TELKOM
NIKA
, Vol. 11, No. 12, Decem
ber 20
13, pp.
7044
~70
5
1
e-ISSN: 2087
-278X
7044
Re
cei
v
ed
Jun
e
29, 2013; Revi
sed Aug
u
st
8, 2013; Accepted Augu
st
20, 2013
Multiple Objective Optimizations for Energy
Management System u
nder Uncertainties
Mian Xing
1
, Ling
Ji*
2
, Baiting Xu
3
1
School of Co
mputer, Mathe
m
atical a
nd Ph
ysic
al Sc
i
ence
s
, North Chin
a Electric Po
w
e
r Univers
i
t
y
Beiji
ng, 10
22
0
6
, Chin
a,
Ph
./F
a
x
: +0
10
-5
19
63
3
45
2
School of Eco
nomics a
nd Ma
nag
ement, Nor
t
h Chin
a Electri
c
Po
w
e
r Un
iver
sit
y
Beiji
ng, 10
22
0
6
, Chin
a, Ph./Fax: +
0
1
0
-51
9
6
367
5
3
Electric Po
w
e
r
Researc
h
Insitute, Guang
don
g Electric Po
w
e
r Grid Corp
or
ation
Guangz
ho
u 51
000
0, Guang
d
ong, Ch
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: xin
g
mi
an1
@
126.com
1
, hdj
ili
ng@
126.com
*
2
, xub
a
itin
g0
401
@12
6
.com
3
A
b
st
r
a
ct
Rece
ntly, micr
o-grid
g
a
ins
more and
more
concer
ns, bec
ause
it is
flexi
b
le
and
e
n
viro
n
m
e
n
tal
l
y
fri
e
n
d
l
y
. Op
tim
i
z
a
ti
on
o
f
the
d
i
strib
u
t
ed
g
e
n
e
r
a
t
o
r
s
o
p
e
r
a
t
i
o
n
in
m
i
cro
-
g
r
i
d
i
s
a
co
mp
l
i
c
a
t
e
d
and
chall
e
n
g
in
g tas
k
, a multi o
b
jec
t
ive opti
m
al
mo
del w
a
s
d
e
si
gn
ed to cut
off the op
erati
on co
st, improv
e th
e
econ
o
m
ic be
n
e
fits and red
u
c
e the emissi
on. How
e
ver,
the rando
mn
ess of the renew
abl
e en
er
gy
gen
eratio
n
and
loa
d
de
ma
nd
mak
e
s th
e d
e
c
i
sion
pr
oc
ess
muc
h
mor
e
co
mp
licat
ed. C
h
a
n
ce c
onstrai
ne
d
progr
a
m
min
g
(CCP) w
a
s e
m
ploy
ed to d
eal
w
i
th these unc
ertainti
es. Besi
des, the satisf
action
degr
ee
of
the d
e
cisi
on w
a
s take
n i
n
to c
onsi
derati
o
n
to
coor
din
a
te
th
e
conflicts
a
m
o
n
g
differ
ent targ
ets. T
h
roug
h th
e
w
e
ighted satisf
action d
egre
e
and co
ordi
nate
degre
e
, t
he multi-o
b
jectiv
e pr
ogra
m
mi
ng ca
n be transfor
m
ed
into sin
g
l
e
-ob
j
ective pro
g
ra
mmi
ng. T
o
ga
in
the so
luti
on o
f
the opti
m
i
z
a
t
i
on pro
b
l
e
m, genetic a
l
g
o
rith
m
w
a
s utili
z
e
d t
o
search for the
opti
m
al strate
gy. T
o
verify the val
i
d
i
ty of the pr
opos
ed
mo
de
l, an e
n
e
r
gy
m
a
nagem
e
nt system
of micro-grid with five types
distributed gener
ators was
taken as the case study.
T
he results in
di
cate the effe
cti
v
eness of the p
r
opos
ed
meth
o
d
.
