TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 16, No. 3, Dece
mbe
r
2
015, pp. 401
~ 408
DOI: 10.115
9
1
/telkomni
ka.
v
16i3.906
7
401
Re
cei
v
ed Se
ptem
ber 3, 2015; Re
vi
sed
Octob
e
r 18, 2
015; Accepte
d
No
vem
ber
5, 2015
Optimized Operation-Planning of a Microgrid with
Renewable Sources an
d Vehicle to Grid
Asad
Waq
a
r
*
, Shaorong
Wang, Qa
sim Kamil Mohsin, Muhammad Zahid
State Ke
y
L
a
b
o
rator
y
of Adva
nced El
ec
trom
agn
etic Eng
i
ne
erin
g and T
e
ch
nol
og
y,
Huaz
hon
g Un
i
v
ersit
y
of Sci
e
n
c
e and T
e
chno
log
y
, W
uha
n, Hub
e
i, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:asad
w
a
q
a
r@
hust.edu.c
n
A
b
st
r
a
ct
T
he microgr
id
w
i
th renew
ab
le so
urces p
o
ssesses stab
ili
ty issues. Duri
ng the
grid-c
o
nnecte
d
mo
de, th
ese
i
ssues
are tak
en c
a
re
by th
e exter
nal
gr
id. H
o
we
ve
r
i
n
ca
se
o
f
i
s
la
nd
in
g
,
th
e d
i
stribu
ted
gen
erators w
i
t
h
in th
e
micr
og
rid, hav
e to ta
ke care
of the
s
e issu
es i
n
d
e
pen
de
ntly. It needs
ad
ditio
n
a
l
backu
p lik
e die
s
el ge
ner
ation
or battery stor
age, w
h
ic
h i
n
c
r
eases the
ove
r
all ca
pital
and
operati
on cost
s.
W
i
th the
interv
entio
n
of the
V
2
G storag
e, th
ese c
o
sts
ca
n
be s
a
ve
d to
so
me
exte
nt. Ho
w
e
ver si
mi
lar t
o
t
h
e
renew
ab
le so
u
r
ces like w
i
nd
and sol
a
r, the pow
er fr
om V2G is also
fluctuatin
g w
h
i
c
h may lea
d
th
e
micr
ogri
d
tow
a
rds an
unec
on
omical
op
erati
on. T
heref
or
e
an exte
nsive
o
perati
on-p
l
a
nni
ng is n
e
e
d
e
d
to
dea
l w
i
th thes
eunc
ertainti
es,
for the
micr
o
g
rid to
be
ec
o
n
o
m
ic
ally v
i
ab
l
e
. In this co
ntext, the stoch
a
stic
progr
a
m
min
g
has
be
en
ap
pli
ed to
ac
hiev
et
he
opti
m
u
m
re
sults. T
he st
oc
hastic sc
en
ario
s for w
i
nd
sp
e
ed,
solar r
adi
atio
n, V2G pow
er a
n
d
lo
ad fl
uctuati
on h
a
ve
be
en
gen
erate
d
usi
n
g the M
a
rkov c
hai
n Mont
e Ca
rl
o
meth
od. T
h
e o
p
timi
z
e
d
o
pera
t
ion-p
l
an
ni
ng
a
i
ms
to
mi
ni
mi
ze the t
o
tal
net
prese
n
t cost,
si
z
e
of th
e fix
e
d
storage a
nd fossil fue
l
e
m
is
sions su
bject to constr
ai
nts. T
he simul
a
tion
s have be
en
perfor
m
e
d
usi
n
g
Matlab/Si
muli
n
k
, HOMER an
d Excel. T
h
e s
i
mulati
on r
e
su
l
t
s show
that the V
2
G techn
o
lo
gy su
bstanti
a
ll
y
decre
ase t
he t
o
tal
net
prese
n
t
cost. Moreov
er for s
u
ch
a
microgri
d
th
e tot
a
l
net pr
ese
n
t
cost an
d foss
il
fue
l
emissio
n
s conf
lict w
i
th each o
t
her.
Ke
y
w
ords
: V2
G, operation-
pl
ann
ing,
micro
g
r
id, Markov ch
ain Mo
nte Carl
o met
hod, o
p
ti
mi
z
a
t
i
o
n
Copy
right
©
2015 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
In the comin
g
years the
traditional p
o
w
er
system
architectu
re
will be repl
a
c
ed by
decentrali
ze
d
dispe
r
sed p
o
we
r so
urce
s calle
d di
stributed gen
erators
(DGs
). This distri
bu
ted
gene
ration
wi
ll be inte
grated di
re
ctly into the m
ediu
m
/low voltag
e net
works a
nd
will colle
ctively
form a mi
crogrid. T
he
microgrid i
s
then a foot
-p
ri
nt power syst
em
that
will be located at
the
downstream
of the distribution sy
stem. The benefit will be the
suppl
y of the local load by local
gene
ration. It will redu
ce the line losse
s
and net
work co
nge
stion
and hen
ce will improve t
h
e
reliability of the power sy
stem.
The di
stribut
ed gen
eratio
n (DG) i
s
fueled fr
om distributed
e
nergy
r
e
sourc
e
s (
D
ERs)
.
The DERs like wind an
d solar re
so
urce
s are inh
e
re
n
t
ly fluctuating in nature. Th
e environm
en
tal
con
d
ition
s
of
wind
sp
eed
a
nd sola
r radi
ation cau
s
e t
he outp
u
t po
wer to be
flu
c
tuating
alwa
ys
and create di
sturb
a
n
c
e sit
uation
s
.
