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Appl
ied P
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neer
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I
J
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l.
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,
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.
4
,
Dec
em
b
er
2
0
2
1
,
p
p
.
3
4
7
~
3
5
4
I
SS
N:
2252
-
8
7
9
2
,
DOI
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1
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v
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.
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.
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347
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354
347
J
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e
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h
ttp
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//ij
a
p
e.
ia
esco
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co
m
O
ptima
l
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ceme
nt
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nd sizi
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of di
stribute
d genera
ti
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n f
o
r los
s
minim
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ABC
o
ptimi
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M
a
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la
v
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De
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n
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,
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y:
R
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J
u
n
15
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2
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R
ev
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J
u
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2
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g
2
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Th
e
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ted
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ra
ti
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n
(DG
)
re
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rs
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se
o
f
t
h
e
n
e
a
rb
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n
it
s
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ll
g
e
n
e
ra
ti
o
n
o
r
in
th
e
sle
e
fe
lze
n
tres
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v
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n
s
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a
v
e
s
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o
w
n
t
h
a
t
u
n
fit
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h
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ice
o
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n
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o
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o
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t
h
e
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c
a
n
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d
to
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g
e
r
sy
ste
m
su
ffe
re
rs
th
a
n
DG
'
s
su
ffe
re
r
s.
P
u
b
l
ic
se
rv
ice
s
a
re
a
lrea
d
y
a
v
a
il
a
b
le
b
e
fo
re
th
e
h
ig
h
lo
ss
o
f
e
n
e
rg
y
lo
ss
a
n
d
o
f
th
e
m
e
d
io
c
re
v
o
lt
a
g
e
p
r
o
fil
e
,
i
n
p
a
rti
c
u
lar
d
e
v
e
lo
p
in
g
c
o
u
n
tri
e
s
c
a
n
n
o
t
t
o
lera
te
a
n
y
in
c
re
a
se
in
lo
ss
e
s.
F
ro
m
o
p
ti
m
a
l
a
ll
o
c
a
ti
o
n
,
p
u
b
li
c
se
rv
ice
s
in
th
e
re
d
u
c
ti
o
n
o
f
sy
ste
m
lo
ss
e
s
i
m
p
ro
v
e
ten
sio
n
a
d
ju
stm
e
n
t
a
n
d
imp
ro
v
e
d
e
li
v
e
ry
re
li
a
b
il
it
y
.
Th
is
a
rti
c
le
a
ims
to
m
in
ima
li
z
e
th
e
a
n
n
u
a
l
sy
ste
m
'
s
a
n
n
u
a
l
l
o
ss
t
h
ro
u
g
h
t
h
e
a
p
p
ro
p
riate
p
o
sit
io
n
in
g
a
n
d
siz
e
o
f
t
h
e
DG
u
n
it
s.
Th
e
a
rti
f
icia
ls
b
e
e
c
o
lo
n
y
(ABC)
o
f
EP
A
a
re
i
n
sp
i
re
d
b
y
t
h
e
b
e
h
a
v
i
o
r
o
f
th
e
API
fe
e
d
i
n
g
,
th
is
m
e
th
o
d
is
i
n
c
re
d
i
b
ly
c
o
n
v
e
n
ti
o
n
a
l,
a
stro
k
e
o
r
a
p
e
o
p
late
d
sto
c
h
a
stic
o
p
ti
m
iz
a
ti
o
n
a
lg
o
rit
h
m
to
m
e
e
t
th
e
so
lu
t
io
n
o
f
th
e
sp
e
c
ifi
e
d
p
ro
b
lem
.
At
M
ATLAB
,
a
p
ro
b
a
b
i
li
stic
a
p
p
r
o
a
c
h
is
sim
u
late
d
to
re
a
c
h
th
e
targ
e
t
in
d
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tes
th
a
t
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h
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e
o
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e
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e
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e
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n
tag
e
t
h
a
t
t
h
e
situ
a
ti
o
n
in
wh
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h
t
h
e
lo
a
d
p
o
we
r
is co
n
sid
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re
d
c
o
n
sta
n
t
.
K
ey
w
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r
d
s
:
Ar
tific
ial
b
ee
co
lo
n
y
Dis
tr
ib
u
ted
g
en
er
atio
n
Op
tim
izatio
n
tech
n
iq
u
es
R
ea
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p
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wer
Vo
ltag
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R
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u
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T
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s
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c
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a
rticle
u
n
d
e
r th
e
CC B
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-
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li
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se
.
C
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r
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s
p
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A
uth
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r
:
Ma
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h
u
Vala
v
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Dep
ar
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f
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lectr
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lectr
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ity
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d
Me
d
ical
Scien
c
es
SH
-
1
8
,
B
h
o
p
al
-
I
n
d
o
r
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R
o
ad
,
Op
p
.
Oil Fed
Plan
t (
M.
P),
Pac
h
am
a,
Ma
d
h
y
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Pra
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esh
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I
n
d
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m
ail: v
m
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g
m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
E
lectr
ical
d
is
tr
ib
u
tio
n
s
y
s
tem
is
o
n
e
in
ev
er
y
o
f
t
h
e
in
te
g
r
al
p
a
r
ts
o
f
g
r
i
d
.
I
t’
s
an
s
w
er
ab
le
f
o
r
d
eliv
er
in
g
p
o
wer
t
o
th
e
c
o
n
s
u
m
er
s
as
ec
o
n
o
m
ically
a
n
d
r
eliab
ly
as
p
o
s
s
ib
le.
T
h
e
elec
tr
ical
g
r
id
is
d
ev
el
o
p
in
g
f
r
o
m
a
s
y
s
tem
with
lar
g
e
ce
n
tr
alize
d
g
en
er
ato
r
s
in
to
a
s
y
s
tem
with
s
m
aller
g
en
e
r
ato
r
s
in
te
r
co
n
n
ec
ted
at
lo
wer
v
o
ltag
e
lev
els.
T
h
e
f
ac
ilit
y
f
l
o
w
is
th
u
s
c
h
an
g
e
d
f
r
o
m
ce
n
tr
alize
d
in
to
b
id
i
r
ec
tio
n
al
p
o
wer
f
lo
w.
E
n
e
r
g
y
r
eso
u
r
ce
s
in
ter
co
n
n
ec
ted
with
i
n
th
e
MV
o
r
L
V
d
is
tr
ib
u
tio
n
g
r
id
is
th
o
u
g
h
t
as
d
is
tr
ib
u
ted
g
e
n
er
atio
n
(
DG)
[
1
]
.
Oth
er
co
m
m
o
n
n
am
es
ar
e
d
e
ce
n
tr
al,
d
is
p
er
s
ed
o
r
em
b
e
d
d
e
d
g
en
er
atio
n
.
So
m
e
d
is
tr
ib
u
te
d
g
en
er
ato
r
s
ap
p
ly
s
u
s
tain
ab
le
en
er
g
y
,
i.e
.
,
m
ic
r
o
-
tu
r
b
in
es
(
b
io
g
as,
o
p
tim
ize
d
u
s
e
o
f
f
u
el
,
C
HP)
,
alter
n
ativ
e
en
er
g
y
an
d
p
h
o
to
v
o
ltaic.
T
h
ese
e
n
er
g
y
r
e
s
o
u
r
ce
s
f
ac
ilit
ate
to
ad
j
u
s
t
to
t
h
e
Ky
o
to
p
r
o
to
co
l
[
2
]
-
[
5
]
.
Dis
tr
ib
u
ted
g
en
er
atio
n
also
in
cr
ea
s
e
th
e
d
eg
r
ee
o
f
p
r
o
d
u
ce
d
p
o
wer
wh
ic
h
ca
n
b
e
t
h
e
an
s
wer
to
f
u
lf
ill
in
cr
ea
s
ed
p
o
wer
co
n
s
u
m
p
tio
n
with
in
th
e
s
o
ciety
.
B
y
g
en
er
atin
g
p
o
wer
lo
ca
lly
,
th
e
en
er
g
y
ef
f
icien
cy
in
cr
ea
s
es
th
an
k
s
to
r
e
d
u
ce
d
tr
an
s
m
is
s
io
n
lo
s
s
e
s
.
T
h
e
in
s
t
allatio
n
p
r
o
ce
s
s
is
s
h
o
r
ter
f
o
r
DG
th
an
f
o
r
b
ig
ce
n
tr
alize
d
p
lan
ts
,
lik
e
ato
m
ic
p
o
wer
p
la
n
ts
.
C
u
s
to
m
er
s
ar
e
g
iv
en
th
e
ch
an
ce
to
p
r
o
v
id
e
t
h
eir
o
wn
elec
tr
icity
s
o
as
to
c
u
t
b
ac
k
th
eir
e
n
er
g
y
ex
p
en
s
es.
T
h
e
s
itu
atio
n
o
f
th
e
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
c
e
(
DE
R
)
h
as
th
u
s
m
a
n
y
im
p
ac
ts
.
B
y
in
jectin
g
p
o
wer
lo
ca
lly
,
th
e
v
o
ltag
e
g
ain
s
in
th
is
in
ter
co
n
n
ec
tio
n
p
o
in
t.
T
h
i
s
will
a
to
n
e
f
o
r
v
o
ltag
e
s
ag
s
b
u
t
m
ay
ad
d
itio
n
ally
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l
Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
4
7
–
354
348
ca
u
s
e
o
v
er
-
v
o
ltag
e
p
r
o
b
lem
s
.
T
h
e
ass
em
b
ly
r
ate
o
f
d
is
t
r
ib
u
ted
g
en
e
r
atio
n
m
ig
h
t
in
s
o
m
e
ca
s
es
h
av
e
co
r
r
elatio
n
to
th
e
clim
atic
co
n
d
itio
n
s
[
6
]
.
T
h
e
ab
ilit
y
g
en
e
r
ated
f
r
o
m
win
d
d
e
p
en
d
s
o
f
t
h
e
win
d
s
p
ee
d
an
d
th
er
ef
o
r
e
t
h
e
p
r
o
d
u
ctio
n
r
ate
f
r
o
m
a
s
o
lar
ce
ll
d
ep
en
d
s
o
n
t
h
e
s
u
n
ir
r
ad
iatio
n
.
