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an
y
elec
tr
ical
p
o
w
er
s
y
s
te
m
ca
n
b
e
d
iv
id
ed
in
to
th
r
ee
p
r
in
cip
a
l
f
u
n
ct
io
n
al
zo
n
e
s
n
a
m
el
y
h
ie
r
ar
ch
ical
lev
el
(
1
)
,
h
ier
ar
ch
ical
le
v
el
(
2
)
,
an
d
,
h
i
er
ar
ch
ical
lev
el
(
3
)
as
s
h
o
w
n
in
Fi
g
u
r
e
1
[
1
]
.
I
n
elec
tr
ical
p
o
w
er
s
y
s
te
m
s
,
t
w
o
ap
p
r
o
ac
h
es
ar
e
u
s
ed
to
as
s
ess
th
e
s
y
s
te
m
r
el
iab
ilit
y
,
o
n
e
o
f
th
e
m
is
b
a
s
ed
o
n
t
h
e
co
m
p
o
n
en
t
s
h
i
s
to
r
ical
a
n
d
th
e
o
th
er
is
b
ased
o
n
p
r
ed
ictiv
e
ass
es
s
m
e
n
t [
2
]
.
Fig
u
r
e
1
.
E
lectr
ical
p
o
w
er
s
y
s
t
e
m
h
ier
ar
c
h
ical
le
v
els d
iag
r
a
m
I
n
th
e
p
ast
f
e
w
y
ea
r
s
,
r
esear
c
h
er
s
f
o
c
u
s
ed
o
n
p
r
o
b
ab
ilit
y
a
n
d
r
eliab
ilit
y
as
s
es
s
m
e
n
t
o
f
t
h
e
elec
tr
ical
p
o
w
er
s
y
s
te
m
i
n
ca
s
e
o
f
g
e
n
e
r
atio
n
,
tr
an
s
m
is
s
io
n
,
a
n
d
d
is
tr
ib
u
tio
n
b
y
u
s
in
g
d
if
f
er
en
t
tec
h
n
iq
u
es
to
ac
h
ie
v
e
th
e
ai
m
s
.
B
o
u
s
s
ah
o
u
a
a
n
d
E
l
m
ao
u
h
ab
[
3
]
,
p
r
esen
ted
a
n
ass
es
s
m
en
t
o
f
th
e
elec
tr
ical
p
o
w
er
tr
an
s
m
is
s
io
n
s
y
s
te
m
r
eliab
ili
t
y
b
y
u
s
i
n
g
b
lo
ck
d
iag
r
a
m
an
d
g
r
ap
h
th
eo
r
i
es
f
o
r
I
E
E
E
9
b
u
s
s
y
s
te
m
.
T
h
e
r
esu
lts
s
h
o
w
th
a
t,
th
e
e
f
f
ec
t o
f
t
h
e
c
lass
if
ica
tio
n
o
f
n
o
d
es a
cc
o
r
d
in
g
to
t
h
eir
r
el
iab
ilit
y
,
th
e
ef
f
ec
t
o
f
d
is
co
n
n
e
ctio
n
s
o
f
n
o
d
es a
n
d
tr
an
s
m
is
s
io
n
b
r
an
c
h
es
o
n
r
eli
ab
ilit
y
.
B
ab
u
et
a
l.
[
4
]
,
p
r
o
p
o
s
ed
th
e
r
eliab
ilit
y
ass
e
s
s
m
e
n
t
f
o
r
a
co
m
p
o
s
ite
g
en
er
atio
n
s
y
s
te
m
f
o
r
R
T
S_
3
_
b
u
s
,
R
T
S_
6
_
b
u
s
,
an
d
R
T
S
_
2
4
_
b
u
s
s
y
s
te
m
s
u
s
in
g
p
r
o
b
a
b
ilit
y
p
er
f
o
r
m
a
n
ce
in
d
ex
w
it
h
cr
itical
co
n
ti
n
g
e
n
c
ies.
T
h
e
r
esu
lts
s
h
o
w
th
e
e
f
f
e
ctiv
e
n
ess
o
f
t
h
is
tec
h
n
iq
u
e
to
id
en
tify
t
h
e
w
ea
k
p
o
in
ts
f
o
r
s
y
s
te
m
s
’
d
ev
elo
p
in
g
r
ein
f
o
r
ce
m
e
n
t
w
a
y
s
.
A
b
d
u
l
k
ar
i
m
et
a
l.
[5
]
,
u
s
ed
b
lo
ck
d
i
ag
r
a
m
tec
h
n
iq
u
e
to
ass
es
s
th
e
co
n
f
i
g
u
r
ati
o
n
o
f
m
i
cr
o
g
r
id
s
y
s
te
m
an
d
s
tu
d
ied
th
e
i
m
p
ac
t
o
f
r
en
e
w
ab
le
g
en
er
a
tio
n
’
s
co
m
p
o
n
e
n
t
s
o
n
s
y
s
te
m
r
eliab
ili
t
y
.
T
h
e
r
es
u
lts
s
h
o
w
t
h
at,
t
h
e
r
eliab
ilit
y
i
n
d
ices
d
ec
r
ea
s
ed
in
ca
s
e
o
f
u
s
i
n
g
d
iesel
g
en
er
ato
r
.