Whil
e
in grid
-con
necte
d mo
de
, these
sou
r
ces
are
contro
lled
as PQ
gen
erators which
mean
s that t
hey have to
provide
wh
atever po
we
r t
hey have. Ho
wever
durin
g the i
s
l
andin
g
of the
microgri
d
, the
Vf mode
i
s
a
c
tivated at
ce
rtain b
u
se
s
which
mean
s t
hat
the voltage and frequ
eccy
has to be maintaine
d
. Du
ring this mo
d
e
the additio
nal sou
r
ce
s like
diesel gene
ra
tion or battery energy storage or a
com
b
ination of b
o
th is need
e
d
to balance the
power sy
ste
m
.
The capital
co
st of the dies
el gen
eration is lo
w,
howev
e
r
it hashigh o
p
e
r
ation and
maintena
nce
co
st. More
over the di
esel
gene
ration
i
s
too much no
isy and it ha
s the pro
b
lem
of
carbon
emi
ssions. The
s
e e
m
issi
on
s cont
ribute
to
be
t
he
mai
n
sou
r
ce of
glo
bal warming. On the
other hand
th
e
battery storage
h
a
s high investment
cost but it
s op
eration
and
maintena
nce
co
st
is lo
we
r tha
n
the di
esel
gene
ratio
n
. Also th
e b
a
ttery sto
r
ag
e re
sp
on
se
s more qui
ckl
y
to a
disturban
ce
than th
e die
s
el gen
erat
ion.
The i
n
terven
tion of ele
c
tri
c
vehi
cle
s
(EVs)
over th
e l
a
st
decade
s h
a
s introd
uced
the co
ncept
of mobile
ba
ttery s
t
orage. This
in turn offers an
eco
nomi
c
ally viable solutio
n
in the form of V2G
stora
ge. The V2G stora
ge is a t
e
rm that defi
nes
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 401 – 408
402
the feedin
g
back of th
e
store
d
e
nerg
y
into the
g
r
i
d
as an
d wh
en ne
ce
ssa
r
y. In most of
the
cou
n
trie
s the
EVs have b
een al
rea
d
y in day to da
y use. Acco
rding to inte
rnational
ene
rgy
agen
cy (IEA) in 2010, th
e EV produ
ction target
was 50,0
00 in
numbe
r. No
w in 201
5, this
prod
uctio
n
target ha
s bee
n increa
sed t
o
896,36
7 nu
mber a
nd in 2020, it is expecte
d to gro
w
to
1,523,36
7 nu
mber. Thi
s
rapid in
cre
a
se
of the EV
m
a
rket sha
r
e
can be utilize
d
in the form
o
f
V2G storage
to balan
ce th
e power sy
stem.
The V2G sto
r
age offe
rs a
lot of benefits to t
he power syste
m
like di
strib
u
ted stora
ge,
off-pea
k
po
wer
storage
to
use
it for pe
a
k
shav
in
g, le
velling of flu
c
tuating
rene
wable
ene
rgy
and
for spin
ning rese
rves [1
-3]. The backu
p provide
d
by the V2G sto
r
a
ge ca
n vary from second
s
to
hours
dep
end
ing u
pon th
e
situation
an
d
the availabl
e
V2G capa
city. The avail
abl
e V2G
ca
pa
ci
ty
or in othe
r word
s availabl
e power cap
a
city (
APC)
of the V2G is also fluctu
ating due to
the
rand
om plu
g
-i
n pattern
s an
d hen
ce it is
stocha
st
ic in
nature.
Ho
we
ver ba
sed o
n
the mobility and
plug-i
n
patte
rn, som
eho
w
APC ca
n be
estimate
d. Acco
rdi
ng to
[4-5], an int
e
rme
d
iate b
o
d
y
kno
w
n
a
s
a
n
agg
re
gator i
s
n
eed
ed,
which
contract
s
with th
e E
V
owner for
profit a
nd
pe
nalty
function
s. Th
e vehi
cle
owner
also tell
s the a
ggrega
tor ab
out hi
s potential
dri
v
ing an
d plu
g
-i
n
patterns
.
So far,not
so mu
ch
re
search i
s
ava
il
able
on th
e
optimized
o
peratio
n-plan
ning
of
microgri
d
with rene
wabl
e
sou
r
ces an
d
V2G. However
som
e
a
u
th
ors have
fo
cu
sed
on
the
po
wer
cap
a
city e
s
timation of V
2
G. The a
u
thors in
[3]
use
d
a dyn
a
mic
sched
u
ling metho
d
for
cha
r
gin
g
/dischargi
ng of
E
V
s
by ren
e
wable so
urce
s ba
sed
on
the lo
ad fo
re
ca
sting m
o
d
e
l.
Acco
rdi
ng to
the authors this model
-b
ase
d
algo
rith
m ensu
r
e
s
the ch
arg
eabi
lity of
the EV to
desi
r
ed
SOC
before
de
part
u
re
and
in thi
s
way it al
so
improve
s
the
accuracy
of the V2G
po
wer
estimation.
T
he a
u
tho
r
s i
n
[4] h
a
ve e
s
timated
the
po
we
r
cap
a
c
ity by u
s
in
g
the
pro
babil
i
ty
distrib
u
tion
of the pl
ug-i
n
pattern. T
he
EVs with
sa
me plu
g
-in
p
r
obability hav
e be
en
clu
s
tered
together.
