Internati
o
nal Journal
of App
lied Power E
n
gineering
(IJAPE)
Vol.
2, No. 3, Decem
ber
2013, pp. 125~
140
I
S
SN
: 225
2-8
7
9
2
1
25
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
/
IJAPE
A Simple Approach for Optima
l Generation Scheduling to
Maximize GENCOs Profi
t
Using PPD Table and ABC
Algorithm under Deregulated
E
nvironment
K. Aso
k
a
n
, R.
Ash
o
k
kum
ar
Department o
f
Electrical Engin
e
ering, Annamalai
University
, Anna
malai Nagar
,
Tamil Nadu
, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 8, 2013
Rev
i
sed
Au
g 1, 201
3
Accepted Aug 18, 2013
In this paper
an attempt has
been
made
to
solve the prof
it based unit
com
m
itm
ent problem
(P
BUC)
u
s
ing pre-prep
ared
power demand (PPD) table
with an artifi
c
i
a
l bee colon
y
(
A
BC) algorithm
.
The P
P
D
-ABC algorithm
appears to be a r
obust and reliab
l
e op
timization algorithm for the solution of
PBUC problem. In a deregulated env
i
ronment, gener
a
tion
companies
(GENCOs) has t
h
e choice to bu
y or
sell from Ind
e
penden
t
S
y
stem Operator
(ISO), in
addition to g
e
ner
a
tin
g power on
its
own. The profit based un
it
com
m
itm
ent problem
is
cons
idered as
a stochast
ic optim
iz
ation problem
in
which the objective is to maximize their own profit and the d
ecisions ar
e
needed
to s
a
tis
f
y
th
e s
t
and
a
rd o
p
erat
ing cons
tra
i
nts
.
The P
B
UC problem
is
solved b
y
the pr
oposed methodo
log
y
in
two stag
es. In
the first step,
the unit
com
m
itm
ent scheduling
is perfo
r
m
ed b
y
consider
ing th
e pre-prep
ared power
demand (PPD) table
and th
en th
e problem
of fu
el cost and r
e
venue functio
n
is solved using
ABC Algorith
m. The PPD table suggests th
e operator
to
decid
e
the units to be put into generation ther
e b
y
reducing th
e co
mplexity
of
the problem. Th
e proposed appr
oach is
demonstrated on 10 units 24 hour and
50 units 24 hour
test s
y
stems and numeri
cal resu
lts are tabu
lated. Simulation
result shows that this approa
ch
effe
c
tive
l
y m
a
xi
m
i
zes the GEN
C
O’s profit
than
those obtained b
y
o
t
her
optimizing methods.
Keyword:
Deregu
latio
n
Gene
rat
i
o
n c
o
m
p
any
PPD tab
l
e an
d
ABC algo
rithm
Pr
of
it Based UC
Pro
f
i
t
m
a
xim
i
zat
i
on
of
GE
NC
O
Copyright ©
201
3 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
:
K. As
oka
n,
Department o
f
Electrical Engin
e
ering
,
Ann
a
m
a
lai Un
iv
ersity,
Ann
a
malai Nag
a
r,
Tam
i
l
n
adu,
I
n
di
a.
Em
a
il: aso
k
a
n
e
ee@g
m
ail.co
m
NO
MEN
C
LA
TURE
PF
total profit of
GENC
Os
RV
total r
e
venue
of
GE
NCOs
TC
total generation c
o
st
of
GE
NCO
s
P
it
real
powe
r
output of
i
th
Ge
ne
rator
P
Dt
forecasted syste
m
dem
a
nd during
hour t
P
it
max
m
a
x
i
mu
m l
i
m
i
t
o
f
i
th
un
it du
r
i
ng
h
our
o
f
t
P
it
min
mi
n
i
mu
m l
i
m
i
t
o
f
i
th
u
n
it du
r
i
ng
h
our
o
f
t
SP
t
f
o
reca
sted m
a
rket price at hour
of
t
ST
st
art up c
o
st
T
num
b
er
of tim
e Periods
c
onsi
d
ere
d
PPD
p
r
e-p
r
epa
r
e
d
po
wer
dem
a
nd t
a
bl
e
RPP
D
re
duced
p
r
e
-
p
r
epa
r
e
d
po
w
e
r dem
a
nd
t
a
bl
e
ABC
artificial b
e
e co
lon
y
I
n
crem
ental cost
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-87
92
IJAPE Vol.
2, No. 3, D
ecem
ber 2013:
125 –
140
12
6
N
num
ber
of
ge
nerat
i
n
g
uni
t
s
a
i
, b
i
, c
i
cost c
o
-e
fficient
o
f
i
t
h
ge
nerat
o
r
GENCO
ge
nerat
i
o
n C
o
m
p
any
TRANSC
O
t
r
ansm
i
ssi
on C
o
m
p
any
DI
SCO
di
st
ri
b
u
t
i
o
n C
o
m
p
any
R
i
(t
)
R
e
serve
of
i
th
g
e
n
e
r
a
ting
un
it du
r
i
n
g
hou
r
of
t
SR
(t
)
s
p
inning
reser
v
e duri
ng hour
of t
X
it
unit status
1.
INTRODUCTION
In
a v
e
rtically
in
tegrated
u
tility
en
v
i
ron
m
e
n
t,
th
e obj
ectiv
e
o
f
Un
it Commi
t
m
en
t (UC) inv
o
l
v
e
s
sch
e
d
u
ling
th
e g
e
n
e
rators apart fro
m
satisfyin
g
th
e
system
co
n
s
train
t
s.
Th
e
Un
it co
mmit
m
en
t p
e
rform
s
th
e
sch
e
d
u
ling
p
r
ocess in
a u
tility for m
i
n
i
m
i
z
i
n
g
th
e t
o
tal gen
e
ration
co
st
ov
er th
e tim
e
p
e
riod
[1
]-[2
]
. Th
e
in
trodu
ctio
n
o
f
d
e
reg
u
l
ation
an
d
restru
cturin
g
i
n
El
ectric p
o
wer syste
m
creates a co
mp
etitiv
e o
p
e
n
mark
et
scenari
o
. T
h
e
gene
rat
i
o
n co
m
p
any
adopt
s
Uni
t
C
o
m
m
i
tm
ent
for m
a
xi
m
i
zi
ng t
h
ei
r o
w
n
pr
ofi
t
i
n
st
ead o
f
m
i
nim
i
zi
ng t
h
e
t
o
t
a
l
gene
rat
i
o
n cost
of t
h
e ce
nt
ral
i
zed
po
we
r sy
stem
. This
pr
o
b
lem
is referre
d as P
r
o
f
it Based
Uni
t
C
o
m
m
i
tment
(PB
U
C
)
p
r
obl
em
. Profi
t
B
a
sed U
n
i
t
C
o
m
m
itm
ent
i
s
defi
ne
d as a
m
e
tho
d
w
h
i
c
h sc
h
e
dul
es
t
h
ei
r ge
nerat
o
r
s
econ
o
m
i
cal
ly based
o
n
f
o
re
cast
e
d i
n
f
o
rm
at
i
on suc
h
as s
p
ot
pri
c
e
,
rese
rv
e pri
ce,
dem
a
nd a
n
d
u
n
it
d
a
ta
w
ith
an
o
b
j
ectiv
e to m
a
x
i
mize th
e
G
E
N
C
O
s
pr
of
i
t
. So, t
h
e so
lu
ti
o
n
m
e
th
o
d
o
l
ogy o
f
PBU
C
prob
l
e
m
seem
s
t
o
be co
m
p
l
e
x t
h
an t
r
a
d
i
t
i
onal
UC
pr
obl
em
. The PB
UC
p
r
o
b
l
e
m
i
s
di
vi
de
d i
n
t
o
t
w
o s
u
b p
r
obl
e
m
s [3]
-
[4]
.
