In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
5
3
8
~1
5
4
6
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1538-1546
1538
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Improved reliability asses
s
ment
of backup battery storage
integrated with power s
upply system
in a buil
d
ing
M
u
h
a
mma
d
Mu
rta
dha
O
thma
n
1
,
M
uha
ma
d
Amirul
N
a
i
m
Mo
hd
J
a
m
a
l
u
ddin,
F
a
i
sal Fa
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z
i
3
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Ismail
Musirin
4
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h
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mmad
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thm
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n
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1
,
2,
3,
4
F
acul
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of Elect
rical
En
g
ineerin
g,
U
n
i
vers
iti T
e
kno
lo
g
i
M
A
R
A
,
M
alay
s
i
a
5
Cen
t
re f
o
r
A
d
v
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P
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er and
En
e
rgy
Research an
d
D
epart
m
e
n
t
o
f
E
lectri
cal an
d
E
lect
ron
i
cs Eng
in
eering,
F
acu
lty
of
En
g
i
neerin
g, U
n
i
vers
i
ti
Putra
Malays
i
a
,
Malays
i
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Au
g
1
9
,
2
018
Re
vise
d F
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b 2,
201
9
Ac
ce
p
t
ed
M
ar 2
4
,
2
019
Th
is
p
aper
p
res
e
n
t
s
th
e
im
pro
v
ed
a
nal
y
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i
s
o
f
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eli
a
bili
ty
f
or
b
a
ttery
s
torage
us
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i
n
pow
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y
s
t
e
m.
T
h
e
r
eli
a
bi
lity
a
ss
essmen
t
of
t
his
p
a
per
i
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clu
d
es
t
h
e
eval
uat
i
on
o
f reli
abil
it
y of
t
he
s
ys
tem
co
m
pon
ents,
batt
ery mo
d
ule and
po
wer
elect
roni
c co
mp
on
ent
s
. Battery
st
o
rage is
con
s
id
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o
n
e
o
f
energy
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torage
and
energ
y
s
ource
t
h
at
c
omm
only
us
ed
i
n
p
o
we
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s
y
stem.
The
ev
alu
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of
t
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r
e
li
a
b
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it
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of
p
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e
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s
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te
ms
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ti
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s
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g
w
i
th
t
he
s
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a
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b
a
t
te
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s
i
s
perf
o
r
med
by
usi
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t
h
e
M
a
rko
v
c
hain
p
roces
s.
T
he
c
om
putatio
n
o
f
t
h
e
reli
abilit
y
i
s
co
ndu
cted
b
y
ref
e
rr
i
ng
t
o
t
he
g
en
er
ated
r
el
iab
i
l
ity
b
l
ock
begi
ns
f
r
o
m
p
ower
s
uppl
y
s
y
stem
.
E
v
e
r
y
part
o
f
th
e
syst
em
i
s
evalu
a
te
d
r
egard
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tw
o
s
p
ecif
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c
st
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t
es
t
hat
are
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n
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r
m
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l
o
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ode.
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u
s
i
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g
th
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a
rkov
m
e
th
od, th
e
sy
s
tem
un
avai
labili
ty
and
f
ail
u
re f
re
q
u
ency
can
b
e
co
mpu
t
e
d
.
K
eyw
ord
s
:
Ba
tt
e
r
y s
t
ora
g
e
Com
m
e
rc
i
a
l pow
er
supp
l
y
(CS
)
En
gine
ge
n
era
t
or
(
EG)
Mark
ov
cha
i
n
R
e
l
i
a
b
i
lit
y
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Mu
ham
m
a
d
M
urta
dha
O
t
h
ma
n,
Fa
cult
y
o
f
E
l
e
c
t
rica
l
En
gine
erin
g,
Un
iv
e
r
sit
i
Tekn
o
lo
gi
M
A
R
A,
4
045
0
Sh
ah
Ala
m,
S
el
a
n
go
r,
M
al
a
y
si
a
.
Em
ail:
ma
ma
t
505m
y
@
yah
o
o
.c
om
1.
I
N
TR
OD
U
C
TI
O
N
Mo
st
o
f
t
h
e
e
l
e
c
trica
l
s
ys
tem
of
a
b
u
ild
i
n
g
is
b
ec
o
m
i
n
g
more
a
d
vanc
e
i
n
its
ope
ra
ti
o
n
d
ue
t
o
i
t
s
depe
n
d
e
n
c
y
on
in
form
at
io
n
a
nd c
o
m
m
un
ica
tio
n tec
h
no
l
o
g
y
(
I
C
T)
t
h
at
h
a
s
i
n
c
re
a
s
ed
i
n
co
mi
ng
y
ea
rs.
Sy
s
t
em
fa
il
ure
s
c
a
u
se
d
b
y
a
s
i
n
g
l
e
m
a
jor
harm
o
ri
gina
t
e
d
fr
om
I
C
T
w
i
l
l
a
ls
o
i
n
s
t
i
g
a
t
e
to
a
m
as
sive
d
isa
s
ter
t
o
t
he
soc
i
et
y
a
nd
ec
onom
ic
o
f
a
c
o
u
n
t
ry
[
1-6].
A
n
e
lectr
i
c
a
l
com
p
o
n
e
n
t
op
e
r
ati
ng
ha
v
i
ng
t
he
c
riter
i
a
o
f
h
ig
h
relia
bi
l
ity
i
s
o
n
e
of
t
he
r
e
a
s
ons
t
ha
t
it
ne
e
d
s
t
o
b
e
pr
o
t
e
c
ted
e
s
p
ec
i
a
l
l
y
un
der
the
e
n
v
i
ro
nm
en
t
of
I
CT
ut
iliz
a
t
i
on.
H
e
n
ce
,
it
is
i
m
p
orta
nt
t
o
m
a
k
e
s
ure
tha
t
t
h
e
c
omm
u
ni
cat
io
n
s
b
ui
l
d
in
gs
a
n
d
d
at
a
ce
nt
ers
t
h
at
opera
te
I
CT e
q
u
i
p
me
n
t
nee
ds to be
s
tab
l
e,
s
u
p
p
lie
d b
y
goo
d
pow
e
r q
u
al
i
t
y and w
ith
ou
t
i
n
t
e
rr
uptio
ns fro
m the
elec
tr
ical
s
u
p
p
l
y
sys
t
em
.
Mo
st
o
f
t
h
e
b
u
i
l
d
i
ngs
m
ay
h
ave
insta
l
led
w
i
t
h
I
CT
t
ha
t
ha
ve
t
o
be
s
up
p
lie
d
by
th
e
pow
er
s
ourc
e
w
i
t
hou
t
i
n
t
e
rru
pt
i
on.
U
s
u
al
l
y
,
t
h
i
s
t
ype
o
f
b
u
i
l
di
n
g
i
s
o
p
er
ati
ng
w
i
t
h
b
ac
ku
p
p
o
w
e
r
so
ur
ces
suc
h
a
s
u
n
in
te
r
r
upta
b
le
pow
e
r
s
up
p
l
i
e
s
(U
P
S
)
.
The
r
efo
r
e,
a
bui
l
di
n
g
h
a
vi
ng
a
b
ac
kup
p
o
w
er
s
up
ply
sy
st
e
m
nee
d
s
a
go
o
d
p
lan
n
i
n
g
t
ha
t
m
u
st
b
e
ta
ke
n
i
n
to
c
on
side
rat
i
o
n
[7-
12].
T
h
is
c
a
n
b
e
ac
hie
v
e
d
w
i
t
h
the
rel
i
a
bi
l
i
t
y
assessm
ent
for
eve
r
y
e
l
ectr
i
c
a
l
c
omp
one
nt
o
f
ba
t
t
er
y
st
orage
,
i
n
v
erter
,
s
w
i
t
c
h,
c
om
m
e
rc
i
a
l
pow
e
r
s
up
p
l
y
an
d
eng
i
ne
g
ener
a
t
or.
H
e
nce
,
t
he
M
a
r
ko
v
m
ode
l
i
s
c
us
toma
rily
u
s
e
d
to
a
na
ly
z
e
t
he
r
el
i
ab
i
lit
y
of
a
p
ow
e
r
s
upp
ly
i
nt
e
g
r
a
te
d
w
ith
t
he
b
at
t
e
ry
s
t
o
rage
.
Th
is
m
e
t
h
o
d
is
w
ide
l
y
use
d
i
n
re
liab
i
li
ty
a
nal
y
s
i
s
of
r
ep
air
a
b
l
e
com
p
o
n
en
ts.
Re
li
a
b
i
l
i
t
y
ca
n
be
d
efi
n
ed
b
y
a
c
o
m
p
le
x
r
e
la
t
i
ons
h
i
p
of
d
es
i
gn,
e
n
v
ir
onme
n
t
,
t
es
t
e
q
uipm
ent,
a
nd
ma
int
e
na
nce
ski
l
l
s
am
o
n
g
s
t
ot
her
i
n
fl
ue
nt
i
a
l
fac
t
or
s
[13-
15].
T
her
e
a
re
nume
r
o
u
s
r
e
se
ar
ches
c
o
n
c
e
rn
in
g
w
ith
the
u
t
i
l
i
z
a
t
i
on
of
M
ark
ov
mo
de
l
for
ana
l
yz
ing
the
r
e
l
i
a
b
ili
ty
o
f
pow
er
s
y
s
tem
a
nd
i
t
s
com
p
o
n
e
n
t
s
[
16
-
18].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Improv
ed re
l
i
a
b
i
lity
a
s
se
ssme
n
t o
f
b
a
c
k
u
p
b
a
t
t
ery
stor
a
g
e
inte
gra
t
ed
… (M
uham
ma
d Mur
t
a
d
ha Ot
hma
n
)
1
539
Th
e
c
o
n
t
i
nuo
us-t
i
m
e
M
a
rkov
c
h
a
i
n
i
s
n
o
r
ma
l
l
y
u
sed
i
n
t
h
e
r
e
l
i
a
b
ility
assessment
of
batt
e
ry
s
to
rag
e
i
nteg
r
a
ted
wi
th
p
o
w
er
s
up
ply
sy
st
e
m
o
f
a
b
u
il
din
g
. R
el
i
a
bi
lity
p
ro
bl
ems
i
n
pow
er
sy
s
te
ms ar
e
u
sua
l
ly
o
c
c
u
r
r
e
d ba
se
d o
n
di
scr
e
te
i
n
s
y
st
em
a
nd
c
o
nti
n
uo
us
i
n
ti
m
e
.