Ke
y
w
ords
:
mi
cro-grid, e
nerg
y
man
a
g
e
m
en
t, uncertainty,
chance co
nstrain
ed pro
g
ra
mmi
ng, multip
l
e
obj
ective
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Due to
the la
ck of the tradi
tional en
ergy
re
sou
r
ce, the
up-trend
of e
nergy
pri
c
e
a
nd the
publi
c
con
c
e
r
ning
on
so
cial e
n
viron
m
ent, the e
l
ectri
c
p
o
wer system
faces
signifi
can
t
transfo
rmatio
n from the convention
a
l h
i
era
r
chical
structure to the
innovativ
e flat stru
cture. I
n
the former, concentrate
d large p
o
wer stations
(li
k
e therm
a
l po
we
r, hydroel
ectric and n
u
cl
e
a
r
power) are t
he main
forms. And the
total numb
e
r
of the
s
e la
rge p
o
wer
st
ations i
s
sm
all,
therefo
r
e, ele
c
tri
c
ity power is eve
n
tuall
y
tr
ansporte
d
to the en
d
use
r
tho
ugh
long-dista
n
ce
transmissio
n netwo
rk a
nd large
-
a
r
ea di
stribution net
wo
rk
. While mic
r
o-grid is
the typic
a
l form of
the
latter, wh
ich mainly co
nsi
s
t
of
di
stri
buted
gen
era
t
ors, i
n
cl
udin
g
wi
nd tu
rbin
e (WT
)
, ph
ot
o
voltaic (PV),
diesel
engi
ne (DE), mi
cro tu
rbi
nes (MT)
and f
uel cell (F
C) [1]. The future
developm
ent
of distributi
on ene
rgy gains mo
re
a
nd more
co
nce
r
n, incl
ud
ing the relati
ve
techn
o
logy of
micro-grid, t
he forecastin
g of
the
re
ne
wabl
e en
ergy, t
he problem
s of di
stri
bute
d
gene
ration
conne
cting
ele
c
tri
c
g
r
id, the
evaluatio
n of
the mi
cro-gri
d
op
eratio
n a
nd
so
on. T
h
e
operator and
manag
er would
utili
ze prop
er
ene
rg
y manage
me
nt tools to
coordi
nate th
e
distrib
u
ted en
ergy,
tra
n
sfo
r
mer su
bstatio
n
s and
en
erg
y
storage
sy
stem for the
b
o
th pu
rpo
s
e
s
of econ
omy and enviro
n
me
ntal friendly.
Schola
r
s h
o
m
e a
nd
abro
ad h
a
ve d
one
abu
nda
nt re
sea
r
ch
on th
e
ene
rgy m
a
n
ageme
n
t
of micro gri
d
from several
different poi
nts of view,
whi
c
h
can
b
e
divided int
o
mid-l
ong te
rm
prog
ram
m
ing
and sh
ort term prog
ram
m
ing acco
rd
i
ng to planni
n
g
hori
z
on. From the form
er
perspe
c
tive,
the dete
r
min
a
tion of l
o
ca
tion an
d
cap
a
city an
d th
e expa
nd
progra
mming
of
distrib
u
ted ge
neratio
n in the micro grid.
In [2
], a modified teachi
ng-learni
ng ba
e
d
optimizatio
n
algorith
m
is p
r
opo
se
d to determin
e
the optimal pl
a
c
e
m
ent and
size of DG units. As to the later,
history lite
r
at
ure
studie
d
th
e po
wer
opti
m
ization
of
e
a
ch type
of di
stribute
d
ge
n
e
ration i
n
mi
cro
-
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Multiple Obje
ctive O
p
tim
i
zations for En
erg
y
Man
age
m
ent System
unde
r… (Mi
a
n Xing)
7045
grid to th
e ai
m of cutting t
he cost, imp
r
oving the
reli
ability and mi
nimum the
e
m
issi
on
s. Pa
per
[3] propo
se
s Signaled P
a
rtical S
w
a
r
m Optimization to ad
dre
ss th
e en
ergy resou
r
ce
s
manag
eme
n
t problem
con
s
ide
r
ing
sto
r
a
ge d
e
vice
s.
Most
of the
s
e research
es have ta
ke
n t
h
e
energy ma
na
gement
of mi
cro
-
g
r
id
a
s
a
determi
na
cy
i
s
sue. Study
d
ealing
with
th
e un
ce
rtaintie
s
in the
ene
rgy
mana
gem
en
t system
is n
o
t that mu
c
h
.
Paper [4] pres
ents
a
robus
t
optimiz
a
tion
method to d
e
termin
e the
optimum ca
pacity of DG
in the face
of unce
r
tain
energy dema
nd.
Ho
wever,
in
fact
due
to
the i
n
trin
sic intermitten
cy and
un
ce
rtainty of wi
n
d
po
we
r
an
d
photovoltai
c
power a
nd th
e ran
dom
ne
ss in the
dem
a
nd si
de, the
strategy got from dete
r
mina
te
model m
a
y b
e
not o
p
timu
m, even o
u
t of the op
er
ati
on limits. T
h
e
s
e
uncertai
n
ties
have a
great
impact o
n
the
deci
s
ion m
a
king p
r
og
re
ss and ma
ke it
more
com
p
licated, thus it is ne
ce
ssary to
c
o
ns
ider them in the model.
