Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
8,
No.
2,
April
2018,
pp.
837
–
844
ISSN:
2088-8708
837
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Non-integer
IMC
Based
PID
Design
f
or
Load
Fr
equency
Contr
ol
of
P
o
wer
System
thr
ough
Reduced
Model
Order
Idamakanti
Kasir
eddy
,
Abdul
W
ahid
Nasir
,
and
Arun
K
umar
Singh
Department
of
Electrical
&
Electronics
engineering,
NIT
Jamshedpur
,
India
Article
Inf
o
Article
history:
Recei
v
ed:
May
31,
2017
Re
vised:
Jan
7,
2018
Accepted:
Feb
2,
2018
K
eyw
ord:
model
order
reduction
genetic
algorithm
non-inte
ger
IMC
filter
rob
ust
control
load
frequenc
y
control(LFC)
ABSTRA
CT
This
paper
deals
with
non-inte
ger
internal
model
control
(FIMC)
based
proportional-
inte
gral-deri
v
ati
v
e(PID)
design
for
load
frequenc
y
control
(LFC)
of
single
area
non-
reheated
thermal
po
wer
system
under
parameter
di
v
er
gence
and
random
load
disturbance.
Firstly
,
a
fractional
second
order
plus
dead
time(SOPDT)
reduced
system
model
is
ob-
tained
using
genetic
algorithm
through
step
error
minimization.
Secondly
,
a
FIMC
based
PID
controller
is
designed
for
single
area
po
wer
system
based
on
reduced
system
model.
Proposed
controller
is
equipped
with
single
area
non-reheated
thermal
po
wer
system.
The
resulting
controller
is
tested
using
MA
TLAB/SIMULINK
under
v
arious
conditions.
The
simulation
results
sho
w
that
the
controller
can
accommodate
system
parameter
uncertainty
and
load
disturbance.
Further
,
simulation
sho
ws
that
it
maintains
rob
ust
performance
as
well
as
minimi
zes
the
ef
fect
of
load
fluctuations
on
fre
quenc
y
de
viation.
Finally
,
the
pro-
posed
method
applied
to
tw
o
area
po
wer
system
to
sho
w
the
ef
fecti
v
eness.
Copyright
c
2018
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Idamakanti
Kasireddy
National
Institute
of
T
echnology
Jamshedpur
,
Jamshedpur
,
India.
Email
ID:
2015rsee002@nitjsr
.ac.in,
kasireddy
.nit@gmail.com
1.
INTR
ODUCTION
Generally
,
electric
po
wer
system
is
studied
in
terms
of
generation,
transmission
and
distrib
ution
systems
in
which
all
generators
are
operated
synchronously
at
nominal
frequenc
y
to
meet
the
demand
load.
The
frequenc
y
de
viation
in
the
po
wer
system
is
mainly
due
to
mismatch
between
the
generation
and
load
plus
losses
at
e
v
ery
second.
There
may
be
small
or
lar
ge
frequenc
y
de
viation
based
on
the
mismatch
between
generation
and
load
demand.
These
mismatches
due
t
o
random
load
fluctuations
and
due
to
lar
ge
generator
or
po
wer
plant
tripping
out,
f
aults
etc.
respecti
v
ely
.
Ho
we
v
er
,
de
viations
could
be
positi
v
e
or
ne
g
at
i
v
e.
The
role
of
load
frequenc
y
control(LFC)
is
to
mitig
ate
frequenc
y
perturbation.
Thus
the
po
wer
system
will
operate
normally
[1,
2].
This
can
be
achie
v
ed
by
adopting
a
auxiliary
controller
in
addition
to
the
primary
control(Go
v
ernor).
From
literature[1,
2],
con
v
entional
controller
is
used
as
auxiliary
or
secondary
control.
T
o
get
the
parameters
of
this
controller
,
the
po
wer
system
is
modeled
and
simulated
using
MA
TLAB.
This
paper
deals
with
the
model
ing
of
po
wer
system
through
fractional
order
dif
ferential
equations
and
design
of
controller
.
The
fractional
order
dynamic
system
is
characterized
by
dif
ferential
equations
in
which
the
deri
v
ati
v
es
po
wers
are
an
y
real
or
comple
x
numbers.
The
approach
of
fractional
order
study
is
mainly
used
in
the
area
of
mathematics,
control
and
ph
ysics
[3].
