Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
10
,
No.
4
,
A
ugus
t
2020
,
pp.
3862
~
38
68
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v10
i
4
.
pp3862
-
38
68
3862
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om/i
nd
ex
.ph
p/IJ
ECE
Adaptiv
e mana
gement
of techn
ical cond
ition
of
p
ower transf
ormers
V.
M. L
evin
1
,
A.
A. Y
ahy
a
2
1,2
Depa
rtment
of
Ene
rg
y
,
Novos
i
b
irsk
State
T
ec
h
nic
a
l
Univer
si
t
y
,
Russ
ia
2
Engi
ne
eri
ng
Pr
oje
c
ts De
par
tment,
Univ
ersity
of
Technol
og
y
,
Ir
a
q
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
N
ov
21
, 201
9
Re
vised
Feb
1
2
,
2020
Accepte
d
Fe
b 24
, 202
0
Ensuring
reliab
l
e
oper
a
ti
on
of
p
ower
tra
nsform
e
rs
as
par
t
of
el
e
ct
ri
c
power
fac
i
li
t
ie
s
is
assigned
to
the
m
ai
nt
ena
nc
e
and
r
epair
s
y
st
em,
whos
e
importa
n
t
components
are
dia
gnosti
cs
an
d
m
onit
oring
o
f
the
t
ec
hni
cal
condi
ti
on
.
Monitori
ng
allo
ws
y
ou
to
answ
er
t
he
qu
esti
on
of
whethe
r
th
e
tra
nsform
er
abnor
m
al
ities
a
nd
how
to
do
they
m
ani
f
est
,
whil
e
di
agno
stic
s
allow
det
ermining
th
e
nat
ure
,
the
sev
er
ity
of
the
prob
lem
,
det
ermine
th
e
ca
use
and
poss
ibl
e
conse
q
uenc
es.
The
article
pre
sen
ts
th
e
result
s
of
th
e
aut
hor’s
r
ese
arc
h
on
cr
e
at
ing
an
a
lgori
t
hm
for
ada
pti
v
e
cont
ro
l
of
th
e
techni
cal
condi
ti
on
of
po
wer
tra
nsform
er
s
using
dia
gno
stic
and
m
onitoring
data.
The
dev
el
op
ed
al
gorit
hm
imple
m
ent
s
the
de
ci
s
ion
-
m
aki
ng
pro
ce
dure
for
ensuring
the
re
liable
ope
ration
of
oil
-
filled
tr
ansform
er
equi
pm
ent
as
par
t
o
f
the
subs
ta
t
ions
of
el
e
ct
r
ic
power
fac
i
li
t
ie
s.
The
d
e
ci
sion
-
m
aki
ng
p
roc
edur
e
is
base
d
on
the
m
et
hod
of
sta
tis
ti
ca
l
Ba
y
es
ia
n
ide
nt
ifica
t
ion
t
he
sta
te
s
o
f
a
tra
nsform
er
b
ase
d
on
th
e
res
ult
s
of
dissolve
d
gas
anal
y
sis
(
DG
A)
in
oil
.
The
m
et
hod
is
cha
ra
cteri
z
ed
b
y
high
re
liabilit
y
of
re
cogni
z
ing
def
e
ct
s
in
the
tra
nsform
er
and
the
ability
to
ada
pt
th
e
p
roba
bil
i
ties
of
t
he
obt
ai
ne
d
soluti
ons
to
the
newl
y
r
ec
e
iv
e
d
dia
gnosti
c
informati
on.
Th
ese
result
s
il
lustrate
the
eff
ec
t
ive
ness
of
th
e
develope
d
app
roa
ch
and
the
p
oss
ibi
li
t
y
of
it
s a
pp
li
c
at
ion
in
the ope
r
at
ion
of
oil
-
f
il
l
ed
t
ran
sfo
rm
er
equi
pm
ent.
Ke
yw
or
d
s
:
Ad
a
ptive al
gor
it
h
m
Diag
nosti
cs
Disso
l
ved g
a
s
analy
sis
Mon
it
ori
ng
Power
t
ransf
orm
er
Stat
ist
ic
al
iden
ti
ficat
ion
Tech
nical
condi
ti
on
Copyright
©
202
0
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Amm
ar Abdul
azee
z Y
a
hya,
Dep
a
rtm
ent o
f Ener
gy,
Nov
os
ib
ir
sk St
at
e
Tech
nical
U
ni
ver
sit
y
,
20 K
a
rl Mar
x
a
venue,
No
vosibirs
k Ob
la
st
63
0073, N
ovos
i
bi
rsk
,
Russia
.
Em
a
il
:
a
m
m
ara
zez384
@g
m
ai
l
.co
m
1.
INTROD
U
CTION
The
iss
ues
of
e
nergy
-
sa
ving
a
nd
e
ff
ic
ie
nt
use
of
li
m
i
te
d
re
so
urces
i
n
the
el
ect
ric
power
industry
are
qu
it
e
urge
nt
a
nd
rele
van
t.
Also
,
they
a
re
inext
ricably
li
nk
e
d
with
th
e
issues
of
e
nsuri
ng
the
f
unct
ion
al
reli
abili
ty
o
f
powe
r faci
li
ti
es and the
operati
on
al
reli
abili
ty
o
f
e
quipm
ent
[
1
-
7
]
.
T
his lead
s to
the
ide
ntific
at
ion
of
a
n
ef
fecti
ve
strat
egy
f
or
m
anag
in
g
the
pro
du
ct
io
n
ass
et
s
of
e
nergy
enter
pr
ise
s,
i
n
dev
el
op
i
ng
al
gorithm
s
for
assessi
ng
the
te
ch
nical
conditi
on
of
equ
i
pm
ent,
m
akin
g
decisi
ons
on
the
ty
pe
and
m
agn
it
ude
of
op
e
rati
onal
i
m
pacts,
et
c.