If a
n
ag
gregato
r
is un
able
to
fulfill the
cont
ractu
a
l
req
u
irement, a
pe
n
a
lty is im
po
sed
unde
r differe
nt penalty categori
e
s. In thi
s
way the p
r
o
f
it function is
maximize
d. T
he auth
o
rs in
[5]
have divided
the EV plug-i
n
possibilitie
s by using th
re
e types of ca
r parks at
offices, re
creation
a
l
places and homes.
They
have mo
deled the m
obility by trip
chai
ns and the dri
v
ing patterns are
profiled
ba
se
d on the
su
rveyed dat
a.
Acco
rdi
ng to
the autho
rs
the ca
r pa
rks
at office
s and
homes have
maximum plug-in availability. The aut
hors in [6] have proposed the real time sm
art
c
h
arging algorithm for the
PEVs
from renewable
energy with cons
iderat
ion of
V2G regulation
servi
c
e. Thi
s
cha
r
gin
g
algo
rithm minimi
zes the im
pa
ct
of chargi
ng
by the grid a
nd at the sa
me
time re
gulate
s
the
fre
que
ncy of th
e
grid.
Ho
wev
e
r
none
of t
he m
entione
d research
has
con
s
id
ere
d
the eco
nomi
c
implicatio
ns of
t
he V2G from a microgri
d
operatio
npoi
nt of view.
In this pa
per
the autho
rs h
a
ve forme
d
a
n
optimizatio
n model fo
r t
he op
eratio
n-planni
ng
of microg
rid
as a
multi
-
obje
c
tive mi
nimizatio
n
p
r
oblem. Th
e
multi-obj
ectiv
e
s in
clu
de t
h
e
minimization
of the total n
e
t pre
s
e
n
t co
st, size of th
e fixed sto
r
a
ge an
d fossil
fuel emi
ssi
o
n
s
subj
ect to the
con
s
traints.T
he sto
c
h
a
sti
c
scena
rio
s
for the time seri
es d
a
ta of wi
nd spee
d, sol
a
r
radiatio
n, V2G po
wer
and
load fluctu
ation have
b
e
e
n
gen
erate
d
by usin
g the
Markov chai
n
Monte Ca
rlo method.
T
he stocha
st
ic ch
ance con
s
trai
ned pro
g
ra
m
m
ing
i
s
u
s
e
d
to
deal with
t
he
uncertainties.
The confidence level from the c
hance constrai
nts
gives the minimum availability
of the fluctuating po
wer fro
m
rene
wa
ble
sou
r
ces a
nd
V2G.
The re
st of the pape
r is organi
zed a
s
follows
. Sectio
n II descri
b
e
s
the modified
CIGRE
benc
h
mark
mic
r
ogrid model. Sec
t
ion III d
e
sc
ribes
t
he
probabilis
t
ic
es
timations
of the power from
V2G sto
r
a
ge
and
ren
e
wabl
e so
urce
s. S
e
ction IV fo
rmulates the
stocha
stic ch
a
n
ce
co
nst
r
ain
e
d
model for the
operatio
nal
planni
ng. Section V so
lve
s
the exampl
e probl
em an
d discu
s
ses t
h
e
simulat
i
o
n
re
sult
s.
S
e
ct
ion
V
I
draws t
he
con
c
lu
sio
n
s.
2. Microgrid Model
The mi
cro
g
rid
is mod
e
lled
based on th
e
CIGRE’
s be
n
c
hma
r
k dist
ri
bution sy
ste
m
[7] and
is shown in F
i
gure
1. It is con
n
e
c
ted to
an extern
al g
r
id via a stati
c
switch and
a tran
sform
e
r at
the
poi
nt
of comm
on co
u
p
ling (PCC).
The DERs
compri
se
of wind
tu
rbine
s
(wind
)
, sola
r PV
array (PV), di
esel g
ene
rati
on (DGEN), fixed ener
gy stora
ge (FS),
V2G (V2G
) and lo
cal loa
d
s.
The utilize
d
V2G storage
is com
p
o
s
ed
of a fleet
of
120 EVs. It i
s
assum
ed t
hat there a
r
e
five
different types of EVs accordin
g to the rating of
the batterie
s
. Th
e Table 1 sh
ows the tech
nical
detail of the generation sou
r
ce
s with
thei
r possibl
e co
nfiguratio
ns.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Optim
i
zed Op
eration
-
Plan
n
i
ng of a Micro
g
rid with
Ren
e
wa
ble Sou
r
ces an
d… (A
sad Wa
qar)
403
3. Genera
tio
n
of Stoch
a
s
t
ic Scenario
s
To gene
rate the future time seri
es d
a
ta
fo
r the wind spe
ed, sola
r
radiatio
n, V2G power
and loa
d
fluctuation, the Markov
ch
ain
Monte Ca
rlo
method is
u
s
ed.
Within this meth
od, the
sampli
ng is
perfo
rmed u
s
ing the the Metrop
olis
-Hasting
s algo
ri
thmthat dra
w
s sam
p
le
s from
compl
e
x asymmetric probability di
stri
butions. A
c
cording to [8], t
he algorithm
first proposes
a
possibl
e ne
w state x* in the Ma
rk
ov chain, ba
se
d on a p
r
eviou
s
state x
(
t-1
)
, according to
the
prop
osal dist
ribution q
(
x*|x(t-1
)).
The al
gorithm a
c
ce
pts or
reje
cts the prop
ose
d
state ba
se
d on
the den
sity of
the target di
stri
bution p(x) evaluated at x*.