To d
eal
with t
he u
n
certainti
e
s
of
wind
po
we
r,
ph
otovol
taic p
o
wer an
d de
mand
sid
e
, this
pape
r tri
e
s to
find the
o
p
timal
strategy
to co
or
dinate
the storage
and
t
r
an
sform of el
ect
r
ici
t
y
power
with th
e po
we
r de
m
and fo
r the
combine
d
b
e
n
e
fits of op
era
t
ion co
st, e
c
o
nomic be
nefits
and envi
r
onm
ent pollution.
The chan
ce
constraine
d progra
mming i
s
employed to
deal with th
e
uncertaintie
s
and
fin
d
the
optimal soluti
on.
Be
side
s,
the satisfa
c
tion of
de
ci
sio
n
ma
ke
rs i
s
a
l
so
taken into
co
nsid
eratio
n for the multiple
obje
c
tive pro
b
lems.
2.
Proposed Dy
namic
O
v
er
modulation Metho
d
Most un
ce
rta
i
nties can b
e
simulate
d b
y
proba
bilisti
c metho
d
like pro
bability den
sity
function,
who
s
e p
a
ra
meters can e
s
tima
ted thoug
h hi
story data
an
d the an
alysi
s
of sy
stem'
s
future develo
p
ment. Stoch
a
stic p
r
og
ra
mming,
fuzzy prog
rammin
g
, dynamic p
r
og
rammi
ng an
d
robu
st o
p
timization
are th
e main m
e
th
ods to
han
dl
e the un
ce
rta
i
nties [5
-10].
So far, chan
ce
con
s
trai
nts
prog
ram
m
ing
ha
s b
een
appli
ed in
seve
ral
aspect
s
in
el
ectri
c
ity sy
ste
m
su
ccessfully. The
mathe
m
atical
mod
e
l of
cha
n
ce
co
nst
r
aints
prog
ram
m
ing
via p
r
oba
bili
stic
method is d
e
s
cribe
d
as foll
owin
g:
_
_
mi
n
..
P
r
{
(
,
)
}
Pr
{
(
,
)
0
}
i
f
st
f
x
f
gx
(1)
Whe
r
e,
x
and
are
the
de
cision ve
ctor
an
d ra
ndo
m vector respe
c
tively;
(,
)
f
x
is the
obj
ect
function;
(,
)
i
g
x
is the ra
ndom
constraint fun
c
tion;
Pr
{
}
is the probability of events;
and
are the confi
den
ce level of con
s
traint
condi
tio
n
and the obje
c
t function, which a
r
e set in
advan
ce;
f
is the minimum
value of obje
c
t function u
n
der the
confid
ence level at
.
To find
the
solutio
n
of
this
ch
an
ce
con
s
trai
nt p
r
ogra
mming,
geneti
c
al
gorithm is
introdu
ce
d h
e
re. In geneti
c
algo
rithm, the fitnes
s rul
e
s of biologi
cal evolution a
nd inform
atio
n
excha
nge me
cha
n
ism
of chrom
o
some
s in
pop
ulatio
n
are
co
mbine
d
togethe
r to
search fo
r the
bes
t solution in c
o
mplic
a
ted s
p
ac
e. Its
s
pecifi
c
step
s
are de
scri
bed
as followi
ng:
1) Initiali
zatio
n
. The
num
b
e
r of
chro
mo
some
s,
crossover p
r
o
babil
i
ty and mut
a
tion p
r
ob
abilit
y
are the inp
u
t para
m
eters in
genetic al
gorithm.
Initial in
dividual are g
enerated ran
domly.
2) Ca
rry out
the simulatio
n
for ea
ch chrom
o
so
me i
n
the popul
ation, and test
if it meets the
cha
n
ce con
s
traint
conditio
n
. If satisfied,
enter
i
n
to th
e next step,
o
t
herwi
se,
ne
w ge
neration
will be ge
nerated thoug
h mutation ope
ration, and thi
s
step
will be
repe
ated.
3) Sel
e
ct th
e
ch
rom
o
som
e
s m
e
t with
the
cha
n
ce
co
nstrai
nt condi
tion, and
calculate its obj
e
c
t
function valu
e.
4) Ch
oo
se th
e elites from t
he pop
ulation
.
5) Cond
uct th
e mutation o
p
e
ration
and
crossove
r o
peration amo
ng t
hese elite
s
, a
s
a result, we
obtain a ne
w
gene
ration.
6) Continue
above op
erat
ion until the
maximum nu
mber of itera
t
ions, othe
rwi
s
e, we
sh
oul
d
repe
at the ste
p
s from 2 to 4
.