M
ost
well
-
know
n
s
ci
entifi
c
stu
die
s
offer
a
ta
ct
ic
al
(situati
on
al
)
appr
oach
t
o
s
olv
in
g
these
pro
blem
s,
wh
ic
h
ge
ne
rall
y
giv
es
posit
ive
resu
lt
s
[
8,
9
].
H
ow
e
ve
r,
the
ob
viou
s
pr
efe
re
nce
is
fo
r
a
un
i
fied,
sci
entifi
cal
ly
based
s
olu
ti
on
f
or
assessi
ng
the
t
echn
ic
al
c
ondi
ti
on
of
el
ect
ric
al
equ
i
pm
ent,
m
aking
decisi
ons
on
it
s
tro
uble
-
f
ree
operati
on
a
nd
th
ei
r
al
gorithm
ic
an
d
s
of
t
war
e
[
10
-
13
].
O
ne
of
the
prom
isi
ng
area
s
that
cl
aim
to
receive
sci
e
nt
ific
al
ly
based
pr
act
ic
al
so
l
utions
[
14,
15
]
,
is
base
d
on
t
he
a
pp
li
c
at
ion
of
the m
et
ho
ds
of the the
ory
of s
ta
ti
sti
ca
l cl
assif
ic
at
ion
a
nd
pa
tt
ern
r
ec
ogniti
on.
Of
al
l
the
ty
pes
of
eq
ui
pm
e
nt
of
power
pl
ants
and
el
ect
ric
netw
orks,
trans
form
er
equ
ipm
ent
is
the
m
os
t
com
p
le
x,
re
spo
ns
ibl
e
an
d
ex
pe
ns
iv
e.
Fail
ur
e
s
of
powe
r
tra
ns
f
or
m
er
(
PT
)
a
re
re
la
ti
vely
rar
e,
but
t
hey
le
ad
to
serio
us
con
se
quence
s:
vio
la
ti
on
s
of
te
chnolo
gica
l
pr
oces
ses,
unde
rs
upply
of
el
ect
rici
t
y,
increase
d
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Ad
ap
ti
ve
man
ageme
nt
of tech
nical c
onditi
on
o
f
po
we
r
tra
nsf
or
mers
(
V. M
. Lev
in
)
3863
losses.
In
this
r
egard,
t
he
diag
no
sis
a
nd
m
on
it
or
in
g
of
PT
play
an
im
po
rtan
t
ro
le
in
e
nsuri
ng
t
he
op
e
rati
on
of
current
in
form
at
ion
on
the
c
urren
t
sta
te
.
O
ne
of
the
m
os
t
info
rm
at
ive
m
et
ho
ds
f
or
the
early
detec
ti
on
of
oil
-
fill
ed
P
T
de
fects
is
a
c
hrom
at
og
raphic
analy
sis
of
gas
es
diss
olv
e
d
i
n
oil
[
16
-
21
]
.
D
issolve
d
gas
a
naly
sis
(
DGA
)
al
lo
ws,
without
tur
ning
off
the
PT
,
to
detect
up
to
70%
of
def
ect
s
in
el
e
m
ents
of
the
act
ive
par
t,
suc
h
as ele
ct
rical
d
i
scharges
and
over
heati
ng
of
va
rio
us
degrees
of intensit
y.
The
DGA
te
ch
nique
ope
rates
with
m
easur
ed
con
ce
ntrati
ons
(A
i,
i
=
1,
.
.,7
)
of
gases
diss
ol
ved
i
n
oil:
H2,
CH
4,
C2
H4,
C2
H2,
C2H6,
C
O2,
CO,
as
well
as
with
est
ablished
li
m
i
t
values
(A
m
axi)
[22
-
25]
.
By
the m
et
ho
dolo
gy [2
6], the
stat
e is assesse
d
acc
ordin
g
t
o t
he
f
ollo
wing c
rite
ria:
-
The
c
rite
rio
n o
f bou
nd
a
ry co
nc
entrati
ons all
ows to
r
e
veal th
e sig
ns
of a
de
velo
ping
def
ec
t;
-
The
crit
erio
n
of
relat
ion
s
of
pa
irs
of
c
on
ce
nt
rati
on
s
of
c
harac
te
risti
c
gases
al
lows
us
to
de
te
rm
ine
the
type
of the
def
ect
;
-
The
c
rite
rio
n
of
the
relat
iv
e
rate
of
cha
ng
e
of
c
once
ntrati
on
al
lo
w
s
us
to
e
stim
at
e
the
degre
e
of
dev
el
op
m
ent of the
d
e
fect a
nd it
s
danger f
or the c
on
ti
nue
d op
e
rati
on
of
P
T.
Desp
it
e
t
hese
ad
van
ta
ges,
D
GA
ha
s
a
sig
nifica
nt
dra
wb
ac
k
-
th
e
relat
ively
low
reli
abi
li
ty
of
the esti
m
a
te
s obtai
ned.
2.
IDENTIF
YI
N
G THE T
EC
HNICAL
ST
ATE OF
PT B
Y DG
A
To
inc
rease
t
he
reli
abili
ty
of
as
sessin
g
t
he
sta
te
of
P
T
by
D
G
A,
i
t
is
reco
m
m
e
nd
e
d
t
o
us
e
a g
e
ner
al
iz
ed
s
ta
te
iden
ti
fier
(
GS
I
), w
hich
is
cal
culat
ed usin
g
c
onvoluti
on:
G
=
∑
(
A
i
A
m
ax
i
)
2
∑
A
i
A
m
ax
i
7
i
=
1
⁄
7
i
=
1
(1)
The
us
e
of
GSI
[
27
]
gu
a
ra
ntees
the
f
ollo
wing
set
of
a
dv
a
nt
ages,
ve
ry
sig
ni
ficant
from
the
po
i
nt
of
view o
f
the
classi
ficat
ion
tas
k:
-
Com
pactness
of
the
descr
i
ption
an
d
gen
e
ra
li
zed
assessm
e
nt
of
the
vecto
r
of
m
easur
e
d
con
ce
ntrati
ons
of
diag
nosti
c g
ase
s;
-
In
c
reasin
g
the
sensiti
vity
of
t
he
trai
t
to
cha
nges
in
th
e
com
po
sit
io
n
a
nd
c
on
ce
ntrati
ons
of
gases
ca
us
e
d
by
the o
cc
urre
nce
of a
def
ect
i
n
t
he
P
T;
-
Si
m
plici
ty
o
f
f
or
m
ing
class
di
cho
t
om
ie
s an
d sim
plifyi
ng
the
cond
it
io
ns
for t
heir
li
nea
r
se
pa
rab
il
it
y.
