TELKOM
NIKA
, Vol.13, No
.2, June 20
15
, pp. 413 ~ 420
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i2.1472
413
Re
cei
v
ed
Jan
uary 21, 201
5
;
Revi
sed Ma
rch 2
6
, 2015;
Acce
pted April 10, 2015
Optimization of Power System Scheduling Based on
SCEM-UA Algorithm
Zi Yang Qiang*
1
, Feng Ping Wu
2
, Jia Rui Dong
3
, Ru
i Dong Hen
g
4
1,2
School of Business Adm
i
nis
t
ration, Hoh
a
i
Un
ivers
i
t
y
, C
h
a
ngzh
ou 2
130
2
2
, P. R. China
3
Business sch
ool, Ho
hai U
n
iv
ersit
y
, Na
nj
ing
210
09
8, P. R.
Chin
a
4
Universit
y
of Bath, Bath
BA2 7AY, United Kingdom
*Corres
p
o
ndi
n
g
author, em
ail
:
16382
94
20
3
@
qq.com
1
, w
f
p
@
hh
u.edu.c
n
2
, djr@nu
ist.edu.
cn
3
A
b
st
r
a
ct
Due to th
e w
o
rld
’
s i
n
cre
a
sin
g
l
y serio
u
s e
ner
gy
crisis, sh
ortage
of reso
urc
e
s, and
env
iro
n
menta
l
degr
adati
on, tr
aditi
ona
l p
o
w
e
r system
ana
l
ysis an
d
sch
e
duli
ng
opti
m
i
z
ation
metho
d
s
have f
a
ced
n
e
w
challenges. This article examines the featur
es of
optimal sc
heduling
of power
system
c
o
ntaining cascade
hydro
pow
er, a
nd
establ
ish
e
s
a sc
hed
uli
n
g
mo
de
l b
a
se
d
on th
e S
huffle
d
C
o
mpl
e
x Ev
oluti
on M
e
trop
olis
(SCEM-UA) al
gorith
m
. T
h
is
mo
de
l takes th
e cost of p
o
w
e
r
gen
erati
on, e
m
iss
i
on
of
g
a
s
eous
po
lluta
nts, an
d
the char
acteris
t
ics of the ge
nerators ful
l
y i
n
to acco
unt. Constra
i
nts on
the c
han
ges in
ther
mo
el
ectric
gen
erator p
o
w
e
r outp
u
t w
e
re add
ed to the
set of cons
trai
nt cond
itions,
reduc
i
ng th
e i
m
p
a
ct of ther
ma
l
power fluctuations
on the power system
. Here, the SCEM
-UA algo
rithm
was used to solve the
problem
of
optim
al power
system
scheduli
ng
and render
the m
o
del ca
pable of global optim
i
z
at
ion s
e
arches. Analys
es
o
f
sim
u
l
a
te
d ca
se
s
h
a
v
e dem
on
stra
te
d tha
t
th
e
SC
EM-
U
A a
l
gor
ith
m
can r
e
solv
e th
e co
nflict b
e
tw
een
conver
genc
e s
pee
d an
d glo
b
a
l searc
h
cap
a
b
ility, incr
eas
i
n
g the glo
b
a
l
se
arch cap
abi
lity of the mo
del.
Ke
y
w
ords
:
Po
w
e
r System Sched
uli
ng, SCE
M-UA Algorit
h
m
, Multi Ch
ai
n Reserv
oirs
1. Introduc
tion
Since the joi
n
t powe
r
system sche
du
ling
optimiza
t
ion is stoch
a
stic, dynam
ic, and
involves time
-delay,
studie
s
at h
o
me
an
d ab
ro
a
d
hav
e bee
n
carrie
d out o
n
the
developm
ent
of
power gen
eration scheme
s
a
nd
power
system
sche
duling [
1
]. Co
mmonly u
s
e
d
method
s i
n
cl
ude
the eq
ual i
n
creme
n
tal
method,
dynamic pr
ogra
mming, lin
e
a
r
pro
g
ra
m
m
ing, La
gra
ngian
relaxation, t
he ge
netic
algorith
m
, a
nd the p
a
rti
c
le swarm optimizatio
n (PSO)
al
go
ri
thm.
Ho
wever, the
s
e algo
rithm
s
all have their own lim
itati
ons o
n
solvin
g the probl
e
m
of sche
duli
n
g
optimizatio
n
of hydrothe
rmal po
wer
sy
stem
s. The e
qual in
creme
n
tal method
only sati
sfies the
necessa
ry co
ndition
s for t
he obj
ective
function to
ta
ke the
minim
u
m value, n
o
t
the suffici
e
n
t
con
d
ition
s
. Dynami
c
pro
g
rammi
ng [2
] suffers
f
r
o
m
the cu
rse of dimen
s
ion
a
lity. Linear
prog
ram
m
ing
[3] requi
re
s linear
sim
p
lification of t
he p
r
oble
m
s to
be
solved, the
r
e
b
y redu
cin
g
the
accuracy
of t
he
cal
c
ulatio
n
.
