Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
5
,
No
. 5, Oct
o
ber
2
0
1
5
,
pp
. 94
8~
95
6
I
S
SN
: 208
8-8
7
0
8
9
48
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
A M
a
thematical Model
for Mini
mizing Add-On Operational
Cos
t
in Electri
c
al Power System
s Using Design of
Experim
e
nts
Approach
Z
a
karia Al-Omari
*
, A. Hamz
eh*,
Sade
q A. Hamed
*
, A.
Sand
ouk
**
, G.
A
l
da
h
i
m
**
* Electr
i
cal
Engineering
Depar
t
ment, Facu
lty
of
E
ngineer
ing, Al-
A
hliy
y
a
Amman University
, Jord
an
** Electr
i
cal Po
wer Engin
eer
ing
Depart
me
nt,
Dama
sc
us Uni
v
e
r
si
ty
,
Jorda
n
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 12, 2015
Rev
i
sed
Ju
l 15
,
20
15
Accepte
d
J
u
l 28, 2015
One of the k
e
y
functions of th
e Distribution S
y
stem Operators
(DSOs) o
f
ele
c
tri
cal powe
r
s
y
s
t
em
s
(EP
S
)
is
to m
i
nim
i
ze the tr
ans
m
is
s
i
on and
distribution po
wer losses and conse
quently
the operational cost. This
objec
tive
can be
reach
ed b
y
ope
rating th
e s
y
s
t
e
m
in an optim
al
m
ode which
is performed b
y
adjusting
contr
o
l para
m
e
t
e
rs
s
u
ch as
on-load
tap ch
ange
r
(OLTC) setting
s
of transform
e
rs, genera
tor e
x
cit
a
tion l
e
vels,
and VAR
compensators switching
. The d
e
viation
from ope
ra
ti
on opt
i
m
a
l
ity
wi
ll
re
sul
t
in addi
tiona
l lo
sses and additio
nal oper
a
tion
a
l
cost of th
e po
wer s
y
stem
.
Reduction of
the
operation
a
l cos
t
increas
es
the p
o
wer s
y
s
t
em
effi
cien
c
y
and
provides a significant redu
ctio
n in to
tal energ
y
consump
tion. This paper
proposes a mathematical model
for mi
nimizing the additional (add-on) costs
based on Design of Expe
riments (DOE). Th
e relation b
e
tw
een add-on
operational costs
and OLTC settings is
establis
hed b
y
means of regression
statisti
cal
ana
l
y
s
is. The dev
e
lop
e
d m
ode
l is applied to a 20-bustest network.
The regr
ession curve fitting
procedur
e r
e
quires simulation
experiments
which have b
een
carried out b
y
the
DigSilent Po
werFactor
y
13.2
Program for
performing network power flow. The resu
lts
s
how the effect
iv
enes
s
of the
m
odel. The
res
e
arch work ra
is
es
the im
portan
ce
the power s
y
s
t
e
m
operatio
n
m
a
nagem
e
nt of
the EP
S
where t
h
e Dis
t
ribution
S
y
s
t
em
Operato
r
can avo
i
d
the add-on oper
a
tion
a
l costs b
y
continuous correction to get an operation
m
ode close
to op
tim
alit
y.
Keyword:
Ad
d-
o
n
op
erat
i
onal
c
o
st
s
Power system
losses
Regressi
on statistical analysis
Tap-c
h
a
nge
r se
t
t
i
ngs
Copyright ©
201
5 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
:
Zakaria Al-
O
m
a
ri,
Electrical Engi
neeri
n
g De
part
e
m
ent, Faculty
of
E
ngi
neeri
n
g, Al
-
A
hl
i
y
y
a
Am
m
a
n
U
n
i
v
e
r
si
t
y
,
A
l
-
A
h
liyya Amman
U
n
iv
er
sity Po
st Of
f
i
ce, Zip
cod
e
1
9328
(
A
mm
an
Jo
rd
an)
.
Em
a
il: alo
m
ari
_
zak
aria@yaho
o
.co
m
1.
INTRODUCTION
Technical power losses ca
use
d
m
a
inly by the resi
stan
ce of EPS co
m
p
o
n
en
ts in
clud
e losses in
the
t
r
ansm
i
ssi
on, s
ubt
ransm
i
ssi
on
, di
st
ri
b
u
t
i
o
n
s
y
st
em
co
m
pon
ent
s
, a
n
d i
n
t
h
e co
n
n
ect
i
o
n
l
i
nks
f
r
o
m
di
st
ri
but
i
o
n
t
o
con
s
um
ers. Tran
sm
i
ssi
on and
Di
st
ri
b
u
t
i
o
n l
o
sses i
n
t
h
e
devel
o
pe
d co
unt
ri
es are i
n
r
a
nge
fr
om
4-1
2
% [
1
,
2
]
, wh
ile lo
sses
m
a
y in
crease to
ov
er
3
0
%
i
n
o
t
h
e
r co
untri
e
s. Technical losses a
r
e possi
ble to com
pute
and
cont
rol
,
p
r
o
v
i
d
ed t
h
e
dat
a
o
f
t
h
e c
once
r
ned
p
o
we
r system
in
clu
d
i
ng
l
o
ad
p
r
o
f
ile is av
ailable.
