Inter
national
J
our
nal
of
A
pplied
P
o
wer
Engineering
(IJ
APE)
V
ol.
14,
No.
2,
June
2025,
pp.
319
∼
327
ISSN:
2252-8792,
DOI:
10.11591/ijape.v14.i2.pp319-327
❒
319
Optimal
placement
of
DGs
in
a
multi-feed
radial
distrib
ution
system
using
actor
-critic
lear
ning
algorithm
Neelakanteshwar
Rao
Battu
1
,
Sur
ender
Reddy
Salkuti
2
1
Department
of
Electrical
and
Electronics
Engineering,
V
allurupalli
Nagesw
ara
Rao
V
ignana
Jyothi
Institute
of
Engineering
and
T
echnology
(VNR
VJIET),
Hyderabad,
India
2
Department
of
Railroad
and
Electrical
Engineering,
W
oosong
Uni
v
ersity
,
Daejeon,
Republic
of
K
orea
Article
Inf
o
Article
history:
Recei
v
ed
Jan
3,
2023
Re
vised
No
v
6,
2024
Accepted
No
v
28,
2024
K
eyw
ords:
Actor
-critic
learning
Distrib
uted
generation
Distrib
ution
system
Netw
ork
reconguration
Reinforcement
learning
ABSTRA
CT
Multi-feed
radial
distrib
ution
systems
are
used
to
reduce
the
losses
in
the
sys-
tem
using
reconguration
techniques.
Reconguration
can
reduce
the
losses
in
the
system
only
to
a
certain
e
xtent.
Introduction
of
distri
b
ut
ed
generators
has
v
astly
impro
v
ed
the
performance
of
distrib
ution
systems.
Distrib
uted
generators
can
be
used
for
reduction
of
loss,
the
impro
v
ement
of
the
v
oltage
prole,
and
reliability
enhancement.
Distrib
ution
generators
play
a
vital
role
in
reducing
the
losses
in
the
distrib
ution
system.
Placement
of
distrib
uted
generators
in
a
multi-
feed
system
is
a
comple
x
task
to
be
solv
ed
using
classical
optimization
methods.
Classical
optimization
techniques
may
sometimes
f
ail
to
pro
vide
a
con
v
er
ged
so-
lution.
Installation
of
distrib
uted
generators
at
suitable
locations
in
a
multi-feed
system
is
found
in
this
pape
r
using
the
actor
-critic
learning
algorithm.
Actor
-
critic
learning
approach
uses
temporal
dif
ference
error
as
a
signal
in
making
judgements
re
g
arding
actions
to
be
tak
en
for
future
states
in
ac
cordance
with
re
w
ards
that
ha
v
e
been
obtained
by
applying
the
present
polic
y
.
The
approach
is
applied
to
a
standard
16-b
us
distrib
ution
system
for
reduction
of
system
losses,
and
the
results
are
discussed.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Surender
Reddy
Salkuti
Department
of
Railroad
and
Electrical
Engineering,
W
oosong
Uni
v
ersity
Jayang-dong,
Dong-gu,
Daejeon
34606,
Republic
of
K
orea
Email:
surender@wsu.ac.kr
1.
INTR
ODUCTION
Distrib
uted
generation
(DG)
has
been
playing
a
vital
role
in
the
electric
po
wer
system
for
the
pas
t
fe
w
years
[1].
It
has
led
to
se
v
eral
benets
lik
e
en
vironmenta
l
protection
in
case
of
rene
w
able
DG,
deferment
of
feeder
upgradation
under
load
gro
wth,
v
oltage
prole
enhancement,
reduction
in
losses,
and
in
reliability
enhancement
of
the
system
[2].
An
e
xtensi
v
e
research
has
been
made
till
no
w
for
single
DG
placement
,
and
relati
v
ely
little
w
ork
has
been
done
in
the
case
of
multiple
DG
placement.
DG
placement
using
a
fuzzy
logic
approach
has
been
done
in
[3].
