TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 5932 ~ 5937
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.558
6
5932
Re
cei
v
ed
Jan
uary 6, 2014;
Re
vised Ma
rch 19, 2014; A
c
cepted Ap
ril 2, 2014
Estimation of Voltage Sag Loss Based on Blind Number
Theory
Fan Li-Gu
o
1,2
*, Zhang Yan-Xia
1
1
Ke
y
L
abor
ator
y of Smart Grid
of Ministr
y
of
Educ
ati
on, T
i
anjin U
n
iv
ersit
y
,
T
i
anjin 30
00
72
, China
2
Departme
n
t of Economic Ma
nag
ement, Nor
t
h Chin
a Electri
c
Po
w
e
r Un
iver
sit
y
, Bao
d
in
g 0
710
03, Ch
ina
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: flgflg20
10@
1
63.com
A
b
st
r
a
ct
Serio
u
s p
o
w
e
r qua
lity issu
es
and
hu
ge
econ
omic l
o
ss ca
n
be ca
use
d
by
voltag
e sa
g. It
’
s
hel
pf
u
l
for grid cor
por
ation to
esti
ma
te voltag
e sag
loss.
Volta
ge
sag a
nd i
n
flue
nce of
se
nsitiv
e eq
uip
m
ent a
r
e
ana
ly
z
e
d
in th
e pa
per. An
estimatio
n
method
of vo
ltag
e sag l
o
ss ba
sed o
n
bli
nd
nu
mb
er theory
i
s
prop
osed, w
h
ic
h takes t
he s
a
g
mag
n
itu
de
a
nd
durati
on
as
its main
char
a
c
teristic par
a
m
eters. F
i
rst Eu
clid
distanc
e an
d r
e
lativ
e
clos
e d
egre
e
betw
e
e
n
the sag
ma
gni
tude a
nd d
u
rat
i
on of vo
ltag
e
sag sa
mp
les
a
nd
thresho
l
d v
a
lu
es is c
a
lcu
l
ate
d
b
a
sed
on
T
O
PSIS. According t
o
rel
a
tive
similar
i
ty de
gre
e
，
prob
abl
e va
lu
e
,
credi
bil
i
ty an
d
me
an v
a
lu
e of
voltag
e sa
g l
o
ss are th
en
c
a
l
c
ulate
d
a
nd
inf
l
ue
nce
of unc
e
r
tainty factor c
an
be cons
ider
ed.
Examp
l
e a
nal
ysis show
s that loss estimati
o
n
meth
od is a feasi
b
le a
nd a
p
plica
b
l
e
for mo
st
sensitiv
e eq
uip
m
e
n
ts.
Ke
y
w
ords
:
vol
t
age sag, l
o
ss estimatio
n
, blin
d nu
mb
er, cred
ibil
ity
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
ti
on
With
comp
uter, ele
c
tro
n
ic equip
m
ent
s
and
spe
ed control device and so on
a
r
e
appli
ed
widely in bot
h indu
stry an
d daily life, th
e deman
d of power qu
ality more an
d m
o
re
con
c
ent
rate
voltage sa
g [1-2] etc tran
sient power q
u
a
lity. On
the basi
s
of forei
gn re
se
arch,
voltage sa
g h
a
s
been maj
o
r p
o
we
r quality issue
s
of impacting e
quip
m
ents
safe o
peratio
n. The
impact of voltage
sag o
n
users and so
ciety is be
comin
g
more
signifi
cant. Though t
he co
nne
ctio
n betwe
en po
wer
sou
r
ces and power con
s
u
m
ption
eq
uip
m
ents
i
s
not
bro
k
en
off by voltage sag, the times of
voltage sag i
s
far more th
an bla
c
kout.
Therfo
re
l
o
sses
cau
s
e
d
by
voltage
sag
are m
o
re severe
than by blackout in some
ca
se
s. Acco
rding to
re
sea
r
ch
s of foreig
n agen
cie
s
, 80 percent of the
cu
stome
r
co
mplaints are compl
a
ints caused
by vol
t
age sag in
develop
ed
co
untry. Econ
o
m
ic
loss [3] i
s
attributable
to vo
ltage
sag
co
sts ten
s
of
billi
ons of
dolla
rs every ye
ar i
n
ind
u
st
rial
a
n
d
comm
ercial fields.