Th
e v
a
l
u
e of po
wer lo
sses is
o
n
e
o
f
th
e
k
e
y
in
d
i
cato
r
s for q
u
a
lity o
f
EPS o
p
e
ration
.
Op
erat
o
r
s
o
f
p
o
wer system
s
m
a
k
e
certain
t
h
at th
e system is o
p
e
rating
in
or close to
an
op
tim
al
m
o
d
e
, so
t
h
at th
e
qu
ality
an
d
reliab
ility
o
f
supp
ly to
co
n
s
u
m
ers are ensu
red
.
Fr
o
m
th
e v
i
ewpo
in
t of cu
sto
m
ers, th
e EPS sho
u
l
d
d
e
liv
er
electrical en
erg
y
with
h
i
gh
p
o
wer qu
ality in
term
s
o
f
voltag
e
and
frequ
e
n
c
y, h
i
g
h
reliab
ility, an
d
min
i
m
a
l
cost
[
3
,
4,
5
,
6
]
. M
o
re
ove
r, t
h
e gree
n
h
ouse
em
i
ssi
ons o
f
t
h
e
gene
rat
i
o
n s
y
st
em
shoul
d
be re
d
u
ced
acc
or
di
n
g
to
in
tern
ation
a
l reg
u
l
ation
s
[7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
948
–
9
56
94
9
Any
va
ri
at
i
ons
i
n
t
h
e powe
r
s
y
st
em
confi
g
u
r
at
i
on or i
n
t
h
e
l
o
ad p
r
o
f
i
l
e
al
on
gsi
d
e t
h
e no
nsy
m
m
e
t
r
y
an
d non
lin
earit
ies o
f
EPS can cau
se d
e
v
i
ation
fro
m
th
e id
eal o
p
tim
al
m
o
d
e
.
Th
is
d
e
v
i
atio
n
resu
lts in
ad
d-on
po
we
r l
o
sses
and c
o
nse
que
n
t
l
y
addi
t
i
onal
ope
rat
i
o
nal
co
st
of s
u
ppl
i
e
d
el
ect
ri
cal
energy
. T
o
e
nha
n
ce t
h
i
s
situ
atio
n
,
t
h
e lo
ad
bu
s vo
ltages sho
u
l
d
b
e
m
a
in
tain
ed
with
i
n
sp
eci
fied
limits. Th
is go
al can
b
e
ach
i
ev
ed b
y
a
set of actions
s
u
ch as c
ontrolling
ge
nerators
excitati
on, swit
ching
reacti
v
e powe
r
com
p
ensators
, and a
d
justing
o
n
lo
ad
lin
e tap
ch
ang
e
r (OLTC)
o
f
grid
tr
an
sfo
r
m
e
r
s
[8
, 9, 10
, 11
].
Thi
s
pape
r
foc
u
ses
o
n
m
i
nim
i
zi
ng t
h
e
ad
d
-
on
p
o
w
er l
o
ss
es an
d
op
erat
i
onal
c
o
st
s
by
adj
u
st
i
n
g t
h
e
OLTC
of
gri
d
t
r
ans
f
o
r
m
e
rs. The
basi
s o
f
t
h
e st
u
d
y
m
e
t
h
o
dol
ogy
i
s
t
h
e De
si
g
n
o
f
Ex
peri
m
e
nt
s (DOE
)
approach
whic
h hel
p
s to
detect th
e im
pact of inputs-fa
ctors
on the
outp
u
t
-resp
o
n
s
e
wh
ile realizing
the
o
b
j
ectiv
es. Th
i
s
statistical th
eo
ry
foun
d its a
ppl
i
cat
i
o
ns i
n
m
a
ny
areas i
n
c
l
udi
n
g
EPSs
[
1
2]
.
2.
POWER
LOS
S
ES VE
RS
US
CO
NTR
O
L
FACT
OR
S
To
ob
tain
th
e p
o
wer
lo
sses
∆
as a f
u
nct
i
o
n
o
f
c
ont
r
o
l
para
m
e
t
e
rs (f
o
r
e
x
am
pl
e OLTC
s
e
t
t
i
ng
o
f
tran
sform
e
r
i
who
s
e valu
e co
rresp
ond
s t
o
i
t
s tu
rn
s ratio
), let us assu
m
e
th
at th
e lo
ad profile of a
power
syste
m
is changed from
m
-v
arian
t
to(
m+
1
) v
a
rian
t
wit
h
op
ti
m
a
l
lo
sses
∆
corres
ponding t
o
, and
∆
co
rre
sp
o
ndi
ng
t
o
, resp
ectively. If th
e contro
l
p
a
ram
e
ters of th
e seco
nd
m
o
d
e
(
m+1
) h
a
s
som
e
value
w
h
i
c
h i
s
not
t
h
e
opt
i
m
al
fact
or,
t
h
e l
o
sses
w
o
ul
d
be
∆
lead
in
g to
add
itio
n
a
l l
o
sses
as fo
llows:
∆
∆
(1
)
In g
e
n
e
ral equatio
n
(1) can
be written
as
(2
)
an
d, in ter
m
s o
f
ad
d-
on
op
er
at
io
n
a
l co
st, as:
∗
(3
)
whe
r
e,
act
ual
ad
d-
o
n
po
we l
o
sses
f
o
r
(
m+
1
)-m
od
e f
o
r t
r
ans
f
orm
e
r
time
d
urati
o
no
f
m+
1
l
o
ad
m
o
d
ede
finedbythe
d
ail
y
loa
dpr
o
f
ile
B
c
o
s
t
o
fener
gyUS
D/kWh
From
t
h
e ab
o
v
e-m
e
nt
i
one
d
equat
i
o
ns
, we
can o
b
se
rve a
rel
a
t
i
ons
hi
p
b
e
t
w
een a
d
d
-
on
ope
rat
i
o
nal
cost
an
d th
e
sw
itch
i
ng
-steps nu
m
b
er
o
f
each
tr
an
sf
or
m
e
r
.