Th
is
i
s
t
h
e
r
e
ason
t
ha
t
c
o
n
t
i
n
uo
us-
tim
e
Ma
r
k
o
v
c
ha
i
n
i
s
s
u
i
t
a
b
l
e
f
o
r
r
e
lia
bi
l
ity
a
nal
y
s
i
s
o
f
b
a
t
t
e
r
y
s
tor
a
ge
i
nte
g
r
a
te
d
w
i
t
h
p
ow
e
r
s
up
ply
.
E
l
e
c
t
ri
c
a
l
pa
r
t
s
lik
e
g
e
n
e
rat
o
r
,
r
e
c
t
i
f
i
e
r
,
i
nv
erte
r,
a
n
d
un
int
e
rru
pt
ab
l
e
p
o
w
er
s
up
ply
(
U
P
S
)
t
e
n
d
t
o
h
a
v
e
pr
o
b
lem
s
c
o
n
t
i
n
u
o
u
sly
in
i
t
s
t
ate
s
un
t
il
a
tr
a
n
sit
i
on
occ
u
r
s
w
h
i
ch
c
ha
n
g
e
th
e
pr
o
b
lem
d
i
s
c
r
e
t
e
ly
t
o
anot
h
e
r
st
at
e.
A
M
arko
v
c
h
ain
i
s
a
m
a
them
at
ica
l
s
ys
tem
inv
o
l
vi
ng
t
he
t
r
a
n
s
it
i
ons
f
r
o
m
o
n
e
sta
t
e
t
o
a
not
h
e
r
a
c
c
o
r
di
ng
t
o
c
e
rt
a
i
n
p
r
ob
ab
ili
st
i
c
r
u
l
e
s.
T
he
M
a
r
ko
v
cha
i
n
is
b
a
s
i
c
al
l
y
c
o
n
s
t
r
u
cte
d
b
ase
d
on
t
h
e
s
t
a
t
e
s
o
f
t
h
e
M
a
r
kov
mo
d
e
l
.
E
v
e
r
y
s
t
a
t
e
c
o
n
s
is
ts
o
f
fa
i
l
u
r
e
r
a
t
e
a
nd r
e
pair
r
ate
an
d
it
i
s
d
e
t
er
m
i
ne
d
b
y
ob
ser
v
a
t
i
o
n
in
a
s
pe
c
i
fic
ti
m
e
[
13-
1
5
]
.
The
r
e
a
r
e
tw
o
ty
pes
of
c
on
f
i
g
u
r
a
t
i
o
n
o
f
r
e
lia
bi
li
ty
w
hic
h
a
r
e
s
e
r
ies
a
nd
p
a
r
a
l
l
e
l
sy
st
em
s
.
F
o
r
s
e
r
i
e
s
s
y
st
e
m
s
,
i
t
on
ly
can
f
u
n
c
tio
n
pr
ope
r
l
y
if
a
ll
of
t
he
c
om
p
one
n
t
s
i
nvo
lve
d
f
u
n
c
t
i
on
pr
o
p
erl
y
.
In
c
o
n
tra
s
t
wit
h
t
he
p
ara
lle
l
s
y
stem
s,
ot
her
c
o
m
p
o
n
e
n
t
s
a
r
e
s
ti
l
l
o
p
e
r
a
ti
ng
d
ur
i
n
g
w
h
i
c
h
the
othe
r
c
o
m
po
ne
nt
i
s
fa
il
i
ng
to
o
pe
r
a
te.
I
n
o
t
h
er
w
or
ds,
the
wh
o
l
e
sys
t
e
m
w
il
l
n
o
t
op
e
r
ate
when
t
he
r
e
i
s
fa
i
l
ur
e
fo
r
all
o
f
t
h
e
c
o
m
pone
n
t
s.
B
l
o
ck
d
iagr
am
o
f
pow
e
r
sup
p
l
y
sys
t
e
m
f
or
A
C
fe
ed
in
g
a
s
s
how
n
in
F
i
g
ur
e
1.
F
i
gur
e
1.
B
l
o
c
k
d
i
a
gr
am
o
f
pow
e
r
s
upp
l
y
s
y
s
tem
for
A
C
f
e
e
di
n
g
An
uni
nt
erru
pt
ibl
e
p
o
w
e
r
s
up
pl
y
(UP
S
)
an
d
sta
ndb
y
g
e
n
e
r
a
to
rs
a
r
e
u
s
ua
ll
y
inte
gr
at
ed
w
i
t
h
th
e
pow
e
r
s
up
p
l
y
ins
t
al
le
d
in
a
b
ui
l
d
in
g
[
1
9-
2
2
]
.
I
n
d
esi
g
nin
g
a
n
d
pla
n
ni
ng
the
bac
k
up
p
o
w
e
r
s
up
pl
y
sys
t
em
,
i
t
ha
s
t
o
b
e
i
n
st
a
lle
d
wi
t
h
h
igh
l
y
cost-ef
f
ec
t
i
ve
i
n
v
es
tm
en
t.
U
P
S
syst
em
i
s
widely
u
se
d
to
m
ake
sure
t
he
power
qua
lit
y
a
n
d
s
u
s
t
a
i
na
ble
p
o
w
e
r
su
pp
l
i
e
d
t
o
th
e
elec
t
r
i
c
a
l
s
ys
t
e
m
o
f
a
bu
il
d
i
n
g
.
I
t
i
s
p
o
s
si
bl
e
t
o
e
qui
p
th
e
UP
S
w
i
t
h
l
on
g
ba
tte
r
y
b
ac
k-
u
p
tim
e
an
d
sm
al
l
i
n
i
t
s
s
izi
n
g.
U
P
S
s
ys
tem
s
w
it
h
a
l
o
n
g
er
l
a
s
ti
n
g
o
f
ba
t
t
er
y
ba
ck-
u
p
time
c
a
n
pr
o
v
i
de
b
o
t
h q
u
a
l
i
t
y
a
nd
r
e
li
a
b
l
e
p
ow
e
r
back
u
p
to t
h
e
e
l
ectr
i
c
a
l
sys
t
em
o
f a bu
ild
in
g [2
3-2
5
]. A new
me
t
h
od
fo
r
c
a
l
c
u
l
a
t
i
ng
t
h
e
un
av
ail
a
bil
i
t
y
U
s
y
s
a
nd
f
a
ilu
re
f
r
e
q
u
e
ncy
of
p
o
w
e
r
s
u
ppl
y
sy
st
e
m
w
i
t
h
ba
c
kup
st
or
age
ba
t
t
er
y
is
i
n
t
r
o
d
u
c
e
d
t
o
a
c
h
i
e
ve
a
p
r
e
c
i
se
r
esu
lt.
B
y
u
sing
t
h
e
s
a
m
e
po
wer
su
pp
ly
s
y
s
t
e
m
c
o
n
f
ig
u
r
at
io
n,
t
he
oper
a
t
i
o
n
o
f
t
h
e
sta
t
e
t
r
ans
iti
on
i
s
c
ha
n
g
ed
s
o
t
h
a
t
a
b
et
ter
c
a
lc
ula
t
i
on
ca
n
be
m
ade
.
I
n
c
o
n
t
r
a
st t
o
t
h
e
bas
i
c ap
pr
oa
c
h
,
the new
a
ppr
oac
h
ha
s
t
h
e
t
r
a
ns
i
ti
on
w
h
e
r
e
the
bac
k
u
p
b
at
t
e
r
y
stor
a
ge h
as
t
o
be
r
echa
r
ged
w
h
e
n
e
xce
e
d
in
g
th
e
ba
ck
u
p
t
i
m
e
be
f
o
r
e
c
o
n
ti
n
u
e
r
e
pa
ir
in
g
th
e
in
t
e
r
r
u
p
t
e
d
c
om
po
ne
nt
s.
O
n
t
h
e
ot
her
ha
n
d
,
t
h
e
new
m
e
t
h
o
d
g
ive
s
a
n
a
ccur
a
t
e
v
a
l
ue
f
or
t
he
c
alc
ula
t
io
n
of
t
he
u
na
vai
l
a
b
i
lit
y
U
s
ys
a
nd
f
a
ilur
e
f
r
e
que
n
c
y.
2.
RESEARCH METHOD
Th
is
s
e
c
t
i
o
n
w
il
l
e
x
p
l
a
i
n
o
n
t
he
calc
u
l
a
tio
n
of
c
o
n
tin
uo
us-t
ime
M
a
r
ko
v
chai
n
t
h
a
t
u
se
d
to
d
eterm
i
n
e
the
una
va
i
l
a
b
il
ity
o
f
a
p
o
w
e
r
sys
t
e
m
a
nd
a
l
s
o
t
he
r
el
i
a
bi
lit
y
a
ss
e
ssmen
t
of
b
a
t
t
e
ry
s
t
o
r
a
ge
o
p
e
rati
ng
c
o
n
d
it
ion
use
d
a
t
a
spec
ific
b
ac
k
u
p
ti
m
e
.
The
fol
l
o
w
in
g
s
u
bsec
ti
on
w
i
l
l
d
e
s
c
r
i
b
e
t
h
o
r
oug
hl
y
on
t
he
cal
c
u
la
t
i
on
o
f
Mar
k
ov
cha
i
n
r
e
qu
ir
e
d
f
or
r
e
l
i
a
b
ili
t
y
a
sse
ss
m
e
nt
o
f
ba
t
t
er
y
sto
r
a
ge
i
nt
e
g
r
a
ted
w
i
t
h
p
ow
e
r
s
upp
l
y
s
yste
m.
2
.
1
.