Con
si
der
at
io
n
(1)
as
a
discre
te
rand
om
var
ia
ble
dete
rm
ine
s
the
p
os
sibil
it
y
of
ge
ner
at
i
ng
sta
ti
sti
cal
sam
ples
(S
S)
ba
sed
on
the
pr
oto
c
ols
of
m
ulti
-
ye
ar
D
GA
of
the
co
ns
ide
re
d
sin
gle
P
T
or
a
gro
up
of
t
he
sam
e
ty
pe
trans
form
ers
ope
rati
ng
unde
r
com
par
a
ble
co
ndit
ion
s.
An
im
po
rta
nt
pro
per
ty
of
s
ta
ti
sti
ca
l
sa
m
ples
is
their
suf
fici
ent
representat
ive
ness.
T
he
sam
ples
com
bin
e
DGA
pr
oto
c
ols,
acco
rd
i
ng
t
o
wh
ic
h,
acc
ord
ing
t
o
the
crit
eria
of
[26],
a
dev
el
opin
g
de
fect
is
pr
e
dicte
d,
or
it
s
absen
ce
.
Th
us,
init
ia
l
con
di
ti
on
s
are
f
or
m
ed
for
sp
li
tt
ing
the
s
et
of
possible
sta
te
s
of
the
PT
i
nto
two
m
utu
al
ly
op
posit
e
cl
asses
P1
-
“
norm
”
and
P
2
-
“dev
ia
ti
ons
fro
m
the
norm
”.Th
e
ap
pea
ran
ce
of
cl
ass
dich
ot
omi
es
in
the
f
or
m
of
tw
o
ge
ner
al
ly
interse
ct
ing
intervals
on t
he
posit
ive sem
i
-
axis
G
∈
[
0
-
∞
)
leads t
o
the
fo
rm
ulati
on
of t
wo fundam
ental
q
ue
st
ion
s:
1.
Wh
e
re sh
ou
l
d I
dr
a
w
the
bo
unda
ry
betwee
n t
he
cl
asses
of s
ta
te
s o
f
t
he
P
T
and ho
w
to
g
et
it
?
2.
How
m
uch
is
it
advisable
t
o
in
tro
du
ce
PT st
at
e cla
sses fo
r
th
ei
r
subse
quent
reli
able ide
ntific
at
ion
?
Stud
ie
s
[27,
28]
hav
e
est
a
blished
that
the
Ba
ye
sia
n
cl
a
ss
ifie
r
(
2)
is
best
su
it
ed
for
desc
ribi
ng
the bo
unda
ry be
tween t
he
cl
as
ses:
G
max
1
=
M
1
σ
2
2
−
M
2
σ
1
2
+
√
D
σ
2
2
−
σ
1
2
(2)
or it
s sim
plified
m
od
el
(3)
G
max
1
=
M
1
+
k
σ
1
(3)
Her
e:
M
1,
M
2,
σ
2
1
,
σ
2
2
m
at
he
m
a
ti
c
al
expect
at
ion
s
an
d
sta
nd
a
r
d
de
viati
on
s
SS
G
in
cl
asses
P
1
a
nd
P
2
resp
ect
ively
,
D
–
functi
on
of
li
ste
d
par
a
m
et
ers,
k
-
e
m
pirically
com
pu
ta
ti
on
al
co
ns
ta
nt
from
2
-
3
range
.
A
pr
e
re
qu
isi
te
for
the
correct
app
li
cat
io
n
of
(2)
an
d
(3)
is
sing
le
-
m
od
e
an
d
two
-
pa
ram
eter
distrib
utio
n
of
S
S
distrib
utions
i
n
bo
t
h
cl
asses
of
sta
te
s,
w
hi
ch
in
m
os
t
pra
ct
ic
al
cases
is
fu
lfil
le
d.The
de
finiti
on
G
max
1
of
(
3)
al
lows
y
ou
to
adjust
it
s
value
base
d
on
t
he
m
ini
m
u
m
total
er
ror
of
dia
gn
os
is,
min
(
ε
1
+
ε
2
)
,
w
her
e
ε
1
and
ε
2
“f
al
se
al
arm
”
a
nd
“
def
ect
om
i
ssion
”
,
res
pecti
vely
.
Figure
1
sh
ows
the
hist
ogram
s
of
relat
ive
fr
eq
ue
ncie
s
SS
G
f
or
cl
asses
P1
a
nd
P
2,
c
om
pi
le
d
from
s
a
m
ples
of
protoco
ls
DGA
blo
ck
PT
ty
pe
T
DN
-
25
0000/2
20
f
or
20
ye
ars
of
op
e
ra
ti
on
from
19
94
to
20
13.
Th
e
figure
c
le
arl
y
sh
ows
the
in
te
rsecti
on
of
t
he
histo
gram
s
of
bo
t
h
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p
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g,
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ol.
10
, No
.
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,
A
ugus
t
2020
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3862
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3868
3864
cl
asses,
wh
ic
h
represe
nts
the
t
otal
erro
r
of
di
agnosis.
As
is
well
know
n,
a
n
inc
rease
i
n
t
he
nu
m
ber
of
cl
asses
of stat
es lea
ds
t
o
a
dec
rease i
n co
nf
i
den
ce
in t
heir
ide
ntific
at
ion
.
Fig
ure
1. Histo
gr
am
s o
f
r
el
at
ive
fr
e
qu
e
ncies
G
In
[
29
]
,
it
was
co
nv
i
ncin
gly
sh
ow
n
that
t
he
m
os
t
app
r
op
riat
e
opti
on
is
the
dich
oto
m
y
of
cl
asse
s
(P
1
a
nd
P2
)
.
