TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 3, March 2
015,
pp. 458 ~ 46
6
DOI: 10.115
9
1
/telkomni
ka.
v
13i3.713
2
458
Re
cei
v
ed O
c
t
ober 5, 20
14;
Revi
se
d De
cem
ber 3, 201
4; Acce
pted Janua
ry 2, 20
1
5
Utilizing the Optimization Algorithm in Cascaded H-
Bridge Multilevel Inverter
M.Suresh Ku
m
a
r*, Ram
a
n
i
Kannan
K.S.Rangas
am
y Co
lle
ge of T
e
chno
log
y
/ An
n
a
Univ
ersit
y
,
K.S.R Kalvi Na
gar, T
i
rucheng
ode,
Nam
a
kkal
-
627
215/C
h
e
n
nai, INDIA
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: sureshme
pe
d13
@gma
il.co
m
A
b
st
r
a
ct
T
h
is p
aper
pro
pose
d
th
e e
l
i
m
inati
on
of u
nde
si
red
har
monic
in
a C
a
sca
de
d H-Bri
d
g
e
Mu
lti-Lev
e
l
Inverter by
us
ing
Sel
e
ctive
Har
m
on
ic E
l
i
m
inati
on-Pu
lse
W
i
dth Mo
dul
at
ion
strategy
w
i
th pr
ogra
mme
d
Particle Swarm
Optim
i
z
a
tion algo
rith
m. In Selectiv
e H
a
rmonic E
l
i
m
i
natio
n Puls
e W
i
dth Modu
lat
i
on
techni
qu
e, PSO algorith
i
m i
s
used to de
termi
ne t
he n
on-li
ne
ar trans
cend
enta
l
equ
ation to prec
i
s
e
obli
gatory
sw
itchin
g a
ngl
es f
o
r el
i
m
in
ate l
o
w
order
ha
rm
on
i
cs an
d re
du
ce
th
e
To
ta
l
Harm
on
i
c
D
i
s
to
rtio
n
from th
e i
n
ver
t
er outp
u
t volt
age
w
a
vefor
m
w
h
ile
mainta
i
n
in
g the
req
u
i
r
ed fu
nda
ment
al vo
ltag
e at t
h
e
desir
ed va
lu
e. Co
mp
utation
a
l
result
s ar
e va
lidat
e that th
e
prop
osed
meth
od d
oes c
o
mp
etently e
l
i
m
i
nat
e
the low
ord
e
r har
mo
nics a
n
d
also res
u
lte
d
in min
i
mu
m
Total Har
m
o
n
i
c
Distortion v
a
lu
e. The res
u
lts
expos
ed that t
he pr
opos
ed
meth
od c
an a
c
hiev
e efficaci
ously to th
e o
p
timal so
luti
on
mor
e
rap
i
dly
tha
n
other al
gorit
hms
.
Ke
y
w
ords
:
multi-lev
e
l
inv
e
rter, sel
e
ctive
h
a
rmonic
e
l
i
m
i
n
ation
p
u
lse
w
i
dth
mo
du
latio
n
,
particl
e sw
ar
m
opti
m
i
z
at
ion, to
tal har
mo
nic di
stortion
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
At the pre
s
e
n
t
time, severa
l studie
s
sh
o
w
that the
ele
c
tri
c
al e
nergy dema
nd
can
rai
s
ed
expone
ntially and
al
so
ele
c
tri
c
al
ene
rgy
is
an
immen
s
ely p
r
ized
o
ne in
the to
d
a
y market. In
the
year of
2001
to 203
0 e
n
e
r
gy the
statistical revi
ew
show th
at the
total ene
rgy
co
nsu
m
ption
is
elevated 1
6
% from 5
0
% [1-2]. Mo
stly this probl
em a
r
ise
s
d
ue to the
li
mited qu
antity o
f
electri
c
al
ene
rgy and al
so
raised p
r
ice
of oil pr
og
re
ssively. He
nce it create
d
a new te
ch
ni
cal
improvem
ent
for re
du
ce th
e total ene
rgy
con
s
um
pt
ion
and in
crea
se
the po
wer
q
uality. This n
e
w
techni
cal
sce
nario
sho
w
s t
hat the
re
sult
of
continu
o
u
s
d
e
velopm
e
n
t to imp
r
ove
efficien
cy in
all
indu
strial a
n
d
con
s
um
er a
pplication
s
. Therefo
r
e it int
r
odu
ce
d
inverters
in th
e po
wer
co
nversi
on
system
and
it is con
s
id
er a
s
mo
st
recogni
ze
d a
pplication in
power
ele
c
tronics. Va
ri
ous
resea
r
che
s
a
r
e con
s
ide
r
ed
on to gro
w
in
g the quality of output voltage with lo
wer value of T
o
tal
Harmoni
c
Di
stortion
(T
HD) [23]. Depen
d up
on thi
s
d
e
veloping
d
e
m
and
for
hig
h
po
we
r i
n
ve
rter
system, m
u
lti-level inve
rte
r
s
have
been
tech
nol
ogi
ca
lly advanced
in re
ce
nt de
cade from b
o
th
aca
demi
c
an
d indu
stry are
a
s.