Pow
e
r
s
u
p
p
ly
sy
s
tem w
i
th
ba
ck
up
ba
t
t
ery
sto
r
a
g
e
I
n
t
h
i
s
sec
t
i
on,
t
he
e
va
l
u
a
tio
n
of
r
e
lia
bil
ity
f
or
a
pow
er
s
u
p
p
l
y
s
yste
m
is
i
ntr
o
d
u
c
e
d
b
y
a
p
p
l
y
i
n
g
t
he
Mar
k
ov
p
r
o
ce
ss
me
th
od
w
h
i
c
h
i
n
cl
u
d
es
t
h
e
r
elia
b
i
l
i
t
y
a
s
s
essm
ent
o
f
b
a
t
t
e
r
y
s
t
o
r
a
g
e
.
M
a
r
k
o
v
p
r
o
c
e
s
s
i
s
a
m
e
tho
d
t
ha
t
us
es
t
he
s
tate
t
r
a
ns
i
t
i
ons
f
or
f
a
i
l
u
r
e
s
f
o
r
ever
y
c
om
p
o
ne
n
t
i
n
v
o
l
ved
in
o
r
d
e
r
t
o
cr
e
a
te
a
M
ar
ko
v
d
i
ag
ra
m
a
n
d
a
se
t
o
f
p
rob
a
b
ilit
i
e
s
th
at
c
a
n
b
e
g
e
n
e
ra
t
e
d
fo
r
ev
er
y
s
t
a
t
e
tr
a
n
sit
i
on
t
h
e
r
e
l
i
a
b
i
lit
y
e
v
a
l
ua
t
i
on.
I
t
is
i
mpor
ta
nt
t
o
co
ns
i
d
e
r
t
h
e
b
ac
ku
p
tim
e
for
the
o
p
e
r
ati
on
o
f
b
a
t
te
r
y
s
tor
a
ge.
F
i
gur
e
2
s
h
o
w
s
the
co
nfi
g
u
r
a
t
i
o
n
o
f
p
o
w
e
r
s
up
ply
sy
st
e
m
w
i
t
h
b
ac
kup
b
a
t
t
e
ry
s
to
ra
g
e.
F
ro
m
th
e
co
nfi
g
u
r
a
t
i
o
n
,
f
a
i
l
u
re
m
od
e
f
o
r
e
v
er
y
c
o
m
p
o
n
e
nt
i
n
t
h
e
sys
t
e
m
i
s
class
i
f
i
e
d
a
nd
r
e
pr
esen
te
d
i
n
t
o
r
e
lia
b
i
l
i
t
y
b
l
o
c
k
s
s
h
o
w
n
i
n
F
i
gur
e
3.
F
or
t
he
CS/EG
b
l
ock,
i
t
re
presen
ts
t
h
e
c
omm
e
r
c
ial
p
o
w
e
r
su
p
p
l
y
p
ara
lle
l
w
it
h
e
m
e
r
gency
e
n
g
i
ne
g
e
n
e
r
at
or
.
The
n
,
bl
oc
k
A
,
B
a
nd
C
r
e
pr
e
s
en
t
as
t
he
U
P
S
c
om
pone
n
t
s
a
nd
t
h
e
fa
i
l
ur
e
s
t
ha
t
affec
t
eac
h
b
l
oc
k
ar
e
pr
ese
n
te
d
i
n
Ta
b
l
e
1.
B
y
r
e
fer
r
in
g
F
i
g
u
r
e
3
,
CS
/EG
an
d
bl
oc
k
A
,
a
nd
a
l
s
o
b
a
t
t
e
r
y
a
n
d
b
l
o
c
k
B
i
s
c
o
n
n
e
c
t
e
d
i
n
s
e
r
i
e
s
.
T
h
e
tw
o
br
anc
h
e
s
a
r
e
c
onnec
t
e
d
t
o
a
junct
i
on
a
n
d
i
s
s
er
ies
w
i
t
h
b
lo
c
k
C.
CS: C
o
m
m
e
r
cial
P
ower
S
upp
ly
EG: Engine-
g
e
n
er
ator se
t
S
W
:
S
w
i
t
c
hge
ar
UPS: Un
i
nter
ru
pt
a
b
le po
w
er su
pply
BATT
: Bat
ter
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
5
3
8
–
1
546
1
540
Ta
ble
1.
C
omp
one
n
t
s
f
o
r
e
ach
b
loc
k
o
f
pow
e
r
s
upp
ly
s
yst
e
m
w
i
t
h
bac
kup
b
atter
y
s
t
o
r
a
g
e
B
l
o
c
ks
M
a
i
n
F
a
ilure
M
od
e
CS / E
G
Outa
g
e
, S
t
a
r
t-up f
a
ilure
A
Thy
r
is
tor
(o
pe
n), MCCB, Filte
r
B
C
T
h
y
r
i
s
tor
(
s
hort
)
,
I
nve
r
t
e
r
MC
C
B
, Filt
e
r
,
Re
a
c
to
r
F
i
gur
e
2.
P
ow
er
s
upp
ly
s
yste
m
conf
ig
ur
at
i
o
n
with
b
ack
u
p
s
tora
ge
b
a
tter
y
F
i
gur
e
3.
Rel
i
a
bil
i
t
y
b
lo
ck
d
ia
gr
am
o
f
pow
er
sup
p
l
y
sys
t
e
m
w
it
h
ba
c
k
u
p
b
a
tter
y
s
tora
ge
2
.
2
.
R
e
l
i
a
bi
li
t
y
c
a
l
c
u
l
a
ti
o
n
f
o
r
t
h
e
p
o
w
er
s
u
p
pl
y
s
y
s
t
e
m
w
i
t
h
b
a
ck
up
ba
ttery
sto
rag
e
The
rel
i
ab
i
lit
y
calc
u
l
a
tio
n
fo
r
the
powe
r
s
upp
l
y
s
y
s
t
e
m
wit
h
b
a
c
k
u
p
b
a
t
t
e
r
y
s
t
o
r
a
g
e
i
s
c
o
m
p
r
i
s
e
d
w
i
t
h
t
he
t
r
a
ns
i
tio
n
o
f
f
a
i
l
u
r
e
f
or
e
ver
y
b
lo
ck
t
ha
t
fa
lls
u
nder
t
wo
c
ond
i
tio
ns
a
nd
t
hi
s
re
fe
rs
t
o
Fig
Err
or
!
Referen
c
e
so
u
r
ce no
t
fo
un
d.
ur
e 3.
The
f
ir
st
c
on
di
ti
on
is
t
h
e
tr
a
ns
it
ion
w
h
er
e the
fa
i
l
ur
e
o
c
c
u
rs at
bl
o
c
k a
but
ther
e
is
s
t
ill
p
o
wer
sup
p
l
i
e
d
from
t
h
e
b
ac
ku
p
ba
tter
y
s
t
o
ra
ge
v
i
a
b
l
o
c
k
B
s
h
o
w
n
i
n
F
i
g
Error
!
R
ef
ere
nc
e
sou
rce
n
ot
f
ou
nd
.
ur
e
3.
T
h
i
s
f
i
r
s
t
co
nd
i
t
i
on
is
r
epr
e
sen
t
ed
by
sta
t
e
tr
a
n
s
i
t
i
on
P2
s
ho
wn
i
n
Fig
Er
ror
!
Refe
re
nc
e
s
o
ur
ce
n
o
t
f
o
u
n
d
.
ur
e
4.
T
h
e
s
ec
on
d
t
r
ans
iti
o
n
i
s
w
h
er
e
the
f
a
i
l
ur
e
ha
ppe
ned
a
t
b
lo
ck
A
a
n
d
ba
tte
r
y
st
o
r
a
ge
e
xcee
ds
t
he
ba
c
ku
p
t
i
m
e
sh
o
w
n
in
F
i
g
Erro
r
!
R
efe
r
e
n
ce
sour
c
e
not
fou
nd.
ur
e
3.
This
sta
t
e
of
tr
a
n
sit
i
on
fa
lls
u
n
d
er
b
lo
c
k
P
3
show
n
i
n
F
ig
Error!
R
eferen
ce
s
o
u
r
ce
n
ot
f
ound.
ure
4.
F
or
t
hi
s
type
o
f
i
n
t
e
r
r
u
p
t
i
o
n
,
t
h
e
f
a
i
l
u
r
e
r
a
t
e
i
s
d
e
r
i
v
e
d
f
r
o
m
a
n
e
q
u
a
t
i
o
n
t
h
a
t
d
ep
end
s
o
n
t
h
e
b
a
tt
e
r
y
st
orag
e
b
acku
p
time
a
s
gi
ve
n
i
n
(
1)
.
P
r
i
o
r
t
o
t
he
a
f
o
r
e
me
ntio
ne
d
tw
o
c
ond
i
t
i
ons
,
th
e
s
t
a
t
e
t
r
a
n
s
i
t
i
o
n
P
1
r
e
p
r
e
s
e
n
t
s
a
s
t
h
e
r
e
i
s
n
o
in
ter
r
up
tio
n
o
f
p
o
w
er
s
u
p
p
l
y.
I
n
F
i
g
Erro
r
!
Referen
ce
so
u
r
ce
n
o
t
f
o
und.
ur
e
3,
t
he
t
r
a
n
s
iti
o
n
f
r
o
m
sta
t
e
P
3
toP
1
h
ap
pe
ned
w
h
en
b
loc
k
A
i
s
r
e
pa
ir
ed
w
i
t
ho
u
t
r
ec
har
g
i
n
g
the
b
at
t
e
ry
s
t
o
rag
e
t
h
a
t
ex
c
e
e
d
s
th
e
b
acku
p
t
i
m
e
as
s
ho
wn
i
n
Fi
g
Err
or!
Ref
ere
nc
e
sourc
e
n
ot
f
oun
d
.
ur
e
3.
I
n
F
i
g
Error
!
R
ef
ere
nc
e
sourc
e
n
ot
f
ou
nd
.
ur
e
4,
the
r
e
pair
r
a
t
e
of
μ
1
i
s
set
for
the
tra
n
si
t
i
o
n
f
rom
P
3
t
o
P
1
.
In
p
ar
tic
ula
r
,
t
h
e
tr
a
n
s
i
t
i
on
fr
om
P
2
t
o
P
3
i
s
s
e
t
t
o
be
α
1
a
nd
f
r
o
m
P
2
t
o
P
1
i
s
se
t
t
o
b
e
β
1
.
