Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 1, No. 2,
February 20
1
6
, pp. 249 ~
254
DOI: 10.115
9
1
/ijeecs.v1.i2.pp24
9-2
5
4
249
Re
cei
v
ed
De
cem
ber 8, 20
15; Re
vised Janua
ry 1
0
, 20
16; Accepted
Jan
uary 20, 2
016
Optimal DG Pla
cement with the
Aim of Profits
Maximization
Sobhan Do
r
a
haki
Youn
g Res
ear
chers an
d Elite
Club, Bush
ehr
br
anch, Islami
c Azad Univ
ers
i
t
y
, Bush
ehr, Iran
E-mail: Sob
h
a
ndor
ahak
i@gm
ail.com
A
b
st
r
a
ct
Using
distri
but
ed g
e
n
e
ratio
n
pow
er pl
ants is
co
mmon
due t
o
adv
anta
ges s
u
ch as syste
m
capac
ity
rele
ase, vo
ltag
e su
pport
an
d
reduc
ed
en
erg
y
loss
es i
n
p
o
w
er netw
o
rks. Prior to t
he cr
e
a
tion
of d
i
strib
u
te
d
gen
eratio
n pl
a
n
ts (DG), econ
omic calc
ulati
o
n is ne
ede
d in
order to fin
d
th
e opti
m
u
m
loca
tion. In this stu
d
y,
IEEE 57 bus t
e
st system is
eval
uate
d
usi
n
g tw
o index
of LMP an
d CP.
Then, the o
p
timal l
o
cati
on o
f
distrib
u
ted
gen
eratio
n pl
ants i
s
studie
d
i
n
ex
peri
m
e
n
tal
net
w
o
rk. F
i
nally, the effects of D
G
correct locat
i
o
n
on bus
es LMP
after DG install
a
tion is stud
ie
d
.
Ke
y
w
ords
: dis
t
ributed g
e
n
e
ra
tion, consu
m
er
payment (CP)
,
optima
l
pow
e
r
flow
, location
al margi
n
a
l
pri
c
e
(LMP)
Copy
right
©
2016 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
tion
Distri
buted
g
eneration pla
n
ts can
be
consi
dered
as plant
s that
complete
larg
e central
power pla
n
ts
[1, 2]. In
the last de
cad
e
, since
the p
o
wer ma
rket ha
s progr
es
se
d
t
o
rest
r
u
ct
u
r
i
n
g
from m
onop
o
l
y state, po
wer h
a
s be
en t
r
an
sform
ed f
r
om
servi
c
e
st
ate to p
r
od
uct. In this
reg
a
r
d,
profit maximi
zation
ha
s be
en inve
stigat
ed for th
e o
w
ners of
cent
ral po
wer pla
n
t
s and
DG a
s
th
e
unde
rlying issue. It has a great effect on su
ccess
or fai
l
ure of po
we
r plants in p
o
wer market.
Optimal DG
placement i
s
one of the
ke
y factor
s fo
r
distrib
u
ted g
e
neratio
n pla
n
ts. If this
is not
don
e
corre
c
tly, it will not
offer a go
od
profi
t
for DG o
w
ners a
nd
will
gene
rate
se
riou
s
probl
em
s
for power networks. The co
rrect location of
DG
will increa
se the
stabil
i
ty of power
grid
[3]. It can sup
port voltage a
gain
s
t the sig
n
ificant
ba
ckd
r
op of voltage
in overload time [1]. On th
e
other ha
nd,
the Optimal DG Place
m
ent r
edu
ce
s the lines conge
stion
and obstru
c
tion
signifi
cantly [
4
]. That i
s
more
stu
d
ie
s have
bee
n
done
on
different
aspe
cts of
DG
correct
loc
a
tion.
Cap
a
city inv
e
stment
plan
ning of di
stri
but
ed g
ene
ration un
der
comp
etitive electri
c
ity
market fro
m
the pe
rspe
ctive of a
di
stributio
n
co
mpany i
s
p
r
opo
sed i
n
Referen
c
e
[5]. In
Referen
c
e [6
], a method has b
een p
r
ese
n
ted for
optimum de
si
gn of netwo
rk co
nne
cted
DG
system
s d
u
e
to the
size
and
DG
type in
order
to solve th
e
relia
bility and e
n
vironm
ental
probl
em
s. In
Referen
c
e [7]
,
a metho
d
h
a
s b
een
provided fo
r DG l
o
catio
n
u
s
ing
GA in o
r
d
e
r
to
minimize a
c
tive power l
o
sse
s
in
distri
b
u
tion net
wo
rk. in Refe
ren
c
e [8] Optimal
placement
of DG
with La
ngran
gian b
a
sed
approa
ch u
s
i
ng tradi
tio
nal
pool b
a
sed
OPF and v
o
ltage
stabili
ty
con
s
trai
ned
OPF formulat
ions i
s
pro
p
o
s
ed.