Multi-level inverter i
s
a
well-kno
w
n p
o
w
er conversi
on te
chniq
u
e
to provid
e the Step
output voltage thus it similar as
sine wa
ve with
minimum value o
f
THD [23-2
4
]. In
focus to the
appli
c
ation a
r
eas of multi
-
l
e
vel inverter,
it purpo
seful i
n
the mediu
m
and hig
h
voltage ap
plication
like Flexible
AC Transmi
s
sion System
s (FACTS),
compressors,
mills, c
onvey
ors, laminators,
UPS system
s, bro
a
d
c
a
s
ting amplifie
r
and ind
u
st
ria
l
drive. In ge
neral m
u
lti-le
vel inverter h
a
s
been catego
ri
zed into thre
e types: Diod
e-Cl
amp Mu
lt
i-Level Invert
er (DCM
LI), Flying Cap
a
ci
tor
Multi-Level
In
verter (F
CML
I
),
and Ca
sca
ded H-B
r
idg
e
Multi-L
e
vel I
n
verter (CHB
MLI). Th
e ma
in
of advantage
of multi-level inverter is e
s
sentia
lly com
pare
d
with th
e traditional t
w
o-l
e
vel voltage
inverter, it
provide
step
o
u
tput voltage
, it pr
o
d
u
c
e high po
wer
q
uality,
lowe
r harm
oni
c
val
ue,
better ele
c
tro
m
agneti
c
co
mpatibility and lowe
r switching lo
sses [8
].
In multi-level inverter, ha
rmonic p
r
o
b
le
m is
the sign
ificant one
wi
th
distre
ss the output
voltage an
d
augme
n
ted l
e
vel of switching
strat
egy.
So many m
e
thod
s like si
ne-tri
angl
e PWM
(SPWM
)
,
Opt
i
mal
Mini
miza
tion
of
T
o
tal Harmoni
c Di
stortion (OM
T
HD) and
Sel
e
ctive Ha
rmo
n
ic
Elimination Pulse Wi
dth Modulatio
n (SHE-PWM
) are
execute
d
for
harm
oni
c elimination in m
u
lti-
level inverte
r
.
In SPWM
m
e
thod i
s
ve
ry
effective
for o
b
se
rved t
he i
n
verter outp
u
t voltage b
u
t t
h
is
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Utilizin
g the Optim
i
zation Algorithm
in Ca
scade
d
H-Bridge Multile
vel Inverte
r
(M.Sure
s
h Ku
m
a
r)
459
method have
can ca
used
high swit
chi
ng
lo
ss be
cause of hig
h
swit
chin
g freque
ncy [9]. In
OMTHD
can
only pro
c
e
s
s all harm
oni
cs in identical
manne
r
to re
duce the T
H
D, but it can
not
con
s
id
er th
e i
m
porta
nce of
lower
ord
e
r
harm
oni
cs,
higher o
r
de
r h
a
rmo
n
ics [1
1
-
12]. SHE
-
PWM
is a
mo
st eff
e
ctive m
e
tho
d
to eli
m
inat
e lo
w o
r
d
e
r
harm
oni
c
s wi
th low switch
ing freque
ncy,
improve
outp
u
t po
wer qu
a
lity and
cost
of filter is
saved for invert
e
r
s [1
3]. Some
other meth
o
d
s
like
Ne
wton-Rap
h
son (N-R) m
e
thod [1
4], Walsh fun
c
tion
s [15] a
nd Block-pul
s
e fun
c
tion
s
[16]
are i
n
volved
in the h
a
rmonic elimin
ation p
r
o
c
e
s
s in m
u
lti-le
vel inverter.