Kh
ar
e
et
a
l.
[
6
]
,
p
r
o
p
o
s
ed
th
e
r
eliab
ilit
y
ev
al
u
atio
n
f
o
r
h
y
b
r
id
r
en
e
w
ab
le
g
e
n
er
atio
n
s
y
s
t
e
m
u
s
i
n
g
f
au
lt
tr
ee
tech
n
iq
u
e.
S
h
alas
h
et
a
l.
[
7
]
,
ev
alu
a
ted
th
e
p
o
w
er
s
y
s
te
m
g
en
er
atio
n
i
n
d
ices
u
s
i
n
g
m
u
lt
i
ag
en
t
m
o
d
el
a
n
d
co
m
p
ar
ed
t
h
e
r
es
u
lts
w
it
h
t
h
at
r
esu
lted
b
y
t
h
e
an
a
l
y
t
ical
ap
p
r
o
ac
h
.
T
h
e
r
esu
lt
s
s
h
o
w
t
h
e
e
f
f
ec
t
iv
e
n
es
s
o
f
tech
n
iq
u
e
to
d
ec
id
e
i
n
cr
ea
s
i
n
g
o
r
d
ec
r
ea
s
in
g
ca
p
ac
it
y
a
n
d
lo
ad
s
.
A
d
e
f
ar
ati
a
n
d
B
an
s
al
[
8
]
,
f
o
cu
s
ed
o
n
th
e
ec
o
n
o
m
ic
s
id
e
an
d
en
v
ir
o
n
m
en
tal
b
en
e
f
its
o
f
s
y
s
te
m
r
elia
b
ilit
y
ass
e
s
s
m
e
n
t
w
it
h
r
en
e
wab
le
g
en
er
ato
r
s
.
T
h
e
r
esu
lt
s
s
h
o
w
t
h
e
ad
v
a
n
ta
g
es
o
f
u
s
in
g
t
h
e
g
r
ee
n
b
u
ild
i
n
g
s
an
d
r
en
e
w
ab
le
en
er
g
ies
i
n
m
icr
o
g
r
id
o
n
r
eliab
ilit
y
.
B
o
u
r
ez
g
an
d
Me
g
lo
u
li
[
9
]
,
u
s
ed
C
/C
++
to
cr
ea
te
d
is
j
o
in
t
s
u
m
o
f
p
r
o
d
u
ct
al
g
o
r
ith
m
f
o
r
e
v
alu
ati
n
g
th
e
p
o
w
er
d
is
tr
ib
u
tio
n
s
y
s
te
m
to
av
o
id
th
e
d
is
ad
v
an
ta
g
e
o
f
Mo
n
te
C
ar
l
o
tech
n
iq
u
e.
K
u
n
ai
f
i
an
d
R
e
in
d
er
s
[
1
0
]
,
p
r
o
p
o
s
ed
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I
n
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&
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R
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ilit
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3649
th
e
r
eliab
ilit
y
ev
al
u
atio
n
f
o
r
e
lectr
ic
s
u
p
p
l
y
I
n
d
o
n
esia
s
y
s
te
m
b
y
co
llecti
n
g
th
e
s
u
r
v
e
y
s
a
n
d
m
ea
s
u
r
e
m
en
t
th
e
elec
tr
ic
p
ar
am
eter
s
f
r
o
m
co
n
s
u
m
er
s
id
es.
T
h
e
r
eliab
ilit
y
ev
alu
atio
n
f
o
r
b
o
th
d
is
tr
ib
u
tio
n
s
y
s
te
m
w
h
ic
h
h
as
lo
w
v
o
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g
e
v
er
s
u
s
t
h
e
tr
a
n
s
m
is
s
io
n
s
y
s
te
m
w
h
ich
h
a
s
h
ig
h
v
o
ltag
e
p
r
esen
ted
i
n
[
1
1
]
,
[
1
2
]
.
A
l
m
u
h
a
m
a
in
i
an
d
Al
-
Sa
k
k
a
f
[
1
3
]
,
p
r
o
p
o
s
ed
th
e
r
eliab
ilit
y
ev
al
u
atio
n
o
f
d
i
s
tr
ib
u
tio
n
s
y
s
te
m
in
m
icr
o
g
r
i
d
w
it
h
o
u
t
i
n
s
tal
led
d
is
tr
ib
u
ted
g
en
er
ato
r
s
an
d
w
i
th
in
s
talled
d
is
tr
ib
u
ted
g
e
n
er
ato
r
s
in
clu
d
i
n
g
t
h
e
ca
lcu
lat
io
n
o
f
th
e
r
eliab
ilit
y
in
d
ices
o
f
t
h
e
s
y
s
te
m
.
T
h
e
r
esu
lt
s
s
h
o
w
th
e
ac
cu
r
ate
a
n
d
ef
f
ec
t
iv
e
n
es
s
o
f
u
s
ed
m
e
th
o
d
f
o
r
r
eliab
ilit
y
ev
alu
a
tio
n
w
it
h
v
o
ltag
e
v
io
lat
io
n
s
L
i
u
a
n
d
Sin
g
h
.