T
h
e
fi
rst
s
u
b
-
pr
obl
em
i
s
the
det
e
r
m
in
ati
o
n of
statu
s
of
th
e g
e
n
e
ratin
g
u
n
its an
d secon
d
sub-
pr
ob
lem
is th
e
det
e
rm
i
n
at
i
on of
o
u
t
p
ut
po
we
rs of com
m
it
t
e
d uni
t
s
.
Earlier, classical
m
e
thods suc
h
as [5]
-
[
1
1
]
Priority
List (PL), Dy
nam
i
c Prog
ram
m
i
ng (D
P), Bra
n
c
h
-
B
o
u
n
d
, M
i
xed
Int
e
ge
r Pr
og
r
a
m
m
i
ng (M
IP
) and La
gra
n
g
i
an rel
a
xat
i
o
n (LR
)
we
re use
d
t
o
sol
v
e t
h
e
UC
problem
.
A
m
o
ng the
s
e m
e
thods, the P
r
iority List
m
e
thod
[6] is a sim
p
le
m
e
thod
but the
quality of sol
u
tion is
ro
u
g
h
.
The
Dy
nam
i
c Progra
m
m
i
ng [7]
i
s
a fl
exi
b
l
e
m
e
t
hod t
o
s
o
l
v
e t
h
e
UC
p
r
o
b
l
e
m
.
Thi
s
ap
pr
oac
h
feat
ure
s
t
h
e cl
assi
fi
cat
ion
of
gene
rat
i
ng
uni
t
s
i
n
t
o
r
e
l
a
t
e
d gr
ou
ps s
o
as t
o
m
i
nim
i
ze t
h
e num
ber of
uni
t
com
b
i
n
at
i
o
n
s
w
h
ich
m
u
st b
e
tested
w
ithout p
r
eclud
i
n
g
t
h
e op
ti
m
a
l p
a
th
. Th
e d
y
n
a
m
i
c
p
r
og
r
a
mm
in
g
tech
n
i
q
u
e
invo
lv
es
h
u
g
e
co
m
p
u
t
atio
n
a
l ti
m
e
to
o
b
t
ain
th
e so
lu
tio
n
b
ecau
s
e of
its co
m
p
lex
d
i
men
s
io
n
a
lity with
larg
e
num
b
e
r o
f
gene
rat
i
n
g u
n
i
t
s
. A
not
her a
p
p
r
oac
h
has
bee
n
p
r
esen
ted
for so
lv
i
n
g
t
h
e un
it co
mmit
m
e
n
t p
r
ob
lem b
a
sed
on
b
r
an
ch
an
d bo
und
techn
i
ques [8
]. Th
e meth
od
in
cor
p
o
r
ates ti
m
e
-
d
ep
en
d
e
n
t
star
t
-
up co
sts, d
e
m
a
n
d
and
reser
v
e co
nst
r
ai
nt
s and m
i
nim
u
m
up and
do
w
n
t
i
m
e
co
nst
r
ai
nt
s
.
The
pri
o
ri
t
y
ord
e
ri
ng
of t
h
e u
n
i
t
s
i
s
not
necessa
ry
i
n
t
h
i
s
t
echni
que
.
Lagra
n
ge R
e
l
a
xat
i
on m
e
t
hod
[1
1]
pr
o
v
i
d
es
fast
sol
u
t
i
on
but
s
o
m
e
t
i
m
e
s i
t
suffe
rs f
r
o
m
num
eri
cal
con
v
e
r
ge
nce p
r
o
b
l
e
m
especi
al
l
y
when t
h
e p
r
o
b
l
e
m
i
s
nonc
on
ve
x. B
e
si
des
,
t
h
i
s
m
e
t
hod st
ro
ngl
y
depe
n
d
s
on
t
h
e t
ech
ni
q
u
e
use
d
t
o
up
dat
e
Lagra
n
ge m
u
l
t
i
p
l
i
e
rs. M
a
ny
r
e
searche
r
s
deal
i
ng
wi
t
h
LR
a
r
e usi
n
g s
u
b
g
r
a
d
i
e
nt
t
echni
q
u
e f
o
r s
o
l
v
i
n
g t
h
i
s
p
r
o
b
l
e
m
.
