TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5096 ~ 51
0
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.521
0
5096
Re
cei
v
ed
No
vem
ber 2
6
, 2013; Re
vi
sed
March 20, 20
14; Accepted
April 2, 2014
Transformer State Assessment Method Based on Fuzzy
and Evidence T
h
eories
Xie Jiangho
ng
1
, Wang Haipeng
1
, Nie Dexin
2
, Song
You
2
, Cai Wei
*
2
1
State Grid Shan
xi El
ectric Po
w
e
r C
o
mpa
n
y
,
T
a
i
y
u
an 03
00
01, Chi
na;
2
State Grid Electric Po
w
e
r Re
search
Institute
,
W
uhan 43
007
4, Chin
a)
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: cai
w
ei
@
w
h
u
.
edu.cn
A
b
st
r
a
ct
Accurate a
nd r
e
lia
bl
e assess
me
nt of pow
er
equi
p
m
e
n
t op
eratio
n state is
the pre
m
is
e a
nd b
a
sis
for ma
inte
nanc
e of pow
er sys
tem state. T
h
is
article
b
u
il
ds the transfor
m
er body
state as
sessment
mod
e
l
base
d
on fu
zzy and ev
ide
n
c
e
theori
e
s taki
ng 50
0kV oi
l-
i
m
mers
ed trans
former
as the
obj
ect of resea
r
ch.
T
he repres
ent
ative p
a
ra
mete
rs in pr
ev
entiv
e test are sel
e
ct
ed as state a
ssessment in
di
cators by maki
n
g
referenc
e to the factory valu
e
s
and thres
hol
d-crossin
g
val
u
es of w
h
ich the
indic
a
tor nor
mali
z
a
ti
on is carr
ie
d
out
to deter
mi
n
e
the de
grees
of
me
mb
ershi
p
of eac
h i
n
d
i
ca
tor relativ
e
to
d
i
fferent state
a
ssessment l
e
v
e
ls
usin
g fu
zz
y
ev
alu
a
tion
metho
d
. T
hese i
ndic
a
tors are
divi
d
ed i
n
to three
sub-ev
ide
n
ce
bod
ies, i.e. ga
s
dissolv
ed
in o
i
l
,
oilati
on test a
nd e
l
ectrica
l
te
st,
and infor
m
a
t
ion co
mbin
atio
n of these thr
e
e sub-
evid
enc
e
bod
ies is carri
ed out usi
ng e
v
ide
n
ce theory
to further
assess the oper
ati
on state
of transformer bo
dy. T
he
effectiveness
of this assess
me
nt mod
e
l a
ppli
ed
in st
ate
assess
me
nt o
f
transformer
body
is verifi
e
d
b
y
exa
m
p
l
e an
aly
s
is
of
th
e data
of
a 50
0kV
tra
n
sformer.
Th
i
s
a
sse
ssm
e
n
t
mo
d
e
l
ha
s cl
e
a
r
i
d
ea
s an
d do
esn’
t
nee
d too much
historica
l
data;
it provides
a n
e
w
metho
d
for transformer sta
t
e assess
ment.
Ke
y
w
ords
: po
w
e
r transforme
r
, fu
zz
y
ev
al
uat
ion,
evi
d
e
n
ce theory, state as
sessment
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Along with t
he co
ntinuo
u
s
imp
r
oveme
n
t of powe
r
transmissio
n and tran
sformatio
n
voltage g
r
ad
es
and
grid
cap
a
citie
s
, th
e safe an
d
stable op
eration of p
o
wer
system i
s
fa
cing
great
ch
allen
ges. A
s
the
core
equip
m
e
n
t of po
wer transmi
ssion
a
nd tra
n
sfo
r
m
a
tion sy
stem,
the
operation
stat
e of p
o
wer transfo
rme
r
di
rectly affe
ct
s t
he
safe
ope
ration level
of
the whole
po
wer
system. A
c
cu
rate
and
reli
a
b
le a
s
se
ssm
ent of o
p
e
r
ati
on
state of
p
o
we
r tr
an
sformer to
di
sco
v
er
the
potential hazards of
transformer
and reduce the
probability of
tr
ansformer f
aults i
s
helpf
ul to
improve the
safe operation
level of the whole gri
d
.
It can be kno
w
n from the tran
sform
e
r st
ate ev
aluatio
n indicato
rs given by literature [1]
that: the amount of information of power tran
sf
orm
e
r state is large and refle
c
ts the operati
on
state of transformer o
n
different levels.
Howeve
r, d
ue to the inaccura
cy of measure
m
ent and
imperfe
ction
of evaluatio
n
criteria,
the
r
e i
s
gre
a
t uncertainty o
f
the state asse
ssm
ent o
f
transfo
rme
r
.
