TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 16, No. 1, Octobe
r 201
5, pp. 30 ~ 3
7
DOI: 10.115
9
1
/telkomni
ka.
v
16i1.870
1
30
Re
cei
v
ed
Jul
y
1, 2015; Re
vised Augu
st
2, 2015; Acce
pted Augu
st 19, 2015
Quality Enhancement of AC Chopper Using Genetic
Algorithm
S. Mahendran*, I. Gnanambal, A. Mahes
w
ari
K.S.R
Colle
ge
of T
e
chnol
og
y,
T
i
ruchen
go
de,
T
a
milna
du, India, +
91-0
4
2
8
8
274
74
1
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: drmahe
ndra
n
s
@gmai
l
.com
A
b
st
r
a
ct
T
h
is pa
per
ma
i
n
ly d
eals w
i
th t
he d
e
sig
n
of A
C
cho
pper
usi
ng Gen
e
tic Al
g
o
rith
m b
a
sed
h
a
rmoni
c
eli
m
i
nati
on tec
hni
que. Gen
e
ti
c Algorith
m
is
used to ca
lc
ul
a
t
e opti
m
u
m
sw
itching a
n
g
l
es to eli
m
i
nate l
o
w
e
r
order h
a
r
m
on
i
cs in the outp
u
t
voltage. T
o
tal
Harmon
i
c Dis
t
o
rtion of o
u
tpu
t
voltage is ca
l
c
ulate
d
from th
e
obtai
ne
d sw
itchin
g an
gles
a
nd als
o
ad
opt
ed in th
e
pro
p
o
sed fitn
ess functio
n
. Co
mp
arative a
n
a
l
ysi
s is
ma
de for the
sw
itching an
gl
es obtai
ne
d b
y
the
New
t
on
Raphs
on
met
hod a
nd th
e prop
osed Ge
n
e
tic
Algorit
h
m
. T
he an
alys
is re
veals th
at the
prop
ose
d
tec
hni
que
is
on
par w
i
th co
nv
entio
nal
meth
od
.
Additi
ona
lly, the Genetic Alg
o
r
ithm a
ppro
a
ch
offers
less comp
utatio
nal b
u
r
den, gu
arant
e
ed gl
oba
l opti
m
a
in
m
o
st c
a
ses
and f
a
ster convergence. The propos
ed m
e
t
hod is
simulat
ed
in
Matlab/Sim
u
link
m
o
del and
the results sho
w
s that the propose
d
metho
d
w
o
rks
w
i
th high effectiven
ess
,
accuracy and
rapi
dity.
Ke
y
w
ords
: AC
chop
per, ge
ne
tic algor
ith
m
, p
u
lse w
i
dth
m
o
d
u
lati
on (PW
M), selective
har
monic e
l
i
m
i
nati
o
n
(SHE)
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Perform
a
n
c
e of electri
c
al system utilities
are improve
d
due to the rece
nt advancement
s
in the devel
o
p
ment of p
o
wer
semi
con
d
u
c
tor
swit
ch
es.
Some of the
advantag
es
o
ffered by u
s
in
g
su
ch devices are quick re
spo
n
se, smal
ler in size
an
d need
s low
power for co
ntrol circuit
r
y. AC
voltage controller i
s
the
wi
dely used p
o
w
er
ele
c
tro
n
i
c
controll
er
b
e
ca
use of
its
simpli
city and
th
e
ability of controlling large amo
unt of
power
economically [1
]. AC voltage controll
ers are
increa
singly u
s
ed in
seve
ra
l application
s
su
ch a
s
indu
strial h
eating
system
s, motor soft starters,
lighting
cont
rol, Energy-sa
v
ing c
ontrol
o
f
indu
ction m
o
tor d
r
ive,
Co
mpen
sation
o
f
an u
nbala
n
ced
sup
p
ly and e
x
citation syst
em of bru
s
hle
ss m
o
tor [2-3].