Even t
hou
g
h
, t
h
e s
o
l
u
t
i
on o
b
t
a
i
n
e
d
f
r
o
m
gradi
e
nt
-
b
ased m
e
t
hod suf
f
er
s
fr
om
conver
g
e
n
ce pr
o
b
l
e
m
and al
way
s
get
s
st
uck i
n
t
o
a l
o
cal
opt
im
u
m
. In or
de
r t
o
ove
r
c
om
e
t
h
ese pr
o
b
l
e
m
s
,
m
a
ny
st
ochast
i
c
o
p
t
i
m
i
zati
o
n
s
suc
h
as
[
12]
-[
19]
genet
i
c
a
l
go
ri
t
h
m
[12]
-
[
1
3
]
,
M
e
m
e
ti
c al
go
ri
t
h
m
[14
]
, Ant
co
lon
y
op
tim
i
zatio
n
[15
]
,
Particle swarm
o
p
t
i
m
iza
tio
n
[16
]
-[17
] an
d Mu
ller meth
od
[18
]
-[19
] were
i
n
t
r
o
d
u
ced
i
n
t
o
po
we
r
sy
st
e
m
opt
im
i
z
at
i
on. The
s
e
m
e
t
hods
begi
n wi
t
h
a po
p
u
l
a
t
i
o
n
of
st
art
i
n
g p
o
i
n
t
s
, use
onl
y
t
h
e
o
b
jec
t
i
v
e fu
nct
i
o
n i
n
f
o
rm
at
i
on, a
n
d sea
r
ch a
sol
u
t
i
o
n
i
n
paral
l
el
usi
n
g
ope
ra
t
o
rs
bo
rr
o
w
e
d
fr
o
m
n
a
tur
a
l b
i
o
l
ogy. Th
ese m
e
th
o
d
s
ar
e seem
s
to
b
e
f
a
st an
d r
e
liab
l
e, b
u
t
it h
a
s a p
r
ob
lem o
f
co
nv
erg
e
n
ce
on
l
a
rge s
cal
e p
o
w
er
sy
st
em
probl
em
. Hy
b
r
i
d
m
e
t
hods s
u
c
h
as LR
-M
I
P
[2
0
]
, LR
-G
A
[
21]
an
d LR
-EP
[
2
2]
-[
2
3
]
have
bee
n
use
d
f
o
r s
o
l
v
i
n
g t
h
e
PB
UC
pr
o
b
l
e
m
s
In
t
h
i
s
a
r
t
i
c
l
e
,
a si
m
p
l
e
m
e
t
h
od
f
o
r
m
a
xim
i
zi
ng t
h
e
pr
o
f
i
t
o
f
GENC
Os
i
s
de
vel
o
pe
d
ba
sed
o
n
P
r
e-
pre
p
are
d
Po
we
r Dem
a
nd
(PP
D
) t
a
bl
e w
ith
an
Artificial Bee Co
lon
y
(ABC)
algorithm. The
prepa
r
ation
of
PPD t
a
bl
e si
m
p
l
i
f
i
e
s t
h
e s
o
l
u
t
i
o
n
m
e
t
hodo
l
ogy
of
Pr
ofi
t
B
a
sed
Uni
t
C
o
m
m
i
tm
ent
pr
obl
em
i
rrespec
t
i
v
e of
d
i
m
e
n
s
io
n
a
lity
o
f
t
h
e system size. Also
th
e ex
ecu
tio
n
ti
m
e
o
f
th
e pro
p
o
s
ed
ap
pro
a
ch
is red
u
c
ed wh
en
co
m
p
ared
with th
e ex
istin
g
m
e
th
od
s.
Th
e pro
p
o
s
ed
PPD-
ABC approach has bee
n
tested
on two test sys
t
e
m
s
and num
e
rical results a
r
e
pres
ented t
o
prov
e
the effective
n
e
ss of the
proposed m
e
thod
.
2.
PROBLEM FORMUL
ATION
2.
1
Tra
d
itiona
l
unit co
mmitment pro
b
lem
In t
h
e
past
,
U
C
i
s
defi
ne
d a
s
a m
e
t
hod t
o
sche
dul
e
ge
ner
a
t
o
rs ec
o
nom
ical
l
y
i
n
a p
o
w
e
r sy
st
em
i
n
or
der t
o
m
eet
the re
q
u
i
r
em
ent
s
of
l
o
a
d
an
d s
p
i
n
ni
n
g
re
ser
v
e. Tra
d
i
t
i
onal
UC
can
be
def
i
ned m
a
t
h
em
ati
cal
l
y
as an op
timizat
io
n
prob
lem
as
fo
llo
ws:
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2
A S
i
mp
le App
r
o
a
c
h
f
o
r
Op
tima
l
Gen
e
ra
tion
S
c
h
e
du
lin
g
to
Ma
ximize
GEN
C
Os Pro
fit Usi
n
g PPD (K. Aso
k
an
)
12
7
The ob
jec
t
ive
func
tion
(1)
Constr
aint
s
The
fol
l
o
wi
n
g
con
s
t
r
ai
nt
s m
u
st
be sat
i
s
fi
e
d
du
ri
n
g
t
h
e
opt
i
m
i
zat
i
on pr
oce
ss:
1.
Power
balance constraint
N
i
t
D
it
it
P
X
P
1
T
t
..
..........
2
,
1
(
2
)
2.
Spi
nni
ng
rese
r
v
e c
onst
r
ai
nt
N
i
t
t
D
it
i
SR
P
X
P
1
max
T
t
........
2
,
1
(
3
)
Ge
nerat
i
o
n l
i
m
it
const
r
ai
nt
max
min
i
i
i
P
P
P
N
i
.......
2
,
1
(
4
)
4. M
i
ni
m
u
m
up an
d
do
w
n
-t
i
m
e con
s
t
r
ai
nt
s
N
i
N
i
..........
1
.
..........
1
(5
)
2.
2 Pr
ofi
t
b
a
se
d unit c
o
mmitment
problem
Th
e obj
ectiv
e is to
d
e
term
in
e th
e g
e
n
e
rating
u
n
it sch
e
du
les for m
a
x
i
mizin
g
th
e pro
f
it o
f
Gen
e
ration
C
o
m
p
ani
e
s su
bject
t
o
al
l
pre
v
ai
l
i
ng c
onst
r
a
i
nt
s such as l
o
a
d
dem
a
nd, s
p
i
n
ni
n
g
rese
rve a
n
d m
a
rket
pri
ces. The
t
e
rm
pro
f
i
t
i
s
defi
ne
d as t
h
e d
i
ffere
nce bet
w
een re
ven
u
e
o
b
t
a
i
n
ed
fr
om
sal
e
of ene
r
gy
wi
t
h
m
a
rket
pr
i
ce and
to
tal
o
p
e
rating
co
st o
f
t
h
e g
e
neratin
g
co
m
p
an
y.
The ob
jec
t
ive
func
tion
Th
e
PBUC can b
e
m
a
th
em
a
tic
ally fo
rm
u
l
ated
b
y
th
e fo
llowin
g
equ
a
tion
s
.
Maximize
TC
RV
PF
(6)
T
t
N
i
it
t
it
X
SP
P
RV
11
(
7
)
T
t
N
i
it
it
it
X
ST
X
P
F
TC
11
.
)
(
(
8
)
Th
e to
tal
o
p
eratin
g
co
st,
o
v
er th
e en
tire sch
e
du
ling
p
e
r
i
o
d
is th
e su
m o
f
pr
odu
ction co
st an
d star
t
-
u
p
/
shu
t
do
wn
co
st fo
r all th
e
u
n
its.
Here, the shu
t
do
wn
co
st is co
n
s
i
d
ered
as eq
ual to
zero
fo
r all un
its. The
pr
o
duct
i
o
n c
o
s
t
of
t
h
e sc
he
dul
ed
uni
t
s
i
s
gi
ve
n i
n
a
qua
d
r
at
i
c
f
o
rm
2
)
(
.
it
i
it
i
i
it
it
P
C
P
b
a
P
F
Min
(
9
)
Constraints
1.
