TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5086 ~ 50
9
5
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.555
4
5086
Re
cei
v
ed
Jan
uary 1, 2014;
Re
vised Ma
rch 20, 2014; A
c
cepted Ap
ril 2, 2014
Determining LBMP through Optimal Power Flow in the
Electric Power Business
Hermag
asa
n
t
os Zein*
1
, Yusra Sabri
2
, Er
w
i
n
D
e
r
m
aw
an
3
1
Energy
Conversion Engin
eer
ing Dept., State Poly
t
e
chnic of B
andung (POLBAN), B
andung, Indonesia
2
Electrica
l
Eng
i
neer
ing ST
EI,
Institute T
e
c
hnolo
g
y
of Band
u
ng (IT
B
), Bandung, Ind
ones
ia
3
Electrical Engineer
ing Dept., Un
versit
as Muhammadiy
a
h, Cempaka Putih,
Jakarta, Indones
ia
Corresp
on
din
g
author, e-mai
l
: hemag
a_s@Y
aho
o.co.id
*1
, yusra.sabr
i@
ym
ail.com
2
,
er
w
i
n
derm
a
w
a
n@
ya
hoo.com
3
A
b
st
r
a
ct
T
he e
nergy
cri
s
is h
a
s g
o
t th
e seri
ous
atte
ntio
n
of ex
pert
s
sinc
e the
mi
ddl
e19t
h ce
ntu
r
y. Many
efforts w
i
th significa
nt progr
e
sses has b
e
e
n
yield
ed to
obtai
n its soluti
on, s
u
ch as tech
no
l
ogy d
e
vel
o
p
m
e
n
t
and d
i
versific
ation of pri
m
ary ener
gy
source
s, but the threat
of the energ
y
crisis has no
t been ab
le to
b
e
avoided.
E
a
rly tahun 19
90, attention of ex
per
ts ar
e focused
on energy s
a
vings
, operating
efficienc
ies and
transpar
ency. As a result, they have reco
mme
n
d
ed ch
ang
ing the e
l
ectric
pow
er busin
es
s of the mon
o
p
o
l
y
system
to the
m
a
rk
et system, com
p
et
ition. In a com
p
etitiv
e system
, the
problem
s
w
ill
be
m
o
re c
o
m
p
lex
,
espec
ial
l
y in t
h
e en
ergy
price
throug
h o
p
ti
mi
z
a
t
i
o
n
.
One of
the po
pu
lar e
nergy
prici
ng
meth
ods to
day
is
LBMP, Locati
ona
l Base
d
Margin
al Pric
e
,
w
h
ich has
bee
n successf
ully a
p
p
lie
d b
y
New
York, US.
Genera
lly, it is
deter
mi
ne
d th
roug
h ED, Ec
o
n
o
m
ic
Disp
a
tch, calcu
l
ati
ons.
In this c
a
se,
Operator
must d
o
the compl
i
cate
d adj
ustments, especi
a
lly for cong
estio
n
conditi
ons, so that thier results
can be ap
pli
e
d t
o
the netw
o
rk. The si
mul
a
tio
n
results, both he
avy and l
i
ght l
oads, show
e
d
that t
he OPF
w
i
th step redu
ctio
n
can w
o
rk w
e
ll. Co
mpar
in
g w
i
th ED has to
d
one s
o
me
a
d
ju
stments b
e
ca
u
s
e a few
contr
a
ints w
e
re o
u
t of
their li
mits.
Ke
y
w
ords
:
co
mp
etitio
n, ener
gy price,
opti
m
i
z
a
t
i
on, step re
ductio
n
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The en
ergy crisi
s
is a
se
rio
u
s p
r
oble
m
that
must be
so
lved, either n
o
w an
d in the
future.
Tech
nolo
g
ica
l
efforts to improve pla
n
t effici
ency ha
s been
started
sin
c
e the 19t
h centu
r
y an
d
rea
c
he
d its
culmination
after a
combi
n
e
d
- cy
cle
pl
an
t with high eff
i
cien
cy ha
s b
een fou
nd. But
the threat of
energy sh
ort
age
s pe
rsi
s
t
today, whi
c
h
is cau
s
ed
by the re
se
rves
of fossil
ene
rgy
more
an
d m
o
re
sh
arply d
i
minishi
ng
wh
ile dem
and
g
r
owth
rose sharply i
n
line
with
popul
ation
gro
w
th an
d i
ndu
strial. As
a re
sult, the
price of en
er
gy (foss
il) in
the future is
very diffic
u
lt to
estimate alth
ough
ene
rgy
from re
ne
wa
ble en
ergy
so
urces
ha
s be
en attempted
in the pa
st th
ree
decade
s. Be
ginnin
g
in 1
990, expe
rts have focu
sed attention
on en
ergy
savings, o
perating
efficien
cie
s
a
nd tran
sp
are
n
cy, and th
ey sug
g
e
s
t a ch
ange i
n
the b
u
sin
e
ss of el
ectri
c
po
we
r f
r
om
monop
oly sy
stem to a m
a
rket
system
(comp
e
tition)
,
[1, 2]. Until now ma
ny co
u
n
tries that ha
ve
been
su
ccessfully running t
he com
petitio
n, su
ch as th
e USA, UK, Australi
a, etc.