T
h
i
s
rel
a
t
i
on
ca
n be
p
r
e
d
i
c
t
e
d by
use o
f
l
i
n
ear re
g
r
essi
o
n
pr
oce
d
u
r
e
ba
sed
o
n
dat
a
acq
ui
re
d f
r
o
m
desi
gne
d e
x
peri
m
e
nt
s.
3.
STATISTI
C
A
LLY-
D
ESI
G
NED
E
X
PE
RIME
NTS
A
N
D
REG
R
ES
SION
Experim
e
ntal
design is a stat
istical
theory that addre
sses t
h
e
design
an
d
an
alysis o
f
exper
i
m
e
n
t
s. I
n
an ex
peri
m
e
nt
al
st
udy
, one
o
r
m
o
re fact
o
r
s (i
n
d
epe
n
dent
variables) are c
h
ange
d so
that
the factors influence
anot
her
va
riabl
e
refe
rre
d to
as
the (
r
esp
o
n
se
varia
b
le),
or
si
m
p
ly
t
h
e resp
o
n
se i
s
obt
ai
ne
d
.
The
dat
a
obt
a
i
ned
by
co
n
duct
i
ng
t
h
e e
x
peri
m
e
nt
s i
s
a
n
al
y
zed
by
re
g
r
essi
on
. R
e
gressi
o
n
a
n
al
y
s
i
s
ser
v
es t
o
i
d
e
n
t
i
f
y
t
h
e
rel
a
t
i
ons
hi
p
be
t
w
een a de
pe
n
d
ent
vari
abl
e
(
r
esp
o
n
se) a
n
d one
or m
o
re i
nde
pe
nde
nt
va
ri
abl
e
s (
f
act
o
r
s
)
. A
l
i
n
ear or
no
nl
i
n
ear re
g
r
essi
o
n
m
odel
of t
h
e
rel
a
t
i
onshi
p i
s
hy
pot
hesi
zed
,
and t
h
e re
gr
es
si
on c
o
ef
fi
ci
en
t
s
are
cal
cul
a
t
e
d usi
ng t
h
e e
xpe
ri
m
e
nt
al
dat
a
and t
h
e l
east
-
s
qua
re m
e
t
hod
t
o
devel
o
p a
n
est
i
m
a
t
e
d regressi
o
n
equat
i
o
n.
Ex
pe
ri
m
e
nt
al
dat
a
are t
h
e
n
em
pl
oy
ed t
o
det
e
rm
in
e if th
e m
o
d
e
l is satisfacto
r
y.
If th
e m
o
d
e
l is fo
und
t
o
be sat
i
s
fact
ory
,
t
h
e est
i
m
at
ed re
gres
si
o
n
eq
uat
i
o
n ca
n be
use
d
t
o
pre
d
i
c
t
t
h
e v
a
l
u
e o
f
t
h
e
de
p
e
nde
nt
vari
a
b
l
e
’s
gi
ve
n
val
u
es
f
o
r
t
h
e i
nde
pe
nde
nt
vari
a
b
l
e
s [
1
3]
.
Th
e po
lyn
o
m
ia
l
regression
m
o
d
e
l
…
,
,
…
,
(4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
A Ma
t
h
ema
tical Mod
e
l fo
r
Min
i
mizing
Add
-
On Op
era
tion
a
l Co
st in
Electrica
l Po
wer …
(Za
k
a
r
ia Al-O
ma
ri)
95
0
can
b
e
ex
pressed
i
n
m
a
trix
fo
rm
in
term
s of a
d
e
sign m
a
t
r
ix
, a
respon
se v
ect
o
r
, a
pa
ram
e
t
e
r vect
or
,
and a
vector
of
ra
nd
om
err
o
rs
. T
h
e
ro
w
o
f
an
d
will co
n
t
ain th
e
x
and
y
v
a
lu
es
for
th
e
dat
a
sam
p
le. Th
en th
e m
o
d
e
l can
be written
as a
syste
m
o
f
lin
ear equ
a
tio
ns [12
,
15
,
16
]:
n
3
2
1
f
2
1
0
f
n
2
n
n
f
3
2
3
3
f
2
2
2
2
f
1
2
1
1
n
3
2
1
a
a
a
a
x
x
x
1
x
x
x
1
x
x
x
1
x
x
x
1
y
y
y
y
(5
)
wh
ich
wh
en
u
s
in
g
pu
re
m
a
tri
x
n
o
t
ation
is written
as
(6
)
The vect
o
r
of
e
s
t
i
m
a
t
e
d
pol
y
n
o
m
i
al
regr
essi
o
n
c
o
ef
fi
ci
ent
s
(
u
si
n
g
or
di
na
ry
l
east
-
sq
uares
m
e
t
hod
)
i
s
:
(7
)
Th
e
fin
a
l
regressio
n
m
o
d
e
l fittin
g
th
e exp
e
rimen
t
al d
a
ta is:
(8
)
Equ
a
tio
n
(2
)
t
h
at show
s ad
d-
on
lo
ss
as a fu
nct
i
o
n
of
can
be consi
d
ered a
s
a relat
i
on
bet
w
ee
n a
d
d
-
o
n
l
o
ss a
n
d
swi
t
chi
n
g st
e
p
num
ber
o
f
OLTC
s
e
t
t
i
ng
whi
c
h c
a
n
be
det
e
rm
i
n
ed as:
(9
)
whe
r
e,
i
s
po
si
t
i
on
st
e
p
of
OLTC
o
f
t
r
a
n
sf
orm
e
r
i
.