And ba
sed
o
n
this, research of
tran
sformer state
a
s
se
ssm
ent me
thods
ha
s be
en
con
d
u
c
ted
by many
schol
a
r
s at h
o
me
a
nd a
b
ro
ad. B
a
yesia
n
n
e
twork [2-3] a
s
sessment
met
hod
take
s the hi
storical, cu
rrent
and fu
ture st
ates of tra
n
sf
orme
r into
co
mpre
hen
sive
con
s
id
eratio
n
to
determi
ne the comp
reh
e
n
s
ive state of transfo
rme
r
b
y
Bayesian n
e
twork. But this a
sse
ssm
ent
method n
eed
s a la
rge
a
m
ount of hi
storical
dat
a
as trai
ning
sample of Ba
yesian n
e
two
r
k.
Suppo
rt vect
or ma
chi
n
e
[4-6] a
sse
ssment m
e
th
od with
goo
d fitting and
gene
rali
zati
on
capabilities can map the highly
non-linear input and
output func
tions and
can well appropri
a
te
the mappi
ng
of transfo
rm
er op
eratio
n
state from
st
ate inform
ation. This m
e
thod al
so n
e
eds
certai
n samp
les for traini
ng and
excessively
harden
s the tre
a
tment of a
s
sessme
nt state
boun
dary. G
r
ey target th
e
o
ry [7] rates the
state
of transfo
rme
r
in
stand
ard
fault
free
mod
e
a
nd
use
s
the g
r
ey target contributio
n d
egre
e
a
s
th
e weig
ht of quantity of state. Fuzzy
comp
re
hen
si
ve evaluation
method co
nd
ucts fu
zzy
ev
aluation no
rm
alizatio
n of each a
s
se
ssm
ent
indicator
to
obtain
th
e membe
r
ship vector
an
d t
hen
co
ndu
ct
s
com
p
o
s
itional o
peration
of
membe
r
ship
vectors of all indicators to obtain
the co
mpre
hen
sive evaluation re
sult. In addition,
there a
r
e lite
r
atures
asse
ssi
ng
the
sta
t
e of transfo
rmer throug
h
matter-eleme
n
t theory [11
],
clou
d theo
ry [12], set pai
r a
nalysi
s
[13] a
nd core
vecto
r
spa
c
e [14]
method
s, etc.
The a
ppli
c
ation
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Tran
sfo
r
m
e
r State Asse
ssm
ent Method Bas
ed o
n
Fu
zzy an
d Evid
ence… (Xie
Jiangh
ong
)
5097
of these m
e
thods greatly
facilit
ates and devel
ops t
he
transform
e
r state as
sessment research,
and the
s
e me
thods al
so pl
ay an importa
nt role in actu
al appli
c
ation
s
.
Evidence the
o
ry [15-1
6
] is an imp
o
rt
ant unc
ertain
ty inference
method; it attache
s
importa
nce t
o
the
subj
ect
i
vity of evidence
e
s
tima
tio
n
a
s
well a
s
empha
si
ze
s t
he o
b
jectivity of
eviden
ce. It effectively co
mbine
s
the d
i
fferent
information thro
u
gh accu
mulat
i
on of eviden
ce
s
and continu
o
u
s shrin
k
a
g
e
of the set of assu
mptio
n
s an
d ha
s stron
g
de
ci
sion tre
a
tme
n
t
capability. Wi
th 500kV
oil-i
mmersed
transformer as t
he object of
research, thi
s
article
considers
the tran
sfo
r
m
e
r
state a
s
se
ssment a
s
a
multi-
attribute
de
cisio
n
-m
a
k
ing
problem
and
build
s t
he
transfo
rme
r
b
ody state
assessment
mod
e
l ba
sed
on
fuzzy and
evi
den
ce the
o
ri
es
acco
rdin
g
to
the sel
e
cte
d
tran
sform
e
r body
state
asse
ssment
paramete
r
s whi
c
h a
r
e
rep
r
e
s
entati
v
e
para
m
eters i
n
preventativ
e test a
nd a
r
e divided i
n
to thre
e sub
-
eviden
ce b
o
d
i
es a
c
co
rding
to
cha
r
a
c
t
e
ri
st
ic
s.
2. Selection of As
ses
sment Indica
tor
s
A relevant in
dustri
a
l
stand
ard
divides th
e tran
sformer into five part
s
, i.e. body,
bushing
shell, tap
p
ing
swit
ch, cooli
ng sy
stem, n
on-el
ec
t
r
ic
q
uantity prote
c
tion a
nd
co
ndu
cts the
st
ate
asse
ssm
ent resp
ectively. This a
r
ticle
specifi
c
ally
asse
sses the
st
ate of in
sul
a
tion of tran
sformer
body, and it can be a refe
rence for state
assessme
nt method
s of other pa
rts.