Pre
vious
study
[4],
the
optimal
placement
of
DGs
in
a
microgrid
has
been
performed.
Probabilistic
placement
of
DG
has
been
performed
in
[5]
considering
uncertainties.
DG
planning
using
the
enhanced
search
group
algorithm
is
done
in
[6].
DG
planning
using
a
Monte
Carlo
simulation
has
been
done
in
[7].
Distrib
ution
system
planning
to
minimize
the
cost
of
operation,
considering
reliability
aspects,
has
been
proposed
in
this
w
ork.
A
mix
ed
inte
ger
linear
programming
(MILP)
model
for
optimal
placement
of
DGs
along
with
switches
and
tie-lines
is
proposed
in
[8].
An
algorithm
for
the
enhancement
of
netw
ork
resilience
has
been
introduced
in
[9].
An
articial
hum-
mingbird
algorithm
for
optimal
placement
of
rene
w
able
sources
is
presented
in
[10].
Netw
ork
reconguration
J
ournal
homepage:
http://ijape
.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
320
❒
ISSN:
2252-8792
of
radial
distrib
ution
systems
for
the
enhancement
of
v
oltage
has
been
discussed
in
[11].
An
optimal
placement
of
DGs
for
the
enhancement
of
reliability
has
been
discussed
in
[12].
Optimal
placement
of
DGs
considering
the
CIGRE
benchmark
has
been
e
xplained
in
[13].
Optimal
placement
of
DG
considering
netw
ork
recon-
guration
for
reliability
impro
v
ement
is
dis
cussed
in
[14].
Optimal
placement
of
a
wind
f
arm
for
reliability
enhancement
is
sho
wn
in
[15].
Optimal
placement
of
DG
for
stability
impro
v
ement
is
discussed
in
[16].
Optimal
placement
of
tie-lines
and
DGs
to
minimize
post-outage
operations
is
disc
ussed
[17].
Opti-
mal
placement
of
rene
w
able
sources
in
a
microgrid
is
discussed
in
[18].
The
result
in
[19],
a
method
to
impro
v
e
distrib
ution
system
reliability
,
has
been
discussed
using
the
distr
ib
uted
generators
a
v
ailable
in
the
system.
A
multi-objecti
v
e
planning
of
DGs
and
rene
w
ables
in
a
microgrid
is
proposed
in
[20].
A
mix
ed
inte
ger
linear
programming
(MILP)
technique
for
optimal
placement
of
char
ging
stations
is
proposed
in
[21].
Dynamic
net-
w
ork
reconguration
in
coordinat
ion
with
switchable
capacitor
banks
has
been
discussed
in
[22].
Simultaneous
placement
of
shunt
capacitors
and
DG
units
has
been
proposed
in
[23].
Harris
Ha
wks’
optimization
for
optimal
placement
of
DGs
is
discussed
in
[24].
Rene
w
able
DG
inte
gration
to
grid
has
been
discussed
in
[25].
DG
place-
ment
considering
a
lar
ge
scale
disturbance
is
discussed
in
[26].
Optimal
sizing
and
placement
of
rene
w
ables
using
metaheuristic
technique
has
been
discussed
in
[27].
Most
of
the
w
ork
a
v
ailable
in
the
literature
is
on
single
DG
placement,
and
mostly
heuristic
techniques
ha
v
e
been
used.
No
v
elty
in
this
paper
is
multiple
DG
placement
in
a
multi-feed
system
and
solving
the
problem
using
a
no
v
el
approach
called
actor
-critic
(A
C)
learning
algorithm.
A
C
is
an
e
xtension
to
the
reinforcement
learning
(RL)
algorithm,
which
is
based
on
the
Mark
o
v
decision
process
(MDP)
[28].
RL
can
be
e
xpected
to
gi
v
e
gratifying
re
sults
in
the
case
of
a
comple
x
problem
ha
ving
a
lar
ge
number
of
states.