The
precision
of
modeling
is
accomplished
using
the
theory
of
fractional
calculus[4].
In
vie
w
of
abo
v
e
f
act,
inte
ger
operators
of
traditi
onal
control
methods
h
a
v
e
been
replaced
by
concept
of
fractional
calculus[5,
6].
Man
y
modern
controllers
for
LFC
as
secondary
controllers
ar
e
a
v
ailable
lik
e
sliding
mode
control[7],
tw
o
de
gree
of
freedom
PID
controller[8],
fuzzy
controller[9],
microprocessor
based
adapti
v
e
control
strate
gy[10]
and
direct-indirect
adapti
v
e
fuzzy
controller
technique[11,
12,
13].
It
can
be
observ
ed
that
po
wer
system
parameters
may
alter
due
to
aging,
replacement
of
system
units
and
modeling
errors,
as
a
consequent
problem
to
design
a
optimum
secondary
controller
becomes
a
challenging
w
ork.
From
literature,
it
is
noticed
that
rob
ust
controller
is
inert
to
system
parameter
alteration.
Thus,
a
good
rob
ust
controller
design
is
needed
to
tak
e
care
of
parameter
uncertainties
as
well
as
load
disturbance
in
po
wer
system.
In
literature,
lot
of
rob
ust
control
methods
are
presented
for
disturbance
rejection
and
parameter
alteration
J
ournal
Homepage:
http://iaescor
e
.com/journals/inde
x.php/IJECE
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A
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a
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,
DOI:
10.11591/ijece.v8i2.pp837-844
Evaluation Warning : The document was created with Spire.PDF for Python.
838
ISSN:
2088-8708
for
LFC.
Still
a
v
ast
research
is
going
on
internal
model
control(IMC)
by
researchers
due
to
its
simplicity
.
W
ith
the
tw
o
de
gree
of
freedom
IMC(TDF
IMC)[14],
both
set
point
tracking
and
load
disturbance
rej
ection
can
be
achie
v
ed.
As
a
consequent
,
IMC
controller
design
is
an
ideal
choice
for
secondary
controller
for
LFC.
Sax
ena[15]
designed
a
TDF
IMC
for
LFC
using
approximation
techniques
lik
e
P
ade’
s
and
Routh’
s,
which
moti
v
ated
to
adopt
the
fractional
IMC-PID
controller
as
a
secondary
controller
and
is
design
based
on
a
fractional
reduced
order
model
of
a
system.
2.
REDUCTION
METHOD
FOR
SINGLE
AREA
THERMAL
PO
WER
SYSTEM
This
section
deals
with
framing
of
fractional
order
model
of
a
single
area
po
wer
system
using
a
step
error
minimization
technique
through
genetic
algorithm.
This
is
se
gre
g
ated
into
follo
wing
subsections.
2.1.
System
in
v
estigated
The
proposed
w
ork
deals
with
modeling
of
the
po
wer
system
to
design
secondary
controller
.
Due
to
this
pur
-
pose,
a
single
area
non-reheated
therm
al
po
wer
system
has
been
cons
idered[1].
The
thermal
po
wer
system
equipped
with
dif
ferent
units
lik
e
generator
G
P
(
s
)
,
turbine
G
t
(
s
)
,
go
v
ernor
G
g
(
s
)
,
boiler
etc.
and
their
dynamics
are
gi
v
en
by
(1)
G
g
(
s
)
=
1
T
G
s
+
1
;
G
t
(
s
)
=
1
T
T
s
+
1
;
G
p
(
s
)
=
K
P
T
P
s
+
1
(1)
Figure
1.
Single
area
po
wer
system
linear
model
The
block
diagram
of
a
single
area
po
wer
system
is
sho
wn
in
Fig.
1,
where
P
d
is
Load
disturbance(in
p.u.MW),
X
G
is
Change
in
go
v
ernor
v
alv
e
position,
P
G
is
Change
in
generator
output(in
p.u.MW),
u
is
Control
input,
R
is
Speed
re
gulation(in
Hz/p.u.MW)
and
f
(
s
)
is
Frequenc
y
de
viation(in
Hz).
The
o
v
erall
transfer
function
is
attained
as
Case1:
From
Fig.
1
assume
f
(
s
)
=
f
1
(
s
)
when
P
d
(
s
)
=
0
,
the
corresponding
transfer
function
is
G
1
(
s
)
.
Case2:
From
Fig.
