Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 3
,
Ju
n
e
201
6, p
p
. 1
294
~ 13
04
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.1
014
7
1
294
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
An Adaptive Neuro-Fuzzy Inf
erence System in Assessment of
Technical L
o
ss
es
in Di
stribution Networks
D
r
aga
n M
l
aki
ć
1
, Srete
Nikol
ovs
ki
2
,
Goran Knež
evi
ć
2
1
Ele
c
tri
c
power
com
p
an
y HZ-HB Inc.
M
o
s
t
ar
, N
ovi Tr
avnik
,
Bos
n
ia
and Her
zego
v
ina
2
Department of Power
Engineer
i
ng,
F
acu
lt
y of El
ectr
i
ca
l E
ngineer
ing, Osijek, Cro
a
tia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 10, 2015
Rev
i
sed
Feb
17
, 20
16
Accepted
Feb 27, 2016
The losses in distribution networks ha
ve alwa
y
s
been ke
y elem
ents
in
predicting
investment, plannin
g
work,
evalu
a
ting
the eff
i
ciency
an
d
effectiven
ess of a network.
This
pape
r elaborates on the use of fuzzy
logic
s
y
s
t
em
s
in an
al
yz
ing th
e d
a
ta
f
r
om
a particular
substation
area predicting
losses in the lo
w voltage n
e
tw
ork. The d
a
t
a
c
o
lle
cted from
th
e fie
l
d were
obtain
e
d from
the Autom
a
tic
Meter Re
ading
(AMR) and Autom
a
tic Met
e
r
Ma
na
ge
me
nt (A
MM) sy
ste
m
s.
The
AMR
s
y
st
e
m
is full
y im
pl
em
ented
in
EPHZHB and integra
t
ed within t
h
e netw
ork infrastructure at seco
ndar
y
level
substations 35/1
0kV and 10(20
)/0.4
kV. The
AMM sy
ste
m
is pa
rtially
im
plem
ented in
the are
a
s
of ele
c
tri
cal
energ
y
cons
um
ers
;
p
r
ecis
e
l
y
, i
n
accoun
ting m
e
te
rs. Dail
y inform
ation ga
ther
ed fr
om
thes
e s
y
s
t
em
s
is
of great
value for the calculation of techn
i
cal
and non-technical losses. Fu
zzy
logic in
com
b
ination
wi
th the
Artif
ici
a
l Neura
l
Netw
orks im
plem
ent
e
d vi
a th
e
Adaptive Neuro
-
F
u
zz
y
Inf
e
ren
c
e S
y
s
t
em
(ANF
IS
) is
us
ed. Finall
y,
F
I
S
S
ugeno, F
I
S
M
a
m
d
ani and
ANF
IS
are
com
p
ared with
the
m
e
as
ured da
t
a
from
s
m
art m
e
te
rs
and pr
es
ented
with
th
eir errors and
graphs
.
Keyword:
Ada
p
tive ne
uro-fuzzy
i
n
fe
rence
syste
m
Artificial in
tellig
en
ce
Lv
d
i
str
i
bu
tion
n
e
twor
k
R
e
mo
t
e
me
t
e
r
r
e
a
d
in
g
Technical loss
es
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Srete Nikolovs
ki,
Depa
rt
m
e
nt
of Po
wer En
gi
nee
r
i
n
g,
Faculty of Elec
trical Engin
eering, J
o
sip
Juraj Strossm
ay
er Un
i
v
ersity of
Osij
ek
,
K
.
Trp
i
mir
a
2B, 310
00
O
s
ij
ek
, C
r
o
a
tia.
Em
a
il: srete.n
i
k
o
l
o
v
sk
i@et
fos.hr
1.
INTRODUCTION
Und
e
rstand
ing o
f
losses in
an
electricity n
e
twork
has al
way
s
bee
n
ess
e
nt
i
a
l
due t
o
l
o
sses
di
rect
l
y
resu
lting
i
n
the in
crease
o
f
an
electricity p
r
ice and
in
d
i
rectly
en
erg
y
efficien
cy [1
]-[2
]
. Electricity
lo
sses
occur in trans
f
orm
e
rs, powe
r lines,
loads, reactors, ca
pacitors and ot
her network c
o
mpone
n
ts [3]-[4]. For
t
h
ei
r asses
s
m
e
nt
, ei
t
h
e
r
a
n
al
y
t
i
cal
com
put
at
ion
o
r
m
easure
m
ent
m
e
t
hods
are
used
[
5
]
.
A
n
al
y
t
i
cal
com
p
ut
i
n
g
assum
e
s t
h
e kn
owl
e
dge
o
f
t
h
e
equi
val
e
nt
sc
h
e
m
e
for
vari
ou
s net
w
or
k el
e
m
ent
s
;
t
h
ei
r ph
y
s
i
cal
pro
p
ert
i
es and
te
m
p
o
r
al ch
ang
e
s
o
f
electrical q
u
a
n
tities (cu
r
ren
t
s, vo
ltages) in
curren
t
facilities, wh
ile m
easu
r
in
g
m
e
th
od
s
r
e
qu
ir
e m
easu
r
in
g
equ
i
p
m
en
t,
its in
stallatio
n
(
calib
r
a
tion
,
co
nf
igu
r
ation)
an
d r
e
g
u
l
ar
r
e
adin
g
[
6
]-[7
].
In
o
r
d
e
r
to correctly predict the losse
s for
fu
ture
fa
cilities within a distribution
ne
twork, it is necessa
ry to
use bot
h
m
e
thods a
n
d t
h
eir indi
vidual adva
nta
g
es. As with
a
n
y approxim
a
tion,
am
biguities and uncertai
n
ties are
pos
si
bl
e;
henc
e, er
ro
rs
m
a
y
occu
r.
H
o
wev
e
r,
A
N
FI
S
has
bee
n
use
d
i
n
m
a
ny
en
gi
neer
i
ng a
p
pl
i
cat
i
o
n
s
a
n
d
esp
ecially in
distrib
u
tion
and sm
art n
e
tw
ork
s
for m
o
d
e
llin
g electricity d
e
m
a
n
d
[8
]-[9], fau
lt
d
i
agnosis [1
0
]
and
fa
ul
t
l
o
cat
i
on
[1
1]
.
Very
few
pa
pers
de
al
wi
t
h
di
st
ri
b
u
t
i
o
n
l
o
sses e
s
t
i
m
a
t
i
on usi
n
g
AN
FI
S [
12]
.
In t
h
i
s
p
a
p
e
r,
fu
zzy l
o
g
i
c
will b
e
used
in
o
r
d
e
r t
o
im
p
l
e
m
en
t ANFIS
for com
p
u
t
atio
n
o
f
l
o
sses in
a l
o
w v
o
ltag
e
d
i
str
i
bu
tio
n netw
or
k.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
An A
d
apt
i
ve N
e
ur
o F
u
zzy
I
n
f
e
rence
Syst
em
i
n
Assess
me
nt
of
Tec
hni
c
a
l
L
o
sses i
n
.
.
.
.
(
D
r
a
g
a
n
Ml
aki
c
)
1
295
2.
LOSSES IN L
V
DIST
RIBUTION
NETWORK
From
t
h
e pers
pect
i
v
e o
f
a n
e
t
w
o
r
k
ope
rat
o
r
,
l
o
sses are
inevitable costs of the tra
n
sm
ission of
electrical en
erg
y
th
roug
h
a distrib
u
tion
n
e
twork causing
ad
d
ition
a
l lo
ad
s in
th
e power
syste
m
. Gen
e
ral
l
y, th
e
t
e
rm
l
o
sses
m
e
an t
h
e di
f
f
ere
n
ce bet
w
ee
n t
h
e
am
ount
o
f
el
ect
ri
cal
energy
t
h
at
has ent
e
red
i
n
t
o
t
h
e di
st
ri
but
i
o
n
sy
st
em
and t
h
e
m
easured a
m
ount
of el
ec
t
r
i
cal
energy
whi
c
h i
s
del
i
v
ered t
o
c
u
st
o
m
ers. Losse
s can be
cat
ego
r
i
zed as
t
echni
cal
an
d
no
n-t
e
c
hni
cal
l
o
sses [
1
]
.