Estimating
re
aso
nably lo
sse
s
of voltag
e sa
g
will h
e
lp for formi
ng con
s
en
su
s ab
out
seri
ou
sne
s
s
of voltage
sa
g bet
wee
n
p
o
we
r
system
and users,
a
pplying esse
ntial
refe
re
nce
to
deal
with volt
age
sa
g an
d
applying
de
ci
sion
ba
sis for po
wer gri
d
constructio
n
.
Curre
n
tly ma
n
y
method
s
of e
s
timating
lo
sse
s
of
voltag
e sag
are propo
sed
by scholars
at h
o
m
e a
nd
ab
ro
ad. It
inclu
d
e
s
thre
e cate
go
rie
s
: losse
s
e
s
tima
tion of voltag
e sa
g ba
se
d
on loa
d
sen
s
i
t
ive curve [4
-6],
losse
s
estim
a
tion of voltage sag ba
sed on proba
b
ilistic meth
o
d
[7-8], losses e
s
timatio
n
of
voltage sa
g b
a
se
d on qu
ali
t
y loss [9].
Voltage sa
g can
cau
s
e la
rge economi
c
loss and h
a
s
been maj
o
r p
o
we
r quality issue
s
.
It’s important
reali
s
tic me
a
n
ing for
study
ing volt
age sag losse
s
. An
method of e
s
timation voltage
sag
lo
sses fo
r alm
o
st
sen
s
itive equipm
e
n
ts b
a
sed
on
blind
nu
mbe
r
the
o
ry [1
0] i
s
p
r
e
s
e
n
ted i
n
the pape
r on
the basis of
summa
rizi
ng
current
re
se
arche
s
. The method could
effectively a
n
d
easily a
s
sess the econ
omi
c
loss cau
s
ed
by voltage sag.
2.
Caus
es of
Voltage Sag
and Voltage
Sag Tolerance Abilit
y
Cur
v
e
Voltage sag i
s
defined according to IEEE
standard: power
freque
ncy voltage effective
value dives t
o
0.9p.u.~0.
1
p.u. and re
co
vers n
o
rm
al value after short du
ration
of 10ms~1mi
n
at
some
wh
ere in power
syst
em. Whe
n
sh
ort-circui
t faul
ts, transfo
rm
ers
and
cap
a
c
itors switchi
ng,
swit
che
s
ma
nipulating a
n
d
large
capa
city induction
motors sta
r
ti
ng happ
en, a bran
ch
current
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Estim
a
tion of
Voltage Sag
Loss Based o
n
Blind Num
b
er The
o
ry (F
a
n
Li-Gu
o
)
5933
increa
se
s wit
h
in a sh
ort term an
d the
n
volt
age sa
g happ
en
s. Thereinto sh
ort-circuit fau
l
ts,
lightning
and
indu
ction
motors sta
r
ti
ng are maj
o
r cau
s
e
s
of
voltage sa
g. Gene
rally
th
e
influen
ce
s of voltage sag
on equipm
e
n
ts are
rela
t
ed to sen
s
itivity of equipments. The
more
sen
s
itive the
equip
m
ent
s
for voltage
sag a
r
e, t
he
bigge
r the
e
c
on
omic lo
ss is. Fo
r diffe
rent
equipm
ents t
he sen
s
itivity of use
r
s i
s
measured by
sele
cted m
o
st
se
nsitive e
quipme
n
ts d
u
r
ing
the manufa
c
turing p
r
o
c
e
s
s acco
rd
in
g to experie
ntial data. Then
ma
x
U
、
mi
n
U
、
ma
x
T
、
mi
n
T
are
defined
and
voltage tole
ra
n
c
e
are
a
[3] of
se
nsitive
u
s
e
r
s i
s
sh
owed i
n
Fig.1
acco
rding to volta
g
e
toleran
c
e
cu
rve of sensitiv
e equipm
ents.
Figure 1. Voltage Sag Tol
e
ran
c
e Ar
e
a
s
of Sensitive Equipme
n
ts
In Figure 1
D re
gion
rep
r
esents th
at equipm
ent
fa
ults
are not certai
nly
ca
u
s
ed by
voltage sag
a
nd E region
repre
s
e
n
ts th
a
t
equipm
ent
faults
are
cert
ainly ca
used
by voltage
sa
g.
A, B, C regi
ons rep
r
e
s
en
t uncertai
n
ty regi
on. Th
e
influences o
f
voltage sa
g on users and
equipm
ents
are u
n
certai
n
t
y in A, B,
C region.