The main drawb
a
cks of the AC voltage cont
rolle
rs usin
g cla
s
sical techni
q
ues for
gene
rating
th
e firing
angl
e
s
a
r
e in
crea
sed ha
rmo
n
ic conte
n
t
and
poor
po
we
r
f
a
ctor. He
nce th
e
PWM ba
sed
AC ch
oppe
r
wa
s propo
se
d as an alte
r
native solutio
n
for the AC
voltage co
ntroller
to re
du
ce th
e ab
ove m
e
ntioned
d
r
awbacks [4
]. In
PWM
ba
se
d AC chop
p
e
r, p
h
a
s
e
co
ntrol
techni
que i
s
adopted to
prod
uce outp
u
t voltage wi
th same in
p
u
t frequen
cy.
Phase
cont
ro
l
techni
que i
s
use
d
only for the n
a
turally commut
a
ted switchin
g device
whi
c
h lea
d
s to
low
efficien
cy an
d poor
perfo
rmance. For t
he low o
u
t
put
voltage, this type of AC ch
oppe
r gen
era
t
e
s
con
s
id
era
b
le
amount
of ha
rmoni
c di
sto
r
tion in th
e
loa
d
cu
rrent
whi
c
h
can
drasti
cally dete
r
io
rate
the po
we
r q
uality delivered fro
m
the
power sy
stem. At pre
s
ent, the dev
elopme
n
t of
fast
swit
chin
g de
vices a
nd mi
cro
p
rocesso
r
s permits
sy
nthesi
z
in
g; pulse
width m
odulatio
n (PWM)
techni
que ca
n be use
d
to enha
nce the perfo
rman
ce
of
this circuit [5]. One of th
e most pop
ular
PWM a
dopte
d
in A
C
cho
pper ci
rcuit i
s
“fixed
-du
r
at
ion PWM”. T
H
D value
ob
tained from t
h
is
PWM techniq
ue is mu
ch b
e
tter than tha
t
of phas
e
co
ntrol techniq
u
e
[6]. Howev
e
r, to enha
nce
the pe
rform
a
nce
of AC ch
oppe
r, vario
u
s
strategi
es
were p
r
op
osed for imp
r
ov
ing the
qualit
y o
f
output voltag
e.
AC cho
ppe
r
circuit empl
o
y
s forced co
mmutated de
vices o
r
self
-comm
u
tating
device
s
.
The sy
stem
perfo
rman
ce
is furthe
r imp
r
oved u
s
i
ng
variou
s ha
rm
onic elimi
nati
on tech
niqu
e
s
in
the AC chop
per. Th
e co
m
m
on characte
ristic
of
the Selective Harmonic Elimi
n
ation Pulse Width
Modulatio
n
(SHEPWM
)
m
e
thod i
s
th
at t
he
waveform
analysi
s
i
s
pe
rforme
d usin
g
Fo
urie
r
th
e
o
ry
[7]. Set of n
online
a
r tra
n
s
cend
ental e
quation
s
a
r
e
derived f
r
om
the ouput
waveform a
n
d
the
solutio
n
is
o
b
tained
usi
n
g an ite
r
ative
pro
c
e
dure,
mostly by Newton
–Raph
son meth
od.
This
method i
s
de
rivative base
d
techni
que
and may en
d
in local o
p
tima; further, right sele
ction
of
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Quality Enh
a
n
cem
ent of AC Ch
opp
er Us
ing G
eneti
c
Algorithm
(S. Mahen
dran)
31
initial values
alone
will gu
arante
e
conv
erge
nce in
th
e solutio
n
s.
Another a
p
p
r
oach uses
Walsh
function
s wh
ere solving
li
near equ
atio
ns
in
stea
d of
solving
nonli
near t
r
an
sce
ndental
equa
tions
and optimi
z
e
s
the swit
chi
ng angle
s
. Intelligent tech
nique
s may be used to solve the com
p
lex
mathemati
c
al
proble
m
s [8-12].