Loa
d
dem
a
nd con
s
t
r
ai
nt
N
i
t
D
it
it
P
X
P
1
N
i
1
(
1
0)
T
t
N
i
it
it
it
X
ST
X
P
F
TC
11
.
)
(
,
,
i
i
i
i
Tdown
Toff
Tup
Ton
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ecem
ber 2013:
125 –
140
12
8
2.
Gen
e
rator lim
i
t
s
con
s
trai
n
t
max
min
i
i
i
P
P
P
N
i
1
(
1
1
)
3.
Sp
inn
i
ng
r
e
serv
e
co
nstr
ain
t
N
i
it
it
SR
X
R
1
T
t
1
(
1
2)
4.
M
i
nim
u
m
up/
d
o
w
n
t
i
m
e const
r
ai
nt
s
,
,
i
i
i
i
Tdown
Toff
Tup
Ton
N
i
N
i
..........
1
.
..........
1
(13)
3.
SOLUTION METHODOL
OGY
It is ex
p
e
rien
ced
from th
e literatu
res, th
at m
o
st
o
f
th
e
p
r
ev
ailin
g
al
g
o
rith
m
s
h
a
v
e
lim
i
t
ati
o
n
s
t
o
p
r
ov
id
e
op
ti
mal so
lu
tion
.
Therefo
r
e, th
is p
a
p
e
r is fo
cu
sed
to
deriv
e
a
simp
le ap
pro
a
ch to
im
p
r
ov
e
GENCOs
pr
ofi
t
u
n
d
er
de
reg
u
l
a
t
e
d e
nvi
r
onm
ent
.
Fo
r t
h
i
s
, a t
a
bl
e nam
e
l
y
pre-
pre
p
are
d
p
o
w
er
dem
a
nd i
s
pre
p
are
d
usi
n
g
the unit data,
forecasted
pric
e and
syste
m
dem
a
nd. T
h
e
PPD ta
ble ide
n
tifies the
c
o
mmitm
ent of units a
n
d
th
en
ABC al
g
o
rith
m
is p
r
escrib
ed to
so
l
v
e t
h
e fu
el cost and
rev
e
nu
e
fun
c
tio
n. Rem
a
in
in
g p
a
rt of t
h
e article is
descri
bed
as
fo
l
l
o
ws.
3.
1.
Mathematiac
al m
o
del
of
Pr
e-prep
ared Power Dem
a
nd
(PPD) table
A c
o
m
p
lete algorithm
i
c steps
to pre
p
are t
h
e
PPD table is
gi
ven bel
o
w.
1.
The m
i
nim
u
m
and m
a
ximum
val
u
es of
l
a
m
bda are ca
l
c
ul
at
ed fo
r al
l
generat
i
n
g
u
n
i
t
s
at
t
h
ei
r
m
i
nim
u
m
and
m
a
xim
u
m
out
put
po
we
rs
(
P
im
in
, P
im
a
x
). Two lam
bda
values
are
pos
s
ible for each
gene
rat
i
n
g uni
t
s
.
The
val
u
e of lam
bda (
) are
est
i
m
at
ed by
usi
n
g t
h
e
f
o
l
l
o
wi
n
g
e
quat
i
ons
i
i
i
i
j
c
c
b
p
2
1
2
min
min
(14)
(1
5)
2.
The
l
a
m
bda val
u
es
are a
r
r
a
nge
d i
n
asce
n
d
i
ng
o
r
de
r a
n
d
l
a
bel
t
h
em
as
j
(
w
here j
=
1
,
2
…
2N
)
.
3.
The
o
u
tp
ut
p
o
we
rs
fo
r all
g
e
nerat
o
rs
at ea
ch
j
valu
e are
calcu
lated
u
s
ing
th
e fo
rm
u
l
atio
n
(16)
4.
T
h
e
m
i
nim
u
m
and
m
a
xim
u
m
out
p
u
t
p
o
w
er
o
f
ge
nerat
o
rs
are
fi
x
e
d as
f
o
l
l
o
w
s
.
(i
) F
o
r m
i
nim
u
m
out
put
po
we
r l
i
m
i
t
If
min
i
j
th
en
set
0
ji
p
(
1
7)
i
i
ji
c
b
p
2
i
i
i
i
j
c
c
b
p
2
1
2
max
max
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A S
i
mp
le App
r
o
a
c
h
f
o
r
Op
tima
l
Gen
e
ra
tion
S
c
h
e
du
lin
g
to
Ma
ximize
GEN
C
Os Pro
fit Usi
n
g PPD (K. Aso
k
an
)
12
9
If
min
i
j
th
en
set
min
i
ji
p
p
(
1
8)
(ii)
For m
a
x
i
m
u
m
o
u
t
pu
t po
wer lim
i
t
If
max
i
j
th
en
set
max
i
ji
p
p
(19)
5.
Lam
bda
(
) v
a
lu
e, ou
tpu
t
po
wers (
P
ji
) a
n
d sum
of output
powe
rs (SOP)
for each
are listed
in
the
t
a
bl
e i
n
asce
n
d
i
ng
o
r
de
r.
Thi
s
t
a
bl
e i
s
re
fe
rre
d as
Pre
-
pre
p
ar
ed P
o
wer
Dem
a
nd
(
PPD
) t
a
bl
e.
To
illu
strate the p
r
ep
aration
of PPD Tab
l
e, a typ
i
cal 1
0
un
i
t
syste
m
is co
nsid
ered
and
u
n
it d
a
ta are shown
i
n
Table -1.
Tabl
e
1.
Fuel
c
o
st
a
n
d
ge
nerat
o
r
l
i
m
i
t
s
dat
a
for
1
0
u
n
i
t
sy
st
em
Un
it
a
($
)
b
($
/MW
)
c
($
/MW
2
)
P
imin
(
MW
)
P
ima
x
(M
W)
1
1000
16.
19
0.
0004
8
150
455
2
970
17.
26
0.
0003
1
150
455
3
700
16.
60
0.
0020
0
20
130
4
680
16.
50
0.
0021
1
20
130
5
450
19.
70
0.
0039
8
25
162
6
370
22.
26
0.
0071
2
20
80
7
480
27.
74
0.
0007
9
25
85
8
660
25.
92
0.
0041
3
10
55
9
665
27.
27
0.
0022
2
10
55
10
670
27.
79
0.
0017
3
10
55
Tabl
e
2.
Asce
n
d
i
n
g
or
der
val
u
es o
f
l
a
m
bda f
o
r
t
e
n
ge
nerat
i
ng
u
n
i
t
s
The asce
n
d
i
n
g
or
der
val
u
es
of
l
a
m
bda a
r
e
gi
ven
i
n
Tabl
e
-
2.