O
n
t
he
o
the
r
h
an
d,
t
he
o
per
a
tio
n
o
f
s
ta
te
t
r
a
ns
i
t
i
o
n
fr
om
P
6
to
P
7
i
s
re
l
a
ti
v
e
ly
s
i
m
il
ar
t
o
th
e
st
at
e
tra
n
sit
i
o
n
fro
m
P2
t
o
P3
s
ho
wn
in
F
i
g
E
r
r
o
r
!
R
ef
erenc
e
s
our
ce
not
found
.
ur
e
4.
T
he
o
nl
y
d
i
ffe
r
e
nc
e
i
s
t
ha
t
t
h
e
fa
il
ur
e
is
o
cc
ur
r
e
d
at
C
S
/
EG
b
lo
c
k
a
nd
t
h
e
r
e
i
s
st
ill
b
a
c
kup
s
upp
l
y
f
ro
m
ba
tte
r
y
s
t
o
r
a
ge
t
ha
t
f
l
ow
s
t
h
r
o
u
gh
bl
oc
k
B
sh
ow
n
i
n
F
ig
E
r
r
o
r
!
R
e
f
eren
ce
s
our
c
e
n
o
t
f
o
und.
ur
e
3.
I
n
Fi
g
Erro
r
!
Reference
so
urce
n
o
t
f
o
und.
ure
4,
t
h
e
t
r
a
n
s
i
t
i
o
n
fr
om
s
tat
e
P
6
t
o
P
7
is
h
a
ppe
ned
w
h
e
n
t
h
e
ope
r
a
ti
o
n
o
f
b
a
tt
e
r
y
i
s
e
xce
e
d
in
g
the
bac
kup
t
i
me
d
ur
i
ng
t
h
e
fa
il
u
r
e
o
f
a
t
C
S
/EG
bl
o
c
k
th
at
r
e
f
e
r
s
to
Fi
g
Err
or!
Ref
ere
nc
e
sou
r
c
e
n
ot
f
ound.
u
r
e
3
.
T
h
e
r
e
fo
re,
t
h
e
failu
r
e
rate
i
s
ref
e
r
r
ed
a
s
α
2
f
o
r
t
h
e
s
t
a
t
e
tr
a
n
smiss
i
on
f
r
o
m
P
6
t
o
P
7
,
a
nd
t
h
e
sta
t
e
tr
ans
i
t
i
on
f
r
o
m
P6
t
o
P
1
pr
e
s
en
t
e
d
b
y
β
2
.
I
n
F
ig
Error
!
R
ef
ere
nc
e
sou
rce
n
ot
f
ound.
ur
e
4,
t
he
t
r
a
ns
it
ion
f
r
o
m
sta
t
e
P
7
t
o
P
1
h
a
ppe
ne
d
w
h
e
n
C
S
/
EG
b
l
o
c
k
i
s
r
e
pa
ir
ed
w
it
hou
t
r
echa
r
gi
ng
t
h
e
bat
t
er
y
st
or
a
g
e
t
h
a
t
e
xc
ee
ds
t
he
b
a
c
k
u
p
t
i
m
e
as
show
n
in
F
ig
Err
or
!
Refe
re
nce
sou
r
ce
n
ot
f
o
un
d.
ur
e
3.
I
n
F
i
g
Err
or
!
Refe
ren
ce
s
ource
n
ot
f
ound
.
ur
e
4,
t
he
r
epa
i
r
r
a
te
o
f
μ
4
i
s
set
f
o
r
the
t
r
ans
iti
on
from
P7
t
o
P
1
.
T
h
e
r
e
f
ore,
t
he
f
ai
l
u
re
r
ate
fo
r
state
t
r
ans
iti
o
n
f
ro
m
P
2
t
o
P3
,
an
d
a
l
s
o
f
ro
m
P6
t
o
P7
c
a
n
b
e
c
o
mpu
t
e
d
by
u
s
i
ng
(
2
)
and
(
3
)
.
F
r
om
(
2)
a
nd
(
3
)
ar
e
de
r
i
ve
d
fr
om
(
1)
.
The
f
a
ilur
e
r
ate,
λ
f
or
al
l
th
e
s
t
a
t
e
t
r
an
si
tio
ns
i
s
gi
v
e
n
a
s
f
ro
m
the
ma
nua
l
da
t
a
.
The
re
pair
r
a
t
e
o
f
μ
a
nd
β
for
al
l
t
h
e
s
t
at
e
t
r
a
nsi
t
i
ons
a
r
e
c
alcu
la
te
d
by
usi
n
g
t
h
e
e
q
ua
tio
ns
whic
h
will
b
e
d
i
s
c
u
sse
d
in
S
e
c
ti
o
n
II.
C.
I
n
othe
r
si
tua
t
ion
whe
r
e
by
CS
/
E
G
and
b
l
oc
k
A
is
oper
a
t
i
ng,
w
hil
e
bl
oc
k
B
is
i
n
fa
ilur
e
,
he
n
c
e
t
h
e
three
-
p
h
ase
sys
t
e
m
i
s
s
til
l
r
e
c
e
i
v
in
g
t
h
e
ele
c
t
ri
c
sup
p
ly
f
ro
m
th
e
C
S
/
E
G.
T
h
i
s
c
a
n
be
r
e
f
e
r
r
e
d
t
o
F
i
g
ur
e
3.
T
her
e
f
o
r
e
,
the
sta
t
e
tr
a
n
si
tio
n
fr
om
P
1
t
o
P
4
s
how
s
the
fa
il
ur
e
o
f
b
l
o
c
k
B
a
nd
vice
-
v
er
sa
a
s
d
e
pi
c
t
e
d
i
n
F
i
gu
r
e
4
.
I
n
F
igur
e
3,
t
he
f
a
ilur
e
o
f
b
l
o
c
k
C
m
ay
c
a
u
se
t
o
a
com
p
le
te
i
n
t
er
rup
tion
o
f
e
l
e
c
tr
ica
l
s
u
p
p
l
y
to
t
he
t
hr
e
e
-
pha
se
s
ys
tem
.
T
he
f
a
i
l
u
r
e
o
f
blo
c
k
C
i
s
r
e
pr
e
s
en
ted
by
t
h
e
sta
t
e
t
r
ans
i
t
i
o
n
fr
om
P
1
t
o
P
5
s
ho
wn
in Figu
re
4
. By
re
p
a
irin
g blo
c
k C, th
e
CS/EG o
r
ba
c
k
up
ba
tte
ry
st
o
rage
wil
l su
p
p
ly
t
h
e
p
owe
r
to
t
he
t
hr
ee
-
p
h
a
se
s
ys
tem
dep
i
cte
d
i
n
F
i
gur
e
3.
H
enc
e
,
by
r
e
pa
i
r
i
n
g
t
he
b
l
o
ck
C
,
th
e
sta
t
e
tra
n
sit
i
on
fro
m
P5
to
P
1
is
i
ncur
r
e
d
and
it
c
a
n
be
obs
er
ved
i
n
F
igur
e
4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Improv
ed re
l
i
a
b
i
lity
a
s
se
ssme
n
t o
f
b
a
c
k
u
p
b
a
t
t
ery
stor
a
g
e
inte
gra
t
ed
… (M
uham
ma
d Mur
t
a
d
ha Ot
hma
n
)
1
541
F
i
gur
e
4.
M
ar
kov
cha
i
n
di
a
g
r
a
m
of
pow
e
r
s
up
p
l
y
s
y
st
e
m
w
it
h
bac
k
u
p
b
at
t
e
ry
s
t
o
rag
e
The
M
a
r
k
o
v
c
h
a
i
n
d
ia
gr
a
m
f
or
t
he
p
ow
er
s
up
p
l
y
s
y
s
t
e
m
w
ith
b
a
c
k
u
p
ba
t
t
e
r
y
st
or
a
g
e
g
i
ve
n
in
F
i
g
u
r
e
4
i
s
us
ed
t
o
de
r
i
ve
t
h
e
t
r
a
nsi
t
i
o
n
a
l
p
r
oba
bi
l
i
t
y
m
atr
i
x
give
n
i
n
(
5)
.
The
n
,
the
tr
a
n
s
i
t
i
ona
l
pr
o
b
a
b
i
l
i
t
y
m
a
tr
ix
i
s
use
d
t
o
c
a
lcu
l
a
t
e
t
h
e
pr
oba
b
ili
t
y
o
f
eve
r
y
sta
t
e.
∙
∙
(
1
)
∙
(
2
)
/
∙
/
/
(
3
)
(4
)
(5
)
Th
e
f
a
ilu
re
freq
u
e
n
c
y
fo
r
th
e
sy
stem
c
an
b
e
ref
e
r
r
ed
t
o
the
sta
te
t
r
a
ns
iti
on
to
a
t
o
t
a
l
f
a
ilur
e
t
hat
is
fro
m
P2
t
o
P3
,
P
1
to
P
5
,
an
d
P6
to
P7
.
2
.
3
.
Estima
tio
n
o
f rep
a
i
r ra
te,
μ
Ta
b
l
e
2
repr
esent
s
t
he
f
a
i
l
u
re
r
ate
λ
for
every
sta
t
e
t
r
ans
i
t
i
o
n
s
how
n
in
F
igur
e
4.
T
h
e
r
epa
i
r
r
a
te
f
o
r
sta
t
e tra
n
si
t
i
o
n
i
s es
ti
m
a
te
d ba
se
d on t
h
e m
ean tim
e t
o
re
p
a
i
r
(
M
T
T
R
)
g
i
v
e
n
i
n
e
qua
t
i
on (
6
)
.
MTT
R is
d
e
f
i
n
e
d
a
s
t
he
a
ve
r
a
ge
tim
e
neede
d
t
o
r
e
pa
i
r
a
n
y
c
ompo
ne
nt
s
tha
t
a
r
e
f
a
i
l
e
d
t
o
ope
r
a
te
a
nd
r
e
tur
n
b
a
c
k
t
o
n
o
r
m
al
ope
r
a
ti
n
g
c
on
d
i
t
i
on
s
[7]
.