1
assume
f
(
s
)
=
f
2
(
s
)
when
u
(
s
)
=
0
,
the
corresponding
transfer
function
is
G
2
(
s
)
.
Applying
the
theory
of
superposition
principle
to
po
wer
system
model,
the
o
v
erall
transfer
function
is
gi
v
en
by
(2)
f
(
s
)
=
f
1
(
s
)
+
f
2
(
s
)
=
G
1
(
s
)
u
(
s
)
+
G
2
(
s
)
P
d
(
s
)
(2)
The
aim
is
to
fi
n
d
control
la
w
u
(
s
)
=
K
(
s
)
f
(
s
)
which
mitig
ates
the
ef
fect
of
load
alteration
on
frequenc
y
de
viation,
where
K
(
s
)
is
fractional
IMC-PID
controller
.
2.2.
Fractional
system
r
epr
esentation
This
subsection
deals
with
the
fractional
order
systems
through
which
it
can
de
v
elop
a
proposed
model
for
po
wer
plant
to
design
a
secondary
controller
.
The
representation
for
a
linear
time
in
v
ariant
fractional
order
dynamic
system[16]
is
gi
v
en
as
,
H
(
D
0
1
::::
n
)
y
(
t
)
=
F
(
D
0
1
::::
m
)
u
(
t
)
(3)
H
(
D
0
1
::::
n
)
=
n
X
k
=0
a
k
D
k
;
F
(
D
0
1
::::
m
)
=
m
X
k
=0
b
k
D
k
(4)
IJECE
V
ol.
8,
No.
2,
April
2018:
837
–
844
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
839
where
y
(
t
)
and
u
(
t
)
are
output
and
input
v
ectors
respecti
v
ely
and
D
is
dif
ferential
operator
.
k
,
k
are
the
order
of
deri
v
ati
v
es.
a
k
and
b
k
are
coef
ficients
of
deri
v
ati
v
es,
a
k
;
b
k
R
.
Here
H
;
F
Fractional
dynamic
systems.
The
transfer
function
of
fractional
order
dynamic
system
is
obtained
by
applying
Laplace
transform
to
(3)
and
(4)
(initial
conditions
are
zero)
and
is
gi
v
en
as
(5)
G
3
(
s
)
=
P
m
k
=0
b
k
(
s
)
k
P
n
k
=0
a
k
(
s
)
k
(5)
2.3.
Design
of
pr
oposed
system
The
full
order
t
ransfer
function
of
single
area
po
wer
system
is
obtained
from
(1)
and
(2),
which
is
gi
v
en
by
(6)
G
1
(
s
)
=
K
P
T
P
T
T
T
G
s
3
+
(
T
P
T
T
+
T
T
T
G
+
T
G
T
P
)
s
2
+
(
T
P
+
T
T
+
T
G
)
s
+
(1
+
K
P
=R
)
(6)
substitute
t
he
v
alues
of
T
P
=
20
sec,
T
T
=
0.3
sec,
T
G
=
0.08
sec,
R
=
2.4,
K
P
=
120
from
[14]
in
(6),
we
get
G
1
(
s
)
as
(7)
A
(
s
)
=
G
1
(
s
)
=
250
s
3
+
15
:
88
s
2
+
42
:
46
s
+
106
:
2
(7)
The
equation
(7)
represents
inte
ger
higher
order
model
which
is
con
v
erted
to
fractional
order
model
assumed
to
be
A
0
(
s
)
Consider
fractional
SOPDT
reduced
model
A
0
(
s
)
gi
v
en
by
(8)
A
0
(
s
)
=
K
1
e
Ls
s
b
+
ps
c
+
q
(8)
Time(sec)
0
1
2
3
4
5
6
7
8
9
10
Amplitude
-0.5
0
0.5
1
1.5
2
2.5
3
Full order
Fractional SOPDT
Routh's approximation
Pade's approximation
1
1.5
2
2.5
3
3.5
4
4.5
5
2
2.2
2.4
2.6
2.8
Figure
2.
Comparison
of
step
responses
of
full
order
model
with
fractional
SOPDT
,
Routh
and
P
ade
approximation
Here
the
order
of
A
0
(
s
)
is
less
than
the
A
(
s
)
and
is
in
fractional
form.