This p
ape
r p
r
opo
se
s a min
i
mization te
ch
nique a
s
siste
d
with a g
ene
tic algo
rithm i
n
ord
e
r
to redu
ce the com
putat
ional bu
rde
n
associ
ated
with Ne
wto
n
-Raph
so
n method.Th
e dual
obje
c
tives of geneti
c
algo
ri
thm are obtai
ning opt
imu
m
switching a
n
g
les a
nd outp
u
t voltage with
low T
HD. V
a
riou
s
swit
ch
ing angl
es
a
r
e ide
n
ti
fied
throug
h the
different ste
p
s
of GA. The
prop
osed
alg
o
rithm
cal
c
ul
ates th
e
swit
ching
angl
es e
v
en beyo
nd t
he p
o
int
whe
r
e othe
r m
e
th
ods
fail to converge. Modulatio
n index may rea
c
h unity
without resultin
g in failure of convergen
ce
.
Based
on the
switching
an
gles, PWM p
u
lse
s
a
r
e ge
n
e
rated
and a
pplied to the
AC ch
opp
er f
e
d
singl
e p
h
a
s
e
indu
ction
m
o
tor. Simul
a
tion
re
sults of
output
volta
ge a
n
d
cu
rre
n
t, spe
e
d
an
d
Torq
ue a
r
e p
r
ese
n
ted a
nd
analysed in t
he re
sult a
nd
discu
ssi
on
se
ction. A co
mp
arative an
alysis
betwe
en con
v
entional NR
method an
d GA method is tabulated.
2. AC Chopp
er Bas
e
d on
SHEPWM
AC ch
opp
er d
r
iving a capa
citor-sta
r
t ind
u
ction
r
un m
o
tor is
sho
w
n i
n
the Figu
re
1. In this
circuit, IGBTs are used a
s
semi
con
d
u
c
tor switch
es a
nd are m
a
rke
d
as S
1
and
S
2
. Switc
h
(S
1
) is
use
d
fo
r
con
nectin
g
the
source
to lo
a
d
an
d
swit
ch
(S
2
) i
s
empl
oyed to f
r
ee
-whe
el the
lo
ad
c
u
rr
en
t, w
h
en
S
1
is switched OFF.
Switch
(S
1
)
i
s
turn
ed
O
N
at
variou
s
swit
chin
g
an
gles,
α
1
,
α
2
,…
α
k-1
a
nd turned
OF
F at
β
1
,
β
2
…
β
k
per qu
arte
r cycl
e. In this
ca
se, in
put supply voltage
is
cho
ppe
d into
segm
ents
an
d output volta
ge level is
de
cide
d by the ratio between
ON a
nd OF
F
of
the power
se
micon
d
u
c
tor
swit
ch. Ch
op
per mo
de of
operation can
be reali
z
e
d
by using two AC
swit
che
s
, one
conn
ecte
d in
serie
s
an
d the other in pa
rallel with the l
oad a
s
sh
own in Figure 1.
The outp
u
t voltage of the
AC ch
opp
er
with k
pul
se
s
per h
a
lf cycl
e
is sho
w
n in
Figure 2.
The switching
angle
s
a
r
e
symmetrical
wi
th respe
c
t to
π
/2. The outp
u
t voltage ca
n be exp
r
e
s
sed
usin
g Fou
r
ier
seri
es a
s
:
n
n
n
n
o
o
t
n
B
t
n
A
a
V
1
1
)
sin(
)
cos(
(1)
Whe
r
e n
= 1, 2, 3,
Figure 1. AC Cho
ppe
r ba
sed IM Drive
Fi
gure 2. Output Voltage o
f
AC chopp
er
Due
to the
sy
mmetry of th
e wave eve
n
harm
oni
cs are ab
se
nt. Further, the
coef
fi
ci
ents
of A
n
and a
o
are ze
ro. Th
us, the above equation redu
ces to:
The value of Bn is com
put
ed as:
....
5
,
3
,
1
,
)
sin(
1
n
where
t
n
B
V
n
n
o
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 1, Octobe
r 2015 : 30 – 3
7
32
1
,
)
1
(
)
1
sin(
)
1
(
)
1
sin(
2
2
/
...
,
...