Du
r
i
n
g
wea
t
h
e
r
co
n
d
itio
n
s
,
th
e
war
m
th
p
r
o
d
u
ctio
n
m
ay
in
cr
e
ase
an
d
in
C
HP
p
lan
ts
th
e
f
ac
ilit
y
p
r
o
d
u
ctio
n
th
e
n
also
in
cr
ea
s
es.
A
p
ar
ticu
lar
u
n
p
r
e
d
ictab
ilit
y
o
f
d
is
tr
ib
u
ted
g
en
er
ated
p
o
wer
is
in
tr
o
d
u
ce
d
th
an
k
s
to
th
e
wea
th
e
r
co
r
r
elatio
n
.
E
v
er
y
d
a
y
,
a
d
ete
r
m
in
is
tic
an
aly
s
i
s
o
f
th
e
ch
ar
g
e
f
lo
w
is
p
er
f
o
r
m
e
d
to
ex
am
i
n
e
th
e
ap
p
e
ar
an
ce
an
d
o
p
er
atio
n
o
f
th
e
g
r
id
.
I
n
o
r
d
er
to
ca
lcu
late
th
e
s
y
s
tem
s
tates
an
d
p
er
f
o
r
m
an
ce
c
u
r
r
e
n
ts
,
th
e
d
eter
m
in
is
tic
lo
ad
cu
r
r
en
t
u
s
es
th
e
d
ef
in
e
d
v
al
u
es
o
f
p
o
wer
g
e
n
er
atio
n
an
d
f
ea
tu
r
es
o
f
th
e
g
o
o
d
s
o
f
a
p
ar
ticu
lar
n
etwo
r
k
co
n
f
ig
u
r
atio
n
[
7
]
.
T
h
e
ac
c
u
m
u
latio
n
o
f
DG
u
n
its
to
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
,
th
e
s
y
s
tem
with
Hito
r
m
is
s
an
d
HitiTim
ity
is
in
jecte
d
[
8
]
.
I
n
to
talin
g
o
f
th
e
u
n
ce
r
tain
e
n
er
g
y
o
f
th
e
in
jecte
d
DG,
th
e
r
e
ar
e
m
an
y
m
o
r
e
u
n
ce
r
tain
ties
in
a
n
ex
tr
e
m
e
g
r
id
in
an
e
x
tr
em
e
g
r
id
,
b
ec
au
s
e
o
f
:
(
i)
Vo
latilit
y
o
f
d
e
m
an
d
f
o
r
a
f
ee
,
(
ii)
C
h
an
g
es
in
n
etwo
r
k
co
n
f
ig
u
r
a
tio
n
,
(
iii)
Gen
er
ato
r
e
r
r
o
r
,
(
i
v
)
T
h
e
DG
u
n
its
in
ject
i
n
ter
m
itten
t
elec
tr
icity
in
th
e
g
r
id
.
As
a
r
esu
lt,
th
e
d
eter
m
in
is
tic
ap
p
r
o
ac
h
is
n
o
t
s
u
f
f
ic
ien
t
to
i
n
v
esti
g
ate
th
e
s
tr
u
ctu
r
e
o
f
th
e
f
ash
io
n
,
an
d
th
e
r
ef
o
r
e
,
th
e
r
esu
lts
o
f
a
d
eter
m
in
is
tic
lo
ad
s
tr
ea
m
ca
n
p
r
o
v
id
e
a
n
o
n
-
r
ea
lis
tic
ev
alu
at
io
n
o
f
th
e
s
tr
u
ctu
r
e
p
r
esen
tatio
n
[
9
]
-
[
1
2
]
.
Fo
r
o
p
e
r
atio
n
al
p
r
ep
ar
atio
n
is
s
u
es,
s
u
ch
as
th
e
v
alu
atio
n
o
f
th
e
co
n
s
is
ten
cy
o
f
s
y
s
tem
ar
r
an
g
em
e
n
t
o
r
th
e
s
tr
ateg
y
o
f
th
e
latest
lin
k
s
,
it
is
r
eq
u
i
r
ed
t
o
ev
alu
ate
th
e
r
o
ad
cu
r
r
en
ts
o
f
s
p
ec
tr
u
m
o
f
co
s
ts
.
Fo
r
p
r
ac
tical
p
r
o
b
lem
s
,
it
is
n
o
t
p
o
s
s
ib
le
to
co
n
tain
in
d
iv
i
d
u
al
lo
ad
s
tr
ea
m
s
f
o
r
ea
ch
l
o
ad
ch
a
n
g
e
f
o
r
th
e
f
o
llo
win
g
r
ea
s
o
n
s
:
(
i)
Pro
h
i
b
itio
n
cr
ed
it
o
f
ca
lcu
latio
n
s
.
L
o
a
d
cu
r
r
en
ts
ar
e
r
eq
u
ir
ed
f
o
r
th
e
n
etwo
r
k
with
n
o
d
e
an
d
b
y
d
if
f
e
r
en
t
lo
ad
v
alu
es
at
ea
ch
n
o
d
e,
(
ii)
Dif
f
icu
lties
to
in
v
esti
g
ate
an
d
m
an
u
f
ac
tu
r
e
th
e
o
u
tco
m
es
o
f
s
ev
er
al
lo
ad
cu
r
r
en
ts
.
T
o
r
e
q
u
est
u
n
ce
r
tain
ty
,
m
at
h
em
atica
l
ap
p
r
o
ac
h
es
a
r
e
o
f
ten
u
s
ed
,
s
u
ch
as
th
e
"p
r
o
b
ab
ilis
tic
ap
p
r
o
ac
h
".
A
p
r
o
b
a
b
ilis
tic
ap
p
r
o
ac
h
in
clu
d
es
a
s
tr
o
n
g
m
at
h
em
atica
l
b
ac
k
g
r
o
u
n
d
;
T
h
er
e
f
o
r
e,
it
ca
n
b
e
ap
p
lie
d
to
th
e
p
o
we
r
g
r
i
d
to
ex
am
in
e
th
e
s
y
s
tem
s
tatu
s
s
y
s
tem
[
1
3
]
-
[
1
6
]
.
Pro
b
ab
ilis
tic
ap
p
r
o
ac
h
es
m
ay
b
e
ap
p
lied
t
o
th
e
ev
alu
atio
n
o
f
t
h
e
d
is
tr
ib
u
ted
g
en
e
r
atio
n
.
I
n
s
tead
o
f
ac
q
u
ir
in
g
s
o
m
e
m
ea
s
u
r
em
en
t,
t
h
e
r
esu
lt
with
th
e
d
eter
m
in
is
tic
lo
ad
f
lo
w
with
e
x
tr
em
e
v
al
u
es
o
f
th
e
in
p
u
t
f
ile
,
th
e
p
r
o
b
ab
ilis
tic
lo
ad
f
lo
w
a
p
p
r
o
ac
h
(
PLF)
ca
n
s
o
lv
e
th
e
r
an
d
o
m
p
r
o
b
lem
o
f
th
e
DG
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
T
h
ese
ty
p
es
o
f
s
tu
d
ies
g
iv
e
a
m
o
r
e
g
en
er
al
p
ictu
r
e
an
d
co
m
p
lete
s
tr
ess
ef
f
ec
ts
w
ith
r
esp
ec
t
to
th
e
d
eter
m
in
is
tic
f
ee
d
s
to
ck
ap
p
r
o
ac
h
.
Stu
d
ies
[
1
7
]
s
ay
s
th
at
th
e
s
in
g
u
lar
v
alu
es
o
f
t
h
e
co
v
er
im
ag
e
ar
e
m
o
d
if
ied
a
f
ter
a
p
p
ly
in
g
DW
T
with
th
e
s
in
g
u
lar
v
alu
es
o
f
t
h
e
wate
r
m
ar
k
im
a
g
e.
A
u
th
o
r
an
al
y
s
ed
p
r
o
p
o
s
ed
AB
C
o
p
tim
izatio
n
alg
o
r
ith
m
is
ap
p
lied
to
a
s
tan
d
ar
d
1
4
-
b
u
s
an
d
57
-
b
u
s
s
y
s
tem
[
1
8
]
.
Au
t
h
o
r
d
is
cu
s
s
ed
ab
o
u
t
im
p
lem
atatio
n
o
f
q
u
ad
r
atic
p
r
o
g
r
am
m
in
g
(
Q
P)
wh
en
ap
p
lied
f
o
r
33
b
u
s
s
y
s
tem
[
1
9
]
.
C
r
o
wse
ar
ch
alg
o
r
ith
em
[
2
0
]
u
s
ed
t
o
ch
ec
k
th
e
r
o
b
u
s
tn
ess
o
f
th
e
s
y
s
tem
s
tatis
tica
l
an
aly
s
is
h
as
b
ee
n
d
o
n
e
wh
ic
h
s
h
o
ws
th
e
r
o
b
u
s
tn
ess
o
f
t
h
e
alg
o
r
ith
m
.
Y
P
Ob
u
lesu
d
is
cu
s
s
ed
b
ased
o
n
o
b
s
er
v
atio
n
th
at
v
o
ltag
e
p
r
o
f
i
le
at
th
e
b
u
s
es
is
im
p
r
o
v
ed
af
ter
in
s
tallin
g
two
DG
s
b
y
d
ec
r
ea
s
in
g
th
e
p
o
wer
lo
s
s
es
o
f
th
e
s
y
s
tem
to
2
.
1
6
8
1
MW
[
2
1
]
.
R
esear
ch
b
ased
o
n
id
en
tific
atio
n
o
f
lo
ca
tio
n
o
f
DGs
u
s
in
g
I
n
d
ex
Vec
to
r
m
eth
o
d
[
2
2
]
.
T
h
e
p
r
o
p
o
s
ed
tech
n
i
q
u
e
d
e
m
o
n
s
tr
at
ed
o
n
1
5
b
u
s
R
DN.
Au
th
o
r
d
is
cu
s
s
ed
ab
o
u
t
weig
h
tin
g
m
eth
o
d
an
d
p
en
alty
f
u
n
ctio
n
ap
p
r
o
ac
h
f
o
r
lo
ca
tio
n
o
f
DG
[
2
3
]
.
Placem
en
t
o
f
DG
an
d
s
izin
g
alo
n
g
with
ca
p
ac
ito
r
is
an
aly
ze
d
wit
h
DL
F m
eth
o
d
[
2
4
].