With
a su
itab
l
e
scalin
g
of t
h
e v
e
rtical ax
is,
Equ
a
tio
n (2) can
b
e
written
as
. Th
e
v
a
lu
es
o
f
add
ition
a
l op
eration
a
l co
st
can
b
e
co
m
p
uted
b
y
ru
n
n
i
n
g a
po
w
e
r fl
ow s
o
ft
wa
re f
o
r t
h
e E
P
S
wi
t
h
vari
ous
l
o
ad
m
odes an
d d
e
si
g
n
ed
ex
peri
m
e
nt
s con
cerni
n
g
th
e sets
o
f
OLTC of tran
sformers.
To a
p
pl
y
a re
gressi
o
n
a
n
al
y
s
i
s
, a re
g
r
essi
on
m
odel
sh
o
u
l
d
fi
rst
be se
l
ect
ed. R
e
g
r
es
si
on m
odel
s
esti
m
a
te
y
v
a
lu
es fo
r kno
wn
x
val
u
e
s
. T
h
e
se
con
d
o
r
de
r
pol
y
nom
i
a
l
regres
si
on
m
odel
i
s
s
e
l
ect
ed as:
(1
0)
Usi
n
g t
h
e l
east
sq
uare
s m
e
t
hod, t
h
e
no
rm
al
equat
i
o
ns
are
f
o
rm
ul
at
ed as:
(1
1)
These
n
o
rm
al
equat
i
o
ns
ha
ve
u
n
i
q
ue s
o
l
u
t
i
o
ns
pr
o
v
i
d
e
d
t
h
at
is
d
i
stin
ct.
Th
e curv
e fittin
g
can
b
e
p
e
rfo
rm
ed
b
y
Matl
ab
u
s
ing
th
e too
l
bo
x
cf
t
ool
(
x
data,
y
dat
a
)
wh
ich
op
en
s
Cu
rv
e Fittin
g
Too
l
with
d
a
ta, factors
x
data
and
y
dat
a
.
x
data
a
nd
y
data
m
u
st be vectors
of t
h
e sam
e
size.
Th
e
resu
lts i
n
clu
d
e
v
a
lu
es of con
s
tan
t
s a’
s
an
d th
e i
n
d
i
cat
o
r
s of
g
ood
n
e
ss of fit:
SSE,
R
2
,
ad
ju
s
t
ed
R
2
and
RM
SE
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
948
–
9
56
95
1
Th
e
regressi
o
n
m
o
d
e
l in
terms of f
acto
r
s an
d r
e
sp
on
se of
tr
an
sfo
r
m
e
r
is rep
r
esen
ted as:
,
(1
2)
whe
r
e
,
and
re
prese
n
t
and
, respectively.
4.
CASE ST
UDY
4.
1
T
e
st
Ne
t
w
ork
The el
ect
ri
cal
net
w
or
k use
d
i
n
t
h
i
s
st
u
d
y
i
s
gi
ve
n i
n
Fi
g
u
r
e
1. It
co
nsi
s
t
s
of 2
0
buse
s
,
20
bra
n
c
h
es
and
1
0
t
r
ans
f
or
m
e
rs, 5
o
f
w
h
i
c
h a
r
e e
qui
ppe
d
wi
t
h
OLTC
s.
Fi
gu
re
1.
Si
n
g
l
e
Li
ne
di
ag
ram
o
f
t
h
e
t
e
st
net
w
o
r
k
The i
n
put
data
are s
u
mmarized in Ta
bles 1,
2 a
n
d 3.
Tabl
e 1. Dat
a
of
t
h
e 2
0
–
b
u
s
t
e
st
net
w
or
k
Bus No.
PL (
M
W)
PG (
M
W)
Bus No.
PL (
M
W)
PG (
M
W)
1 0.
00
0.
00
11
0.
00
0.
00
2 40.
00
100.
00
12
0.
00
0.
00
3 45.
00
100.
00
13
40.
00
18.
60
4 40.
20
100.
00
14
0.
00
0.
00
5 30.
00
100.
00
15
0.
00
0.
00
6 0.
00
0.
00
16
0.
00
0.
00
7 0.
00
0.
00
17
0.
00
0.
00
8 0.
00
0.
00
18
0.
00
0.
00
9 36.
20
16.
50
19
70.
00
26.
60
10
63.
80
28.
80
20
65.