The
Ma
rk
ov
chai
n d
r
a
w
s
sa
mple
s
s
u
ch
that at any gi
ven point i
n
ti
me t,
the probability of moving from
x(t-1)
x
(
t) mu
st
be
equal
to t
he
probability of moving from
x(t-1)
x(t)
and thi
s
co
n
d
ition is
kno
w
n a
s
reversibility or deta
iled
balan
ce.
The
Metro
poli
s
-Ha
s
ting
s al
g
o
rithm
deal
s with
a
s
ymm
e
tric propo
sa
l dist
ributio
ns by
impleme
n
ting
an addition
al
corre
c
tion fa
ctor
c,
define
d
from the propo
sal di
strib
u
tion as.
Table 1. Te
ch
nical
Detail
s of Gene
ration
Sources
Sr. #
Genera
tio
n
So
u
r
ce
Possible
Co
nfig
uratio
ns
1
Wind Turbine (k
W)
1500, 3000,
450
0, 6000, 750
0
2
Solar PV Arra
y (
k
W)
500, 1000, 1
500,
2000
3
Diesel Generatio
n (kW)
500, 600, 70
0, 8
00, 900
4
Fixed Sto
r
age (k
Wh)
500, 1000, 1
500,
…., 6500
5
V2G T
y
pe 1
(kWh)
35, 70, 105,
……
…., 735
6
V2G T
y
pe 2
(kWh)
32, 64, 96,…
…
…
..., 672
7
V2G T
y
pe 3
(kWh)
24, 48, 72,…
…
…
..., 504
8
V2G T
y
pe 4
(kWh)
56, 112, 158,
…
…
..., 1176
9
V2G T
y
pe 5
(kWh)
16.5, 31, 49.5
,
….
…, 346.5
Figure 1. Microgrid m
odel
c=
q
x
t-
1
|x
*
q
x
*
|x
t-
1
(
1
)
The correction factor adjusts the transi
ti
on operator to ensure that the probability o
f
moving from
x
(t-1)
x
(t)
i
s
e
qual to th
e p
r
obability of m
o
ving fro
m
x
(t-
1
)
x
(t)
, no
ma
tter the h
o
w the
prop
osal dist
ribution is.
Usi
ng this al
gorithm, the
future time serie
s
data fo
r ea
ch year i
s
gen
erate
d
for wind
spe
ed, clea
rn
ess index (so
l
ar rea
d
iation
), V2G
powe
r
(plug-i
n
pattern
) and loa
d
fluctuation.T
he
expected values are then estima
ted by using the probability di
stributions. The two param
eter
Weib
ull distri
bution is u
s
e
d
for win
d
sp
eed, Beta
distribution is
used for cl
earn
e
ss index an
d the
Normal di
stri
bution is u
s
e
d
for V2G plu
g
-in patte
rn a
nd load flu
c
tu
ation.
The output wi
nd po
wer
can
be cal
c
ulate
d
from followi
ng equ
ation
s
[9].
P
W
t
=
1
2
⍴
Av
t
3
C
p
(
2
)
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KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 401 – 408
404
P
W
t
=
0
P
w
v-
v
ci
v
r
-v
ci
P
w
0
(
3
)
Whe
r
e
P
W
t
is the output power of
wind turbi
ne at time t,
⍴
is the air d
e
n
s
ity in kg/m3, A is
the swe
a
p
area in
m2,
v
t
i
s
the
wind
sp
eed i
n
m/
s
at time t
and
C
p
is
th
e powe
r
coeffici
ent. The
power
cu
rve
in Equation
(3) fu
rt
he
r
explain
s
the
output po
we
r of wind tu
rbine at different
spe
e
d
s
. In Equation (3)
v is the mea
n
wind
spe
ed, v
r
is the rated
wind
spe
ed, v
ci
is the cut in
wind
spe
ed a
nd v
co
is the cut
out wind
spe
ed.
The two pa
ramete
r Wei
bull pro
babili
ty distributio
n is the most app
rop
r
i
a
te and
recomme
nde
d di
strib
u
tion
for
wind
spee
d data
a
nalysis [10].
This i
s
b
e
cau
s
e
it
gives
a
better fit
for measured monthly probability density distri
bu
tions than other
statis
tical functions. The
Weib
ull pro
b
a
b
ility density functio
n
is giv
en as:
f
v
t
=
k
c
v
c
k-1
exp
-(
v
c
)
k
(
4
)
Whe
r
e f
v
t
is th
e pro
bability
den
sity functi
on of win
d
speed
v
t
, k is a
dimen
s
ionl
e
ss
Weib
ull para
m
eter an
d c i
s
the Wei
bull
scal
e
par
am
eter in m/s. T
he value
s
of k and
c ca
n be
comp
uted fro
m
Equation (5) and
(6).
k=
σ
µ
-1.086
(
5
)
c=
µ
ɼ
1+k
-1
(
6
)
Whe
r
e µ is th
e mean value
and
σ
is the
stand
ard d
e
viation.
The
o
u
tput solar
PV po
wer stro
ngly
d
epen
ds
upo
n
sol
a
r
ra
diation [10
-
11]
an
d can
be
cal
c
ulate
d
fro
m
following e
quation
s
.
P
PV
t
=G
t
P
PV
max
(
7
)
G
t
=K
t
G
t
ex
(
8
)
G
t
ex
=I
sc
1+0
.