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
k
ey
o
b
jectiv
e
o
f
th
is
wo
r
k
is
to
an
aly
ze
th
e
p
r
o
b
a
b
ilis
tic
lo
ad
f
lo
w
a
p
p
lied
t
o
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
an
d
p
lan
th
e
lo
ca
tio
n
a
n
d
s
izin
g
o
f
DGs f
o
r
ex
tr
em
e
l
o
s
s
s
av
in
g
.
T
h
e
d
is
tr
ib
u
tio
n
s
y
s
tem
is
co
n
s
id
er
ed
to
b
e
a
r
a
d
ial
s
y
s
tem
with
W
in
d
-
b
ased
DG
co
n
n
ec
ted
to
it
an
d
with
u
n
ce
r
tain
lo
a
d
d
em
an
d
.
T
h
is
in
clu
d
es
p
r
o
b
a
b
ilis
tic
m
o
d
elin
g
o
f
:
Po
wer
in
jecte
d
b
y
W
in
d
-
b
ased
DG.
Un
ce
r
tain
l
o
ad
d
em
an
d
o
n
ea
c
h
b
u
s
.
T
h
e
v
ar
io
u
s
to
o
ls
u
s
ed
f
o
r
th
e
ev
alu
atio
n
o
f
th
e
p
r
o
b
lem
ar
e:
B
ac
k
war
d
-
f
o
r
war
d
s
wee
p
in
g
lo
ad
-
f
lo
w
(
B
FS
L
)
alg
o
r
ith
m
an
d
ar
tific
ial
b
ee
c
o
lo
n
y
(
AB
C
)
alg
o
r
ith
m
.
2
.
1
.
Dis
t
ributio
n
g
ener
a
t
io
n
Dis
tr
ib
u
tio
n
G
en
er
atio
n
s
a
r
e
c
u
r
r
en
tly
in
cr
ea
s
in
g
an
in
cr
ea
s
in
g
in
ter
est
o
f
all
ac
t
o
r
s
in
t
h
e
elec
tr
icity
m
ar
k
et.
I
n
r
ec
en
t
y
ea
r
s
,
o
f
co
u
r
s
e,
th
an
k
s
to
ec
o
n
o
m
ic,
ec
o
lo
g
ic
al
an
d
p
o
liti
ca
l
r
ea
s
o
n
s
,
th
e
s
tan
d
ar
d
in
s
tallatio
n
,
ch
ar
ac
ter
ized
b
y
t
h
e
p
r
o
d
u
ctio
n
o
f
ce
n
tr
al
m
ass
en
er
g
y
a
n
d
l
o
n
g
,
lo
n
g
tr
a
n
s
m
is
s
io
n
n
etwo
r
k
s
is
s
till
s
u
p
p
o
r
ted
b
y
th
e
en
e
r
g
y
R
eso
u
r
ce
s
to
th
e
d
is
tr
ib
u
tio
n
n
e
two
r
k
,
a
s
u
itab
le
co
m
m
o
n
f
o
l
d
ed
as
a
d
is
tr
ib
u
te
d
g
en
er
atio
n
(
DG)
.
I
t
s
h
o
u
ld
b
e
ad
d
ed
t
h
at
in
r
ec
en
t
y
ea
r
s
,
D
G
p
en
etr
atio
n
h
as
b
ec
o
m
e
in
d
is
tr
ib
u
tio
n
s
y
s
tem
s
in
a
m
an
n
e
r
f
aster
th
at
ac
h
iev
e
s
th
e
m
ax
im
u
m
lim
it o
f
th
e
ap
p
r
o
v
e
d
co
n
n
ec
tio
n
s
in
m
a
n
y
c
o
u
n
tr
ies,
wh
ich
ar
e
m
an
ag
ed
b
y
th
e,
ap
p
r
o
ac
h
t
o
t
h
e
s
tan
d
a
r
d
p
ass
iv
e
n
etwo
r
k
s
.
T
h
er
ef
o
r
e,
o
v
er
th
e
y
ea
r
s
,
it
a
p
p
r
o
ac
h
es
s
tr
u
ctu
r
e
n
etwo
r
k
s
,
d
esig
n
an
d
f
u
n
ctio
n
m
u
s
t
r
ad
ically
b
e
m
o
d
if
ied
in
an
e
x
tr
em
ely
m
a
n
n
er
,
w
h
ile
th
e
g
en
e
r
atio
n
s
h
o
u
ld
b
e
co
n
s
id
er
ed
as
a
n
in
teg
r
al
p
ar
t
o
f
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
y
s
tem
.
I
n
v
es
tm
en
ts
an
d
im
p
o
r
tan
t
r
esear
ch
ar
e
t
h
en
n
ee
d
ed
to
th
e
elec
tr
ical
R
en
ew
d
is
tr
ib
u
tio
n
s
ec
to
r
,
ac
h
iev
e
a
k
i
n
d
o
f
"self
-
h
ea
lin
g
"
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
tima
l p
la
ce
men
t a
n
d
s
iz
in
g
o
f d
is
tr
ib
u
ted
g
en
era
tio
n
f
o
r
lo
s
s
min
imiz
a
tio
n
u
s
in
g
…
(
Ma
d
h
u
V
a
la
va
la
)
349
d
is
tr
ib
u
tio
n
s
y
s
tem
th
at
n
o
t
o
n
ly
allo
ws
m
an
ag
em
en
t
o
f
lar
g
e
g
r
o
u
p
s
o
f
en
er
g
y
r
es
o
u
r
ce
s
,
b
u
t
also
.
,
I
n
cr
ea
s
ed
lev
el
o
f
s
er
v
ice
q
u
al
ity
.
Dis
tr
ib
u
ted
g
en
er
atio
n
(
DG)
is
n
o
t
a
n
ew
n
o
tio
n
,
b
u
t
it
is
a
g
r
o
win
g
tech
n
iq
u
e
to
p
r
o
v
id
e
en
er
g
y
to
th
e
s
k
ill
s
y
s
tem
'
s
h
ea
r
t.
I
t
is
p
r
im
ar
ily
d
ep
en
d
en
t
o
n
t
h
e
in
s
tallatio
n
an
d
o
p
er
atio
n
o
f
a
lim
ited
p
o
r
tf
o
lio
o
f
elec
tr
ical
elec
tr
icity
u
n
its
,
co
m
p
ac
t
a
n
d
clea
n
u
p
in
o
r
d
e
r
to
clo
s
e
an
elec
tr
ic
ch
ar
g
e
(
clien
t)
.
Dis
tr
ib
u
ted
g
en
er
atio
n
(
DG)
will
b
e
in
cr
ea
s
in
g
ly
im
p
o
r
tan
t
in
an
ex
t
r
em
ely
ex
p
o
n
e
n
t
e
n
v
ir
o
n
m
en
t
f
o
r
v
ar
i
o
u
s
r
ea
s
o
n
s
:
(
a)
th
e
b
u
y
er
ca
n
p
r
o
v
id
e
th
e
b
u
y
er
in
th
e
p
lan
n
in
g
an
d
d
ev
elo
p
m
e
n
t
o
f
in
d
e
p
en
d
e
n
ce
in
s
tallatio
n
an
d
f
lex
ib
ilit
y
.
T
h
is
is
p
ar
ticu
lar
ly
im
p
o
r
tan
t
f
o
r
s
en
s
itiv
e
an
d
s
o
p
h
is
ticated
lo
ad
s
in
en
v
ir
o
n
m
en
t
s
s
u
b
ject
to
in
ter
r
u
p
tio
n
s
a
n
d
d
ec
r
ea
s
es.
(
b
)
T
h
e
e
n
er
g
y
co
s
ts
g
en
er
ated
b
y
DG
d
ec
r
ea
s
e
co
m
p
etitiv
e
wit
h
elec
tr
icity
s
u
p
p
lied
b
y
th
e
g
r
id
.
E
lectr
icity
co
m
p
an
ies
ca
n
g
en
er
ate
c
r
itical
p
o
in
ts
in
t
h
e
g
r
id
,
esp
ec
ially
n
ea
r
b
y
ex
p
e
n
s
es.
T
h
is
lead
s
to
s
ig
n
if
ican
t
s
av
in
g
s
with
in
t
h
e
elec
tr
ical
d
is
tr
ib
u
tio
n
in
f
r
a
s
tr
u
ctu
r
e,
esp
ec
ially
ex
ten
s
io
n
s
.
(
c)
allo
ws
an
in
d
ep
en
d
en
t
elec
tr
icity
g
en
er
atio
n
o
f
a
co
n
s
u
m
er
,
p
o
s
s
ib
ly
a
l
ess
ex
p
en
s
iv
e
r
ate,
wh
ich
s
av
es
th
e
ca
lcu
latio
n
o
f
u
tili
ty
.
E
x
ce
s
s
en
er
g
y
is
p
u
b
li
s
h
ed
in
th
e
co
m
m
o
d
ity
m
ar
k
et
an
d
o
b
tain
ed
with
a
p
r
o
f
it.
(
d
)
W
ith
r
ed
u
ctiv
e
co
s
ts
,
in
d
ep
en
d
en
t
en
er
g
y
p
r
o
d
u
ce
r
s
ca
n
in
s
tall
th
e
g
en
er
atio
n
an
d
co
n
n
ec
t
th
e
m
to
th
e
s
y
s
tem
g
r
i
d
to
s
ell
en
e
r
g
y
with
p
r
o
f
its
.
(
e
)
T
h
e
p
o
ten
tial
f
ile
is
to
p
r
o
v
id
e
a
n
u
m
b
e
r
o
f
titl
es
id
en
tifie
d
as
p
r
o
f
it
r
esu
lts
.
I
n
d
e
p
en
d
e
n
t
en
er
g
y
g
en
er
ato
r
s
ca
n
also
p
r
o
v
i
d
e
th
ese
s
er
v
ices
as
co
n
s
u
m
er
s
with
an
in
d
ep
en
d
en
t g
e
n
er
atio
n
.
B
ef
o
r
e
en
ter
in
g
a
d
is
tr
ib
u
ted
g
en
er
atio
n
s
ch
em
e,
a
t
r
an
s
m
is
s
io
n
d
ef
in
itio
n
o
r
a
m
in
i
m
u
m
o
f
a
f
u
n
ctio
n
al
f
r
am
e
o
f
th
e
d
is
tr
ib
u
ted
g
e
n
er
atio
n
m
u
s
t
b
e
p
lace
d
.