The
remaining
content
of
the
paper
is
di
vided
into
the
follo
wing
s
ections:
i)
Section
2
brief
about
the
proposed
methodology;
ii)
Section
3
deals
with
problem
formulation;
iii)
Section
4
describes
the
solution
methodology;
i
v)
Section
5
follo
wed
by
a
discussion
on
the
results;
v)
Section
6
gi
v
es
the
conclusion
of
the
w
ork.
2.
REINFORCEMENT
LEARNING
Reinforcement
learning
(RL)
is
a
goal-directed
method
that
tackles
a
problematic
situation
through
interaction.
It
basically
consists
of
an
agent
and
an
en
vironment.
The
learner
and
decision
mak
er
is
kno
wn
as
the
agent,
and
e
v
erything
outside
it
is
kno
wn
as
the
en
vironment.
RL
maps
the
situations
to
actions
to
enhance
the
re
w
ard
signal.
During
the
learning
process,
the
agent
gets
information
about
the
present
en
vironment’
s
state,
s
t
∈
S
at
time
step
‘
t
’.
On
the
basis
of
this
state
agent
decides
the
action,
a
t
∈
A
(
s
t
)
to
be
tak
en
and
recei
v
es
a
re
w
ard,
r
t
+1
one
time
step
later
and
enters
into
a
ne
w
state
s
t
+1
.
This
is
sho
wn
in
Figure
1.
Figure
1.
Architecture
of
reinforcement
learning
This
process
of
the
agent
deciding
the
action
to
be
tak
en,
the
en
vironment
reciprocating
to
these
actions
and
presenting
ne
w
re
w
ards
and
states
tak
es
place
for
each
time
step
and
during
each
time
step,
the
agent
does
mapping
between
the
present
state
and
the
probability
of
deciding
each
possible
action
when
the
agent
is
in
this
state.
This
mapping
i
s
kno
wn
as
Agent’
s
Polic
y
,
represented
as
π
(
s
t
,
a
t
)
.
Agent,
based
on
the
e
xperience
changes
its
polic
y
.
The
objecti
v
e
of
the
RL
agent
is
to
maximize
the
sum
of
re
w
ards
o
v
er
the
long
run.
These
reinforcement
learning
algorithms
use
the
v
alue
function,
V
π
(
s
)
,
to
estimate
“ho
w
good
it
is
for
the
agent
to
tak
e
a
particular
action
for
a
present
state”.
V
π
(
s
)
represents
the
e
xpected
v
alue
of
return
when
the
system
be
gins
in
state
s
and
then
follo
ws
a
polic
y
π
.
Mathematically
,
this
can
be
represented
as
(1).
V
π
(
s
)
=
E
π
{
R
t
|
s
t
=
s
}
=
E
π
{
∞
X
j
=0
γ
k
r
t
+
j
+1
|
s
t
=
s
}
(1)
Int
J
Appl
Po
wer
Eng,
V
ol.
14,
No.
2,
June
2025:
319–327
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Appl
Po
wer
Eng
ISSN:
2252-8792
❒
321
Where,
V
π
(
s
)
is
the
v
alue
function
of
a
polic
y
π
,
E
π
is
the
e
xpected
v
alue
for
a
gi
v
en
polic
y
,
γ
is
the
discount
f
actor
,
and
r
t
+
j
+1
is
the
re
w
ard
g
ained
when
agent
mo
v
es
from
state
s
t
+
j
to
state
s
t
+
j
+1
.
Solving
a
problem
using
reinforcement
learning
in
v
olv
es
nding
an
optimal
v
alue
function,
which
is
e
xpressed
as
(2).
V
∗
(
s
)
=
max
(
V
π
(
s
))
,
∀
s
∈
S
(2)
Where,
V
∗
(
s
)
is
the
optimal
v
alue
function.
3.
PR
OPOSED
METHODOLOGY
The
DG
placement
problem
in
this
w
ork
is
solv
ed
using
the
actor
-critic
(A
C)
learning
method.