The
step
error
minimization
technique[17,
1
8]
through
Genetic
Algorithm(GA)[19,
20]
is
utilized
to
obtain
parameters
of
A
0
(
s
)
are
gi
v
en
as
K
1
=
16
:
385
;
L
=
0
:
095
;
b
=
1
:
897
,
c
=
0
:
962
;
p
=
1
:
954
;
q
=
7
:
031
.
This
is
done
through
MA
TLAB
&
simula-
tion.
Thus
the
attained
reduced
fractional
model
A
0
(
s
)
is
A
0
(
s
)
=
16
:
385
e
0
:
095
s
s
1
:
897
+
1
:
954
s
0
:
962
+
7
:
031
(9)
The
step
responses
of
original
model,
proposed,
P
ade’
s
approximation
and
Routh’
s
approximation
are
compared
and
sho
wn
in
Fig.
2.
The
performance
i
nde
x
ITSE
of
proposed
P
ade’
s
and
Routh,s
methods
are
0.0015,
0.027
and
0.06
respecti
v
ely
.
From
Fig.
2
and
abo
v
e
ITSE
v
alues,
it
is
observ
ed
that
the
response
of
proposed
method
is
v
ery
closer
to
full
order
model(original).
Non-inte
g
er
IMC
Based
PID
Design
for
Load
F
r
equency
Contr
ol
of
P
ower
...
(Idamakanti
Kasir
eddy)
Evaluation Warning : The document was created with Spire.PDF for Python.
840
ISSN:
2088-8708
(a)
(b)
Figure
3.
Block
diagram
of
a)
IMC
configuration
b)
equi
v
alent
con
v
entional
feedback
control
3.
FRA
CTION
AL
IMC
CONTR
OLLER
DESIGN
3.1.
Inter
nal
Model
Contr
ol
In
this
section,
model
based
IMC
method
for
load
frequenc
y
controller
design
is
considered,
which
is
de
v
eloped
by
M.
Morari
and
co
w
ork
ers
[21,
22].
The
block
diagram
of
IMC
structure
is
sho
wn
in
Fig.
3a,
where
C
I
M
C
(
s
)
is
the
controller
,
P
(
s
)
is
the
po
wer
plant
and
P
m
(
s
)
is
the
predicti
v
e
plant.
Fig.
3b
sho
ws
block
diagram
of
con
v
entional
closed
loop
control.
From
Fig.
3a
and
Fig.
3b,
we
can
relate
C
(
s
)
and
C
I
M
C
(
s
)
as
C
(
s
)
=
C
I
M
C
(
s
)
1
C
I
M
C
(
s
)
P
m
(
s
)
(10)
Steps
for
IMC
controller
design[23]
are
as
follo
ws.
Step1:
The
plant
model
can
be
represented
as
P
m
=
P
+
m
P
m
(11)
where
P
m
=
minimum
phase
system
and
P
+
m
=
non-minimum
phase
system,
lik
e
zeros
in
right
side
of
S-plane
etc.
Step2:
The
IMC
controller
is
C
I
M
C
(
s
)
=
1
P
m
f
(
s
)
;
f
(
s
)
=
1
(1
+
c
s
+1
)
r
(12)
where
f
(
s
)
is
lo
w
pass
filter
with
steady
state
g
ain
of
one
where
c
is
the
desired
closed
loop
time
constant
and
r
is
the
positi
v
e
inte
ger
,
r
1,
which
are
chosen
such
that
C
I
M
C
(
s
)
is
ph
ysically
realizable.
Here
r
is
tak
en
as
1
for
proper
transfer
function.
The
FIMC
controller
is
designed
for
fractional
SOPDT
is
gi
v
en
by
(9)
via
method
discussed
belo
w
.
Consider
the
system
[23],
is
gi
v
en
by
(13)
P
m
(
s
)
=
k
e
s
a
2
s
+
a
1
s
+
1
;
>
(13)
where
:
0
:
5
1
:
5
,
:
1
:
5
2
:
5
,
=
time
delay
.
Here
a
2
=
2
and
a
1
=
2
.
Using
(11),
the
in
v
ertible
part
of
P
m
(
s
)
is
P
m
(
s
)
=
k
a
2
s
+
a
1
s
+
1
(14)
Using
(12),
the
Fractional
IMC
controller
is
C
I
M
C
(
s
)
=
a
2
s
+
a
1
s
+
1
k
1
(1
+
c
s
+1
)
(15)
substitute
(15)
in
(10),
then
the
con
v
entional
controller
C
(
s
)
is
e
v
aluated
and
simplified
as
C
(
s
)
=
a
2
s
+
a
1
s
+
1
k
(
c
s
+1
+
s
)
(16)
where
e
s
is
approximated
as
(1
s
)
using
first
order
T
aylor
e
xpansion[23].