I
n
g
en
er
al,
h
e
p
r
escr
ib
ed
th
at
an
y
i
n
teg
r
ate
d
p
o
wer
g
e
n
er
atio
n
tec
h
n
o
lo
g
y
i
n
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
s
co
m
p
lies
with
th
e
d
is
tr
ib
u
ted
g
en
e
r
atin
g
u
m
b
r
ella.
T
h
e
n
am
es
"d
is
tr
ib
u
ted
"
an
d
"d
is
p
er
s
ed
"
ar
e
u
s
ed
in
te
r
ch
an
g
ea
b
ly
.
Yo
u
ca
n
also
class
if
y
d
is
p
er
s
ed
g
en
er
atio
n
tec
h
n
o
lo
g
ies as r
en
ewa
b
le
an
d
n
o
t similar
d
is
tr
ib
u
to
r
s
.
R
en
ewa
b
le
tech
n
o
lo
g
ies
in
clu
d
e:
(
i)
s
o
lar
,
p
h
o
to
v
o
ltaic
o
r
t
h
er
m
o
-
(
ii)
g
eo
th
e
r
m
al
an
d
o
c
ea
n
win
d
.
No
m
in
al
ca
b
in
tech
n
o
lo
g
ies
in
clu
d
e:
(
i)
C
o
m
b
u
s
tio
n
e
n
g
i
n
e
(
I
C
E
)
(
ii)
C
o
m
b
in
ed
c
y
cle
(
iii)
C
o
m
b
u
s
tio
n
tu
r
b
in
e
(
iv
)
Mic
r
o
-
T
u
r
b
in
e
(
v
)
Fu
el
ce
ll.
T
h
e
d
is
tr
ib
u
ted
g
en
er
atio
n
m
u
s
t
n
o
t
b
e
co
n
f
u
s
ed
w
ith
r
en
ewa
b
le
p
r
o
d
u
ctio
n
.
Als
o
d
is
tr
ib
u
ted
g
en
er
atio
n
tech
n
o
lo
g
y
is
r
en
ewa
b
le
o
r
n
o
t; Af
ter
all,
s
o
m
e
d
is
tr
ib
u
ted
p
r
o
d
u
ctio
n
tech
n
o
lo
g
ies co
u
ld
co
n
tr
ib
u
te
s
ig
n
if
ican
tly
to
cu
r
r
en
t p
o
llu
tio
n
p
r
o
b
lem
s
if
it is
co
m
p
letely
u
s
ed
.
2.
2
.
P
r
o
blem
f
o
rm
ula
t
io
n
T
h
e
DG'
s
p
o
s
itio
n
an
d
d
im
e
n
s
io
n
s
ca
n
r
esu
lt
in
a
s
ig
n
if
i
ca
n
t
lo
s
s
o
f
p
o
wer
a
n
d
a
lo
wer
v
o
ltag
e
p
r
o
f
ile.
I
t
is
n
o
t
r
ec
o
m
m
e
n
d
e
d
to
en
ter
th
e
n
etwo
r
k
'
s
DG
o
f
v
er
y
h
i
g
h
ca
p
ac
ity
.
T
h
e
DGS
p
lace
d
in
th
e
n
etwo
r
k
m
u
s
t
h
av
e
a
to
tal
ca
p
ac
ity
th
at
is
co
n
s
u
m
ab
le
in
s
i
d
e
t
h
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
An
y
attem
p
t
to
b
u
il
d
h
ig
h
ca
p
ac
ity
DG
r
eso
u
r
ce
s
in
o
r
d
er
to
e
x
p
o
r
t
p
o
wer
to
th
e
o
p
p
o
s
ite
s
tatio
n
(
in
v
er
ted
en
er
g
y
f
l
o
w
f
r
o
m
th
e
s
u
b
s
tatio
n
)
r
esu
lts
in
a
s
ig
n
if
i
ca
n
t
lo
s
s
.
T
h
e
n
etwo
r
k
c
o
n
f
ig
u
r
atio
n
an
d
lo
ad
s
o
f
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
p
lay
a
cr
itical
r
o
le
in
d
eter
m
i
n
in
g
th
e
id
ea
l
s
ize
o
f
th
e
DG
f
o
r
th
e
lo
west
s
y
s
tem
lo
s
s
.
T
h
e
ap
p
licatio
n
is
f
o
r
m
u
lated
to
m
ee
t
two
g
o
als.
First
s
e
lec
t
a
s
u
itab
le
lo
ca
tio
n
wh
er
e
th
e
lo
s
s
o
f
th
e
s
y
s
tem
b
ec
o
m
es
m
in
im
al;
s
ec
o
n
d
s
ca
lcu
lates th
e
o
p
tim
u
m
DG
s
iz
e
f
o
r
th
e
m
in
im
u
m
s
y
s
tem
lo
s
s
.
T
h
is
s
eg
m
en
t
p
r
esen
ts
th
e
p
r
o
p
o
s
al
f
o
r
a
p
r
o
b
ab
ilis
tic
d
ef
in
i
tio
n
f
o
r
a
q
u
esti
o
n
o
f
th
e
o
r
g
a
n
izatio
n
o
f
th
e
L
DC
with
th
e
m
ea
n
in
g
o
f
th
e
s
tu
d
io
f
r
am
ewo
r
k
.
T
h
e
ju
s
tific
atio
n
o
f
th
e
p
r
o
p
o
s
ed
s
tr
at
eg
y
is
to
f
o
r
ce
th
e
ap
p
r
o
v
al
m
o
d
el
f
o
r
th
e
tast
in
g
o
f
tr
ials
at
th
e
d
eter
m
in
is
tic
co
n
d
itio
n
s
o
f
t
h
e
id
ea
l
f
o
r
c
e
(
OPF).
T
h
u
s
,
t
h
e
m
ea
s
u
r
em
en
t
o
f
th
e
d
y
n
am
ic/
r
ec
eiv
in
g
f
o
r
ce
o
f
th
e
f
o
r
ce
c
o
n
d
itio
n
s
(
3
.
9
-
3
.
1
0
)
is
ad
ap
t
ed
to
th
e
e
n
tire
s
u
m
o
f
cir
c
u
m
s
tan
ce
s
.
Fo
r
ea
ch
E
x
p
r
ess
,
th
e
e
n
tr
y
o
f
DG
B
r
ee
ze
DG
h
as
m
o
d
if
ied
t
h
e
u
n
its
o
f
ag
e
th
e
ag
e
o
f
ag
e,
wh
ile
th
e
tr
o
u
b
le
o
f
th
e
B
u
r
e
au
is
d
etec
ted
an
d
th
e
r
ef
o
r
e
weig
h
ted
with
th
e
lik
elih
o
o
d
o
f
th
e
ev
e
n
t
o
f
t
h
is
cir
cu
m
s
tan
ce
d
u
r
in
g
t
h
e
f
u
ll
y
ea
r
to
esti
m
ate
liv
elin
ess
d
is
aster
.
T
h
e
id
ea
l
d
is
tr
ib
u
tio
n
s
o
f
DG
elem
en
ts
ar
e
n
o
t
in
s
talled
b
y
s
to
n
e,
f
o
r
ea
ch
o
p
er
atin
g
s
tate
co
m
p
lete
en
er
g
y
d
is
aster
s
ar
e
lim
ited
w
ith
o
u
t
th
e
f
ac
t
th
at
f
r
am
e
lim
its
ar
e
ab
u
s
ed
.
T
h
e
f
o
ll
o
win
g
ass
u
m
p
tio
n
s
a
r
e
m
ad
e
in
o
r
d
e
r
to
co
n
s
tr
u
ct
an
a
p
p
r
o
p
r
iate
p
lan
n
in
g
ap
p
r
o
ac
h
t
h
at
d
eter
m
in
es th
e
id
ea
l
f
u
el
m
ix
t
u
r
e
f
o
r
r
en
ewa
b
le
DG
u
n
its
:
−
T
h
e
s
am
e
b
u
s
ca
n
b
e
co
n
n
ec
te
d
to
m
o
r
e
th
an
o
n
e
ty
p
e
o
f
DG.
−
T
h
e
p
o
wer
f
ac
to
r
o
f
all
DG
u
n
its
is
th
e
s
am
e.
W
h
y
B
ec
au
s
e
d
is
tr
ib
u
tio
n
s
y
s
tem
s
o
f
ten
in
v
o
lv
e
m
u
ltip
le
lo
ca
tio
n
s
,
th
e
lo
ca
tio
n
h
as
li
ttle
m
an
n
er
o
n
th
e
p
r
o
d
u
ctio
n
au
t
h
o
r
ity
o
f
win
d
a
n
d
s
o
lar
DG.
2.
3
.
O
bje
c
t
iv
e
f
un
ct
io
n
Un
d
er
all
o
p
e
r
atio
n
al
co
n
d
itio
n
s
,
th
e
p
u
r
p
o
s
e
o
f
th
e
p
lan
n
in
g
f
o
r
m
u
latio
n
is
to
r
e
d
u
ce
a
n
n
u
al
en
er
g
y
lo
s
s
es in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
=
∑
=
1
×
(
)
×
8760
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l
Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
4
7
–
354
350
W
h
er
e
P
lossg
is
to
tal
p
o
wer
lo
s
s
es in
th
e
o
r
g
an
izatio
n
d
u
r
in
g
s
tate
g
.
2.
4
.
Co
ns
t
ra
ints
2
.
4
.
1
.
P
o
wer
flo
w
equa
t
io
ns
,
1
+
∑
(
,
)
=
1
×
,
−
(
,
+
1
)
×
=
∑
,
×
,
×
×
(
+
=
1
,
−
,
)
∀
,
,
…
(
2
)
,
1
−
(
,
+
1
)
×
,
=
−
∑
,
×
,
×
×
(
+
,
−
,
)
=
1
∀
,
,
…
(
3
)
wh
er
e
P
D
G
t,
i
-
T
h
e
r
ated
p
o
wer
o
f
th
e
t
th
win
d
-
b
ased
DG
th
at
is
co
n
n
ec
ted
to
b
u
s
i.