T
echni
cal
l
o
sse
s i
n
t
h
e com
pone
nt
s o
f
t
h
e
po
we
r
syste
m
can be
categorized as
voltage
-depe
n
dent l
o
sses
and cu
rren
t-d
e
p
e
nd
en
t l
o
sses. The latter are th
e
resu
lts
of t
h
e
fl
o
w
of
cur
r
ent
t
h
r
o
ug
h t
h
e
com
p
o
n
e
n
t
s
o
f
t
h
e
po
we
r sy
st
em
and d
e
pen
d
o
n
t
h
e
l
e
vel
o
f
net
w
or
k
usa
g
e
,
i
.
e. o
n
t
h
e a
m
ount
of
t
r
a
n
sfer
red
ene
r
gy
or
t
h
e
pre
v
i
o
us c
u
r
r
ent
.
V
o
l
t
a
ge-
d
e
p
en
de
nt
l
o
sses
,
whi
c
h ar
e
co
nstan
tly presen
t in th
e
n
e
t
w
ork, ar
e t
h
e
results of t
h
e
maintenance
of th
e
electricity syste
m
in a
constant
state o
f
o
p
e
ratio
n
a
l read
in
ess to
supp
ly cu
sto
m
ers with
electricity [2]. These incl
ude l
o
sses i
n
tra
n
sform
e
r
cores
,
dialectical losses of ca
bles
and capac
itor ba
nks. Als
o
, technical lo
s
s
es de
pen
d
o
n
t
h
e l
e
ngt
h an
d
cros
s
section of
the cables. Non-technical
l
o
sses are otherw
ise
k
nown as co
mmercial lo
sses
since their c
o
s
t
s are
soci
al
i
zed i
n
st
ead o
f
di
rect
l
y
char
gi
n
g
net
w
or
k o
p
e
r
at
or
s and s
u
ppl
i
e
rs
[4
]
,
[5]
.
U
n
a
u
t
h
or
i
zed co
nsum
pt
i
on
o
f
electricity refers to th
e
un
au
t
h
orized in
terv
en
tio
n of th
e meters and
illegal co
nn
ection
s
. It is very
d
i
ffi
cu
lt to
est
a
bl
i
s
h t
h
e
exact
am
ount
of s
u
c
h
l
o
ss
es si
nce m
o
st
of t
h
em
are pr
o
b
abl
y
u
n
d
et
ect
ed.
Unm
easure
d
con
s
um
pt
i
on i
s
us
ual
l
y
associ
at
ed wi
t
h
p
u
b
l
i
c
l
i
ght
i
n
g. T
h
e
cal
cul
a
t
i
on
pr
o
cedu
r
e ca
n
oft
e
n
be i
n
acc
urat
e
d
u
e
t
o
:
m
easurem
ent
er
r
o
rs,
c
o
l
l
ect
i
on a
n
d
pr
oc
essi
ng
o
f
da
ta read
ing
s
, wh
i
c
h
are
related
to
th
e rest
of
n
on-
technical losse
s. A calculation m
e
t
hod
de
pends
on t
h
e availability of
m
easured
dat
a
. In m
o
st count
ries,
technical loss
es are calc
u
lated “ex-post”
by the
volta
g
e
lev
e
ls
[5
],[7
]. At
vo
ltag
e
lev
e
ls,
wh
ere each
measurem
ent site has a continuous m
easure
m
ent, losse
s are calculated hourly base
d
on t
h
e obtaine
d
rea
d
ings.
In m
e
di
um
and l
o
w
vol
t
a
ge net
w
or
ks, t
h
e
m
a
jori
t
y
of m
easurem
ent
po
i
n
t
s
are eq
ui
p
p
e
d wi
t
h
c
o
n
v
e
n
t
i
ona
l
measuring de
vices that are periodically
read. In suc
h
case
s
, technical los
s
es i
n
po
wer l
i
nes an
d t
r
an
sf
orm
e
rs
can
be cal
cul
a
t
e
d
by
usi
n
g
va
ri
o
u
s m
a
t
h
em
at
i
cal
m
e
t
hod
s.
It
use
d
t
o
b
e
c
o
m
m
e
rci
a
l
l
y
used;
h
o
w
eve
r
,
i
t
has
not bee
n
use
d
s
i
nce
the appearance of
di
gital
sm
art
meters
.
3.
AUTOMATIC METER READING
AND ADVA
NCE
METER MANAGEME
NT
SYSTE
M
Pri
o
r t
o
t
h
e
A
M
R
and
AM
M
sy
st
em
s, v
a
ri
o
u
s c
o
m
p
l
e
x m
e
t
hods
of
app
r
oxi
m
a
t
i
on o
f
l
o
sses i
n
d
i
stribu
tio
n
n
e
twork
s
were
used
. Nowad
a
y
s
, calcu
lating
i
s
b
a
sed on
raw
d
a
ta
with
vo
ltag
e
lev
e
ls t
h
at are
tak
e
n
in
to
acco
u
n
t
in
th
e calcu
latio
n
of losses. Th
e AM
R an
d
AMM syste
m
s are c
o
n
s
tan
tly activ
e an
d
ad
ap
tab
l
e to
en
d-u
s
ers. A
v
e
ry i
m
p
o
r
tan
t
ch
aracteristic
of th
ese two
syst
e
m
s is co
n
tin
uity in
th
e activ
ities o
f
readi
ng a
n
d t
h
ei
r wi
t
h
dra
w
al
fr
om
a dat
a
ba
se. De
pe
ndi
ng
on
t
h
e
need
s o
f
us
ers
,
i
n
t
h
i
s
case t
h
e
di
st
ri
b
u
t
i
o
n
of electrical energy, m
e
ters that are
placed in the LV fee
d
e
r
s can serve as
readouts acquired in di
ffe
rent
tim
e
-
i
n
t
e
rval
s
(m
i
nut
e, ho
u
r
, day
)
.
For e
x
am
pl
e, t
h
e co
ns
um
pt
i
on i
n
k
W
h f
o
r a
peri
od
, w
h
i
c
h
m
a
y
not
be l
e
ss t
h
an
15 m
i
nut
es (
w
i
t
h
t
h
e pa
ram
e
ters f
o
r t
h
e m
e
ter can
go
u
p
t
o
1
m
i
n
.
), wh
ich is su
fficien
t
to calcu
late th
e ho
urly
lo
sses on
so
m
e
p
a
rt of th
e n
e
t
w
ork, can
b
e
easily calcu
late
d
.
Th
is
p
a
p
e
r
d
o
e
s no
t tak
e
in
to
acco
u
n
t
voltag
e
l
e
vel
s
ab
ove
0.
4 k
V
beca
use
of t
h
e com
p
l
e
x
i
t
y
of f
u
zzy
m
odel
s
. Th
e dat
a
t
o
be
rea
d
ev
ery
day
i
n
t
h
e
AM
R
syste
m
are on a server locate
d
in th
e Di
st
ri
but
i
o
n EP H
Z
-
H
B
bui
l
d
i
ng i
n
M
o
st
ar [1
3]
. The dat
a
can b
e
rea
d
out
wi
t
h
a
del
a
y
of
24
h
o
u
rs
[1
3]
. T
h
e
dat
a
fr
om
t
h
e A
M
M
sy
st
em
ar
e o
n
t
h
e sam
e
serv
er
un
de
r
anot
her
d
o
m
ain
so th
ey are sep
a
rated b
y
fun
c
tion
a
lity. Th
e
LV d
i
strib
u
tion
area
ex
em
p
lified
in th
is
p
a
p
e
r is co
v
e
red
fr
om
t
h
e subst
a
t
i
on t
o
t
h
e en
d cu
st
om
ers w
i
t
h
sm
art
m
e
t
e
rs f
o
r m
easuri
ng el
ect
ri
ci
t
y
cons
um
pt
i
on. T
h
e dat
a
u
s
ed
in
th
is p
a
p
e
r are tak
e
n
directly fro
m
th
e serv
er, wh
ich read
s th
e m
e
te
rs in
stalled
in
th
e sub
s
tation
an
d
t
h
e
en
d
cu
st
o
m
ers with
ou
t an
y
m
o
d
i
ficatio
n
of th
e
d
a
ta. The
situ
atio
n
p
r
esen
ted
i
n
th
is
p
a
p
e
r is illu
strated
in
Fi
gu
re 1
.