[
1
4
]
,
p
r
esen
ted
r
eliab
ilit
y
e
v
al
u
atio
n
f
o
r
co
m
p
o
s
ite
p
o
w
er
s
y
s
te
m
r
eliab
ilit
y
an
d
ta
k
e
n
i
n
to
ac
co
u
n
t
t
h
e
ef
f
ec
t
o
f
w
ea
t
h
er
.
T
h
e
DC
_
OP
F,
m
i
n
i
m
al
c
u
t
s
et,
a
n
d
Ma
r
k
o
v
p
r
o
ce
s
s
ar
e
u
s
ed
to
ca
lcu
late
t
h
e
s
y
s
te
m
r
eliab
ilit
y
i
n
d
ices
a
n
d
th
e
b
o
u
n
d
s
o
f
r
eliab
ilit
y
i
n
d
ices.
T
h
o
m
p
s
o
n
et
al
.
[
1
5
]
p
r
o
p
o
s
ed
r
eliab
ili
ty
e
v
alu
a
tio
n
a
n
d
co
s
t
o
f
HVD
C
tr
an
s
m
is
s
io
n
in
ter
co
n
n
ec
tio
n
f
ee
d
er
s
w
it
h
u
s
i
n
g
MM
C
co
n
v
er
ter
u
s
i
n
g
Mo
n
te
C
ar
lo
s
i
m
u
latio
n
m
e
th
o
d
.
R
e
n
et
a
l
.
[
1
6
]
,
p
r
o
p
o
s
ed
th
e
r
elia
b
ilit
y
e
v
al
u
atio
n
o
f
n
in
e
m
icr
o
g
r
id
s
y
s
te
m
ta
k
i
n
g
i
n
to
ac
co
u
n
t
th
e
i
n
s
u
f
f
icien
t tr
an
s
m
i
s
s
io
n
ca
p
ac
it
y
o
f
t
h
e
s
y
s
t
e
m
u
s
i
n
g
B
a
y
e
s
ia
n
n
et
w
o
r
k
b
ased
u
n
i
f
ied
m
o
d
eli
n
g
(
B
NB
UM
)
m
et
h
o
d
.
T
h
e
r
e
s
u
lt
s
s
h
o
w
t
h
e
i
m
p
o
r
tan
t
r
o
le
o
f
u
s
in
g
t
h
e
en
er
g
y
s
to
r
ag
e
a
n
d
en
er
g
y
d
is
p
atc
h
s
t
r
ateg
y
o
n
r
eliab
ili
t
y
ev
al
u
atio
n
.
R
a
g
h
u
w
an
s
h
i
a
n
d
A
r
y
a
[
1
7
]
u
s
ed
Ma
r
k
o
v
a
n
d
f
r
eq
u
en
c
y
d
u
r
atio
n
m
et
h
o
d
s
to
ass
es
s
t
h
e
r
eliab
ilit
y
in
d
ice
s
o
f
h
y
b
r
id
en
er
g
y
s
y
s
te
m
in
c
lu
d
i
n
g
d
ie
s
el,
P
V,
an
d
b
atter
y
.
P
h
a
m
et
a
l.
[
1
8
]
p
r
e
s
en
ted
th
e
r
eliab
ili
t
y
e
v
alu
a
ti
o
n
f
o
r
m
icr
o
g
r
id
s
y
s
te
m
w
it
h
m
u
ltip
le
b
atter
y
s
to
r
ag
e
u
n
d
er
v
ar
io
u
s
d
y
n
a
m
i
c
o
p
er
atio
n
ca
s
es
u
s
i
n
g
Ma
r
k
o
v
tech
n
iq
u
e.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
an
al
y
z
es
th
e
r
eliab
ilit
y
o
f
elec
tr
ical
p
o
w
er
s
y
s
te
m
g
e
n
er
atio
n
b
ased
o
n
th
e
f
ail
u
r
e
an
d
r
ep
air
r
ates
o
f
ea
ch
u
n
it
o
f
g
en
er
ato
r
s
.
T
h
er
e
ar
e
t
w
o
m
ai
n
ca
teg
o
r
ies
o
f
elec
tr
ical
s
y
s
te
m
r
eliab
ilit
y
as
s
ess
m
e
n
t
tec
h
n
iq
u
es,
o
n
e
o
f
t
h
e
m
is
s
i
m
u
lati
o
n
o
r
Mo
n
te
C
ar
lo
tech
n
iq
u
e
an
d
th
e
o
th
er
is
an
al
y
tical
m
o
d
el.
Si
m
u
latio
n
ap
p
r
o
a
ch
es
esti
m
ate
t
h
e
elec
tr
ical
in
d
icato
r
s
b
y
s
i
m
u
lati
n
g
ac
t
u
al
elec
tr
ica
l
s
y
s
te
m
an
d
r
a
n
d
o
m
b
e
h
av
io
r
o
f
t
h
e
s
y
s
te
m
[
1
9
]
.
An
al
y
tic
al
ap
p
r
o
ac
h
es
r
ep
r
esen
t
t
h
e
e
lectr
ical
s
y
s
te
m
b
y
m
at
h
e
m
a
tical
m
o
d
el
a
n
d
ass
e
s
s
t
h
e
in
d
icato
r
s
o
r
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eliab
ilit
y
f
r
o
m
t
h
is
m
o
d
el
b
y
u
s
i
n
g
m
a
t
h
e
m
a
tical
a
n
al
y
s
is
.