00
28.
20
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
A Ma
t
h
ema
tical Mod
e
l fo
r
Min
i
mizing
Add
-
On Op
era
tion
a
l Co
st in
Electrica
l Po
wer …
(Za
k
a
r
ia Al-O
ma
ri)
95
2
Tabl
e 2.
B
r
anc
h
es dat
a
of
t
e
st
net
w
o
r
k
Branch No.
Fro
m
Bus
To Bus
Ser
i
es Im
pedance (p.
u
)
T
a
p Setting
M
VA R
a
ting
R X
1.
1
6
0.
0000
0
0.
1300
0
-
500.
00
2.
2
14
0.
0000
0
0.
1100
0
-
500.
00
3.
3
15
0.
0000
0
0.
1100
0
-
500.
00
4.
4
16
0.
0000
0
0.
1100
0
-
500.
00
5.
5
17
0.
0000
0
0.
1100
0
-
500.
00
6.
6
7
0.
0570
0
0.
1737
0
-
150.
00
7.
6
12
0.
0415
8
0.
1614
4
-
150.
00
8.
6
14
0.
0530
0
0.
1270
0
-
150.
00
9.
7
8
0.
0301
8
0.
0919
6
-
150.
00
10.
7
20
0.
0000
0
0.
1260
0
1.
0681
100.
00
11.
8
9
0.
0000
0
0.
1200
0
1.
0681
80.
00
12.
8
18
0.
0509
1
0.
1532
6
-
150.
00
13.
11
10
0.
0000
0
0.
1260
0
1.
0681
80.
00
14.
11
12
0.
0617
3
0.
1859
6
-
150.
00
15.
11
15
0.
0207
9
0.
0633
5
-
150.
00
16.
12
13
0.
0000
0
0.
1074
0
1.
0681
63.
00
17.
15
16
0.
0288
4
0.
0878
7
-
150.
00
18.
16
17
0.
0737
6
0.
2247
9
-
150.
00
19.
17
18
0.
0663
9
0.
2023
1
-
150.
00
20.
18
19
0.
0000
0
0.
1260
0
1.
0681
100.
00
Tabl
e
3.
Dat
a
of
t
h
e t
r
a
n
s
f
o
r
m
e
rs an
d m
ode
s l
o
sses
Transf
or
m
e
r
No
1
2
3
4
5
6
7
8
9
10
-
-
-
-
-
0.
078
8 0.
078
8 0.
078
8 0.
078
8 0.
078
8
0.
1515
0.
1515
0.
1136
0.
1136
0.
1136
4.
000
4.
000
4.
000
4.
000
4.
000
-
-
-
-
-
4.
078
8 4.
078
8 4.
078
8 4.
078
8 4.
078
8
-
-
-
-
-
4.
15
76 4.
15
76 4.
15
76 4.
15
76 4.
15
76
-
-
-
-
-
4.
2364
4.
2364
4.
2364
4.
2364
4.
2364
4.
3152
4.
3152
4.
3152
4.
3152
4.
3152
-
-
-
-
-
4.
3949
4.
3949
4.
3949
4.
3949
4.
3949
M
ode
1
(
O
pti
m
al)
0.
1515
0.
1515
0.
1136
0.
1136
0.
1136
4.
3949
4.
3949
4.
0000
4.
0000
4.
0000
∆
;
M
W
19.
565
M
o
d
e
2
(
P
e
a
k
)
0.
1515
0.
1515
0.
1136
0.
1136
0.
1136
4.
0000
4.
0000
4.
2364
4.
0000
4.
0000
∆;
M
W
31.
68
OL
T
C
:
-
-
-
5 5 5 5 5
Fi
gu
re
2 sh
o
w
s Loa
d
M
o
de (
m
)–
op
tim
a
l
an
d
(
m+1
)
-
p
e
ak)
po
wer
losses in
M
W
,
w
ithou
t pr
op
er
tap
p
i
n
g
of
th
e 5 tran
sfo
r
m
e
rs .
Fi
gu
re
2.
P
o
we
r L
o
sses
o
f
m
odes
m
an
d (
m+
1
)
Loa
d
va
rent
s
0
1
2
3
4
5
6
7
8
9
10
M
ode
(
m
)
-O
p
tim
al Load
;
70%
M
ode
(
m+
1
)
-Peak Load
7
0%
100%
19.565
M
W
31.68
M
W
8
Hours
7
Hours
Load m
ode
capacity;
[%]
Powe
r sy
ste
m
losse
s;
[MW]
Ti
m
e
peri
o;
[Hours]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
948
–
9
56
95
3
Th
e
5
sing
le-facto
r test scen
ario
s ar
e
sh
ow
n
i
n
Tabl
e
4,
fr
o
m
whi
c
h t
h
e fi
t
t
e
d reg
r
essi
on
cur
v
es a
r
e
obt
ai
ne
d
by
M
a
t
l
a
b.
Table
4.
Single-Factor Test
Sc
enari
o
for L
o
a
d
Mode
(
m+
1
)
Scenarios
T6
TC setting
T7
TC setting
T8
TC setting
T9
TC setting
T
10
TC setting
Δ
P
MW
δ
P
MW
1 1
0
0
0
0
38.
24
6.
56
2 2
0
0
0
0
35.
46
3.