As c
a
n be see
n
, t
h
e ener
gy
fl
o
w
fr
om
t
h
e subst
a
t
i
on t
o
t
h
e e
n
d cust
om
ers i
s
com
p
l
e
m
e
nt
ed wi
t
h
inevitable tec
h
nical losses
of
electrical
ener
gy
. T
h
ere
f
ore,
i
f
o
n
e i
nvest
s
i
n
a
ne
w L
V
ne
t
w
o
r
k
o
r
m
a
i
n
tai
n
t
h
e
ex
istin
g on
e, on
e
n
eeds to kno
w th
e ex
ten
t
of th
ese lo
sses.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
9
4
– 13
04
1
296
Fi
gu
re
1.
G
r
ap
hi
cal
p
r
esent
a
t
i
on
o
f
t
h
e L
o
w
Vol
t
a
ge
net
w
o
r
k
The
prese
n
t
e
d
l
o
w
vol
t
a
ge ar
ea co
nsi
s
t
s
o
f
di
ffe
re
nt
co
nd
uct
o
rs wi
t
h
t
h
e
m
o
st
prese
n
t
one
s bei
ng
7
0
mm
2
, 50 m
m
2
and
3
5
m
m
2
.
Each sm
art
m
e
t
e
r i
s
i
n
st
al
l
e
d o
n
pol
e
posi
t
i
ons
just
i
n
fr
ont
of a c
o
n
s
u
m
er’s
object such as
a house,
works
h
op, etc.
so
o
t
h
e
r
co
ndu
ctor
s s
m
aller
th
an
35
mm
2
are connected a
f
ter observe
d
m
e
t
e
rs and t
h
ey
do n
o
t
i
n
fl
uence l
o
sses.
A si
n
g
l
e
l
i
n
e di
ag
ram
for a di
st
ri
b
u
t
i
on
LV area
, pre
v
i
ousl
y
di
scuss
e
d
,
i
s
pr
esent
e
d
i
n
Fi
g
u
r
e 2.
Fi
gu
re
2.
Si
n
g
l
e
l
i
n
e di
a
g
ram
of
t
h
e
di
st
ri
b
u
t
i
on
LV
net
w
o
r
k a
r
ea
Th
e coun
ters
with
th
eir respectiv
e characte
r
istics used in t
h
e AMR and
AMM syste
m
s
are defi
ned i
n
t
h
e st
an
dar
d
s I
E
C
62
0
5
3
-
22 a
nd
IEC
62
0
5
3
-
23
, as
prese
n
t
e
d i
n
Ta
bl
e 2
.
T
h
e t
a
bl
e s
h
o
w
s
st
anda
rd
s o
f
l
o
sses
in electrical energy m
easurement; ther
efo
r
e, th
is m
i
stak
e
n
eeds to
b
e
tak
e
n
i
n
to
con
s
id
eration
during
d
a
t
a
acqui
ri
n
g
. T
h
e
m
e
t
e
rs used t
o
m
easure t
h
e el
ect
ri
ci
t
y
consu
m
pti
on by
c
u
st
om
ers are m
o
st
l
y
200
9 ge
ne
r
a
t
i
on;
yet, they are gradually being
replaced
by a new ge
neration. More
detailed
characte
r
istics of the m
e
ters are not
listed
.
Also
, th
e co
mm
u
n
i
catio
n
tech
no
logies u
s
ed
fo
r tran
sm
issio
n
o
f
d
a
ta fro
m
rem
o
te
sites wh
ere th
e
meters are inst
alled are
not el
aborated on i
n
this pa
per.
Table
2. C
h
ara
c
teristics accuracy
Measuring accura
c
y
Speed
(rp
m
)
Active ener
gy accor
ding to I
E
C 62053-
22
Class 1/Class 2
Reactive ener
gy accor
d
ing to I
E
C 62053-
23
Class 2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
An A
d
apt
i
ve N
e
ur
o F
u
zzy
I
n
f
e
rence
Syst
em
i
n
Assess
me
nt
of
Tec
hni
c
a
l
L
o
sses i
n
.
.
.
.
(
D
r
a
g
a
n
Ml
aki
c
)
1
297
4.
F
U
ZZY
L
O
G
I
C
Fuzzy logic is
a conce
p
t m
u
ch m
o
re
natural than
one
m
i
g
h
t
t
h
i
n
k
.
R
ece
nt
l
y
, a
num
ber
o
f
di
ffe
re
nt
appl
i
cat
i
o
ns
of
f
u
zzy
l
o
gi
c h
a
ve si
gni
fi
ca
nt
l
y
i
n
crease
d
.
A
ppl
i
cat
i
o
ns
ran
g
e
fr
om
cons
u
m
er pr
o
duct
s
s
u
ch
as
ca
m
e
ras, camcorders,
was
h
ing m
achines
and m
i
crow
aves t
o
c
ont
r
o
l
i
n
du
st
ri
al processes
,
m
e
dical
i
n
st
rum
e
nt
at
i
on,
deci
si
o
n
s
u
pp
o
r
t
sy
st
em
s an
d a c
h
oi
ce of
p
o
r
t
f
ol
i
o
[8]
.
Fuzzy
l
o
g
i
c has t
w
o
di
ffe
rent
m
eani
ngs
. H
o
weve
r, i
n
a
br
o
a
der se
nse,
f
u
z
z
y
l
ogi
c i
s
alm
o
st
sy
n
ony
m
o
u
s
wi
t
h
t
h
e t
h
e
o
ry
of
fuzzy
set
s
- t
h
e
th
eory related
to
th
e class o
f
o
b
j
ects with
in
d
i
stin
ct bo
rd
ers in
wh
ich
the
m
e
m
b
ersh
ip is d
e
ter
m
in
ed b
y
a
degree.
The
r
efore
,
fuzzy logic in
th
e n
a
rro
w
sen
s
e is a b
r
an
ch
of the fu
zzy log
i
c. On
e relativ
el
y n
e
w
app
r
oach
t
o
m
a
nagem
e
nt
i
s
t
h
e a
pp
lication
o
f
a fu
zzy co
ntro
ller.
Fu
zzy
co
n
t
ro
llers are
syste
m
s th
at activ
ely
reg
u
l
a
t
e
dy
na
m
i
c envi
ro
nm
ent
[
9
]
.
A
pr
ot
o
t
y
p
i
cal
exam
ple i
s
a t
e
m
p
erat
ure c
o
nt
rol
l
e
r
on t
h
e i
n
put
s
f
r
om
a
t
e
m
p
erat
ure se
nso
r
.
It
set
s
t
h
e engi
n
e
t
e
m
p
erat
ure c
o
nt
rol
devi
ces t
o
co
ol
or
warm
envi
r
onm
ent
[8]
,
[9]
.
T
h
e
g
e
n
e
ral sch
e
me of a
fu
zzy con
t
ro
ller is illu
st
rated
i
n
Fi
g
u
re
3
.
Fi
gu
re
3.