A
C
learning
method
is
an
e
xtension
to
the
reinforcement
learning
problem.
A
C
learning
embeds
reinforcement
learning
in
it.
In
actor
-critic
architecture,
the
polic
y
selects
acti
ons,
hence,
it
is
termed
as
an
actor
,
and
the
estimated
v
alue
function
i
s
termed
as
the
critic,
as
it
criticizes
the
actions
tak
en
by
the
polic
y
.
Learning
is
done
in
an
on-polic
y
manner
,
the
critic
must
learn
about
and
must
criticize
the
polic
y
that
is
presently
follo
wed
by
the
actor
.
The
criticism
made
is
in
the
form
of
temporal
dif
ference
(TD)
error
,
hence,
this
method
comes
under
temporal
dif
ference
methods.
TD
error
acts
as
a
scalar
signal
for
the
output
gi
v
en
by
critic
and
helps
in
learning
process
that
tak
es
place
between
actor
and
critic
as
sho
wn
in
Figure
2.
Figure
2.
Architecture
of
actor
-critic
learning
Mathematically
TD
error
,
δ
t
is
gi
v
en
as
(3).
δ
t
=
r
t
+1
+
γ
V
(
s
t
+1
)
−
V
(
s
t
)
(3)
Where,
δ
t
is
temporal
dif
ference
and
r
t
+1
is
the
re
w
ard
g
ained
when
agent
mo
v
es
from
s
t
to
s
t
+1
state.
If
TD
error
is
positi
v
e,
the
tendenc
y
to
select
an
action
a
t
in
future
should
be
strengthened
and
if
it
is
ne
g
ati
v
e
the
tendenc
y
to
select
an
action
a
t
in
future
should
be
weak
ened.
This
is
done
by
updating
the
tendenc
y
as
(4).
p
(
s
t
,
a
t
)
←
p
(
s
t
,
a
t
)
+
β
δ
t
(4)
Where,
p
(
s
t
,
a
t
)
is
the
tendenc
y
to
select
an
action
a
t
in
future
when
state
is
s
t
and
β
is
the
step
size
parameter
.
Polic
y
is
e
v
aluated
using
Gibbs
softmax
method
as
(5).
π
t
(
s,
a
)
=
e
p
(
s,a
)
B
X
b
=1
e
p
(
s,b
)
(5)
Where,
π
t
(
s,
a
)
is
the
polic
y
corresponding
to
state
s
t
and
action
a
t
.
The
state
v
alues
are
updated
as
(6).
Optimal
placement
of
DGs
in
a
multi-feed
r
adial
distrib
ution
system
...
(Neelakanteshwar
Rao
Battu)
Evaluation Warning : The document was created with Spire.PDF for Python.
322
❒
ISSN:
2252-8792
V
(
s
t
)
←
V
(
s
t
)
+
α
δ
t
(6)
Where,
α
is
the
step
size
parameter
.
4.
PR
OBLEM
FORMULA
TION
It
is
assumed
that
the
distrib
ution
system
and
the
DGs
to
be
placed
in
the
system
are
o
wned
by
the
same
utility
.
This
paper
focuses
on
nding
the
suitable
locations
(
D
G
l
oc
)
and
si
zes
(
D
G
siz
e
)
of
DGs
in
each
feeder
that
reduce
the
total
system
real
po
wer
loss
(TPL).
Mathematically
,
it
can
be
e
xpressed
as
(7).
M
in
{
T
P
L
(
D
G
l
oc
,
D
G
siz
e
)
}
(7)
Subject
to
belo
w
mentioned
constraints.
4.1.
V
oltage
constraints
Installation
of
DG,
though
reduces
real
po
wer
loss
compared
to
the
base
case,
sometimes
it
may
result
in
v
oltage
violations
at
some
b
uses.
Hence,
there
is
a
need
to
put
a
constraint
on
the
node
v
oltages.