78
3 3
0
0
0
0
34.
77
3.
09
4 4
0
0
0
0
34.
08
2.
40
5 5
0
0
0
0
33.
53
1.
85
6 0
1
0
0
0
39.
86
8.
18
7 0
2
0
0
0
39.
66
7.
98
8 0
3
0
0
0
39.
57
7.
89
9 0
4
0
0
0
39.
42
7.
74
10
0
5
0
0
0
39.
21
7.
53
11
0
0
1
0
0
36.
70
5.
02
12
0
0
2
0
0
34.
49
2.
81
13
0
0
3
0
0
33.
82
2.
14
14
0
0
4
0
0
33.
44
1.
76
15
0
0
5
0
0
32.
44
0.
759
16
0
0
0
1
0
39.
68
8.
00
17
0
0
0
2
0
38.
15
6.
471
18
0
0
0
3
0
36.
12
4.
439
19
0
0
0
4
0
35.
894
4.
214
20
0
0
0
5
0
34.
63
2.
95
21
0
0
0
0
1
39.
66
7.
98
22
0
0
0
0
2
39.
16
7.
48
23
0
0
0
0
3
39.
17
7.
49
24
0
0
0
0
4
39.
18
7.
50
25
0
0
0
0
5
39.
21
7.
53
From
Fi
gure
3 i
t
i
s
obvi
o
u
s
t
h
at
t
h
e t
r
ansfo
r
m
e
rs 7 and 1
0
ha
ve ne
gl
i
g
i
b
l
e
effect
s on ad
d-
o
n
ope
rat
i
o
nal
co
st
s, w
h
i
l
e
t
h
e
t
r
ans
f
o
r
m
e
rs 6
,
8
,
an
d
9 a
r
e
con
s
i
d
ere
d
a
s
cri
t
i
cal
com
ponent
s
.
T
h
ere
f
o
r
e,
we
check t
h
e m
u
ltifactor sce
n
ari
o
s of
t
r
ans
f
or
m
e
rs 6, 8 a
nd
9. T
h
e n
u
m
b
er of t
h
ese sce
n
a
r
i
o
s s
h
o
u
l
d
be
2^
3 = 8
.
Th
e
po
wer
flow for th
ese scen
ari
o
s
resu
lt in v
a
lu
es
o
f
po
wer
lo
sses an
d ad
d-o
n
co
sts as
sh
own
in Tab
l
e 5
.
Fig
u
re
3
.
Fitted
regression
curv
es of t
h
e
5
si
n
g
l
e-factor test
scen
ario
s
C
add
= 185.6
n
2
-
1728.5
n +
5134.1
C
add
=
107.11
n
2
-
1117.7
n +
3496.3
C
add
=
93.486
n
2
-
1252.9
n +
5650.7
C
add
=
23.2
n
2
-
188.48
n +
4751
C
add
= 42.4
n
2
-
303.68
n +
4698.4
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
12
34
5
OLTC
Settings
Add-on Operational
Costs,
dependi
ng
on the step of OLTC
for
each
tran
sfo
r
m
e
r, USD
Transform
e
r 6
Transform
e
r 8
Transform
e
r 9
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
A Ma
t
h
ema
tical Mod
e
l fo
r
Min
i
mizing
Add
-
On Op
era
tion
a
l Co
st in
Electrica
l Po
wer …
(Za
k
a
r
ia Al-O
ma
ri)
95
4
Tab
l
e
5
.
M
u
ltifacto
r
Test Scen
ari
o
s
for Lo
ad
Mod
e
(
m+
1
)
Scenarios No;
T6
T8
T9
Δ
P
; M
W
δ
P
; M
W
1
44.
425
12.
745
2 +
35.
054
1.
107
3
+
38.
444
6.
764
4
+ 39.
65
7.
97
5
+ +
37.
85
6.
17
6 +
+
+
31.
73
0.
05
7 +
+
32.
207
0.
527
8 +
+ 34.
536
2.
856
Fig
u
re
4
shows Lo
ad
fl
o
w
resu
lts of power
lo
sses an
d
a
dd-on
p
o
wer l
o
sses o
f
Mu
ltifacto
r Ex
perim
e
n
t
s for
Loa
d
M
ode
(
m+1
) loa
d
.
Fig
u
re
4
.
Lo
ad
flow resu
lts
o
f
po
wer l
o
sses and
ad
d
-
o
n
po
wer
l
o
sses of Mu
ltifacto
r
Exp
e
rim
e
n
t
s
for Lo
ad
M
ode
(
m+
1)
Th
e gr
ap
h
i
cal ch
ar
t of
add-
on
op
eration
a
l lo
sses an
d
ad
d-o
n
o
p
e
ration
a
l co
sts o
f
m
u
lti
-factor test
scenari
o
s
for L
o
ad Mode
(
m+
1)
i
s
sh
o
w
n
i
n
Fi
gu
re
5.
Fi
gu
re
5.