In this paper, LMP and
CP i
ndices
are studied totall
y. T
hen, IEEE 57 bus test system
buses
are ra
nke
d
ba
se
d
on the
s
e t
w
o
indicators. O
p
timal DG Pl
acem
ent i
s
e
v
aluated u
s
in
g a
contin
uou
s lo
op. Finally, th
e effects of
DG
co
rre
ct lo
cation
on b
u
ses L
M
P after DG in
stallati
on
are stu
d
ied.
2. Local Mar
g
inal Price (LMP)
Local Ma
rgin
al Pri
c
e
(LM
P
) is the l
a
g
r
angi
an
multipliers a
s
so
ci
ated
with th
e a
c
tive
power flow e
quation
s
for e
a
ch b
u
s in th
e system.
Usually, LMP co
nsi
s
ts of thre
e parts a
s
foll
ows
[9]:
1) The m
a
rgi
nal co
st of ge
nerato
r
s pro
d
u
ction
2) The
co
st of losses
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 249 – 254
250
3) The
co
st of lines de
nsity and ob
stru
cti
o
n
Con
s
id
erin
g the ca
se of re
al power s
pot
price at bu
s i
,
LMP is given by:
∑
(1)
,
,
(2)
In Equation (1) an
d (2
),
λ
is marginal
co
st of ene
rg
y produ
ction
in a refe
ren
c
e bus,
λ
,
λ
is the co
st
of losses
an
d
λ
,
μ
,
is the in
cremental
co
st-pe
r-
con
g
e
s
tion of
lines [1]. LMP
index i
s
use
d
a
s
u
s
eful
to
ol in
ord
e
r to
ran
k
th
e u
s
e
d
network
bu
ses. A
c
cordi
n
g
l
y,
the load bu
ses a
r
e ran
k
e
d
in desce
ndi
ng order of
L
M
Ps with the
first node in
the ord
e
r a
s
the
best candi
dat
e for DG pl
acement as
sho
w
n bel
ow.
.
.
.
(3)
Table 1 sho
w
s ran
k
in
g of network bu
se
s from 1 to 5 base
d
on LMP
index:
Table 1. Ra
n
k
ing n
e
two
r
k
buses b
a
sed
on LMP index
LMP
Bus number
Rank
48.38
31
1
47.77
33
2
47.60
32
3
47.40
34
4
47.02
35
5
3. Consume
r
Pa
y
m
ent Index (CP)
Con
s
um
er P
a
yment (CP)
is one
of the
importa
nt fact
ors i
n
the pla
c
eme
n
t of distributed
gene
ration
system
s. Acco
rding to equ
at
ion 4, it can b
e
said that CP
is as a prod
uct of LMP [1].
.
.
.
(4)
The flo
w
rate
is in
clu
ded i
n
CP in
dex; i
t
s logi
c i
s
tha
t
the bu
s flo
w
is ve
ry impo
rtant for
DG lo
cation
with the aim of maximizin
g
prod
ucer p
r
ofits. It is important t
hat in that if LMP is
alone
as
abo
ve and the
r
e
is no
or low
con
s
um
er i
n
bus, the
profit of DG o
w
n
e
r
will be
sm
all;
therefo
r
e the
bus
ca
nnot b
e
offered fo
r
DG in
sta
ll. Ta
ble 2 sho
w
s
ranki
ng of net
work b
u
ses from
1 to 5 ba
sed
on CP in
dex. Table 2
analy
s
is
sh
ows
tha
t
the most CP
is for b
u
s
12
and the
r
efo
r
e
,
bus 1
2
is sele
cted for
study
from CP inde
x persp
ective
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Optim
a
l DG Placem
ent wi
th the Aim of
Profits Ma
xim
i
zation (S
obh
an Do
rah
a
ki
)
251
Table 2. Ra
n
k
ing n
e
two
r
k
buses b
a
sed
on CP index
CP
LMP
Bus number
Rank
16333.33
43.32
377
12
1
6065.48
40.43
150
8
2
5074.42
41.95
121
9
3
3109.33
41.45
75
6
4
1869.24
43.47
43
16
5
4. Studied Net
w
o
r
k
Implementa
tion a
nd Simulation
The s
t
udied
network
of this
res
e
arc
h
is
IEEE 57 bus tes
t
s
y
s
t
em.