The followi
ng
prin
ciple
s
sh
all be followe
d by
the sele
ction of asse
ssment indi
cators: (1)
High
sen
s
itivity, i.e. the minor
ch
ang
e o
f
equipm
ent
state
shall
be
able
to
cau
s
e
the sig
n
ificant
cha
nge of qu
antity of state; (2)
Hi
gh reli
ability, i.e. th
e cha
nge
of asse
ssm
ent
i
ndicator shall
be
able to
a
c
curately refle
c
t t
he
cha
nge
of
equi
pment
state; (3) Pra
c
ticability, i.e. the a
s
sessm
ent
indicators sh
all be conv
enient for t
e
sting; (4)
Variou
s a
ssessment in
di
cators
shall
be
indep
ende
nt
of ea
ch
othe
r a
nd
refle
c
t
the fe
atur
e
s
of tra
n
sfo
r
m
e
r from
different a
s
pe
cts
as
much
a
s
po
ssible. And
ba
sed
on thi
s
, the qu
antities
of
part
states
of gas
dissolv
ed in oil, oil
a
tion
test an
d
ele
c
trical
test
of t
r
an
sform
e
r b
ody a
r
e
sel
e
cted
as the
asse
ssm
ent i
ndicators i
n
t
h
is
article. As
sh
own in Ta
ble
1:
Table 1 T
r
an
sform
e
r Body
St
ate Assessment Indicato
rs
Transform
er Bod
y
State
Gas dissolved in
oil
Total h
y
d
r
ocarbo
n content
H
y
dr
ogen conten
t
Acety
l
en
e conten
t
Oilation test
O
il dielectr
ic los
s
Oil breakdo
w
n
v
o
ltage
Moistur
e
in oil
Furfu
r
al
Electrical test
Direct current
resistance unbalance rate
Winding dielectric loss
Polarization index
Iron core g
r
oundi
ng current
3. Indicator
Quan
tiza
tion
and State Di
v
i
sion
3.1. Asse
ss
ment Indicator Normaliza
t
ion
Powe
r tran
sf
orme
r body i
s
a very co
m
p
licat
e
d
syst
em. Variou
s
asse
ssm
ent i
ndicators
reflect
the
o
peratio
n
stat
e of tran
sfo
r
mer fr
o
m
d
i
fferent
side
s and
differe
nt asse
ssme
n
t
indicators h
a
v
e different u
n
it mea
s
ures. Before
the asse
ssm
ent of
tran
sform
e
r bo
dy state
by
comp
re
hen
si
ve use of these a
s
sessm
ent indica
to
rs, norm
a
lizati
on of assessment indicators
shall be
con
d
u
cted. In this article, the normali
za
tio
n
of assessme
nt indicato
rs i
s
co
ndu
cted
by
use
of relativ
e
crackin
g
de
gree
s. As fo
r
the asse
ssm
ent indi
cators of whi
c
h the
indicator valu
es
are the small
e
r the better,
su
ch a
s
cont
ent of hydr
og
en in oil, the cal
c
ulatio
n of relative cra
c
king
degree
s is ca
rrie
d
out usi
n
g formula (1):
0
0
01
10
1
0
1
r
r
nr
r
r
xx
xx
x
xx
x
xx
xx
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5096 – 51
03
5098
1
0
10
01
0
1
0
r
r
nr
r
r
xx
xx
x
xx
x
xx
xx
(
2
)
As for th
e a
s
se
ssm
ent in
d
i
cators
of whi
c
h th
e indi
cat
o
r valu
es are
the la
rge
r
th
e better,
su
ch a
s
oil breakdo
wn voltage, t
he cal
c
ulation of rel
a
tive cra
c
kin
g
deg
ree
s
is
carrie
d out u
s
ing
formula (2).
In formula
s
(1) and
(2),
x
r
is the actu
al measured val
ue of asse
ssment indicato
r
e
r
,
x
nr
is
the normali
ze
d value,
x
0
and
x
1
are no
rmalize
d
thre
shold value
s
.
x
1
is dete
r
min
ed by prevent
ive
test pro
c
e
dure, and the ex
pre
ssi
on of a
c
tual me
asure value of asse
ssm
ent
indi
cator
beyon
d the
stipulate
d
value sh
all aro
u
se the
attention.
x
1
is t
he facto
r
y value of a
s
se
ssment indi
cator.
Acco
rdi
ng to the tran
sform
e
r a
sse
ssme
nt guidelin
es
and field surv
ey data, the thre
shol
d valu
es
of various a
s
se
ssm
ent indi
cators of 500
kV
tran
sform
e
r body a
r
e shown in Tabl
e 2.