033cos
360n
365
sin
α
t
(
9
)
sin
α
t
=sin
ϕ
sin
δ
+c
os
ϕ
co
s
δ
cos
ω
t
(
1
0
)
Whe
r
e P
PV
t
, P
PV
max
, G
t
, K
t
, G
t
ex
rep
r
e
s
ent out
put PV power at time t, maximum PV power,
hori
z
ontal
ra
d
i
ation at time
t, clearness i
ndex an
d extraterrest
rial ra
diation respe
c
tively. I
sc
is th
e
sola
r
con
s
tan
t, n is th
e day
of a yea
r
,
α
i
s
the
altitude
of the
sun,
δ
is
th
e d
e
c
lin
atio
n
o
f
th
e s
un
and
ω
is the
hour a
ngle.
The cle
a
rn
ess index re
pre
s
ent
s an inde
x that the
G
t
ex
suf
f
e
rs by
f
a
ct
o
r
s s
u
c
h
as
cl
oud
s
and tempe
r
at
ure. The
clea
rne
ss in
dex follows a beta
distrib
u
tion a
nd is given a
s
:
f
K
t
=
ɼ
a+b
ɼ
a
ɼ
b
K
t
a-1
1-K
t
b-1
(
1
1
)
a=
µ
2
1-
µ
σ
2
-
µ
(
1
2
)
b=
a(1-µ)
µ
(
1
3
)
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TELKOM
NIKA
ISSN:
2302-4
046
Optim
i
zed Op
eration
-
Plan
n
i
ng of a Micro
g
rid with
Ren
e
wa
ble Sou
r
ces an
d… (A
sad Wa
qar)
405
Whe
r
e µ is th
e mean value
and
σ
is the
stand
ard d
e
viation.
The output
V2G storage
powe
r
stron
g
ly
depend
s upon the st
ate of charg
e
of the
plugg
ed-i
n
EVs and can
be cal
c
ulate
d
by modifi
ed Coulom
b co
unting metho
d
[12] using
the
followin
g
equ
ation.
P
V2G
t
=
W
V2G
t
t
=S
OC
t
=S
O
C
t-1
+
I
c
t
Q
n
∆
t
(
1
4
)
Whe
r
e I
c
, SO
C an
d Q
n
rep
r
esent
the co
rre
cted cu
rre
n
t,
state of
charg
e
a
nd th
e ch
arge
s
t
ored in the battery res
p
ec
tively.
The V2G plu
g
-in patte
rn a
nd load flu
c
tuation follo
w a Normal di
stribution a
nd i
s
given
as:
f
V2G
t
=
1
σ
V2G
√
2
π
e
-
V2G-
µ
V2G
2
2
σ
V2G
2
(
1
5
)
f
P
Lt
=
1
σ
L
√
2
π
e
-
P
L
-µ
L
2
2
σ
L
2
(
1
6
)
Whe
r
e µ is th
e mean an
d
σ
is the stand
ard deviatio
n
.
4. Chanc
e
Constr
ained P
r
ogramming
Stocha
stic
ch
ance con
s
trai
ned p
r
og
ram
m
i
ng was i
n
trodu
ced
by Charn
e
s
and
Coo
pers
[13] and
it
co
ntains the
st
och
a
sti
c
va
ri
able
s
in
the
con
s
trai
nts. T
he
stocha
stic varia
b
le
s in
the
con
s
trai
nts should b
e
met with som
e
co
nfiden
ce level
.
In cu
rrent p
r
oblem th
e m
u
ltiple obj
ecti
ves in
clud
e t
he minimi
zati
on of the
total net
pre
s
ent cost
(NPC), size
of the fixed
storag
e and
fossil fuel e
m
issi
on
s [15]. They can be
expre
s
sed a
s
min
f
1
=ß
k
w
+k
pv
+k
fs
+k
V2
G
+k
G
+k
DGEN
(
1
7
)
minf
2
=
∑
E
G
+E
DGEN
T
t=
1
(
1
8
)
minf
3
=
∑
fs
T
t=
1
(
1
9
)
s
.t.
Pr
∑
.
∑
.
T
t=
1
N
i=1
P
L
t
-P
G
t
-P
w
it
-P
pv
it
-P
DGEN
it
-P
V2G
it
≤
1
≥α
1
(
2
0)
Pr
∑
.
∑
P
w
it
+P
pv
it
≤
2
T
t=
1
N
i=1
≥α
2
(
2
1
)
∑
.
∑
.
P
w
it
+P
pv
it
+P
DGEN
it
+P
V2G
it
+P
G
t
≥
P
L
t
T
t=
1
+P
RES
N
i=1
(
2
2
)
SOC
min
≤
SOC
≤
SOC
max
(
2
3
)
P
DGEN
mi
n
≤
P
DGEN
≤
P
DGEN
ma
x
(
2
4
)
DS
w
i
nd+pv
+DGEN+fs+V2G
≤
DS
max
(
2
5
)
Whe
r
e the E
quation
(17
)
, (18
)
and
(1
9) rep
r
e
s
ent
th
e three
obje
c
tive function
s. k is the
total co
st in
$ and
ß is the net
pre
s
e
n
t co
st facto
r
. The
su
bscripts
w, pv, fs, V2G a
nd
G
rep
r
e
s
ent
win
d
, sol
a
r, fixed
sto
r
age,
vehi
cle to
gri
d
a
n
d gri
d
re
spe
c
t
i
vely. The tot
a
l cost
s in
clu
d
e
the capital, repla
c
eme
n
t, operation
an
d main
te
nan
ce, fuel,
ene
rgy not
se
rv
ed a
nd
emissio
n
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 401 – 408
406
co
st
s.