The
gene
ral
sc
hem
e
o
f
a
fuzzy
re
gul
at
o
r
Fu
zzy r
easo
n
i
n
g
is th
e pr
o
c
ess o
f
fo
r
m
u
l
atin
g
a sp
ecif
i
c
m
a
p
p
i
n
g
input to
an
o
u
t
pu
t u
s
ing
fu
zzy
l
ogi
c. M
a
p
p
i
n
g t
h
e
n
p
r
o
v
i
d
e
s
a
basi
s
used
t
o
m
a
ke a de
ci
si
on
o
r
t
o
n
o
t
i
ce pat
t
e
r
n
s.
The
p
r
o
g
ram
,
w
h
i
c
h
wi
l
l
be
used
t
o
c
r
e
a
t
e
a fuzzy
sy
st
em
, i
s
M
a
t
L
ab
20
1
0
a [
1
4]
. The
part
of
M
a
t
L
ab t
o
be
use
d
i
n
t
h
i
s
pa
per i
s
a
to
o
l
box
con
s
istin
g
of th
e ANFIS Ed
itor
wh
ich
is u
s
ed
to
train
and
test th
e fu
zzy syste
m
b
y
d
e
fau
lt ru
les
GUIDE – a se
t of tools that
are use
d
to c
r
e
a
te inte
rfaces
and t
h
e M-file
editor
use
d
to write progra
mming
code
s. T
h
e t
w
o t
y
pes
of
fuzz
y
reaso
n
i
n
g ca
n be ca
rri
e
d
ou
t
wi
t
h
i
n
t
h
e t
o
ol
b
ox
- M
a
m
d
ani
an
d S
uge
n
o
t
y
pe.
Th
ese t
w
o typ
e
s of
th
e r
eason
in
g syst
em
differ in t
h
e
way t
h
ey set out
res
u
lts. T
h
e
proce
ss of
fuzzy
rea
s
oni
ng
con
s
i
s
t
s
o
f
fi
v
e
part
s:
fuzzi
fi
cat
i
on
of i
n
p
u
t
vari
a
b
l
e
s, t
h
e
use
of
fu
zzy
o
p
erat
ors
(
A
N
D
or
OR
)
,
i
m
pl
icat
i
ons
of t
h
e prem
is
e in conse
q
ue
nce, t
h
e aggre
g
ation eff
ect in acc
ordance
with the
rules and de
fuzzification.
ANFIS
stands
for the a
d
a
p
tive net
w
ork
fuzzy reas
onin
g system
or se
m
a
ntically eq
ual, a
d
aptive
fuzz
y
reaso
n
i
n
g ne
ur
o-sy
st
em
.
4.
1.
Devel
o
pme
n
t
of the
ANFI
S
model
Th
e
b
a
sic
ANFIS m
o
d
e
l, as
sh
own
in Figure
4
,
is illu
strated
in
fiv
e
b
l
ock
s
o
f
learn
i
ng stag
es
[1
1
]
[1
2]
. T
h
i
s
m
odel
i
s
an exam
pl
e of t
h
e A
N
F
I
S de
vel
o
pm
ent
m
odel
f
o
r a
p
o
w
er
rest
o
r
at
i
o
n
pl
an t
h
at
co
nsi
s
t
s
of
t
w
o i
n
p
u
t
s
a
n
d
t
w
o m
e
m
b
ersh
i
p
f
u
nct
i
ons
.
Fi
gu
re
4.
A
ba
si
c AN
FI
S m
odel
wi
t
h
t
w
o i
n
put
dat
a
a
n
d
t
w
o M
F
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
9
4
– 13
04
1
298
So,
t
h
ere are four fuzzy
‘IF-T
H
EN’
ru
les to
sh
ow th
e relatio
n
s
h
i
p
b
e
tw
een
fau
lts lo
catio
n
s
in
‘x, y
’
coordinates. T
h
ere are
five s
t
ages
o
f
th
e
ANFIS op
eration
a
l p
r
o
cess that
in
clu
d
e
fu
zzificatio
n
,
‘IF-THEN’
rul
e
s,
n
o
r
m
a
li
zat
i
on,
de
fuzzi
fi
cat
i
on a
n
d
n
e
u
r
o
n
a
d
di
t
i
on.
As illustrate
d i
n
Fi
gure
4, the
fuzzification stage is
l
o
cated at the
first
stage
of recei
ving the input
sig
n
a
l. Its
fun
c
tio
n
is t
o
co
nv
ert th
e i
n
pu
t sign
al to
a fu
zzy sig
n
a
l
wh
ere t
h
e sign
al is yield
e
d v
i
a t
h
e inpu
t sid
e
of
t
h
e M
F
cu
r
v
e, de
fi
ne
d
by
a
ppl
y
i
n
g
t
h
e
f
o
l
l
owi
n
g e
q
uat
i
o
ns:
X
i
(x
) =
(
1
)
Y
i
(y)
=
(
2
)
whe
r
e,
Xi(x) a
n
d Yi(y
) are
fuzzed
values
for each i
n
put data, while ai, bi a
n
d ci are t
h
e M
F
pa
ram
e
ters for t
h
e
respective
re
presentation of t
h
e m
i
ddle,
wi
dth and
slope
of the c
u
rve.
These
param
e
ters are va
ried
accordingly to get a su
itable curve in orde
r to
get a fuzz
y signal.
An
out
put
si
g
n
al
f
r
om
t
h
e fuzzi
fi
cat
i
on st
age be
com
e
s i
nput
t
o
t
h
e st
age of t
h
e ‘IF
-TH
E
N
’
r
u
l
e
. I
n
t
h
i
s
st
age, t
h
e
fu
zzy si
g
n
a
l is
g
a
in
ed
b
y
using
th
e equ
a
tion
(3) to (6
).
R
1
=X
1
(x)
*
Y
1
(y
)
(
3
)
R
2
=X
2
(x)
*
Y
2
(y
)
(
4
)
R
3
=X
3
(x)
*
Y
1
(
y
)
(5
)
R
4
=X
4
(x)
*
Y
2
(y
)
(6)
R1, R
2
, R
3
a
n
d R
4
are
real
values for e
v
ery
‘IF-T
h
e
n
’ rule.
Fu
rt
h
e
r, th
e
ou
tpu
t
sign
al fro
m
th
e stag
e o
f
‘IF-THEN’
ru
le
will b
e
an
i
n
pu
t sig
n
a
l to
th
e
n
o
rm
aliza
tio
n
stag
e. In
th
is
stag
e, ev
ery gain
ed
sign
al is d
i
v
i
d
e
d
to
the to
tal o
f
a gain
ed
sign
al by th
e
fo
llowing
equ
a
tio
n
:
N
i
=
i
T
R
R
i=1,
2,
3,
4
(
7
)
Whe
r
e:
R
T
=
R
1
+ R
2
+ R
3
+ R
4
.
The
ne
xt proc
ess is signal defuzzification i
n
whic
h
th
e ou
tpu
t
sign
al fro
m
the norm
alization stage
becom
e
s an input signal to t
h
is de
fu
zzifica
tion stage.
In this stage, a
norm
alized signal is gained a
g
ain
th
ro
ugh
a lin
ear eq
u
a
tion
t
h
at
is form
ed
f
r
o
m
th
e MF of
th
e
o
u
t
p
u
t
sign
al as show
n in
t
h
e
f
o
llow
i
ng
equ
a
tio
n
.
G
i
= N
i
(p
i
x +
q
i
y + r
i
)
i=1,
2,
3,
4
(8)
with
pi,
qi and
ri are t
h
e MF
p
a
ram
e
ters for
the linea
r sig
n
al
.
Th
e last p
r
o
c
ess in
th
e ANFIS
o
p
e
ratio
n
is called
n
e
u
r
o
n
ad
d
ition
in wh
ich
all d
e
fu
zzificatio
n
si
gnal
s
Gi
a
r
e
adde
d t
oget
h
er
as s
h
o
w
n
bel
o
w:
OT =
Ʃ
G
i
i=
1,
2,
3,
4
(9)
OT is a pred
icted
v
a
lu
e.
5.