Substation
b
uses
are
tak
en
as
r
eference,
and
v
oltages
at
thes
e
b
uses
are
maintained
at
1
p.u.
In
accordance
with
ANSI
C84.1,
v
oltages
at
remaining
b
uses
are
constrained
amid
0.95
p.u.
and
1.05
p.u.
[29],
[30].
That
can
be
e
xpressed
as
(8).
0
.
95
≤
V
n
≤
1
.
05
(8)
Where,
V
n
is
the
v
oltage
at
load
b
us
n
.
4.2.
Real
and
r
eacti
v
e
po
wer
balance
According
to
IEEE
Std
1547-2003
[31],
DG
connected
in
the
distrib
ution
system
should
operate
at
unity
po
wer
f
actor
.
Therefore,
the
real
po
wer
consumed
by
load
and
losses
in
each
feeder
is
fed
from
grid
and
DG,
connected
to
the
respecti
v
e
feeder
,
whereas
reacti
v
e
po
wer
load
and
associated
losses
are
supplied
by
the
grid
alone.
Hence,
the
po
wer
balance
equations
for
real
and
reacti
v
e
po
wers
can
be
e
xpressed
as
(9)-(10).
P
g
r
id
m
+
P
D
G
m,n
=
P
l
oad
m
+
P
l
oss
m
(9)
and
Q
g
r
id
m
=
Q
l
oad
m
+
Q
l
oss
m
(10)
Where,
P
g
r
id
m
is
the
r
eal
po
wer
supplied
by
the
grid
to
feeder
m
,
P
D
G
m,n
is
MW
capacity
of
DG
placed
at
b
us
n
in
feeder
m
,
P
l
oad
m
is
the
real
po
wer
load
connected
to
feeder
m
,
P
l
oss
m
is
the
real
po
wer
loss
in
feeder
m
,
Q
g
r
id
m
is
the
reacti
v
e
po
wer
supplied
by
the
grid
to
feeder
m
,
Q
l
oad
m
is
the
reacti
v
e
po
wer
load
connected
to
feeder
m
,
and
Q
l
oss
m
is
reacti
v
e
po
wer
loss
in
feeder
m
.
4.3.
DG
po
wer
constraints
DG
solution
resulted
from
the
optimization
algorithm
should
be
a
positi
v
e
v
alue
and
it
should
be
a
less
than
a
maximum
v
alue.
Hence,
this
condition
can
be
e
xpressed
as
(11).
0
≤
P
D
G
m,n
≤
P
D
G
max
(11)
Where,
P
D
G
max
is
the
maximum
limit
of
P
D
G
.
5.
SOLUTION
METHODOLOGY
This
paper
discusses
multiple
DG
placements
in
a
multi
-feed
system.
The
objecti
v
e
is
to
place
a
DG
in
each
fe
eder
at
an
optimal
location
with
an
optimal
size
that
minimizes
the
total
system
losses.
In
case
of
a
multi-feed
system,
the
situations,
possible
load
in
each
feeder
,
and
the
actions
to
be
tak
en,
a
combination
of
DG
locations
and
sizes
of
it
in
each
feeder
,
will
increase
with
the
increase
in
the
size
of
the
system.
In
such
a
situation,
it
w
ould
be
better
to
use
a
technique
that
decides
on
the
solution
by
mapping
e
xisting
states
with
possible
act
ions.
The
reinforcement
algorithm
m
aps
the
s
tates
to
actions
and
maximizes
the
v
alues
of
a
polic
y
that
leads
to
maximum
e
xpected
return.
A
C
algorithm
is
an
impro
v
ement
to
reinforcement
learning,
and
since
it
embeds
the
features
of
both
dynamic
programming
and
Mont
e-Carlo
methods.
This
method
has
been
adopted
to
solv
e
the
problem
of
DG
installation.
Int
J
Appl
Po
wer
Eng,
V
ol.
14,
No.