In co
mpetitio
n, ele
c
tric e
nergy
pri
c
in
g
is
a bi
g i
s
sue. In
spite
of a fe
w m
e
thods in
determi
ning t
he ene
rgy pri
c
e
s
have be
e
n
widely pu
bl
i
c
ized, su
ch a
s
the metho
d
of spot pri
c
in
g
and no
dal p
r
i
c
ing.
Until no
w, a pop
ula
r
method
i
s
LB
MP method, [3]; and this m
e
thod ha
s b
e
en
tested in p
r
a
c
tice i
n
the
United State
s
; it is
used i
n
the elect
r
ic
power b
u
si
ne
ss i
n
Ne
w Y
o
rk.
Und
e
r thi
s
m
e
thod, the p
r
i
c
e of e
n
e
r
gy
depe
nd
s on
t
he characte
ri
stics of
the lo
cation.
Ho
we
ver,
the determi
na
tion of LBMP
until now, a
s
use
d
by
NYISO, still base
d
on EDM. In this method, th
e
loss
system i
s
a
problem
that
will
be
so
lved sepa
rate
ly at a late
r stage.
The
oth
e
r wea
k
n
e
ss is
necessa
ry ad
justment
s a
g
a
in if
the results can
not
be ap
plied to
the sy
stem
becau
se p
o
ssible
occur viol
ations of the con
s
traint
s, su
ch
as
a few lin
es a
r
e ove
r
flow. Settleme
n
t throug
h the
adju
s
tment
can be
asce
rta
i
ned that t
he
result
s will
not
fall to the opt
imal pri
c
e. T
h
is conditio
n
wil
l
make the
situ
ation of unfair competition.
Econo
mic di
spatch meth
od
used in the
deter
mi
nation
of LBMP not nece
s
sarily
be able
to work qui
ckly becau
se n
eed the adj
u
s
tment
s that
can ta
ke lon
ger if the re
sults ca
n not
be
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Determ
inin
g LBMP throug
h Optim
a
l Power Fl
ow
in t
he Electri
c
Powe
r… (He
r
m
agasanto
s
Zein)
5087
applied to the gri
d
. If violations of constrai
nt
s
occur from EDM result
s, the ISO will
m
a
ke
adju
s
tments
to the results u
n
til they
can
be
re
cei
v
ed by g
r
id.
The
othe
r
wea
k
n
e
ss i
s
that
probl
em of l
o
sse
s
mu
st
be complet
e
d se
pa
rately
at a later stage. If the grid i
s
robu
st (or
unlimited
), EDM appli
c
atio
n is better be
cau
s
e it is si
mpler a
nd faster wo
rk [4].
In the operati
on of the po
wer
sy
stem
must meet th
e con
d
itio
n
s
of system co
nstrai
nts,
bus voltage
l
i
mit, curre
n
t l
i
mit ea
ch lin
e an
d p
o
wer limit of e
a
ch ge
nerator.
Another thing
is
losse
s
is a
p
r
oble
m
that
can not
be ig
nore
d
in
th
e
electri
c
po
we
r bu
sin
e
ss b
e
ca
use the
r
e
is
alway
s
as n
a
turally, whe
r
e
the amount is about 5%.
The metho
d
that can ove
r
come the
we
akn
e
sse
s
EDM is OPF me
thod. Conve
n
t
ionally,
the method i
s
very sl
ow,
so it is difficult to
implem
ent to marke
t
system. But experts h
a
v
e
develop
ed thi
s
metho
d
in orde
r to wo
rk more
qui
ckly, such a
s
the OPF with
step re
du
ction
develop
ed by [5]
that can work faste
r
(Table 1)
. Thi
s
table sh
ows the run
n
ing
time compa
r
iso
n
between OP
F with step treduction
and conventional OPF. Then,
this method will be used to
determi
ne LB
MP to market
mecha
n
ism as in Figu
re 1
.
Table 1. Ru
n
n
ing time of OPF
Parameter
Electric Pow
e
r S
y
st
em
Remarks
Bus Number.
4
15
19
225
Run Time (scond
)
0.01
0.22
0.46
474.29
Step reduction
Run Time (scond
)
0.02
0.45
0.88
1153.68
Conventional
Figure 1. Mekanism
e LBM
P
with OPF
In this me
cha
n
ism, i
nde
pe
ndent
se
rvice
ope
ra
to
r
(ISO)
run
s
OPF
prog
ram
after data
of
energy dema
nds by DISCO, ener
gy
-offers by GENCO and gri
d
co
nstrai
nts hav
e been obtai
n
ed.
In this ca
se,
the prog
ram
OPF yields n
odal pri
c
e
s
(NPs), the qu
ota of gene
ra
tors a
nd lo
sses.
W
h
er
e
th
es
e
r
e
su
lts
c
a
n be
a
s
c
e
r
t
a
i
n
ed to
b
e
a
p
p
lie
d dire
ctly on t
he sy
stem, it is cau
s
ed
by all
con
s
trai
nts h
ad met.
To re
alize thi
s
ide
a
, this p
aper
pre
s
e
n
ts
a
numeri
c
a
l
simulatio
n
calcul
ation for electri
c
power
syste
m
that contai
ned in
the Fi
gure
2. In th
is
simulatio
n
create
s
two
different l
o
a
d
s,
namely a
hea
vy and a light
load.