ASSES
S
ME
NT OF TECHNICAL
LOSSE
S
The
data to
be use
d
from
the serve
r
s c
o
llected
fro
m
th
e
m
e
ters are the to
tal co
nsum
p
t
io
n
for a
cert
a
i
n
peri
o
d
of t
i
m
e of
0.
4
kV
si
de
o
f
t
h
e
sub
s
t
a
t
i
on a
n
d
t
h
e t
o
t
a
l
co
ns
u
m
pti
on
of
co
ns
um
ers con
n
ect
ed t
o
t
h
e su
bst
a
t
i
on
fo
r t
h
e sam
e
p
e
ri
o
d
[1
1]
,[
1
2
]
.
Al
l
cons
um
p
tio
n
is exp
r
essed
in
kWh. Th
e g
o
a
l is to
create as
precise
ANFIS as it can
be. Furt
her, the sm
allest possibl
e s
a
m
p
les, in this
case the sam
p
le of
15 m
i
nutes, are
t
a
ken,
as
pre
s
e
n
t
e
d i
n
Ta
bl
e
5
.
T
h
e
peri
o
d
o
f
l
earni
ng
, t
r
ai
ni
ng
an
d t
e
st
i
n
g
AN
FIS
w
o
rk
i
s
t
h
ree
m
ont
hs.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
An A
d
apt
i
ve N
e
ur
o F
u
zzy
I
n
f
e
rence
Syst
em
i
n
Assess
me
nt
of
Tec
hni
c
a
l
L
o
sses i
n
.
.
.
.
(
D
r
a
g
a
n
Ml
aki
c
)
1
299
Tabl
e
5. T
h
e
c
a
l
c
ul
at
ed l
o
s
s
f
o
r
t
h
e sam
p
l
e
s
of
1
5
m
i
nut
es
Ti
m
e
Custo
m
er
consu
m
ption (
k
Wh)
Substation
(k
Wh
)
Lo
sses
% (kW
h
)
2015-
1-
1 0
0
:15
8.
8587
5
9.
50
7.
24
0.
6412
5
2015-
1-
1 0
0
:30
8.
4077
5
10.
00
18.
94
1.
5922
5
2015-
1-
1 0
0
:45
8.
1867
5
8.
50
3.
83
0.
3132
5
2015-
1-
1 0
1
:00
8.
1757
5
9.
50
16.
20
1.
3242
5
2015-
1-
1 0
1
:00
8.
1757
5
9.
50
16.
20
1.
3242
5
2015-
1-
1 0
1
:15
8.
1435
0
8.
50
4.
38
0.
3565
2015-
1-
1 0
1
:30
7.
9385
0
8.
50
7.
07
0.
5615
2015-
1-
1 0
1
:45
7.
9175
0
8.
75
10.
51
0.
8325
2015-
1-
1 0
2
:00
8.
1835
0
8.
25
0.
81
0.
0665
2015-
1-
1 0
2
:15
6.
8490
0
8.
00
16.
81
1.
1510
Th
e lo
sses i
n
th
e electr
i
cal en
erg
y
o
f
t
h
e d
i
str
i
b
u
tion
syste
m
ar
e th
e r
a
ti
o
of
en
er
g
y
p
a
ssed
thr
ough
t
h
e s
ubst
a
t
i
o
n
and
ene
r
gy
t
h
a
t
con
s
um
ers ha
ve t
a
ke
n t
h
r
o
u
g
h
t
h
ei
r
m
e
t
e
rs:
10
0%
TP
T
EE
G
E
(10)
G
–
to
tal losses exp
r
essed as a p
e
rcen
tag
e
(%);
E
T
–
en
erg
y
th
at is record
ed on
th
e m
e
ters o
f
th
e sub
s
tatio
n
(kWh);
E
P
– e
n
e
r
gy t
h
at is recorded on
the
m
e
ters of
cust
om
ers (k
Wh
).
The
value
G is calculated e
v
ery 15 m
i
nutes duri
n
g
a
day
aim
i
ng at
bui
l
d
i
ng a
p
r
eci
se
kn
o
w
l
e
d
g
e
base ANF
I
S
will be built upon. In
order t
o
reduce e
n
orm
ous
am
ount
of
data, the decision is to take sa
m
p
les.
Fo
r th
e pu
rpo
s
e of th
is p
a
p
e
r, 178
sam
p
les
for trai
n
i
ng
FIS and
80
sam
p
les for testing
FIS are cho
s
en. Th
e
best
e
x
am
pl
es are t
h
ose
t
h
at
com
e
from
di
f
f
ere
n
t
seas
o
n
al
pe
ri
o
d
s a
n
d
di
ffe
rent
t
i
m
es of a
day
a
n
d
ni
ght
i
n
or
der
t
o
p
r
o
p
er
l
y
m
odel
t
h
e l
o
w
vol
t
a
ge
net
w
or
k
[1
2]
.
It is i
m
p
o
r
tan
t
to
stress th
at th
e g
r
eater the n
u
m
b
e
r o
f
sa
m
p
les, FIS will b
e
m
o
re ac
cu
rate; yet
,
calculation time is
m
u
ltipli
ed.
Whe
n
yo
u calculate all
the sam
p
les
l
o
sses, it is necessary to define the
t
r
ans
f
o
r
m
e
r bay
und
er re
vi
e
w
. De
fi
ni
ng t
h
e t
r
ansf
o
r
m
e
r
bay
m
eans
m
a
ki
n
g
base c
h
ar
act
eri
s
t
i
c
s dat
a
whi
c
h
i
n
cl
ude
s cr
oss
sect
i
ons ra
n
g
i
ng
fr
om
t
h
e subst
a
t
i
o
n t
o
t
h
e end c
u
st
om
ers, l
e
n
g
t
h
of a
con
d
u
ct
o
r
, t
y
pe o
f
material they are m
a
de of (C
u,
Al),
num
ber of c
ons
um
ers, "dis
persi
on"
of c
ons
um
ers, t
e
m
p
erature for each
sam
p
le an
d
rel
a
tiv
e hu
m
i
d
ity
for each
sam
p
le. So
m
e
o
f
th
ese ch
aracteristics are
no
t so im
p
o
r
tan
t
fo
r t
h
e lo
ss
calculation but
m
a
y be considere
d
as factors that a
ffec
t
t
h
e el
ect
ri
c
con
s
um
pt
i
on and c
onse
q
uent
l
y
t
h
e
budget. Most of the cha
r
acte
r
istics can
b
e
f
o
und
on
th
e sch
e
m
e
sh
o
w
ing
the feeder (Figure 2) and
weather
co
nd
itio
ns wh
i
c
h
can
b
e
foun
d
on
th
e local weath
e
r con
d
ition
s
p
r
o
v
i
d
e
r. It is n
ecessary to
calcu
l
a
te th
e
fo
rm
ul
a (1
0)
f
o
r
1
7
8
sam
p
l
e
s i
n
o
r
de
r t
o
det
e
rm
i
n
e t
h
e
kn
o
w
l
e
d
g
e
ba
se.
Am
ong t
h
e rec
o
r
d
e
d
dat
a
, t
h
e
colum
n
s suc
h
as the cross se
ction of
the ca
bles (70, 50,
35
m
m
2), the air tem
p
erature
(T),
h
u
m
i
dity (H
),
num
ber
of c
o
n
s
um
ers (C
N)
,
t
h
e su
bst
a
t
i
o
n
(SS
)
-
r
egi
s
t
e
re
d
at
t
h
e su
bst
a
t
i
on
k
W
h
% -
p
e
rcent
a
ge o
f
l
o
sses
fro
m
SS to
co
n
s
u
m
ers will b
e
in
serted
.