Fi
nal
l
y
t
h
e
PPD
Tabl
e
i
s
p
r
epa
r
ed
b
y
applying the a
b
ove al
gorithmic
st
eps a
n
d
s
h
ow
n i
n
Ta
bl
e
–
3.
3
.
2
.
Ma
th
e
m
a
t
i
c
a
l mo
d
e
l
o
f
R
e
d
u
c
ed
P
r
e-p
r
e
p
a
r
ed
Po
we
r
D
e
ma
nd
(RP
P
D
)
ta
b
l
e:
The
Forecaste
d price
plays an im
portant rol
e
in
pre
p
aring t
h
e RPPD Ta
bl
e. Because
GE
NCOs yield
profit
only when t
h
e
forec
a
sted price at the gi
ven hou
r is m
o
re than the i
n
crem
ental fuel c
o
st
of t
h
e
gene
rat
o
rs.
Th
ere are two
ways to fo
rm
th
e RPPD tab
l
e
fro
m
th
e PPD tab
l
e
.
1.
From
the PPD table, two
rows are selecte
d
for
the predi
c
ted powe
r de
mand, s
u
ch t
h
at the powe
r
d
e
m
a
n
d
lies wi
th
in
th
e Su
m
o
f
Po
wers
(SOP) lim
its. Th
e co
rresp
ond
ing
rows
are
considered
k
and
1
k
.
2.
Here
, two
ro
ws co
rre
sp
o
n
d
s
to the f
o
rec
a
sted
price are selected from
th
e PPD tab
l
e .So
th
at
forecasted
p
r
ice
falls within
th
e i
n
crem
en
tal
cost. T
h
e rows
are
consi
d
ered as
l
and
1
l
.
S.No
λ
S.No
λ
S.No
λ
S.No
λ
1
16.
33
6
17.
12
11
22.
54
16
27.
51
2
16.
58
7
17.
35
12
23.
48
17
27.
78
3
16.
63
8
17.
54
13
26.
00
18
27.
82
4
16.
68
9
19.
90
14
26.
37
19
27.
87
5
17.
05
10
20.
99
15
27.
31
20
27.
98
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IJAPE Vol.
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ecem
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140
13
0
Tabl
e 3. Pre
-
p
r
epare
d
p
o
we
r dem
a
nd
(
P
P
D
)
t
a
bl
e
f
o
r
1
0
u
n
i
t
24 h
o
u
r
sy
st
e
m
s
(In
c
lud
i
ng
g
e
nerato
r limits,
min
i
m
u
m
u
p
and do
wn
tim
e co
n
s
train
t
s and
i
n
itial statu
s
o
f
gen
e
rat
o
rs)
T
h
e
r
efo
r
e
,
th
e
Re
d
u
c
ed
Pre
-
p
r
epa
r
ed
P
o
we
r
Dem
a
nd (RP
P
D
) ta
ble is
fo
r
m
ed by
a)
If the
row
l
k
,
th
en th
e R
P
PD
tab
l
e is fo
rm
ed
b
y
co
nsid
eri
n
g
th
e op
tion
1
.
b
)
If
the
ro
w
k
l
,
t
h
en t
h
e R
P
PD
t
a
bl
e i
s
f
o
rm
ed
by
ch
o
o
si
n
g
t
h
e
opt
i
o
n
2.
The R
P
PD
Ta
b
l
e fo
r
vari
ous
p
o
we
r
dem
a
nds
are
devel
ope
d
and
s
h
o
w
n
i
n
t
h
e Ta
bl
e -
4
t
o
Tabl
e -
8
.
Tabl
e
4. R
P
PD
Tabl
e
fo
r
Fo
re
cast
e
d
Dem
a
nd o
f
70
0 M
W
t
o
8
5
0
M
W
λ
($
/MW
)
P
1
(M
W)
P
2
(M
W)
P
3
(M
W)
P
4
(M
W)
P
5
(M
W)
P
6
(M
W)
P
7
(M
W)
P
8
(M
W)
P
9
(M
W)
P
10
(M
W)
SOP
(M
W)
16.
33
150
455
0
0
0
0
0
0
0
0
605.
00
16.
58
455
455
0
0
0
0
0
0
0
0
910.
00
Tabl
e
5. R
P
PD
Tabl
e
fo
r
Fo
re
cast
e
d
Dem
a
nd o
f
95
0 M
W
t
o
1
1
5
0
M
W
Tabl
e 6.
R
P
PD
Tabl
e fo
r Fo
re
cast
e
d Dem
a
nd
o
f
12
0
0
M
W
t
o
13
0
0
M
W
λ
($
/MW
)
P
1
(M
W)
P
2
(M
W)
P
3
(M
W)
P
4
(M
W)
P
5
(M
W)
P
6
(M
W)
P
7
(M
W)
P
8
(M
W)
P
9
(M
W)
P
10
(M
W)
SOP
(M
W)
16.
68
455
455
0
42.
65
0
0
0
0
0
0
952.
65
17.
05
455
455
112.
50
130
0
0
0
0
0
0
1152.
5
0
λ
($
/MW
)
P
1
(M
W)
P
2
(M
W)
P
3
(M
W)
P
4
(M
W)
P
5
(M
W)
P
6
(M
W)
P
7
(M
W)
P
8
(M
W)
P
9
(M
W)
P
10
(M
W)
SOP
(M
W)
19.
90
455
455
130
130
25.
12
0
0
0
0
0
1195.
1
2
20.
99
455
455
130
130
162
0
0
0
0
0
1332.
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
APE
I
S
SN
:
225
2-8
7
9
2
A S
i
mp
le App
r
o
a
c
h
f
o
r
Op
tima
l
Gen
e
ra
tion
S
c
h
e
du
lin
g
to
Ma
ximize
GEN
C
Os Pro
fit Usi
n
g PPD (K. Aso
k
an
)
13
1
Tabl
e 7.
R
P
PD
Tabl
e fo
r Fo
re
cast
e
d Dem
a
nd
o
f
14
0
0
M
W
Tabl
e 8.
R
P
PD
Tabl
e fo
r Fo
re
cast
e
d Dem
a
nd
o
f
15
0
0
M
W
Now, it is n
ecessary to
form
t
h
e Red
u
ced
Sch
e
du
lin
g U
n
i
t
s
(R
SU) t
a
bl
e w
h
i
c
h ex
pl
ai
ns t
h
e st
at
us o
f
co
mmitted
u
n
i
ts. Th
e RSU tab
l
e is ob
tain
ed fro
m
RPPD t
a
b
l
e b
y
sub
s
titu
tin
g th
e
b
i
n
a
ry v
a
lu
es
su
ch
a way
t
h
at
i
f
any
el
em
ent
i
n
t
h
e t
a
bl
e i
s
non ze
ro
,
t
h
en i
t
i
s
repl
a
ced by
1
.