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h
er
e
ar
e
m
o
r
e
an
al
y
tical
tec
h
n
iq
u
e
s
u
s
ed
to
co
m
p
u
te
t
h
e
r
eliab
ilit
y
o
f
elec
tr
ical
p
o
w
er
s
y
s
te
m
s
u
c
h
as
b
lo
ck
d
iag
r
a
m
,
Ma
r
k
o
v
p
r
o
ce
s
s
,
f
au
lt
tr
ee
a
n
al
y
s
i
s
,
e
v
en
t
tr
ee
a
n
al
y
s
i
s
,
m
i
n
i
m
al
c
u
t
s
et,
m
i
n
i
m
al
tie
m
et
h
o
d
,
an
d
p
ath
tr
ac
in
g
m
e
th
o
d
[
2
0
]
.
T
h
is
p
ap
er
p
r
esen
ts
t
h
e
r
eliab
i
lit
y
a
s
s
e
s
s
m
e
n
t
o
f
g
e
n
er
atio
n
f
o
r
I
E
E
E
_
E
P
S_
2
4
_
b
u
s
s
y
s
te
m
u
s
i
n
g
a
n
ad
v
an
ce
d
Ma
r
k
o
v
p
r
o
ce
s
s
a
n
d
b
lo
ck
s
d
iag
r
a
m
tec
h
n
iq
u
es.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
lo
g
y
ac
h
ie
v
ed
th
e
r
eliab
ilit
y
e
v
alu
a
tio
n
u
s
i
n
g
th
e
b
est
tech
n
iq
u
e
f
o
r
p
r
o
b
a
b
ilit
ies
s
t
u
d
y
i
n
g
,
n
a
m
el
y
Ma
r
k
o
v
ch
ain
p
r
o
ce
s
s
.
A
l
s
o
ass
es
s
ed
th
e
r
eliab
ilit
y
i
n
d
ice
s
lo
s
s
o
f
lo
ad
p
r
o
b
a
b
ilit
y
(
L
OL
P
)
an
d
lo
s
s
o
f
lo
ad
ex
p
ec
ta
tio
n
(
L
O
L
E
)
.
T
h
e
Ma
r
k
o
v
p
r
o
ce
s
s
b
ased
o
n
t
h
e
tr
an
s
itio
n
b
et
w
ee
n
p
r
o
b
ab
ilit
y
s
tate
s
a
s
e
x
p
lain
ed
in
s
ec
tio
n
3
.
T
h
e
ch
alle
n
g
e
i
n
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
t
h
e
in
f
i
n
it
y
n
u
m
b
er
o
f
f
ail
u
r
es
p
r
o
b
ab
ilit
y
s
tates
d
u
e
to
th
e
lar
g
e
n
u
m
b
er
o
f
g
en
er
atio
n
u
n
it
s
.
T
h
e
m
e
th
o
d
o
v
er
co
m
e
to
th
e
ch
al
len
g
e
b
y
u
s
i
n
g
th
e
b
lo
ck
d
iag
r
a
m
tec
h
n
iq
u
e
to
r
ed
u
ce
th
e
n
u
m
b
er
o
f
ele
m
en
t
s
a
s
d
is
c
u
s
s
ed
i
n
s
ec
tio
n
2
.
T
h
e
p
r
o
p
o
s
ed
s
t
u
d
y
a
n
al
y
ze
s
th
e
r
esu
lt
s
an
d
ca
lcu
late
s
t
h
e
f
r
eq
u
en
c
y
,
m
ea
n
d
u
r
atio
n
o
f
f
ailu
r
e
s
tate
s
f
o
r
s
y
s
te
m
,
t
h
e
m
ax
i
m
u
m
a
n
d
m
i
n
i
m
u
m
f
r
eq
u
e
n
c
y
a
n
d
d
u
r
atio
n
o
f
f
ail
u
r
e
p
r
o
b
ab
ilit
y
s
tate.
T
h
e
p
r
o
b
a
b
ilit
y
o
f
g
en
er
atio
n
ca
p
ac
it
y
s
ta
te
w
h
ich
r
e
m
ain
ed
i
n
s
er
v
ice
an
d
k
ep
t
o
u
t
o
f
s
er
v
ice
f
o
r
ea
ch
p
r
o
b
ab
ilit
y
s
tate
o
f
f
ail
u
r
e,
s
y
s
te
m
r
eliab
i
lit
y
a
s
s
e
s
s
m
e
n
t,
a
n
d
s
y
s
te
m
r
e
liab
ilit
y
in
d
ice
s
a
r
e
d
is
cu
s
s
ed
in
s
ec
tio
n
4
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
B
lo
ck
dia
g
ra
m
T
h
e
b
lo
ck
d
iag
r
am
m
e
th
o
d
is
u
s
ed
to
ass
ess
t
h
e
to
tal
s
y
s
te
m
r
el
iab
ilit
y
a
n
d
an
al
y
ze
th
e
p
r
o
b
a
b
ilit
y
o
f
s
y
s
te
m
's
f
a
ilu
r
e
[
2
1
]
.