The
Lag
ran
g
ian
relaxa
tio
n
[4] meth
od
has o
scill
atio
ns, eve
n
sing
ular
points, in the
solutio
n
process. The g
e
n
e
tic
alg
o
rithm
[5] and the
PSO [6] algorithm have we
ak
global
search
ca
pability, a
nd m
a
y ea
sil
y
fall into
a l
o
cal
optimal
solution.
Con
s
eque
ntly, non
e of
these al
gorith
m
s can a
ccu
rately solve the pr
obl
em of optimal po
we
r system
sch
edulin
g.
In orde
r to overcome the
shortcomin
gs
of
powe
r
sy
stem sche
dulin
g optimization and it
s
corre
s
p
ondin
g
solutio
n
s
of traditional
model
s [7], this pape
r prop
oses a
powe
r
sy
stem
sched
uling o
p
timization
model whi
c
h
take
s
t
he
eco
nomi
c
be
nefits, ene
rg
y efficiency
and
environ
menta
l
benefits i
n
to co
nsi
deration. A ne
w o
b
jective fun
c
t
i
on, i.e. obje
c
tive functio
n
of
pollution emi
ssi
on
s, is added to the
objective
functio
n
base
d
on the convention
a
l coal
con
s
um
ption
co
sts. In this way, unde
r the premi
s
e o
f
effectively e
n
su
ring
safe operation of the
power
syste
m
, the numb
e
r of the
r
moe
l
ectri
c
ge
ne
ra
tor sta
r
ts a
n
d
stop
s can b
e
minimi
zed,
and
water
re
sou
r
ces can b
e
used efficiently. This may
al
so red
u
ce poll
u
tant emissio
n
s from
ele
c
tric
power
comp
a
n
ies. Thi
s
pa
per al
so u
s
e
s
the SC
EM-UA [8] global optimization
al
gorithm to
sol
v
e
the mod
e
l. The SCEM
-UA alg
o
rithm
is a
glob
al
optimization
algo
rithm th
at com
b
ine
s
the
advantag
es
o
f
Shuffled Co
mplex Evolution (S
CE-U
A) algo
rithm a
n
d
Ma
rkov
ch
a
i
n Monte
Ca
rl
o
(MCM
C) met
hod.
With the
SCEM-UA
algo
rithm, in the
pro
c
e
s
s of
e
v
olution the
compl
e
xes a
r
e
not
partitione
d in
to multiple sub-com
p
lexe
s. Inst
ead,
a Markov chain is
con
s
tructed
so that
parameters evolve toward
the ta
rget posterior
probability distributi
on [9
]. SCEM-UA algorithm is
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 413 – 42
0
414
a glob
al opti
m
ization
alg
o
rithm
with
strong
ro
b
u
st
ness. It ca
n
re
solve the
confli
ct bet
wee
n
conve
r
ge
nce spe
ed an
d gl
obal search
capability effi
ci
ently and so
facilitate dive
rsity within th
e
popul
ation, improvin
g the global
sea
r
ch
ability of the
algorith
m
.
2.
Mathem
atica
l
Model
for
Optimal Sch
e
duling o
f
Po
w
e
r Sy
stem Co
ntaini
ng
Casc
ad
e
H
y
dropo
w
e
r Station
s
2.1. Objectiv
e func
tion
Optimal po
wer system
scheduli
ng
m
o
d
e
ls ba
sed
on
green
e
c
on
o
m
y no l
ong
er merely
pursue e
c
o
n
o
mic be
nefits [10]. Inste
ad, they
pursue
comp
re
hen
sive ben
efits that co
ver
eco
nomi
c
, social, enviro
n
mental, an
d other
be
n
e
fits. This sche
duling m
ode allo
ws
the
hydroel
ect
r
ic gene
rato
rs
and the th
ermoele
c
tri
c
g
enerators in
the gri
d
to
interrelate
and
compl
e
me
nt each other’
s
advantage
s to achiev
e the maximum
benefits of the system.