At
t
he
sam
e
tim
e,
the
cl
ass
P
2
c
onsis
ts
of
tw
o
s
ubset
s
P
2
1
-
“m
inor
dev
ia
ti
ons”
and
P
2
2
-
“si
gn
i
ficant
(cr
it
ic
al
)
devi
at
ion
s”,
be
tw
een
w
hich
t
he
re
is
al
so
a
n
inter
face.
A
ccordin
g
to
[
29
],
the
bounda
ry
be
tween
these
s
ub
s
et
s
ca
n
be
adequate
ly
de
s
cribe
d
by
t
he
e
xpressi
on
max
1
=
M
1
+
k
σ
1
su
bj
ect
to
the
re
pr
ese
ntati
ven
ess
of
the
sam
ple
i
n
the
cl
ass
P
2.
T
he
possi
bili
ty
of
ob
ta
ini
ng
t
he
boun
da
ries
of
the
div
isi
on
of
cl
asses
on
the
po
sit
ive
hal
f
-
l
ine
of
the
si
gn
G
m
akes
it
po
ssible
to
form
t
he
f
ollow
i
ng
c
rite
ria
and r
ules
for
id
entify
ing
PT
sta
te
s:
-
if,
G
≤
G
max
1
then
"
norm
al
";
-
if,
G
max
1
≤
G
<
G
max
2
then
"
m
ino
r de
viati
on
s";
-
if,
G
>
G
max
2
then
“S
ign
ific
a
nt (
c
riti
cal
)
de
viati
ons
”.
The
f
or
m
ed
de
ci
sion
r
ules
est
ablish
a
on
e
-
to
-
one
c
orres
pondence
betwee
n
the
quantit
at
iv
e
m
easur
e
of
the
ge
ner
al
i
zed
trai
t
an
d
th
e
char
act
erist
ic
s
of
th
e
operati
on
al
sta
te
PT
.
The
loa
d
of
th
e
PT
is
an
im
p
or
ta
nt
op
e
rati
onal
fa
ct
or
t
hat
in
flu
ences
t
he
te
m
per
at
ur
e
re
gim
e
of
it
s
op
e
rat
ion
a
nd,
as
a
resu
lt
,
t
he
res
ults
of
the tec
hnic
al
co
ndit
ion
assess
m
ent u
sin
g
the
D
G
A
m
et
ho
d.
A
sig
nifica
nt incr
ease i
n
the
PT curre
nt loa
d
(
I
load
)
even
in
a
tra
ns
f
or
m
er
in
the
“n
or
m
al
”
sta
te
causes
an
increase
d
he
a
t
gen
erat
io
n
and
an
i
ncr
e
ase
in
the
co
ncen
tr
at
ion
s
of
hydro
carbo
n
gases
ty
pical
fo
r
ov
erh
eat
in
g:
С
Н
4,
С2
Н
4,
С2
Н6,
w
hich
in
crease
s
the
pro
ba
bili
ty
of
an
er
rone
ou
s
dia
gnos
is.
In
or
der
t
o
i
ncr
ease
the
re
li
abili
ty
of
ide
ntifyi
ng
the
st
at
e
of
"dev
ia
ti
on
f
rom
the
no
rm
al
,"
it
is
adv
isa
ble
to
est
ablis
h
a
co
rr
el
at
io
n
de
pe
nd
e
nce
G
max
1
(К
load
),
give
n
the
stoc
hasti
c
pro
per
ti
es
of
these
va
riables
.
A
neces
sary
c
onditi
on
f
or
ac
hieving
this
go
al
is
the
form
a
ti
on
of
two
ti
m
e
-
synchro
nized
sta
ti
sti
cal
sa
m
ples o
f
the SS
G
a
nd
К
load
= I
load
\
I
l .nominal
in class P1
.
Her
e
I
l.nom
inal
is
the
nom
inal
c
urren
t
of
the
low
volt
age
wi
nd
i
ng
PT
.
Dete
rm
inati
on
of
th
e
co
rr
el
at
io
n
functi
ons
M
1(К
load
),
σ1
(К
load
),
t
he
cal
c
ulati
on
of
t
he
desir
ed
de
pende
nce
G
max
1
(К
load
)
by
th
e
ex
pr
e
ssio
n
(
3),
the app
roxim
ation
of the
obtai
ned set
of
calc
ulati
on
points
by the a
naly
ti
cal
ex
pressi
on
:
G
max
1
= α ex
p [β К
loa
d
]
,
(4)
w
he
re
α
,β
ar
e
con
sta
nts
of
appr
ox
im
at
ion
,
rep
re
sent
the
se
qu
e
nce
of
so
lvi
ng
the
se
t
ta
sk
.
As
a
re
su
lt
of
the
us
e
of
(4),
an
adap
ti
ve
i
den
ti
ficat
io
n
of
the
sta
te
of
the
PT
is
prov
i
ded,
de
pendin
g
on
it
s
cur
re
nt
load
current,
at w
hi
ch
the
conce
ntr
at
ion
s
of d
ia
gnos
ti
c g
ase
s ar
e
m
easur
ed
b
y
D
GA an
d
t
he G
value
is
calc
ul
at
ed.
3.
PRACTI
CA
L
IM
PLE
MEN
TATION
OF
THE
ORETI
C
AL PO
SITIO
NS
3.1
.
M
on
i
to
ri
ng
th
e
st
at
e
of
PT
on
th
e
dynamics
of ch
ange
th
e
g
e
ner
aliz
ed t
rait
Con
si
der
the
pr
act
ic
al
im
pl
e
m
entat
ion
of
ada
ptive
c
on
t
ro
l
of
the
te
c
hn
ic
al
c
onditi
on
of
P
T
on
the
exam
ple
of
the
operati
ng
histor
y
of
t
he
blo
c
k
tra
nsfo
rm
er
TDN
-
2500
0/220
in
NTP
S
-
5
(
N
ovos
ibir
s
k
Ther
m
al
Po
we
r
Stat
ion
-
5).