7) The b
e
st chrom
o
some
s found in the
whol
e pro
c
e
s
s are th
e optimal strate
gie
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 12, Dece
mb
er 201
3: 704
4 – 7051
7046
2.1. The des
c
ription of o
b
ject fu
nctio
n
The o
peration ma
nage
ment of mi
cro
-
g
r
id
sh
o
u
ld me
et b
o
th econo
m
y
and
environ
menta
l
protectio
n
targets [11
-
1
3
], in other
wo
rd
s, we sh
ould
minimize the operation cost
as
well
a
s
t
he g
a
s emi
s
sion
s. It is
obviou
s
ly th
at the mi
cro
grid
en
ergy mana
gem
e
n
t
optimizatio
n i
s
a m
u
lti-o
b
je
ctive problem
, includi
ng th
e fuel
co
st of di
stri
buted g
enerators,
th
e
start an
d stop
cost of units
and the
pu
rchasi
ng cost from main g
r
id.
CO
2
, SO
2
and NO
2
are the
main emi
s
sio
n
, while th
e
cost of
wind tu
rbine
and
ph
otovoltaic p
o
w
er is
relativ
e
low, a
nd th
eir
emission
is
n
early
zero. So in thi
s
pa
p
e
r,
we only
consi
der the g
eneration
co
st and emi
s
sio
n
co
st of MT, FC and
DE.
1. The obje
c
t of minimum o
peratio
n co
st
Con
s
id
erin
g the fuel co
st, the sta
r
t and stop
co
st of un
its and the p
u
rch
a
si
ng
cost
from
main gri
d
, the obje
c
tive
function tri
e
s to opt
imi
z
e the output
powe
r
of e
a
ch di
stri
but
ed
gene
rato
r an
d the storage
batterie
s
, aim
i
ng at
the minimizing the to
tal operatio
n co
st.
1,
,
,
=
1
=1
=1
=
1
,,
,,
,
=
1
=1
=1
mi
n
=
+
+
+
++
P
r
GE
F
C
MT
mm
m
T
D
E
it
F
C
i
t
M
T
it
t
iii
TI
T
s
hut
i
t
st
art
i
t
u
t
t
ti
t
fC
C
C
Cos
t
Cos
t
P
i
c
e
(2)
(1) Die
s
el
ge
nerato
r
The fuel co
st
of diesel g
e
n
e
rato
r at time t is usually e
x
presse
d as:
2
()
()
()
tt
t
DE
Gi
G
i
Gi
CP
a
P
b
P
c
(3)
Whe
r
e,
t
Gi
P
is th
e output
power of the
Gi
th
diesel ge
nera
t
or at time
t;
a, b an
d c
are co
nsta
nts
determi
ned b
y
the type of
diesel gene
ra
to
r, here a
=
0.
0547, b
=
1.73
62, c=3.245
6.
(2) F
uel cell
Duri
ng the no
rmal op
eratio
n of fuel cell, t
he relation
sh
ip betwe
en fu
el con
s
um
ption an
d
the output po
wer
can b
e
d
e
scrib
ed a
s
:
=1
()
=
c
t
t
t
F
Ci
FC
FC
i
f
u
e
l
t
F
Ci
P
CP
L
(4)
Whe
r
e,
F
C
C
is the fuel ope
rati
on cost;
t
FC
i
P
is the output po
wer of fuel
cell;
c
f
uel
is the p
r
ice of
the ga
s fu
el,
set a
s
3.58
￥
/m
3
;
L
is th
e lo
w h
eating
val
ue of
ga
s,
FCi
is
the utilization efficient
of fuel, here
FCi
L
=
8
.1.
(3) Mi
cr
o ga
s turbine
=1
()
=
c
t
t
t
MT
i
MT
M
T
i
gas
t
M
Ti
f
P
CP
L
HV
(5)
Whe
r
e,
M
T
C
is the natural ga
s operatio
n co
st;
t
M
Ti
P
is the output powe
r
of the MTi
th
micro gas
turbine at time
t
;
c
g
as
is the price of natural gas, 2.05
￥
/m
3
;
M
Ti
is the efficiency of the MTi
th
micro ga
s turbine,
f
L
HV
is the lowe
r cal
o
rifi
c value,
M
Ti
f
LH
V
=7.
6
.
(4) Start an
d stop cost
,i
,
-
1
,
ma
x
(
0
,
U
-
U
)
s
hu
t
i
t
i
t
Co
s
t
(6)
sta
r
t,i
,
-
1
,
ma
x
(
0
,
U
-
U
)
it
i
t
Cos
t
(7)
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ctive O
p
tim
i
zations for En
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Man
age
m
ent System
unde
r… (Mi
a
n Xing)
7047
Whe
r
e,
,
U
it
is th
e state va
ria
b
l
e of the i
th
u
n
it at time t, 0 mea
n
s the
unit ha
s b
een
sh
ut do
wn,
and 1 mea
n
s
the unit is at runnin
g
statu
s
.