No
tice th
at
th
ere is n
o
co
n
s
um
p
t
io
n
in
kWh
fo
r co
nsu
m
ers. Th
e
reason
is th
at
th
is is already co
n
t
ained with
in
th
e reg
i
stratio
n
o
f
en
erg
y
with
in th
e sub
s
tatio
n and
th
e
perce
n
t
a
ge
of l
o
sses t
o
be cal
cul
a
t
e
d. S
o
,
da
t
a
i
nput
s a
r
e cr
oss sect
i
o
n o
f
t
h
e cabl
e
s
,
T, H
,
C
N
, a
nd S
S
,
whi
l
e
th
e o
u
t
p
u
t
, lo
sses in
p
e
rcen
tag
e
(%), co
m
e
s
fro
m
th
e FIS syste
m
[1
1
]
,[12
]. Th
e in
fo
rm
atio
n
th
at is th
rown
away is the
dat
e
and tim
e. The reas
on
is th
at
th
e tim
e is irrelev
a
n
t
co
nsidering
th
e tem
p
eratu
r
e and
humid
ity
characteristics because it can be determ
ined that losses
are unrelated to date but relat
e
d to t
h
e conditions
unde
r whic
h the LV net
w
ork is worki
n
g, whic
h m
a
ke
s inputting
data in MatLab
Works
p
ace m
u
ch easier.
After ed
itin
g
t
h
e
d
a
ta
p
r
esentatio
n
,
t
h
e tab
l
e is m
a
d
e
and
afterwa
r
ds i
n
s
e
rted i
n
to MatLab
Works
p
ac
e. T
h
e
obs
er
ved
s
ubst
a
t
i
on a
r
eas
ha
v
e
cha
r
act
eri
s
t
i
c
s p
r
ese
n
t
e
d i
n
Tabl
e
6.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
9
4
– 13
04
1
300
Tab
l
e 6
.
I
npu
t d
a
ta
of
tr
an
sf
ormer
ar
ea
Cables Te
m
p
e
r
ature
Hu
m
i
dity
Custo
m
er
nu
m
b
er
Substation Losses
70 m
m
2
50
m
m
2
35
m
m
2
oC
%
kW
h
%
6000
1200
2500
-
3
12
110
9.
5
7.
24
6000
1200
2500
-
3
12
110
10
18.
94
6000
1200
2500
-
3
12
110
8.
5
3.
83
6000
1200
2500
-
3
12
110
9.
5
16.
2
6000
1200
2500
-
3
12
110
8.
5
4.
38
6000
1200
2500
-
3
12
110
8.
5
7.
07
6000
1200
2500
-
3
12
110
8.
75
10.
51
6000
1200
2500
-
3
12
110
8.
25
0.
81
6000
1200
2500
-
3
12
110
8
16.
81
6000
1200
2500
-
3
12
110
7.
25
9.
67
6000
1200
2500
-
3
12
110
7.
25
9.
3
6000
1200
2500
-
3
12
110
7
7.
69
6000
1200
2500
-
3
12
110
6.
75
11.
96
6000
1200
2500
-
3
12
110
6.
5
3.
85
6000
1200
2500
-
3
12
110
7.
25
18.
68
6000
1200
2500
-
3
12
110
6.
5
7.
69
6000
1200
2500
-
3
12
110
5.
75
-
4
.
84
6000
1200
2500
-
3
12
110
6.
25
2.
55
6000
1200
2500
-
3
12
110
7
14.
59
6000
1200
2500
-
3
12
110
6.
5
6.
81
6000
1200
2500
-
3
12
110
6.
75
0.
75
6000
1200
2500
-
3
12
110
6.
75
4.
25
6000
1200
2500
-
3
12
110
7.
75
19.
4
6000
1200
2500
-
2
16
110
7
6.
47
Upon
co
m
p
leti
o
n
of sam
p
ling
,
t
h
e
d
a
ta
n
e
ed
to
b
e
fed
i
n
t
o
MatLab
wh
ere th
e ANFIS
b
u
ild
i
n
g is
done. Fi
rst, the data are translated so that the Data
Im
por
t
e
r reco
g
n
i
zes and sa
ves t
h
e
m
as t
h
e kno
wl
e
d
g
e
b
a
se. It is cru
c
ial to
clean
th
e in
form
at
io
n
of "d
irt" th
at o
n
ly b
r
in
g
s
co
nfu
s
ion
and
un
necessary d
e
lays in
th
e
calculation
of t
h
e fuzzy rules. In t
h
is
exam
ple, the sam
p
les that have
val
u
e
"0" are
bad
be
cause the
r
e wa
s no
con
s
um
pt
i
on, i
.
e. t
h
e
di
st
ri
b
u
t
i
on
net
w
or
k
was
out
of t
h
e
ope
rat
i
o
n
or t
h
e m
e
t
e
r di
d n
o
t
m
easure;
t
h
eref
ore
,
t
h
e dat
a
are n
o
t
val
i
d
. He
nc
e, dat
a
pr
oces
si
ng ne
eds t
o
be d
one
pri
o
r
t
o
t
h
e AN
FIS
t
r
ai
ni
n
g
. I
n
ad
di
t
i
on,
bef
o
re
p
r
ocessi
ng
t
h
e
dat
a
, "cl
eani
n
g"
of t
h
e
t
a
bl
e k
n
ow
ledg
e b
a
se,
t
h
at po
llu
te
th
e kn
ow
ledg
e b
a
se,
need
s
t
o
be
do
ne.
C
l
ean
i
ng i
s
d
o
n
e m
a
nual
l
y
by
fi
n
d
i
n
g
val
u
es t
h
at
are
not
good e
x
am
ples for the assessm
ent and are
pos
si
bl
e err
o
rs
i
n
m
e
t
e
r readi
n
g. It
i
s
nec
e
ssary
t
o
g
o
t
h
r
o
ug
h t
h
e da
t
a
t
a
bl
e, l
ook
fo
r val
u
e
s
t
h
a
t
are
abn
o
r
m
a
l
,
li
ke faul
t
s
i
n
t
h
e
di
st
ri
but
i
o
n
net
w
or
k
or s
w
i
t
c
hi
ng
o
f
l
i
n
e b
r
ea
kers et
c.
, an
d
del
e
t
e
t
h
em
from
t
h
e
specim
e
n. When the ba
se sa
m
p
le
is ready for the
A
N
FI
S t
r
ai
ni
n
g
,
ope
n t
h
e A
N
F
I
S E
d
i
t
o
r
fr
om
t
h
e com
m
a
nd
line and im
port the data t
h
at
are
pre
p
are
d
for t
h
e trai
ni
n
g
.
Fi
g
u
re
5
sh
ow
s t
h
e i
m
port
e
d
dat
a
w
h
e
n
pres
ent
e
d
i
n
t
h
e AN
FI
S Edi
t
o
r acc
om
pani
ed by
t
h
e m
o
st
of
wo
r
k
o
n
AN
FIS
,
t
r
ai
ni
n
g
, t
e
st
i
n
g
,
chec
ki
n
g
, m
a
nagi
n
g
er
r
o
r
and training e
poc
hs
. After c
r
eating
ANFIS, it is necessa
ry to train FIS to success
f
ully
m
eet the crite
ria of
accuracy. For testing
pu
rpose
s
, the
table c
r
e
a
ted from
the sa
m
e
data as t
h
e table to creat
e FIS
was
use
d
.
The
criterio
n
of accu
racy
d
e
p
e
nds on
th
e
u
s
ers
who
will u
s
e t
h
e ab
ov
e FIS
syste
m
. Th
e satisfacto
r
y lev
e
l
o
f
an
erro
r d
e
p
e
n
d
s
o
n
th
e
kn
owled
g
e
b
a
se
u
s
ed to
create FI
S, t
h
e m
e
th
o
d
s
u
s
ed
for m
o
d
e
lin
g and
u
s
er sen
s
itiv
ity.
Fi
gu
re
5.
A
N
F
I
S E
d
i
t
o
r,
w
h
i
c
h c
r
eat
es a
fuz
z
y
sy
st
em
t
h
at
i
s
base
d
on
t
h
e
ent
e
re
d
dat
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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ECE
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S
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8-8
7
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8
An A
d
apt
i
ve N
e
ur
o F
u
zzy
I
n
f
e
rence
Syst
em
i
n
Assess
me
nt
of
Tec
hni
c
a
l
L
o
sses i
n
.
