Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
43
9
~
44
6
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.9
182
4
39
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
Econ
omi
c
Valuat
ion of
P
o
wer and Energy Loss
es i
n
Distribution Networks
Smaj
o Bisa
nov
i
c*
, M
e
rsiha
Sa
ma
rdzic*
*,
D
a
mir Aga
n
ov
ic*
* Public Enterpr
i
se Elektropr
ivreda of Bosnia
and
Herzegovina d.d. –
Sarajevo,
B
o
snia and
Herzegovina
** Faculty
of
Electr
i
cal
Engineer
ing, Univ
er
si
ty
of Sa
ra
je
vo, Bo
snia and
Her
zegov
ina
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 11, 2015
R
e
vi
sed Dec 6,
2
0
1
5
Accepted Dec 26, 2015
This paper pr
esents a framewo
rk for
determining the price of
power and
energ
y
at
each node in distribu
tion ne
twork as
well as the price of ener
g
y
los
s
e
s
in the
i
r
el
em
ents
. Th
e pro
pos
ed fram
e
work is
bas
e
d
on th
e con
cept
o
f
the r
a
dial structure network and
gives one appr
oach
to solving
the pricin
g
problem that is
based on pur
chase price
of power and
energ
y
at the network
supply
point. In
this way
it is p
o
ssibl
e to deter
m
ine the econo
mic value of
energ
y
los
s
e
s
whether in th
e ne
twork as
a whole or in particular voltag
e
levels. The model has been successfully
te
ste
d
and re
sults from
te
st studie
s
are r
e
ported.
Keyword:
D
i
str
i
bu
tio
n n
e
tw
or
k
P
o
w
e
r
a
n
d
en
er
g
y
lo
s
s
e
s
Pr
ice at th
e n
e
t
w
or
k nod
e
P
r
ic
e
o
f
en
er
g
y
lo
s
s
e
s
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
:
Sm
ajo Bisanovic,
Pu
bl
i
c
Ent
e
rp
ri
se
El
ekt
r
o
p
ri
vr
eda of
B
o
s
n
i
a
and
He
rze
g
o
v
i
n
a d.
d. – Sara
j
e
vo
,
Vilson
ovo
setaliste 1
5
,
71
0
0
0
Sa
raje
v
o
, B
o
s
n
i
a
an
d
Herze
g
ovi
na.
Em
a
il: s.b
i
sano
v
i
c@elek
tropriv
red
a
.b
a
1.
INTRODUCTION
R
e
searche
r
s’ a
t
t
e
nt
i
on has be
en occ
upi
e
d
b
y
est
i
m
a
t
i
on of po
we
r and e
n
er
gy
l
o
sses i
n
di
st
ri
but
i
o
n
n
e
two
r
k
s
long sin
ce. Th
e greatest ef
f
o
r
t
s
w
h
en
it co
m
e
s to
esti
m
a
tio
n
of
pow
er
an
d
en
er
g
y
lo
sses ar
e
conce
n
trate
d
on e
n
ergy los
s
e
s
assessm
ent on a yea
r
ly
basi
s and
powe
r l
o
sses assessm
ent at m
a
xim
u
m
load in
t
h
e net
w
or
k [
1
]
.
The nee
d
fo
r p
o
we
r an
d
ener
gy
l
o
sses esti
m
a
tio
n
arises fro
m
th
e fo
llowing
reaso
n
s:
opt
i
m
i
zati
on o
f
ex
pa
nsi
o
n an
d f
u
rt
her
de
vel
opm
ent
of t
h
e
di
st
ri
b
u
t
i
o
n
n
e
t
w
o
r
k
,
ch
oi
ce
of
o
p
t
i
m
a
l
l
o
cat
i
o
n
and
si
zi
ng of d
i
st
ri
but
ed ge
ne
rat
o
r
s
an
d
c
o
m
p
en
sat
i
on de
vi
ces,
dy
nam
i
c
n
e
t
w
o
r
k reco
n
f
i
g
u
r
at
i
o
n
an
d v
o
l
t
a
ge
o
p
tim
izat
io
n
in d
i
strib
u
tion
n
e
twork, an
alysis o
f
th
e n
e
tw
ork efficien
cy an
d p
e
rfo
r
m
a
n
ces, etc. In
ad
d
ition
,
i
n
a co
m
p
etitiv
e an
d dereg
u
l
ated
en
v
i
ron
m
en
t th
e
qu
ality o
f
lo
sses estim
ati
o
n is cru
c
ial
fo
r fair co
m
p
etitio
n
i
n
electricity
mark
ets.