The
obje
c
tive function of the o
p
timal po
we
r sy
stem
sched
uli
ng mo
del b
a
sed on
green
eco
nomy i
s
a
s
follows
:
2
11
mi
n
2
(P
)
m
in
(
P
)
si
n(
e
(
P
P
)
)
(P
)
t
sj
TN
tt
t
js
j
j
j
s
j
j
s
j
tj
tt
j
j
sj
s
j
j
j
sj
P
t
js
j
j
Fa
b
P
c
dP
e
(1)
Her
e
,
(t
)
sj
P
– the o
u
tput of the jth thermoel
e
c
tri
c
gen
erat
or in the tim
e
interval t(MW);
(t
)
sj
P
– the output
of level i hydroele
c
tric p
o
we
r statio
n in the time interv
al t (MW);
,,
,
,
j
jj
j
j
ab
c
d
e
–
fuel con
s
ump
t
ion characte
ristic
co
effici
e
n
ts of th
erm
o
-ele
ctri
c p
o
wer pl
ant j;
,,
,
j
jj
j
– e
m
issi
on
coeffici
ents in
the mathema
t
ical model fo
r gas
e
m
issio
n
s by therm
o
electri
c
po
we
r plant j.
2.2. Cons
trai
nts
Variabl
e con
s
traint
s a
r
e i
m
porta
nt to the reali
z
ation
of optimal
sche
duling
mo
del. Only
whe
n
the
co
nstrai
nts
are
satisfie
d, th
e re
sult
of o
p
timized
sch
edulin
g be
co
me u
s
eful in
a
pra
c
tical
way
.
The optimal powe
r
syste
m
sch
eduli
n
g
model ba
se
d on gre
en e
c
on
omy has
a
numbe
r of co
nstrai
nts [11]-[12].
First, co
nstrai
nt of electricit
y balancin
g is
the requirem
ent that in one scheduli
ng
perio
d,
the total po
wer ge
ne
rated
by all the hy
droel
ect
r
ic
an
d therm
oele
c
tric g
ene
rators in the
po
wer
system e
qual
s the load d
e
m
and of the g
r
id.
11
1
1
1
(t
)
(
t
)
(t
)
TM
T
N
T
sj
hi
L
tj
t
i
t
PP
P
(2)
Secon
d
, du
e
to the hydraul
ic conn
ectio
n
betwe
en
u
p
st
ream and do
wn
strea
m
reservoirs,
the output p
o
w
er of casca
de hyd
r
opo
wer
stati
on
can
be represent
ed by
the p
o
w
er flow
and
the
stora
ge capa
city of the rese
rv
oir. Thi
s
is called t
he co
nstraint
of hydropo
wer o
u
tput. The
quad
ratic fun
c
tion of the o
u
tput power o
f
ca
scad
e hydrop
ower
station is a
s
follo
ws:
22
1
,
2,
3
,
4,
5,
6
,
(V
)
C
(
q
)
C
V
q
C
V
Cq
C
tt
t
t
t
t
hi
i
h
i
i
hi
i
h
i
h
i
i
h
i
t
ih
i
i
PC
(3)
Her
e
,
1
,
i2
,
i
3
,
i4
,
i
5
,
i
6
,
i
,,
,,
,
CC
C
C
C
C
are th
e hydro
e
le
ctric conver
sio
n
factors of the cascad
e
hydrop
ower station,
and
t
hi
V
and
t
hi
q
are the re
servoi
r
cap
a
city and power flow in time i
n
terval t,
r
e
spec
tively.
Third, the co
nstrai
nt of powe
r
bala
n
ce is
the requ
ireme
n
t that
at any time,
the total
output po
wer
of all generators in the
s
ystem must equ
al the system
load.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Optim
i
zation of Power S
y
stem
Scheduli
ng Base
d on
SCEM-UA Algorithm
(Zi Yang Qia
ng)
415
11
(t
)
(
t
)
P
(
t
)
MN
sj
hi
L
ji
PP
(4)
Fourth, the
st
orag
e
capa
cit
y
of a hydro
e
l
e
ctri
c p
o
wer
station i
s
det
ermin
ed by t
he initial
cap
a
city, nat
ural inflo
w
a
nd the di
sch
a
rge flo
w
of
the hydro
e
le
ctri
c po
we
r. This i
s
called
the
con
s
trai
nt of water b
a
lan
c
e.