Whe
r
e
a
s bi
ddin
g
of
each ge
nerator d
e
libe
r
atel
y different fro
m
one an
other,
either in on
e locatio
n
or bet
wee
n
location
s.
2. Res
earc
h
Method
In the elect
r
i
c
po
we
r bu
siness is
not
fully follow conve
n
tional
eco
nomi
c
p
r
oble
m
s
becau
se the
r
e are
som
e
th
ing that sh
oul
d be con
s
id
e
r
ed, such as
losse
s
natu
r
a
lly that can n
o
t
be igno
re
d a
nd the sy
ste
m
is limited
(l
ike eve
r
y Ge
nco i
s
not fre
e
to enter th
e
power g
r
id
). Due
to these
prob
lems,
we n
e
ed a m
e
thod
that ca
n
resolve co
mplet
e
ly the probl
ems. T
h
is
pa
per
prop
oses a
model
of det
ermin
a
tion L
B
MP that
ca
n a
c
commo
d
a
te dem
and
-sup
ply, losse
s
a
n
d
limited syste
m
. Furtherm
o
re, the market mechani
sm
prop
osed i
n
the Figure
1, which in
this
pape
r is u
s
ed
to determine
LBMP.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5086 – 50
95
5088
In the Figure
1, every DISCO do
es e
n
e
r
gy dem
a
nd to ISO in the form of po
we
r capa
city
and it
s en
ergy pri
c
e.
Wh
ile every
GENCO d
o
e
s
e
nergy
offer t
o
ISO in th
e
form
of po
wer
cap
a
city an
d
its en
ergy p
r
ice.
Then
ISO ru
ns
the
OPF prog
ra
m to produ
ce NP, L
o
sse
s
of
system
an
d
gene
rato
r
ca
pacitie
s th
at are
con
n
e
c
ted to
the
sy
stem. After the OPF
results
obtaine
d then
ditermine LB
MP at each lo
cation
with the followin
g
co
ndition
s.
a)
For the no
rm
al case, LBMP is the sam
e
at
every location an
d is equal to the highest NP
s
y
s
t
em, that is
:
system
max
NP
LBMP
(
1
)
b)
For
the co
ng
estion ca
se, LBMP
is
det
ermin
ed by t
he value
of the high
est
NP in ea
ch
loc
a
tion, that is
:
locatoni
max
NP
LBMP
(
2
)
c)
If the location is only comp
ose
d
of DISCO al
one or
without NP in that location, then LBMP
determi
ned b
y
exported po
wer to
that lo
cation, that is:
}
k
location
power to
export
that
locations
i
,
{LBMP
max
LBMP
ik
k
(3)
Whe
r
e: LBM
P
ik
is
LBMP from loc
a
tion i that exported
s
o
me power t
o
loc
a
tion k
.
d)
In case of co
nge
stion, having determi
ne
d LB
MP at each location a
nd further
co
nge
stion co
st
can b
e
determined, that is:
)
LBMP
(LBMP
P
B
j
i
im
ij
c
(
4
)
3.
Resul
t
s and
Analy
s
is
3.1.
Simulation
Figure 2 is t
he ele
c
tri
c
p
o
we
r sy
stem
that
is take
n as the n
u
m
eri
c
al si
mul
a
tion to
evaluate the
prop
osed m
e
thod. Thi
s
sy
stem
con
s
i
s
ts of 7 bu
se
s
with three
se
parate
lo
catio
n
s.
In Location 1
con
s
i
s
ts of
3 bu
se
s (1, 2 and
5),
a
n
d
3 Ge
ncos
con
n
e
c
ted to
Bus 1, 2
an
d 5.
Location 2
co
nsi
s
ts of 3 b
u
s
e
s
(3, 4 a
n
d
7), and 2
Ge
nco
s
conn
ect
ed to Bus 4
a
nd 7. Wh
erea
s
at Locatio
n 3 con
s
i
s
ts of on
e bus that co
nsi
s
t of only load.
Figure 2. 7 Buse
s System
Furthe
rmo
r
e,
Table 2 and
3 contain th
e data
of electri
c
power
systems with t
he ba
sic
100MVA an
d
20kV. Tabl
e
2 contain
s
data that co
ns
i
s
ts of en
e
r
gy offers
by GENCO in
unit
Rp/M
Wh, an
d the cont
rai
n
s are the limits of the
active and the
reactive po
wer. While T
a
ble 3
contai
ns the
data of each line of grid.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Determ
inin
g LBMP throug
h Optim
a
l Power Fl
ow
in t
he Electri
c
Powe
r… (He
r
m
agasanto
s
Zein)
5089
The next ste
p
wa
s forme
d
some
cal
c
ul
ation ca
se
s o
f
the electri
c
power syste
m
above,
namely to
si
mulate the
case
of co
ng
estion
and
n
o
t con
g
e
s
tio
n
. The
simul
a
tion re
sult
s are
descri
bed in
detail as follo
ws:
Table 2. Offer and Co
nstrai
n GENCO
No.Bus GENC
O Offer
(Rp/MWh
)
P
(pu)
Q
(pu
)
Location
1 G1
9.6
0.30<P<1.30
-1.80<Q<1
.
80
1
2 G2
15.3
0.20<P<1.20
-1.25<Q<1
.
25
1
4 G4
8.8
0.25<P<1.80
-1.03<Q<1
.