In
t
o
d
a
y
’
s m
a
rk
et, d
i
stri
b
u
tion
u
tilitie
s,
sup
p
liers, d
i
stribu
tio
n
n
e
twork
op
erat
o
r
s,
as
well
as consum
ers,
expect estim
ation
of losses
wi
th highest
acc
uracy. Correct a
llocation
of los
s
es is necessa
ry for
cor
r
ect
al
l
o
cat
i
o
n
o
f
c
o
r
r
es
po
ndi
ng
co
st
s. T
h
e l
o
sses i
n
di
st
ri
but
i
o
n
net
w
or
k m
u
st
be
fa
i
r
l
y
al
l
o
cat
ed a
m
on
g
all co
n
s
u
m
ers an
d
d
i
stri
b
u
t
ed
g
e
n
e
rat
o
rs. In
recen
t
lite
ratu
re, reg
a
rd
in
g
lo
sses co
st
s allo
catio
n
,
sev
e
ral
m
e
t
hods
ha
ve
been
pr
op
ose
d
,
s
u
ch
as p
o
st
age
st
am
p
[
1
-
3
]
,
M
W-m
i
l
e
[4]
,
ci
rcui
t
ba
sed
a
n
d pr
o
p
o
r
t
i
onal
shari
n
g [5]. R
ecently,
there
has
been propose
d
a m
odifie
d
propor
tional
sha
r
ing proce
d
ure [6] base
d
on
the
al
l
o
cat
i
on
of e
n
t
i
r
e l
o
sses t
o
con
s
um
ers di
sr
egar
di
n
g
t
h
e i
n
fl
uence
of
di
s
t
ri
but
e
d
ge
ne
ra
t
o
rs
usi
n
g t
h
e
basi
c
pr
o
p
o
r
t
i
onal
s
h
ari
ng
pri
n
ci
pl
e. Seco
n
d
l
y
,
m
a
rgi
n
al
p
r
oc
edu
r
es
hav
e
b
een ext
e
nsi
v
el
y
pr
op
ose
d
i
n
or
der t
o
sen
d
effi
ci
ent
e
c
on
om
i
cal
si
gn
al
s t
o
t
h
e
m
a
rket
agent
s
. M
a
r
g
i
n
al
m
e
t
hods
req
u
i
r
e a sl
ack
bus
desi
g
n
at
i
o
n an
d
do
n
o
t
assi
gn
a
r
bi
t
r
a
r
i
l
y
po
we
r l
o
ss
es
bet
w
ee
n
pr
o
duce
r
s a
n
d c
o
n
s
um
ers [
1
]
.
Al
l
o
cat
i
o
n
o
f
l
o
sses c
o
st
s
i
n
di
st
ri
but
i
o
n
net
w
or
ks i
s
a com
p
l
e
x p
r
obl
em
wh
ose
im
port
a
nc
e
in
creased
in
com
p
et
itiv
e
m
a
r
k
et and
in
n
e
tworks with
h
i
gh
p
e
n
e
tration
of
d
i
stri
b
u
t
ed
gen
e
rat
o
rs [7
]. Prici
ng
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
. 2, A
p
ri
l
20
16
:
43
9 – 4
4
6
44
0
of di
st
ri
b
u
t
i
on
net
w
or
k i
n
cl
u
d
e
s t
h
e al
l
o
cat
i
on of ca
pi
t
a
l
and o
p
erat
i
n
g co
st
s t
o
users (c
o
n
sum
e
rs, ge
ner
a
t
o
rs
)
of t
h
e net
w
o
r
k
i
n
fai
r
a
nd e
q
ui
t
a
bl
e
m
a
nner
,
t
a
ki
n
g
i
n
t
o
c
o
ns
i
d
erat
i
o
n t
h
at
e
ach u
s
er i
s
c
h
a
r
ge
d f
o
r t
h
ose
cost
s
only
for
whic
h they are
res
ponsible.
Marginal cost
pricing
is the m
o
st
widely accepte
d
conce
p
t
for ac
hieving
th
is. By d
e
fin
i
tio
n
,
th
e m
a
rg
in
al co
st o
f
a
go
od
or serv
ice is th
e in
crease in
th
e to
tal c
o
st o
f
p
r
ov
id
ing
th
e
good or service as a result of a rela
tiv
ely s
m
all
in
crease in
th
e rate of ou
tpu
t
o
f
th
e
goo
d
o
r
serv
ice [7
]. In
o
r
d
e
r to
allo
cate p
o
wer losses in
d
i
stribu
tion
n
e
two
r
k
s
with
d
i
stribu
ted
gen
e
ration
,
th
e co
n
c
ep
t o
f
m
a
rg
i
n
al
lo
ss co
efficients is in
tro
d
u
c
ed
[8-1
0]. Thes
e
coe
fficients
measure
t
h
e
ch
ang
e
i
n
t
o
tal activ
e
p
o
wer
lo
sses
cause
d by m
a
r
g
inal cha
nge
s in consum
ption and/or ge
nerat
i
on of active and reac
tive power at each node in
t
h
e di
st
ri
but
i
o
n
net
w
o
r
k
.
In t
h
i
s
pa
per
we pr
o
p
o
s
e a sim
p
l
e
m
e
t
hod
ol
o
g
i
cal
fram
e
wo
rk t
h
at
det
e
rm
i
n
es pri
ces of p
o
w
er a
n
d
energy at each node
of the
distri
bution network, as we
ll as the econom
ic value of energy losses
in the
net
w
or
k el
em
ent
s
. Gi
ve
n i
t
s
sim
p
l
i
c
i
t
y
,
pro
pos
ed
fram
e
wor
k
ca
n be
ve
ry
usef
ul
f
o
r
a qui
c
k
l
o
sses
cost
s
assessm
ent
,
as a pa
rt
of
l
o
s
s
es co
st
s al
l
o
c
a
t
i
ng
pr
oce
d
u
r
es f
o
r
net
w
o
r
k
user
s a
n
d
i
n
ot
he
r a
ppl
i
c
at
i
ons
rega
rdi
n
g
di
st
ri
but
i
o
n
net
w
o
r
k
,
su
ch
as
opt
i
m
i
zat
i
on o
f
de
ve
l
opm
ent
an
d
o
p
erat
i
o
n.
Thi
s
pa
per
i
s
o
r
ga
ni
zed
as f
o
l
l
o
ws.
Sect
i
o
n
2 pr
o
v
i
d
es th
e
math
e
m
atica
l
fo
rm
u
l
atio
n
o
f
t
h
e
p
r
ob
lem.
In Sect
i
o
n 3 a
r
e prese
n
t
e
d t
h
e
resul
t
s
fr
om
several
case
stud
ies. Th
e con
c
lu
sion
s and
po
in
t to
fu
t
u
re research
are o
u
tlin
ed
in Sectio
n
4
.
2.