P
Gg,
i
-
B
u
s
i
r
ec
eiv
ed
ac
tiv
e
p
o
wer
f
r
o
m
t
h
e
s
u
b
s
tatio
n
.
Q
G
g,
i
-
B
u
s
i r
ec
eiv
ed
r
ea
ctiv
e
elec
tr
icity
f
r
o
m
th
e
s
u
b
s
tatio
n
.
PDi
-
B
u
s
i h
as th
e
h
ig
h
ac
tiv
e
lo
ad
.
QDi
–
B
u
s
i h
as th
e
h
ig
h
r
ea
ct
iv
e
lo
ad
.
Vg
,
i
–
B
u
s
I
h
as th
e
v
o
ltag
e
d
u
r
in
g
s
tate
g
.
n
-
T
h
e
o
v
er
all
q
u
an
tity
o
f
b
u
s
es in
th
e
s
y
s
tem
.
2
.
4
.
2.
P
o
wer
lo
s
s
equa
t
io
ns
=
0
.
5
×
∑
∑
×
[
(
,
)
2
+
(
,
)
2
−
2
×
,
×
,
×
(
,
−
=
1
=
1
,
)
]
∀
,
,
(
4
)
2
.
4
.
3
.
B
ra
nch c
urre
nt
equa
t
i
o
ns
,
=
|
|
×
[
(
,
)
2
+
(
,
)
2
−
2
×
,
×
,
×
(
,
−
,
)
]
1
/
2
∀
,
,
(
5
)
wh
er
e
I
g,
ij
is
th
e
c
u
r
r
en
t i
n
th
e
f
ee
d
er
co
n
n
ec
tin
g
b
u
s
s
es i
an
d
j d
u
r
in
g
s
tate
g
.
2
.
4
.
4
.
Sla
ck
bu
s
v
o
lt
a
g
e
a
nd
a
ng
le
(
a
s
s
um
ed
t
o
be
bu
s
1
)
,
1
=
1
.
0
,
1
=
0
.
0
.
(
6
)
3
.
2
.
5
.
Vo
lt
a
g
e
lim
it
s
a
t
lo
a
d
bu
s
e
s
0
.
90
≤
,
≤
1
.
10
∀
∉
(
7
)
2
.
4
.
6
.
F
ee
der
ca
pa
cit
y
lim
it
s
0
≤
,
≤
(
8
)
2
.
4
.
7
.
Dis
cr
et
e
s
ize
o
f
wind
-
ba
s
ed
DG
,
=
,
∀
∈
∈
(
9
)
wh
er
e
a
i
-
T
h
e
in
teg
er
v
a
r
iab
le.
P
r
-
T
h
e
o
n
e
-
co
lu
m
n
m
atr
ix
o
f
len
g
th
m
i
n
clu
d
es a
ll r
atin
g
s
o
f
th
e
av
ailab
le
win
d
tu
r
b
in
es.
B
-
T
h
e
s
et
o
f
ca
n
d
id
ate
b
u
s
es
to
co
n
n
ec
t D
Gs.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
tima
l p
la
ce
men
t a
n
d
s
iz
in
g
o
f d
is
tr
ib
u
ted
g
en
era
tio
n
f
o
r
lo
s
s
min
imiz
a
tio
n
u
s
in
g
…
(
Ma
d
h
u
V
a
la
va
la
)
351
2
.
4
.
8
.
M
a
x
im
um
penet
ra
t
io
n o
n e
a
ch
bu
s
∑
,
≤
∀
=
1
(
1
0
)
W
h
er
e
P
bus
is
th
e
m
ax
im
u
m
al
lo
wab
le
p
en
etr
atio
n
o
n
ea
ch
b
u
s
.
2
.
4
.
9
.
M
a
x
im
um
penet
ra
t
io
n o
f
DG
un
it
s
in t
he
s
y
s
t
em
T
h
e
m
ax
im
u
m
p
en
etr
atio
n
li
m
it
will
b
e
ca
lcu
lated
b
ased
o
n
th
e
av
er
a
g
e
p
en
etr
atio
n
o
f
th
e
win
d
-
b
ased
DG
.
∑
∑
×
,
≤
×
∑
=
1
=
1
=
1
(
1
1
)
wh
er
e
x
d
e
n
o
tes th
e
m
a
x
im
u
m
p
en
etr
atio
n
,
lim
it e
x
p
r
ess
ed
a
s
a
p
er
ce
n
tag
e
o
f
p
ea
k
lo
ad
.
2.
5
.
Art
if
ici
a
l
bee
co
lo
ny
a
l
g
o
rit
hm
T
h
e
r
esear
ch
b
eh
av
i
o
r
o
f
th
e
b
ee
in
s
p
ir
ed
th
e
ar
tific
ial
alg
o
r
ith
m
o
f
th
e
b
ee
co
lo
n
y
.
T
h
is
ap
p
r
o
ac
h
is
a
s
to
ch
asti
c
co
n
s
tr
u
ctiv
e
o
p
ti
m
izatio
n
m
eth
o
d
f
o
r
e
x
tr
em
el
y
o
b
v
i
o
u
s
an
d
r
esil
ien
t
co
n
s
u
m
p
tio
n
co
n
s
u
m
p
tio
n
.
T
h
e
b
ee
ar
tific
ial
co
lo
n
y
is
d
iv
id
ed
b
y
th
e
AB
C
alg
o
r
ith
m
in
to
th
r
ee
ca
teg
o
r
ies:
u
s
ed
API
s
,
p
ass
er
s
-
b
y
an
d
s
co
u
ts
.
W
eig
h
ts
th
e
API
s
r
ep
r
esen
t
h
alf
o
f
th
e
co
lo
n
y
wh
ile
p
ass
er
s
-
b
y
ar
e
f
o
r
m
e
d
f
r
o
m
t
h
e
o
th
er
h
al
f
.
T
h
e
am
o
u
n
t
o
f
q
u
an
tity
o
f
ea
c
h
f
o
o
d
s
o
u
r
ce
s
y
m
b
o
lizes
th
e
q
u
a
lity
(
f
itn
ess
)
o
f
th
e
ass
o
ciate
d
s
o
lu
tio
n
,
s
in
ce
th
e
p
o
s
itio
n
o
f
a
p
o
wer
s
o
u
r
ce
r
e
f
er
s
to
a
s
o
lu
tio
n
th
at
is
p
o
s
s
ib
le
o
n
th
e
o
p
tim
izatio
n
p
r
o
b
le
m
.
T
h
e
n
u
m
b
er
o
f
e
m
p
lo
y
ee
s
c
o
r
r
esp
o
n
d
s
to
th
e
n
u
m
b
e
r
o
f
f
o
o
d
s
o
u
r
ce
s
.
W
h
en
th
e
API
s
lea
v
e
a
p
o
wer
s
o
u
r
ce
,
th
e
p
r
e
v
io
u
s
ly
u
s
ed
b
e
e
b
e
co
m
es
a
s
co
u
t.
First,
th
e
AB
C
p
r
o
ce
d
u
r
e
wo
u
ld
cr
ea
te
an
in
itial
p
o
p
u
latio
n
th
at
is
d
is
cr
im
in
ated
ag
ain
s
t
b
y
ca
s
e
P
(
C
=
0
)
S
NO
f
o
o
d
s
itu
atio
n
s
,
wh
er
e
Sn
is
th
e
s
ize
o
f
th
e
f
o
o
d
s
o
u
r
ce
s
.
E
ac
h
Xi
s
o
lu
tio
n
(
i
=
1
,
2
,
3
,
3
,
.
.
.
,
Sn
)
co
u
ld
b
e
a
d
im
e
n
s
io
n
ca
r
r
ie
r
ca
lled
th
e
n
u
m
b
er
o
f
o
p
tim
izatio
n
p
ar
am
eter
s
.
Af
ter
in
itializatio
n
,
th
e
s
o
lu
tio
n
p
o
p
u
latio
n
is
ac
c
=
1
.
2
.
3
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
,
MCN
o
f
th
e
s
tate
r
esear
ch
o
f
API
wo
r
k
o
f
API
wo
r
k
an
d
s
co
u
t.
A
u
s
ed
b
ee
c
an
ch
an
g
e
th
e
a
n
s
wer
to
y
o
u
r
s
to
r
e
b
ased
o
n
lo
ca
l
f
ac
ts
an
d
test
th
e
v
alu
e
o
f
th
e
n
ew
s
o
u
r
ce
f
itn
ess
.
I
f
th
e
n
ew
h
as
a
g
r
ea
ter
p
h
y
s
ical
s
h
ap
e
th
an
th
e
p
r
ev
io
u
s
o
n
e,
th
e
d
ed
icate
d
b
ee
lear
n
s
th
e
n
ew
an
d
f
o
r
g
ets
th
e
o
ld
m
an
.
Oth
er
wis
e,
y
o
u
r
em
em
b
er
th
e
lo
ca
tio
n
o
f
th
e
p
r
ev
io
u
s
o
n
e.
I
f
all
th
e
API
s
u
s
ed
h
av
e
co
m
p
leted
th
e
s
ea
r
ch
,
in
f
o
r
m
th
e
p
en
d
r
an
ts
o
n
t
h
e
n
ec
tar
lev
els
an
d
r
estau
r
an
ts
.
An
o
b
s
er
v
er
e
v
alu
ates
th
e
n
ec
tar
d
ata
r
elea
s
ed
b
y
all
th
e
API
s
u
s
ed
an
d
s
elec
ts
a
p
o
wer
s
o
u
r
ce
with
a
p
r
o
b
ab
ilit
y
th
at
co
r
r
esp
o
n
d
s
to
th
e
q
u
a
n
tity
o
f
q
u
a
n
tity
.
T
h
e
o
b
s
er
v
er
c
an
m
o
d
if
y
th
e
p
o
in
t
o
f
m
em
o
r
y
an
d
ex
am
i
n
e
th
e
n
ec
ta
r
o
f
t
h
e
q
u
an
tity
o
f
th
e
s
o
u
r
ce
o
f
th
e
c
an
d
id
ates a
n
d
th
e
r
en
ted
b
ee
.
I
f
th
e
am
o
u
n
t
o
f
n
ec
tar
is
g
r
ea
ter
th
an
th
e
p
r
ev
i
o
u
s
o
n
e,
t
h
e
b
ee
will
lear
n
th
e
n
ew
p
o
s
itio
n
an
d
f
o
r
g
et
th
e
o
ld
wo
m
a
n
.