I
t
ca
n
b
e
ac
h
iev
ed
u
s
in
g
r
ep
r
esen
t
in
g
t
h
e
s
y
s
te
m
an
d
its
co
m
p
o
n
e
n
t
s
b
y
g
r
ap
h
ica
l
r
ep
r
esen
tatio
n
w
i
th
d
i
v
id
i
n
g
th
e
s
y
s
te
m
to
s
m
alle
s
t
g
r
o
u
p
s
.
T
h
e
in
ter
co
n
n
ec
ted
g
r
o
u
p
m
a
y
b
e
i
n
s
e
r
i
e
s
,
p
a
r
a
l
l
e
l
,
s
e
r
i
e
s
p
a
r
a
l
l
e
l
,
o
r
p
a
r
a
l
l
e
l
s
e
r
i
e
s
c
o
n
n
e
c
t
i
o
n
s
.
A
l
l
o
f
t
h
e
s
e
c
o
m
b
i
n
a
t
i
o
n
s
a
r
e
u
s
e
d
t
o
a
c
h
i
e
v
e
t
h
e
s
o
l
u
tio
n
.
2
.
1
.
1
.
Series c
o
m
bin
a
t
io
n
T
h
e
s
y
s
te
m
r
eliab
ilit
y
m
a
y
b
e
co
n
s
i
s
ti
n
g
o
f
i
n
ter
co
n
n
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ted
g
r
o
u
p
o
f
e
x
p
o
n
e
n
tial
f
u
n
c
tio
n
w
h
ic
h
i
s
ch
ar
ac
ter
ized
b
y
f
ail
u
r
e
r
ate.
T
h
e
f
ai
lu
r
e
o
f
a
n
y
co
m
p
o
n
e
n
t
ca
u
s
e
s
t
h
e
w
h
o
le
s
y
s
te
m
t
o
f
ail.
T
h
e
s
y
s
te
m
s
h
o
w
n
in
F
ig
u
r
e
2
co
n
s
is
ts
o
f
n
co
m
p
o
n
e
n
ts
i
n
s
er
ies co
n
n
ec
tio
n
.
ea
ch
co
m
p
o
n
e
n
t
h
as
f
ail
u
r
e
an
d
r
ep
air
r
ate.
C
1
C
2
C
3
C
n
-
1
C
n
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
a
m
co
n
s
i
s
ts
o
f
n
co
m
p
o
n
e
n
ts
co
n
n
ec
ted
in
s
er
ies
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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11
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5
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2
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T
h
e
s
y
s
te
m
r
eliab
ili
t
y
an
d
f
ai
l
u
r
e
r
ate
f
o
r
s
er
ies
co
m
p
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n
e
n
ts
ar
e
ca
lcu
lated
as
s
h
o
w
n
in
(
1
)
,
(
2
)
,
an
d
(
3
)
[
20
]
,
[
22
]
,
[
23
].
R
sys
(
t)
=
−
(
1
)
R
ser
=
∏
=
1
(
2
)
λ
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λ
i
=
1
(
3
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2
.
1
.
2
.
P
a
ra
llel c
o
m
bi
na
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T
h
e
s
y
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te
m
s
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w
n
i
n
Fi
g
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r
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3
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n
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ar
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n
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t
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ea
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co
m
p
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n
en
t
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as
f
ail
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r
e
an
d
r
ep
air
r
ates.
T
h
e
f
a
ilu
r
e
o
f
a
n
y
co
m
p
o
n
e
n
t
d
o
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ca
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s
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h
e
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h
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ail
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ca
u
s
es t
h
e
w
h
o
le
s
y
s
te
m
to
f
ai
l [
5
]
.
C
1
C
2
C
3
C
n
-
1
C
n
Fig
u
r
e
3
.
B
lo
ck
d
iag
r
a
m
co
n
s
i
s
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n
co
m
p
o
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n
ts
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in
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allel
T
h
e
s
y
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te
m
r
eliab
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n
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ailab
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in
(
4
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-
(
7
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[
5
]
.
R
par
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1
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n
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Q
p
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i
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5
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R
par
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6
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1
λ
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λ
1
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λ
2
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….
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[
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2
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λ
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3
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[
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λ
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4
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-
………….
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+
[
(
-
1
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n+
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n
n
1
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2
.
2
.
M
a
rk
o
v
pro
ce
s
s
T
h
e
an
al
y
tical
m
o
d
el
p
r
esen
t
s
clea
r
l
y
r
ep
r
esen
tatio
n
o
f
al
l
th
e
s
tates
o
f
a
s
y
s
te
m
an
d
also
th
e
tr
an
s
itio
n
b
et
w
ee
n
t
h
ese
s
tate
s
[
3
]
,
[
24
]
.
T
h
r
ee
s
tep
s
ar
e
r
eq
u
ir
ed
to
ac
h
iev
e
t
h
e
an
al
y
t
ical
Ma
r
k
o
v
m
o
d
el
w
h
ic
h
ar
e
n
a
m
ed
ze
r
o
o
n
e
m
a
tr
ix
co
n
s
tr
u
ctio
n
,
tr
an
s
itio
n
M
ar
k
o
v
m
atr
ix
,
a
n
d
s
o
lv
in
g
t
h
e
Ma
r
k
o
v
eq
u
atio
n
.