50
2
5 G5
5.3
0.20<P<0.60
-1.25<Q<1
.
25
1
7 G7
10.5
0.25<P<1.60
-1.50<Q<1
.
50
2
Table 3. Line
Data
From i
To j
R (pu)
X (pu)
Y
(
pu)
S
ma
x
(pu)
1 2
0.05
0.06
0.02
0.90
1 5
0.08
0.30
0.03
0.80
2 3
0.20
0.50
0.03
0.50
2 5
0.10
0.10
0.02
0.60
2 6
0.05
0.10
0.025
0.90
3 4
0.05
0.10
0.025
0.70
3 7
0.02
0.05
0.03
0.86
4 7
0.04
0.03
0.02
0.90
5 6
0.10
0.30
0.03
0.50
6 7
0.25
0.55
0.01
0.50
3.1.1. Case
-1
: Cong
es
tion
This
ca
se
op
erate
s
in
hea
vy load co
ndi
tions
re
sultin
g in cong
esti
on on th
e
co
nne
cting
line bet
wee
n
the two lo
cati
ons. T
h
is
hea
vy load wa
s
shown by the
Table 4,
both
the active a
n
d
the rea
c
tive powe
r
.
Table 4. Loa
d
and Lo
cation
No. Bus
P (pu)
Q (pu
)
Location
1 0.80
0.55
1
2 0.70
0.35
1
3 0.60
0.30
2
4 0.70
0.25
2
5 0.60
0.40
1
6 0.90
0.50
3
7 0.80
0.50
2
(a) Solutio
n
by
EDM
The
cal
c
ulati
on results
of EDM fo
r th
e case can
be
seen
in
the fllowin
g
tables.
Econo
mic
Di
spat
ch results are sho
w
n
in Tabel
5(a). The
re
su
lts of the ru
nning lo
ad fl
ow
prog
ram
are
sho
w
n in th
e Tabel 5
b
, wh
ere g
ene
ratin
g
bus volta
g
e
s
are set 1 p
u
and b
u
s 7
as
swi
ng bu
s.
Whe
r
ea
s the
next tables
are to
che
ck
sy
st
em
con
s
t
r
aint
s,
p
o
w
e
r
f
l
ow limit
s of
t
h
e
transmissio
n rea
c
tive power limits of ge
nerato
r
s, and
voltage limits of the buse
s
.
Table 5. The
Re
sults of EDM
(a) Po
we
r opt
imal of gene
rators
GE
NC
O
λ
(RP/MW
)
P
mi
n
(MW
)
P
opt
(MW
)
P
ma
x
(MW
)
G1
9.60
30.1
130.0
130.0
G2
15.3
20.0
0.0
120.0
G4
8.80
25.3
180.0
180.0
G5
5.30
20.0
60.0
60.0
G7
10.25
25.5
130.0
160.0
Total load = 500.
0 MW
Note: gene
rator
at bus 2 lost in the auction.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5086 – 50
95
5090
(b) Voltag
e a
nd po
wer b
e
sed on EDM
No.
Bus
V
(k
V)
δ
(degri)
P
g
(MW
)
Q
g
(MW
)
P
d
(MW
)
Q
d
(MW
)
1
20.0
0.000
130.0
89.1
80.0
55.0
2
19.0 0.13
0.0
0.0 70.0
35.0
3
19.5 0.402
0.0
0.0
60.0 30.0
4
20.0 0.466
180.0
-45.4
70.0 25.0
5 20.0
-0.08
60.0
120.7
60.0
40.0
6
17.9 0.011
0.0
0.0
80.0 50.0
7
20.0 0.427
159.5
138.3
80.0 50.0
Losses =29.5+j 17.7 MVA
529.5
302.7
500.0
285.0
(c) Ch
eck line
con
s
traint
s
From
i
To
j
P
ij
(MW
)
Q
ij
(MVar)
S
ij
(MVA)
S
ij
(max
)
(MVA)
Remar
ks
1 2
29.4
59.5
66.4
90
-
1 5
20.6
-20.5
29.1
80.0
-
2 3
-50.4
24.4
56.0
50.0
Over
2 5
-13.8
-33.8
36.5
60.0
-
2 6
21.4
39.8
45.2
90.0
-
3 4
-59.2
7.0
59.6
70.0
-
3 7
-58.2
-25.4
63.5
86.0
-
4 7
48.9
-62.6
79.5
90.0
-
5 6
5.2
32.8
33.2
50.0
-
6 7
-55.7
22.3
60.0
50.0
Over
(d)
Che
c
k rea
c
tive power
contraint
s
of generators
GE
NC
O
Q
mi
n
(MVar)
Q
op
t
(MVar)
Q
ma
x
(MVar)
Remar
ks
G1
-180.1
89.1
180.1
-
G4
-150.3
-45.4
150.3
-
G5
-125.4
120.7
125.4
-
G7
-150.5
138.3
150.5
-
(e)
Che
c
k voltage co
ntraint
s
No.
Bus
V
mi
n
(k
V)
V
opt
(k
V)
V
ma
x
(k
V)
Remar
ks
1 18.0
20.0
22.0
-
2 18.0
19.0
22.0
-
3 18.0
19.5
22.0
-
4 18.0
20.0
22.0
-
5 18.0
20.0
22.0
-
6 18.0
17.9
22.0
Lo
w
7 18.0
20.0
22.0
(b) Solution
by
OPF
The cal
c
ul
ation re
sults of
OPF for the ca
se
can b
e
seen in the fllo
wing tabl
es.