T
h
e
s
e co
st
s ca
n
b
e
cal
c
ulat
e
d
a
c
cor
d
ing
to th
e
mathem
atica
l
formul
ation
s
of [14]. E
G
a
nd
E
DGEN
are the emissi
on
s from the extern
al
grid an
d the diesel gen
e
r
ation.
The Equ
a
tio
n
(20
)
a
nd (21)
sho
w
th
e ch
an
ce
co
nstrai
nts. Th
e ch
an
ce
co
nstrai
nt in
Equation (20) states t
hat the po
wer
pro
v
ided by the V2G
storage
must be e
n
o
ugh to mitiga
te
the differen
c
e of power b
e
twee
n the g
enerati
on a
n
d
load. So th
e differen
c
e
betwe
en the
load
and all
ge
ne
ration sou
r
ces
must be at
l
east equ
al
to
the
1
limit/error with a confiden
ce
l
e
vel
equal
to
α
1. Similarly
the cha
n
ce con
s
t
r
aint
in
Equ
a
ti
on (21
)
states that outp
u
t p
o
we
r of th
e
wind
and
sol
a
r
ge
neratio
n m
u
st
be
at-lea
st e
qual to
limit
2 with
a
confi
den
ce l
e
vel e
qual to
α
2. T
he
con
s
trai
nt in
Equation
(2
2) sh
ows the
p
o
we
r
balan
ce
equ
ation
in
whi
c
h th
e tot
a
l ge
ne
ration
by
all the so
urce
s mu
st be at
most eq
ual to
the l
oad a
nd
reserve
po
we
r. The
con
s
traint in Equati
on
(23
)
en
sures that all the stora
ge dev
ice
s
ar
e o
p
e
r
ated withi
n
the limits instructed
by the
manufa
c
turer. The
con
s
traint in Equ
a
tion (24) en
su
res that the
diesel ge
ne
ration is op
erated
within th
e limi
t
s in
stru
cted
by the m
anuf
acturer.
Simil
a
rly the
con
s
traint i
n
Eq
uat
ion
(25
)
ensu
r
es
that the operational plan
ni
ng is carri
ed
out within the
deployment
spa
c
e.
5. Example Problem and
Simulation Resul
t
s
In the examp
l
e problem, a
microg
rid h
a
s
to
b
e
integ
r
ated to
a co
mmunity dist
ribution
system
which
is supplie
d
b
y
an
external
gri
d
.
Th
e e
s
t
i
mated
pea
k
value of
the l
oad i
s
10
57
kW
and its ave
r
a
ge value i
s
4
54 kW. The
e
x
ternal g
r
id h
a
s
cap
a
city shortag
e
p
r
obl
em due to
kn
own
as well a
s
ra
ndom outa
g
e
s
. The tariff of buying ele
c
tri
c
ity from the external g
r
id is 0.2 $/kWh
and
sellin
g e
l
ectri
c
ity to e
x
ternal g
r
id i
s
0.19
$/kWh. The
sam
e
tariff also
a
pplie
s to en
e
r
gy
excha
nge
wi
th V2G storage. The p
e
nalty for ca
p
a
city sho
r
tag
e
is 0.2 $/kWh. Numero
us
simulatio
n
s h
a
ve been pe
rformed u
s
ing
Matlab/
Simulink, HOME
R and Excel, and followin
g
are
the observati
ons:
1)
Whe
n
the loa
d
dema
nd is
sup
p
lied by t
he
extern
al g
r
id with n
o
capa
city sho
r
tage,
the
total NPC
is 107
880
40 $.
Ho
weve
r with
a kno
w
n
capa
city sh
ort
age
of 49.2
%, the total
NPC
rea
c
he
s to 1
0543
499 $.
Similarly with
a kno
w
n
ca
pacity sh
orta
ge of 60.3
%, the total
NPC
decrea
s
e
s
to 1049
1614
$.
2)
An 1100 kW
of diesel generation is
requir
ed to fulfill
the capacity
shortage of 100 %.
Similarly a
9
00
kW of di
e
s
el
gen
eratio
n is re
qui
red
to fulfill the
cap
a
city
sho
r
tage of
49.2
%.
Whe
n
thi
s
di
esel
gen
eration i
s
utilized,
the total
NP
C rea
c
he
s to
171
2977
0 $
and
ope
rati
ng
hours of di
e
s
el g
ene
ratio
n
co
unt to 4
379 h
r
s.
In t
he current e
x
ample p
r
obl
em the capa
city
sho
r
tage of 4
9
.2% is use
d
for all scena
ri
os.
3)
With the
a
d
d
ition of
a fi
xed sto
r
a
ge
of
100
0 kWh, the total
NPC re
ache
s to
1837
7890
$ and the op
erating hou
rs
o
f
diesel ge
ne
ration
count t
o
4376 h
r
s. By increa
sin
g
the
size of fixed
storage
to 60
0
0
kWh the
total NPC re
ach
e
s to 2
446
48
50 $ a
nd the
operating h
o
u
r
s
of diesel g
e
n
e
ration
count
to 436
7 h
r
s.
This
minim
a
l decre
ase is be
cau
s
e
of
the re
ason th
at
fixed storag
e is also getting
char
ge po
we
r by the diese
l
generation.