MAT
H
EM
AT
ICAL
FO
R
M
ULATIO
N
O
F
THE P
R
OB
LEM
In ord
e
r t
o
p
r
esen
t m
a
th
e
m
atical
m
o
d
e
l fo
r power and en
erg
y
l
o
sses v
a
l
u
atio
n in
d
i
stribu
tion
n
e
two
r
k
s
, it is
su
itab
l
e to start
with
sim
p
le d
i
strib
u
tion
n
e
two
r
k
with
n
no
des, as illu
strated
in Figure
1
.
Fi
gu
re
1.
Si
m
p
l
e
conce
p
t
of
d
i
st
ri
but
i
o
n
net
w
o
r
k
wi
t
h
n
no
des
For
val
u
at
i
on
po
we
r an
d ene
r
gy
l
o
sse
s acc
or
di
n
g
t
o
t
h
e
m
e
t
hod
ol
o
g
i
c
a
l
appr
oac
h
t
h
at
fol
l
o
ws, i
t
i
s
necessa
ry to determine eco
n
o
m
i
c val
u
e of
1 k
W
(
P
)
a
nd 1 k
W
h (
W
) at each node of the
distributi
on
netw
or
k (1,2,
.
.
.,
n
).
2.
1
Cal
c
ul
ati
o
n o
f
P
a
r
a
mete
r
P
Eco
nom
i
c
val
u
e of
1
k
W
(
P
) at each
node
of t
h
e
network accordin
g t
o
Figure
1 ca
n be determ
ined
st
art
i
ng f
r
o
m
the p
u
rc
hase
pr
i
ce of 1 k
W
at
no
de 1
,
P1
, (
a
t
t
h
e net
w
o
r
k
sup
p
l
y
poi
nt
)
and c
o
st
s f
o
r t
r
ans
f
er
po
we
r t
o
part
i
c
ul
ar
no
de i
n
t
h
e
net
w
or
k.
If
t
h
e p
u
r
chase
pri
ce
P1
at node
1 is known, the
n
the ec
onom
ic
val
u
e
o
f
po
wer
at
t
h
e e
n
d
o
f
s
ect
i
on
1–
2,
at
no
de
2,
can
be
det
e
rm
i
n
ed as
fol
l
o
ws:
PP
P
21
1
2
(1
)
whe
r
e
P12
is
increm
ent of the econom
ic value
of power
t
h
at is transm
itted
from
node
1
to node
2.
Inc
r
em
ent
P12
represe
n
t
s
t
h
e an
n
u
al
cost
s rel
a
t
e
d t
o
a
m
ort
i
zati
on, m
a
i
n
t
e
nan
ce an
d
ot
her
fi
xe
d
cost
s f
o
r sect
i
on
1–
2,
i
P12
, pl
us cost
s
fo
r
po
wer l
o
sses
in
th
is sectio
n
,
p
P12
. The annual costs
i
P12
fo
r
sect
i
on
1
–
2
are
gi
ve
n a
s
f
o
l
l
o
ws:
P
P
12
12
12
2
10
0
i
(2
)
whe
r
e:
12
i
s
fi
xe
d a
n
nual
c
o
st
s
fact
or
f
o
r
sect
i
o
n
1
–
2
,
[%]
;
I
12
is purch
ase
v
a
lu
e
of th
e equ
i
p
m
en
t for sectio
n
1
–
2
(cap
ital co
sts), [$
];
P
2
i
s
p
o
w
er
t
r
a
n
sfe
rre
d t
o
no
d
e
2 at
m
a
xi
m
u
m
l
o
ad,
[
k
W
]
.
12
2/
3
4
/
5
nn
-2
/
-
1
n-
2
n-
1
n
34
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Econ
omic Va
lua
tio
n o
f
Po
wer an
d En
erg
y
Lo
sses i
n
Distrib
u
tion
Networks (S
.
Bisan
o
v
i
c
)
44
1
Th
e co
sts
related
to power lo
sses in
sectio
n 1–
2 are g
i
v
e
n as fo
llo
ws:
P
P
P
P
12
1
12
2
p
(3
)
whe
r
e
P
12
is
p
o
wer lo
sses i
n
section
1–
2 at
m
a
x
i
m
u
m
lo
ad
,
[kW
]
.
Acco
r
d
i
n
g t
o
e
quat
i
o
ns
(
2
)
an
d
(3
), e
q
uation
(1
) obtain
s
the
follo
win
g
fo
rm
:
P
PP
P
PP
12
12
1
2
1
21
22
100
(4
)
Each kW whi
c
h is trans
f
erred to
node 2 is charge
d at the cost
of t
r
ansm
i
ssi
on t
o
t
h
at
no
de.
Eco
nom
i
c
val
u
e of 1
k
W
at
t
h
e en
d o
f
t
h
e f
o
l
l
o
wi
ng sect
i
o
n, at n
o
d
e
3, is fo
und
in
a co
m
p
letely
an
alo
gou
s
way
.
In the
ge
neral
case, for the
se
ction
(
n
–1
)–
n
,
o
r
fo
r nod
e
n
, i
t
can
b
e
written
:
P
PP
P
PP
(
1
)
(
1)
(
1
)
(
1)
(1
)
10
0
nn
nn
nn
n
nn
nn
(5
)
P
PP
P
PP
(1
)
(
1
)
(1
)
(
1
)
1
22
100
kk
k
k
kk
k
n
kk
nn
kk
(6
)
whe
r
e:
(
k
–1)
k
is fixed
ann
u
al c
o
sts
fa
ctor
fo
r sectio
n
(
k
–1
)–
k
, [%]
;
I
(
k
–1)
k
i
s
p
u
rc
ha
se val
u
e
of t
h
e
equi
pm
ent
fo
r
t
h
e sect
i
o
n (
k
–1
)–
k
(cap
ital co
sts), [$
];
P
k
is pow
er tr
an
sf
er
r
e
d
t
o
n
ode
k
a
t
ma
x
i
mu
m
l
o
a
d
,
[
k
W
]
;
P(
k
–1)
is economic value
of
1
kW at node
(
k
–1
),
[$
/kW
]
.