It is
express
ed as
follows
:
1
(t
1
)
V
(
t)
q
(
t)
t
Q
(t)
t
Q
(
t)
t
ii
i
i
i
V
(5)
Fifth, under
norm
a
l circu
m
stan
ce
s, the uppe
r
limit of generato
r
output is t
he rated
output, and
the lowe
r limit is the minimum sta
b
l
e
output. This is called the co
nstraint
of
gene
rato
r out
put.
mi
n
m
a
x
(t
)
(
t)
(t
)
hi
hi
hi
PP
P
(6)
mi
n
m
a
x
(t
)
(
t
)
(t
)
sj
sj
sj
PP
P
(7)
Sixth, the constraint of po
wer fl
ow is exp
r
esse
d as foll
ows.
mi
n
m
a
x
(t
)
(
t
)
(t
)
h
i
hi
hi
QQ
Q
(8)
Seventh, the con
s
trai
nt of
rese
rvoir
stora
ge ca
pa
city is expresse
d a
s
follows.
mi
n
m
a
x
(t
)
(
t
)
(t
)
hi
h
i
hi
VV
V
(9)
Eighth, the co
nstrai
nt of the output cha
n
g
e
of t
hermoel
ectri
c
gen
erators i
s
expressed a
s
follo
ws.
mi
n
max
(t
)
m
ax(P
(t
),
P
(
t
1
)
P
)
(
t
)
P
(
t
1
)
(
t
)
m
i
n
(P
(t
),
P
(
t
1
)
P
)
(
t
)
P
(
t
1
)
dow
n
sj
sj
sj
sj
sj
sj
tu
p
sj
sj
sj
sj
sj
sj
PP
PP
(10)
(t
)
i
V
–wate
r
storag
e of level i
po
wer statio
n in
time inte
rval
t (m
3
);
(t
)
i
q
–the na
tural inflo
w
of level i
po
wer
station
pe
r unit
time
(m
3
/s
);
(t
)
i
Q
–the work flow of level i power stati
on per unit
time (m
3
/s
);
(t
)
L
P
–load p
o
wer
at time t (MW);
max
(t
)
hi
P
,
mi
n
(t
)
hi
P
–the u
p
per a
nd lo
we
r limits of the
output of level i hydroele
c
tric po
wer
stati
on at time t, resp
ectively (MW);
max
m
in
(t
),
(
t
)
sj
sj
PP
–the up
per
and lo
wer li
mits of the output of level i thermoel
e
c
tri
c
po
wer
station at time t, respe
c
tively
(MW
)
;
ma
x
m
i
n
(t
)
,
Q
(
t
)
hi
hi
Q
–the up
per a
nd lo
we
r limits of the
powe
r
flow
o
f
level i hydro
e
lectri
c p
o
we
r
station at time t, respe
c
tively (m
3
/s
);
ma
x
m
i
n
(t),
V
(
t
)
hi
h
i
V
–the upp
er an
d lowe
r limits of the stora
ge
cap
a
city of level i hydroele
c
tri
c
power
station at time t, respe
c
tivel
y
(m
3
);
,
do
w
n
u
p
s
js
j
PP
–the la
rge
s
t
decli
ning an
d
rising
rate of gene
rato
r uni
ts j.
3. SCEM-UA
Algorithm
3.1. Shuffled
Complex Ev
olution Metr
opolis Algori
t
hm
The S
C
EM-UA algo
rithm
was
develop
ed
by Du
an
et a
l
. and first p
u
b
lish
ed in
19
92. With
this alg
o
rithm
,
a larg
e initi
a
l ra
ndom
sa
mple fa
c
ilitates the
explo
r
ation of the
p
a
ram
e
ter
sp
a
c
e,
increa
sing
th
e ch
an
ce
of finding th
e gl
o
bal optim
um
of the p
r
escri
bed d
e
n
s
ity functio
n
. The
use
of a n
u
mbe
r
of pa
rallel
seq
uen
ce
s
with diffe
rent
starting
poi
nts fa
cilitates
an in
depe
nd
ent
exploratio
n of the sea
r
ch space, and ca
n give
the opt
imization p
r
o
b
lem mo
re th
an one
regi
o
n
of
attraction [13
]. In
this way
,
heuristi
c tests can be u
s
ed to dete
r
mine wh
ethe
r the seq
uen
ce
s
conve
r
ge
nce of the sequ
en
ce
s to a limiting dist
ributio
n has b
een a
c
hieve
d
. By using
compl
e
xes,
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ISSN: 16
93-6
930
TELKOM
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Vol. 13, No. 2, June 20
15 : 413 – 42
0
416
the coll
ectio
n
of inform
ation ab
out the
sea
r
ch
spa
c
e gathe
re
d b
y
each
indivi
dual
seq
uen
ce
durin
g the ev
olution proce
ss
can b
e
co
nsoli
dat
ed. T
he sh
uffling o
f
these compl
e
xes en
han
ces
the survivab
ility of the se
que
nces thro
ugh
gl
obal
sh
arin
g
of the
inf
o
rmatio
n g
a
i
ned
indep
ende
ntly by each p
a
rallel
se
que
nce. Thi
s
se
ries
of ope
ra
tions
can p
r
odu
ce a
rob
u
st
colle
ction of MCM
C
sam
p
les ca
pabl
e of facilitat
ing efficient and effective searche
s
of the
para
m
eter sp
ace
[14].