2,
June
2025:
319–327
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Appl
Po
wer
Eng
ISSN:
2252-8792
❒
323
5.1.
Ev
aluation
of
states
A
standard
16-b
us
distrib
ution
system
with
3
feeders,
sho
wn
in
Figure
3,
is
used
to
apply
the
actor
-
critic
learning
approach
for
minimization
of
t
otal
system
real
po
wer
losses.
In
this
gure,
solid
lines
encircled
with
number
s
1-13
are
sectionalizing
branches,
and
the
dashed
lines
encircled
with
numbers
14-16
are
tie
branches
of
the
system
for
the
base
case.
T
otal
po
wer
losses
produced
in
the
system
for
each
possible
DG
location
and
quantum
represent
states.
Location
set
{
b
1
,
b
2
,
b
3
}
represents
a
state
in
this
paper
,
where:
b
1
=
{
n
∀
n
=
4
,
5
,
6
,
7
}
(12)
b
2
=
{
n
∀
n
=
8
,
9
,
10
,
11
,
12
}
(13)
b
3
=
{
n
∀
n
=
13
,
14
,
15
,
16
}
(14)
Figure
3.
Single
line
diagram
of
a
16-b
us
radial
distrib
ution
system
5.2.
Ev
aluation
of
actions
In
this
paper
,
DG-connected
b
us
beha
v
es
lik
e
a
PQ
b
us.
The
minimum
v
alue
of
DG
capacity
is
tak
en
as
0
MW
.
0
MW
indicat
es
a
case
of
no
DG
placement.
The
maximum
capacity
of
DG
in
each
feeder
is
limited
to
30%
of
the
load
in
the
feeder
to
mak
e
proper
utilization
of
the
present
substation
sunk
cost
[32].
DG
sizes
are
chosen
to
be
positi
v
e
inte
gers
from
a
practical
point
of
vie
w
.
The
Cartesian
product
of
location
set
{
b
1
,
b
2
,
b
3
}
and
DG
capacity
set
{
c
1
,
c
2
,
c
3
}
represents
the
possible
actions
in
this
paper
.
Real
po
wer
load
on
feeder
1,
feeder
2,
and
feeder
3
are
8.5
MW
,
15.1
MW
,
and
5.1
MW
,
respecti
v
ely
.
5.3.
Ev
aluation
of
r
ewards
F
or
each
state-action
pair
,
real
po
wer
losses
are
e
v
aluated
for
the
best
congurati
o
n
of
the
sys
tem.
Reciprocal
of
total
system
real
po
wer
losses
is
tak
en
as
a
re
w
ard
for
a
particular
state-action
pair
.
r
t
+1
=
1
T
P
L
(15)
The
mathematical
procedure
of
agent
making
transition
between
dif
ferent
states,
by
taking
actions
according
to
the
polic
y
(actor)
and
correction
of
thes
e
actions
by
v
alue
function
(critic)
is
gi
v
en
in
o
wchart
in
Figure
4.
F
or
the
policies
and
v
alues
obtained
using
the
actor
-critic
algorithm,
the
optimum
v
alue
is
obtained
using
(2).
State-action
pair
corresponding
to
this
optimal
v
alue,
kno
wn
as
optimal
polic
y
,
π
∗
gi
v
es
the
DG
solution
for
each
feeder
.
Optimal
placement
of
DGs
in
a
multi-feed
r
adial
distrib
ution
system
...
(Neelakanteshwar
Rao
Battu)
Evaluation Warning : The document was created with Spire.PDF for Python.
324
❒
ISSN:
2252-8792
Is
?
Sele
ct a
n
in
iti
al
ac
tio
n
ran
dom
ly
No
Yes
Read the input
data
Initially selec
t a state randomly
from se
t of possible states
Select an
ac
ti
on
Set time
count, t
= 1
Evalua
te
the
r
ewa
rd
Evaluate the temp
or
al di
ffere
nce
Eva
l
uate the tendenc
y
to
s
e
lect
the pres
ent
action in
futur
e
Evalua
te
Policy
matrix
Evaluate V
a
lue matrix
Set tendenc
y
of
s
e
lecting any
actio
n to be eq
ual
in
it
iall
y.