Table 2. No
rmalize
d
Thre
shol
d Value
s
of State Asse
ssment Indicators
Assessment Indi
cator
x
0
x
1
Total h
y
d
r
ocarbo
n content (uL/L
)
50
150
H
y
dr
ogen conten
t (uL/L)
30
150
Acety
l
en
e conten
t (uL/L)
0
5
Oil dielectric loss (%)
0
2
Oil breakdo
w
n
v
o
ltage (kV)
70
50
Moisture in oil (mg/L)
0
15
Furfu
r
al (mg/L
)
0
4
Direct current
resistance unbalance rate (
%
)
0
2
Winding dielectric loss ((%)
0
0.6
Polarization index
2
1.5
Iron core g
r
oundi
ng current
(A)
0
0.1
3.2. State Gr
ading
The tra
n
sfo
r
mer
state is gene
rally di
vided in
to fo
ur stat
e grad
es: no
rmal
state S1,
attention
state S2, a
bno
rmal
state S3
and
seri
ou
s
state S4.
No
rmal
state m
e
ans that: vari
ous
asse
ssm
ent i
ndicators of tran
sform
e
r a
r
e sta
b
le
an
d
within the
warnin
g value
s
and attentio
n
values
stipula
t
ed by the proce
dure, the transfo
rm
e
r
can ope
rate n
o
rmally; atten
t
ion state me
ans
that: the cha
nging
tren
ds of on
e o
r
more
a
s
sessment indi
cat
o
rs devel
op
approa
chin
g
the
stand
ard
limi
t
values but
haven’t
exceede
d the
st
anda
rd li
mit
values, th
e t
r
an
sform
e
r can
contin
ue the
operation a
n
d
the monito
ring
sha
ll
be
enha
nce
d
; a
bnormal
state mean
s that
: a
certai
n a
s
se
ssment i
ndi
cat
o
r h
a
s
relativ
e
ly larg
e cha
nge a
nd h
a
s
excee
ded
or
slightly excee
ded
the sta
nda
rd
limit value, th
e op
eratio
n
shall b
e
m
onitored
an
d
rep
a
ir
sh
all be
sche
dule
d
to
be
carrie
d out a
s
app
ro
priate
; serio
u
s
stat
e mean
s that
: an importa
nt asse
ssm
e
n
t indicato
r h
a
s
seri
ou
sly exceede
d the
st
anda
rd li
mit
value, an
d p
o
we
r-off rep
a
i
r shall
be
sche
dule
d
to
be
carrie
d out as soon a
s
po
ssible.
4. Transform
e
r Body
State Ass
essme
n
t Model Ap
ply
i
ng Fuzz
y
and Ev
idence Theorie
s
Acco
rdi
ng to the asse
ssm
ent indicato
r
sele
ct
ion met
hod in Sectio
n 1, the asse
ssment
indicators of tran
sform
e
r
b
ody are
divid
ed into t
he
qu
antities of p
a
rt states
of th
ree sub-evide
n
ce
bodie
s
, i.e.: gas di
ssolved i
n
oil (sub-eviden
ce bo
dy 1), oilation test
(su
b
-evid
e
n
c
e body 2) a
n
d
electri
c
al
test
(sub-eviden
ce body
3). E
a
ch
su
b-
evid
ence bo
dy co
nsi
s
ts of
sev
e
ral
asse
ssm
e
n
t
indicators (Ta
b
le 1
)
. The
worki
ng
step
s
of tr
an
sform
e
r bo
dy state
as
se
ssm
ent model ba
sed
on
fuzzy an
d eviden
ce theo
ri
es are: 1) Ob
tain the
actu
al values of variou
s a
s
sessment indi
cat
o
rs
and
co
ndu
ct
the n
o
rm
ali
z
ation,
determine the
de
gree
of m
e
mbershi
p
of
each a
s
se
ssment
indicator to th
e state of tra
n
sformer
usi
n
g fuzzy
theory; 2) Dete
rmi
ne the d
egre
e
of memb
ership
of each sub-eviden
ce bod
y to
t
he state of transformer; 3) Cond
uct the evide
n
ce infe
ren
c
e of
each sub
-
evi
den
ce b
ody
usin
g evide
n
c
e the
o
ry
to
obtain the
a
s
se
ssm
ent
sta
t
e of tran
sformer
body. The det
ailed working
pro
c
e
ss of a
s
se
ssm
ent mo
del is sho
w
n i
n
Figure 1.
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TELKOM
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Tran
sfo
r
m
e
r State Asse
ssm
ent Method Bas
ed o
n
Fu
zzy an
d Evid
ence… (Xie
Jiangh
ong
)
5099
Figure 1. Tra
n
sformer Bo
d
y
State Assessment Mo
del
4.1. Degre
e
of Member
s
h
ip of Ass
e
s
s
ment Indica
tor
This a
r
ticle
determi
ne
s the state
s
of
va
riou
s a
s
se
ssm
ent
in
dicat
o
rs
usi
n
g f
u
z
zy
evaluation m
e
thod which overcome
s th
e pro
b
le
m of
exce
ssive h
a
r
deni
ng of a
s
se
ssm
ent sta
t
e
boun
dary tre
a
tment of other evalu
a
tion method
s.