.
.
.
(
D
r
a
g
a
n
Ml
aki
c
)
1
301
In
th
is case, th
ree epo
c
h
s
are su
fficien
t to train
an
d
will tak
e
a lev
e
l
o
f
an
erro
r to 5
%
. In
the
properties of FIS, the m
e
m
b
er
sh
i
p
fu
n
c
tion
d
a
ta are presen
ted
.
It is p
o
ssib
le to
m
a
n
u
a
lly ch
an
g
e
t
h
e typ
e
,
sco
p
e an
d pa
r
a
m
e
t
e
rs of t
h
e
fu
nct
i
on i
t
s
el
f
i
f
t
h
e
m
e
m
b
ershi
p
f
unct
i
o
ns
do
not
co
rres
p
o
n
d
t
o
t
h
e l
e
vel
o
f
sen
s
itiv
ity o
f
t
h
e data th
at it rep
r
esen
ts.
Figure 6
show
s th
e
ANFIS Mod
e
l
Ru
les g
e
n
e
rated
fro
m
th
e im
p
o
rted
d
a
ta.
Dep
e
nd
ing
on
t
h
e inpu
t d
a
ta tun
i
ng
and
m
e
m
b
ersh
ip
fun
c
tion
s
ru
les can
b
e
m
o
re or less gen
e
rated
.
It i
s
best
t
o
ha
ve m
o
re
r
u
l
e
s t
o
co
ver m
o
st
o
f
i
n
put
si
t
u
at
i
ons
but
i
t
i
s
i
m
pos
si
bl
e t
o
c
o
ver t
h
em
al
l
,
so co
nt
i
nue
d
devel
opm
ent
o
f
A
N
F
I
S
i
s
o
f
great
i
m
port
a
n
ce.
Fi
gu
re
6.
The
s
t
ruct
u
r
e
of
the created ANFIS
m
odel
Fi
gu
re
6
dem
onst
r
at
es
ho
w t
h
e st
ruct
ure
A
N
F
IS m
odel
c
r
e
a
t
e
d FI
S l
o
o
k
s.
C
l
earl
y
, a l
o
t
of
r
u
l
e
s are
u
s
ed
for 7
inpu
ts an
d
1
ou
tpu
t
. Co
nsid
ering
th
e in
fo
rm
ati
o
n
u
s
ed
for creatin
g
FIS, th
e p
o
ssi
b
ilities o
f
fu
zzy
logic a
r
e clear. The
num
b
er of create
d
“if-then
” ru
les is
2
,
18
7,
wh
ich
is
no
t a lo
t if th
e
nu
m
b
er of th
e en
tered
sam
p
les is co
n
s
id
ered
. Fi
g
u
re 7
shows th
e
me
m
b
ersh
ip
fu
n
c
tio
ns fo
r
inpu
t no
. 7, wh
ich
is a r
e
g
i
ster
ed
f
l
ow
through the s
u
bstation.
Now, test FIS is cre
a
ted due to the
data
which are loade
d
into
t
h
e works
p
ace.
As ca
n
be seen i
n
Fi
g
u
re
8, a st
an
da
rd er
r
o
r t
e
st
i
n
g FI
S i
s
29
.1
6
2
8
.
It is a grea
t erro
r
from
the pers
pective
of the
di
st
ri
b
u
t
i
on sy
st
em
. The erro
r of 3
0
%
po
ur
ed i
n
t
o
ene
r
gy
l
o
sses i
s
si
gni
fi
cant
.
I
n
or
de
r t
o
red
u
ce t
h
e
erro
r
,
in
trodu
ctio
n
o
f
m
o
re sa
m
p
les an
d
tak
i
ng
sam
p
les
fro
m
several
di
f
f
ere
n
t
peri
o
d
s ha
ve t
o
be do
ne.
A
s
t
h
e
n
u
m
b
e
r and
q
u
ality o
f
sam
p
les in
crease,
FIS
will b
e
m
o
re accu
rate.
Fig
u
re
7
.
Memb
ersh
ip fun
c
tion
inpu
ts for registered
en
erg
y
th
ro
ugh
th
e sub
s
tatio
n
Figure
8. The
test res
u
lts of the created FIS
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
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08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
9
4
– 13
04
1
302
C
r
eat
i
ng FI
S f
o
r t
h
e assessm
ent
of p
h
y
s
i
cal
beha
vi
or i
s
an
evol
vi
ng
pr
oc
ess;
fuzzy
l
ogi
c i
s
based on
t
h
e kn
o
w
l
e
d
g
e
base, w
h
i
c
h i
s
im
prove
d wi
t
h
m
o
re expe
ri
ence. It
i
s
im
po
rt
ant
t
o
n
o
t
i
ce t
h
at
t
h
i
s
m
e
t
hod can
onl
y
cal
cul
a
t
e
t
echni
cal
l
o
sse
s fo
r a cert
a
i
n
LV fee
d
er
fo
r a cert
a
i
n
pe
r
i
od
of t
i
m
e under ce
rt
ai
n we
at
her
,
clim
ate and technical re
quire
m
ents.
Eve
n
t
h
o
u
gh l
o
sses
m
a
y
i
n
cl
ude a
no
n
-
technical aspect, the m
e
thod in
this case can c
l
early separate
the technical from
non
-t
ech
n
i
cal
l
o
sses. Aft
e
r pe
rf
orm
i
ng
t
h
e sim
u
l
a
t
i
on fo
r a
certain
p
e
riod
,
th
e resu
lts ob
tain
ed
fro
m
th
e si
m
u
latio
n
are c
o
m
p
ared
with the m
easur
ed a
c
tual values
. In the
event that deviates
m
o
re th
an a specifie
d
a
llowable thres
hol
d (in t
h
is
case, to conside
r
the error counters
,
cu
rren
t tran
sform
e
rs, th
e ap
plicatio
n
itself, wh
ich
h
a
s
a cl
ear mistake), there is
a prese
n
ce of non-tec
hnical
lo
sses in
t
h
e LV n
e
t
w
o
r
k
wit
h
a +/- error that was m
e
n
tio
ned
.
C
r
eatin
g FIS Sug
e
no
and
FIS Mam
d
an
i is v
e
ry
si
m
ilar to
creatin
g
ANFIS excep
t wh
en
creatin
g
MF.
[2
],[11
]
-[13
]. In
ANFIS Ed
ito
r, in
MatLab
, n
e
w
FIS is
created and fi
nally Sugeno or Ma
m
d
ani are to be chos
en
.
Th
e d
i
fferen
c
e is in
th
e o
u
t
pu
t fun
c
tion
.
M
a
m
d
an
i
pr
o
v
i
d
es t
h
e c
hoi
ce
bet
w
ee
n
several
o
u
t
p
ut
fu
nct
i
o
ns s
u
c
h
as t
r
i
m
f, gau
s
sm
f, zm
f, et
c. and
S
uge
n
o
gi
ves
us
t
w
o c
h
oi
ces
-
co
nst
a
nt
o
r
l
i
n
ear
.