(1) Ge
nerate
sample. Sa
mple s poi
nts
12
,,
,
s
randomly from the prio
r distrib
u
tion
and compute
the posteri
or density
(1)
(
2
)
(
)
(|
,
(
|
)
,
,
(
|
)
s
py
p
y
p
y
of each p
o
int usi
ng equ
ation (2
)
or (3
).
(2) Ran
k
p
o
ints. Sort the s points in
or
de
r of decreasi
ng po
st
erior den
sity and store
them in a
r
ra
y D
1:
,
1
:
1
sn
, whe
r
e
n is the
num
ber
of param
eter
s
,
s
o
that the firs
t row of D
rep
r
e
s
ent
s the point with the high
est po
sterio
r de
nsit
y.
(3) Initialize parall
e
l sequences. Initiali
ze t
he sta
r
tin
g
points of th
e parall
e
l se
q
uen
ce
s,
12
,,
,
,
q
SS
S
su
ch t
hat
k
S
is D
[,
1
:
1
]
kn
, where
1,
2
,
,
kq
. Partition into
complexes. Partition
the s p
o
ints
of D into
q
complexe
s
12
,,
,
,
q
CC
C
e
a
ch
containi
n
g
m
point
s,
such
that th
e
first
compl
e
x co
ntains
eve
r
y
(1
)
1
qj
ra
nked
point, th
e second
co
mplex
co
ntain
s
every
(1
)
2
qj
ra
nked
point of D, an
d so on, where
1,
2
,
,
.
j
m
(4) Evolve each
sequ
en
ce. Evolve each of the parallel seq
uen
ces a
c
cordi
n
g
to the
Sequen
ce Ev
olution Metro
polis al
gorith
m
outlined be
low.
(5) S
huf
f
l
e c
o
mplex
e
s.
U
npa
ck all
co
mplex
e
s
C
b
a
ck into D, ra
nk the poi
nts
in orde
r of
decrea
s
in
g p
o
steri
o
r de
nsity, and resh
uffle the
s points into q compl
e
xes a
c
cordi
ng to the
pro
c
ed
ure sp
ecified in
step
4.
(6) Ch
eck converg
e
n
c
e. Che
c
k
the
G
e
lman and
Rubin
(G
R) co
nverge
nce
statistic. If
conve
r
ge
nce crite
r
ia are sa
tisfied,
stop; otherwise ret
u
rn to ste
p
5.
4. Case Stud
y
In ord
e
r to v
e
rify the fea
s
ibility of the prop
osed al
g
o
rithm, typica
l daily load
d
a
ta of a
certai
n are
a
from July 20,
2012 to Jul
y
31,
2012 are used to analyze the o
p
timal operation
probl
em of the power
system in this
area. Th
e
po
wer
system i
n
this are
a
consi
s
ts of three
thermo
ele
c
tri
c
po
wer pl
ant
s, Pinghai Po
wer Plant, Sh
aoyang Po
we
r Plant, and Xiayong Power
Plant, and three ca
scade h
y
dropo
we
r st
ations. The sche
duling p
e
riod bega
n on
July 20, 2012
and
end
ed
o
n
July 31,
20
12, coverin
g
a total of
12
days. Ea
ch
sche
duling
int
e
rval i
s
o
ne
day.