Selet Va
lues of each
state to zero
initia
lly
tt
+
1
|V
(
s
)
-
V
(
s
)
|
<
0
Stop the
e
xecution
of pro
g
r
am
E
n
te
r in
to
t
h
e new
s
t
a
t
e
Figure
4.
Flo
wchart
for
actor
-critic
learning
method
6.
RESUL
TS
The
information
obtained
for
DG
soluti
on
in
each
feeder
using
A
C
approach
is
sho
wn
in
T
able
1.
The
v
oltage
proles
at
v
arious
b
uses
before
and
after
the
placement
of
DG
is
sho
wn
as
a
plot
in
Figure
5.
V
oltages
at
substation
b
uses
are
maintained
at
1
p.u.
Apart
from
the
substation
b
uses,
there
is
a
signicant
impro
v
ement
in
v
oltages
at
other
b
uses.
Real
po
wer
loss
in
the
system
and
minimum
node
v
oltage
in
the
system,
with
and
with-
out
DG,
are
sho
wn
in
T
able
2.
Percentage
reduction
in
losses
compared
to
the
base
case
without
DG
is
found
to
be
48.35%
and
the
minimum
node
v
oltage
has
impro
v
ed
from
0.9568
p.u.
to
0.9710
p.u.
after
placement
of
DG.
Int
J
Appl
Po
wer
Eng,
V
ol.
14,
No.
2,
June
2025:
319–327
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Appl
Po
wer
Eng
ISSN:
2252-8792
❒
325
T
able
1.
Optimum
location
and
size
of
DGs
Feeder
no.
Optimum
location
Optimum
size
(MW)
1
7
3
2
12
5
3
16
2
T
able
2.
T
otal
real
po
wer
loss
and
minimum
node
v
oltage
Case
T
otal
real
po
wer
loss
in
MW
Minimum
node
v
oltage
(p.u.)
W
ithout
DG
0.5995
0.9568
W
ith
DG
0.3097
0.9710
Figure
5.
V
oltages
at
v
arious
b
uses
with
and
with
out
DGs
in
a
16-b
us
distrib
ution
system
7.
CONCLUSION
In
case
of
a
multi-feed
system,
the
problem
of
multiple
DG
placement
comes
out
with
se
v
eral
combi
-
nations
of
DG
locations
and
sizes.
Reinforcement
learning
and
actor
-critic
l
earning
algorithms
ha
v
e
a
feature
of
mapping
situations
with
possible
actions.
These
algorithms
nd
a
potential
application
in
case
of
comple
x
and
uncertain
situations.
Actor
-critic
learning
algorithm
embeds
the
features
of
reinforcement
learning,
dynamic
programming,
and
Monte-Carlo
approaches.
Hence
the
problem
of
optimal
placement
of
DGs
in
a
multi-feed
system
is
solv
ed
in
this
paper
using
act
or
-critic
learning
algorithm.
In
actor
-critic
learning
algorithm,
actions
tak
en
by
the
polic
y
(actor)
are
corrected
by
the
v
alue
function
(critic).
The
approach
is
applied
to
a
standard
16-
b
us
radial
distrib
ution
system
for
minimization
of
system
real
po
wer
losses.
The
results
obta
ined
are
discussed
for
both
the
cases
of
with
and
without
DG.
FUNDING
INFORMA
TION
This
research
w
ork
w
as
supported
by
“W
oosong
Uni
v
ersity’
s
Academic
Research
Funding
-
2024”.
A
UTHOR
CONTRIB
UTIONS
ST
A
TEMENT
This
journal
uses
the
Contrib
utor
Roles
T
axonomy
(CRediT)
to
recognize
indi
vidual
author
contrib
u-
tions,
reduce
authorship
disputes,
and
f
acilitate
collaboration.