2.
2
Cal
c
ul
ati
o
n o
f
P
a
r
a
mete
r
W
Eco
nom
i
c
val
u
e
of 1 k
W
h (
W
) at each node of t
h
e
network acc
ordi
ng to
Figure
1 can be determ
ine
d
st
art
i
ng
fr
om
the p
u
r
c
hase
p
r
i
ce of
1 k
W
h
at
t
h
e no
de
1,
W1
, (at
t
h
e n
e
t
w
o
r
k s
u
ppl
y
poi
nt
) a
nd c
o
st
s of
energy losse
s
in appropriat
e secti
ons
o
f
t
h
e di
st
ri
but
i
on
net
w
o
r
k
.
As t
h
e c
o
st
s
associ
at
ed
w
i
t
h
t
h
e
am
ort
i
zat
i
on,
m
a
i
n
t
e
nance a
nd
ot
he
r fi
xe
d cost
s as wel
l
as po
wer l
o
s
s
es
rel
a
t
e
d t
o
t
h
e econ
o
m
i
c val
u
e of 1
kW
at each node in the distribution net
w
ork, the ec
onomic value of 1 kWh of electrical energy at the
ap
pro
p
riate nod
es
will affect
o
n
l
y en
erg
y
losses. Th
e i
n
itial assu
m
p
tio
n
i
n
d
e
term
in
in
g
p
a
ram
e
ter
W
n
is
th
e
existence
of e
q
uality between the econo
m
i
c
value
of the e
n
ergy acce
pted
at
the begi
nni
ng of the one se
ction
and t
h
e economic value of e
n
ergy delive
r
e
d
in the sam
e
peri
od at the e
nd
of this sect
ion.
If the acc
epted
am
ount
of e
n
e
r
gy
du
ri
n
g
t
h
i
s
peri
od at
t
h
e
begi
nni
ng
o
f
s
ect
i
on
1-
2 i
s
W
1
, with
th
e price
W1
, the econom
i
c
v
a
lu
e
of
1
kWh
at t
h
e en
d of
th
is sec
tio
n,
w
h
er
e
th
e
d
e
liv
e
r
ed
en
er
g
y
is
W
2
, wit
h
th
e price
W2
, ca
n
be
det
e
rm
i
n
ed acc
or
di
n
g
t
o
t
h
e
e
quat
i
o
n:
WW
WW
11
2
2
(7
)
Since
WW
W
21
1
2
(8
)
whe
r
e
W
12
is
en
erg
y
lo
sses i
n
section
1–
2,
fro
m
eq
u
a
tion
(7)
fo
llows:
WW
W
WW
1
21
11
2
(9
)
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
. 2, A
p
ri
l
20
16
:
43
9 – 4
4
6
44
2
Eco
nom
i
c
val
u
e of
1
k
W
h at
t
h
e en
d
of t
h
e
fol
l
o
wi
n
g
sect
i
o
n
,
t
h
e t
r
ans
f
o
r
m
a
ti
on 2/
3, at
no
de
3, i
s
f
oun
d in
a co
m
p
letely an
alog
ou
s
w
a
y:
WW
W
WW
W
WW
W
W
WW
21
2
32
1
22
3
1
1
2
22
3
(1
0)
In
t
h
e ge
neral
case,
f
o
r no
de
n
, it can
b
e
wri
tten
:
WW
W
WW
(1
)
1
(1
)
(
1
)
2
k
n
kk
k
n
k
(1
1)
All eq
u
a
tion
s
fo
r d
e
term
in
in
g
p
a
ram
e
ters
P
and
W
are d
e
riv
e
d
for case illu
strated
in
Fig
u
re 1
wit
h
a directional ‘t
ransm
i
ssion’
of ener
gy conta
i
ning lines a
n
d trans
f
orm
e
rs
, and
whic
h are connected to each
ot
he
r f
r
om
t
h
e hi
g
h
er t
o
l
o
we
r v
o
l
t
a
ges.
H
o
weve
r, t
h
ese e
quat
i
o
ns ca
n
b
e
use
d
f
o
r a
p
pr
op
ri
at
e v
o
l
t
a
ge
l
e
vel
,
co
nsid
eri
n
g
t
h
at all
th
eir v
a
ri
ab
les are related
with
th
is
vol
t
a
ge l
e
vel
(va
r
i
a
bl
e cost
s,
po
wer
,
ene
r
gy
, l
o
sses).
In this
way it i
s
possi
ble to determine the ec
onom
ic va
lue of
1
kW and 1 kWh at
each
node
of t
h
e
distribution
net
w
or
k.
2.
3
Cal
c
ul
ati
o
n o
f
P
a
r
a
mete
r
s
P
and
W
in R
a
di
al Ne
tw
ork w
i
th
m
o
re
M
a
in Sec
t
ion
s
M
odel
p
r
ese
n
t
e
d by
eq
uat
i
o
n
s
(6) a
nd
(1
1)
can be ge
ne
ral
i
zed f
o
r any
n
u
m
ber of
m
a
i
n
sect
i
ons (
o
n
e
main
sectio
n
is illu
strated
b
y
si
m
p
lified
sch
e
me in
Fig
u
r
e 1 to
d
e
term
in
e t
h
e v
a
lu
e
o
f
th
e p
a
ram
e
ters
P
and
W
at each node of the
network). The
sim
p
lified sc
hem
e
with N m
a
in secti
ons is illustra
ted in Fi
gure
2. The
param
e
ters
P
and
W
fo
r a
n
y
section
(
j
=
1,
...,
N
)
ca
n
be
determ
ined as
f
o
llow
s
:
P
PP
P
PP
()
()
()
(
)
(1
)
(
1
)
(1
)
(
-
1
)
()
1
()
()
22
(
1
,
.