Table 6. The
Re
sults of O
P
F
(a) Voltag
e a
nd po
wer b
e
sed on OPF
No.
Bus
V
(k
V)
δ
(degri)
P
g
(MW
)
Q
g
(MW
)
P
d
(MW
)
Q
d
(MW
)
1 21.0
0.000
130.0
50.2
80.0
55.0
2 20.7
-0.015
20.0
76.0
70.0
35.0
3 21.4
0.211
0.0
0.0
60.0
30.0
4 22.0
0.251
180.0
13.7
70.0
25.0
5 20.9
-0.004
60.0
47.3
60.0
40.0
6 19.7
-0.021
0.0
0.0
80.0
50.0
7 21.7
0.231
122.9
73.2
80.0
50.0
Losses =12.9-j 24.6 MVA
512.9
260.4
500.0
285.0
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Determ
inin
g LBMP throug
h Optim
a
l Power Fl
ow
in t
he Electri
c
Powe
r… (He
r
m
agasanto
s
Zein)
5091
(b) Po
we
r flow in line
From
i
To
j
P
ij
(MW
)
Q
ij
(MVar)
S
ij
(MVA)
S
ij
(max
)
(MVA)
Remar
ks
1 2
27.7
0.8
27.7
90
-
1 5
22.3
-0.1
22.3
80.0
-
2 3
-37.5
11.5
39.3
50.0
-
2 5
-10.7
1.1
10.7
60.0
-
2 6
25.7
38.9
46.6
90.0
-
3
4
-50.4
-7.2
50.9
70.0
-
3 7
-50.1
-10.1
51.1
86.0
-
4 7
-58.2
-15.3
60.5
90.0
-
5 6
11.4
16.9
20.4
50.0
-
6 7
-44.4
8.9
45.3
50.0
-
The
re
sults
o
f
OPF metho
d
sho
w
ed th
a
t
there
wa
s n
o
violation of con
s
trai
nts a
nd
they
can
be
dire
ctl
y
accepted
b
y
the system.
The follo
win
g
table i
s
a
d
e
tailed
com
p
arison
of the
two
method
s.
Table 7. Co
m
paratio
n Re
sults between
EDM and OP
F
Item EDM
OPF
1. Number
of line over load
2
0
2. Number
of bus
voltage out of constrain
1
0
4. GENC
O at
bu
s 2
off
on
5 .Losses
5,74%
2,51%
Table
7
sh
o
w
s that th
e
OPF meth
od
is better tha
n
the
EDM
b
e
ca
use n
o
vi
olation
of
system
con
s
traints a
nd l
o
sses
di
re
ctly obtain
ed
by a
small
e
r p
e
rcentag
e. T
hen
LBMP e
a
ch
locatio
n
and
cap
a
city of e
a
ch GE
NCO
can b
e
det
e
r
mined di
re
ctly. The results by OPF are
sho
w
in two table
s
belo
w
:
Table 8. Power for Lo
catio
n
1
No.
Bus
DISCO
(MW
)
GE
NC
O
(MW
)
Offer
(Rp/MWh)
1 80
130
9.60
2 70
20
15.30
5 60
60
5.30
Total 210
210
-
Notes:
Max
i
mum NP
= 15.30 RP / MW
h
P
im
= 0 MW
P
ex
= 0MW
OPF re
sult
s f
o
r lo
catio
n
1
are
co
ntaine
d
in
Tabl
e 5
shows that
th
e
power
gen
erated is
great th
an th
e po
wer dem
ande
d at tha
t
location, o
r
in this
ca
se
there i
s
n
o
i
m
port o
r
exp
o
rt
power. So LB
MP for this l
o
cation fall
s o
n
the p
r
ice
of
the high
est o
ffer of GENCO that ha
s be
en
won in the a
u
c
tion, whi
c
h i
s
LBMP
1
= 15
.30 Rp/M
Wh
Table 9. Power for Lo
catio
n
2
No.
Bus
DISCO
(MW
)
GE
NC
O
(MW
)
Offer
(Rp/MWh)
3 60
0.0
0.00
4 70
180
8.80
7 80
123
10.50
Total 210
303
-
Notes:
Max
i
mum NP
= 10.50 RP / MW
h
P
im
= 93 MW
P
ex
= 0MW
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5086 – 50
95
5092
OPF re
sult
s f
o
r lo
catio
n
2
are
co
ntaine
d
in
Tabl
e 6
shows that
th
e
power
gen
erated is
great tha
n
the power d
e
m
ande
d at that location,
o
r
i
n
this case L
o
catio
n
2 im
ports
po
wer
93
MW to lacation 3. So LBMP for this loc
a
tion falls
on t
he p
r
ice of th
e high
est
offer of GE
NCO t
hat
has b
een
wo
n in the aucti
on, whi
c
h is L
B
MP
2
= 10.50 Rp/M
Wh.