Ag
ain
C
(
s
)
is
decomposed
into
FIMC
PID
filter
via
technique
discussed
belo
w
.
Multiplying
and
di
viding
RHS
of
(16)
by
s
C
(
s
)
=
(
a
2
s
+
a
1
s
+
1)
k
(
c
s
+1
+
s
)
s
s
(17)
IJECE
V
ol.
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2,
April
2018:
837
–
844
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IJECE
ISSN:
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841
substitute
a
2
=
2
and
a
1
=
2
in
(17)
and
rearranged
as,
C
(
s
)
=
[
s
1
1
+
(
c
=
)
s
][
2
k
(1
+
1
2
s
+
2
s
)]
(18)
where
first
part
is
fractional
filter
and
second
part
is
fractional
PID
controller
.
3.2.
FIMC
to
single
ar
ea
non-r
eheated
po
wer
system
T
o
design
FIMC,
the
(9)
can
be
re-framed
in
the
form
of
(13)
is
A
0
(
s
)
=
2
:
3303
e
0
:
095
s
0
:
142
s
1
:
897
+
0
:
2676
s
0
:
962
+
1
(19)
From
(13),(18)
and
(19),
we
get
=
0
:
3768
,
=
0
:
095
,
k=2.3303,
=
1
:
897
,
=
0
:
962
,
=
0
:
3551
substituting
abo
v
e
v
alues
in
(18),
the
fractional
IMC-PID
filter
for
single
area
po
wer
system
is
C
(
s
)
=
s
0
:
038
1
+
10
:
526
c
s
1
:
21(1
+
3
:
736
s
0
:
962
+
0
:
5305
s
0
:
935
)
(20)
The
v
alue
of
c
and
are
selected
in
such
a
w
ay
,
that
it
minimizes
tracking
error
and
achie
v
es
rob
ust
performance.
4.
RESUL
TS
AND
DISCUSSIONS
In
this
section,
a
model
with
proposed
system
and
its
controller
is
designed
in
simulation
and
an
e
xtensi
v
e
simulation
is
carri
ed
out.
In
this
model
an
performance
inde
x
ISE
is
accompanied
to
determine
the
error
of
frequenc
y
de
viation.
Based
on
ISE,
Ov
ershoot,
undershoot
and
settling
time,
we
choose
best
and
c
.
The
obtained
parameters
and
c
are
=0.22
and
c
=0.02
Time(Sec)
0
1
2
3
4
5
6
7
8
9
10
Frequency Deviation(Hz)
×
10
-3
-12
-10
-8
-6
-4
-2
0
2
4
Saxena method for Routh's approximation
Proposed method for fractional SOPDT
Saxena method for Pade's approximation
Figure
4.
Comparison
of
response
of
po
wer
system
using
proposed
with
other
methods
T
o
e
v
aluate
performance
a
step
load
disturbance
P
d
(
s
)
=0.01
is
applied
to
a
single
area
po
wer
system
as
sho
wn
in
Fig.
1.
The
frequenc
y
de
viation
f
(
s
)
of
proposed
method
in
comparison
with
P
ade’
s
and
Routh’
s
method
under
nominal
case
is
sho
wn
in
Fig.
4.
It
is
clear
from
Fig.
4
that
the
frequenc
y
de
viation
of
the
system
for
proposed
controller
due
to
load
disturbance
is
diminished
compared
to
P
ade’
s
and
Routh’
s
approximation
methods.
The
performance
inde
x
of
proposed
and
other
tw
o
methods
are
compared
and
sho
wn
in
T
able
1
under
nominal
case.
From
T
able
1
it
is
observ
ed
that
the
performance
inde
x
ISE
is
significantly
lo
w
as
compared
with
other
methods.
T
able
1.
Comparison
of
performance
inde
x
for
proposed
and
other
reduced
models
under
nominal
and
50%
Uncer
-
tainty
cases
Methods
Nominal
case
50%
Uncertainty
case
Lo
wer
bound
Upper
bound
ISE
ISE
ISE
P
ade’
s
approximation(Sax
ena)
8
:
4
10
4
9
:
1
10
3
8
:
4
10
3
Routh’
s
approximation(Sax
ena)
8
:
7
10
4
9
:
2
10
3
8
:
9
10
3
Proposed
method
1
:
4
10
5
8
:
44
10
6
6
:
8
10
6
Non-inte
g
er
IMC
Based
PID
Design
for
Load
F
r
equency
Contr
ol
of
P
ower
...