T
o
ca
lcu
late
th
e
p
r
o
b
ab
ilit
y
o
f
th
e
s
y
s
te
m
,
an
al
y
tica
l M
ar
k
o
v
m
o
d
el
m
u
s
t b
e
estab
lis
h
ed
in
th
r
ee
s
tep
s
.
2
.
2
.
1
.
Z
er
o
o
ne
M
a
rk
o
v
m
a
t
rix
Su
p
p
o
s
e
an
elec
tr
ical
s
y
s
te
m
h
as
t
h
r
e
e
g
e
n
er
ato
r
co
m
p
o
n
e
n
ts
G1
,
G2
,
an
d
G3
as
s
h
o
w
n
i
n
Fi
g
u
r
e
4
,
th
er
ef
o
r
e
t
h
er
e
w
i
ll
b
e
2
3
=
8
s
t
ates.
T
h
e
elec
tr
ical
co
m
p
o
n
e
n
t
s
tate
s
ar
e
O
n
an
d
O
f
f
o
r
0
a
n
d
1
,
r
esp
ec
tiv
e
l
y
.
T
h
e
ze
r
o
m
ea
n
s
n
o
c
h
an
g
e
i
n
th
e
ca
s
e
an
d
t
h
e
co
n
n
ec
t
io
n
is
O
n
.
T
h
e
o
n
e
m
ea
n
s
t
h
e
s
ta
te
ch
a
n
g
ed
a
n
d
th
e
co
n
n
ec
tio
n
is
O
f
f
.
T
h
e
s
tate
p
r
o
b
ab
ilit
ies
ar
e
li
s
ted
in
T
ab
le
1
,
ze
r
o
o
n
e
Ma
r
k
o
v
m
atr
i
x
in
f
er
r
ed
f
r
o
m
th
e
s
tat
e
p
r
o
b
a
b
ilit
ies
as
s
h
o
w
n
in
t
h
e
T
ab
le
1
.
Fro
m
th
e
tab
le,
it
is
n
o
ticed
th
at
th
e
t
h
r
ee
co
m
p
o
n
en
ts
ar
e
o
p
er
ates
in
ca
s
e
o
f
s
tate
1
,
f
ir
s
t
co
m
p
o
n
e
n
t
f
ails
a
n
d
o
th
er
co
m
p
o
n
e
n
t
s
o
p
er
ate
in
ca
s
e
o
f
s
tate
2
,
s
ec
o
n
d
co
m
p
o
n
e
n
t
f
ail
s
an
d
o
th
er
co
m
p
o
n
e
n
t
s
o
p
er
ate
in
ca
s
e
o
f
s
tate
3
,
f
ir
s
t
a
n
d
s
ec
o
n
d
co
m
p
o
n
en
t
s
f
ail
a
n
d
t
h
ir
d
o
n
e
o
p
er
ates
in
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
R
elia
b
ilit
y
a
s
s
ess
men
t fo
r
elec
tr
ica
l p
o
w
er g
en
era
tio
n
s
yst
em
b
a
s
ed
o
n
…
(
A
.
A
.
Ta
w
fiq
)
3651
ca
s
e
o
f
s
tate
4
,
t
h
ir
d
co
m
p
o
n
en
t
f
ail
s
an
d
o
t
h
er
co
m
p
o
n
en
ts
o
p
er
ate
in
ca
s
e
o
f
s
tate
5
,
f
ir
s
t
an
d
t
h
ir
d
co
m
p
o
n
e
n
t
s
f
ail
a
n
d
s
ec
o
n
d
o
n
e
o
p
er
ates
i
n
ca
s
e
o
f
s
tate
6
,
s
ec
o
n
d
an
d
th
ir
d
co
m
p
o
n
e
n
t
s
f
a
il
a
n
d
f
ir
s
t
o
n
e
o
p
er
ates
in
ca
s
e
o
f
s
tate
7
,
a
n
d
T
h
r
ee
co
m
p
o
n
e
n
ts
f
ai
l
i
n
ca
s
e
o
f
s
tate
8
.
Af
ter
s
tates
d
ete
r
m
in
a
tio
n
,
t
h
e
ze
r
o
o
n
e
m
atr
ix
h
av
e
co
n
s
tr
u
c
ted
f
r
o
m
t
h
e
lis
t
o
f
s
ta
tes
b
y
tr
an
s
it
io
n
o
n
l
y
f
r
o
m
O
n
s
tate
to
O
f
f
s
tate
f
o
r
ea
ch
ca
s
e.
T
h
e
d
im
e
n
s
io
n
s
o
f
ze
r
o
o
n
e
m
atr
ix
ar
e
eq
u
al
to
i a
n
d
j
w
h
ic
h
ar
e
eq
u
al
to
2
an
d
3
,
r
esp
ec
tiv
el
y
.
Fig
u
r
e
4
.
T
h
r
ee
g
en
er
ati
o
n
co
m
p
o
n
en
ts
s
y
s
te
m
T
ab
le
1
.
L
is
t o
f
s
tate
s
f
o
r
th
r
e
e
s
y
s
te
m
co
m
p
o
n
en
t
s
S
t
a
t
e
s
C
o
mp
.
(
1
)
C
o
mp
.
(
2
)
C
o
mp
.