Whe
r
ea
s LB
MP at Locatio
n-3 can be
ca
lculate
d
by Table 6b a
s
th
e followin
g
:
a)
From L
o
catio
n
1: P
26
= 25
.6 MW a
nd
P
56
=11.4 M
W
. When
red
u
c
ed
with lo
ss total, the
n
total imported
powe
r
from L
o
catio
n
1 to Locatio
n 3 is
ex
13
P
= 35.6 M
W
.
b)
From L
o
catio
n
2: P
76
= 44.4 MW. So tot
a
l importe
d p
o
we
r from
Lo
cation
2 to L
o
catio
n
3 is
ex
23
P
= 44.4 M
W
c)
By using equ
ation 3, then
h
15.30Rp/MW
10.50}
{15.30,
ax
LBMP
3
m
The follo
win
g
table
sh
ows
the compa
r
i
s
on of th
e
sim
u
lation
re
sult
s of th
e two
method
s.
Colum
n
4
of
the table
co
n
s
ist
s
of th
e
calcul
at
ion
re
sults after EDM re
sult
s adj
usted
by givi
ng
quota to G2, as lo
ser b
a
se
d on EDM re
sults, 30 MW.
Table 10. Co
mparation Re
sults b
e
twe
e
n
EDM and O
P
F
No. Item
EDM
EDM)*
OPF
1
Number of line o
v
er flow
2
0
0
2
Number of
bus voltage is violated
1
0
0
3
Number of
GEN
C
O is out contrai
n
t
0
0
0
4
Condition of G2
at bus 2
Off
on
on
5 Losses
5.74%
3.7%
2.5%
6
Quota of
G1
at b
u
s 1 [MW]
130.0
130.0
130.0
7
Quota of
G2
at b
u
s 2 [MW]
0.0
30.0
20.0
8
Quota of
G4
at b
u
s 4 [MW]
180.0
180.0
180.0
9
Quota of
G5
at b
u
s 5 [MW]
60.0
60.0
60.0
10
Quota of
G7
at b
u
s 7 [MW]
159.5
129.5
123.0
11
LBMP at Location 1 [Rp/MWh]
10.5
15.3
15.3
12
LBMP at Location 2 [Rp/MWh]
10.5
10.5
10.5
13
LBMP at Location 3 [Rp/MWh]
10.5
15.3
15.3
Note:
)* aft
e
r adjusted
Whe
r
ea
s
co
n
gestio
n
co
st i
s
ve
ry ea
sy
calcul
ated
with
usi
ng
equ
ation 4
after LB
MP for
each location
has dete
r
min
ed, that is fro
m
OPF results:
ex
21
P
=37.5 M
W
: CC
21
=37.5x4.8
0
= Rp 180.0
0
ex
23
P
=44.4 M
W
: CC
23
=44.4x4.8
0
= Rp 213.1
2
So CC=Rp 3
93.12
3.1.2. Case
-2
: Normal
In this
ca
se t
he g
r
id lo
ad i
s
ma
de lig
hte
r
than
case-1
as
set fo
rth i
n
Tabl
e 11.
T
hen it i
s
done d
e
termi
nation LBMP bersad
a
sarka
n
OPF metho
d
.
Tabel 11. Lo
a
d
and Lo
catio
n
No.
Bus
P
d
(pu)
Q
d
(pu)
Location
1 0.64
0.44
1
2 0.56
0.28
1
3 0.48
0.24
2
4 0.56
0..20
2
5 0.48
0.32
1
6 0.56
0.40
3
7 0.64
0.40
2
(a) Solutio
n
by
OPF
The followi
ng
tables contai
n the re
sults
of runnin
g
O
P
F prog
ram.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Determ
inin
g LBMP throug
h Optim
a
l Power Fl
ow
in t
he Electri
c
Powe
r… (He
r
m
agasanto
s
Zein)
5093
Table 12. Re
sults of OPF f
o
r No
rmal
Ca
se
(a) A
c
tive power at Lo
cati
on 1
No.
Bus
DISCO
(MW
)
GE
NC
O
(MW
)
Offer
1 64
130
9.60
2 56
0
15.30
5 48
60
5.30
Note:
- Maximum
NP
= 9.60 Rp/MWh
-P
ex
=22 MW
-P
im
= 0 MW
(b) A
c
tive power at Lo
cati
on 2
No.
Bus
Demand
(MW
)
GE
NC
O
(MW
)
Offer
3 48
-
-
4 56
180
8.80
7 64
29
10.50
Note:
- Maximum
NP
= 10.50 Rp/MW
h
-P
ex
=41
MW
-P
im
= 0 MW
On the
Lo
cati
on 1: G
e
n
c
o,
G2, on
the b
u
s 2
is l
o
se b
e
ca
use it wa
s too
expen
si
ve, 15.3
Rp/M
Wh, a
n
d
two
othe
rs
get maximum
quota
with
a
total po
we
r
of 190
MW. P
o
we
r
sup
p
ly i
s
smalle
r than
the total de
mand, 224M
W. This la
ck of supply as much as 3
4
MW ha
s be
en
covered from
the generat
ors at Lo
cati
on 2. The
maximum NP at Location 1
,
9.6Rp/MWh
,
is
offered by G
E
NCO
at Bus 1.
Location-2: G
enco in the
b
u
s 4
ha
s a m
a
ximu
m qu
ota of 180
MW
due to its offe
r is ve
ry
low a
nd
Gen
c
o in
Bus 7
has
a q
uota
29MW un
der the maximu
m ca
pa
city beca
u
se a
rat
h
e
r
expen
sive. So produ
cing
power of
Lo
cation 2 i
s
20
9MW
whi
c
h i
s
mo
re tha
n
t
he total de
m
and,
168M
W. It is over-su
pply is as m
u
ch as
41MW a
nd
maximum NP
is 10.5Rp/MWh.