Thoug
h all t
hese
method
s hav
e some d
r
a
w
backs to solve this harm
o
nic problem.
In N-R meth
od have req
u
i
re
initial gue
ss,
can
not give
o
p
timum
soluti
on a
nd
diverg
ence p
r
obl
em
s. Walsh fun
c
tion an
d Blo
c
k-
pulse fun
c
tio
n
have o
n
ly d
e
termini
ng lin
ear e
quat
io
ns, in the event
of non-li
nea
r tran
sce
nde
ntal
equatio
ns
are
difficult to find well
switchi
ng re
sult.
In rece
nt times,
many evoluti
o
nary al
go
rith
ms
s
u
c
h
as
Genetic
Algorithms
(GA), Bee Algorit
hms
(BA) and Ant
Colony Sys
t
ems
(ACS
) have
been
employ
ed in h
a
rm
on
ic elimin
ation
pro
c
e
s
s of
multi-level in
verter. Results indi
catio
n
that
the propo
se
d
method
can
su
cce
ssfully
eliminate
ce
rtain n
u
mb
er of ha
rmo
n
ics a
nd th
e ou
tput
voltage wavef
o
rm with lo
we
r total harmo
nic di
stortion
value.
In this pa
pe
r, the Particl
e
Swarm
Optim
i
zation
(PSO) algorith
m
ca
n be p
r
o
g
ram
m
ed in
SHE-PWM method for e
s
timate the tran
scend
ental
e
quation of switching a
ngle
s
to finding the
optimal soluti
on. This
prop
ose
d
metho
d
can
wo
rk
out the
optimal solution
of swit
chin
g
an
gles for
eliminate t
h
e
low o
r
de
r
h
a
rmo
n
ics
an
d minimi
ze
the T
H
D valu
e p
r
ofici
ently co
mpa
r
ed
with
iterative method
s and th
e re
sultant theory a
ppr
oa
ch. Simulatio
n
re
sults
can
be sh
own wit
h
conve
n
tional
desi
gn of 7-le
vel CHBMLI to
sho
w
the validity of prop
ose
d
method.
2. Configur
a
t
ion of The
Cascad
ed
H-Bridge Multi-L
e
v
e
l In
v
e
rter
A CHBM
L
I compa
r
ed
wit
h
FCMLI an
d DCMLI, it
pre
s
ente
d th
at the me
rits su
ch
as
modula
r
ity layout, smalle
r numbe
r of co
mpone
nts,
ab
sen
c
e
of extra clam
ping
di
ode
s or volta
g
e
balan
cing
ca
pacito
r
s and t
he num
be
r of
output voltag
e level can b
e
ea
sily adju
sted. In CHBM
L
I,
the pe
riod
of
swit
che
s
tu
rn
ON
and
OFF
pro
c
e
s
s can
be do
ne i
n
on
ly once
pe
r
cycle so it
sim
p
ly
solving the
switchi
ng lo
ss
probl
em. In Figure 1
sh
o
w
n that the CHBMLI hav
e serie
s
of H bri
d
ge
(sin
gle
-
pha
se
full-bri
dge
) i
n
verter
units.
Each full
-inv
erter
H-bri
d
g
e
ca
n p
r
od
uce thre
e different
voltage outp
u
ts: +
V
dc
, 0,
and
−
V
dc
. On
the other ha
nd, in Figu
re
2 has sh
own the stairca
s
e
output voltag
e wavefo
rm
of CHBM
L
I. Therefor
e, th
e level of CHBMLI is mea
s
ured in
2
S
+ 1,
whe
r
e
S
is th
e num
be
r of
dc
so
urce
s.