ℎ
⁄
(
6
)
The
MTT
R
f
or
C
S
/
EG
i
s
ass
u
m
e
d
t
o
b
e
1
0
h
our
s
for
e
v
e
r
y
r
e
pa
i
r
c
o
n
d
it
io
n,
a
nd
f
or
b
loc
k
A
,
B
an
d
C
ar
e
as
sum
e
d
t
o
b
e
5
h
o
u
rs
f
or
e
very
r
e
p
ai
r
c
ond
it
i
on.
T
h
e
M
T
T
R
for
b
a
t
t
er
y
i
s
e
st
im
ated
t
o
be
2
h
o
u
rs
o
f
r
e
pair
c
on
di
ti
o
n
.
Ther
efor
e,
t
he
r
epair
r
a
te
f
or
e
a
c
h
bloc
k
c
a
n
b
e
ca
l
c
ula
t
e
d
by
us
in
g
t
h
e
fo
l
l
ow
in
g
eq
ua
t
i
o
n
s.
/
0
.
1
ℎ
⁄
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
5
3
8
–
1
546
1
542
,
,
0
.
2
ℎ
⁄
(
8
)
0
.
5
ℎ
⁄
(
9
)
Ta
ble
2.
F
a
i
l
u
r
e
r
ate
λ
for
eve
r
y state
trans
i
ti
on
Bl
o
c
k
s
F
a
i
l
u
r
e
r
at
e
λ
CS
/ E
G
2.
5
1
0
A
71
0
B
C
31
0
91
0
The
o
b
t
a
i
ne
d
r
e
pair
r
a
t
es
μ
a
n
d
failu
re
r
ates
λ
w
i
ll
b
e
u
se
d
in
t
he
s
t
a
te
t
r
a
ns
it
ion
ma
t
r
ix
o
f
Marko
v
ch
a
i
n
in
(5
)
t
o
ca
l
c
ul
at
e th
e
p
r
o
b
a
bi
l
iti
e
s
o
f ev
ery
st
at
e
.
2
.
4
.
Imp
r
o
v
e
d relia
bili
t
y
a
s
s
ess
m
en
t
o
f
p
o
w
er su
pply
sy
ste
m
wi
t
h ba
ck
u
p
b
a
ttery
s
t
o
ra
g
e
Th
is
s
ec
t
i
o
n
i
ll
ustr
ates
a
n
ew
a
pp
r
o
ach
u
se
d
to
d
es
i
gn
t
h
e
Mar
k
o
v
c
ha
i
n
d
ia
gr
am
t
ha
t
r
e
pr
e
s
e
n
t
s
t
h
e
c
h
an
ges
in
t
he
oper
a
tio
n
of
p
ow
er
s
up
pl
y
sy
stem
w
ith
b
ac
k
up
ba
t
ter
y
s
tor
a
ge.
The
r
efor
e,
c
han
g
es
o
f
M
a
r
k
o
v
c
h
ai
n
d
i
a
g
ra
m
from
F
igur
e
4
can
b
e
se
en
i
n
F
i
gur
e
6.
B
y
re
fer
r
i
ng
t
o
F
i
gur
e
4,
t
he
o
n
l
y
c
h
a
nges
m
a
d
e
a
r
e
r
e
fe
r
r
i
ng
t
o
t
he
s
ta
te
t
r
a
ns
i
t
i
o
n
fr
om
P
3
t
o
P
1,
a
n
d
a
l
s
o
fr
o
m
P7
t
o
P1.
T
h
is
m
ea
ns
t
ha
t
the
sta
t
e
tra
n
si
ti
o
n
i
s
c
h
an
ge
d
fr
om
P
3
to
P
2
an
d
a
l
so
f
r
o
m
P
7
t
o
P
6
s
how
n
in
F
i
gur
e
6.
I
n
F
i
g
u
r
e
6,
t
he
s
ta
t
e
t
r
a
nsiti
o
n
f
r
o
m
P
3
t
o
P2
r
es
emb
l
an
ce
d
u
r
i
n
g
t
h
e
f
a
i
l
u
r
e
of
b
lo
ck
A
a
n
d
b
a
t
t
ery
,
t
he
b
a
t
ter
y
i
s
gi
ve
n
e
n
o
u
gh
t
i
m
e
t
o
r
e
c
h
ar
g
e
a
n
d
the
n
i
t
i
s
c
o
n
n
ected
t
o
t
h
e
sy
st
e
m
onc
e
the
com
p
o
n
e
n
t
s
i
n
bl
ock
A
i
s
r
e
p
a
i
r
e
d
a
n
d
t
h
i
s
r
e
f
e
r
r
i
n
g
t
o
F
i
g
u
r
e
3
.
The
r
ef
or
e,
t
he
n
ew
s
ta
t
e
t
r
a
ns
it
i
o
n
be
tw
ee
n
P
2
a
nd
P
3
can
b
e
ob
se
r
v
ed
i
n
F
i
gur
e
5
an
d
F
i
gu
r
e
6
.
F
i
gur
e
5.
M
ar
k
ov
cha
i
n
f
o
r
th
e
new
st
a
t
e
tr
a
n
s
i
t
i
on
be
t
w
e
e
n
P
2
a
nd
P
3
B
y
r
ef
er
r
i
ng
t
o
t
he
M
a
r
ko
v
chai
n
d
i
a
g
r
a
m
show
n
i
n
F
igur
e
5,
t
he
s
to
c
h
a
s
ti
c
t
r
an
si
t
i
on
al
p
rob
a
bili
ty
m
a
tr
ix
f
or
t
he
n
ew
s
tate
t
r
a
n
s
i
t
i
on
be
t
w
e
e
n
P
2
a
nd
P
3
i
s
gi
ven
i
n
(
1
0
)
.
1
0
1
0
1
(
10)
The
new
sta
t
e
pr
o
b
a
b
ili
t
y
P
1,
P
2
and
P
3
g
i
v
e
n
i
n
(
1
1
)
,
(
12)
a
nd
(
1
3
)
are
d
eriv
ed
f
ro
m (
1
0
)
.
(
11)
(
12)
(
13)
F
r
om
(
14)
,
(
15)
a
nd
(
16)
a
r
e
de
r
i
v
e
d
d
ir
e
c
t
l
y
fr
om
t
he
M
ar
k
o
v
c
ha
in
d
i
a
g
r
am
g
ive
n
i
n
F
i
gur
e
5.
1
2
(
14)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Im
prove
d
re
li
a
b
i
l
ity a
ssessm
e
n
t
of
b
a
cku
p
b
a
ttery
st
ora
g
e
i
n
te
gr
a
t
e
d
… (
M
u
ham
m
a
d Mur
t
a
d
ha O
t
hm
a
n
)
1
543
2
1
3
(
1
5
)
3
2
(
1
6
)
S
o
lve
(
10)
t
o
de
term
i
n
e
t
h
e
bat
t
e
r
y
fa
il
ure
r
a
te,
λ
Batt
er
y
,
w
h
ic
h
depe
n
d
s
on
t
he
b
ac
ku
p
t
i
m
e
g
i
v
e
n
in (17).
F
rom
(17
)
is bas
i
ca
lly
o
rigi
na
t
e
d f
r
om (1).
∙
∙
(17)
F
i
gure
6.
A
n
e
w
Ma
r
kov d
i
a
g
ra
m
for
pow
er
sup
p
l
y
syste
m
w
ith
b
ac
kup
b
at
t
e
ry
st
o
ra
g
e
It
i
s
w
o
rt
h
to
m
e
n
t
i
o
n
t
ha
t
t
h
e
sta
t
e
t
r
ans
i
t
i
o
n
i
s
al
so
c
ha
nge
d
fr
om
P
7
to
P
6
s
h
ow
n
in
F
ig
ure
6.
I
n
Fi
g
u
r
e
6
,
t
he
s
t
a
t
e
t
ra
nsiti
on
f
ro
m
P7
t
o
P
6
s
ho
ws
d
u
r
in
g
t
h
e
f
a
i
lu
r
e
o
f
CS
/E
G
a
n
d
b
a
t
t
e
r
y
,
th
e
ba
t
t
e
r
y
is
g
i
v
e
n
en
oug
h
ti
me
t
o
rec
h
arge
a
nd
t
h
e
n
it
i
s
c
onn
e
c
t
e
d
b
ack
t
o
t
h
e
syst
em
o
n
c
e
th
e
C
S
/
E
G
i
s
r
e
p
ai
re
d
an
d
th
i
s
r
eferrin
g
t
o
F
i
gure
6.
The
s
t
oc
has
t
ic
t
rans
it
ion
a
l
proba
b
i
l
i
ty
m
a
t
r
i
x
f
o
r
the
for
t
h
e
ne
w
M
a
rk
o
v
c
ha
i
n
o
f
po
w
e
r
supp
ly
syste
m
w
it
h
ba
cku
p
b
a
tter
y
st
o
ra
ge is g
i
ve
n
i
n
(18).
/
/
/
/
1(
)
0
0
1(
)
0
0
0
0
01
0
0
0
0
00
1
0
0
0
00
0
1
0
0
00
0
0
1
(
)
00
0
0
0
1
AB
C
C
S
E
G
A
B
C
C
S
E
G
A
A
B
a
tte
ry
Bat
t
e
r
y
B
a
tte
ry
Batt
e
r
y
B
B
C
C
CS
E
G
C
S
EG
Bat
t
e
r
y
B
att
e
ry
B
at
te
ry
Bat
t
e
r
y
P
(
1
8
)
The
pro
b
ab
i
lit
y for e
v
ery
st
a
t
e
is used
t
o
ca
l
c
u
la
te t
he
risk
o
f
t
h
e sys
t
em
a
nd i
s
gi
v
e
n
in
(19) u
nt
i
l
(25).
/
/
/
(
1
9
)
(
2
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
153
8
– 1
546
1
544
(2
1
)
(2
2
)
(2
3
)
/
⁄
⁄
(
2
4
)
(
2
5
)
The
u
n
a
v
ai
la
bi
lit
y
o
f
t
he
t
hree
-phase
s
yste
m
,
U
sy
s
,
is
t
he
s
um
o
f
t
h
e
p
r
oba
b
i
l
itie
s
of
s
ta
te
f
ac
in
g
com
p
le
te
f
a
i
lu
re.