The s
t
udied
network
has 7 g
ene
ra
tor bu
s and 5
0
load bu
s. T
he mo
st am
o
u
nts of a
c
tive losses o
c
cu
r in line 8-9 a
s
3.36 MW [9]. Figure 1 s
hows
I
EEE 57-
bus
network
s
t
andard.
Figure 1. IEEE 57 bus te
st system
5. Cost Fu
nc
tion and Incr
emental Cos
t
of Studie
d
DGs
Distri
buted
g
eneration p
o
w
er
plant
s a
r
e vari
o
u
s ty
pes that e
a
ch has it
s o
w
n cost
function. It is
clea
r that in
crea
sed
co
st functio
n
of DG po
wer
plan
t leads to
red
u
ce
d DG owner
profit. Table
3 sh
ows cost function co
efficient
s
of studie
d
DG. Figure 2 sho
w
s
dra
w
in
gs of
studie
d
DG i
n
Table 3.
Differentiation
of Figure
2 functio
n
s le
ad
s to increm
e
n
tal co
st gra
p
h.
Figure 3 sh
o
w
s the in
cre
m
ental co
st.
Table 3. Co
st
function coef
ficients of stu
d
ied DGs
DG No
.
0
15
0.002
DG 1
0
19
0.004
DG 2
0
20
0.04303
DG 3
0
20
0.25
DG4
0
30
0.1
DG 5
0
40
0.01
DG 6
0
43
0.003
DG 7
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ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 249 – 254
252
Figure 2. Co
st functions of
studie
d
DG
s
Figur
e 3. Incremental cost
cha
r
a
c
teri
stics of
studie
d
DG
s
6. Maximize DG O
w
n
e
r Benefi
t
One of the importa
nt issues of di
strib
u
t
ed gen
e
rati
on pla
c
eme
n
t
is DG o
w
n
e
r profit
maximizatio
n
. In this pape
r, profit maximization
of DG own
e
r i
s
studied u
s
ing
contin
uou
s lo
op
method.
OPF (Optimal
Power Flow)
is
solved in grid
in
order to
get the ma
ximum benefit.
Where,
λ
i
s
a
c
hieve
d
after DG in
st
allation. Th
e
profit
of
DG
o
w
ne
r i
s
o
b
tai
ned from Eq
u
a
tion (5) usi
n
g
λ
and
that is obtained fro
m
OPF.
(5)
In above equ
ation,
is LMP after DG placem
ent,
is DG prod
ucti
vity power a
n
d
C(
) is DG co
st function. In Equation (5),
and
are
variables; therefo
r
e, their chang
e
lead
s to profi
t
chang
e. For example, if
we lo
ca
te DG6, profit ch
ange
s graph
of Equation (5) is
sho
w
n by Fig
u
re 4. The
amount equ
als to zero, OPF
proble
m
is solved, output
and
are
set in Eq
uation (5)
an
d the p
r
ofit is cal
c
ulate
d
in
orde
r to find
the optimal
and
in a
bus. Th
en, 0.
5 MW i
s
ad
d
ed to
and
O
P
F is solved
with ne
w
and
.
amounts are
set a
gain
in
e
quation
5
and
the p
r
ofit i
s
calcul
ated;
the
loop
will
cont
inue
as lon
g
as th
e p
r
ofit
o
f
next step be
comes le
ss than previo
us
step (Profit2
>Profit1) that is call
ed maxi
mum po
wer p
o
int.
Figure 4. DG
6 locatio
n
in Equation (5)
6.1. Maximizing the Bene
fit from LMP Index Pers
pe
ctiv
e
As it was de
scribe
d, LMP is one of the sele
ction ind
i
ce
s of bus i
n
orde
r to create DG
index. Acco
rding to Table
1, the most
LMP of I
EEE 57 bus test system is rel
a
ted to bus
31.
Acco
rdi
ng to
Figure 5, it
can
be
said
t
hat
co
rre
ct
l
o
cat
i
o
n
of
D
G
in n
e
t
w
o
r
k
bus
e
s
lead
s
t
o
redu
ce
d am
o
unt of LMP.
Figure 5
sho
w
s
LMP
st
atus of
network bu
se
s b
e
fo
re a
nd afte
r
the
locatio
n
of DG6 an
d DG7.