2. The obje
c
t of minimum e
m
issi
on
2
1
2,
,
2
2
,
,
3
2,
,
1
12
,
,
2
2
,
,
3
2
,
,
mi
n
(
+
)
+
TI
it
it
i
t
ti
Ut
Ut
i
t
f
p
CO
p
S
O
p
NO
pC
O
p
S
O
p
N
O
(8)
Whe
r
e,
2,
,
it
CO
,
2,
,
it
SO
and
2,
,
it
NO
are the variou
s emissio
n
of unit i at
time t.
2,
,
Ut
CO
,
2,
,
Ut
SO
,
2,
,
it
NO
are the emi
s
sion of main
grid at time t.
p
1
=
0
.023, p
2
=7, p
3
=9.
3. Multiple target tran
sform
a
tion
To deal with
the multi objective optimi
z
ati
on p
r
obl
e
m
, it is usual
ly transforme
d
into
singl
e obje
c
ti
ve optimizati
on problem.
The maximu
m value
ma
x
k
f
and
minimum val
ue
mi
n
k
f
of
each individu
al goal ca
n be optimal calcul
ated.
Ho
wever, there
are som
e
conflicts am
on
g
them,
and here we em
ploy
wei
ghti
ng
techniq
u
e
com
b
inin
g
with di
stan
ce fun
c
tion.
By
combi
n
ing th
e wei
ghted
sum of satisfa
c
tion d
egree (WSSD)
with coo
r
din
a
tion degree (CD), the
optimal functi
on ca
n be tra
n
sformed into
:
=1
K
kk
k
k
WSSD
s
A
D
S
D
(9)
Whe
r
e,
k
SD
indicates the satisfaction de
gre
e
to the k
th
goal.
mi
n
max
mi
n
m
ax
max
m
i
n
max
1
-
=
-
0
kk
kk
kk
k
k
kk
kk
ff
ff
SD
f
f
f
ff
ff
(10
)
Table 1. The
Satisfaction
Deg
r
ee
Satisfaction Degree
Not Satisf
y
i
ng
Little Sa
tisfy
i
ng
Satisfy
i
ng
Very
Satisf
y
i
ng
SD
k
[0, 0.5)
[0.5, 0.75)
[0.75, 1)
1
Considering
k
SD
sho
u
ld arriv
e
at its mini
mum value
*
k
SD
at least, there will be an
addition
al co
nstrai
nt con
d
i
t
ion:
*
kk
SD
S
D
(11
)
**
1
/
K
kk
k
k
A
DS
D
S
D
(12
)
*
*
0
1
kk
k
kk
i
f
SD
SD
s
f
SD
SD
≥
(13
)
K-dimension Euclidean
di
stanc
e
will be utilized to
coordi
nate the relationshi
p
among
each single goal, the coordination degree
(CD)
will be calculated as follows:
12
CD
d
d
(14
)
Whe
r
e,
2
max
=1
1
2
mi
n
=1
-
=
-
K
kk
k
K
kk
k
f
f
f
o
r
M
I
N
o
bj
e
c
t
f
un
c
t
i
o
n
d
f
f
f
or
M
A
X
o
bj
e
c
t
f
unct
i
o
n
,
2
ma
x
m
i
n
2
=1
=-
K
kk
k
df
f
.
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4 – 7051
7048
2.2. The Des
c
ription of
Constr
aint Co
ndition
The main
con
s
traint
conditi
ons a
r
e de
scribed an
d anal
yzed a
s
follo
wing:
1. Load bal
an
ce
,,
,
,
,
,
TS
i
t
i
t
jt
jt
u
t
D
t
ij
PU
P
U
P
P
(15
)
Whe
r
e,
,
D
t
P
is the total a
c
tu
al load
dema
nd un
der the
micro g
r
id a
t
time t;
is t
he loa
d
p
u
r
c
h
as
ed
fr
om ma
in
gr
id
, if
,
>0
ut
P
, that means power lo
ad i
s
pu
rcha
sed f
r
om mai
n
gri
d
, while,
if
,
<0
ut
P
, that indica
tes micro g
r
id
sell the ele
c
tricity to the main grid.
2. The limits of distribute
d
gene
rato
rs
mi
n
m
a
x
,
ii
t
i
PP
P
(16
)
Whe
r
e,
min
i
P
and
ma
x
i
P
are the lo
we
r and up
per lim
its of the ith unit resp
ectivel
y
.