4)
With the ad
di
tion of 1500
kW
of wind
a
nd 150
0 kW
of sola
r ge
ne
ration, the tot
a
l
NPC de
crea
ses to 166
785
30 $ and the
operating ho
urs
of diesel
gene
ration
co
unt to 2755 h
r
s.
In this ca
se t
he si
ze of th
e fixed stora
ge is
2
000
kWh. As the
percenta
ge o
f
the rene
wa
ble
fraction
is i
n
crea
se
s, the
count of the
o
peratin
g h
ours of the
die
s
el gen
eratio
n
decre
ase. With
7500
kW of wind a
nd 2
0
0
0
kW of the solar g
ene
rati
on, the total NPC in
crea
ses to 25
766
5
20 $
and the o
p
e
r
ating hou
rs o
f
the diesel
g
eneration
co
u
n
t to 1421 h
r
s. In this case the si
ze of
the
fixed stora
g
e
is ke
pt con
s
tant
at 200
0 kWh. For t
he sa
me situ
at
ion if the size of the fixed
stora
ge is in
cre
a
sed to 6
000 kWh, th
e tota
l NPC i
n
crea
se
s to 2929
9760
$ and the op
erating
hours of the d
i
esel g
ene
rati
on furthe
r de
cre
a
se to 128
6 hrs.
5)
For the
same
model, the d
i
esel g
ene
rati
on ha
s bee
n
eliminated a
n
d
the minimu
m
cap
a
city
sho
r
tage of
9.3%
is fou
nd. Thi
s
is th
e
ca
se
whe
n
the l
o
a
d
is fulfilled b
y
the 75
00
kW of
wind a
nd 200
0 kW of the solar ge
ne
ratio
n
in parall
e
l to the external
grid. A fixed
stora
ge of 90
00
kWh is
utilize
d
for thi
s
case. Also the to
tal NPC fo
r
current case is increa
sed
to
2712
2368
$
and
the ope
rating
hours of the
diesel gen
era
t
ion cou
n
t
to zero. On the
other h
and if
the si
ze of th
e
rene
wa
ble fraction
and fi
xed storage
is de
crea
sed
,
the total NPC also de
crea
se b
u
t it will
increa
se the
cap
a
city sh
ortage.
6)
The ca
pa
city sho
r
tage p
r
o
b
lem will pe
rs
ist until an
d unle
ss the g
e
neratio
n ca
pa
city
is in
crea
sed.
But becau
se
of the
con
s
traint of the
de
ployment
sp
a
c
e
any furth
e
r
in
crea
se in
the
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Optim
i
zed Op
eration
-
Plan
n
i
ng of a Micro
g
rid with
Ren
e
wa
ble Sou
r
ces an
d… (A
sad Wa
qar)
407
rene
wa
ble f
r
action
is not
possibl
e
so t
he tu
rned
off
die
s
el
gen
eration h
a
s to
be tu
rned
o
n
to
overcome the
capa
city sho
r
tage p
r
obl
e
m
.
7)
With the ad
di
tion of the 10
00 kWh V2
G
st
ora
ge al
ong
with 200
0 kW of sol
a
r, 7
500
kW of wi
nd a
nd 600 kW of
diesel ge
ne
ration, the total NPC de
cre
a
se
s to 2088
7310 $ an
d the
operating
ho
urs of th
e die
s
el
gen
eratio
n count to
16
07 h
r
s.
In thi
s
ca
se
the fixe
d sto
r
ag
e i
s
kept
zero. As the
ca
pa
city of V2G
storag
e is in
cre
a
sed
to 2000
kWh with sa
me
capa
city
of
gene
ration, t
he total
NPC furthe
r de
creases t
o
15
5
5845
0 $
and
the op
erating hou
rs of di
esel
gene
ration fu
rther d
e
crea
se to 1473. With same ca
p
a
city of gene
ration, if the size of the V2G
stora
ge i
s
fu
rther in
crea
se
d, the total
NPC will
de
cre
a
se
furthe
r
a
nd
same
is true for op
erati
n
g
hours of the d
i
esel g
ene
rati
on.
From the
syn
t
hesi
z
ed SO
C time serie
s
dat
a for the
V2G sto
r
ag
e
based on th
e
plug-i
n
pattern
s, it is found that th
e value of lim
it
1 is minim
a
l and e
qual t
o
0.0000
1. It is a
s
sumed th
at
the EVs of
same
categ
o
ry have same
plug
-in p
a
ttern to
simplify
the si
mulatio
n
s. Th
e g
r
ap
h in
Figure 2
sho
w
s
relatio
n
shi
p
between th
e co
nfiden
ce
level
α
1 and the
V2G cap
a
city.
The
g
r
aph
sho
w
s that th
ere i
s
al
ways a co
nfiden
ce
level
of 19
% of sup
p
lying po
wer by the V2G
stora
g
e
and a
s
V2G
cap
a
city in
creases thi
s
co
nfiden
ce leve
l will also in
crea
se. Th
e g
r
aph i
n
Fig
u
re 3
sho
w
s the
rel
a
tionship b
e
twee
n the
co
nfiden
ce leve
l
α
1 a
nd th
e
total NPC. T
he g
r
aph
sho
w
s
that as the confiden
ce lev
e
l
α
1 increa
ses, the total NPC de
crea
ses an
d at a level of 24 %, th
e
total NP
C
stabilizes. T
he
reason i
s
that
as
more
and
more EVs are plugged
in to provide
power
,
the utilization
of the other gene
ration
sou
r
ces
de
creases,
so th
e total NPC
also d
e
cre
a
ses.