An
o
b
s
er
v
er
s
el
ec
ts
a
n
u
tr
itio
n
al
s
o
u
r
ce
f
u
lly
b
ased
o
n
th
e
p
r
o
b
ab
ili
ty
v
alu
e
ass
o
ciate
d
with
th
e
s
u
p
p
ly
s
o
u
r
ce
ass
o
ci
ated
with
th
e
f
o
llo
win
g
f
o
r
m
u
lawh
ef
ites
wh
o
s
e
p
h
y
s
ical
v
alu
e
v
alu
e
o
f
th
e
I
-
I
T
H
s
o
lu
tio
n
b
ased
o
n
th
e
am
o
u
n
t
o
f
n
ec
tar
o
f
t
h
e
I
-
T
H
p
o
s
itio
n
.
T
h
e
AB
C
co
u
l
d
u
s
e
th
e
f
o
llo
win
g
m
o
d
if
icatio
n
f
o
r
m
to
cr
ea
te
a
n
ew
f
o
o
d
p
o
s
itio
n
f
r
o
m
th
e
p
r
ev
io
u
s
o
n
e.
W
h
en
K
an
d
J
g
en
er
ate
r
an
d
o
m
clu
es,
b
u
t
K
s
h
o
u
ld
d
if
f
er
f
r
o
m
I
.
ca
n
h
an
d
le
th
e
av
ailab
ilit
y
o
f
a
r
ep
lace
m
en
t
p
o
wer
o
f
Xij
a
n
d
u
s
e
a
b
ee
to
v
is
u
ally
v
iew
th
e
co
m
p
ar
is
o
n
o
f
two
f
o
o
d
p
r
o
d
u
cts.
As
ca
n
b
e
s
ee
n
f
r
o
m
th
e
e
q
u
atio
n
s
m
en
t
io
n
ed
ab
o
v
e,
th
u
s
r
ed
u
cin
g
th
e
d
i
f
f
er
en
ce
b
etw
ee
n
th
e
p
a
r
am
eter
s
o
f
th
e
p
a
r
am
eter
s
Xij
an
d
XKJ,
th
u
s
d
i
s
tu
r
b
ed
o
n
th
e
Xij
p
o
s
itio
n
.
As
a
r
esu
lt,
th
e
s
ize
o
f
th
e
tem
p
ests
is
r
ed
u
ce
d
wh
en
s
ea
r
ch
i
n
g
f
o
r
th
e
o
p
tim
al
s
o
lu
tio
n
in
th
e
s
ea
r
ch
r
o
o
m
.
T
h
e
ab
a
n
d
o
n
ed
f
o
o
d
s
o
u
r
ce
o
f
b
ee
s
w
o
u
ld
h
av
e
b
ee
n
r
ep
lace
d
b
y
a
n
ew
f
o
o
d
s
ea
r
ch
s
o
u
r
ce
b
y
Sco
u
ts
.
T
h
e
b
eh
av
io
r
o
f
th
e
f
ee
d
s
ea
r
ch
is
em
u
lated
in
th
e
AB
C
alg
o
r
ith
m
b
y
r
an
d
o
m
ly
g
en
er
atin
g
a
p
o
wer
o
u
tlet
an
d
g
e
n
er
atin
g
an
ex
ch
an
g
e
o
f
a
d
is
co
n
n
ec
te
d
p
l
u
g
with
a
r
ep
lace
m
en
t
b
ase.
I
f
a
co
m
p
etitiv
e
ad
v
an
tag
e
ca
n
n
o
lo
n
g
er
b
e
in
cr
ea
s
ed
af
ter
a
n
u
m
b
er
o
f
c
y
cl
es,
th
e
n
u
tr
itio
n
al
s
o
u
r
ce
m
u
s
t b
e
ab
an
d
o
n
ed
.
T
h
e
d
ef
au
lt n
u
m
b
er
o
f
cy
cles c
alled
"lim
it" f
o
r
th
e
task
o
f
th
e
A
B
C
a
lg
o
r
ith
m
is
a
cr
itical
co
n
t
r
o
l p
ar
am
eter
.
I
f
th
e
s
o
u
r
ce
s
p
ec
if
ied
a
n
d
J
is
,
th
e
s
co
u
t
f
in
d
s
a
n
ew
f
o
o
d
s
o
u
r
ce
to
r
ep
lace
it.
T
h
is
m
eth
o
d
is
o
f
te
n
d
e
f
in
ed
b
ec
au
s
e
it
g
en
er
ates
ev
er
y
n
ew
VI
J
s
o
u
r
ce
p
o
s
itio
n
,
wh
i
ch
ev
alu
ates
th
e
ar
tific
ial
b
e
e
an
d
co
m
p
ar
e
s
its
p
h
y
s
ical
s
h
ap
e
with
th
e
p
r
ev
i
o
u
s
o
n
e.
I
f
th
e
n
ew
s
o
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r
ce
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f
f
o
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is
s
o
g
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o
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b
etter
th
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t
h
e
o
ld
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an
,
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e
o
ld
m
an
ca
n
b
e
r
ep
lace
d
in
its
m
e
m
o
r
y
.
Oth
e
r
wis
e,
h
e
h
o
ld
s
th
e
o
ld
m
an
in
h
is
m
em
o
r
y
.
As
y
o
u
ca
n
s
ee
f
r
o
m
th
e
p
r
ev
io
u
s
ex
p
lan
atio
n
,
t
h
e
AB
C
alg
o
r
ith
m
h
as
th
r
ee
cr
itical
co
n
tr
o
l
p
a
r
am
eter
s
:
th
e
n
u
m
b
er
o
f
f
o
o
d
s
o
u
r
ce
s
(
SN)
,
th
e
v
alu
e
o
f
th
e
lim
it ""
an
d
th
e
m
a
x
im
u
m
n
u
m
b
er
o
f
cy
cle
(
MCN)
.
a.
B
eg
in
b
y
p
o
p
u
latin
g
th
e
p
o
p
u
l
atio
n
o
f
s
o
lu
tio
n
s
x
ij,
I
=
1
,
2
,
.
.
.
.
,
SN,
j =
1
,
2
,
.
.
.
.
,
D.
b.
Ass
es
s
th
e
p
o
p
u
latio
n
'
s
f
itn
ess
.
c.
Set th
e
C
y
cle
to
1
d.
Dev
elo
p
n
ew
x
ij so
lu
tio
n
s
f
o
r
th
e
em
p
lo
y
e
d
b
ee
s
an
d
ass
ess
th
eir
f
itn
ess
e.
Fo
r
th
e
em
p
lo
y
ed
b
ee
s
,
u
s
e
th
e
g
r
ee
d
y
s
elec
tio
n
p
r
o
ce
s
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l
Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
4
7
–
354
352
f.
Fo
r
ea
ch
s
o
lu
tio
n
Vij,
ca
lcu
late
th
e
p
r
o
b
ab
ilit
y
v
alu
es Pij.
g.
Fro
m
th
e
s
o
lu
tio
n
s
x
i
p
i
ck
ed
b
ettin
g
o
n
Pi,
cr
ea
te
f
r
esh
s
o
lu
ti
o
n
s
x
ij f
o
r
o
b
s
er
v
e
r
s
an
d
ass
ess
th
eir
f
itn
ess
.
h.
Fo
r
th
e
s
p
ec
tato
r
b
ee
s
,
u
s
e
th
e
g
r
ee
d
y
s
elec
tio
n
tech
n
iq
u
e.
i.
I
d
en
tify
a
n
ab
a
n
d
o
n
ed
r
esp
o
n
s
e
f
o
r
th
e
s
co
u
t a
n
d
r
ep
lace
it
with
a
r
an
d
o
m
ly
g
e
n
er
ated
s
o
l
u
tio
n
x
ij.
j.
W
r
ite
d
o
w
n
th
e
m
o
s
t e
f
f
icien
t
s
o
lu
tio
n
.
k.
C
y
cle
is
eq
u
al
to
C
y
cle+
1
.
l.
R
ep
ea
t step
s
(
4
)
th
r
o
u
g
h
(
1
1
)
u
n
til C
y
cle
=
MCN is r
ea
ch
ed
.
m.
Sh
o
w
th
e
b
est s
o
lu
tio
n
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
ar
tific
ial
b
ee
c
o
lo
n
y
alg
o
r
ith
m
was
test
ed
o
n
th
e
b
u
s
s
y
s
tem
s
I
E
E
E
3
3
an
d
I
E
E
E
1
1
8
t
o
s
ee
h
o
w
ef
f
ec
tiv
e
it
is
.
T
h
e
A
B
C
o
p
tim
izatio
n
m
eth
o
d
was
u
s
ed
in
th
e
MA
T
L
AB
7
.
1
s
o
f
twar
e
f
o
r
th
is
p
r
o
b
lem
,
an
d
all
p
r
o
g
r
a
m
s
wer
e
p
er
f
o
r
m
ed
o
n
a
3
.
0
0
GHz
GB
,
I
n
tel
C
o
r
e
2
Du
o
PC
R
AM
.
T
h
e
f
o
llo
win
g
wer
e
m
ea
s
u
r
ed
as test ca
s
e
s
:
C
ase
1
: I
n
th
is
ca
s
e,
th
e
GD
u
n
it to
p
r
o
v
id
e
o
n
ly
an
ac
tiv
e
s
u
p
p
ly
,
ie
th
e
p
o
wer
f
ac
to
r
o
f
t
h
e
u
n
it.
C
ase
2
:
I
n
th
is
ca
s
e,
t
h
e
DG
u
n
it
to
g
en
er
ate
ac
tiv
e
en
er
g
y
th
at
r
ea
ctiv
ates
th
e
m
ain
ten
an
ce
o
f
a
p
o
wer
f
ac
to
r
o
f
0
.
8
.
T
h
ese
two
test
ca
s
es
ar
e
ca
r
ef
u
lly
e
x
am
in
ed
,
an
d
t
h
e
r
esu
lts
ar
e
co
m
p
ar
ed
an
d
c
o
n
tr
asted
with
AB
C
o
p
tim
izatio
n
.
3
.
1
.