Acco
rdi
ng to fuzzy mathe
m
atic theory,
the
informatio
n of different state grad
es of a
s
sess
me
nt indicato
rs
can
be expre
s
sed
by membership
function
s. Th
e co
mmon
m
e
mbe
r
ship fu
nction
s a
r
e t
r
iangul
ar m
e
mbershi
p
fun
c
tion, tra
p
e
z
o
i
dal
membe
r
ship
function, semi-tra
pe
zoid
and semi-ridge combi
n
ation memb
ership fun
c
ti
on.
Trian
gula
r
m
e
mbe
r
ship fu
nction
is rel
a
tively
rough
i
n
the
determ
i
nation
of sta
t
e gra
de,
whi
l
e
trape
zoid
al
membe
r
ship
function
is
e
a
sy to
cau
s
e
inform
ation
loss. Thi
s
a
r
ticle u
s
e
s
se
mi-
trape
zoid
an
d semi
-ri
dge
combi
nation
membe
r
ship
function to
determi
ne th
e informatio
n
of
different
state
grad
es
of va
riou
s a
s
sessment indi
cato
rs, a
nd the m
e
mbe
r
ship fu
nction i
s
d
e
fined
as:
1
12
11
2
21
2
1
11
()
s
i
n
[
(
)
]
22
2
0
nr
n
r
nr
nr
nr
xa
aa
x
xa
x
a
aa
xa
(3)
12
12
21
22
3
34
34
43
11
sin
[
(
)
]
22
2
()
1
11
sin
[
(
)
]
22
2
nr
nr
nr
nr
nr
n
r
aa
x
ax
a
aa
x
ax
a
aa
x
ax
a
aa
(4)
34
34
43
34
5
56
56
65
11
sin
[
(
)
]
22
2
()
1
11
sin[
(
)
]
22
2
nr
n
r
nr
nr
nr
nr
aa
x
ax
a
aa
x
ax
a
aa
x
ax
a
aa
(5)
5
56
45
6
65
6
0
11
()
s
i
n
[
(
)
]
22
2
1
nr
nr
nr
nr
nr
xa
aa
x
xa
x
a
aa
xa
(6)
In formul
as
(3
)~
(6),
x
nr
i
s
th
e no
rmali
z
ed
value of a
s
se
ssment in
dica
tor
e
r
;
μ
1
(
x
nr
)~
μ
4(
x
nr
)
are the
deg
re
es of m
e
mbe
r
shi
p
of a
s
se
ssment indi
ca
tor e
r
relative to four
different
state gra
des
S1~
S
4. a
1
~a
6
are
bo
und
ary values bet
wee
n
differen
t
state g
r
a
d
e
s
. Acco
rdin
g
to releva
nt fu
zzy
rule
s, the values of a1
~a
6 are sele
cted
as 1/10, 3/10,
4/10, 6/10, 7/10 and 9/1
0
.
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4: 5096 – 51
03
5100
4.2. Degre
e
of Member
s
h
ip of Sub-e
v
i
dence Bod
y
The d
egree
s of memb
ership
μ
1
(
x
nr
)~
μ
4
(
x
nr
)
of a
s
sessment i
ndi
cat
o
r e
r
relative
to four
different state
grade
s can b
e
determi
ned
from formul
as (3)~(6
). The
mathemati
c
al
expressio
n
o
f
degree of me
mbershi
p
of
sub-evid
en
ce body
is:
1
()
(
)
(
)
m
ij
i
n
r
r
r
E
xx
(
7
)
In whic
h,
μ
i
(
E
j
) is the
de
gree
of mem
bership
of su
b-evide
n
ce b
ody
j
relative to s
t
ate
grad
e
i
.
μ
i
(
x
nr
) is the de
gre
e
of membe
r
ship of a
s
sessment indi
cat
o
r er in
sub
-
eviden
ce bo
d
y
j
relative to st
ate gra
de
i
.
ω
(
x
r
) is the
weig
ht of indicator
er.
Th
e weig
ht of each indi
cato
r is
determi
ned u
s
ing exp
e
rt d
e
ci
sion meth
od. In this art
i
cle, the state
of transform
er is divide
d into
four g
r
a
d
e
s
, therefo
r
e, th
e value
s
sel
e
cted
fo
r i
a
r
e 1,
2, 3
an
d 4.