..,
)
100
jj
j
j
kk
kk
k
k
k
j
n
jj
kk
nn
kk
j
N
(1
2)
WW
W
WW
()
(1
)
()
1
()
()
(1
)
(
1
)
2
(
1
,
.
..,
)
j
k
j
n
jj
kk
k
n
k
j
N
(1
3)
Fi
gu
re
2.
Si
m
p
l
e
conce
p
t
of
d
i
st
ri
but
i
o
n
net
w
o
r
k
wi
t
h
N m
a
i
n
sect
i
o
ns
2.
4 E
c
on
omi
c
Val
u
e
o
f
L
o
ss
es
The ec
o
nom
i
c
val
u
e
o
f
po
w
e
r
P
and
en
er
g
y
W
at
each node of
the
network can be use
d
t
o
det
e
rm
i
n
e t
h
e econ
o
m
i
c val
u
e of t
h
e l
o
s
s
es.
If t
h
e am
ount
of
p
o
we
r l
o
ss
es at
t
h
e t
i
m
e
of m
a
xim
u
m
load i
n
1
2
1
2
2
2
N
2/
3
11
2/
3
22
2/
3
NN
4/
5
11
4/
5
22
4/
5
NN
(-
2
)
/
(
-
1
)
nn
11
(-
2
)
/
(
-
1
)
nn
22
(-
2
)
/
(
-
1
)
nn
NN
(2
)
n-
1
(2
)
n-
2
(2
)
n-
N
(1
)
n-
1
(1
)
n-
2
(1
)
n-
N
n
1
n
2
n
N
3
1
3
2
3
N
4
1
4
2
4
N
5
1
5
2
5
N
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Econ
omic Va
lua
tio
n o
f
Po
wer an
d En
erg
y
Lo
sses i
n
Distrib
u
tion
Networks (S
.
Bisan
o
v
i
c
)
44
3
net
w
or
k f
o
r se
ct
i
on (
k
–1
)–
k
is
P
(
k
–1)–
k
, and t
h
e am
ount
of e
n
er
gy
l
o
ss
es i
n
t
h
i
s
sect
i
on i
n
t
h
e co
ns
i
d
ere
d
peri
od
i
s
W
(
k
–1)–
k
, th
en
co
sts of th
e lo
sses in
th
is sectio
n can
b
e
d
e
term
in
ed
as fo
llo
ws:
PW
CP
W
(1
)
(
1
)
(
1
)
(
1
)
(1
)
lo
s
s
kk
kk
k
k
k
k
(1
4)
The am
ount
of
ener
gy
l
o
sse
s
can
be ex
p
r
es
sed
by
p
o
we
r
l
o
sses at
t
h
e t
i
m
e
of m
a
xim
u
m
l
o
ad an
d
equi
val
e
nt
t
i
m
e d
u
rat
i
o
n
of
t
h
e pea
k
l
o
sses:
WP
(1
)
(
1
)
(1
)
kk
k
k
kk
(1
5)
whe
r
e
(
k
–1)–
k
is equ
i
v
a
len
t
time d
u
ratio
n of
th
e p
e
ak
l
o
sses,
th
en
eq
u
a
ti
o
n
(1
4) can
b
e
written
in
th
e fo
rm:
PW
CP
P
(1
)
(
1
)
(
1
)
(
1
)
(1
)
(
1
)
lo
s
s
kk
kk
k
k
k
k
k
k
(1
6)
Eco
nom
i
c
val
u
e o
f
t
h
e
ene
r
gy
l
o
sses
can
be
f
o
u
n
d
fr
om
t
h
e equat
i
o
n
(
1
6
)
a
s
f
o
l
l
o
ws:
P
W
C
W
(1
)
(
1
)
(1
)
(
1
)
(1
)
(
1
)
lo
s
s
kk
k
kk
k
kk
kk
c
(1
7)
and i
t
dep
e
n
d
s
on t
h
e e
qui
val
e
nt
t
i
m
e
durat
i
on o
f
t
h
e pea
k
l
o
sses
an
d pa
r
a
m
e
t
e
rs
P
and
W
. Fo
r lo
ng
er ti
me
(
f
o
r
whic
h the loa
d
dia
g
ra
m
is
m
o
re uni
fo
rm
), eco
nomic value of the energy
lo
sses in
th
e approp
riat
e
sect
i
on i
s
l
o
we
r. E
quat
i
o
n (
1
7) ca
n be
use
d
fo
r t
h
e act
ual
t
a
ri
ff sy
st
em
.
Net
w
or
k l
o
sse
s can be
val
o
ri
zed by
actu
a
l tariff syste
m
in
a way
th
at p
a
ram
e
ter
P
is tariff ele
m
ent for
po
we
r an
d pa
ram
e
ter
W
is tariff ele
m
en
t
for en
erg
y
.
The m
a
in
d
i
fficu
l
t
y in
app
lication
o
f
equ
a
tion
(1
7) is th
e
un
kno
wi
n
g
th
e lo
ad d
i
ag
ram
o
f
n
e
twork
ele
m
ents. If the load
diagram is not accessi
ble, unlike
val
u
es
of
delivere
d
ene
r
gy and
maxim
u
m
power, the
n
equi
val
e
nt
t
i
m
e d
u
rat
i
o
n
of
t
h
e pea
k
l
o
sses
can
be calc
u
la
ted according t
o
em
piric relation,
for e
x
am
ple:
2
m
m
0
,
17
0
,
83
T
T
T
(1
8)
3.