The
com
p
l
e
te
f
ai
l
u
re
i
s
ha
ppe
ne
d
w
h
e
n
t
her
e
i
s
n
o
p
ow
er
s
up
ply
b
e
c
a
use
o
f
t
h
e
b
at
ter
y
stor
age
exce
e
d
in
g
t
h
e
bac
k
u
p
t
im
e
d
u
r
i
ng
t
h
e
fai
l
ure
of
C
S
/
EG,
bl
oc
k
A
or
b
l
o
c
k
C
t
ha
t
re
fe
rs
t
o
F
i
g
u
r
e
3
.
F
o
r
this
s
it
ua
t
i
on,
t
he
U
sy
s
c
alcu
la
te
d
b
y
r
eferr
i
n
g
t
o
t
h
e
summ
ati
o
n
o
f
P
3,
P
5
and
P7
r
epr
e
s
ent
i
ng
as
a
com
p
le
te fa
i
l
u
r
e
f
or
t
he
three
-
pha
se
sys
t
e
m
give
n i
n
(
26).
3
5
7
(
2
6
)
The
fa
il
ure
fr
eque
nc
y
for
the
sys
t
em
c
a
n
b
e
referr
ed
t
o
t
h
e
st
a
t
e
t
ra
nsit
i
on
t
o
a
t
ota
l
f
a
i
l
u
re
t
ha
t
is
from
P
2 to P
3, P
1
t
o
P
5,
a
nd
P
6
to P
7
give
n i
n
(
27
)
.
1
2
6
(2
7
)
3.
RESULT
S
A
N
D
ANALY
S
IS
Th
is
s
ec
tio
n
w
i
l
l
d
i
s
cus
s
o
n
the
re
lia
bi
li
ty
a
sse
s
sm
e
n
t
ba
se
d
o
n
the
una
va
ila
b
i
lit
y
and
fa
i
l
ure
fre
que
nc
y
for
bo
t
h
o
f
t
h
e
bas
i
c
an
d
i
m
pro
v
e
d
M
ar
k
o
v
c
ha
i
n
o
f
po
wer
su
pp
l
y
s
yst
e
m
wi
th
t
h
e
b
ack
up
b
a
t
t
e
ry
stor
age.
T
he
p
r
oba
b
ili
ty
f
or
e
ac
h
sta
t
e
of
t
he
b
as
ic
M
ark
o
v
c
ha
i
n
a
n
d
t
h
e
n
e
w
M
a
r
k
o
v
c
h
a
i
n
o
f
p
o
w
e
r
s
u
p
p
l
y
w
ith
t
he back
u
p
b
a
t
tery
s
t
o
r
a
ge
a
n
d
t
he
c
a
l
c
u
la
te
d
va
l
u
e
i
s
t
ab
u
l
at
ed in
Ta
ble
3.
T
he
t
o
t
a
l
p
roba
b
ili
t
y
o
f bas
i
c
appr
oa
ch of p
o
w
e
r
supp
l
y
w
it
h the bac
k
up batter
y
sto
r
a
ge i
s obt
a
i
n
e
d i
n
a large
val
ue tha
t is
7
.
55
1
0
and
t
h
i
s
c
on
c
e
pt
i
s
i
n
co
rre
c
t
si
nc
e
th
e
v
a
lu
e
sh
oul
d
b
e
l
i
m
i
t
e
d
to
a
u
n
i
t
y
v
a
l
ue
.
There
f
ore
,
a
n
i
m
prove
d
ve
rs
ion
o
f
Mark
ov
cha
i
n for pow
e
r
sup
p
l
y w
i
th t
he
b
ac
ku
p
ba
tter
y
sto
ra
ge i
s
i
n
tro
d
u
c
e
d
a
nd i
s
sho
w
n
in F
i
gur
e
6
.
Tab
l
e
3.
P
roba
bil
i
t
y
for
e
ve
ry s
tate
o
f
ba
si
c
a
nd impr
o
v
e
d
Mar
k
ov
c
ha
in
f
or
pow
er
s
upp
ly
with
t
he backup b
at
ter
y
st
o
ra
ge
S
t
a
t
e
P
r
o
b
a
b
ilit
y of the
ba
s
i
c
met
ho
d
(p
.u
.)
Proba
bili
ty
o
f
the
i
m
prove
d
m
e
thod
(
p
.
u
.
)
P1
0.9
7
5
0
.
975
P2
7.5
4
5
10
1.
4
1
0
P3
5
8.194
1
0
P4
1.5
10
1.
5
1
0
P5
4.5
10
4.
5
1
0
P6
1
.
601
1
0
0
.
024
P7
1
0
8.194
1
0
B
y
u
s
i
n
g
(
2
6
)
t
h
a
t
r
e
f
e
r
s
t
o
t
h
e
b
a
s
i
c
a
p
p
r
o
a
c
h
o
f
p
o
w
e
r
s
u
p
p
l
y
w
it
h
t
h
e
b
acku
p
b
a
tter
y
s
tora
ge
,
the
c
a
l
c
ul
a
t
ed
u
n
a
v
a
i
l
a
b
ilit
y
fo
r
t
h
e
o
p
e
r
at
i
n
g
c
o
ndi
tio
n
o
f
t
h
r
ee
-
p
h
ase
sy
stem
i
s
15
a
n
d
t
h
i
s
i
s
r
e
f
e
r
r
i
n
g
t
o
t
h
e
bat
t
ery
bac
k
up
t
im
e
o
f
3
h
our
s.
B
y
usi
ng
(2
6)
t
ha
t
re
fer
s
t
o
th
e
i
m
pro
v
e
d
a
p
p
roac
h
of
p
ow
e
r
s
upp
l
y
w
ith
t
h
e
bac
k
u
p
bat
tery
st
o
r
a
ge,
the un
avai
la
b
i
l
ity for
t
he
ope
rat
i
n
g
co
ndi
ti
o
n
of
t
hree
-p
h
a
se
s
y
s
t
e
m
i
s
4.5
10
and
t
h
i
s
i
s al
so
r
eferri
n
g
t
o
th
e
b
att
e
ry
b
ac
kup
t
ime
o
f
3
h
ou
rs.
T
h
e
variation of
U
sy
s
at e
v
er
y t
i
m
e
in
t
e
r
va
l fo
r both
bas
i
c
an
d
im
pr
ove
d
a
ppr
oac
h
o
f
p
o
w
e
r
su
pp
l
y
w
it
h
the
bac
k
u
p
b
at
t
e
r
y
s
t
o
r
a
g
e
c
a
n
b
e
o
b
s
e
r
v
e
d
v
i
a
F
i
g
u
r
e
7
and
F
i
g
u
re
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Improv
ed re
l
i
a
b
i
lity
a
s
se
ssme
n
t o
f
b
a
c
k
u
p
b
a
t
t
ery
stor
a
g
e
inte
gra
t
ed
… (M
uham
ma
d Mur
t
a
d
ha Ot
hma
n
)
1
545
F
i
gur
e
7.
V
ar
i
a
tio
n
of
U
sy
s
a
t e
v
ery
tim
e
i
n
te
r
v
al f
or
the
ba
si
c
a
p
pr
o
a
c
h
o
f
p
o
w
e
r
supp
ly
w
ith
t
he
b
ac
k
u
p
bat
t
e
r
y
st
or
a
g
e
F
i
gur
e
8.
V
ar
ia
tio
n
of
U
sy
s
a
t
ever
y
t
i
m
e
i
nt
e
r
val
for
the
im
pr
ove
d
appr
oa
ch
o
f
po
w
e
r
suppl
y
w
i
t
h
t
he
ba
ck
u
p
ba
tte
ry
storage
The
r
e
s
u
l
t
s
si
gn
i
f
y
t
h
a
t
t
he
i
mpr
o
ve
d
ap
pr
oac
h
o
f
p
o
w
e
r
supp
l
y
w
i
t
h
t
h
e
b
a
c
k
u
p
b
a
t
t
e
r
y
s
t
o
r
a
g
e
pr
ovi
des
a
per
s
ua
sive
l
y
acc
ur
ate
r
e
su
l
t
o
f
U
sys
i
n
c
o
n
t
rast
wi
t
h
t
h
e
p
ecul
i
ari
t
i
e
s
la
rg
e
v
a
l
u
e
i
n
t
h
e
res
u
l
t
o
f
U
sy
s
ob
ta
ine
d
b
ase
d
on
the
b
a
si
c
a
ppr
oac
h
o
f
p
o
w
er
s
upp
l
y
w
i
t
h
t
he
b
a
c
k
u
p
b
a
t
te
r
y
s
t
o
r
a
ge.
The
fa
i
l
ur
e
fr
eque
nc
y
of
2
.
43
9
10
a
nd
8.77
9
10
f
or
t
he
b
asic
a
nd
impr
o
v
ed
c
o
n
ce
p
t
o
f
pow
er
s
up
pl
y
w
i
t
h
t
he
b
a
c
k
up
ba
tte
r
y
s
t
o
r
a
ge
a
r
e
obta
i
ne
d,
r
espe
ct
ive
l
y.
T
he
f
a
i
l
u
r
e
f
r
e
q
u
en
c
y
v
a
l
u
e
o
f
8
.
77
9
10
i
s
c
h
o
s
en
b
eca
u
s
e
i
t
is
o
bt
a
i
ned
bas
e
d
o
n
t
he
a
c
c
u
r
a
t
e
e
sti
m
a
t
i
o
n
of
t
ot
a
l
s
ta
te
p
r
o
ba
bi
lit
y
an
d
U
sys
d
e
t
er
mine
d
b
y
r
e
f
er
r
i
ng
to
t
h
e
im
pr
o
v
ed
a
p
p
r
o
a
c
h
o
f
p
ow
er
sup
p
l
y
w
ith
t
h
e
b
a
c
ku
p
ba
tte
r
y
s
t
o
r
a
ge
.
4.