T
h
erefo
r
e e
qui
pment fault
s
and p
r
od
uction
interruption
could be
cau
s
ed by voltage
sag an
d equi
pments
coul
d
not be influe
nce
d
obviou
s
l
y
.
3.
Loss Esti
mation Mod
e
l of Voltage
Sag Base
d on Blind Nu
mber Theory
3.1.
The Mea
n
ing of Blind
Number The
or
y
Un
certai
nty inclu
d
e
s
ra
n
domne
ss, fuzzi
ne
ss, u
n
a
s
certainty a
nd grayne
ss. Blind
informatio
n p
e
rform
s
a
bove two cla
s
sification o
r
mo
re uncertain in
formation
s
. Blind numb
e
r
can
be considered credi
bility f
unction [11-14] of interval
distri
but
ion.
If object perf
orm
s
uncertain,
actual val
ue
of obje
c
t is
n
o
t alway
s
poi
nt val
ue but i
n
terval value
in the nei
ghb
orho
od of
poi
nt
value. If interval value can
be rep
r
e
s
ent
ed by interva
l
numbe
r
x
and
0,
1
is credibility of
interval, blind
numbe
r is
compo
s
ed
by interval
di
strib
u
tion from a
numbe
r of
int
e
rval nu
mbe
r
i
x
and credi
bility
i
.
Suppo
se
A
I
is
interval g
r
ey
numb
e
r
set
:
i
A
I
and
0,
1
i
,
1,
2
,
,
in
.
f
x
is grey fun
c
tion of
A
I
:
,,
1
,
2
,
,
0,
ii
x
xi
n
fx
其他
(1)
Whe
r
e
1
ii
x
x
,
1
1
n
i
i
. Function
f
x
is a blin
d numbe
r.
i
is credibility of
i
x
.
is total credibi
lity of
f
x
.
n
is degree of
f
x
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 593
2 –
5937
5934
3.2.
Algorith
m
of Blind Number
Suppo
se blin
d
num
be
r
,,
1
,
2
,
,
0,
ii
x
xi
m
Af
x
其他
an
d
,,
1
,
2
,
,
0,
ij
y
yj
n
Bg
y
其他
, *
is algo
rithm a
r
ithmetic o
perators th
at rep
r
esent
＋，
－，
，
×÷
.
A new
mn
deg
re
e blind
numb
e
r is form
ed
by algorith
m
of
A
and
B
and p
r
e
s
ente
d
by
prob
able valu
e matrix
X
and credibility
matrix
Y
.
n
j
n
m
j
m
m
m
n
i
j
i
i
i
n
j
y
y
y
y
x
y
x
y
x
x
y
x
y
x
y
x
x
y
x
y
x
y
x
x
X
1
1
1
1
1
1
1
1
*
n
j
n
m
j
m
m
m
n
i
j
i
i
i
n
j
Y
1
1
1
1
1
1
1
1
*
(
2
)
The
sam
e
el
ements a
r
e
rega
rd
ed
as a valu
e a
n
d
proba
ble v
a
lue
are
a
r
range
d in
seq
uen
ce in
prob
able val
u
e matrix
X
. If
i
x
has
i
S
difference p
o
sition
s in
se
quen
ce in
probabl
e
value matrix
X
, the sum of
the element
s of
i
S
co
rrespo
nding p
o
sitio
n
s is
reg
a
rd
ed as
i
r
in
credibility matrix
Y
and se
qu
ence
12
,,
,
k
rr
r
is obtai
ned. The *
of blind num
ber
A
and blin
d
numbe
r
B
c
a
n
be
r
e
pr
es
e
n
t
ed
a
s
:
,,
1
,
2
,
,
0,
ii
rx
x
i
k
xA
B
其他
(3)
3.3.
Algorith
m
of Blind Number
Suppo
se
a
and
b
are re
al
nu
mbers and
ab
.
,
ab
is
sign
ed by
2
ab
cou
r
s
e
.
Mean value o
f
blind numbe
r
A
and blind nu
mber
B
are
cal
c
ulated a
s
follows.
其他
,
0
,
,
1
1
m
i
i
i
i
i
x
x
x
x
f
E
A
E
(4)
其他
,
0
,
,
1
1
n
j
j
j
j
j
y
y
x
y
g
E
B
E
(5)
其他
,
0
,
,
,
11
1
1
m
i
n
j
j
j
j
i
i
i
y
y
x
x
z
B
E
A
E
B
A
E
(6)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Estim
a
tion of
Voltage Sag
Loss Based o
n
Blind Num
b
er The
o
ry (F
a
n
Li-Gu
o
)
5935
3.4.