Fo
r FI
S Mam
d
an
i,
th
ree
M
F
s a
r
e c
hos
en
,
nam
e
ly ga
ussm
f, t
r
i
m
f and
g
a
ussm
f as sh
own
i
n
Figu
re
9. For FIS Su
g
e
n
o
, th
ree MF
s
are cho
s
en
and it will b
e
a lin
ear typ
e
as shown
i
n
Fi
gu
re 1
0
. M
F
s of sev
e
n i
n
p
u
t
s
are t
h
e sam
e
i
n
bot
h
of t
h
ese reaso
n
i
n
g
sy
st
em
s. Tem
p
erat
ure
,
h
u
m
i
di
t
y
and
reg
i
stered
kWh
in th
e sub
s
t
a
tio
n
i
n
flu
e
n
c
e th
e
o
u
t
pu
t MF th
e m
o
st. Th
e
reason
fo
r
th
is is in th
e t
y
p
e
s
o
f
con
d
u
ct
o
r
s i
n
s
t
al
l
e
d i
n
t
h
e L
V
di
st
ri
but
i
on
net
w
or
k a
nd t
h
e num
ber
of c
ons
um
ers of
el
ect
ri
cal
ener
gy
bei
n
g
th
e sam
e
m
o
st of th
e tim
e, so
it
d
o
e
s
n
o
t
i
n
fl
u
e
n
c
e lo
sses du
ri
n
g
tim
e
o
n
a
d
i
fferen
t
lev
e
l. Th
e syst
e
m
is
integrate
d
with the a
pplication
using s
u
c
h
interface.
Fi
gu
re
9.
M
e
m
b
ers
h
i
p
f
u
nct
i
o
ns
of
t
h
e M
a
m
d
ani
o
u
t
p
ut
Fi
gu
re
1
0
. M
e
m
b
ershi
p
fu
nct
i
ons
o
f
t
h
e
S
u
g
e
no
o
u
t
p
ut
6.
CO
MP
ARI
S
O
N OF
THE
RESULTS
Whe
n
t
h
e a
ppl
ication with FIS Mam
d
ani, FIS Suge
no
and
ANFIS are i
n
tegrate
d
int
o
the exec
utabl
e
file, th
e co
m
p
arison
of th
e
measu
r
ed d
a
ta fro
m
th
e
field (sm
a
rt
m
e
ters) with t
h
e calc
u
lated
ones
fr
om
the
appl
i
cat
i
o
n ca
n be
d
one
. F
o
r
exam
pl
e, 80
m
easured
spec
im
en and
80 c
a
lculated va
l
u
e
s
from
the application
are t
a
ke
n
an
d
prese
n
t
e
d
i
n
Fi
gu
re
1
1
a
n
d
12
. T
h
ere
i
s
a cle
a
r
diffe
re
nce i
n
acc
uracy
bet
w
een three m
e
thods.
Er
ro
rs -1
.29
%
f
o
r
A
N
FI
S,
-2
.5
6% fo
r FIS
Ma
m
d
an
i and
-
1
.
0
9
%
f
o
r
FIS Su
g
e
no
ar
e reco
rd
ed
acco
r
d
i
ng
to
th
e g
e
n
e
rated
resu
lts. FIS Su
g
e
no
h
a
s th
e lo
west record
ed
erro
r. In
ad
d
ition
,
th
e tren
d
o
f
FIS Sug
e
no
is
m
o
st
ly
neut
ral
of
spe
c
i
m
en tim
e t
h
at
i
s
not
pr
om
i
s
i
ng f
o
r
l
o
n
g
er
pe
ri
o
d
of
ap
p
r
o
x
i
m
ati
on.
F
u
rt
he
r a
n
al
y
s
i
s
sho
w
s t
h
at
A
N
F
IS
has t
h
e be
st
t
r
end acc
or
d
i
ng t
o
t
h
e m
e
asure
d
val
u
es f
r
o
m
AM
R
but
has ba
d res
u
l
t
s
i
n
t
h
e
begi
nni
ng
. F
I
S
M
a
m
d
ani
has
t
h
e st
eadi
e
st
t
r
en
d b
u
t
t
h
e
hi
ghe
st
err
o
r
.
Th
e devi
at
i
o
n o
f
t
h
e err
o
rs dec
r
eases
for longer s
p
ec
im
en. The
rea
s
on is that
the l
o
nge
r
s
p
eci
m
e
n
,
t
h
e
b
e
tter
p
e
riod
resu
lts. In th
at
way, it can
n
o
t
be ignore
d, e
s
pecially whe
n
the asses
s
ment declares
t
h
e co
u
r
se o
f
expe
nses i
n
si
d
e
t
h
e i
nve
st
m
e
nt
o
r
m
a
i
n
t
e
nance
o
f
t
h
e
di
st
ri
b
u
t
i
on
net
w
o
r
k
.
Er
ro
rs
of
-1
.2
9
%, -
2
.
5
6
% an
d -
1
.
0
9% are
g
r
eat
st
art
i
n
g
p
o
i
nt
s f
o
r
fu
rt
he
r re
searc
h
on
t
h
e
FI
S s
y
st
em
. The f
u
z
z
y
-
base
d a
p
p
r
oxi
m
a
t
i
on m
e
tho
d
i
s
o
n
e
o
f
t
h
e easi
e
st
a
n
d
fast
est
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
An A
d
apt
i
ve N
e
ur
o F
u
zzy
I
n
f
e
rence
Syst
em
i
n
Assess
me
nt
of
Tec
hni
c
a
l
L
o
sses i
n
.
.
.
.
(
D
r
a
g
a
n
Ml
aki
c
)
1
303
gr
owi
n
g
m
e
t
hods f
o
r t
h
e assessm
ent
.
In concl
u
si
o
n
, we
can su
gge
st
a
com
b
i
n
at
i
on o
f
several
m
e
t
h
ods i
n
o
r
d
e
r to
p
r
ov
id
e b
e
tter
o
v
e
rall resu
lts th
an
th
e o
n
es ob
tain
ed. Tak
i
n
g
m
o
re sam
p
les o
f
th
is ap
p
lication
and
com
b
ining the
m
will provid
e
results that are
m
o
re accurat
e
. Also,
the
voting m
echanism for all 3-inferenc
e
m
e
t
hods
can
b
r
i
ng a
bet
t
e
r
t
r
e
n
d
.
Fi
gu
re
1
2
.
G
r
a
phi
c
p
r
esent
a
t
i
on
o
f
m
easure
d
a
n
d
cal
cul
a
t
e
d l
o
sses i
n
t
h
e
LV
di
st
ri
b
u
t
i
o
n
net
w
or
k
Figure 13.
T
h
e
error betwee
n the
m
easured a
n
d
calcu
lated lo
sses i
n
t
h
e LV
d
i
stribu
tio
n
n
e
two
r
k
7.
CO
NCL
USI
O
N
The
pape
r d
e
s
c
ri
bes t
h
e
ad
v
a
nt
ages
of
usi
ng
f
u
zzy
l
ogi
c
t
o
ap
pr
o
x
i
m
ate l
o
sses
on t
h
e
l
o
w
vol
t
a
ge
electricity distribution netw
ork. The
m
e
thod accuracy de
pe
nds
on the s
p
e
c
ific practical exam
ples to be used
as refe
rence
s
because m
easure
m
ent data are
use
d
to cr
eate
knowledge ba
s
e
s, which a
r
e furt
her
use
d
to
deri
ve
m
e
m
b
ershi
p
fu
nct
i
o
n
s
. I
n
l
o
n
g
-t
erm
app
r
o
x
i
m
at
i
on, t
h
e b
e
s
t
m
e
t
hod i
s
A
N
FI
S bec
a
use
as speci
m
e
n gr
ows i
n
num
ber, it bec
o
m
e
s close to r
eal
m
easured values, whic
h lo
wers
do
w
n
the err
o
r p
e
rce
n
tag
e
. In com
p
aris
on t
o
Sug
e
no
an
d
M
a
m
d
an
i, ANFIS is th
e easie
st to
up
grad
e
from train
i
n
g
d
a
ta. Its app
licatio
n
is no
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ited
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ent
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e d
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two
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in new weath
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r con
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ition
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or
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est
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m
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put
ed
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h
A
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S.
ACKNOWLE
DGE
M
ENTS
We
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l
d lik
e to
th
ank
th
e Dep
a
rt
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e
nt fo
r
Distrib
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tion
o
f
Electrical
En
er
g
y
H
Z
-H
B
I
n
c.
Mo
star for
allowing
us t
o
use t
h
e Sm
ar
t Meter grid
i
n
frastru
cture.
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