As there are three
sub
-
eviden
ce b
o
d
i
es in
asse
ssment mod
e
l, the value
s
sel
e
cted fo
r j a
r
e 1, 2 an
d 3.
m is the
num
ber
of asse
ssm
e
n
t indicato
rs
in sub
-
evid
e
n
ce
body; as obtained f
r
o
m
Table 1: t
he num
bers
o
f
asse
ssm
ent i
ndicators in
v
a
riou
s
su
b-eviden
ce
bodi
e
s
in
a
s
sessm
ent mo
del
are respe
c
tively: 3,
4 and 4. The
weig
hts of asse
ssm
ent indi
cato
r e
r
in various
sub
-
evid
ence bodi
es
are:
Gas di
ssolve
d in oil: {0.26
97, 0.1780, 0.
5223
}
Oilation test: {0.171
0, 0.19
64, 0.1964, 0.
4362
}
Electri
c
al test
: {0.2828, 0.1
720, 0.172
0, 0.3732
}
4.3. Ev
idence Combina
t
ion Theor
y
Evidence
co
mbination the
o
ry, also kno
w
n a
s
DS the
o
ry, is an un
certainty infere
nce a
nd
treatment me
thod. Evidence combi
natio
n theory
is b
a
se
d on the
combi
nation
of evidences
and
updatin
g of belief functio
n
s a
nd de
scribe
s
the u
n
c
ertai
n
ty thro
ugh the
con
c
ept
s such as
identificatio
n frame, ba
sic
belief distri
bu
tion f
unction,
belief functio
n
, plausi
b
ility and co
nfide
n
ce
interval [17].
4.3.1. Basic Defini
tions
The ba
sic d
e
finitions of evi
den
ce combi
nation theo
ry are a
s
follows:
Definition 1:
assume th
at:
Θ
is the ide
n
tification fra
m
e and the
b
a
si
c belief di
stributio
n
function
m i
s
the m
appi
ng from
the
set 2
Θ
→
[0,
1
], and
A
. If
①
()
0
m
and
②
()
1
A
mA
are sati
sfied,
m(A) is call
e
d
the basi
c
b
e
lief distrib
u
tion function of
event A an
d
expre
s
ses th
e deg
re
e of b
e
lief of evide
n
ce
to A.
All the
sets satisfying
m(A)>0 are call
ed
fo
cal
element
s, an
d the union of
all the focal element
s in frame
Θ
is
call
ed the co
re.
Definition
2: the functio
n
Bel
：
2
Θ
→
[0,1] defined
by
A
an
d
()
()
BA
B
el
A
m
B
is call
ed the
confide
n
ce functio
n
on
Θ
and expresses the d
egre
e
of
belief to the truene
ss of A.
Definition
3:
assume
Bel
：
2
Θ
→
[0,1] to
be the
confid
ence fun
c
tion
on
Θ
, for
A
;
the functio
n
Pls
：
2
Θ
→
[0,1
] defined
by
()
1
(
)
Pl
s
A
Be
l
A
is called the
plausibility function
of
Bel.
Definition 4:
for
A
, the interval [Bel(A), pl
s(A)] is
call
ed
the co
nfiden
ce interval of
A.
4.3.2. Ev
idence Combin
ation
Con
s
id
erin
g
that different
sub
-
evide
n
ce bodi
es ha
ve
different relative
imp
o
r
tance,
confid
en
ce functio
n
α
is introdu
ced t
o
corre
c
t the conf
id
en
ce
distributio
n before evid
e
n
ce
combi
nation.
()
(
)
()
1
mA
m
A
m
(8)
m’(A) is the
correcte
d co
nfiden
ce fun
c
tio
n
value; m’(
Θ
) is the co
nfiden
ce di
strib
u
tion of
uncertain evi
den
ce.
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TELKOM
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ISSN:
2302-4
046
Tran
sfo
r
m
e
r State Asse
ssm
ent Method Bas
ed o
n
Fu
zzy an
d Evid
ence… (Xie
Jiangh
ong
)
5101
Given the co
nfiden
ce fun
c
tions of different
evidence
bodie
s
in the same id
ent
ification
frame, the combine
d
con
f
idence functi
on ca
n be
calcul
ated u
s
i
ng the combi
nation rule. The
basi
c
combin
ation rule i
s
a
s
follows:
1
1
11
1
11
()
(
)
()
(
)
1(
)
(
)
n
n
nn
AA
A
n
nn
AA
mA
m
A
mm
A
mA
m
A
(9)
After the co
mbined
confi
den
ce fun
c
ti
on of
diffe
re
nt
sub
-
evid
e
n
ce bodi
es has been
determi
ned, t
he a
s
sessme
nt target det
ermin
a
tion can be
con
d
u
c
ted u
s
ing th
e co
rrespond
ing
inferen
c
e
rule
. The basi
c
in
fe
renc
e rule is
as
follows
:
1
2
()
(
)
()
()
(
)
ij
i
mF
mF
m
mF
m
(10)
F
i
is th
e
state
gra
de
obtain
ed by th
e a
ssessment; m
(
F
i
) i
s
the
conf
iden
ce fu
ncti
on valu
e
of assessme
nt result; m(
F
j
) is the co
nfiden
ce fun
c
tion value
s
of other stat
es; m(
Θ
) is
the
uncertain
co
nfiden
ce fun
c
tion value;
ε
1
and
ε
2
are threshold v
a
lue
s
pre
defi
ned a
c
cordi
n
g to
expertise and
technical sta
ndards. In th
is articl
e, the values sele
cted for
ε
1
and
ε
2
are 0.5 a
n
d
0.1 respe
c
tively.