Loss Estimation Mod
e
l
Sensitivity of
equipm
ents i
s
influen
ce
d lots of
eleme
n
t
s that includ
e mounting lo
cation
s,
stru
cture ch
a
r
acte
ri
stics, operat
in
g envi
r
onm
ents, ru
nning
states,
load level an
d sup
p
ly side
in
the circu
m
st
ance of voltage
sag. Th
ese
un
cert
ai
n inform
ation
s
that pe
rform ran
domn
e
ss,
fuzzi
ne
ss, u
n
a
scertai
n
ty a
nd g
r
ayne
ss sh
ow
ch
ar
a
c
teri
stic
of b
lind info
rmati
ons. T
h
e
r
efo
r
e
voltage sa
g tolera
nce curv
es of sen
s
itive equip
m
ent
s appea
r un
ce
rtainty. On the other h
and
the
influen
ce
s of voltage sag
on se
nsitive equipm
ents
appe
ar un
ce
rtainty. Uncert
ain con
d
ition
of
equipm
ent fa
ults o
r
p
r
od
uction interrupti
on could
be i
ndicated by
b
lind nu
mbe
r
t
heory. Th
erefore
the severity
of
voltage sa
g could
be
reflecte
d
by
blind
numb
e
r. Voltage
sa
g lo
ss could
be
estimated by
cal
c
ulatin
g mean value of
blind num
ber.
(1) Stand
ardi
zing d
e
ci
sion
matrix
Firstly, stan
d
a
rdi
z
ing
de
cision m
a
trix
ij
mn
Xx
and a
c
hievin
g a stan
dardi
zed m
a
trix
ij
mn
Yy
,
2
1
1,
2
,
,
;
1,
2
,
,
ij
ij
m
ij
i
x
yi
m
j
n
x
(7)
(2)
Cal
c
ulatin
g weig
hted st
anda
rdi
z
ed m
a
trix
ij
j
i
j
mn
mn
Uu
y
(8)
(3)
Determini
ng Ideal Solut
i
on and
Neg
a
t
ive Ideal Solution
n
u
j
u
u
u
J
j
j
u
J
j
j
u
U
m
i
i
m
i
i
0
0
0
0
1
1
0
,
,
,
2
,
1
min
,
max
(9)
n
u
j
u
u
u
J
j
j
u
J
j
j
u
U
m
i
i
m
i
i
0
0
0
0
1
1
0
,
,
,
2
,
1
max
,
min
(10
)
(4) Cal
c
ulatin
g
Dista
n
ce
m
i
j
u
j
u
D
n
j
i
i
,
,
2
,
1
,
1
2
0
(11)
m
i
j
u
j
u
D
n
j
i
i
,
,
2
,
1
,
1
2
0
(12)
(5)
Cal
c
ulatin
g relative simi
larity degree
of sample
s
*
,1
,
2
,
,
i
i
ii
D
Ci
m
DD
(13)
(6) E
s
timatin
g
prob
able
value and
credibilit
y of voltage sag l
o
sse
s
by produ
ction
interruption cost.
*
1
iA
V
L
CC
(14)
Whe
r
e
i
L
is pro
bable value o
f
voltage sag
losses,
A
V
C
is average valu
e
of produ
ctio
n
interruption cost,
*
C
is relativ
e
simila
rity degree of voltag
e sag.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 593
2 –
5937
5936
(7)
Cal
c
ulatin
g mean value
of blind num
ber an
d Esti
mating losse
s
of voltage sa
g ca
se
s.
i
LL
(15)
Whe
r
e
L
is me
an value
of bl
ind num
be
r o
f
voltage sa
g
losse
s
,
is
cre
d
ibility corre
s
pondi
ng to
prob
able valu
e of voltage sag losse
s
.
4.
Cas
e
Stud
y
A sensitive u
s
er i
s
analy
z
es a
s
ca
se st
udy
in the paper. The sen
s
itive use
r
is subj
ecte
d
to many voltage
sag
duri
ng a
statistics pe
riod. T
h
resh
old value
of cha
r
a
c
teri
stic p
a
ra
mete
r of
voltage
tole
rance curve
of
the se
n
s
iti
v
e users a
r
e
achieved
a
c
co
rding
to hi
stori
c
al
data
of
voltage
sag:
0.8
.