The
r
efo
r
e, i
f
bi
na
ry
val
u
e i
s
zer
o, t
h
en t
h
e
co
rresp
ond
ing
u
n
it is i
n
OFF
state. Similarly
if
b
i
n
a
ry
v
a
l
u
e is 1, th
en
t
h
e
un
it is in
ON state.
For e
x
am
ple, the status
of
ge
nerating
units for
forecaste
d powe
r dem
a
nd of
700
M
W
is as
follows
U
1
U
2
U
3
U
4
U
5
U
6
U
7
U
8
U
9
U
10
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
The dec
o
m
m
i
tm
ent
of uni
t
s
,
Incl
usi
o
n of m
i
ni
m
u
m
up t
i
m
e
and m
i
nim
u
m
do
w
n
t
i
m
e
con
s
t
r
ai
nt
s are
incorporate
d
i
n
the PB
UC
problem
.
3.
3.
De-c
om
mi
tment
o
f
un
i
t
s
The
pr
ofi
t
of
GENC
Os
de
pe
nds
o
n
t
h
e
pr
o
p
er
sche
d
u
l
i
n
g
of
u
n
i
t
s
. S
o
m
e
t
i
m
e
s, t
h
e spi
nni
ng
rese
rv
e
of the
system
is inc
r
eased,
due to t
h
e large
gap
betwee
n
t
h
e selected
lam
b
d
a
v
a
lu
es in the RPPD tab
l
e.
So
, it
is i
m
p
o
r
tan
t
to
no
te th
at th
e d
eco
mm
i
t
m
e
n
t o
f
th
e
u
n
it is n
ecessary to
i
m
p
r
ov
e th
e fin
a
n
c
ial b
e
nefits o
f
GENC
Os.
If the
r
e is any
excessive
spi
nni
ng
rese
rve
,
th
en the R
P
PD table is exa
m
ined. T
h
en t
h
e exce
ssive
u
n
its i
n
th
e RPPD Tab
l
e are
deco
mmitted
after sa
tisfying
the sp
i
n
n
i
n
g
reserv
e con
s
trai
n
t
s.
3.4. Minimum
up time and minimum
down
time
c
o
ns
traints
Th
e
OFF tim
e
o
f
t
h
e un
it is less th
an th
e m
i
n
i
m
u
m
d
o
w
n
-
ti
me, th
en
statu
s
o
f
t
h
at un
it wi
ll b
e
OFF.
Si
m
ilarly
if ON ti
m
e
o
f
th
e
u
n
it is greater
th
an
th
e up
time o
f
th
e
u
n
it, th
en
that un
it will b
e
ON.
All th
ese
u
s
efu
l
in
fo
rm
atio
n
are app
lied
in
RPPD
Tab
l
e to
p
e
rform th
e fin
a
l u
n
it co
mmi
t
m
e
n
t sch
e
du
ling
.
Th
en
Artificial Bee
Co
lon
y
(ABC) alg
o
rith
m
h
a
s
b
een pro
p
o
s
e
d
to s
o
lve t
h
e Ec
onom
ic Dispatch
(ED)
problem
.
3.
5. Ar
ti
fi
ci
al
B
ee
C
o
lo
ny
(A
BC)
A
l
go
rithm
Artificial Bee Co
lon
y
(ABC) is th
e recen
tly d
e
fi
ne
d a
l
go
ri
t
h
m
s
by
Der
v
i
s
Ka
ra
bo
ga i
n
2
0
0
5
,
m
o
t
i
v
a
ted
b
y
th
e in
tellig
en
t
b
e
h
a
v
i
o
r
o
f
h
o
n
e
y bees [24
]
-[25
]. ABC
in
an
op
ti
m
i
z
a
tio
n
too
l
prov
id
es a
po
p
u
l
a
t
i
o
n
-
bas
e
d sea
r
c
h
pr
oc
edu
r
e i
n
w
h
i
c
h
i
n
di
vi
d
u
al
s ca
l
l
e
d f
o
o
d
s
p
o
si
t
i
ons a
r
e m
odi
fi
ed
by
t
h
e a
r
t
i
f
i
c
i
a
l
bees with tim
e
and t
h
e bee
’
s a
i
m
is
to discover the pl
aces
of food s
o
urces
with hi
gh
nectar am
ount and finally
the one
with t
h
e
highest necta
r
.
In
th
e ABC alg
o
rith
m
,
th
e co
lo
n
y
o
f
artifici
a
l b
ees
cont
ai
n
s
of t
h
ree g
r
ou
ps
of bees: employed
bees,
onl
oo
ke
rs an
d
scout
s. T
h
e f
o
o
d
so
u
r
ce re
prese
n
t
s
a p
o
s
s
i
b
l
e
sol
u
t
i
o
n of t
h
e
opt
i
m
i
z
at
i
on p
r
o
b
l
e
m
and t
h
e
nectar am
ount
of a
food s
ource corre
s
ponds to the
quality (fitn
ess
)
of t
h
e ass
o
ciated
solution.
Eve
r
y food
sou
r
ce
has
o
n
l
y
one
em
pl
oy
ed
bee. T
h
us,
t
h
e n
u
m
b
er o
f
e
m
pl
oy
ed bees
or t
h
e
onl
oo
ke
r be
es i
s
e
qual
t
o
t
h
e
num
ber
of
f
o
o
d
s
o
u
r
ces
(s
ol
u
t
i
ons)
.
The
onlooker
bees
eval
uate
the nectar inform
ation and
choo
se a fo
od so
ur
ce d
e
p
e
nd
ing
on
th
e
p
r
ob
ab
ility
v
a
lu
e
asso
ciated
with
th
at fo
od
so
urce (
, calcul
a
ted by t
h
e
foll
owi
n
g expressi
on.
λ
($
/MW
)
P
1
(M
W)
P
2
(M
W)
P
3
(M
W)
P
4
(M
W)
P
5
(M
W)
P
6
(M
W)
P
7
(M
W)
P
8
(M
W)
P
9
(M
W)
P
10
(M
W)
SOP
(M
W)
22.
54
455
455
130
130
162
20
0
0
0
0
1352.
0
0
23.
48
455
455
130
130
162
80
0
0
0
0
1412.
0
0
λ
($
/M
W)
P
1
(M
W)
P
2
(M
W)
P
3
(M
W)
P
4
(M
W)
P
5
(M
W)
P
6
(M
W)
P
7
(M
W)
P
8
(M
W)
P
9
(M
W)
P
10
(M
W)
SOP
(M
W)
27.
31
455
455
130
130
162
80
0
55
10
0
1477.
0
0
27.