A
d
d-
on
o
p
e
r
at
i
onal
l
o
sses a
n
d a
d
d
-
on
o
p
e
r
at
i
onal
cost
s
of
m
u
l
t
i
-fact
or t
e
st
sce
n
a
r
i
o
s
f
o
r
Loa
d
M
ode
(
m+
1)
0
5
10
15
20
25
30
35
40
45
12
34
56
78
44.425
35.054
38.444
39.65
37.85
31.73
32.207
34.536
12.745
1.107
6.764
7.97
6.17
0.05
0.527
2.856
Exsperiements
Scenarios
Power
Losses;
[MW]
Add
‐
on
Power
Losses;
[MW]
0
2
4
6
8
10
12
14
123
4567
8
12.745
1.107
6.764
7.97
6.17
0.05
0.527
2.856
7142
620
3788
4463
3455
28
295
1599
Add-on
Operat
i
onal
Losses;
[M
W
]
Add-on
Operat
i
onal
C
o
st
s;
[USD]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
948
–
9
56
95
5
From
Figure 5 it is obvious that the scena
r
io 6
gives the
m
i
nim
u
m
additional powe
r losses
of
0.05
M
W
and
co
n
s
eq
u
e
n
tly th
e lowest add
-
on
operatio
n
a
l co
st.
Th
is scen
ario
dictates th
at th
e OLTC settin
gs o
f
all
t
h
ree t
r
a
n
s
f
o
r
m
e
rs s
h
o
u
l
d
be a
t
t
h
e hi
gh
p
o
si
t
i
on
(St
e
p
5).
5.
CO
NCL
USI
O
NS
The
pape
r
pre
s
ent
s
a m
a
t
h
em
at
i
cal
m
odel an
d an
al
g
o
ri
t
h
m
of m
i
nim
i
zi
ng t
h
e a
d
d
-
o
n
ope
rat
i
o
nal
real
po
we
r l
o
s
s
es an
d ad
d-
o
n
ope
rat
i
o
nal
co
st
i
n
el
ect
ri
cal
po
we
r sy
st
em
s, base
d o
n
Des
i
gn
of E
x
peri
m
e
nt
s
app
r
oach a
nd
pol
y
n
o
m
i
al
l
i
n
ear re
gressi
on
.
The m
odel
t
a
kes i
n
t
o
c
o
nsi
d
erat
i
o
n t
h
e c
ont
rol
pa
ram
e
ters o
f
OLTC
t
r
ans
f
or
m
e
rs. Ho
we
ver
,
i
t
can easi
l
y
be ext
e
nde
d t
o
c
onsi
d
er
ot
he
r cont
rol
va
ri
abl
e
s such as ge
ner
a
t
o
r
exci
t
a
t
i
on l
e
v
e
l
s
, an
d
VAR
com
p
ensat
o
rs
swi
t
c
hi
n
g
.
T
h
e
devel
ope
d
m
odel
and
al
go
ri
t
h
m
sho
u
l
d
be
bene
fi
ci
al
f
o
r
Di
st
ri
b
u
t
i
o
n
S
y
st
em
Op
erat
or in detecting
critical transfor
m
e
rs and
m
e
et
i
ng
pr
o
p
er
t
a
p
p
i
n
g t
o
m
i
nim
i
ze t
h
e p
o
we
r sy
st
em
add
-
on l
o
sses.
T
h
e m
odel
has
b
een s
u
ccessf
ul
l
y
appl
i
e
d t
o
a t
e
st
net
w
or
k an
d t
h
e
resu
lts
ob
tain
ed
were ex
am
in
ed
an
d d
i
scu
s
sed
.
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i
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rançois
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t
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c
ienc
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edia
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ca
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0
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e
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I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Ma
t
h
ema
tical Mod
e
l fo
r
Min
i
mizing
Add
-
On Op
era
tion
a
l Co
st in
Electrica
l Po
wer …
(Za
k
a
r
ia Al-O
ma
ri)
95
6
BIOGRAP
HI
ES OF
AUTH
ORS
Z
a
karia Al-O
mari
, PhD.El
.E
ng. (IEEE M)
was born in Irb
id Jordan on Ju
ne 3, 1966. He
obtain
e
d his MSc degree (1991), in
Electrical Engineer
ing/Power
fro the Faculty
of Electrical
Engine
ering, Vi
nn
y
t
si
a State Pol
y
t
echn
i
c Institu
t
e
, Ukraine and h
i
s PhD degree from
the Facult
y
of Electrical En
gineer
ing, Vinn
y
t
sia State Un
iversity
, Ukr
a
ine in 1998. Curr
ently
h
e
is an
As
s
i
s
t
ant P
r
ofess
o
r at Elect
ric
a
l
Engineering Department at Facult
y
of Eng
i
neer
ing, Al-Ahliyy
a
Am
ma
n Uni
v
e
r
si
ty
i
n
Amma
n,
Jorda
n
.
Hi
s ma
i
n
in
terests
are minimizing of
power s
y
stem
los
s
e
s
,
renewab
l
e en
erg
y
,
load
forec
a
s
ting,
re
l
i
abil
it
y and
e
ffi
cien
c
y
. H
e
has
published 12
techn
i
ca
l pap
e
rs
in J
ournals
an
d intern
ation
a
l
conferen
ces
.
He
is
a M
e
m
b
er
of IEEE
P
E
S
S
o
ciet
y
Ali Hamz
eh
, P
h
D.El.
E
ng. (
I
E
EE M
)
was
bo
rn in S
y
r
i
a
.