The
ret
ro
s
pect
ive
of
t
he
D
GA
protoc
o
ls
for
20
ye
ars
of
op
e
rati
on
sh
owe
d
an
e
xcess
of
th
e
boun
dar
y
c
oncent
rati
on
s
of
su
c
h
diag
nosti
c
gases
as
С
2
Н
2
,
С
2
Н
4
,
С
Н
4
,
С
2
Н
6
,
in
the
i
nt
erv
al
06.20
06
-
02.20
13,
wh
ic
h
i
ndic
at
es
a
sta
bl
e
therm
al
defec
t,
pres
um
ably
associat
ed
with
a
vi
olati
on
of
the
ci
rcu
la
ti
on
of
m
agn
et
ic
flu
xes
in
the
ste
el
cor
e.
T
he
ind
ic
at
ed
in
te
rv
al
of
oper
at
ion
of
a
PT
with
a
dev
el
op
i
ng
de
fect
can
be
cl
early
ob
se
r
ved
by
the
c
hange
in
the
dynam
i
cs
of
t
he
gen
e
r
al
iz
ed
at
tribu
te
G(
t)
sh
ow
n
in
Fi
g
ure
2.
T
he
resu
l
ts
of
the
m
on
it
or
i
ng
in
f
or
m
t
hat
the
in
vestigat
ed
PT
is
in
a
sta
te
of
"de
vi
at
ion
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p
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g
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S
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88
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8708
Ad
ap
ti
ve
man
ageme
nt
of tech
nical c
onditi
on
o
f
po
we
r
tra
nsf
or
mers
(
V. M
. Lev
in
)
3865
from
the
norm
al
"
(
G
max
1
<G
<
G
max
2
).
I
n
certai
n
pe
rio
ds
of
ti
m
e
,the
sta
te
of
S
T
de
te
rior
at
es
a
nd
go
e
s
int
o
the
cat
egory
of
“crit
ic
al
dev
ia
ti
on
”
(G
>
G
max
2
).
Con
ti
nue
d
ope
ra
ti
on
of
the
PT
in
this
sta
te
is
associat
ed
with
an
inc
rease
d risk of
f
ai
lu
re a
nd
requires
the t
i
m
ely introdu
ct
ion
of a
dequat
e operati
onal
i
m
pacts.
Fig
ure
2.
Mo
nitor
in
g
t
he
sta
tu
s of P
T
b
y
G
(t)
3.2.
Incre
as
e
d ident
i
fica
tio
n a
cc
urac
y
In
the
pro
pose
d
sta
ti
sti
cal
m
o
dels,
the
a
dap
t
at
ion
of
the
rel
ia
ble
identific
a
ti
on
of
the
sta
te
s
of
the
P
T
is
po
ssi
ble,
fir
st,
by
choosin
g
the
val
ue
of
the
com
pu
ta
ti
on
al
const
ant
k
=
2
–
3
by
the
c
rite
rion
m
in
(μ
1
+
μ
2
).
As
al
rea
dy
m
e
ntion
e
d,
t
he
tot
al
diagnosis
e
r
ror
is
vis
ually
the
area
se
par
a
te
d
by
the
bounda
ry
f
un
ct
io
n
G
max
1
from
the
fr
eq
ue
ncy
histogra
m
s
in
each
of
t
he
cl
asses
of
st
at
es
P1
and
P
2
as
sh
own
in
Fig
ure
1
.
Ta
ble
1
sh
ows
the
sel
ect
ion
r
esults
K,
acc
ordi
ng
t
o
w
hic
h
the
m
ini
m
u
m
total
identific
at
ion
er
r
or
(Ԑ
1
+Ԑ
2
)
=1
.15
9%
is
pro
vid
e
d wit
h K=2
.2 an
d
G
max
1
=
0.765
.
Seco
nd
ly
,
a
n
adap
ta
ti
on
of
re
li
a
ble
identific
at
ion
of
PT
st
at
es
can
be
re
al
iz
ed
us
in
g
(
4).
Fig
ur
e
3
sh
ows
the
ap
pro
xi
m
ation
of
the
bounda
ry
functi
on
G
max
1
f
or
the
st
ud
ie
d
P
T
with
coe
ff
ic
i
ents
α
=0
.42
42,
β=0.
7716.
This
all
ow
s
for t
he op
e
rati
onal
ad
a
ptati
on
of
decisi
on rules
on th
e cu
rr
e
nt v
al
ue
К
load
PT.
Table
1.
Sele
ct
ion
res
ults
co
nst
ants
K
№
k
max
1
ε
1
,
%
ε
2
,
%
1
2
0
,73
5
3
,05
1
,15
9
2
2
,2
0
,76
5
0
1
,15
9
3
2
,4
0
,79
6
0
1
,15
9
4
2
,6
0
,82
7
0
1
,49
4
Fig
ure
3.
A
ppr
ox
im
at
ion
of t
he bou
nd
a
ry fu
nction i
n
t
he
st
at
e sp
ace
PT
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S
N
:
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-
8708
In
t J
Elec
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C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
3862
-
3868
3866
3.3.
The i
n
ten
sity o
f
t
he d
ynamic
s
of ch
anges in
t
he
g
e
n
erali
z
ed sign
Assessm
ent
of
the
i
ntensity
of
the
dynam
ic
s
of
c
ha
ng
es
in
t
he
gen
e
ra
li
zed
cha
racter
ist
ic
G
is
appr
opriat
e
in
the
case
whe
n
the
presen
ce
of
a
de
vel
op
i
ng
de
fect
is
predict
ed
an
d
t
he
sta
t
e
of
the
PT
is
char
act
e
rized
a
s
“de
viati
on
f
r
om
the
norm
al”.
I
n
t
his
case
,
there
is
a
nee
d
to
determ
ine
the
de
gr
ee
of
dange
r
of
a
def
ect
f
or
the
fu
rthe
r
op
erati
on
of
PT.