51
455
455
130
130
162
80
0
55
54.
05
0
1521.
0
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-87
92
IJAPE Vol.
2, No. 3, D
ecem
ber 2013:
125 –
140
13
2
Fi
gu
re
1.
Fl
o
w
cha
r
t
f
o
r
p
r
o
p
o
se
d m
e
t
hod
Initialize colony
si
ze, food nu
m
b
er
a
nd fo
od source
position o
f
ABC par
a
m
e
ter
s
Read unit data, For
ecasted price
and sy
stem
de
m
a
n
d
Calculate la
m
bda
values,
output pow
er
s
and su
m
of output power
s (
S
OP)
to form
P
P
D
ta
ble
Ti
m
e
t =
1
Form
RPPD table
using PPD table for
the given tim
e
inter
v
al of sy
stem
d
e
m
a
nd
Form
r
e
duced co
m
m
itted units (
RCU)
table using RPPD table
I
s
ma
x
i
mu
m t
i
me
interval reached
Obtain the reduced co
mm
i
tted units
(
RCU)
table for
24 hour
inter
v
al
Incorporate deco
mm
i
t
m
ent
of
units,
m
i
ni
m
u
m
up and down and tim
e
constr
aints
Form
final unit com
m
it
m
e
nt scheduling
for
24 ho
ur
inter
v
al including all
constr
aints
Call ABC algorith
m
to solve
econo
m
i
c dispatch (
E
D)
subpr
oblem
E
v
aluate fitness fu
nction of the E
D
subpr
oblem
I
s
optim
al
solution reached
Print si
m
u
lation re
sults
Sto
p
Yes
Yes
No
t = t+1
No
Start
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
APE
I
S
SN
:
225
2-8
7
9
2
A S
i
mp
le App
r
o
a
c
h
f
o
r
Op
tima
l
Gen
e
ra
tion
S
c
h
e
du
lin
g
to
Ma
ximize
GEN
C
Os Pro
fit Usi
n
g PPD (K. Aso
k
an
)
13
3
(2
0)
Whe
r
e
fit
i
is
the fitness value
of the s
o
lution i which is proportional to
the nectar am
ount of the food
so
urce i
n
th
e po
sitio
n i and
SN
i
s
t
h
e
num
ber
of
f
o
o
d
s
o
urc
e
s i
s
eq
ual
t
o
t
h
e
num
ber
of
e
m
pl
oy
ed bees.
The
em
ployed
bees
e
x
c
h
ange
th
eir
in
form
at
io
n
with
th
e
on
loo
k
e
rs. In
ord
e
r to
produ
ce a can
d
i
d
a
te
food
p
o
s
ition
fro
m
th
e
o
l
d
o
n
e,
th
e ABC u
s
es
th
e fo
llowing
exp
r
ession
(2
1)
Whe
r
e,
}
.,
..........
2
,
1
{
BN
k
and
}
.,
..........
2
,
1
{
D
j
are ra
ndom
ly
chosen i
nde
xe
s. Although
k
is
d
e
term
in
ed
rand
o
m
ly, it h
a
s to
b
e
d
i
fferen
t
fro
m
i
.
ij
i
s
a ra
n
dom
num
ber
b
e
t
w
een
[0
,
1]
. It
co
nt
r
o
l
s
t
h
e
pr
o
duct
i
o
n o
f
a nei
g
h
b
o
u
r
fo
od s
o
u
r
ce p
o
si
t
i
on aro
u
nd
ij
X
a
nd the m
odification represe
n
t
s
the com
p
arison
o
f
th
e n
e
ighb
ou
r
fo
od
po
sition
s
v
i
su
ally
b
y
t
h
e b
ee.
If a p
r
edet
e
r
m
i
ned
num
ber o
f
t
r
i
a
l
s
does n
o
t
im
pro
v
e a sol
u
t
i
on re
prese
n
t
i
ng a f
o
od s
o
u
r
ce, t
h
en t
h
at
food source is abandone
d a
n
d the em
ployed bee a
sso
ciat
ed with t
h
at food s
o
urce
be
com
e
s a scout
. The
n
u
m
b
e
r of trials fo
r
releasing
a food
source is eq
u
a
l
to
th
e v
a
l
u
e of ‘limit’, wh
ich
is an
im
p
o
r
tan
t
co
n
t
ro
l
param
e
t
e
r of
A
B
C
al
go
ri
t
h
m
.
The l
i
m
it
val
u
e us
ual
l
y
va
ri
es f
r
om
0.
00
1
n
e
D
to
n
e
D
. If the aba
n
done
d
s
o
urce is
ij
X
,
j
(
1
,
2
,.
..
D)
then t
h
e sc
out
discovers a
ne
w food s
o
urce
ij
X
, cal
cul
a
t
e
d
by
usi
n
g
t
h
e e
q
ua
t
i
on.
)
(
)
1
,
0
(
min
max
min
j
j
j
ij
X
X
rand
X
X
(22)
Whe
r
e
min
j
X
and
max
j
X
are th
e m
i
n
i
m
u
m an
d
m
a
x
i
m
u
m li
mits o
f
th
e p
a
ram
e
ter to
b
e
op
tim
ized
.
There
are
four
cont
rol
param
e
ters used
in
ABC alg
o
rith
m
.
Th
ey
are
the
num
b
er of em
ployed
bees
,
num
b
er of
unem
p
l
o
y
e
d
or
onl
oo
ke
r bee
s
, t
h
e l
i
m
i
t
val
u
e and t
h
e c
o
l
o
ny
si
ze. T
hus
,
AB
C
sy
st
em
com
b
i
n
es l
o
cal
searc
h
carri
ed
o
u
t
by
em
pl
oy
ed a
nd
onl
oo
ke
r bee
s
,
an
d gl
obal
sea
r
ch m
a
nage
d
b
y
onl
oo
ker
s
an
d sc
out
s
,
at
t
e
m
p
t
i
n
g
t
o
bal
a
nce e
x
pl
orat
i
o
n a
n
d e
x
pl
oi
t
a
t
i
o
n
p
r
oc
ess.
4.
SIM
U
LATI
O
N
AN
D RES
U
LTS
CO
MP
A
R
ISO
N
Th
e
Pr
e-
pr
ep
ared
po
w
e
r
d
e
man
d
(PPD
) tab
l
e w
ith an ar
tif
i
c
ial b
ee co
lony alg
o
r
ith
m
(
A
BC)
b
a
sed
PBUC is first tested
on
10
u
n
it syste
m
av
ail
a
b
l
e in
th
e literatu
re
[1
8
]
and [23
]
as Case 1
.
It is also
v
a
l
i
d
a
ted
o
n
m
u
ltip
le tes
t
syste
m
s o
f
5
0
un
its in
Case
2
.