(
3
)
D
e
scri
b
e
S
t
a
t
e
1
0
0
0
T
h
r
e
e
c
o
mp
o
n
e
n
t
s o
p
e
r
a
t
e
S
t
a
t
e
2
1
0
0
1
st
c
o
mp
.
f
a
i
l
u
r
e
a
n
d
o
t
h
e
r
c
o
mp
s
o
p
e
r
a
t
e
S
t
a
t
e
3
0
1
0
2
nd
c
o
mp
f
a
i
l
u
r
e
a
n
d
o
t
h
e
r
c
o
mp
s
o
p
e
r
a
t
e
S
t
a
t
e
4
1
1
0
1
st
a
n
d
2
nd
c
o
mp
s fa
i
l
u
r
e
a
n
d
3
rd
o
n
e
o
p
e
r
a
t
e
s
S
t
a
t
e
5
0
0
1
3
rd
c
o
mp
.
f
a
i
l
u
r
e
a
n
d
o
t
h
e
r
c
o
mp
s o
p
e
r
a
t
e
S
t
a
t
e
6
1
0
1
1
st
a
n
d
3
rd
c
o
mp
s
f
a
i
l
e
d
a
n
d
2
nd
o
n
e
o
p
e
r
a
t
e
s
S
t
a
t
e
7
0
1
1
2
nd
a
n
d
3
rd
c
o
m
p
s fa
i
l
e
d
a
n
d
1
st
o
n
e
o
p
e
r
a
t
es
S
t
a
t
e
8
1
1
1
T
h
r
e
e
c
o
mp
s fai
l
e
d
2
.
2
.
2
.
T
ra
ns
it
io
n M
a
rk
o
v
eq
ua
t
io
n
T
h
is
p
ar
t
ex
p
lai
n
s
t
h
e
tr
a
n
s
it
io
n
ca
s
e
f
r
o
m
s
tate
to
o
th
er
.
State
1
r
ep
r
esen
ts
t
h
e
o
n
c
ase
f
o
r
all
co
m
p
o
n
e
n
t
s
an
d
h
as
t
h
r
ee
tr
an
s
itio
n
s
b
y
λ
1
,
λ
2
,
an
d
λ
3
an
d
ea
ch
tr
an
s
i
tio
n
ca
s
e
ca
n
b
ac
k
t
o
p
r
ev
io
u
s
s
tate
b
y
μ
1
,
μ
2
,
an
d
μ
3
,
r
esp
ec
tiv
el
y
.
States
2
,
3
,
an
d
5
h
av
e
t
w
o
tr
a
n
s
it
io
n
s
b
y
λ
2
,
λ
3
,
λ
1
,
λ
3
,
λ
1
,
an
d
λ
2
r
esp
ec
tiv
el
y
an
d
ea
ch
tr
an
s
itio
n
ca
s
e
ca
n
b
ac
k
to
p
r
ev
io
u
s
s
tate
b
y
μ
2
,
μ
3
,
μ
1
,
μ
3
,
μ
1
,
an
d
μ
2
r
esp
ec
tiv
el
y
.
State
s
4
,
6
,
an
d
7
h
av
e
o
n
e
tr
an
s
itio
n
b
y
λ
3
,
λ
2
,
an
d
λ
1
,
r
e
s
p
ec
tiv
el
y
a
n
d
e
ac
h
tr
a
n
s
it
io
n
ca
s
e
ca
n
b
ac
k
t
o
p
r
ev
io
u
s
s
tate
b
y
μ
3
,
μ
2
,
an
d
μ
1
,
r
esp
ec
tiv
el
y
.
S
tate
8
r
ep
r
esen
ts
t
h
e
O
f
f
ca
s
e
f
o
r
all
co
m
p
o
n
e
n
t
s
an
d
h
as
n
’
t
an
y
tr
an
s
itio
n
.
T
h
e
tr
an
s
itio
n
m
a
tr
ix
ca
n
b
e
estab
lis
h
ed
b
y
s
tates tr
an
s
itio
n
as s
h
o
w
n
in
(
8
)
.
(
8
)
T
=
[
0
1
2
0
3
0
0
0
µ
1
0
0
2
0
3
0
0
µ
2
0
0
1
0
0
3
0
0
µ
2
µ
1
0
0
0
0
3
µ
3
0
0
0
0
1
2
0
0
µ
3
0
0
µ
1
0
0
2
0
0
µ
3
0
µ
2
0
0
1
0
µ
3
0
µ
3
0
µ
2
µ
1
0
]
Fro
m
t
h
e
tr
a
n
s
i
tio
n
m
atr
i
x
it
i
s
n
o
tice
d
th
a
t,
t
h
e
d
i
m
en
s
io
n
s
o
f
tr
a
n
s
i
tio
n
m
atr
i
x
ar
e
eq
u
al
to
i
a
n
d
j
(
b
o
th
i
an
d
j
eq
u
al
to
n
u
m
b
er
o
f
s
tates).
T
h
e
ch
an
g
es
in
s
tat
es
ar
e
r
ep
r
esen
ted
in
th
e
m
atr
i
x
b
y
en
ter
i
n
g
eit
h
er
th
e
f
ai
lu
r
e
o
r
r
ep
air
r
ate
w
h
ic
h
r
ep
r
esen
t
th
e
tr
a
n
s
it
io
n
f
r
o
m
s
tate
to
o
th
er
.