3. The tran
smissi
on po
we
r limit betwee
n
main gri
d
a
nd micro gri
d
mi
n
m
a
x
tt
t
PP
P
(17
)
4. Energy sto
r
age d
e
vice
s
As adva
n
ced
ene
rgy
stora
ge d
e
vice
em
erge, th
e e
n
e
r
gy sto
r
a
ge
d
e
vice i
s
playing a
n
increa
singly i
m
porta
nt role
in power
system. It c
an be
used to
store
the elect
r
icit
y powe
r
, whe
n
the ele
c
tri
c
ity pri
c
e
is lo
w,
instea
d, it
ca
n di
scha
rge
the p
o
wer wh
en the
p
r
ice i
s
hi
gh, to
gai
n
more e
c
o
n
o
m
ic ben
efits. At curre
nt, stor
ag
e ba
ttery, Flywheel energy storag
e (FES),
sup
e
rcon
du
cting en
ergy
storage
and
sup
e
r
ca
paci
t
or are the
popul
ar late
-model
ene
rg
y
stora
g
e
tech
nologi
es. In
t
h
is
pap
er,
we di
scu
ss th
e mo
st
com
m
only a
pplie
d batte
ry en
ergy
stora
ge, and t
he rule
s of ch
arge
-di
s
cha
r
g
e
are exp
r
e
s
sed as follo
win
g
:
,,
1
a
r
g
,
a
r
g
,
,
arg
,
,
ar
g
,
1
j
t
j
t
c
h
ej
c
h
ej
t
di
s
c
h
e
j
t
di
s
c
h
e
j
Pt
Pt
(18
)
mi
n
m
a
x
,
jj
t
j
(19
)
ma
x
ar
g
,
,
a
r
g
,
ch
e
j
t
c
h
e
j
PP
(20
)
max
arg
,
,
a
rg
,
disc
h
e
j
t
disc
h
e
j
PP
(21
)
Whe
r
e,
,
j
t
is th
e sto
r
ag
e
cap
a
city of the jt
h battery
at time t;
ar
g
,
,
ch
e
j
t
P
an
d
arg
,
,
disc
h
e
j
t
P
are th
e
cha
r
ge
rate
and di
scharg
e
rate of the
jth battery after
t
;
ar
g
,
ch
e
j
and
ar
g
,
disc
h
e
j
are the
cha
r
ge
efficie
n
cy an
d di
scharg
e
effici
en
cy of the jth
b
a
ttery;
mi
n
j
and
ma
x
j
are the lower limit
and
upp
er limit of the jth
battery;
max
arg
,
ch
e
j
P
an
d
max
arg
,
di
s
c
h
e
j
P
are
the m
a
ximum cha
r
ge rate an
d
discha
rge
rat
e
of the jth battery duri
n
g
t
. These p
a
ram
e
ters are set as:
arg
,
ch
e
j
=8
0%
;
ar
g
,
disc
h
e
j
=85%;
mi
n
j
=240
kW;
ma
x
j
=
1
20
0k
W
;
max
arg
,
ch
e
j
P
=350;
max
arg
,
di
s
c
h
e
j
P
=450.
,
ut
P
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p
tim
i
zations for En
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Man
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m
ent System
unde
r… (Mi
a
n Xing)
7049
2.3. The Unc
e
rtain
t
ies in the Tar
g
et P
o
w
e
r Sy
stem
1. Wind po
we
r
Suppo
se
()
w
Pv
as the outp
u
t p
o
we
r of
wind
turbin
e ge
ne
ration, its
rel
a
tionship
with
wind
spe
ed can be expressed a
s
:
0
()
CF
kk
c
wR
C
R
kk
Rc
RR
F
vv
o
r
v
v
vv
Pv
P
v
v
v
vv
Pv
v
v
(22
)
Whe
r
e,
R
P
is the nominal po
wer of wi
nd tu
rbin
e gen
erator, here set
as 30kW;
C
v
,
F
v
and
R
v
is
the c
u
t-in wind s
p
eed, cut-out wind
s
p
eed
and
rated
wind
s
p
eed, and set as
3m/s
, 25m/s
and
11m/s
re
spe
c
tively. Accord
ing to pa
st st
udie
s
, the probability den
sity function
of wind
sp
ee
d
follows Weibull distri
bution
-1
-(
/
)
()
=
k
k
vc
kv
ve
cc
, where, the
k
is
Wei
bull
sha
pe p
a
ra
m
e
ter [14],
usu
a
lly falls i
n
[1.8,2.8], and c i
s
the
scale pa
ra
mete
r, in this p
a
p
e
r we set the
m
as 2
and 6
.
