
p
p
.
5
7
7
9
-
5
7
8
4
,
2
0
2
0
.
[2
3
]
C.
L
.
T
.
Bo
rg
e
s,
J.
A.
S
.
Dia
s,
“
Re
p
re
se
n
tatio
n
o
f
W
in
d
a
n
d
L
o
a
d
Co
rre
lati
o
n
i
n
No
n
-
S
e
q
u
e
n
ti
a
l
M
o
n
te
Ca
rl
o
Re
li
a
b
il
it
y
Ev
a
lu
a
ti
o
n
,
”
Reli
a
b
il
it
y
a
n
d
Ri
sk
Eva
l
u
a
ti
o
n
o
f
W
in
d
In
t
e
g
ra
ted
P
o
we
r S
y
ste
ms
,
p
p
.
9
1
-
1
0
6
,
2
0
1
3
.
[2
4
]
A
.
M
.
L
e
it
e
d
a
S
il
v
a
,
L
.
A.
F
.
M
a
n
so
,
A
.
A
.
F
lav
io
,
M
.
A
.
d
a
Ro
sa
,
a
n
d
L
.
C.
Re
se
n
d
e
,
“
Co
m
p
o
site
Re
li
a
b
i
li
ty
A
s
se
ss
m
e
n
t
o
f
P
o
w
e
r
S
y
ste
m
s
with
L
a
rg
e
P
e
n
e
tr
a
ti
o
n
o
f
Re
n
e
wa
b
le
S
o
u
rc
e
s,”
Relia
b
il
it
y
a
n
d
Ri
s
k
Eva
lu
a
t
io
n
o
f
W
in
d
In
teg
ra
ted
Po
we
r
S
y
ste
ms
,
p
p
.
1
0
7
-
128
,
2
0
1
3
.
[2
5
]
R.
Bil
li
n
t
o
n
,
a
n
d
R.
N.
A
ll
a
n
,
“
Re
li
a
b
il
it
y
As
se
s
s
m
e
n
t
o
f
L
a
rg
e
El
e
c
tri
c
P
o
w
e
r
S
y
ste
m
s,”
Klu
we
r
Aca
d
e
mic
Pu
b
li
s
h
e
rs
,
1
9
9
8
.
[2
6
]
W
.
L
i,
“
P
ro
b
a
b
il
isti
c
T
ra
n
sm
issio
n
P
lan
n
i
n
g
,
”
IEE
E
Pre
ss
J
o
h
n
W
i
ley
&
S
o
n
s,
NJ
,
US
A,
2
0
1
1
.
[2
7
]
A.
S
.
D
a
lab
e
e
h
,
A
.
A
l
-
M
o
f
leh
,
A.
R.
A
lz
y
o
u
d
,
H.
T
.
Ay
m
a
n
,
“
Eco
n
o
c
m
ica
l
a
n
d
Re
li
a
b
le
Ex
p
a
n
sio
n
A
lt
e
rn
a
ti
v
e
o
f
Co
m
p
o
site
P
o
w
e
r
S
y
ste
m
u
n
d
e
r
Re
stru
c
tu
rin
g
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
t
e
r
En
g
i
n
e
e
rin
g
(
IJ
ECE
),
v
o
l
.
8
,
n
o
.
6
,
p
p
.
4
7
9
0
-
4
7
9
9
,
2
0
1
8
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
An
g
ie
C
a
ta
li
n
a
Ce
p
e
d
a
is
g
ra
d
u
a
ted
o
f
e
le
c
tri
c
a
l
e
n
g
in
e
e
rin
g
f
ro
m
Un
iv
e
rsid
a
d
d
e
lo
s
A
n
d
e
s
(2
0
2
0
)
a
t
Bo
g
o
tá,
Co
l
o
m
b
ia.
His
in
tere
st
f
ield
s
a
re
in
e
lec
tri
c
a
l
p
o
w
e
r
s
y
ste
m
s
a
n
d
tele
c
o
m
m
u
n
ica
ti
o
n
s sy
ste
m
s.
e
-
m
a
il
:
a
c
.
c
e
p
e
d
a
@u
n
ian
d
e
s.e
d
u
.
c
o
M
a
r
io
Alb
e
r
to
Rí
o
s
:
re
c
e
iv
e
d
a
d
e
g
re
e
in
e
le
c
tri
c
a
l
e
n
g
in
e
e
rin
g
i
n
1
9
9
1
a
n
d
a
M
.
S
c
.
De
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
in
1
9
9
2
,
b
o
t
h
f
ro
m
Un
iv
e
rsid
a
d
d
e
lo
s
A
n
d
e
s,
Bo
g
o
tá,
Co
lo
m
b
ia.
He
re
c
e
iv
e
d
a
P
h
.
D.
d
e
g
re
e
in
e
lec
tr
ica
l
e
n
g
in
e
e
rin
g
f
ro
m
INP
G
-
L
E
G
,
Gre
n
o
b
le,
F
ra
n
c
e
,
in
1
9
9
8
,
a
n
d
a
Do
c
to
ra
l
d
e
g
re
e
in
e
n
g
in
e
e
rin
g
f
ro
m
Un
iv
e
r
sid
a
d
d
e
lo
s
A
n
d
e
s,
in
1
9
9
8
.
He
w
o
rk
e
d
a
s
a
c
o
n
su
lt
a
n
t
e
n
g
in
e
e
r
i
n
C
o
n
C
o
l
(
n
o
w
W
S
P
),
Bo
g
o
tá,
Co
lo
m
b
ia,
d
u
rin
g
1
2
y
e
a
rs.
A
lso
,
h
e
w
a
s
a
Re
se
a
rc
h
A
ss
o
c
iat
e
a
t
th
e
Un
iv
e
rsity
o
f
M
a
n
c
h
e
ste
r
(
f
o
r
m
e
rl
y
,
U
M
IS
T
).
Cu
rre
n
tl
y
,
h
e
is
F
u
ll
P
r
o
f
e
ss
o
r
a
t
th
e
De
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
S
c
h
o
o
l
o
f
En
g
in
e
e
rin
g
,
Un
iv
e
rsid
a
d
d
e
lo
s A
n
d
e
s,
Bo
g
o
tá,
a
n
d
d
irec
to
r
o
f
th
e
P
o
w
e
r
a
n
d
En
e
rg
y
Re
s
e
a
rc
h
G
ro
u
p
o
f
th
is
u
n
iv
e
rsity
,
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