It
is
ob
vious
that
the
resu
lt
s
of
su
c
h
an
as
ses
sm
ent
m
ay
aff
ect
the r
es
ults o
f d
eci
sion
-
m
akin
g
a
nd sho
uld
be
r
eflect
ed
in
t
he
crit
eri
on r
el
at
ion
s
hip
s.
by t
he
m
et
ho
d D
G
A
[26
],
an
asse
ssm
ent
of
the
de
gr
ee
of
dange
r
of
a
de
fect
de
velo
pi
ng
in
PT
is
m
a
de
ac
c
ordin
g
to
th
e
relat
ive
r
at
e
of
change
of
co
nc
entrati
ons
of
diag
nosti
c
gas
es
diss
olv
e
d
i
n
oil
V
rel
i
.
To
est
ablish
a
qu
antit
at
ive
m
ea
su
re
of
the
da
ng
e
r
of
a
dev
el
op
i
ng
d
e
fect,
two
m
axim
u
m
per
m
issib
le
values
of
t
he
m
axi
m
u
m
relat
ive
rate
of
increas
e
in
the
con
ce
ntr
at
ion
s
of
cha
ra
ct
erist
ic
gases
are
introd
uced
10%
and
15%
per
m
on
th.
I
f
m
ax
V
rel
i
≥
10
%
per
m
on
th
and
<
15%
per
m
on
th
,
it
is
reco
m
m
e
nd
e
d
to
put
the
PT
on
the
i
nc
reased
c
ontr
ol
by
D
GA,
an
d
i
f
m
ax
V
rel
i
>15%
per
m
on
th,
the
n
it
i
s r
e
qu
i
red to
re
m
ov
e the PT
fr
om
w
ork wit
h
t
he
s
ubseq
ue
nt
plan
ning
of r
e
pa
ir.
4.
ALGO
RITH
M
O
F
ADAP
TIVE ST
ATE CO
NTR
OL
PT
The
de
ci
sion
-
m
aking
al
go
rithm
is
an
or
de
r
ed
seq
ue
nce
of
act
ion
s
ai
m
ed
at
achievin
g
the
set
goal
.
In
this
case,
th
e
go
al
is
to
dev
el
op
reas
on
a
bl
e
and
tim
ely
r
ecom
m
end
at
io
ns
on
the
direc
ti
on
an
d
i
m
po
r
ta
nce
of
operati
on
al
i
m
pacts
on
t
he
P
T
by
the
assessm
ent
of
it
s
cu
rr
e
nt
te
chn
ic
al
c
onditi
on,
determ
ined
us
in
g
the
dev
el
op
e
d
m
od
el
s
and
de
ci
sion
r
ules.
T
he
al
gorithm
of
a
dap
ti
ve
c
on
t
ro
l
of
the
te
ch
ni
cal
sta
te
of
the
PT
a
s
sh
ow
n
in
Fi
g
ur
e
4
i
nclu
des
t
he
foll
ow
i
ng com
pu
ta
ti
on
al
and lo
gical
b
l
oc
ks:
-
colle
ct
ion
a
nd
processi
ng of
da
ta
, th
e
form
at
i
on of
diag
nosti
c stat
ist
ic
s;
-
cal
culat
ion
of
bounda
ry fu
nctions an
d
c
orrel
at
ion
dep
e
nde
nc
ie
s;
-
cal
culat
ion
of
the
curre
nt
va
lue
of
t
he
ge
ne
rali
zed
cha
ra
ct
erist
ic
,
ta
kin
g
into
acc
ount
the
act
ual
lo
ad
on the t
ran
s
f
orm
er;
-
crit
erion assess
m
ent an
d i
de
nt
ific
at
ion
of the
current
operati
on
al
sta
tus
of the tra
nsfo
rm
er;
-
Decisi
on m
ak
ing o
n
t
he natu
r
e of
op
e
rati
ona
l im
pacts o
n t
he
PT.
Fig
ure
4. Al
gorithm
f
or
a
da
ptive contr
ol
of the tech
nical
st
at
e o
f
a
power
trans
form
er
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Ad
ap
ti
ve
man
ageme
nt
of tech
nical c
onditi
on
o
f
po
we
r
tra
nsf
or
mers
(
V. M
. Lev
in
)
3867
Ad
a
ptabili
ty
of
the
de
velo
pe
d
al
gorithm
giv
es,
firstly
,
the
a
bili
ty
to
custo
m
iz
e
the
boundar
y
f
unct
io
n
G_
m
ax^1
by
t
he
co
ndit
ion
of
m
ini
m
u
m
tot
al
identific
at
ion
er
ror,
sec
on
dly,
the
abili
ty
to
ta
ke
into
a
ccount
the
dep
e
ndenc
e
of
the
boun
da
ry
functi
on
on
th
e
act
ual
cu
rr
e
nt
load
PT
G_
m
ax^1
(
Kloa
d)
,
rec
orde
d
durin
g
the
f
or
m
at
ion
of
the
prot
oco
l
f
or
the
a
naly
sis
of
disso
l
ve
d
gases
D
GA.
T
his
al
lo
ws
with
a
high
pro
bab
i
li
ty
to
pro
vid
e
reli
abl
e
identific
at
io
n
of
the
c
urre
nt
te
chn
ic
al
c
onditi
on
of
th
e
PT,
an
d
the
r
e
fore,
the
validit
y
of
the
reco
m
m
end
ed
op
e
rati
ona
l
i
m
pacts
con
c
ern
i
ng
it
.
The
la
un
c
h
of
the
al
gorithm
is
per
f
or
m
ed
at
the
t
i
m
e
of
receipt
of
the
protoc
ol
of
the
cu
rr
e
nt
D
GA
P
T.
Re
-
c
om
pu
ta
ti
on
of
bounda
ry
f
unct
ion
s
an
d
c
orrelat
io
n
dep
e
ndencies
occurs
as
the
s
ta
ti
sti
ca
l
m
a
te
rial
is
up
dated
(DGA
prot
ocol
s),
but
at
le
ast
on
ce
a
ye
ar
.