(Idamakanti
Kasir
eddy)
Evaluation Warning : The document was created with Spire.PDF for Python.
842
ISSN:
2088-8708
4.1.
Rob
ustness
Examining
rob
ustness
of
controller
is
vital
because
modeling
of
system
dynamics
is
not
perfect.
So
we
ha
v
e
chosen
fifty
percentage
uncertainty
in
system
parameters
to
check
rob
ustness
of
controller
.
The
uncertain
parameter
i
,
for
all
i
=
1
;
2
;
::;
5
are
tak
en
as[14].
Here
is
parameter
uncertainty
.
The
lo
wer
bounds
and
upper
bounds
of
system
uncertainty
responses
for
proposed,
P
ade’
s
and
Routh’
s
method
are
sho
wn
in
Fig.
5a
and
Fig.
5b
respecti
v
ely
.
Time (s)
0
2
4
6
8
10
Frequency Deviation (Hz)
#
10
-3
-15
-10
-5
0
5
Proposed
Saxena Routh's approximation
Saxena Pade's approximation
(a)
Time (s)
0
2
4
6
8
10
Frequency Deviation (Hz)
#
10
-3
-15
-10
-5
0
5
Proposed
Saxena Routh's approximation
Saxena Pade's approximation
(b)
Figure
5.
Comparison
of
response
of
po
wer
system
using
proposed
method
with
other
method
for
a)
lo
wer
and
b)
upper
bound
uncertainties
From
Fig.
5a
and
Fig.
5b
,
it
is
noticed
that
the
proposed
controller
is
rob
ust
when
there
is
plant
mismatch
and
system
parameter
uncertainty
.
The
performance
inde
x
ISE
of
proposed
and
other
methods
under
50
%
uncertainty
case
are
compared
and
gi
v
en
in
T
able
1.
It
is
observ
ed
that,
there
is
significant
dif
ference
in
ISE
between
the
proposed
and
P
ade’
s,
Routh’
s.
Thus
proposed
controller
is
more
rob
ust
compared
to
other
tw
o
controllers.
4.2.
Pr
oposed
method
extended
to
tw
o
ar
ea
po
wer
system
Di
P
i
f
1
1
Gi
sT
1
1
Ti
sT
1
Pi
Pi
K
sT
-
Ti
P
Gi
P
-
()
i
Cs
+
i
B
1
i
R
1
B
1
i
T
s
+
i
u
i
A
C
E
C
o
n
t
r
o
l
l
e
r
G
o
v
e
r
n
o
r
T
u
r
b
i
n
e
P
o
w
e
r
s
y
s
t
e
m
A
r
e
a
i
+
+
-
T
i
e
i
P
-
+
1
B
in
T
s
+
+
+
-
()
j
f
j
i
()
i
Figure
6.
Block
diagram
of
multi
area
po
wer
system
The
block
diagram
of
multi
area
po
wer
system
linear
model
is
sho
wn
i
n
Fig.
6.
The
parameter
v
alues
of
model
are
gi
v
en
belo
w[24].
T
P
1
=
T
P
2
=20
secs,
T
T
1
=
T
T
2
=
0.3
secs,
T
G
1
=
T
G
2
=
0.08
secs,
R
1
=
R
2
=
2.4,
K
P
1
=
K
P
2
=120
Here
i=1,2
and
tw
o
area
po
wer
system
is
assumed
to
be
identical
for
simplicity
.
As
follo
wed
abo
v
e
subsections,
the
controller
is
designed
for
tw
o
area
po
wer
system
with
an
assumption
that
there
is
no
tie
line
e
xchange
po
wer(
T
12
=
0
).
The
resulting
FIMC-PID
controller
for
area1
and
area2
of
tw
o
area
po
wer
system
are
gi
v
en
as
(21)
C
1
(
s
)
=
C
2
(
s
)
=
s
0
:
038
1
+
0
:
01
s
0
:
64
1
:
21(1
+
3
:
736
s
0
:
962
+
0
:
5305
s
0
:
935
)
(21)
T
o
e
v
aluate
the
performance
of
controller
,
a
step
load
disturbance
P
d
(
s
)
=0.01
is
applied
to
a
tw
o
area
non
reheated
po
wer
system.