He
rece
ived
the
B.S
c
degr
ee in
Electrical
Engin
eering from the
Aleppo University
, S
y
r
i
a and
an
d his Ph.D degree in electrical
engineering, fro
m University
o
f
Dresden, Germ
an
y, in
19. Curr
entl
y h
e
is a
Full Professor at
Ele
c
tri
cal
Eng
i
n
eering
Depar
t
m
e
nt at
F
acu
lt
y of
Engineering,
Al-
A
hliy
y
a
Amma
n Uni
v
e
r
si
ty
i
n
Amma
n,
Jorda
n
.
His
ma
in inte
re
sts a
r
e
Powe
r
s
y
s
t
em
s
ecurit
y
,
P
o
wer s
y
s
t
em
s
t
abili
t
y
, S
m
art
grids, Integr
atio
n of Distributed
Generations
(w
ind and solar) into electric grid
, Design and
operation of So
lar PV and Wi
nd Turbine s
y
s
t
em
s, Energ
y
Efficiency
and Environmental
Protection and
Operation & Mainten
a
nce of con
v
en
tion
a
l and renewable electric power sy
stems.
He has published 87 technical p
a
pers in Journals
and interna
tiona
l conferen
ces
. H
e
is
a M
e
m
b
er
of IE
EE
PE
S Soc
i
ety
Sade
q Ab
dulla
h Hame
d,
he
is the presiden
t of
AAU since 2011, He received
the B.Sc degr
ee
in
Electrical Power
Engineering fr
om
the Dam
a
s
c
us
Univers
i
t
y
,
M
.
S
c
. in P
o
wer
Elec
troni
cs
and
S
y
stems and Ph.D. in Power
Electronics (A
C Power Conditioning & El
ec
tri
cal M
a
chin
es
Control) from the UMIST, UK. Prof. Hamed h
a
s
published mo
re th
an 25 r
e
search pap
e
rs in
highly
-rank
ed journals and
co
nferences. In
a
ddition
to his
long exper
i
ence in th
e field
of
education as a
university
prof
essor, locally
and
interna
tion
a
ll
y,
he has supervised m
a
n
y
M.Sc
Thes
es
. P
r
of.
S
a
deq Ham
e
d was
the Vic
e
-P
res
i
de
nt for Acad
em
ic
Affairs
& De
an
of the F
a
cult
y
of Engineering at AAU,
also as Dean of Faculty
of
Engineering Techno
logy
,
Al-Balqa’ Applied
University
, Vice Dean
, of
Faculty
o
f
Eng
i
n
eering
and
Technolog
y
and
Chairman of
the
D
e
partm
e
nt o
f
E
l
ec
tric
al
Engin
e
e
r
ing, U
n
iv
ers
i
t
y
of J
o
rdan.
Abba
s San
d
ouk
received
the B
.
Sc (1985), M.Sc. (1994) and
Ph.D (1998) degrees in Electr
ical
P
o
wer Engineer
i
ng from
Dam
a
s
c
us
Univers
i
t
y
, S
y
ri
a. He
is
curre
ntl
y
an As
s
o
ciat
e P
r
ofes
s
o
r at
Electrical Power Engineering D
e
pa
rtm
e
nt
at F
a
cult
y of
M
echa
n
ica
l
&
Ele
c
tri
c
al Eng
i
ne
ering
,
Damascus University
, S
y
ria.
He has published more than 1
0
peer-r
eviewed Journal and
Conferenc
e
pap
e
rs
. His
m
a
in res
earch in
ter
e
s
t
s
are El
ectr
i
c
a
l
m
achines
, P
o
we
r s
y
s
t
em
s
,
and
Renewabl
es
en
erg
y
s
y
s
t
em
s
.
He is
m
e
m
b
er of S
y
rian
En
gineers
S
o
ci
et
y (S
ES
), Energy
Com
m
ittee of S
E
S
-
Branch Dam
a
s
c
us
, W
o
rld W
i
nd Energ
y
Association (WWEA), and Arab
Institute for
Operation
& M
a
int
e
nance in
Arab C
ountries.
Ghada Aldahi
m
recieved h
e
r
B.Sc (1985), M.Sc. (2008) and
Ph.D (2014) degrees in Electrical
P
o
wer Engine
eri
ng from
Dam
a
s
c
us
Univers
i
t
y
,
S
y
ri
a.
S
h
e is
curr
entl
y
a
te
chnic
a
l
s
t
aff m
a
nag
e
r
and lectur
er at
Electrical Engin
eering D
e
partm
e
nt and
M
ech
atr
onics
De
par
t
ment at Damascus
University
, S
y
ria. She has published 8 peer-r
eviewed Journal and Conference papers. Her
res
earch
are
a
s
are El
ec
tric
al P
o
wer S
y
s
t
em
s
,
Dis
t
ributed Gen
e
rat
i
on, Bifur
c
a
tion & Chaos
Theor
y
, Applications to DC-DC Converters, Re
newable
Energ
y
S
y
stems. She is member of
S
y
rian
Engin
eer
s Societ
y (SES)
,
En
erg
y
Com
mitte
e of SES-Br
anch Dam
a
scus,
W
o
rld W
i
nd
Energ
y
Associa
tion (W
W
E
A), and Arab Inst
itute
for Opera
tion & Ma
inte
nance
in Arab
Countries.
Evaluation Warning : The document was created with Spire.PDF for Python.