CONCLUSION
Th
is
p
ape
r
ha
s
pr
e
sen
t
ed
a
n
i
m
pr
ove
d me
th
od
o
f
M
a
r
k
ov c
h
ai
n i
n
e
v
al
ua
ti
n
g
the
relia
b
i
l
i
t
y
of
p
o
we
r
sup
p
l
y
sys
t
em
w
ith
b
ac
ku
p
b
a
t
t
e
r
y
st
or
a
g
e.
T
he
u
na
vai
l
a
b
i
l
i
t
y
a
nd
t
h
e
f
a
i
l
u
re
f
re
qu
en
cy
h
av
e
b
e
en
e
v
a
lu
a
t
ed
by
im
pl
e
m
e
n
ti
ng
the
c
o
n
t
i
n
u
ous-
time
M
a
r
k
ov
c
h
a
i
n
f
o
r
b
o
t
h
b
a
s
ic
a
n
d
i
m
p
r
ove
d
a
p
pr
oac
h
o
f
pow
er
s
upp
l
y
w
i
t
h
t
he
b
a
c
k
u
p
b
at
t
e
r
y
s
tor
a
ge.
The
ca
lc
u
l
ate
d
u
na
va
ila
b
i
l
i
t
y
f
o
r
t
h
e
ne
w
Mar
k
ov
c
h
a
i
n
o
f
pow
e
r
s
upp
l
y
sys
t
em
w
ith
b
a
c
ku
p
bat
t
er
y
s
t
or
age
i
s
4.5
1
0
.
U
n
like
the
ba
sic
m
e
th
o
d
,
the
ne
w
me
thod
pr
ese
n
t
s
t
hat
it
is
i
mpr
ove
d
to
g
e
t
a
n
acc
ur
at
e
r
e
sul
t
f
or
t
he
una
va
ila
b
i
l
i
t
y
of
t
he
s
ys
tem
.
T
he
i
m
p
r
ove
d
m
e
tho
d
a
lso
g
i
v
e
s
a
be
tte
r
r
e
sul
t
o
f
f
a
i
l
ur
e
fr
e
q
u
e
ncy
w
i
th
c
o
m
pute
d
v
a
l
ue
o
f
8
.
77
9
10
.
T
h
e
c
h
a
n
g
e
s
o
f
t
h
e
o
p
e
r
a
t
i
n
g
t
r
an
si
tio
n
wh
e
r
e
th
e
b
a
t
t
e
r
y
has
to
b
e
c
h
arg
e
d
aft
e
r
ex
ce
edin
g
t
h
e
bac
k
up
t
i
m
e
r
e
s
u
lt
in
g
to
a
b
e
tte
r
rel
i
a
b
i
l
i
t
y
a
s
se
ssm
e
nt
o
f
t
h
e
pow
er
s
u
ppl
y
s
y
stem
w
ith
b
ac
ku
p
ba
tte
r
y
s
t
o
r
a
ge.
C
o
gn
iza
n
ce
t
ow
a
r
ds
t
he
i
m
por
t
a
nce
o
f
una
va
il
a
b
ili
t
y
a
nd
f
a
ilur
e
f
r
e
que
nc
y
f
o
r
t
h
e
pow
er
s
up
p
l
y
s
y
s
t
e
m
w
i
t
h
b
ac
ku
p
ba
tter
y
s
to
r
a
ge
w
il
l
r
e
nde
r
to
a
hi
g
h
r
elia
bi
lit
y
thre
e-phase
sy
s
tem
.
ACKNOWLEDGE
ME
N
T
S
Th
is
r
ese
a
r
c
h
w
a
s
su
pp
or
te
d
by
t
h
e
L
o
n
g
-
T
er
m
R
e
se
ar
ch
G
r
a
n
t
(
L
R
GS),
M
in
is
t
r
y
of
E
d
u
c
a
t
ion
Ma
la
ysia
f
or
t
he
p
ro
gr
am
tit
led
"Dec
arb
o
n
i
sa
t
i
o
n
o
f
Gr
i
d
w
ith
a
n
Optim
al
C
o
n
tr
ol
ler
and
Energ
y
Ma
na
gem
e
n
t
f
or
E
ne
r
gy
S
t
or
a
g
e
S
y
ste
m
i
n
M
i
cr
ogr
id
A
p
p
lica
t
i
ons"
w
it
h
pr
oje
c
t
c
o
d
e
6
00-
I
R
MI
/L
RG
S
5/3
(
001/
2
0
1
9
)
.
T
he
a
u
t
h
o
r
s
w
ou
ld
a
l
s
o
l
i
ke
t
o
a
c
k
n
o
w
l
e
dge
T
he
I
nst
i
t
u
t
e
o
f
Resea
rch
Mana
g
e
m
e
nt
&
I
nnova
tio
n
(
I
R
M
I
)
,
U
niver
s
i
t
i
T
e
k
n
o
l
o
g
i
M
A
R
A
(
U
iTM)
,
S
h
a
h
A
lam
,
S
e
l
an
g
o
r,
M
ala
y
s
i
a
for
the
fa
cil
i
t
i
es
pr
ovi
de
d
to
s
u
p
p
o
r
t
o
n
t
h
is
r
e
s
ear
ch.
REFERE
NC
E
S
[1]
T
.
T
s
u
m
u
ra,
K.
H
i
r
os
e,
a
nd
M
.
M
i
no,
“
Ap
plicatio
n
o
f
a
M
arko
v
P
r
ocess
t
o
E
va
l
u
ate
t
h
e
Rel
i
abilit
y
of
t
he
P
ower
S
u
pp
ly
S
ystems
U
ti
li
zin
g
S
t
o
rage
B
atteri
es,
”
35th
Int.
Tel
ecom
m
u
n
.
E
n
erg
y
Co
n
f
. ’S
m
art Po
wer E
f
fic, 2
01
3.
[2]
I.
A
.
Tø
nd
el,
J.
F
oro
s
,
S.
S
.
Ki
ls
kar,
P
.
H
o
k
s
tad,
a
n
d
M
.
G
.
J
a
at
un
,
"
I
n
t
erd
e
pend
enci
es
a
nd
r
eli
a
bilit
y
i
n
t
h
e
c
o
m
b
i
n
e
d
I
C
T
a
n
d
p
o
w
e
r
s
y
s
t
e
m
:
A
n
o
v
e
r
v
i
e
w
o
f
c
u
r
r
e
n
t
r
e
s
e
a
r
c
h
,
"
Ap
pl
ied
co
m
p
u
t
in
g
an
d
informatics,
v
ol.
1
4
,
n
o
.
1,
p
p.
1
7
-
27
,
20
18
.
[3]
S.
C
.
Mü
l
l
er,
H.
G
eo
rg,
J.
J
.
N
u
taro
,
E.
W
idl
,
Y
.
Deng
,
P
.
P
ale
n
s
k
y
,
M.
U
.
A
w
ais,
M
.
Ch
eni
n
e,
M
.
Küch
,
M
.
Sti
f
t
e
r,
a
nd
H
.
Li
n
,
"
Interf
aci
ng
power
s
y
s
t
em
a
nd
i
ct
s
imula
t
o
rs
:
Ch
all
e
ng
es,
stat
e-o
f
-t
he-art,
and
cas
e
stu
d
i
e
s,"
IE
EE
T
rans
acti
o
n
s
o
n S
m
art
Grid,
vo
l
.
9
,
n
o
.
1,
pp.
1
4
-
24
,
20
18
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
153
8
– 1
546
1
546
[4]
D.
S
ch
acht,
S
.
P
a
t
zack,
H
.
V
en
n
e
geert
s
,
S
.
K
ra
h
l
,
an
d
A
.
M
oser,
"
S
e
lect
io
n
of
r
elevant
f
a
ilu
re
m
o
d
e
s
a
nd
s
ys
tem
st
ates
f
or
t
he
e
valu
ati
on
o
f
r
e
l
ia
b
ility
i
n
d
i
s
t
ri
butio
n
grids
depen
d
i
n
g
on
I
CT,
"
C
IRE
D
W
orks
hop
201
6,
p
p
.
9
-4,
20
16
.
[5]
D.
S
ch
a
c
h
t
,
D.
L
eh
man
n
,
H.
V
en
nege
ert
s
,
S.
K
rah
l
,
an
d
A.
M
o
s
er,
"
Mo
del
l
ing
o
f
i
n
t
eractions
b
etw
een
p
o
w
er
sy
st
e
m
a
n
d
c
o
m
m
u
n
i
catio
n
syst
ems
f
o
r
t
h
e
eval
uati
on
o
f
reli
abil
it
y,
"
In
2
01
6
Po
wer Sys
t
em
s Com
put
a
tion
Con
f
eren
ce (
P
SCC)
, p
p
. 1-7
,
2
0
16
.
[6]
H.
L
ei,
and
C.
S
ing
h
,
"
D
evelo
p
i
n
g
a
bench
m
ark
t
e
st
s
y
s
te
m
fo
r
e
lectri
c
pow
e
r
gri
d
c
yber-physical
r
eliabi
lity
st
udies,
"
I
n
IEEE
2
0
1
6
I
n
ternat
ional conference
on
probabilist
i
c methods
appl
i
ed to power
syst
ems
(
P
MA
P
S
)
,
pp
.
1-5
,
2
016
.
[7]
T.
T
su
m
u
ra,
T
.
T
ak
eda,
a
n
d
K
.
Hiro
se,
“A
T
o
o
l
f
o
r
Calcu
l
ating
R
eli
a
bilit
y
of
P
o
w
e
r
S
u
p
p
l
y
fo
r
Inf
o
rm
a
t
io
n
an
d
Com
m
unicatio
n T
echno
lo
gy
S
y
s
tem
s
,
”
I
NTELE
C
’08
,
p
p
.
1
–6
,
2
0
08
.
[8]
P
.
P
al
ens
ky,
a
n
d
D
.
D
i
etri
ch,
"
D
em
and
s
i
de
m
an
ag
em
ent:
D
em
and
r
e
s
po
nse
,
i
n
t
e
l
l
i
g
e
n
t
e
ne
rg
y
sy
ste
m
s,
a
n
d
s
ma
rt
loads,"
I
EEE
Tran
s
act
ion
s
on
Indust
r
ial
In
f
o
rm
atics
,
v
o
l
.
7,
n
o
.
3
, p
p.