5
r
e
spec
tively.
2. Photovoltaic po
wer
Solar
cell is t
he found
ation
and kernel of
photovoltaic
power g
ene
ra
tion system,
who
s
e
output po
wer is clo
s
ely related to lig
ht intens
ity. Su
ffe
r
i
n
g
th
e s
t
r
o
ng
r
a
ndo
mn
es
s
o
f
lig
h
t
intensity, the output powe
r
is also u
n
certain.
According to statistics, duri
ng a
certain pe
rio
d
(one
o
r
several hou
rs) th
e
sun'
s
ray
can
be
reg
a
rd
ed
as Beta
di
stri
bution
app
rox
i
matively, and
its probability density f
unction is described as:
1-
AC
PV
S
T
C
c
t
ST
C
G
P
Pk
T
T
G
(23
)
Whe
r
e,
STC
P
is the maximum
test powe
r
under
stan
dard te
st co
ndition(su
nlig
ht incident
intensity a
s
1
000
W/m
2
, the enviro
n
me
ntal tempe
r
a
t
ure a
s
25
℃
);
A
C
G
is the ill
umination
intensity;
STC
G
is
the illumin
a
tion inte
nsity
unde
r ST
C,
as
100
0W/m
2
,
k
is th
e tem
peratu
r
e
power
coeffi
cient, he
re
set as -0.004
7;
c
T
is the p
anel'
s
workin
g tempe
r
ature;
t
T
is the
referen
c
e te
mperature, 2
5
℃
.
3. Cas
e
Stud
y
In this pap
er,
we si
mulate
a micro gri
d
i
n
clu
d
ing five
types dist
ribu
ted gene
rato
rs, wind
turbine, p
hot
ovoltaic p
o
we
r, fuel cell, diesel
po
wer
a
nd micro
ga
s machi
ne. Th
e upp
er limit
of
physi
cal tra
n
s
missio
n cap
a
city betwee
n
micro g
r
id
and mai
n
gri
d
is 30
kW. T
he time interv
al is
set at 1
ho
ur, whi
c
h me
a
n
s 2
4
p
e
rio
d
s
a
day. The
power l
oad
is
subje
c
ted
to the unifo
rm
distrib
u
tion
with the foreca
sting value a
s
me
a
n
valu
e and 0.1
a
s
the varian
ce.
The output
of
wind
po
wer a
nd ph
otovolta
ic po
we
r i
s
o
beyed to
th
e uniform dist
ri
bution with
±10%
deviatio
n
.
The emi
ssi
on
cost of different gene
rato
r units is liste
d
in Table 2.
Table 2. Emission of Different Gene
rato
r Unit
Gas
CO
2
SO
2
NO
x
External cost discount (
￥
/kg)
0.023
7
9
Fuel cell (kg/MWh)
489
0.0027
0.014
Micro gas turbine
(kg/MWh)
724
0.0036
0.2
Diesel generator
(kg/MWh)
649
0.206
9.89
Main Grid (kg/M
W
h)
1230
0.42
2.35
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e-ISSN: 2
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TELKOM
NIKA
Vol. 11, No
. 12, Dece
mb
er 201
3: 704
4 – 7051
7050
Figure 1 illustrates the 2
4
hour d
a
ily load de
mand
of micro
-
g
r
i
d
. The outpu
t powe
r
of wi
nd
turbine
an
d p
hotovoltaic p
o
we
r i
s
d
e
scribed i
n
Fig
u
re 2.The
confi
den
ce i
n
terva
l
value i
s
set
at
0.9, and the
singl
e obj
ective prog
ram
m
ing an
d m
u
lti obje
c
tive prog
ram
m
in
g are
discu
s
se
d
r
e
spec
tively.
Figure1. 24 h
our daily loa
d
curve of micro-g
r
id
Figure2. The
output po
wer
of wind turbi
n
e
and ph
otovoltaic po
we
r
4. Resul
t
s
Anal
y
s
is
The results f
r
om
singl
e-objective and mult
i-obj
ecti
ve optimizati
on are illustrated in
Table
3
re
sp
ectively. It's o
b
viously th
at
the results
go
t from th
e m
u
lti-obje
c
tive o
p
timization
lie
betwe
en the
corre
s
po
ndi
ng minimum
and maxi
mum value
from the singl
e-o
b
je
ctive
optimizatio
n. Only con
s
id
e
r
ing the ge
ne
ration cost, th
e minmum va
lue is 63
48.1
2
￥
; as to only
con
s
id
erin
g e
m
issi
on, the minmum vule
is 130.58
￥
.