Con
s
e
quently
in Fi
gure 2
shown that th
e outp
u
t voltage
waveform of a 7-level CHBMLI with three isol
ated d
c
so
urce
s (
S
= 3).
Figure 1. Single Phase Ca
scade
d H-B
r
i
dge
Multi-Level In
verter
Figure 2. Stairca
s
e
Output
Voltage Wav
e
form
of CHBMLI
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 3, March 2
015 : 458 – 4
6
6
460
3. Selectiv
e
Harmonic Elimination Str
a
tegy
In SHE-PWM method u
s
ed to comp
uting the no
n-line
a
r tra
n
scen
dental e
q
uation to
finding suffici
ent swit
chin
g angel
s of 11 l
e
vel CHBM
L
I is pre
s
e
n
ted.
In CHBMLI p
r
odu
ce
s o
u
tp
ut
pha
se voltag
e with re
qui
red
swit
chin
g angle
s
. T
o
begin
with
output pha
se voltage
h
a
ve
harm
oni
cs is
pre
s
ente
d
. B
e
sid
e
s in
ca
se of
output
p
hase voltag
e, even
ha
rmo
n
ics i
s
ze
ro
but
odd ha
rmo
n
i
cs
are
criti
c
al
to evaluate. For that
rea
s
on, SHE met
hod can b
e
u
s
ed to
cal
c
ul
ate
the odd
ha
rm
onics in th
e p
hase voltage
by usin
g Fo
u
r
ier
se
rie
s
ex
pan
sion. A
c
cordin
gly Fou
r
i
e
r
seri
es a
nalysi
s
of output ph
ase voltag
e is given by
∑
cos
sin
∞
(
1
)
Con
s
id
erin
g t
he am
plitude
of dc
so
urce
s and
out
put
p
hase voltage
is
sho
w
n i
n
Fi
gure
2,
it would be
written as:
∑
sin
∞
(
2
)
W
h
er
e V
n
is
the amplitu
d
e
an
d voltag
e waveform
of n
th
harm
o
nic
com
pon
e
n
t. In SHE-P
W
M
method, swit
chin
g angl
es
can b
e
assig
ned withi
n
the rang
e of zero an
d
π
/2.Thus
V
n
imp
r
oves
to define odd and even functio
n
is given by
∑
cos
, n=odd and
,
n=eve
n
. The
determin
a
tion of SHE-PWM metho
d
in CHBM
L
I is used to eliminate low o
r
de
r
harm
oni
cs
while othe
r ha
rmonics a
r
e
removed by
u
s
ing filter. In
this pa
per SHE-P
W
M me
thod
can
be p
e
rfo
r
med to elimi
n
ate 3
rd,
5
th,
7
th
harm
oni
cs. I
n
the same
way eliminatin
g the lo
w o
r
d
e
r
harm
oni
cs by
cal
c
ulate the
nonline
a
r tra
n
scen
dent
al
equatio
n of switchi
ng an
gl
es a
r
e p
r
ovid
ed
as
follows
,
(
3
)
5
5
5
(
4
)
7
7
7
(
5
)
In Equation
(4) a
nd (5)
are assig
ned to
be zero for t
he pu
rpo
s
e
o
f
eliminate lo
w o
r
de
r
harm
oni
cs re
spe
c
tively. By mean
s
of M
odulatio
n
Ind
e
x (MI) to
su
gge
st the
fun
damental
volt
age
of V
1
is given as:
(6)
Substituting
Equation (3), (4), (5) into (6
) to get nonlin
ear Equ
a
tion
(7)
can b
e
followe
d:
0
5
5
5
(7)
0
7
7
7
At this in
stan
t optimal
switchin
g a
ngle
s
can
be
kno
w
n a
s
a
1,
a2, a3
must be o
r
iginate
depe
nd up
on
MI. So PSO algo
rithm
can
be p
r
og
rammed
with
SHE metho
d
for dete
r
mi
ng
optimal
switching val
ue to
eliminatin
g l
o
we
r
ord
e
r h
a
rmo
n
ics
and
maintai
ned
the fun
dam
en
tal
voltage value
.