5. Example Analy
s
is
The
asse
ssment o
b
ject
is the
tra
n
sf
orme
r
with
model
of O
D
FPS-2
500
0
0
/500 i
n
a
transfo
rme
r
substatio
n
of
Hub
e
i Provincial El
e
c
tri
c
Powe
r
Comp
any, the p
r
ev
entative test
data
of this tran
sforme
r in
Ma
y 2010
are selecte
d
fo
r th
e a
s
sessme
n
t
of the state
of tran
sform
e
r
body. The a
c
tual valu
es
of its variou
s indicators
, i.e. gas
dissol
ved in oil, oi
lation test a
n
d
electri
c
al te
st are sho
w
n in
Table 3:
Table 3. Prev
entative Test
Data of Tra
n
sformer
Sub-evidence Bod
y
Assessment Indicator
Measured Value
Gas dissolved in
oil
Total h
y
d
r
ocarbo
n content (uL/L
)
70.1
H
y
dr
ogen conten
t (uL/L)
60.5
Acety
l
en
e conten
t (uL/L)
3.6
Oilation test
Oil dielectric loss (%)
0.5
Oil breakdo
w
n
v
o
ltage (kV)
67.1
Moistur
e
in oil (
m
g/L)
9
Furfu
r
al (mg/L
)
3.01
Electrical test
Direct current
resistance unbalance rate (
%
)
1
Winding dielectric loss ((%)
0.53
Polarization index
1.9
Iron core g
r
oundi
ng current
(A)
0.065
Table 4. Co
nfiden
ce Fun
c
ti
on Value
s
of S
ub-evid
en
ce
Bodies befo
r
e the Corre
c
ti
on
Sub-evidence Bod
y
m(A)
S1 S2
S3 S4
1
0.1548
0.2929
0.5095
0.0128
2
0.1979
0.1695
0.5625
0.0701
3
0.0860
0.2274
0.5175
0.1691
Table 5. Co
nfiden
ce Fun
c
ti
on Value
s
of Sub-evid
en
ce
Bodies after
the Corre
c
tio
n
Sub-evidence Bod
y
m(
)
m(A)
S1 S2
S3 S4
1
0.1000
0.1393
0.2636
0.4586
0.0115
2
0.4653
0.1058
0.0906
0.3008
0.0375
3
0.1700
0.0714
0.1887
0.4296
0.1403
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5096 – 51
03
5102
The
normali
zation of
mea
s
ured
value
s
of in
di
cators is cond
ucte
d
usi
n
g
the
ca
lculatio
n
formula of rel
a
tive cra
cki
n
g
degree
s an
d the thre
sho
l
d values of variou
s a
s
sessment indi
cat
o
rs
in Section
2.
Then, the
de
gree
s of m
e
mbershi
p
of
e
a
ch
asse
ssm
ent indi
cator
relative to vari
ous
state gra
d
e
s
are obtai
ned
based on fuzzy evaluat
ion
method to furthe
r obtain
the degre
e
s of
membe
r
ship
of ea
ch
sub-eviden
ce
bod
y relative
to
variou
s
state
grade
s; T
abl
e 4
an
d T
abl
e 5
respe
c
tively sho
w
the co
nfiden
ce fun
c
tion values o
f
various
sub
-
eviden
ce b
o
d
ies b
e
fore
a
n
d
after the co
rrection.
Acco
rdi
ng to the inferen
c
e
rule in formu
l
a (10), the m
a
ximum confi
den
ce functio
n
value
of
su
b-eviden
ce body 1
i
s
0.4586
with
differen
c
e
of less
tha
n
ε
1
f
r
om
all the
ot
her confiden
ce
function val
u
es; the
r
efore, the op
eratio
n state
of tra
n
sformer bo
d
y
can’t b
e
de
termine
d
by t
he
informatio
n o
f
sub
-
evide
n
c
e
body
1 al
one. Simila
rl
y, neither
su
b-evide
n
ce b
ody 2
nor sub-
eviden
ce bo
dy 3 can d
e
termin
e the
operation
state of transformer
body
by themsel
v
es.