.
ma
x
Up
u
,
mi
n
0.3
.
.
Up
u
,
30
ma
x
Ts
,
mi
n
0.1
Ts
,
5.262
t
e
n
t
housa
n
d
y
ua
n
AV
C
. The
weig
ht of sa
g ma
gnit
ude a
nd
dura
t
ion is
re
sp
ectively
0.
8
0
.
2
,
0.
5
0
.
5
and
0.
2
0
.
8
.
Suppo
sing th
at the use
r
is su
bje
c
ted to
four time
s voltage sag
but not pro
ductio
n
interruption. Cha
r
a
c
teri
stic
param
eters of four times
volt
age sa
g a
r
e sh
own as
Table 1.
Table 1. Use
r
s’ Ch
ara
c
te
ristic Paramete
r of Voltage Sag
Case
sag magnitude
duration /s
0.60 8
0.45 25
0.28 0.2
0.80 30
Proba
ble val
ue, credibility
and mea
n
value of
blin
d numbe
r of vo
ltage sa
g lo
sse
s
are
estimated a
n
d
sho
w
e
d
as
Table 2.
Table 2. The
Possi
ble Valu
e, Credi
bility and Mea
n
Va
lue of Blind Numbe
r
of Voltage Sag
Losse
s
case probable
value
credibility
mean value of
blind number
1
2.005
0.3
1.676
1.589
0.5
1.400
0.2
2
3.789
0.3
4.096
4.173
0.5
4.362
0.2
3
3.731
0.3
2.260
2.000
0.5
0.705
0.2
4
1.573
0.3
3.046
3.315
0.5
4.583
0.2
Acco
rdi
ng to results of Ta
ble 2, prob
ab
le va
lue of blind numb
e
r of
the first time and the
se
con
d
time
vary slig
htly, but proba
ble
value of
bli
n
d num
ber of
the third
time
and th
e fou
r
th
time vary ob
viously. Above re
sult illust
rate w
hen
ch
ara
c
teri
stic p
a
ram
e
ter of
voltage sa
g
are
clo
s
e to
or
re
ach l
o
wer limi
t
of threshold
value in volt
age
sag
ca
se
, it contrib
u
te
s to voltag
e sag
losse
s
bigg
er. Meanwhile the influen
ce
of the se
con
d
time voltage sag o
n
u
s
ers
is mo
st se
rio
u
s.
The influen
ce
of the third a
nd fourth time voltage
sag
on users is l
e
ss se
riou
s. The influen
ce
of
the first time voltage sag o
n
use
r
s is m
o
st s
light. Th
ough u
s
e
r
s’ p
r
odu
ction inte
rru
ption are not
cau
s
e
d
by fo
ur time
s volta
ge
sag,
accu
mulative
e
c
o
nomic lo
sses
are
hug
e a
n
d
re
ach to
11.
078
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Estim
a
tion of
Voltage Sag
Loss Based o
n
Blind Num
b
er The
o
ry (F
a
n
Li-Gu
o
)
5937
ten-thou
sa
nd
-yuan
and
la
rge
r
tha
n
lo
sses of
two
times i
n
terruption.
Th
erefore ben
efits
of
improve p
o
wer quality for
use
r
s a
r
e o
b
vious.
5.
Conclu
sion
The meth
od
of estimatio
n
of voltage sa
g loss b
a
sed
on blin
d num
ber th
eory i
s
prop
osed
in the pap
er.
Sag magnitu
de and
duration are co
nsi
d
ered
as m
a
in
cha
r
a
c
teri
stic pa
ramete
rs by
usin
g the vol
t
age sag tol
e
ran
c
e
ability of sen
s
itive
equipm
ent. The ide
a
of
blind nu
mbe
r
is
introdu
ce
d in
voltage
sag
ca
se to
cal
c
ulate
voltag
e sag lo
ss.
Acco
rdi
ng to
pro
babl
e va
lue,
cre
d
ibility of blind numb
e
r, mean value o
f
blind
numbe
r rep
r
e
s
entin
g econ
omi
c
losse
s
of voltage
sag a
r
e calcu
l
ated. Example result sho
w
s that t
he esti
mation metho
d
is feasi
b
le a
nd universal.
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hang Bi
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