Ho
wever fo
r the ca
se of fixed storage, th
e total NPC continuo
usly in
cre
a
ses.
Similarly fro
m
the
synthe
si
zed
wind
spee
d an
d
clea
rn
e
s
s ind
e
x time
seri
es d
a
ta fo
r
wind
and sola
r gen
eration, it is f
ound that the
value of the limit
2 is 0.4
99. It means t
hat alway
s
5
0
%
of the total
re
newable
po
wer i
s
al
way
s
available.
T
h
e graph
in
Fi
gure
4
sh
ows the relation
ship
betwe
en th
e
confid
en
ce le
vel
α
2
and
th
e total
NPC.
The g
r
a
ph
sh
ows that th
ere is always
a
35
% confid
en
ce
level of
sup
p
l
ying the
rene
wabl
e po
we
r
to the g
r
id a
n
d
a
s
this level
increa
se
s, th
e
total NPC increa
se
s be
cau
s
e of the high
in
v
e
st
ment
c
o
st
s of
r
ene
wable source
s.
Figure 2. Con
f
idence level
α
1 vs V2G
ca
pacity
Figure 3. Con
f
idence level
α
1 vs
total NPC
Figure 4. Con
f
idence level
α
2 vs
total NPC
Figure 5. Pareto front “obj
ective functio
n
s”
The ob
se
rvations di
scusse
d abov
e, sho
w
that objecti
ve function
s total NPC an
d fossi
l
fuel emission
s are co
nflicti
ng with ea
ch
other. It
mea
n
s that if the total
NPC in
creases, the fo
ssil
0
1000
2000
3000
4000
5000
6000
7000
18%
23%
28%
33%
V
2
G Ca
p
a
c
ity
(kW
h
)
Balancing by
V2G
Storage
α
1(%)
13000000
15000000
17000000
19000000
21000000
23000000
25000000
27000000
29000000
8
1
82
8
3
84
8
5
86
8
Tot
a
l NPC
($)
α
1 (%)
FS
V2G
13000000
14000000
15000000
16000000
17000000
18000000
19000000
20000000
21000000
22000000
35
55
75
95
Tot
a
l NPC
($)
α
2 (%)
13000000
15000000
17000000
19000000
21000000
23000000
25000000
27000000
0
5
0
100
150
200
Tot
a
l NPC
($)
Fossil fuel
emissions (%)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 401 – 408
408
fuel emi
s
sion
s d
e
cre
a
se.
For
su
ch
a
si
tuation the
r
e
is n
o
singl
e
o
p
timal
solutio
n
availa
ble
a
n
d
Pareto f
r
ont
s
are utilized to find the most near to
the optimal soluti
ons. These most near
to the
optimal soluti
ons are
the
n
on-d
o
min
ant solutio
n
s
whi
c
h m
ean
s th
at they are
th
e be
st solutio
n
s
from the sol
u
tion spa
c
e. T
he sel
e
ctio
n of the most
favorabl
e sol
u
tion from the Pareto front i
s
a
trade
-off an
d
it de
pend
s
upon
the
utility operator a
nd the
state
polici
e
s.
The
Pareto
fro
n
t in
Figure 5 sh
o
w
s the m
o
st
near to the o
p
timal solutio
n
s.
6. Conclusio
n
In this pap
er the optimize
d
ope
ration
-p
lanni
n
g
of a
microgri
d
wit
h
ren
e
wable
sou
r
ces
and V2G
is
carri
ed-out. Th
e re
sults hav
e sh
own t
hat
V2G integ
r
a
t
ion su
bsta
ntially decrea
s
e
s
the total net pre
s
ent
co
st of the micro
g
r
id. Also
alo
n
g
with the integratio
n of re
newable
sou
r
ce
s,
the utilization
of the diesel
gene
ration i
s
minimi
zed an
d hen
ce the e
m
issi
on
s are redu
ce
d. Usi
n
g
the sto
c
ha
sti
c
chan
ce
con
s
train
ed p
r
og
rammin
g
t
he
confid
en
ce le
vel of integra
t
ing the ra
nd
om
sou
r
ces to th
e mi
cro
g
rid
h
a
s
bee
n d
e
te
rmine
d
. It is seen th
at the
r
e is al
ways a
confid
en
ce l
e
vel
of 19 % of supplying p
o
wer by V2G
a
nd this
co
nfid
ence level in
cre
a
ses
as t
he V2G
cap
a
c
ity
increa
se
s. It is also se
en t
hat as thi
s
co
nfiden
ce lev
e
l
incr
ea
se
s t
he t
o
t
a
l NP
C d
e
cr
ea
se
s and
at
a level of 24 % it almost stabilizes. It is also
seen
that there is al
ways a 35 % confidence lev
e
l of
sup
p
lying
po
wer by th
e re
newable
source
s a
nd
as
this confidence
level
inc
r
eases
the total
NPC
also i
n
crea
se
s. So in a
n
u
tshell thi
s
o
perat
io
n-plan
ning
mo
del usin
g
the sto
c
ha
stic ch
an
ce
con
s
trai
ned
p
r
og
rammi
ngd
etermin
e
s th
e
availability
of the power from the fluctu
ating re
ne
wa
ble
sou
r
ces
and
V2G with le
ast net p
r
e
s
ent co
st, whi
c
h p
r
ovide
s
t
he firm b
a
si
s for the robu
st
operation
-
pla
nning of microgrid.
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in
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