The optimal g
eneration cost obtained fro
m
multi-obj
ectiv
e
is 68
54.28
￥
, whi
c
h i
s
7.97% hig
h
e
r
than th
e mi
nimum val
u
e
und
er
sin
g
l
e
-
obje
c
tive pro
g
rammi
ng. While, the optimal emissi
on
value got from multi-obje
c
tive is 142.63
￥
,
whi
c
h is
9.2
4
% highe
r than the mi
ni
mum value
unde
r si
ngle
-
obje
c
tive pro
g
rammi
ng. T
he
optimizatio
n
and
co
ordi
na
tion of the th
ree
obj
e
c
tive
s
simultan
eo
usly ma
ke
al
l the SD
s
well
sat
i
s
fi
e
d
, whi
c
h mea
n
s tha
t
all the objectives excee
d
their setting value
s
of SD
s
.
Table 3. Co
m
pari
s
ion b
e
tween Single a
n
d
Multi-obj
ect
i
ve Optimizati
on Re
sult
s
O
b
jectives
Single-objective
Multi-objective
Min Max
Optimum
SD
s
Gene
ration
Cost(
￥
)
6348.12
7105.62
6854.28
0.6987
Emission(
￥
)
130.58
151.24
142.65
0.5214
WSSD.CD
-
-
0.4356
-
Table 4. Co
m
pari
s
ion a
m
o
ng Differe
nt Confid
en
ce Interval
Confidence inter
v
al value
Gene
ration cost(
￥
)
Emission(
￥
)
WSSD.CD
0.80 6671.35
140.21
0.4251
0.85 6725.20
143.56
0.4298
0.90 6854.28
142.65
0.4356
0.95 6935.12
144.25
0.4510
Beside
s, the
impact
s
of
di
fferent con
fi
d
ence inte
rval
value
s
a
r
e
also
analy
z
e
d
he
re.
Acco
rdi
ng to
Table
4. Th
e
confid
ential v
a
lue i
s
set to
be 0.8
0
, 0.85
, 0.90 a
nd
0.95 respe
c
tively,
and
the gen
e
r
ated solutioi
ns can be
u
s
ed
for
va
riou
s deci
s
io
n opti
ons th
at are
asso
ciated
wi
th
different leve
ls of
risks. It can
be fo
u
nd that the
gene
ration
cost, the e
m
i
ssi
on a
nd th
e
WSSD.CD value ch
ang
e
a little under different co
n
fi
d
e
n
c
e inte
rval values. The high
er the
confid
en
ce in
terval value is, both the gen
erat
ion
co
st and emissio
n
cost will be g
r
e
a
ter.
40
60
80
100
120
1
5
9
13
17
21
h
MW
0
150
300
450
600
750
15
9
1
3
1
7
2
1
w
i
nd turbine
photovoltaic pow
er
kW
h
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Multiple Obje
ctive O
p
tim
i
zations for En
erg
y
Man
age
m
ent System
unde
r… (Mi
a
n Xing)
7051
5. Conclu
sion
In this pape
r,
a multi-obje
c
tive optimiz
ation model
has b
een d
e
v
eloped to coordi
nate
the econo
mi
c an
d e
n
vironmental
problem
s
in
micro g
r
id
energy man
ageme
n
t. The
uncertaintie
s
brou
ght by the rene
wa
ble
ener
gy gene
ration and po
wer d
e
ma
nd are ha
ndle
d
by
cha
n
ce co
nst
r
aint program
ming. The satisfacti
o
n
deg
ree and
coo
r
di
nation de
gre
e
is introdu
ce
d
with the
con
s
ide
r
ation
of
deci
s
io
n ma
kers'
requi
rem
ent. The
sim
u
lation
re
sult
s in
dicate th
e
model i
s
effi
cient
and via
b
le. Thi
s
mo
del p
r
op
os
ed
in this pa
pe
r can
provid
e the d
e
ci
sio
n
make
rs the optimal strateg
y
within feasi
b
le
solutio
n
s.
Howeve
r, the combi
ned h
eat and po
we
r
gene
ration i
s
not consi
dered here. The
genetic
alg
o
r
ithm may be not the best and faste
s
t
method to se
arch for the b
e
st sol
u
tion, and it can b
e
improve
d
in the future.
Ackn
o
w
l
e
dg
ment
This
work wa
s su
ppo
rted i
n
part by NS
FC un
der
Grant No
s. 710
7105
2 and G
r
ant Nos.
7120
1057,
a
s
well
as “th
e
Fu
ndam
ent
al Research
Fund
s fo
r th
e Central
Uni
v
ersitie
s
” un
d
e
r
Grant No
s.
12QX23.
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