,
2
1
2
1
n
n
t
n
n
t
n
V
B
k
m
n
(3)
Whe
r
e V
m
is
the maximum
value of the
input sin
e
wa
ve. The fund
amental
com
pone
nt is giv
e
n
by:
2
/
...
,
...
,
1
2
1
2
1
2
)
sin(
2
k
t
t
V
B
m
(4)
The obj
ectiv
e
is to
fi
nd t
he switching
angle
s
to m
a
ke B
1
=V
0
* and
pe
rfo
r
m sele
ctive
harm
oni
c eli
m
ination
wh
ere
V
0
* is t
he
referen
c
e
output
voltage. Thi
s
i
s
conve
r
ted
to
an
optimizatio
n probl
em.
3. Harmonic
Elimination using Gene
ti
c Algorithm
Geneti
c
Algo
rithms a
r
e
stoch
a
sti
c
opti
m
izat
ion te
ch
nique
s. They
are si
mple,
powerful,
gene
ral
purpose an
d d
e
rivative-fre
e
sto
c
ha
stic
global
opti
m
ization
techniqu
es
(se
a
rch
algorith
m
s) i
n
spi
r
ed
by the la
ws
of n
a
tural
sele
cti
on an
d ge
ne
tics [4]. They
follow
Darwi
n
’s
theory
of evo
l
ution, where
fi
tter individ
uals a
r
e li
kel
y
to survive i
n
a
co
mpetin
g envi
r
onm
e
n
t.
These al
go
rithms
are d
e
ri
vative-free i
n
the
sen
s
e
that they d
o
not ne
ed fu
n
c
tional
de
riva
tive
informatio
n to search
for a set of
sol
u
tion t
hat
mi
nimises (or maximi
se
s) a
given o
b
je
ctive
function. Thi
s
prope
rty
of GAs red
u
ces the
comp
utational
burden,
sea
r
ch time
a
nd al
so
en
abl
es
them to
solve
com
p
lex obj
ective fu
n
c
tio
n
s. In thi
s
Se
ction, vari
ou
s step
s involve
d
in a
GA b
a
sed
approa
ch for
harm
oni
c eli
m
ination in th
e AC cho
ppe
r are expl
aine
d. Variou
s co
mpone
nts of GA
su
ch a
s
ch
ro
moso
me
s,
fi
t
ness fun
c
tion
, reprodu
ctio
n, crosso
ve
r
and m
u
tation
as
appli
ed to
the
present work
are illustrated in the followi
ng section.
The ste
p
s for
formulatin
g a probl
em an
d applying a G
A
are as follo
ws.
1)
Find the number of vari
abl
es specifi
c
to the problem;
this number will be the
numbe
r
of ge
nes in a
chro
moso
me. In t
h
is
appli
c
atio
n the
numb
e
r of varia
b
le
s i
s
the
num
be
r of
controllabl
e switchi
ng an
gl
es. Each chromosome
fo
r this appli
c
at
ion will h
a
ve
six swit
chin
g
angle
s
, viz. (
α
1
,
β
1
,
α
2
,
β
2
,
α
3
&
β
3
).
2)
Set a populat
ion si
ze an
d i
n
itialize the
p
opulatio
n. Hi
gher
popul
ation might in
crease
the rate of
co
nverge
nce bu
t it also incre
a
se
s
the exe
c
ution time.
The sele
ction
of an optimu
m
-
sized
popul
a
t
ion re
quires som
e
exp
e
r
ien
c
e i
n
G
A
. The p
o
p
u
lation in
thi
s
p
ape
r h
a
s 20
chromo
som
e
s, ea
ch
cont
aining
six
swi
t
ching
angl
es
. The p
opul
ation i
s
initiali
zed
with rand
om
angle
s
betwe
en 0
o
and 90
o
taking into con
s
id
eratio
n
the quar
ter-wave symm
e
t
ry of the output
voltage wavef
o
rm.