The
frequenc
y
de
viations
in
area1
&
area2
and
de
viation
in
tie
line
of
proposed
method
IJECE
V
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2,
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2018:
837
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IJECE
ISSN:
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843
Time(s)
0
2
4
6
8
10
"
f1(Hz)
#
10
-3
-10
-5
0
5
Proposed
Wen Tan method
(a)
Time(s)
0
2
4
6
8
10
"
f2(Hz)
#
10
-3
-6
-4
-2
0
2
Proposed
Wen Tan method
(b)
Time(s)
0
2
4
6
8
10
"
P
tie
(p.u.)
#
10
-3
-2
-1
0
1
Proposed
Wen Tan method
(c)
Figure
7.
Responses
of
tw
o
area
po
wer
system
are
compared
with
W
en
T
an
method[24],
which
is
sho
wn
in
Fig.
7.
It
is
clear
from
figures
that
the
de
viations
of
the
po
wer
system
for
proposed
controller
due
to
load
disturbance
is
diminished
compared
to
W
en
T
an
method.
5.
CONCLUSION
A
good
rob
ust
LFC
technique
is
required
to
act
ag
ainst
load
perturbation,
system
parameter
uncertainties
and
modeling
error
.
In
this
paper
a
good
approximation
model
reduction
technique
i.e
step
error
minimization
method
is
adopted
to
desi
gn
a
rob
ust
fractional
IMC
based
PID
controller
for
non-reheated
thermal
po
wer
system.
It
consists
of
fractional
filter
and
fractional
order
PID.
The
tuning
parameters,
time
constant
c
and
non
inte
ger
are
e
v
aluated
to
get
f
ast
settling
time
and
better
o
v
ershoot/undershoot
respecti
v
ely
.
The
simulation
results
sho
wed
that
the
proposed
controller
is
more
rob
ust
and
good
at
set
point
tracking
and
for
disturbance
rejection.
The
performance
of
proposed
method
is
good
when
applied
to
tw
o
area
po
wer
system.
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heating
loads
with
Non-inte
g
er
IMC
Based
PID
Design
for
Load
F
r
equency
Contr
ol
of
P
ower
...
(Idamakanti
Kasir
eddy)
Evaluation Warning : The document was created with Spire.PDF for Python.
844
ISSN:
2088-8708
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BIOGRAPHIES
OF
A
UTHORS
Idamakanti
Kasireddy
recei
v
ed
the
M.T
ech.
de
gree
from
National
Institute
of
T
echnology
,
Jamshed-
pur
,Jharkhand,
India,in
2015.
He
is
currently
w
orking
to
w
ards
the
Ph.D.
de
gree
at
the
Department
of
Electrical
Engineering,
NIT
Jamshedpur
,Jharkhand,
India.
His
research
of
interest
are
Applica-
tion
of
Control
System
in
Po
wer
and
Ener
gy
Systems.
Abdul
W
ahid
Nasir
recei
v
ed
the
M.T
ech.
de
gree
from
B.S.Abdur
Rahman
uni
v
ersity
,Chennai,India,
in
2014.
He
is
currently
w
orking
to
w
ards
the
Ph.D.
de
gree
at
the
Department
of
Electrical
Engineer
-
ing,NIT
Jamshedpur
,Jharkhand,
India.
His
research
interest
are
Process
Control
and
model
based
control.
Arun
K
umar
Singh
recei
v
ed
the
B.Sc.
de
gree
from
the
Re
gional
Institute
of
T
echnology
,
kuruk-
shetra,Haryana,
India,
M.T
ech.
de
gree
from
the
IIT(BHU),V
a
ranasi,UP
,
India,
and
Ph.D.
de
gree
from
the
Indian
Institute
of
T
echnology
,
Kharagpur
,
India.He
has
been
a
professor
in
the
Depart-
ment
of
Elect
rical
Engineering
at
National
Institute
of
T
echnology
,
Jamshedpur
,
since
1985.
His
areas
of
research
interest
in
Control
System,
Control
System
in
Po
wer
and
Ener
gy
Systems
and
Non
Con
v
entional
Ener
gy
.
IJECE
V
ol.
8,
No.
2,
April
2018:
837
–
844
Evaluation Warning : The document was created with Spire.PDF for Python.