Therefore, e
v
idence
com
b
inati
on i
s
condu
cted fo
r the three
sub-evid
en
ce
bodie
s
a
nd t
h
e
confid
en
ce fu
nction valu
es
are obtai
ned,
as sho
w
n in
Table 6:
Table 6 Confi
den
ce Fun
c
ti
on Value
s
after Eviden
ce
Combi
nation
Transform
er Bod
y
m(
)
m(A)
S1 S2
S3 S4
1&2&3
0.0222
0.0705
0.1816
0.6990
0.0267
Table 6
sh
ows the
confid
e
n
ce
distri
buti
on of three
sub-evid
en
ce bodie
s
after eviden
ce
combi
nation.
It can be
seen that: the
confid
en
ce f
unctio
n
value
of state S3
is 0.69
90
with
differen
c
e
of more
than
ε
1
from the
confid
en
ce f
unctio
n
value
s
of all th
e
other
state
s
; the
uncertain evi
den
ce co
nfid
ence functi
o
n
value is 0.0222 an
d is
less than
ε
2
, in addition, the
confid
en
ce fu
nction val
ue
of state S3 i
s
mo
re
tha
n
the un
certai
n
eviden
ce
co
nfiden
ce valu
e.
Therefore, it
can
be obtai
ned fro
m
the
inferen
c
e
ru
l
e
that: the transfo
rme
r
is
in state S3, i
.
e.
abno
rmal
sta
t
e. The a
c
tu
al situ
ation i
s
that:
the
r
e
are
hig
h
te
mperature
ov
erhe
ating t
r
a
c
e
s
arou
nd
the
coil of thi
s
t
r
a
n
sformer a
n
d
ther
e
h
a
s
b
een arc discharg
e
phen
o
m
enon,
there
f
ore,
the ope
ratio
n
of this tran
sformer shall
be mo
ni
tore
d
and th
e rep
a
ir
shall
be
sche
dule
d
to
b
e
carrie
d out as app
rop
r
iate
; thus, the correctn
ess
of the asse
ssment method
in this articl
e is
verified.
6. Conclusio
n
This arti
cle select
s
the
re
pre
s
entative para
m
et
ers i
n
preventive
test
of tran
sforme
r
a
s
asse
ssm
ent i
ndicators for state asse
ssment a
nd
di
vides the
s
e i
ndicators int
o
three diffe
ren
t
sub
-
evide
n
ce
bodie
s
to asse
ss the
ope
ration
stat
e o
f
transfo
rme
r
body by use
of assessm
e
nt
model ba
se
d
on fuzzy and
eviden
ce the
o
rie
s
. It can b
e
obtaine
d from the re
se
a
r
ch i
n
this a
r
ticle
that: 1) Th
e
use
of fuzzy
evaluation m
e
thod in
t
r
eat
ment of un
ce
rtainty pro
b
le
m ca
n overcome
the proble
m
of exce
ssive
hard
eni
n
g
of asse
ssm
ent state
treatme
n
t
of othe
r eval
uation m
e
tho
d
s;
2) Eviden
ce theory
can ov
ercome the o
ne-side
dne
ss of evidence
body in a certain asp
e
ct a
n
d
effectively co
mbine th
e inf
o
rmatio
n of v
a
riou
s
eviden
ce bodie
s
to
allow
th
e state
a
s
sessme
n
t
results
to be more sp
ecifi
c
and
g
r
e
a
tly
redu
ce
the
asse
ssm
ent u
n
c
ertai
n
ty; 3)
The tra
n
sfo
r
mer
body state
a
s
sessme
nt m
odel b
a
sed o
n
fuzzy an
d
eviden
ce the
o
rie
s
h
a
s
cle
a
r p
r
in
ciple
s
and
easily a
c
ce
ssible
asse
ssment indi
cat
o
rs, it
c
an
accurately a
s
sess the
o
peratio
n stat
e o
f
transfo
rme
r
b
ody with
out requiri
ng
a la
rge am
ount
of empi
rical d
a
ta. Thi
s
a
s
se
ssment
mod
e
l
is
also a
ppli
c
abl
e to all the other tra
n
sf
o
r
m
e
r pa
rts o
r
other po
we
r eq
uipment
s.
Ackn
o
w
l
e
dg
ements
This work was supp
orted
by Science
and Te
chn
o
logy Prog
ra
m of Shanxi Powe
r
Corpo
r
ation
(No. K
J
[20
11]
333
) a
nd
Nat
i
onal Ba
si
c
Rese
arch P
r
og
ram
of China
(973
) P
r
og
ra
m
(No.2
009
CB7
2450
7)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Tran
sfo
r
m
e
r State Asse
ssm
ent Method Bas
ed o
n
Fu
zzy an
d Evid
ence… (Xie
Jiangh
ong
)
5103
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