N
U
M
E
RICAL R
E
SU
LTS
The
propose
d
m
a
the
m
atica
l
m
odel
was
s
u
ccess
f
ully
tested on three
dist
ribution ne
tworks
wit
h
sim
p
l
e
confi
g
u
r
at
i
ons a
nd i
n
t
h
i
s
sect
i
on re
sul
t
s
are prese
n
t
e
d. I
n
al
l
t
e
st
cases t
h
e annual
cost
s rel
a
t
e
d t
o
am
ort
i
zat
i
on,
m
a
i
n
t
e
nance a
n
d
ot
her
fi
xe
d
cost
s
of
t
h
e
net
w
o
r
k
el
em
ent
s
are
negl
ect
ed
.
Test c
a
se
1.
Dat
a
f
o
r
t
e
st
c
a
se 1
i
s
gi
ven
i
n
Fi
g
u
r
e
3.
A
ccor
d
i
n
g t
o
m
a
t
h
em
ati
cal
m
odel
gi
ve
n i
n
Sect
i
on
2,
t
h
e
val
u
es o
f
pa
ra
m
e
t
e
rs
P
and
W
for eac
h
node, as
well as
econom
i
c value of e
n
e
r
gy l
o
s
s
es for eac
h
ne
twork
sect
i
on,
are
gi
v
e
n i
n
Ta
bl
e 1
.
Param
e
t
e
rs fo
r
no
de
1 a
r
e:
P1
= 0,106
27
$
/
kW
an
d
W1
= 0,05
983
$
/
kW
h.
Fi
gu
re
3.
Si
m
p
l
e
di
st
ri
b
u
t
i
o
n
net
w
or
k
fo
r t
e
s
t
case 1
S
n
m
P
=
50
kW
P
= 10 kW
Cu
,
n
Fe
,n
= 8
M
V
A
n,
T
=
35/
1
0
,
5
kV
P
ma
x
= 6,
2
M
W
W
=
1
875
0
M
W
h
W
= 9100
M
V
A
r
h
a
r
5
km
;
0,
45
/
k
m
1
2
3
35 kV
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
. 2, A
p
ri
l
20
16
:
43
9 – 4
4
6
44
4
Tab
l
e
1
.
Resu
lts fo
r test case
1
node
node
P
(k
–1)k
P
k
T
m
,
(
k
–1)k
(
k
–1)k
W
(
k
–1)k
W
k
Pk
Wk
c
(k
–1)k
k–1
k
kW
kW
h
h
kW
h
kW
h
$/kW
$/kW
h
$/kW
h
1
2
87,
17
6.
332,
46
3.
024,
2
1.
380,
7
120.
34
5,
40
18.
886.
3
23,
6
0,
1077
3
0,
0602
1
0,
0599
1
2
3
45,
29
6.
200,
00
3.
024,
2
1.
380,
7
136.
32
3,
56
18.
750.
0
00,
0
0,
1085
2
0,
0606
5
0,
0602
9
Test c
a
se
2.
Th
e seco
nd
test case is illu
strated
in
Fi
g
u
re
4
.
Param
e
ters for nod
e 1
are:
P1
= 0
,
11
439 $
/
kW
an
d
W1
= 0,
07
1
2
6
$/
k
W
h.
T
h
e
val
u
es
o
f
pa
ra
m
e
t
e
rs
P
an
d
W
for eac
h
node, as
well
as econom
i
c value
of
energy los
s
es
for each net
w
ork section,
are
give
n i
n
Ta
ble
2. Data nee
d
e
d
for t
h
e calculation is s
p
ecified in
Fi
gu
re 4.
Fi
gu
re
4.
Si
m
p
l
e
di
st
ri
b
u
t
i
o
n
net
w
or
k
fo
r t
e
s
t
case 2
Tab
l
e
2
.
Resu
lts fo
r test case
2
node
node
P
(k
–1)k
P
k
T
m
,
(
k
–1)k
(
k
–1)k
W
(
k
–1)k
W
k
Pk
Wk
c
(k
–1)k
k–1
k
kW
kW
h
h
kW
h
kW
h
$/kW
$/kW
h
$/kW
h
1
2
48,
98
6.
046,
21
2.
450,
0
985,
2
48.
256,
5
7
41.
242.
5
18,
2
0,
1153
2
0,
0713
4
0,
0713
8
2
3
12,
74
2.
000,
00
2.
350,
0
922,
8
11.
755,
8
4
11.
037.
6
00,
0
0,
1160
5
0,
0714
2
0,
0714
7
2
4
33,
47
4.
000,
00
3.
500,
0
1.
755,
7
58.
762,
3
9
30.
134.
4
00,
0
0,
1170
2
0,
0714
8
0,
0714
1
Test c
a
se
3.
Th
e th
i
r
d
test case is illu
strated
in
Figu
re
5
.
Param
e
ters fo
r n
o
d
e
1
are:
P1
= 0
,
1
243
7 $
/
kW
and
W1
= 0
,
09
351
$
/
kW
h. Th
e
v
a
lu
es of
p
a
r
a
m
e
ter
s
P
an
d
W
for eac
h node,
a
s
well as ec
onom
i
c value of
energy
l
o
sses fo
r
eac
h net
w
or
k
sect
i
o
n,
a
r
e gi
ve
n
i
n
Tabl
e 3. Dat
a
neede
d
f
o
r
t
h
e cal
cul
a
t
i
on
i
s
s
p
eci
fi
ed
i
n
Fi
g
u
re
5
.