This
is
du
e
to
t
he
inte
ns
it
y
of
up
dating
sta
ti
sti
cal
sa
m
ples,
w
hich
de
pends
on
th
e
le
vel
of
t
he
hierar
c
hy
of
s
of
t
war
e
and
com
pu
ti
ng
res
ources.
I
n
t
he
case
of
a
ce
ntrali
zed
le
vel o
f
hiera
rc
hy
(t
he
se
rv
e
r
of
th
e
netw
ork
ente
rprise),
sta
ti
sti
cal
sa
mp
le
s
f
or
m
the
DGA
protoc
ols
of
the
sa
m
e
ty
pe
of
tr
ansfo
rm
ers
use
d
in
sim
il
ar
op
e
rati
ng
conditi
ons.
Th
is
ensu
re
s
that
the
sa
m
ples
are
su
f
fici
ently
rep
rese
ntati
ve
at
the
annua
l
op
erati
ng
inter
val
.
In
the
case
of
the
local
hiera
rch
y
le
vel,
the
sa
m
pling
is
carried
ou
t
in
t
he
m
od
e
of
di
agnostic
m
on
ito
ri
ng,
wh
ic
h
is al
s
o
a
ccepta
ble
from
their
represe
nt
at
iveness.
5.
CONCL
US
I
O
NS
Sit
uational
de
ci
sion
s
relat
e
d
to
the
us
e
of
ex
per
t
asses
sm
ents
of
the
degree
of
w
orka
bili
ty
of
ind
ivi
du
al
un
it
s
and
gro
up
s
of
eq
uip
m
ent
of
the
sam
e
ty
pe
giv
e
posit
ive
resu
lt
s,
bu
t
ca
nnot
be
oppos
ed
to
a
un
i
fied,
sci
entifi
cal
ly
-
bas
ed
ap
proac
h
t
o
assessi
ng
t
he
current
sta
t
e
of
el
ect
rical
equ
i
pm
ent,
m
aking
decisi
ons
on
it
s
tro
ub
le
-
f
ree
op
e
rati
on,
a
nd
their
al
gorith
m
ic
and
softw
are.
T
he
pr
opose
d
sta
ti
sti
cal
m
od
el
s,
decisi
on r
ules
and
a
n
al
gorith
m
f
or
ad
a
ptive co
nt
ro
l o
f
the tec
hn
ic
al
con
diti
on
of a pow
e
r
trans
form
er p
ro
vi
de
an
ef
fecti
ve
s
ol
ution
t
o
the
s
pecified
pro
ble
m
s.
The
resu
lt
s
of
their
us
e
i
n
the
pract
ic
e
of
operati
ng
a
powe
r
trans
form
er
are
confirm
ed
by
con
c
rete
exa
m
ples
and
de
m
on
strat
e
a
hig
h
le
vel
of
rel
ia
bili
ty
of
dia
gnos
ti
c
evaluati
ons a
nd the
v
al
id
it
y
of the
r
ec
omm
e
nd
e
d o
per
at
io
na
l effects.
REFERE
NCE
S
[1]
Chern
y
avsk
y
,
G.
I.
,
"A
dap
ti
ve
m
ana
gement
of
the
te
chn
ical
condi
t
ion
and
saf
ety
o
f
oper
a
ti
on
of
co
m
ple
x
techni
c
a
l
s
y
stems
under
re
source
constr
ai
n
t
s
,
"
Ene
rgy
Sav
in
g
, n
o
.
2
,
pp
. 5
-
7
,
2006
.
[2]
Sidel
nikov
L.
G.
,
Sedunin
A.M.
,
S
y
kule
v
A.Yu
,
"
Diagnosti
cs
of
p
ower
tra
nsform
e
rs
without
remo
ving
the
oper
a
ti
n
g
volt
ag
e
,
Tra
nsfo
rm
ers:
oper
ation
,
di
agnosis,
rep
a
ir
and
ext
ension
of
service
l
ife
,
"
Mate
ri
al
s
MN
PK
dedi
c
at
ed
to
the
70
th anni
ver
sar
y
of
Vikt
or
S
okolov:
Ye
k
at
e
ri
nburg
,
pp
.
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-
1
28
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2010
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P.
Jarm
an,
R.
Hooton,
L
.
W
al
ke
r,
Q.
Zhong,
T.
I
shak,
Z.
W
ang
,
"Tra
nsform
er
li
f
e
pre
di
ct
ion
usin
g
dat
a
from
units
removed
from
se
rvic
e
and
the
rm
a
l
m
odel
l
ing,
"
Proc.
CIGR
E
S
ession
,
2010
.
[4]
"IEE
E
Standa
rd
C57.
91
-
2011
,
"
IEE
E
Guide
for
Loading
Mine
ral
-
Oil
-
Imm
ersed
Tr
ansfo
rm
ers
a
nd
Ste
p
-
Voltage
Re
gulat
ors
,
201
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D.
Marti
n,
Y
.
C
ui,
C.
Eka
n
a
y
ak
e,
H.
Ma
,
and
T.
Saha
,
"A
n
updat
ed
m
odel
to
det
ermine
the
l
ife
remai
n
ing
of
tra
nsform
er
insu
la
ti
on
,
"
I
EE
E
Tr
ans.
Powe
r
Del.
,
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p.
395
-
402
,
Feb
.
2015.
[6]
N’cho,
J.
,
Fofan
a,
I.
,
Hadja
d
j,
Y
.
,
and
Berou
al,
A.
,
"
Revi
ew
of
ph
y
sico
che
m
ical
-
base
d
dia
gnosti
c
te
chn
ique
s
for
assess
ing
insula
t
ion
cond
it
ion
in
age
d
tra
nsform
er
s,"
Ene
rgi
es
,
vo
l
.
9
,
367
,
pp
.
1
-
2
9,
2016
.
[7]
Rozga
,
P.