4. Proposed
Particle S
w
a
r
m Optimization Algorith
m
PSO algorith
m
is a n
e
w
h
euri
s
tic
sche
me
expo
sed
by Kennedy
and Ebe
r
h
a
rt
in 199
5
[12]. Esse
ntially PSO alg
o
rithm
wa
s i
n
spi
r
ed
by th
e sociol
ogi
ca
l mann
ers of
food
sea
r
chi
ng
prin
ciple
s
su
ch
as group
of birds an
d fish
man
n
e
r. PSO i
s
a
n
op
erative
and
well
-fou
nde
d
optimizatio
n
algorith
m
for finding th
e o
p
timal solution
of the no
nline
a
r p
r
obl
em
s. In PSO, pa
rticle
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Utilizin
g the Optim
i
zation Algorithm
in Ca
scade
d
H-Bridge Multile
vel Inverte
r
(M.Sure
s
h Ku
m
a
r)
461
has to b
e
a
ssigned
a
s
initi
a
l value
to d
e
t
ermine
the
p
r
oba
ble
sol
u
tion fo
r the
no
n line
a
r
probl
em.
In general PSO can find th
e finest optim
al solutio
n
fro
m
the enter search spa
c
e.
In PSO ,opti
m
al
solution
depe
nd
upo
n
Gbe
s
t
and
Pbest
wh
ere G
best
kn
own a
s
gl
obal
best i
s
den
ote by P
g
= [
p
g1
, p
g2
, .
. .
, p
gD
] and Pbest
kno
w
n a
s
p
e
rson
nel be
st i
s
den
ote by
P
i
=
[p
i1
, p
i2
, . . . , p
iD
]. On
every instan
ce,
p
a
rticle
s ca
n
b
e
up
dated
for finding
the
realisti
c
soluti
on
with re
spe
c
t of position a
n
d
velocity vectors. In
enter
sea
r
ch sp
ace
,
position vect
ors a
s
sum
ed
to
be X
i
= [
x
1
, x
2
. .
. x
D
] and th
e velocity vector V
i
= [
v
1
, v
2
, .
. .
,
v
D
] [13]. Every particle can expa
nd
s
the sea
r
ch criteria be influ
enced
by pre
s
ent be
st val
ue, previo
us
best value a
n
d
experi
ence
o
f
neigh
bori
ng
best valu
e. Using E
quatio
n (8
) an
d (9)
adju
s
t the pa
rticle
s
with re
spe
c
t of velo
city
and po
sition
vectors. The
r
efore the velo
city and po
sition equ
ation i
s
given a
s
:
g
(8)
(9)
Whe
r
e c
1
an
d c
2
a
r
e the
con
s
trai
nts
of cogitative a
n
d
so
cial ta
sk
and
r1 a
nd r
2
are th
e rand
om
values for the
initial solutio
n
of PSO and its
range i
s
within 0 to 1 respe
c
tively [15-16].
5. Problem Formulation
In PSO algorithm ca
n be
excueted to
assume
θ
i
= [
θ
1
,
θ
2
.
. .
θ
s
] be a trial vector
establi
s
hi
ng the
i
th
particle
of the enter swarm to
be d
e
velope
d. The con
s
trai
nts
of
θ
i
kno
w
n the
optimal sol
u
tion for SHE p
r
oble
m
and it
will be acco
mplish
ed du
e
to consi
s
tent
to the variou
s
swit
chin
g an
gle for the m
u
lti-level inve
rter. And
so
step-by-step
pro
c
ed
ure as to be follows to
solving the S
H
E pro
b
lem
with non
-eq
u
a
l dc source
s.
Step 1: Initialize the po
pula
t
ion with app
r
opriate lo
cati
ons a
nd ra
ng
e of velocities.
Step 2: Evaluation the fitness of the spe
c
if
ic pa
rticle i
n
the entire swarm (Pbe
st).
Step 3: Comp
ute the fitness of individual
gl
obal pa
rticl
e
s in the entire swarm
(Gb
e
st).
Step 4: Modify Pbest and
Gbe
s
t Positio
n
based on u
pdating velo
ci
ty constraints
Step 5: Updat
e the particl
e
s
po
sition at
the termin
atio
n of every iteration.
Step 6: Termi
nate the iterat
ion pro
c
e
s
s if
the conditio
n
can get the o
p
timum value
Step 7: Otherwise Go to Step 2.