This
ca
se
st
udy aims to
verify the superi
o
ri
ty of
establi
s
h
e
d
hydrothe
rm
al po
wer
sy
stem
sched
uling
model
ba
sed
on
green
e
c
on
omy in
i
m
provin
g the
overall o
u
tp
ut level of
the
hydroel
ect
r
ic po
wer statio
ns, p
r
om
otin
g con
s
ervati
on of
non
-re
newable
ene
rgy sou
r
ces,
and
improvin
g the
comp
reh
e
n
s
i
v
e econ
omi
c
benefits of
t
he sy
stem. T
he goal i
s
al
so to verify the
effectivene
ss of SCEM-UA
algo
rithm in
solving
l
a
rge-scale g
r
e
en
sche
duling
mo
del with
st
ron
g
nonlinear
characteri
stics. T
able 1
and T
able 2 illust
rate
the reserv
oir
characte
ri
stics coefficient
and the ma
in water ind
i
cators of the ca
sc
ade
hydropo
we
r stations, resp
ectively. The
con
s
um
ption
cha
r
a
c
teri
sti
c
coefficie
n
ts of ther
mal
power pl
ant
units a
r
e
cal
c
ulate
d
by u
s
ing
least
squa
re
s fit based o
n
coal
con
s
u
m
ption data of
power pl
ants
subj
ecte
d to grid
sched
uli
ng in
this area. Th
e ba
sic o
p
e
r
ating pa
rame
ters a
r
e
sho
w
n in T
able
3. Figure 1 shows the n
e
two
r
k
stru
cture of the ca
scade
hy
drop
ower stations.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Optim
i
zation of Power S
y
stem
Scheduli
ng Base
d on
SCEM-UA Algorithm
(Zi Yang Qia
ng)
417
Figure 1. Net
w
ork st
ru
cture of
the cascade hydropo
wer
station
The minim
u
m coal
co
nsumption
co
st of t
he joint
optimal hyd
r
otherm
a
l po
wer
syste
m
sched
uling u
s
ing the two al
gorithm
s can
be dete
r
mine
d by runni
ng t
he SCEM-UA
algorithm
an
d
PSO algorith
m
20 times. Table 4 sh
ows the daily
powe
r
flow of the reservoi
rs (July 20, 2012–
July 31, 201
2) and the re
sults of e
c
on
omically
opti
m
al sched
uli
ng of t
he hydrothe
rmal p
o
we
r
system u
s
ing
SCEM-UA a
l
gorithm an
d PSO algorith
m
. Figure 2
and 3 sh
ow
the total active
power o
u
tpu
t
s of the hydroel
ect
r
ic p
o
we
r sy
stem
, the total active power
outputs of t
he
thermo
ele
c
tri
c
gen
erators, and loa
d
cha
nge
s ov
er the
entire
sch
ed
uling pe
riod
u
s
ing the S
C
E
M
-
UA and PSO algorith
m
s, respe
c
tivel
y
. These re
sults in
dicate that the sum of the daily
hydrop
ower
o
u
tput and
the
r
mal p
o
wer
o
u
tput ca
l
c
ul
ated by SCEM
-UA alg
o
rithm
is e
qual to t
he
total electri
c
ity load, and thus the lo
ad
balan
ci
ng constraint is
well satisfied
.
The operation
sched
uling of
hydrop
ower
plants m
a
inly
involves
adj
usting the
pe
ak loa
d
in o
r
der to mai
n
ta
in a
high-hea
d op
eration of th
e hydr
op
owe
r
plants
so that maximu
m electri
c
ity can b
e
gene
rated
unde
r the sa
me inflow
co
ndition
s. The
optimal
sch
edulin
g of hydrop
ower pl
a
n
ts en
su
re
s the
stable a
nd e
fficient opera
t
ion of therm
oele
c
tric
p
o
wer plant
s. In this way, the use of water
energy resou
r
ce
s du
ring t
he sched
ulin
g perio
d
can
be maximized, and co
al
con
s
umptio
n
o
f
thermal
po
wer pl
ants
ca
n be
re
du
ce
d. Using
the
PSO alg
o
rit
h
m, the
cal
c
ulated total
daily
electri
c
ity ge
nerate
d
can
not bala
n
ce
the total load d
e
man
d
,
and the o
peratio
n of
the
hydroel
ect
r
ic
gene
rato
rs
cannot pl
ay a
n
effective
ro
le in adj
ustin
g
the pe
ak l
oad. Hen
c
e,
the
results a
r
e no
t ideal.
Table 1.Cha
r
acteri
stic
coef
ficients
of cascad
e hydro
p
o
w
er
station
s
8
C
1
C
2
C
3
C
4
C
5
C
6
H
y
dr
oelectric pow
e
r
station 1
-0.0029
-0.31
0.03
1.34
14
-70
H
y
dr
oelectric pow
e
r
station 2
-0.0032
-0.3
0.04
1.14
23
-55
H
y
dr
oelectric pow
e
r
station 3
-0.003
-0.21
0.027
1.44
11.5
-80
Table 2. Main
water en
ergy indicato
rs
of
the ca
scade
hydr
op
ower stations
Table 3. Co
n
s
umptio
n ch
a
r
acte
ri
stic co
efficients of therm
oele
c