,
Piotr
ows
ki,
T
.
,
Ko
zak,
R.
,
"
Expe
ri
en
ce
s
with
de
te
c
tion
of
tr
ansform
er
fa
il
ur
e
bas
ed
on
insulating
o
il
te
sts,"
In
Procee
dings
of
the
201
7
IEEE
19th
Int
ernati
onal
Conf
ere
nce
on
Di
el
e
ct
ric
Liquids
(
ICDL)
,
Manc
hest
e
r,
UK
,
25
–
29
June
2017.
[8]
Aks
enov
Yu
P.,
Golubev
A.V.,
Za
videy
V
.
I.,
Yurin
A.V.,
Ya
roshenko
I.
V.
,
"
The
result
s
of
l
ong
-
te
rm
per
iod
ic
dia
gnostic
s
of
p
ower
tra
nsform
e
rs
,
"
Elec
tro
,
n
o.
1
,
pp
.
28
-
35
,
20
06
.
[9]
Bondare
nko
V
.
E.
and
Shut
enk
o
O.V.
,
"Im
prove
m
ent
of
decision
-
m
aki
ng
proc
edur
es
in
assess
ing
th
e
deg
ree
of
agi
ng
of
tr
ansform
er
oil
s
,
"
ELEC
TRO
, n
o.
1
,
pp
.
17
-
21
,
2009
.
[10]
Y.
Cu
i,
H.
Ma
,
T.
Saha
,
C.
Ekana
y
ake,
D.
Mart
in,
"M
oisture
-
de
pende
nt
the
rm
al
m
odel
li
ng
of
po
wer
tra
nsform
er
,
”
IEE
E
Tr
ans.
Po
wer
Del.
,
vo
l. 31
,
no
.
5
,
pp
.
2140
-
2150,
Oct
.
2016
.
[11]
E.
Müll
ero
vá
,
J.
Hrůza
,
J.
Ve
le
k
,
I.
Ullman,
F.
Stř
íska,
"Lif
e
c
y
c
le
m
ana
gement
of
power
tra
nsform
ers:
Result
s
and
discussion
of
c
as
e
studi
es
,
"
IE
EE
Tr
ans.
El
ectr.
In
sul.
,
vo
l. 22, no.
4,
pp
.
2379
-
238
9,
Aug.
2015.
[12]
D.
Zhou,
Z
.
W
a
ng,
P.
Jarm
an
,
and
C.
Li,
"D
ata
req
u
isit
es
for
tra
nsform
er
stati
stic
al
li
f
etim
e
m
odel
li
ng
-
Pa
rt
II
:
Com
bina
ti
on
of
ran
dom
and
agi
ng
-
relate
d
f
ai
l
ure
s
,
"
IEE
E
Tr
ans.
Powe
r
Del.
,
vol
.
29,
no.
1,
pp.
154
-
160,
Feb.
2014
.
[13]
E.
Ch
iodo, D.
L
aur
ia,
F.
Mottol
a
,
C.
Pis
ani,
"L
ifetime
ch
aract
er
izati
on
via l
ognor
m
al
di
stribu
ti
on
of
tra
nsform
ers
i
n
sm
art
grids:
Des
ign
opti
m
i
za
t
ion
,
"
Appl. Energy
,
vol.
177
,
pp
.
127
-
135,
2016
.
[14]
Le
vin
V.M.
,
"A
stat
isti
ca
l
m
e
tho
d
for
the
re
cognition
of
def
ec
ts
i
n
power
tra
nsfor
m
ers
during
the
i
r
m
ai
nte
nan
ce
as
of
state
,
"
Industrial Ene
rgy
, n
o.
8
,
pp
.
37
-
42
,
201
3
.
[15]
Le
vin
V.M
.
,
"T
he
principle
s
of
stat
isti
cal
id
entificat
ion
in
th
e
proble
m
s
of
diagnos
ing
and
m
onit
oring
o
il
-
fi
ll
e
d
equi
pm
ent
,
Energ
y
:
eff
i
cienc
y
,
rel
i
abi
l
ity
,
safe
t
y
,
"
proc
ee
d
ings
of
the
XX
Al
l
-
R
uss
ian
scie
nt
if
i
c
and
techni
cal,
C
onfe
renc
es
,
T
om
sk
Poly
te
ch
n
ic
Univ
ersity
,
T
om
sk:
Publishing
house
of
To
m
sk
Poly
te
chn
i
c
Univer
si
t
y
,
T.I
,
pp
.
98
-
103
,
201
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
3862
-
3868
3868
[16]
Ortiz
,
F.
,
Ferna
ndez
,
I.
,
Ort
iz
,
A.
,
Ren
edo,
C.
J
.
,
De
lga
do
,
F.
,
and
Ferna
nd
ez,
C.
,
"
He
al
th
Ind
exe
s
for
power
tra
nsform
ers:
A
ca
se
stud
y
,"
I
EEE
E
le
c
tr.
Insul
.
Mag
,
vol
.
32
,
pp
.
7
-
17
,
2016
.
[17]
IEC
Standard,
"
Minera
l
Oil
-
Fill
ed
Elec
tri
c
al
Eq
uipment
in
Serv
ic
e
-
Guid
ance
on
The
Inte
rpr
etation
of
Diss
olved
and
Free
Gases
Anal
y
sis
,
"
6059
9
,
IEC
Stand
ard
:
Gene
ve
,
Sw
itze
rla
nd,
2015.
[18]
Yaha
y
a,
M.S.
,
Azis,
N.
,
Ab
Kadir
,
M.Z
.
A.
,
Jasni,
J.
,
Hair
i,
M.H.
,
Ta
li
b
,
M.A.
,
"
Es
ti
m
at
ion
of
Tra
n
sform
ers
Hea
lt
h
Inde
x
base
d
on
t
he
Markov
Chain
,"
En
ergie
s
,
vol
.
10
,
1824
,
2017
.
[19]
Scat
iggi
o
,
F.
,
Po
m
pil
i,
M.
,
Ca
la
c
ara
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