Name
of
A
uthor
C
M
So
V
a
F
o
I
R
D
O
E
V
i
Su
P
Fu
Neelakanteshw
ar
Rao
Battu
✓
✓
✓
✓
✓
✓
✓
✓
✓
Surender
Reddy
Salkuti
✓
✓
✓
✓
✓
✓
✓
✓
✓
C
:
C
onceptualization
I
:
I
n
v
estig
ation
V
i
:
V
i
sualization
M
:
M
ethodology
R
:
R
esources
Su
:
Su
pervision
So
:
So
ftw
are
D
:
D
ata
Curation
P
:
P
roject
Administration
V
a
:
V
a
lidation
O
:
Writing
-
O
riginal
Draft
Fu
:
Fu
nding
Acquisition
F
o
:
F
o
rmal
Analysis
E
:
Writing
-
Re
vie
w
&
E
diting
Optimal
placement
of
DGs
in
a
multi-feed
r
adial
distrib
ution
system
...
(Neelakanteshwar
Rao
Battu)
Evaluation Warning : The document was created with Spire.PDF for Python.
326
❒
ISSN:
2252-8792
CONFLICT
OF
INTEREST
ST
A
TEMENT
Authors
state
no
conict
of
interest.
INFORMED
CONSENT
Informed
consent
is
not
applicable
to
t
his
paper
as
no
personal
information
of
an
ybody
is
used
in
this
w
ork.
ETHICAL
APPR
O
V
AL
Ethical
appro
v
al
is
not
applicable
to
this
paper
as
the
proposed
w
ork
doesn’
t
use
people
or
animals.
D
A
T
A
A
V
AILABILITY
The
data
that
support
the
ndings
of
this
study
are
a
v
ailable
from
the
corresponding
author
,
[SRS],
upon
reasonable
request.
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BIOGRAPHIES
OF
A
UTHORS
Neelakanteshwar
Rao
Battu
graduated
from
G.
Pulla
Reddy
Engineering
Colle
ge,
K
urnool
in
2001.
He
recei
v
ed
M.T
ech.
de
gree
from
JNTU
Anantapur
in
2004
and
Ph.D.
de
gree
from
IIT
Delhi
in
2016.
He
is
presently
w
orking
as
an
associate
professor
at
VNR
V
ignana
Jyothi
Institute
of
Engineering
and
T
echnology
,
Hyderabad,
T
elang
ana,
India.
His
research
interests
include
distrib
ution
system
planning,
po
wer
system
protection,
and
modelling
of
electrical
machines.
He
can
be
contacted
at
email:
neelakanteshw
arrao
b@vnrvjiet.in.
Sur
ender
Reddy
Salkuti
recei
v
ed
the
Ph.D.
de
gree
in
Electrical
Engineering
from
the
Indian
Institute
of
T
echnology
,
Ne
w
Delhi,
India,
in
2013.
He
w
as
a
postdoctoral
researcher
with
Ho
w
ard
Uni
v
ersity
,
W
ashington,
DC,
USA,
from
2013
to
2014.
He
is
currently
an
associate
professor
with
the
Departm
ent
of
Railroad
and
Electrica
l
Engineering,
W
oosong
Uni
v
ersity
,
Daejeon,
Republic
of
K
orea.
His
current
research
interests
include
mark
et
clearing,
including
rene
w
able
ener
gy
sources,
demand
response,
smart
grid
de
v
elopment
with
inte
gration
of
wind,
and
solar
photo
v
oltaic
ener
gy
sources.
He
can
be
contacted
at
email:
surender@wsu.ac.kr
.
Optimal
placement
of
DGs
in
a
multi-feed
r
adial
distrib
ution
system
...
(Neelakanteshwar
Rao
Battu)
Evaluation Warning : The document was created with Spire.PDF for Python.