3
81
-3
88
,
20
11
.
[9]
H.
C
.
Gil
s
,
Y
.
S
ch
ol
z,
T
.
P
r
eg
g
e
r,
D
.
L.
d
e
Ten
a
,
and
D
.
H
eid
e
,
"
Integ
r
ated
m
o
d
ell
i
n
g
o
f
v
a
riabl
e
r
enewab
le
e
n
e
r
gy
-b
a
s
e
d
powe
r
sup
ply
in
E
u
r
o
p
e
,
"
En
e
r
gy
,
v
o
l.
12
3
,
pp
.
17
3
-18
8
,
2
01
7.
[10]
X.
L
u
o
,
J
.
W
an
g
,
M
.
Doo
n
er,
and
J.
C
larke,
"
Overv
i
ew
o
f
c
u
rrent
d
ev
elo
p
ment
i
n
el
ec
t
r
ical
e
nerg
y
s
t
o
r
age
tech
no
log
i
es
a
nd
t
h
e
a
pp
li
cati
on
po
tential
in
p
o
w
er
s
ys
te
m
o
p
er
at
i
o
n," App
lied
en
erg
y
, vo
l
. 1
37
,
p
p
. 5
11
-53
6
,
20
1
5
.
[11]
M
.
M
oh
am
m
a
di
, R
.
G
h
as
emp
o
u
r
, F
.
R
.
Ast
ar
aei
,
E
.
Ahm
adi
,
A.
Al
i
g
holi
a
n
,
an
d
A
. T
oo
psh
e
kan
,
"Op
t
i
m
al
pl
a
nn
i
n
g
o
f
r
e
n
e
w
a
b
l
e
e
n
e
r
g
y
r
e
s
o
u
r
c
e
f
o
r
a
r
e
s
i
d
e
n
t
i
a
l
h
o
u
s
e
c
o
n
s
i
d
e
r
i
n
g
econ
o
m
i
c
a
n
d
rel
i
ab
ility
c
rit
e
ria,"
International
Jou
r
n
a
l
o
f
El
ectri
cal
Po
wer
&
Ener
gy
S
y
st
ems
,
v
o
l
.
96
,
pp
.
2
6
1
-
2
7
3
,
2
01
8.
[12]
S
.
W
e
item
e
yer,
D
.
Klei
nhan
s
,
L.
S
i
e
mer,
a
nd
C.
A
gert
,
"Optim
al
com
b
i
n
atio
n
of
e
nergy
st
orages
f
or
p
ro
sp
ecti
v
e
po
wer
su
ppl
y
sy
st
ems
based
o
n
R
enew
able
E
n
e
rgy
S
o
urces,
"
J
o
u
rna
l
of
E
ne
rg
y
S
t
orag
e,
vol.
20
,
p
p
.
5
8
1
-
58
9
,
20
18
.
[13]
F
.
W
ayne,
“
P
h
i
los
o
p
h
y
o
f
E
ngineering
Reli
abili
t
y
,
”
pp
.
5
7
9
–58
3,
1
8
32.
[14]
S
.
R
ao
M
,
V
.
N.A
N
a
ik
an,
"Avai
l
ab
ility
m
odel
i
n
g
o
f
re
p
a
irab
le
s
y
ste
m
s
usin
g
Ma
rk
ov
s
yste
m
dy
n
a
mic
s
simulation
,
" Inte
rna
tional Journal
of Qua
lity
&
Reli
a
b
ili
t
y
Man
ag
emen
t
,
vo
l
.
3
2
,
no
.
5
,
p
p
. 5
17
-53
1
, 2
01
5.
[15]
W.
B
a
m
run
g
setth
a
po
ng
,
an
d
A.
P
on
gpu
ll
po
ns
ak,
“
P
aram
et
er
i
n
t
erva
l
esti
mat
i
on
of
s
ystem
re
liabi
li
t
y
f
or
r
e
p
airable
mu
l
t
is
t
a
te
s
e
r
ie
s
-
pa
r
a
l
l
e
l
sy
s
t
e
m
with
f
uzzy
dat
a,” Th
e S
c
ienti
fic W
o
rld
J
ourn
a
l,
v
o
l
.
2
0
1
4
,
20
14.
[16]
R
.
H
.
Z
a
i
n
i
,
M
.
M
.
O
t
h
m
a
n
,
I
.
M
u
s
i
r
i
n
,
A
.
M
o
h
a
m
e
d
,
a
n
d
A
.
H
u
s
s
a
in
.
"
D
etermina
ti
on
of
t
ransmiss
i
o
n
re
liabi
lit
y
m
a
rgin
c
on
si
de
ri
ng
uncert
a
in
tie
s
o
f
s
y
stem
o
perati
ng
c
on
dit
i
o
n
an
d
t
r
ansmissio
n
lin
e
out
age."
E
u
rop
e
an
Tran
sacti
o
n
s
o
n E
l
ect
rical
P
o
w
er,
vol.
21, no
.
1
, pp. 3
80
-39
7
,
2
011.
[17]
N.
A
.
S
a
lim,
M.
M
.
Othm
an,
M
.
S
.
S
e
rwan,
M
.
F
ot
uhi-Fi
r
uzaba
d
,
A
.
S
a
f
d
arian
,
a
nd
I
.
M
u
siri
n,
"
Det
e
rm
i
n
a
t
ion
o
f
avai
labl
e
trans
f
er
capabi
lity
w
it
h
i
m
p
l
i
cat
i
o
n
o
f
cascading
col
laps
e
un
cert
a
in
ty,
"
I
E
T
G
en
eration
,
T
ransmis
s
ion
&
Di
st
ribu
ti
on
,
v
o
l.
8
,
n
o
.
4
,
pp
.
7
0
5
-
71
5,
2
01
4.
[18]
M
.
M
.
Ot
h
m
an,
N.
A
b
d
R
ahm
a
n,
I
.
M
u
si
rin,
M
.
Fotu
hi
-F
iruzab
ad,
a
nd
A
.
Rajabi-G
hahn
avi
e
h,
"
A
h
e
u
r
is
ti
c
rank
in
g
app
r
oach
o
n
cap
acit
y
b
en
ef
it
m
a
r
g
i
n
d
e
termin
ation
u
s
i
ng
P
a
reto
-
bas
e
d
evo
l
u
tio
na
ry
p
rog
r
amm
i
ng
t
echn
i
qu
e,
"
T
h
e
Sc
ie
nt
ific
W
orld
Jou
rna
l
, vo
l
.
20
15
, 20
1
5
.
[19]
T.
T
su
mu
ra,
H.
M
urai
,
K.
H
irose,
a
nd
M
.
Y
a
ma
s
a
ki
,
“Devel
op
ment
of
a
C
a
l
c
u
l
a
ti
n
g
S
y
s
te
m
U
s
in
g
P
o
w
e
r
S
u
pp
ly
Reli
abilit
y
Fi
eld Dat
a
i
n
Jap
a
n,
”
10
th
I
n
t
.
Conf
.
Electr.
P
ower
Qu
a
l
.
Util
., 2
00
9.
[20]
A.
K.
S
huk
la,
K. S
ud
hakar,
a
nd
P
.
Bared
a
r,
"
A co
m
p
rehen
s
i
v
e
rev
iew on
d
es
ig
n
of
b
uil
d
i
n
g
integ
r
ated ph
o
t
ovo
lt
aic
sy
st
e
m
,
"
E
nerg
y
an
d
Bu
il
d
i
ngs
, v
ol
.
1
28,
p
p
.
9
9-1
10,
2
0
1
6
.
[21]
N
.
A
r
s
h
a
d
,
a
n
d
U
.
A
l
i
,
"
A
n
a
n
a
l
y
s
i
s
o
f
t
h
e
e
f
f
e
c
t
s
o
f
r
e
s
i
d
e
n
t
i
al
u
n
i
nt
erpret
able
p
o
w
er
s
up
pl
y
s
y
s
t
e
m
s
on
P
aki
s
t
a
n'
s
po
wer
s
ector,
"
E
nerg
y
f
o
r S
u
stainabl
e
Dev
e
lo
pment
,
v
o
l
.
36
,
p
p
.
1
6-2
1
,
2
01
7.
[22]
M
.
A
ami
r
,
K
.
A
.
Kalw
ar,
and
S
.
M
ek
hil
e
f,
"
Un
in
terrup
t
i
b
le
p
o
w
er
s
up
ply
(u
ps)
sy
ste
m
,"
R
e
n
e
w
a
b
le
a
n
d
S
u
s
t
a
i
n
a
bl
e En
ergy
R
evi
e
w
s
,
vol.
58,
pp.
1
395
-1410
,
2
0
1
6
.
[23]
Q.
H
an,
“Dat
a-teleco
m
P
o
wer
S
y
s
t
e
m
S
o
l
u
t
i
on
Bas
e
d
on
R
el
iab
i
lit
y
Anal
ysis,
”
2
9t
h
Int
.
T
el
e
c
o
m
m
un.
E
nerg
y
Con
f
.
(INT
E
LEC
’0
7),
p
p
.
9
1
7
–
9
22
,
2
007
.
[24]
M
.
A
ami
r
,
K
.
A
.
Kalw
ar,
and
S
.
M
ek
hil
e
f.
"
Un
in
terrup
t
i
b
le
p
o
w
er
s
up
ply
(u
ps)
sy
ste
m
."
R
e
n
e
w
a
b
le
a
n
d
S
u
s
t
a
i
n
a
bl
e En
ergy
R
evi
e
w
s
,
vol.
58,
pp.
1
395
-1410
,
2
0
1
6
.
[25]
X.
L
u
o
,
J
.
W
an
g
,
M
.
Doo
n
er,
and
J.
C
larke,
"
Overv
i
ew
o
f
c
u
rrent
d
ev
elo
p
ment
i
n
el
ec
t
r
ical
e
nerg
y
s
t
o
r
age
tech
no
log
i
es
a
nd
t
h
e
a
pp
li
cati
on
po
tential
in
p
o
w
er
s
ys
te
m
o
p
er
at
i
o
n," App
lied
en
erg
y
, vo
l
. 1
37
,
p
p
. 5
11
-53
6
,
20
1
5
.
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