Co
ns
t
a
nt
m
o
del
I
n
th
is
m
o
d
el
,
b
o
th
t
h
e
lo
ad
d
em
an
d
o
n
th
e
n
etwo
r
k
a
n
d
th
e
p
o
wer
o
u
tp
u
t
o
f
th
e
DGs
to
b
e
in
s
talled
ar
e
co
n
s
id
er
ed
to
b
e
c
o
n
s
tan
t.
3
.
1
.
1
.
Resul
t
s
f
o
r
3
3
bu
s
ra
dia
l dis
t
ributio
n sy
s
t
em
T
h
e
p
r
o
p
o
s
ed
tech
n
i
q
u
e
is
b
e
in
g
test
ed
u
s
in
g
th
e
s
tan
d
ar
d
I
E
E
E
3
3
-
b
u
s
s
y
s
tem
as
a
f
ir
s
t
ex
am
p
le.
T
h
e
s
y
s
tem
'
s
to
tal
ac
tu
al
an
d
r
ea
ctiv
e
p
o
wer
lo
ad
s
ar
e
3
.
7
2
MW
an
d
2
.
3
MV
Ar
,
r
esp
ec
tiv
ely
.
An
attem
p
t
was
m
ad
e
to
d
ep
lo
y
DG
at
d
if
f
e
r
en
t
lo
ca
tio
n
s
i
n
o
r
d
er
to
e
x
am
in
e
th
e
e
f
f
ec
t
o
f
DG
p
lac
em
en
t
at
m
u
ltip
le
lo
ca
tio
n
s
.
Sin
g
le
DG
pla
ce
m
ent
a
nd
T
wo
DG
P
la
ce
m
ent
T
h
e
m
ax
im
u
m
s
ize
o
f
s
in
g
le
DG
u
n
it
is
f
ix
ed
as
3
.
5
MV
A.
T
h
e
test
r
esu
lt
s
f
o
r
b
o
th
ca
s
es
ar
e
a
s
Fig
u
r
e
1
an
d
Fig
u
r
e
2
.
Fig
u
r
e
1
.
Vo
ltag
e
Pro
f
ile
o
f
3
3
b
u
s
s
y
s
tem
f
o
r
s
in
g
le
DG
p
lace
m
en
t
Fig
u
r
e
2
.
Vo
ltag
e
Pro
f
ile
o
f
3
3
b
u
s
s
y
s
tem
f
o
r
two
DG
p
lace
m
en
t
T
h
e
lo
ad
-
f
lo
w
tech
n
iq
u
e
ca
lc
u
lated
s
y
s
tem
r
ea
l
p
o
wer
l
o
s
s
es
to
b
e
2
0
2
.
6
6
k
W
,
with
a
m
in
im
u
m
v
o
ltag
e
o
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9
1
3
1
p
.
u
.
T
h
e
tr
u
e
p
o
wer
lo
s
s
es
in
C
ase
1
an
d
C
ase
2
af
ter
th
e
in
s
tallatio
n
o
f
a
s
in
g
le
DG
wer
e
f
o
u
n
d
to
b
e
1
0
3
.
9
7
k
W
an
d
6
1
.
5
8
k
W
,
r
esp
ec
tiv
ely
.
E
v
en
t
h
e
v
o
ltag
e
m
ag
n
itu
d
es
im
p
r
o
v
ed
,
with
m
in
im
u
m
v
alu
es o
f
0
.
9
4
0
7
p
.
u
an
d
0
.
9
5
8
6
p
.
u
in
C
ase
1
an
d
C
ase
2
,
r
esp
ec
tiv
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
tima
l p
la
ce
men
t a
n
d
s
iz
in
g
o
f d
is
tr
ib
u
ted
g
en
era
tio
n
f
o
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lo
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min
imiz
a
tio
n
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s
in
g
…
(
Ma
d
h
u
V
a
la
va
la
)
353
T
h
e
lo
ad
-
f
lo
w
tech
n
iq
u
e
ca
lc
u
lated
s
y
s
tem
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ea
l
p
o
wer
l
o
s
s
es
to
b
e
2
0
2
.
6
6
k
W
,
with
a
m
in
im
u
m
v
o
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e
o
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0
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9
1
3
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.
u
.
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h
e
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al
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o
wer
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ase
1
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d
C
ase
2
af
ter
th
e
in
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ta
llatio
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f
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e
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o
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n
d
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e
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5
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9
9
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d
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ag
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n
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.
u
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d
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4
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.
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ase
1
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d
C
ase
2
,
r
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Fig
u
r
es
1
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d
2
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em
o
n
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tr
ate
th
e
v
o
ltag
e
p
r
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f
ile
o
f
a
3
3
b
u
s
s
y
s
tem
with
a
s
in
g
le
DG
p
lace
m
e
n
t a
n
d
a
d
o
u
b
le
DG
p
lace
m
en
t
,
r
esp
ec
tiv
ely
.
3
.
1
.
2
.
Resul
t
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f
o
r
a
ra
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l dis
t
ributio
n sy
s
t
em
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h 1
1
8
bu
s
es
An
I
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E
E
1
1
8
-
b
u
s
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ed
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o
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er
ex
am
p
le
f
o
r
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v
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atin
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ested
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e
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icac
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.
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y
s
tem
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s
to
tal
ac
tu
al
an
d
r
ea
ctiv
e
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o
wer
lo
a
d
s
ar
e
2
2
.
7
1
GW
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d
1
7
.
0
4
GVAr
,
r
esp
ec
ti
v
ely
.
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h
e
lo
ad
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f
lo
w
tech
n
iq
u
e
ca
lc
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lated
s
y
s
tem
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l
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o
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es
to
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1
2
9
8
.
3
8
k
W
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m
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im
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m
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.
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e
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al
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wer
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a
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e
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ase
2
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ter
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n
d
9
2
1
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ec
tiv
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v
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e
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o
ltag
e
m
a
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im
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im
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m
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al
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0
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3
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.
u
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d
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0
5
3
p
.
u
in
C
ase
1
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d
C
ase
2
,
r
esp
ec
tiv
ely
.
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h
e
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f
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w
tech
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e
c
alc
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lated
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s
tem
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l
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wer
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8
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m
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.
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m
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is
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o
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e
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l
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o
wer
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s
s
es
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C
ases
1
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d
2
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e
d
eter
m
in
ed
to
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e
8
0
5
.
5
5
k
W
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d
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8
7
.
5
1
k
W
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y
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v
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v
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d
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m
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.
u
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d
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0
5
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.
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ase
1
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ase
2
,
r
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Fig
u
r
e
3
an
d
Fig
u
r
e
4
d
em
o
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ate
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e
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o
ltag
e
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il
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r
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le
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p
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t
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le
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p
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en
t,
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.
Fig
u
r
e
3
.
Vo
ltag
e
Pro
f
ile
o
f
1
1
8
b
u
s
s
y
s
tem
f
o
r
s
in
g
le
DG
Fig
u
r
e
4
.
Vo
ltag
e
Pro
f
ile
o
f
1
1
8
b
u
s
s
y
s
tem
f
o
r
two
DG
4.
CO
NCLU
SI
O
N
T
h
e
ar
tific
ial
b
ee
c
o
lo
n
y
ap
p
r
o
ac
h
is
u
s
ed
in
th
is
s
tu
d
y
to
s
u
g
g
est
a
p
r
o
b
ab
ilis
tic
s
o
lu
tio
n
f
o
r
th
e
o
p
tim
al
p
lace
m
en
t
an
d
s
izin
g
o
f
s
ev
er
a
l
d
is
tr
ib
u
ted
g
en
er
at
io
n
s
.
T
h
e
r
esu
lts
wer
e
co
n
f
ir
m
ed
u
s
in
g
I
E
E
E
-
3
3
an
d
I
E
E
E
-
1
1
8
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
test
e
q
u
ip
m
e
n
t.
I
n
t
h
is
s
tu
d
y
,
two
s
ce
n
ar
io
s
wer
e
e
x
am
in
ed
:
o
n
e
with
o
n
ly
r
ea
l
p
o
wer
in
jectio
n
an
d
th
e
o
th
er
with
b
o
th
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
in
jectio
n
.
W
ith
th
e
in
s
tallatio
n
o
f
DGs,
we
s
ee
a
r
ed
u
ctio
n
in
t
h
e
o
v
er
all
r
ea
l
p
o
wer
lo
s
s
o
f
th
e
s
y
s
tem
in
b
o
th
s
ce
n
ar
io
s
.
W
h
en
th
e
DGs
ar
e
co
n
tr
o
lled
to
in
ject
b
o
th
ac
tu
al
an
d
r
ea
ctiv
e
p
o
wer
,
th
e
lo
s
s
r
ed
u
ctio
n
is
o
b
s
er
v
e
d
to
b
e
g
r
ea
ter
.
T
h
e
p
r
o
b
a
b
ilis
tic
ap
p
r
o
a
c
h
s
h
o
ws
th
at
t
h
e
s
izes
o
f
th
e
DGs
t
o
b
e
in
s
talled
a
r
e
r
e
d
u
ce
d
f
o
r
alm
o
s
t
th
e
s
am
e
p
er
ce
n
tag
e
l
o
s
s
r
ed
u
ctio
n
w
h
e
n
co
m
p
a
r
ed
with
th
e
s
itu
atio
n
wh
er
e
th
e
lo
a
d
an
d
DG
o
u
t
p
u
t
ar
e
co
n
s
id
er
e
d
to
b
e
co
n
s
tan
t.
I
n
t
h
is
wo
r
k
,
I
E
E
E
test
s
y
s
tem
s
h
av
e
b
ee
n
co
n
s
id
er
ed
t
o
v
alid
ate
a
n
d
p
r
o
v
e
t
h
e
s
u
b
s
tan
ce
o
f
th
e
p
r
o
p
o
s
ed
p
r
o
b
ab
ilis
tic
ap
p
r
o
a
ch
.
T
h
is
ca
n
b
e
e
x
ten
d
e
d
to
l
iv
e
r
u
r
al
d
is
tr
ib
u
tio
n
f
ee
d
e
r
s
an
d
ca
n
b
e
u
tili
ze
d
s
u
cc
ess
f
u
lly
to
r
ed
u
ce
th
e
b
u
r
d
en
o
n
th
e
s
u
b
s
tatio
n
as we
ll a
s
o
n
th
e
tr
an
s
m
is
s
io
n
lin
e.