3)
The mo
st im
portant
para
m
eter in
GA i
s
the
co
st fu
nction to
eval
uate the fitne
s
s of
each ch
rom
o
some. Th
e
obje
c
tive of this study
is to minimize
the spe
c
ifie
d lowe
r ord
e
r
harm
oni
cs. T
herefo
r
e the
co
st function
has to be
re
lated to thes
e harmonics
. In this
work
, third
and fifth o
r
de
r ha
rmo
n
ics
pre
s
ent
at th
e outp
u
t
voltage of the
AC
cho
ppe
r h
a
s
to be mi
nimized
or elimin
ated.
Then the cost function (f) can be sele
cte
d
to minimize
.
f(
α
,
β
) =
f(
α
1
,
β
1
,
α
2
,
β
2..
α
k-1
,
β
k
) = e
r
+
hc
(5)
Subject to:
0
≤
α
1
≤
β
1
,
α
2
…
α
k
-1,
β
k
≤
π
/2
Whe
r
e,
2
1
B
V
e
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Quality Enh
a
n
cem
ent of AC Ch
opp
er Us
ing G
eneti
c
Algorithm
(S. Mahen
dran)
33
1
7
5
3
....
k
B
B
B
B
hc
4)
For
ea
ch
ch
romosome
an
output volta
ge
waveform
is
created
u
s
ing
the
swit
chin
g
angle
s
an
d the req
u
ired
harm
oni
c ma
gnitude
s ar
e
calculated u
s
ing F
a
st Fo
urie
r Tra
n
sfo
r
m
(FFT
) tech
niq
ues.
5)
Switchin
g a
n
g
le set produ
cing th
e max
i
mum Fitne
ss Value i
s
the
best
sol
u
tio
n
of
the first iterati
on.
6)
GA is
usually set to
run
fo
r a
ce
rtain n
u
m
ber
of iterat
ions
(1
00 in
this
wo
rk) to fi
nd
swit
chin
g ang
le set. After the first iterati
on, FV
s are u
s
ed to dete
r
mine the ne
w offspring. Th
ese
go throug
h
crossove
r
and
mutation
op
eration
s
and
a n
e
w po
pu
lation i
s
cre
a
t
ed which g
o
e
s
throug
h the same cy
cle st
arting fro
m
FV evaluati
on. The flow ch
art for cal
c
ul
ation of swit
ching
angle
s
is
sho
w
n in Figu
re
3.
Figure 3. Flow ch
art for ca
lculatio
n of switchi
ng an
gles
MATLAB codi
ng is develop
ed for the ap
plicatio
n of GA for voltage
harm
oni
c red
u
ction in
the AC chop
per. T
he
pa
ra
meters of
GA
su
ch
a
s
crossover an
d m
u
tation p
r
ob
a
b
ility, populati
on
size a
nd
num
ber of g
ene
ra
tions
are u
s
u
a
lly sel
e
ct
e
d
as
co
mmon
value
s
give
n i
n
the lite
r
atu
r
e,
or by me
an
s
of a trial a
n
d
error
pro
c
e
s
s to a
c
hieve
the be
st sol
u
tion set. It is observed th
a
t
a
value of
20–
3
0
is ide
a
l for
popul
ation
si
ze; a le
sse
r
va
lue in
crea
se
s the n
u
mbe
r
of iteration
s
.
On
the othe
r h
a
n
d
, a la
rge
nu
mber for pop
ulation
si
ze
d
oes
not de
crease
the
nu
mber of ite
r
at
ions
signi
fi
cantly. The num
ber
of iterations i
s
fi
rs
t
fi
xed at
100, and increased to 100
0 in steps of
100.
In most of th
e operating points, an op
timum
solutio
n
is obtaine
d
aroun
d 100
–400 iteratio
ns.
Hen
c
e, the n
u
mbe
r
of gen
eration
s
is
fi
x
ed at 500. The prob
ability of cro
s
sover i
s
fi
rs
t tak
e
n as
0.9 and then
cha
nge
d to 0.8, 0.7,
0.6 a
nd 0.5. It is o
b
se
rved that the best sol
u
tion for a given
terminatio
n
criterio
n em
erged fo
r 0.8.