It can be
se
en that location of DG6 in
bus
31 ha
s g
r
eate
r effect
s on
netwo
rk b
u
s
LMPs; the re
aso
n
for this
can
b
e
less cost of DG6
co
mpared to DG7.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Optim
a
l DG Placem
ent wi
th the Aim of
Profits Ma
xim
i
zation (S
obh
an Do
rah
a
ki
)
253
If DG7 i
s
l
o
cated in
bu
s
3
1
that the
mo
st cost
s a
m
o
ng
studie
d
DGs
and
its l
o
cation
is
more
acute,
Figure 6 g
r
a
p
h
will b
e
o
b
ta
ined. Fig
u
re
6 graph
sh
ows that in
crea
sed p
r
od
uction
of
DG in a bus l
eads to increased
profit. If
the increase i
s
conti
nued, LMP will be gradually reduced
and L
M
P am
ount will
be
more
than
op
erating
cost
s
that lead
s to
negative
DG.
Figu
re 7
gra
ph
sho
w
s the op
timal size p
e
r each lo
catio
n
of DG in bu
s 31.
Figure 5. LMP chang
es g
r
aph thro
ugh
placement DG6 and
DG7 i
n
bus 3
1
Figure 6. Placeme
n
t of DG7 in bu
s 31
Figure 7. Placeme
n
t of DGs 1
-
7 in bu
s 31
6.2. Maximizing the Bene
fit from CP Index Persp
e
c
t
iv
e
The best bus in IEEE 57-bus ne
twork is bus 12 from CP i
ndex perspectiv
e. Locating
DG in bu
s 1
2
,
bus LMP is
cha
nge
d as
Figure 8 gr
ap
h. Figure 8
shows that co
rrect lo
catio
n
of
DG lea
d
s to redu
ced LMP
of buse
s
.
Figure 8. LMP chang
es g
r
aph thro
ugh
placement DG6 and
DG7 i
n
bus 1
2
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 249 – 254
254
Figure 9 gra
p
h
sho
w
s interest ch
ang
es
per DG
re
si
zi
ng. It can be
found that si
ze an
d
optimum be
n
e
fit of bus 12 (CP Index) is more
co
mpared to b
u
s 31
(L
MP
Index). Figure 10
grap
h sh
ows
the optimum
size per e
a
ch
location of DGs in bu
s 12.
Figure 9. Placeme
n
t of DG7 in bu
s 12
Figure 10. Placem
ent of DGs 1
-
7 in bu
s 12
7. Conclusio
n
One of the i
m
porta
nt issu
es of dist
ribu
ted
gene
ratio
n
placement
is profit maximization
for DG o
w
ne
r. In this pa
pe
r, LMP an
d
CP indicators
were explai
n
ed an
d bu
se
s 31 (LMP Ind
e
x)
and 12 (CP i
ndex)
were
selected for
st
udy usi
ng both indi
ces am
ong IEEE 57
bus test
syst
em
buses. The
n
, optimum si
ze of distribute
d
gene
ration plants wa
s
obtained con
s
i
derin
g
DG
s with
different co
st function
s and
usi
ng co
ntin
uou
s
lo
op
an
d OPF
metho
d
. It is
su
gge
sted th
at futu
re
study is
con
ducte
d in o
r
der to find t
he optimal
si
ze
con
s
ide
r
in
g different o
b
jective fun
c
t
i
ons
inclu
d
ing max
i
mization
of social
welfare
function,
m
a
ximizing
net
wo
rk flow
rate
a
nd u
s
in
g of
DG
in obje
c
tive bus.
Referen
ces
[1]
D Gautam, N
Mithul
ana
ntha
n. Optimal
DG
pl
ac
ement in d
e
reg
u
late
d ele
c
tricit
y
m
a
rket.
Electric Power
System
s Res
e
arch
. 200
7; 77:
1627
–1
636. d
o
i:10.1
0
1
6
/j.ep
s
r.2006.1
1
.01
4
.
[2]
S Dora
haki. A
Surve
y
o
n
Ma
xim
u
m Po
w
e
r
Point T
r
acking
Methods
in P
hotovo
l
taic P
o
w
e
r S
y
stems
.
Bull
etin of Elec
trical Eng
i
ne
eri
ng an
d Infor
m
a
t
ics
. 2015; 4(3)
. Doi:10.12
92
8/eei.v4
i
3.4
46.
[3]
JM Lopez L
e
z
a
ma, A Padil
h
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