In this case there
we
re
no
con
g
e
s
tion
probl
em
s, so
LBMP for th
ree lo
catio
n
s are the
same, ie 10.5
R
P/MWh.
3.2. Analy
ses
In determini
n
g
LBMP, not only the energy pric
e d
e
te
rmine
d
for ea
ch lo
cation b
u
t also
quota ea
ch
Gen
c
o a
s
the
winne
r of the comp
etitio
n
must also b
e
determi
ned
. In this case
the
necessa
ry a
s
suran
c
e th
at the quot
a
of
each Ge
nco that wo
n the
competition m
u
st be
re
ceiv
ed
by the grid. Whe
r
ea
s in
determi
ning
LBMP will b
e
affected by
three comp
onent, ie offer by
GENCO
s
(pri
ce and po
we
r
capa
city
), reque
st by
DISCO
s
(pri
ce
and
p
o
wer capa
city)
an
d grid
con
s
trai
nts. Influen
ce of GENCO
s
an
d DI
SCO
s
can be cl
ea
rl
y seen a
s
a
supply
-
dem
and
relation
shi
p
a
l
one. Ele
c
trical po
wer bu
siness i
s
not th
e sa
me a
s
co
modity bu
sin
e
ss at the
oth
e
r
eco
nomi
c
se
ctors be
cau
s
e
it
have
spe
c
i
a
l
problem
s,
su
ch a
s
th
e l
o
sse
s
can
no
t be avoid
ed
and
grid
are limit
ed in
d
e
liveri
ng p
o
wer fro
m
all
GENCOs to all
DI
SCO. T
he
e
x
istence of
these
spe
c
ificitie
s h
a
s mad
e
bu
si
ness at ele
c
tr
ical po
we
r se
ctor into a uni
que bu
sin
e
ss.
EDM to dete
r
mine LBMP i
s
very sim
p
le
because
is
n
o
t involve gri
d
co
nstraints
so that
the losse
s
ca
n not be directly obtained. In this
metho
d
the loss pro
b
l
em will be
re
solved th
roug
h
load flo
w
cal
c
ulatio
n b
a
se
d on
the
re
sults of
the E
D
M
se
paratel
y. The
re
sult
s of
the
ca
se 1
manunj
ukan that two line
s
were overl
o
a
ded (see T
abl
e
7). This i
s
d
ue to the offer of GENCOs at
Location 2
lo
wer than th
e
offer of GE
NCO
s
at L
o
ca
tion 1. It re
sult
s in
som
e
p
o
w
er that ha
s t
o
be
delivere
d
to L
o
catio
n
1. Ho
wever, the
ca
pacitie
s
of two lines
are
n
o
t quite able
to deliver so
me
power from
Location 2. To solve thi
s
pro
b
le
m
should b
e
do
ne adju
s
tme
n
ts of the re
sults
obtaine
d until
there
are n
o
t line ove
r
lo
aded, ie
by redu
cing th
e
sup
p
ly from
Location 2
a
n
d
accomp
anie
d
addition su
p
p
ly of Locatio
n 1. For exam
ple, if quota of G2 from Location 1 is set
30MW, q
uoita of G7 at Location 2 h
a
s t
o
be red
u
ced
30MW.
EDM metho
d
can
not provide the optim
al re
su
lts
be
cause po
we
r flows in the n
e
twork
are
dete
r
min
ed by
ru
nnin
g
a l
oad
flow p
r
og
ram. In
th
e loa
d
flo
w
progra
m
, the
vo
ltage m
agnitu
de
of the generating buses hav
e to be
set, this
will affect the reat
ive power flows in
the net
work
and
also
will
affe
ct lo
sses.
Especi
a
lly in
he
avy l
oad
co
n
d
itions,
adju
s
ments mu
st
be m
ade
so t
hat
the results of
the EDM ca
n be appli
ed to the netwo
rk.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5086 – 50
95
5094
This i
s
sho
w
n
by Table 1
0
, G2 is a
s
the
lose
r, acco
rdi
ng to the EDM re
sults, ha
ve to be
given a quota
of 30 MW. It
is larg
er tha
n
10 MW fr
o
m
the OPF re
sul
t
s, so favora
b
l
e G2 owne
rs.
Beside
s l
o
sses i
s
gre
a
ter
than 1.2% f
r
o
m
the
OPF re
sult
s, it will
affect ad
ditio
nal q
uota
on
the
G7 as the
swi
ng bu
s so tha
t
its quota is
greate
r
than
6.5 MW from
OPF re
sults.
The dete
r
min
a
tion of LBMP through E
D
M will lea
d
to the following three i
s
sues that
must get seri
ously attentio
n.
1) The
r
e a
r
e
GENCO
s
ben
efited due to the additio
n
of
their quota, such a
s
G2 a
n
d
G7 in ca
se
1
of the simulat
i
on re
sults.
2)
Losses are not
optimal
so cost
of the l
o
sses
will
increase.
It will harm
DIS
C
Os as responsi
ble
to the loss
es
, [6]. This
is
shown by the
s
i
mulation
fo
r ca
se
1, lo
sse
s
in
crea
se
1.2% of optim
al
condition.