S
3,
m
a
x
Th
= 2+j
3
M
V
A
3,
m
= 2350
S
4,
m
a
x
Th
= 4
+
j
5
MV
A
4,
m
= 3500
3 km
;
0,
2
/
k
m
4
k
m
;
0
,
3
/
k
m
5
k
m
;
0
,
2
/
k
m
10 kV
12
3
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Econ
omic Va
lua
tio
n o
f
Po
wer an
d En
erg
y
Lo
sses i
n
Distrib
u
tion
Networks (S
.
Bisan
o
v
i
c
)
44
5
Fi
gu
re
5.
Si
m
p
l
e
di
st
ri
b
u
t
i
o
n
net
w
or
k
fo
r t
e
s
t
case 3
Tab
l
e
3
.
Resu
lts fo
r test case
3
node
node
P
(k
–1)k
P
k
T
m
,
(
k
–1)k
(
k
–1)k
W
(
k
–1)k
W
k
Pk
Wk
c
(k
–1)k
k–1
k
kW
kW
h
h
kW
h
kW
h
$/kW
$/kW
h
$/kW
h
1
2
1
83,
02
4.
529,
35
3.
152,
7
1.
477,
7
122.
68
0,
06
16.
665.
3
99,
6
0,
1266
5
0,
0939
0
0,
0935
9
2
1
3
1
19,
24
2.
610,
11
2.
950,
0
1.
326,
1
25.
513,
2
4
16.
639.
8
86,
4
0,
1275
8
0,
0940
4
0,
0939
9
3
1
4
1
10,
11
2.
600,
00
2.
950,
0
1.
326,
1
13.
406,
3
9
16.
626.
4
80,
0
0,
1280
8
0,
0941
2
0,
0941
4
1
2
2
142,
00
6.
633,
71
3.
192,
2
1.
508,
1
214.
15
6,
21
25.
500.
3
07,
7
0,
1270
3
0,
0940
1
0,
0935
9
2
2
3
2
47,
04
4.
086,
67
3.
420,
3
1.
689,
8
79.
489,
3
7
25.
420.
8
18,
3
0,
1284
9
0,
0946
9
0,
0940
9
3
2
4
2
10,
41
1.
700,
00
3.
150,
0
1.
475,
6
15.
361,
4
7
11.
764.
6
80,
0
0,
1292
8
0,
0948
2
0,
0947
8
3
2
5
2
76,
26
2.
300,
00
3.
620,
0
1.
857,
0
141.
61
6,
87
13.
499.
1
60,
0
0,
1327
5
0,
0956
9
0,
0947
6
4.
CO
NCL
USI
O
NS A
N
D
FUT
URE RESE
A
R
C
H
Thi
s
pa
pe
r p
r
op
ose
d
a si
m
p
l
e
m
e
t
hod
ol
o
g
i
cal
fram
e
wo
rk t
h
at
det
e
rm
i
n
es p
r
i
ces o
f
po
wer a
n
d
energy at each node
of the
distri
bution network, as we
ll as the econom
ic value of energy losses
in the
net
w
or
k el
em
ent
s
. Gi
ve
n i
t
s
sim
p
l
i
c
i
t
y
,
pro
pos
ed
fram
e
wor
k
ca
n be
ve
ry
usef
ul
f
o
r
a qui
c
k
l
o
sses
cost
s
assessm
ent
,
as a pa
rt
o
f
l
o
ss
es cost
s al
l
o
ca
t
i
on
pr
oce
d
u
r
e
s
f
o
r
net
w
o
r
k
users
.
It
i
s
t
r
a
n
sp
are
n
t
an
d c
oul
d
be
p
r
actical fo
r im
p
l
e
m
en
tatio
n
.
App
licatio
n
s
o
n
th
e test
cas
es prese
n
ted i
n
Section 3
pu
t th
ese o
b
j
ectiv
es
in
t
o
p
e
rsp
ectiv
e. In o
r
d
e
r to
en
su
re th
e ap
p
licatio
n of th
e
m
o
d
e
l o
n
real-life
d
i
stribu
tio
n n
e
t
w
ork with d
i
st
ribu
ted
gene
rat
i
o
n, p
r
esent
e
d m
e
t
hodol
ogi
cal
fram
e
wo
r
k
sh
oul
d be m
odi
fi
ed, whi
c
h i
s
fut
u
r
e
researc
h
cha
l
l
e
nge.
Eco
nom
i
cal
ly
effi
ci
ent
net
w
o
r
k
p
r
i
ces s
h
o
u
l
d
be c
o
m
put
ed
by
c
onsi
d
eri
n
g t
h
e
m
a
rgi
n
al
im
pact
of
eac
h
user
on
net
w
or
k co
st
s:
l
o
ads an
d gene
rat
o
rs. T
h
e t
y
pe of use
r
(l
oa
d or
gene
r
a
t
o
r) a
nd t
h
e
p
a
t
t
e
rn of
net
w
or
k us
e
are
key
det
e
rm
i
n
ant
s
of
i
n
di
vi
dual
use
r’s
i
m
pact
o
n
t
h
e
net
w
o
r
k
c
o
st
s.
REFERE
NC
ES
[1]
P.
M.
de
Oliveira-de
Je
sus,
et al.
,
"Cost loss allocation in distr
i
bution networ
ks with high penetration of distributed
renewable gener
a
tion – a comparative stud
y
"
, in
Proceedings of the Internati
onal Conferenc
e
on Renewabl
e
Energies and
Po
wer
, Zarago
za, 2
005.
[2]
D. Shirm
ohamm
adi, and P.R.
Gribik, "Eva
lu
ation of
network capacity
use
for
wheeling t
r
ans
act
ions
",
IEEE
Transactions on
Power Systems
,
vol. 4
,
no
. 4
,
pp
.
1405-1413, 198
9.