4.
1 T
e
s
t
c
a
se:
1
(T
en u
n
i
t
T
e
st S
y
s
t
em)
Thi
s
t
e
st
sy
st
em
adapt
e
d fr
om
[23]
c
o
nsi
s
t
i
ng o
f
t
e
n g
e
nerat
i
n
g u
n
i
t
s
wi
t
h
Twent
y
Four h
o
u
r
sche
duling
periods a
n
d the
fuel cost of
each
gene
rators is e
s
tim
a
ted into
quadratic form
. The
gene
rator data,
forecasted m
a
rket and
dem
a
nd
price a
r
e als
o
conside
r
ed from
the sam
e
reference
.
Tab
l
e
9
.
Un
it Data fo
r Ten
Un
it System
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
P
ma
x
455
455
130
130
162
80
85
55
55
55
P
mi
n
150
150
20
20
25
20
25
10
10
10
a
1000
970
700
680
450
370
480
660
665
670
b
16.
19
17.
26
16.
60
16.
50
19.
70
22.
26
27.
74
25.
92
27.
27
27.
79
c
0.
0004
8
0.
0003
1
0.
0020
0
0.
0021
1
0.
0039
8
0.
0071
2
0.
0007
9
0.
0041
3
0.
0022
2
0.
0017
3
M
i
n up
8
8
5
5
6
3
3
1
1
1
M
i
n down
8
8
5
5
6
3
3
1
1
1
ST
4500
5000
550
560
900
170
260
30
30
3
0
Initial
8
8
-5
-5
-6
-3
-3
-1
-1
-1
SN
n
n
i
i
fit
fit
p
1
)
(
kj
ij
ij
ij
ij
X
X
X
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-87
92
IJAPE Vol.
2, No. 3, D
ecem
ber 2013:
125 –
140
13
4
These
dat
a
are
descri
be
d i
n
Tabl
e-
9 a
nd
T
a
bl
e-
10
. T
h
e f
easi
b
l
e
pa
ram
e
t
e
rs o
b
t
a
i
n
e
d
by
va
ri
o
u
s
p
r
o
cesses fo
r
Artificial Bee
Co
lon
y
(ABC) alg
o
rith
m
ar
e
as follows.
Colony size
=
20
; foo
d
nu
m
b
er
=
10
;
Food source lim
it =100; a
n
d
m
a
xim
u
m
num
ber of iterations = 1000.
The
pr
op
ose
d
PPD
-AB
C
m
e
tho
d
o
l
o
gy
i
s
t
e
st
ed t
o
dem
onst
r
at
e i
t
s
supe
ri
o
r
pe
rf
orm
a
nce on t
e
n u
n
i
t
s
t
w
ent
y
fo
u
r
h
o
u
r
sy
st
em
usi
ng M
A
TLA
B
.
Fi
nal
uni
t
com
m
i
tm
ent sched
u
l
i
n
g a
nd
out
p
u
t
po
wers
o
f
co
mmitted
g
e
nerato
rs are
d
i
sp
layed
in
Tab
l
e -
1
1
and
Table -
12
in d
e
tai
l
. Fro
m
th
is ta
b
l
e, it is ob
serv
ed th
at
th
e
GENC
O decid
e
s
to
shu
t
o
f
f Un
its 7
to 1
0
in
all
the
c
o
mmitment period and t
o
sel
l
power and
re
serve
b
e
low th
e
fo
recasted
lev
e
l in so
m
e
p
e
riod
s. Th
is is
beca
use the
objective of PBUC is
not t
o
m
i
nimiz
e
the
cost
s as bef
o
r
e
, but
t
o
m
a
xim
i
ze t
h
e pro
f
i
t
wi
t
h
rel
a
x
a
t
i
on o
f
t
h
e dem
a
nd ful
f
i
l
l
m
e
nt
and co
n
s
t
r
ai
nt
.
Com
p
arative s
t
udies
ha
ve al
so
bee
n
m
a
de to analyze
t
h
e to
tal co
st, reven
u
e
and profi
t
o
f
Trad
itio
n
a
l an
d
PBUC system. The
num
e
ric
a
l results are
prese
n
ted i
n
Tabl
e -
13
. I
n
o
r
der t
o
ve
ri
fy
t
h
e pe
rf
o
r
m
a
nce
adva
nt
age
s
o
f
PPD
-AB
C
f
u
rt
her
,
t
h
e si
m
u
l
a
t
i
on r
e
sul
t
s
were co
m
p
ared
with
th
at
o
f
o
t
h
e
r op
timizin
g
t
echni
q
u
es
an
d
com
p
ari
s
o
n
re
sul
t
s
are
gi
ven
i
n
Ta
bl
e -
1
4
a
n
d
1
5
.
Fi
g
-
2 e
xhi
bi
t
s
t
h
e
gra
phi
cal
rep
r
ese
n
t
a
t
i
on
of t
o
t
a
l
cost
, re
ven
u
e an
d p
r
of
i
t
.
Al
so Fi
g-
3 c
o
m
p
ares t
h
e pr
ofi
t
of f
o
ur
di
f
f
ere
n
t
opt
i
m
i
z
at
i
on al
go
ri
t
h
m
vi
z.,
trad
itio
n
a
l un
it
co
mmit
m
en
t,
Mu
ller m
e
th
o
d
, p
a
rallel PSO
an
d
n
o
d
a
l AC
O. Fro
m
th
e resu
lts, it is cle
a
r th
at
the proposed
m
e
thods
provides m
a
xim
u
m
profits an
d a
r
e com
p
ared
with thos
e publishe
d in the
recent
literatu
res.
Tabl
e
10
. F
o
re
cast
e
d
Dem
a
nd an
d S
p
ot
P
r
i
ce f
o
r
Ten
U
n
i
t
2
4
Ho
ur
Sy
st
em
Hour
(h
)
Forecasted
De
m
a
nd
(M
W)
Forecasted
Reserve
(M
W)
Forecasted
Mark
et p
r
i
c
e
($
/MWh
)
1
700
70
22.
15
2
750
75
22.
00
3
850
85
23.
10
4
950
95
23.
65
5
1000
100
22.
25
6
1100
110
22.
95
7
1150
115
22.
50
8
1200
120
22.
15
9
1300
130
22.
80
10
1400
140
29.
35
11
1450
145
30.
15
12
1500
150
31.
65
13
1400
140
24.
60
14
1300
130
24.
50
15
1200
120
22.
50
16
1050
105
22.
30
17
1000
100
22.
25
18
1100
110
22.
05
19
1200
120
22.
20
20
1400
140
22.
65
21
1300
130
23.
10
22
1100
110
22.
95
23
900
90
22.
75
24
800
80
22.
55
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