3) Th
e po
we
r flows i
n
the t
r
an
smi
ssi
on
bran
ch
es
are
not equ
al to
the optimal
condition
so th
at
imfluences
co
st allocation o
f
transmi
ssi
o
n
usa
ge, as
stated in [7].
These are three issue
s
ab
ove can b
e
concl
ude
d
that the determin
a
tion of LBMP through EDM is
not fair.
Solution by
O
P
F, it is
defini
t
ely no p
r
o
b
le
m to the
g
r
id.
It ca
n b
e
sho
w
n
by the
re
sults of
two
ca
se
s in
the
above
si
mulation,
bot
h for the
ca
ses
of h
eavy l
oad
and
light
load.
So u
s
i
ng
OPF do
es no
t need
mo
re
adju
s
ment
be
cau
s
e
it is de
finitely the re
sult
can
be
di
rectly a
pplie
d
to
the g
r
id. Th
u
s
LBMP
ea
ch lo
cation
an
d qu
ota e
a
ch
GENCO
that
win
s
th
e
co
mpetition
can
be
dire
ctly determined, as
sh
own in
simula
tion on the Case 1 a
nd Ca
se 2 ab
ove.
4.
Conclu
sion
For the light system
load or
the strong
net
work, the application
of EDM will
not be a
probl
em b
e
cause the o
p
e
r
ator
ca
n run
the load
flo
w
p
r
og
ram
with losse
s
co
vered
by GE
NCO
whi
c
h
has qu
ota bel
ow it
s
maximum a
s
the swin
g bu
s. However,
whe
n
the
he
avy system l
o
a
d
or the
r
e
are
con
g
e
s
tion, then the
ap
pli
c
ation
of
EDM ha
s a fe
w
probl
em
s, su
ch
as l
o
sse
s
that
has
not be
en
covered a
n
d
its re
sults
ca
n not be
di
re
ctly applie
d to the net
work. In this ca
se
the
operator m
u
st look fo
r the
overflow li
ne
s and the
n
det
ermin
e
the
re
ductio
n
of the
i
r po
we
r-flo
ws
with the re
du
ction of qu
otas fo
r the
se
nsitive gen
erators to th
o
s
e lines. It sh
ould be n
o
te
d that
the results
of the adjusme
nts can be
ascertained th
at it will not fall to an opti
m
al pri
c
e. These
con
d
ition
s
wil
l
create the
si
t
uation of an unfair comp
etition.
In determinin
g
LBMP mu
st be cond
uct
ed fairly
to
al
l parti
cipa
nts
of the comp
e
t
ition. In
this case it is req
u
ire
d
opti
m
ization
met
hod that
gua
rantee
s the
re
sults fall
in th
e value
of the
optimum pri
c
e and these result
s sho
u
ld
be able to
be dire
ctly applie
d to the network. In additio
n
,
the optimization metho
d
u
s
ed m
u
st h
a
v
e a run
n
ing
time of less than half an
hour
be
cau
s
e
electri
c
ity market de
sig
n
e
d
in a hour a
head.
Thi
s
paper p
r
op
ose
s
an OPF wit
h
the redu
ction
step that ha
s been d
e
velop
ed by [5] that
has h
ad
the runnin
g
time more q
u
ickly (se
e
Tabl
e 1).
The results o
f
OPF cal
c
ul
ation have
b
een a
b
le
to b
e
asce
rtaine
d
to be ap
plie
d to the
netwo
rk.
But
it has very
complex o
p
tim
i
zati
on
proble
m
s wh
en co
mpared with EDM.
However
with the hel
p of comp
uter t
hat wo
rks very fast
with a large m
e
mo
ry capa
city and
the prog
re
ss in
the devel
ome
n
t of OPF
m
e
thod, the
n
OPF will
be
able to
do
de
terminatio
n L
B
MP as i
ndi
cated
by the above simulatio
n
.
Glossary
of Terms
CC
=
Congestion cost
N
Y
S
O
=
Ne
w
Y
o
rk Service Ope
r
ator
EDM
=
Economic dispat
ch method
OPF
=
Optimal po
w
e
r flow
d
=
demand/load ind
e
x
opt.
=
Optimal index
deg.
=
degree
pu
=
Per unit
DISCO
=
Distribution compan
y
P
=
Active pow
er
g
=
generato
r
inde
x
P
ex
=
Expor o
f
active power
ISO
=
Independent se
r
v
ice operator
P
im
=
Impor of active p
o
wer
GENC
O
=
Gene
rator comp
an
y
Q
=
Reactive power
kV
=
kilo Volt
R
=
Reactance of line
max
.
=
max
i
mum inde
x
Rp
=
Unit currenc
y
min.
=
minimum index
S
=
Amparent po
wer
MVar
=
Mega Var
V
=
Voltage
MW
=
Mega
w
a
tt
X
=
Reactance of line
MWh
=
Mega
w
a
tt ho
ur
Y
=
Admittance of line
No. =
Number
δ
=
Phase angle
NP
=
Nodal price
λ
=
Lagrange coe
fficient
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Determ
inin
g LBMP throug
h Optim
a
l Power Fl
ow
in t
he Electri
c
Powe
r… (He
r
m
agasanto
s
Zein)
5095
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