T
h
e
m
atr
ix
ca
n
b
e
d
iv
id
ed
in
to
th
r
ee
p
ar
ts
d
iag
o
n
al,
u
p
p
er
d
iag
o
n
al,
a
n
d
lo
w
er
d
iag
o
n
al.
A
ll
e
le
m
e
n
t
s
in
n
o
n
-
d
ia
g
o
n
al
p
ar
ts
(
w
h
en
i
i
s
n
o
t
eq
u
al
to
j
)
ar
e
r
ep
r
esen
ted
b
y
th
e
tr
an
s
itio
n
f
r
o
m
f
a
ilu
r
e
to
r
ep
air
r
ate,
v
ice
v
er
s
a,
a
n
d
ze
r
o
[
3
]
.
A
ll
ele
m
e
n
ts
in
d
iag
o
n
al
p
ar
t
(
w
h
e
n
i
is
eq
u
al
to
j
)
,
ar
e
eq
u
al
to
o
n
e
m
i
n
u
s
s
u
m
m
at
io
n
o
f
th
e
o
t
h
er
ele
m
e
n
ts
i
n
its
r
o
w
.
T
h
en
th
e
tr
an
s
itio
n
m
atr
i
x
ch
a
n
g
ed
as
s
h
o
w
n
in
(
9
)
[
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
.
5
,
Octo
b
e
r
2
0
2
1
:
3
6
4
7
-
3659
3652
(
9
)
T
=
[
−
(
1
+
2
+
3
)
1
2
0
3
0
0
0
µ
1
−
(
µ
1
+
2
+
3
)
0
2
0
3
0
0
µ
2
0
−
(
µ
2
+
1
+
3
)
1
0
0
3
0
0
µ
2
µ
1
−
(
µ
2
+
µ
1
+
3
)
0
0
0
3
µ
3
0
0
0
−
(
µ
3
+
1
+
2
)
1
2
0
0
µ
3
0
0
µ
1
−
(
µ
3
+
µ
1
+
2
)
0
2
0
0
0
0
µ
1
0
−
(
µ
3
+
µ
2
+
1
)
1
0
0
0
µ
3
0
µ
2
µ
1
−
(
µ
3
+
µ
2
+
µ
1
)
]
In
(
10
)
ex
p
r
ess
es th
e
Ma
r
k
o
v
eq
u
atio
n
[
25
].
[
]
[
]
=
[
0
]
(
1
0
)
T
r
an
s
p
o
s
e
th
e
m
at
r
ices a
r
e
r
eq
u
ir
ed
an
d
th
e
eq
u
at
io
n
ch
a
n
g
e
d
to
th
at
f
o
r
m
.
(
1
1
)
[
−
(
1
+
2
+
3
)
µ
1
µ
2
0
µ
3
0
0
0
1
−
(
µ
1
+
2
+
3
)
0
µ
2
0
µ
3
0
0
2
0
−
(
µ
2
+
1
+
3
)
µ
1
0
0
µ
3
0
0
2
1
−
(
µ
2
+
µ
1
+
3
)
0
0
0
µ
3
3
0
0
0
−
(
µ
3
+
1
+
2
)
µ
1
µ
2
0
0
3
0
0
1
−
(
µ
3
+
µ
1
+
2
)
0
µ
2
0
0
0
0
1
0
−
(
µ
3
+
µ
2
+
1
)
µ
1
0
0
0
3
0
2
1
−
(
µ
3
+
µ
2
+
µ
1
)
]
×
[
]
=
[
0
]
T
h
e
s
u
m
o
f
all
in
d
i
v
id
u
al
p
r
o
b
ab
ilit
ies
is
eq
u
al
o
n
e
as
s
h
o
w
n
in
(
12
)
as
Ma
r
k
o
v
th
eo
r
y
ass
u
m
p
tio
n
.
B
ased
o
n
th
at
ass
u
m
p
tio
n
,
In
(
11
)
m
u
s
t b
e
r
ep
lace
d
to
(
13
)
[
3
].
P
1
+P
2
+P
3
+P
4
+P
5
+P
6
+P
7
+P
8
=
1
(
1
2
)
[
1
1
1
1
1
1
1
1
1
−
(
µ
1
+
2
+
3
)
0
µ
2
0
µ
3
0
0
2
0
−
(
µ
2
+
1
+
3
)
µ
1
0
0
µ
3
0
0
2
1
−
(
µ
2
+
µ
1
+
3
)
0
0
0
µ
3
3
0
0
0
(
µ
3
+
1
+
2
)
µ
1
µ
2
0
0
3
0
0
1
−
(
µ
3
+
µ
1
+
2
)
0
µ
2
0
0
0
0
1
0
−
(
µ
3
+
µ
2
+
1
)
µ
1
0
0
0
3
0
2
1
−
(
µ
3
+
µ
2
+
µ
1
)
]
×
[
]
=
[
1
0
0
0
0
0
0
0
]
(
1
3
)
T
h
e
in
d
ep
en
d
en
t
p
r
o
b
ab
ilit
y
v
alu
es
P
1
,
P
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