The
proba
b
ility of mutation i
s
fi
rs
t
fi
xed at 0.1.
An
increa
sed val
ue yields
po
or result
s; as this va
lue i
s
decrea
s
e
d
, results g
e
t improve
d
unti
l
it
rea
c
he
s 0.0
6
. The pa
ram
e
ters th
us
sel
e
cted for th
e impleme
n
tatio
n
of GA are g
i
ven in Table
1.
Switchin
g an
gles
cal
c
ulate
d
by GA for di
fferent voltages are plotted
in Figure 4.
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TELKOM
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KA
Vol. 16, No. 1, Octobe
r 2015 : 30 – 3
7
34
Table 1. Para
meters of GA
S.No. Parameters
Values
1. Population
size
30
2. Coding
Binary
3. Number
of
generations
500
4. Selection
schem
e
Combination of
Roulette
w
heel s
e
lection w
i
th elitism
5.
Crossover operat
or
Multipoint crosso
ver
6. Cr
ossover
pr
obability
0.8
7. Mutation
proba
bility
0.06
8.
Termination crite
r
ion
500 iterations
Figure 4. Switchin
g Angle
s
for De
sired O
u
tput Voltage
s
4. Simulation Resul
t
s an
d Discus
s
io
n
Simulation of
AC chop
per
fed indu
ction
motor
we
re p
e
rform
e
d u
s
i
ng MATLAB/
Simulink
softwa
r
e a
nd
is sh
own in Fi
gure
5.
In the simulatio
n
st
udy, all the switch
es a
r
e
consi
dered to
be
ideal. The
fre
quen
cy of out
put voltage i
s
50 Hz. In
thi
s
pa
pe
r, fund
amental freq
uen
c
y switchi
ng
scheme i
s
u
s
ed. In thi
s
method, the
swit
chin
g an
gles
ca
n be
obtaine
d
to
eliminate
so
me
sele
cted h
a
rmonics an
d in turn minimi
zation of total
harmo
nics di
stortion.
Figure 5. Simulation Di
agram of AC Ch
oppe
r fed Ind
u
ction Moto
r
Simulation is
carrie
d out using the switching angl
e sh
own in Figu
re
4. The spe
c
trum of
the output vol
t
age an
d
current is ta
ke
n t
o
dete
r
mi
ne
the Total
Harmonic Di
storti
on (THD) of
AC
cho
ppe
r fed
i
ndu
ction
mot
o
r
drive. T
h
e
sim
u
lation
result
s of
out
p
ut voltage,
curre
n
t an
d t
heir
FFT sp
ectru
m
are p
r
esen
ted in the Figure 6 an
d Fig
u
re 7.
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TELKOM
NIKA
ISSN:
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046
Quality Enh
a
n
cem
ent of AC Ch
opp
er Us
ing G
eneti
c
Algorithm
(S. Mahen
dran)
35
(a)
(b)
Figure 6. (a)
Output Voltag
e Wavefo
rm; (b) FF
T sp
ect
r
um
(a)
(b)
Figure 7. (a)
Output Cu
rre
n
t Waveform;
(b) FFT
spe
c
trum
(a)
(b)
Figure 8. (a)
Rotor Sp
eed
(b) Ele
c
trom
a
gnetic To
rq
ue
From the Fi
g
u
re 6 a
nd Fi
gure
7, it is obs
erved tha
t
the output curre
n
t wave
form is
smooth
e
r tha
n
the
output
voltage. Current fluctu
at
e
up to
0.2
sec and
after th
at they attain
a
0
0.
0
1
0.
02
0.
03
0.
0
4
0.
0
5
0.
06
-
400
-
300
-
200
-
100
0
100
200
300
400
T
i
m
e
i
n
s
econ
d
s
V
o
lta
g
e
in
v
o
lts
0
0.
1
0.
2
0.
3
0.
4
0.