tri
c
plants
j
a
j
b
j
c
j
e
j
f
j
j
j
j
j
min
s
j
P
ma
x
s
j
P
Pinghai Pow
e
r
Plant
100
2.45
0.0012
160
0.0038
4.09
-5.56
0.32
2e-4
3.33
50
200
Shao
y
ang
Po
w
e
r
Plant
120
2.32
0.0010
180
0.0027
2.56
-8.62
0.12
e-6
2
70
300
Xiayong Po
w
e
r
Plant
150
2.1
0.0015
200
0.0035
3.76
-6.71
0.34
e-5
6.37
50
200
mi
n
hj
V
(
43
10
m
)
ma
x
hj
V
(
43
10
m
)
in
i
V
(
43
10
m
)
in
i
V
(
43
10
m
)
mi
n
hj
Q
(
3
4
10
m
d
)
ma
x
hj
Q
(
3
4
10
m
d
)
mi
n
hj
P
(MW
)
ma
x
hj
P
(MW
)
H
y
dr
oelectric pow
e
r
station 1
60
120
78
100
0.1
25
0
90
H
y
dr
oelectric pow
e
r
station 2
40
100
50
80
0.1
25
0
80
H
y
dr
oelectric pow
e
r
station 3
30
120
50
100
0.1
40
0
100
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 413 – 42
0
418
Figure 2. Dail
y output and load dem
and
of
hydrothe
rmal plant usi
ng SCEM-UA
Figure 3. Dail
y output and load dem
and
of
hydrothe
rmal plant usi
ng PSO
Table 4. Re
sults of eco
n
o
m
ic sche
dulin
g of
the hydro
t
hermal p
o
we
r system u
s
in
g SCEM-UA
and PSO alg
o
rithm
s
Date
SCEM-U
A
(
MW)
PSO
(MW)
1
h
P
2
h
P
3
h
P
1
s
P
2
s
P
3
s
P
1
h
P
2
h
P
3
h
P
1
s
P
2
s
P
3
s
P
D
P
7.20
34.70
2.89
0.02
153.72
155.83
99.35
147.34
75.59
36.43
145.86
178.27
27.17
446.42
7.21
34.64
5.61
8.16
153.99
158.11
100.67
134.42
0.39
7.57
168.39
143.51
17.05
461.83
7.22
59.36
3.23
0.00
154.17
156.00
105.66
46.90
117.14
6.71
46.93
159.59
8.74
478.20
7.23
66.72
40.91
0.00
150.87
151.68
100.66
69.03
152.60
36.68
19.52
38.75
101.27
509.04
7.24
31.83
55.37
22.99
147.81
148.50
105.67
39.32
197.93
92.46
62.00
166.65
120.20
514.98
7.25
54.21
26.91
21.73
142.88
144.56
109.04
123.12
6.39
121.96
111.43
104.95
54.21
499.43
7.26
43.48
42.27
22.11
137.88
139.62
108.76
39.21
209.77
52.86
183.33
115.97
24.40
494.15
7.27
31.65
73.28
30.76
132.59
136.70
104.86
71.02
94.74
72.81
99.89
63.85
18.48
503.78
7.28
42.23
55.97
51.96
127.53
131.75
103.22
1.45
141.02
26.29
161.88
165.91
26.21
512.67
7.29
58.10
61.27
57.23
122.52
126.81
98.22
34.09
225.47
12.18
158.06
204.85
58.52
524.24
7.30
62.21
92.79
51.40
117.16
121.90
93.08
20.07
177.75
177.56
80.34
92.26
103.88
537.48
7.31
53.33
84.80
45.63
116.70
123.89
88.60
6.73
117.30
98.14
11.07
165.18
192.20
512.89
Table 5. Opti
mal simul
a
tio
n
results u
s
in
g two optimization algo
rith
ms
Algorithm
Minimum
cost (
$
)
Max
i
mum
cost (
$
)
Average
cost (
$
)
CPU time (min)
Load
balancing
constraint
Water balance
constraint
Constraint on
the change of
po
w
e
r ou
tput
SCEM-UA
5795.89
5903.19
5896.72
2
0
0
0
PSO
7728.83
9649.23
8467.65
16
8.94×10
10
0
371.357
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Optim
i
zation of Power S
y
stem
Scheduli
ng Base
d on
SCEM-UA Algorithm
(Zi Yang Qia
ng)
419
To verify the
effectivene
ss an
d sta
b
ili
ty
of SCE-UA algorith
m
and PSO
algorithm,
figure
s
re
ga
rding the o
p
timal simul
a
tio
n
re
sults afte
r run
n
ing th
e
two algo
rith
ms 20 time
s
were
here
com
p
a
r
ed. As sho
w
n in Tabl
e 5, the values
o
f
the objectiv
e
functio
n
wit
h
SCEM-UA
are
$579
5.89, $
5903.1
9
, an
d $58
96.72,
and th
ose
with PSO
are
$77
28.8
3
, $964
9.23,
and
$846
7.65. Th
e obje
c
tive fu
nction
cal
c
ul
a
t
ed usi
ng S
C
E-UA al
gorith
m
is n
o
table
sup
e
rio
r
to th
at
usin
g PSO al
gorithm i
n
mi
nimum valu
e, avera
ge val
ue an
d maxi
mum value. I
n
additio
n
, SCE-
UA com
p
letel
y
satisfies all
con
s
trai
nt co
ndition
s for h
y
droele
c
tri
c
a
nd therm
oele
c
tri
c
gene
rato
rs,
inclu
d
ing
real
-time loa
d
ba
lanci
ng a
nd
storage
ca
pa
ci
ty const
r
aint
s. The re
sult
s
of cal
c
ulatio
n
s
made u
s
in
g
PSO can
not
satisfy the
constraint of
l
oad b
a
lan
c
in
g or th
e con
s
traint
of po
wer
cha
nge.