RE
F
E
R
E
NC
E
S
[1
]
Y.
M
.
Atwa
,
a
n
d
E.
F
.
El
-
S
a
a
d
a
n
y
,
"
P
r
o
b
a
b
i
li
stic
a
p
p
r
o
a
c
h
fo
r
o
p
ti
m
a
l
a
ll
o
c
a
ti
o
n
o
f
wi
n
d
-
b
a
se
d
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
i
n
d
istr
ib
u
ti
o
n
sy
ste
m
s,"
IET
Ren
e
w,
Po
we
r
Ge
n
e
r
.
,
v
o
l.
5
,
n
o
.
1
,
p
p
.
7
9
-
8
8
,
2
0
1
1
,
d
o
i:
1
0
.
1
0
4
9
/i
e
t
-
rp
g
.
2
0
0
9
.
0
0
1
1
[2
]
F
.
S
.
Ab
u
-
Mo
u
ti
a
n
d
M
.
E.
El
-
Ha
wa
ry
,
"
Op
ti
m
a
l
d
istri
b
u
te
d
g
e
n
e
ra
ti
o
n
a
ll
o
c
a
ti
o
n
a
n
d
siz
i
n
g
in
d
istri
b
u
ti
o
n
sy
ste
m
s
v
ia
a
rti
ficia
l
b
e
e
c
o
lo
n
y
a
lg
o
rit
h
m
,
"
in
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Po
we
r
De
li
v
e
ry
,
v
o
l
.
2
6
,
n
o
.
4
,
p
p
.
2
0
9
0
-
2
1
0
1
,
Oc
t.
2
0
1
1
,
d
o
i:
1
0
.
1
1
0
9
/T
P
WRD.
2
0
1
1
.
2
1
5
8
2
4
6
.
[3
]
J.
O.
Kim
,
S
.
W.
Na
m
,
S
.
K.
P
a
r
k
,
a
n
d
C
.
S
in
g
h
"
Disp
e
rse
d
g
e
n
e
ra
ti
o
n
p
lan
n
i
n
g
u
sin
g
imp
r
o
v
e
d
He
re
fo
rd
Ra
n
c
h
a
lg
o
rit
h
m
,
"
E
lec
tric P
o
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l
.
4
7
,
n
o
.
1
,
p
p
.
6
7
8
–
6
8
3
,
1
9
9
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l
Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
4
7
–
354
354
[4
]
G
a
n
d
o
m
k
a
r,
M
.
Va
k
il
ia
n
a
n
d
M
.
Eh
sa
n
,
"
O
p
ti
m
a
l
d
istr
ib
u
ted
g
e
n
e
ra
ti
o
n
a
ll
o
c
a
ti
o
n
i
n
d
istri
b
u
ti
o
n
n
e
two
rk
u
sin
g
He
re
fo
rd
Ra
n
c
h
a
lg
o
rit
h
m
,
"
2
0
0
5
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
El
e
c
trica
l
M
a
c
h
in
e
s a
n
d
S
y
ste
ms
,
2
0
0
5
,
p
p
.
9
1
6
-
9
1
8
v
o
l.
2
,
d
o
i:
1
0
.
1
1
0
9
/ICE
M
S
.
2
0
0
5
.
2
0
2
6
7
8
.
[5
]
T.
G
riff
in
,
K.
T
o
m
so
v
ic,
D.
S
e
c
re
st
a
n
d
A.
Law
,
"
P
lac
e
m
e
n
t
o
f
d
isp
e
rse
d
g
e
n
e
ra
ti
o
n
sy
ste
m
s
fo
r
r
e
d
u
c
e
d
lo
ss
e
s,
"
Pro
c
e
e
d
in
g
s
o
f
th
e
3
3
r
d
An
n
u
a
l
Ha
wa
ii
I
n
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
S
y
ste
m
S
c
ien
c
e
s
,
2
0
0
0
,
p
p
.
9
p
p
.
-
,
d
o
i
:
1
0
.
1
1
0
9
/HIC
S
S
.
2
0
0
0
.
9
2
6
7
7
3
.
[6
]
K.
Na
ra
,
Y.
Ha
y
a
sh
i,
K.
I
k
e
d
a
a
n
d
T.
As
h
iza
wa
,
"
A
p
p
l
ica
ti
o
n
o
f
tab
u
se
a
rc
h
to
o
p
ti
m
a
l
p
lac
e
m
e
n
t
o
f
d
istri
b
u
ted
g
e
n
e
ra
to
rs,"
2
0
0
1
IEE
E
P
o
w
e
r
En
g
i
n
e
e
rin
g
S
o
c
iety
W
in
t
e
r
M
e
e
ti
n
g
.
Co
n
fer
e
n
c
e
Pro
c
e
e
d
in
g
s
(C
a
t.
No
.
0
1
CH3
7
1
9
4
)
,
2
0
0
1
,
p
p
.
9
1
8
-
9
2
3
v
o
l
.
2
,
d
o
i:
1
0
.
1
1
0
9
/P
ES
W.
2
0
0
1
.
9
1
6
9
9
5
.
[7
]
J.
A.
G
re
a
tb
a
n
k
s,
D.
H.
P
o
p
o
v
i
c
,
M
.
Be
g
o
v
ic,
A.
P
re
g
e
l
j
a
n
d
T.
C.
G
re
e
n
,
"
On
o
p
ti
m
iza
ti
o
n
f
o
r
se
c
u
rit
y
a
n
d
re
li
a
b
il
it
y
o
f
p
o
we
r
sy
ste
m
s
with
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
,
"
2
0
0
3
IEE
E
B
o
lo
g
n
a
P
o
we
r
T
e
c
h
Co
n
fer
e
n
c
e
Pro
c
e
e
d
in
g
s
,
2
0
0
3
,
p
p
.
8
p
p
.
v
o
l
.
1
-
,
d
o
i:
1
0
.
1
1
0
9
/P
TC
.
2
0
0
3
.
1
3
0
4
1
1
1
.
[8
]
T.
K.
A.
Ra
h
m
a
n
,
S
.
R.
A.
Ra
h
im
a
n
d
I.
M
u
sirin
,
"
Op
ti
m
a
l
a
ll
o
c
a
ti
o
n
a
n
d
siz
i
n
g
o
f
e
m
b
e
d
d
e
d
g
e
n
e
ra
t
o
rs,
"
Pro
c
e
e
d
in
g
s.
Na
ti
o
n
a
l
P
o
we
r a
n
d
En
e
rg
y
Co
n
fer
e
n
c
e
,
2
0
0
4
,
p
p
.
2
8
8
-
2
9
4
,
d
o
i:
1
0
.
1
1
0
9
/
P
ECON.2
0
0
4
.
1
4
6
1
6
6
0
.
[9
]
G
.
Ce
ll
i
a
n
d
F
.
P
il
o
,
"
O
p
ti
m
a
l
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
a
ll
o
c
a
ti
o
n
in
M
V
d
istri
b
u
ti
o
n
n
e
two
r
k
s,
"
PICA
2
0
0
1
.
In
n
o
v
a
ti
v
e
C
o
mp
u
ti
n
g
fo
r
Po
we
r
-
E
lec
tric
En
e
rg
y
M
e
e
ts
th
e
M
a
rk
e
t.
2
2
n
d
IEE
E
Po
we
r
E
n
g
i
n
e
e
rin
g
S
o
c
iety
.
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
P
o
we
r
In
d
u
stry
Co
mp
u
ter
Ap
p
li
c
a
ti
o
n
s
(Ca
t
.
No
.
0
1
CH
3
7
1
9
5
)
,
2
0
0
1
,
p
p
.
8
1
-
8
6
,
d
o
i
:
1
0
.
1
1
0
9
/
P
ICA.2
0
0
1
.
9
3
2
3
2
3
.
[1
0
]
G
.
Ce
ll
i
a
n
d
F
.
P
il
o
,
"
M
V
n
e
tw
o
r
k
p
lan
n
i
n
g
u
n
d
e
r
u
n
c
e
rtain
ti
e
s
o
n
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
p
e
n
e
tratio
n
,
"
2
0
0
1
P
o
we
r
En
g
i
n
e
e
rin
g
S
o
c
iety
S
u
mm
e
r
M
e
e
ti
n
g
.
Co
n
fer
e
n
c
e
Pro
c
e
e
d
in
g
s
(
Ca
t.
N
o
.
0
1
CH3
7
2
6
2
)
,
2
0
0
1
,
p
p
.
4
8
5
-
4
9
0
v
o
l.
1
,
d
o
i:
1
0
.
1
1
0
9
/P
E
S
S
.
2
0
0
1
.
9
7
0
0
7
4
.
[1
1
]
G.
Ca
rp
in
e
ll
i,
G
.
Ce
ll
i,
F
.
P
il
o
a
n
d
A.
Ru
ss
o
,
"
Distri
b
u
te
d
g
e
n
e
r
a
ti
o
n
sit
in
g
a
n
d
siz
in
g
u
n
d
e
r
u
n
c
e
rtain
ty
,
"
2
0
0
1
IEE
E
P
o
rto
P
o
we
r T
e
c
h
Pr
o
c
e
e
d
in
g
s (C
a
t.
N
o
.
0
1
EX
5
0
2
)
,
2
0
0
1
,
p
p
.
7
p
p
.
v
o
l.
4
-
,
d
o
i:
1
0
.
1
1
0
9
/P
TC.
2
0
0
1
.
9
6
4
8
5
6
.
[1
2
]
R.
Ka
rk
i
a
n
d
R.
Bil
li
n
to
n
,
"
Co
st
-
e
ffe
c
ti
v
e
win
d
e
n
e
rg
y
u
ti
li
z
a
ti
o
n
fo
r
re
li
a
b
le
p
o
we
r
su
p
p
l
y
,
"
i
n
IE
EE
T
ra
n
sa
c
ti
o
n
s
o
n
E
n
e
rg
y
Co
n
v
e
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9
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3
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a
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4
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.
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.
[1
5
]
A.
S
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rizz
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.
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6
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[1
7
]
B.
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.
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[1
8
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lag
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[1
9
]
L.
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1
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[2
2
]
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.
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.
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R.
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.
[2
3
]
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.
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s,
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m
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me
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.
[2
4
]
A.
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9
9
6
.
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