5
-6
0
-4
0
-2
0
0
20
40
60
Ti
m
e
i
n
se
c
o
n
d
s
C
u
rre
n
t
in
a
m
p
e
re
0
1
2
3
4
5
0
500
1000
1500
Ti
m
e
i
n
se
c
o
n
d
s
Sp
e
e
d
i
n
r
p
m
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TELKOM
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KA
Vol. 16, No. 1, Octobe
r 2015 : 30 – 3
7
36
con
s
tant valu
e. From the n
o
rmali
z
e
d
FF
T analysi
s
sh
own in Fi
gure
6(b) a
nd Fig
u
re 7
(
b), it ca
n
be se
en that
the magnitu
de of lowe
r
orde
r ha
rmo
n
ics are ve
ry low. Rotor Speed cu
rv
e
,
electroma
gne
tic toque
and
cap
a
cito
r voltage of
singl
e
pha
se in
ducti
on moto
r is
shown in Fig
u
re
8 and Figu
re
9.
Figure 9. Cap
a
citor Volta
g
e
Waveform
The fluctu
atio
ns in the
stator current die
out at about
0.2 se
c and
the cu
rre
nts
attain a
fairly con
s
ta
nt value to
rea
c
h their f
u
ll spee
d of 1430 rpm.
Torque h
a
s
an oscillat
i
ng
cha
r
a
c
teri
stic at the
startin
g
in
stant. A n
early
co
n
s
tan
t
electroma
g
n
e
tic torque
is
obtaine
d after a
time of 0.3 se
c.
5. Compara
t
i
v
e
Stud
y
In order to i
ndicate the
useful
ne
ss a
nd
effe
ctiven
ess of th
e
p
r
opo
se
d te
ch
nique,
a
quality factor has to b
e
chosen. Co
ncernin
g
to
voltage an
d current harm
oni
cs amplitu
d
e
s
, the
para
m
eters
u
s
ed
in the
co
mparative
an
alysis are h
a
r
moni
c fa
ctor of n
th
ha
rmo
n
ic
(H
F
n
), tot
a
l
harm
oni
c di
stortion
(T
HD), disto
r
tion fa
ctor
(D
F),
WTHD an
d lo
we
st or
der
h
a
rmo
n
ic
s
(L
OH
).
Perform
a
n
c
e
para
m
eters f
o
r AC chop
p
e
r obtain
ed
from the cal
c
ul
ation and
sim
u
lation is giv
e
n
in Table 2.
Table 2. Perf
orma
nce par
ameters of AC Ch
opp
er
Parameters
Calculated
Simulated
THD (
%
)
26.2
26.69
V1(Volts) 261.1
260.6
WTHD (
%
)
2.97
2.92
DF (
%
)
0.42
0.40
HF3
0.0199
0.0198
HF5
0.0602
0.0595
HF7
0.0713
0.0707
HF9
0.0189
0.0184
HF11
0.191
0.188
HF13
0.1701
0.166
HF15
0.0062
0.0060
HF17
0.0043
0.0041
HF19
0.0277
0.0274
LOH
5th
5th
Table 3
sho
w
s the co
mpa
r
i
s
on of conve
n
ti
onal Newto
n
-Raph
so
n m
e
thod with p
r
opo
sed
GA method.
From th
e Ta
b
l
e 3, it ca
n b
e
con
c
lu
ded
th
at the optimi
z
ation p
r
obl
em
wo
rks
with GA
will be ef
fi
cie
n
t, and its performan
ce i
s
superi
o
r
comp
ared to NR m
e
thod.
0
1
2
3
4
5
0
50
10
0
15
0
20
0
25
0
30
0
T
i
m
e
i
n
s
eco
n
d
s
C
a
pa
c
itor
Volta
g
e
in volts
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TELKOM
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ISSN:
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046
Quality Enh
a
n
cem
ent of AC Ch
opp
er Us
ing G
eneti
c
Algorithm
(S. Mahen
dran)
37
Table 3. Co
m
pari
s
on of Co
nventional
Ne
wton-
Ra
ph
so
n Method wit
h
Propo
se
d GA Method
Harmonic
Orde
r
Ne
w
t
on-
Raphso
n
Method
Proposed
GA Method
HF3
0.15
0.0198
HF5
0.193
0.0595
HF7
0.67
0.0707
HF9
0.71
0.0184
THD (
%
)
35.81%
26.69%
6. Conclusio
n
Geneti
c
algo
rithm based A
C
chopp
er i
s
develop
ed in
whi
c
h lo
we
r orde
r ha
rmo
n
i
cs
are
eliminated by
prope
r sel
e
ction of swit
ching angl
es.