Figure 4 an
d
5 sho
w
the
cha
nge
s in t
he obje
c
tive
function
with
numbe
r of iteration
s
usin
g the
two
algo
rithm
s
,
whi
c
h
de
scrib
e
the
co
nv
ergen
ce
ch
ara
c
teristics
of th
e two
alg
o
rith
ms
in the o
p
timization
proce
ss. T
he S
C
EM-UA al
go
rithm ca
n co
nverge
and
prod
uce go
o
d
optimizatio
n
results aft
e
r a
small
numbe
r
o
f
iterations,
demon
strating converg
ence
cha
r
a
c
t
e
ri
st
ic
s si
gnif
i
c
ant
l
y
bet
t
e
r than
that of the PSO algorit
hm. In s
o
lving the s
h
ort-term
eco
nomi
c
loa
d
sche
dulin
g
for the hyd
r
ot
herm
a
l po
we
r sy
stem, the
re
sult of the
PSO algo
rith
m
may prem
atu
r
ely fall into a
local mini
mu
m. In this
wa
y, it is impossible to find th
e global
opti
m
al
s
o
lution.
Figure 4. Con
v
ergen
ce
cha
r
acte
ri
stics of PSO algorith
m
Figure 5. Con
v
ergen
ce
cha
r
acte
ri
stics of SCEM-UA al
gorithm
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 413 – 42
0
420
5. Conclusio
n
This
pap
er establi
s
h
e
s an
o
p
timal power
syste
m
sch
edulin
g mod
e
l in
the g
r
een
eco
nomy co
ntext.
This model, while
red
u
ci
ng
produ
ction
co
sts an
d emi
s
sion
s
of ga
seou
s
pollutant
s, im
prove
s
flexibi
lity and resp
onse
s
pee
d
of po
wer sy
stem sche
duli
ng. The
present
work ha
s targeted the sh
ortco
m
ing
s
of the PSO
algorithm with resp
ect to joint powe
r
system
sched
uling, l
a
rge
po
pulati
on si
ze, l
ong
cal
c
ulat
io
n time, and
poo
r global
optimi
z
ation
ca
pabi
lity.
It is here
pro
posed that th
e SCEM-UA
algorith
m
be
use
d
with strong
glo
bal search cap
abil
i
ty
and th
e
strat
egy of
pen
alty function
co
nstrai
nt
p
r
o
c
essing
for so
lution. Th
e p
r
opo
sed
meth
od
can produ
ce a
preci
s
e de
script
ion
of the op
eratio
n
domain
bo
u
ndary
of hyd
r
othe
rmal p
o
w
er
system, and
the scheme f
o
r sh
ort-te
rm
joint sch
e
dul
ing optimization of
powe
r
system can
be
prod
uced effectively in order to ma
ke
rational
u
s
e
of hydropo
we
r re
sou
r
ces
while maximi
zin
g
efficien
cy wit
h
re
sp
ect to
co
sts an
d t
herm
a
l p
o
w
e
r f
uel
s.
Fin
a
ll
y
,
a t
y
pical
ca
se
st
udy
wa
s
evaluated to
verify the pra
c
tica
bility of the sol
u
tion to
the sho
r
t-te
rm optimal joi
n
t scheduli
n
g
of
power
syste
m
usi
ng th
e
SCEM-UA al
gorithm.
Re
su
lts
s
h
ow
th
at th
e
SC
EM-U
A a
l
go
r
i
th
m c
an
conve
r
ge after
a small numbe
r
of
iteration
s
,
rea
c
hin
g
sati
sfa
c
tory optimi
z
ation and
while
meeting all the co
nstraint
s of joint sch
edulin
g of
the hydrothe
rm
al powe
r
sy
stem. In terms of
conve
r
ge
nce
effects, calculatio
n time
, and opt
imi
z
ation, the
SCEM-UA al
gorithm i
s
more
effective than the PSO
algorith
m
. The current
m
e
thod provid
es an effecti
v
e and pra
c
tical
solutio
n
of gri
d
sched
uling
fo
r ene
rgy-sa
ving power g
eneration.
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