S
W
=
12
8
15,
88
M
W
h
T
=
343
0
h
m
=
1
,
9
+
j
0
,
2
5
M
V
A
S
W
=
16
6
2
6,48
M
W
h
T
=
29
50
h
m
= 2,
6
+
j
0
,
9
M
V
A
S
W
=
1
1
764
,
6
8 M
W
h
T
=
3
120
h
m
=
1
,
7+
j
0
,
2
5
M
V
A
S
W
=
1
4
4
5
4,00
M
W
h
T
=
281
5
h
m
=
2
,
5+
j
0
,
4
5
M
V
A
S
W
=
134
99,
16
M
W
h
T
=
3
620
h
m
=
2,
3
+
j
0
,
2
M
V
A
Z
=
0,
385
+
j
0,
31
6
p
u
0,
266+
j
0
,
2
08
pu
Z
=
0,
297+
j
0
,
213
pu
Z =
0,
249+
j
0
,
221
pu
Z =
0,33
2
+
j
0
,
3
61
p
u
1
2
1
2
2
3
1
4
1
4
2
5
2
3
2
1
10/
2
0
k
V
20/
10
kV
0,
124
+
j
0,
257
Z =
20/
10
kV
0,
1
2
4
+
j
0
,
257
Z =
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
. 2, A
p
ri
l
20
16
:
43
9 – 4
4
6
44
6
[3]
H.H. Happ, "Co
s
t of
wheeling
methodologies",
IEEE Transactions on Power S
y
stems
, vol. 9
,
n
o
. 1, pp. 147-15
5,
1994.
[4]
A.J. Conejo,
et
a
l
.
,
"Z-bus loss
al
loca
tion",
IEEE
Transactions Power Systems
, vol. 16
, no
. 1
,
pp
. 1
05-110, 2001
.
[5]
J
.
W
.
Bial
ek, "Tr
acing
the flow o
f
ele
c
tri
c
i
t
y
"
,
in
IEE Proceeding
s
Generation, Transmission and
Distribution
,
vol.
143, pp
. 310-32
0, 1996
.
[6]
P.
M.
Costa
,
a
nd M.
Ma
tos,
"Loss
a
lloc
a
tion in
dis
t
ribution network with embedded generation",
IEEE T
r
ansactio
ns
on Powe
r Sy
stems
, vol. 19, no.
1, pp
. 384-389
,
2004.
[7]
K.A. Papadogiannis,
et al.
, "Cost allocation of losses in autonomous pow
er sy
stems
with high penetration of RES",
WSEAS Transactions on pow
er systems
, vol. 4
,
n
o
. 6
,
pp
. 210-22
0, 2009
.
[8]
J.
Muta
le
,
et
al.
, "Allocation of
losses in distribution
s
y
stems with embedded generation", in
I
EE Proceedings
Generation, Transmission and Distribution
, vol.
147, no
. 1
,
pp
. 7
-
14, 2000
.
[9]
P.
M.
De
Olive
i
ra
-de
Je
sus,
a
nd
M.
T.
Ponce
de
Le
a
o
,
"Cos
t loss
allo
ca
tion in
dis
t
ribution
networ
ks with em
bedd
ed
generation: A fu
zzy
approach",
in
Proceedings o
f
IEE Med
P
ower
2004,
Limassol, 2004.
[10]
J.M. Vignolo, and P.M. Sotk
iewicz, "Allo
catio
n of loss costs in distri
bution n
e
tworks: the no
dal factor pricin
g
method",
International Journal of
Pow
e
r
Systems
, vol. 10, no. 10
, pp
. 1-10
, 2004
.
BIOGRAP
HI
ES OF
AUTH
ORS
Smajo Bisanovic receiv
ed the d
e
gree of
Electr
i
cal
Engineer in
1991, MSc degr
ee in 1994
and
PhD degree in 2009 from the Faculty
of Electrical Engin
eer
ing,
Un
iversity
of Sarajevo
, Bosnia
and Herzegov
in
a. He is
as
s
o
cia
t
e profes
s
o
r at th
e F
acult
y of E
l
e
c
tri
cal
Engine
eri
ng, Univers
i
t
y
of Sarajevo, Bosnia and
Herze
govina. His ar
eas of in
terest in
clude operation
,
planning
and
economics of
po
wer s
y
stems an
d
application
of r
e
liability
th
eor
y
to power s
y
s
t
ems.
M
e
rs
iha S
a
m
a
rdzic re
ceiv
e
d a
BS
c degree in
power
elec
tri
cal
engineer
ing for the F
acult
y of
Electrical Eng
i
n
eering
,
Univ
ersity
of Sar
a
jevo
,
Bosnia and
Her
zegovin
a
in
201
4. She
is now
pursuing her
MSc degree
in
the same Faculty
.
Her
res
e
a
r
ch int
e
res
t
s
in
clude
com
puter
simulations and
design an
aly
s
is
applied
to pow
er
s
y
stems.
Dam
i
r Aganovic is received a M
S
c degree in po
wer elec
tri
cal en
gineer
ing from
the Facult
y
of
Electrical
Engin
eering
,
University
of Sarajevo,
B
o
snia and Herzegovina in
2010.
He is currently
purs
u
ing his
P
h
D degree in the s
a
m
e
field at the
s
a
m
e
Univers
ity. He is
an Expe
rt as
s
o
ciat
e for
Power S
y
stem
Operation
Man
a
gem
e
nt
at Pub
lic
Ent
e
rprise
E
l
ektropr
ivreda
o
f
Bosnia
and
Herzegovin
a
. His areas
of in
ter
e
st in
clude
oper
a
tion and p
l
ann
i
ng
of power s
y
s
t
em
s.
Evaluation Warning : The document was created with Spire.PDF for Python.