It is observe
d that the genetic algo
rith
m
wor
k
s ef
fi
cie
n
tly for required output vol
t
age witho
u
t lo
we
r order h
a
rmo
n
ics. A compa
r
i
s
on
is
also
present
ed bet
wee
n
Geneti
c
alg
o
r
ithm an
d Newton
-Raph
son
iterat
ive Method. O
u
tput
voltage T
HD
obtaine
d by
GA method
is 26.69%. It is
observed
that
the GA
meth
od is supe
rior to
the Ne
wton-Rap
h
son iterat
ive Method on seve
ral co
unts. Althoug
h the method
is applied to the
AC ch
opp
er
is gen
eral i
n
nature a
nd
can b
e
ea
sil
y
extended for any num
b
e
r of ha
rmon
ic
elimination.
Referen
ces
[1]
Addo
w
e
es
h K
E
, Moham
ade
i
n
AL. Micr
opr
ocessor
bas
ed
harmo
nic
eli
m
inati
on
in c
h
opp
er t
y
pe
AC
voltag
e reg
u
lat
o
rs.
IEEE Trans. on Power Elec.
2000; 5(
2): 191-
200.
[2]
Kait
w
a
nidv
ila
i
S, Pi
yaru
ngsa
n
P. Lo
w
cost m
i
cropr
oc
essor
base
d
a
l
tern
ati
ng c
u
rrent v
o
lt
age
contro
ller
usin
g ge
netic a
l
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hms and
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al net
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o
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e
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(
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99.
[3]
Hashem GM,
Dar
w
ish MK.
Genera
l
i
z
e
d
sy
mmetric
a
l a
ngl
e PW
M techni
que for ac vo
ltage co
ntroll
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.
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w
er En
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01.
[4]
Sund
ares
w
a
ra
n K, Kumar AP.
Voltage h
a
r
m
o
n
ic e
l
i
m
i
nat
ion i
n
PW
M A.C. chopp
er u
s
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e
n
e
tic
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o
rith
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w
e
r Ap
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04; 151(
1): 26-
31.
[5]
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w
ood AI,
Wei S.
Gen
e
ti
c al
gorith
m
b
a
s
ed s
o
luti
on
i
n
PW
M conv
erter sw
itchin
g.
lEE Proc. Elect
.
Po
w
e
r Ap
pl. 20
05; 152: 4
73-4
78.
[6]
Jegath
e
sa
n V.
Genetic
Alg
o
r
i
thm Bas
ed S
o
lutio
n
i
n
PW
M Conv
erter S
w
itchin
g F
o
r V
o
l
t
age S
ourc
e
Inverter F
eed
in
g an Ind
u
ctio
n Motor Drive.
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a
l
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ch. Devel
o
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m
e
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[7]
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i
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ahee
m HK. Selective harmo
nic
elimin
atio
n of
PW
M AC/AC voltag
e reg
u
l
a
to
r using
h
y
bri
d
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o
a
ch.
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07; 1(
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[8]
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p
a
nan Pi
tchaiVi
ja
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anta Ma
hap
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u
zz
y
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e
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w
e
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e
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e
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n
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uting E
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ang Y
ong-
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ang Bi
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jie.
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y
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F
u
zz
y
Direct T
o
rqu
e
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E
LKOMNIKA T
e
lec
o
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i
c
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mput
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n
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ontro
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i
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o
w
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i
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n
w
i
t Bo
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l s
w
it
chin
g p
a
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-
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o
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e
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n
a
n
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a
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zz
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a
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a
po
w
e
r qua
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anc
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.
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