The ab
ove all
steps i
s
u
s
e
d
to estimate
t
he optimal value, its pr
ocess ca
n be d
e
fined in
fo
llo
w
i
ng
flow
c
h
ar
t. Hen
c
e F
i
gu
r
e
3 s
h
o
w
n
th
at the PSO
flow
ch
art
ref
e
r to
the
op
timal
swit
chin
g ang
les for elimin
ating the lower order
h
a
rm
onic a
nd mini
mizing the T
HD valve. In PSO
algorith
m
can
app
ortion
ed
the rand
om p
a
rticle
s fo
r t
h
e initial
co
nst
r
aints for eva
l
uate the
be
st
solutio
n
d
e
p
end
upo
n th
e up
gra
d
ing
of po
sition
a
nd velo
city p
a
ram
e
ters. E
a
ch
po
sition
an
d
velocity value
can imp
r
ove
the new fi
ne
st best value in SHE-PWM method.
Figure 3. PSO algorith
m
F
l
ow Chart
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TELKOM
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KA
Vol. 13, No. 3, March 2
015 : 458 – 4
6
6
462
6. Anal
y
s
is o
f
Simulation Resul
t
s
At the insta
n
t pro
p
o
s
ed
11
level
CHBM
L
I ca
n b
e
si
mulated
by u
s
ing
Matlab/
Simulink
tool box. Here com
pare the TH
D re
sult
of conventio
n
a
l 5-level CHBMLI and propo
sed 1
1
le
vel
CHBM
L
I pro
g
ramm
ed PS
O algo
rithm
with SHEP
WM method
using MATLAB/
Simulink
syst
em.
In five levels CHBMLI,
ca
rrie
r
wave
pu
lse
width
mo
dulation
meth
od
can
be
u
s
ed to
be
pul
se
gene
ration di
vision. In Figure 4 expo
se
d that t
he magnitude of ou
tput phase v
o
ltage of 5 level
CHBM
L
I. In
Figure 5 sho
w
n that the THD value of
5 level CHB
MLI by Fast Fouri
e
r Tran
sform
analysi
s
. In
prop
osed S
H
EPWM meth
od, PSO alg
o
rithm h
a
s
b
een u
s
e
d
to
determi
ne t
h
e
optimum solu
tion for estim
a
te the req
u
i
red
swit
chin
g angle
s
. Th
erefo
r
e PSO
prog
ram
ca
n be
written in m
-
file editorial bl
ock by usin
g
Matl
ab tool box. Therefo
r
e PSO prog
ram ca
n insi
st
ed
with p
r
op
er initialized t
he n
o
. of l
e
vels,max
imu
m
iteratio
n,n
o
.of. swit
chi
n
g a
ngel
s
and
modulatio
n i
ndex. In Ta
b
l
e 1
sho
w
s t
he bl
ock
con
s
traint fo
r th
e PSO al
gorithm. The P
S
O
algorith
m
ca
n
be prog
ram
m
ed by usin
g if-else
state
m
ent and for l
o
op conditio
n
.
Figure 4. Output Phase Vo
ltage of 5-Lev
el CHBM
L
I
Figure 5. THD re
sult of 5 Level CHBM
LI
Table 1. Prog
ram Paramet
e
r OF PSO Algorithm
S.no
Name
of t
h
e PS
O co
nstrai
nts
Qua
n
ti
t
y
Ra
nge
1.
Sources
05
2.
Levels
11
3.
Voltage Value
100 V
4.
Modulation
Index
0.1-1
5.
Max
Ite
ration
1000
6.
Intialize
Population
300
7.
Voltage
Magnitu
de
0.02
8.
Size of Modulation Index
10
9. .
Required
Frequ
e
n
cy
50
Hz
0
50
0
1000
150
0
2
000
2500
3000
3500
40
00
4500
5000
-250
-200
-150
-100
-50
0
50
100
150
200
250
Ti
m
e
i
n
m
s
e
c
I
n
v
e
r
t
er
V
o
l
t
ag
e i
n
V
o
l
t
s
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TELKOM
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ISSN:
2302-4
046
Utilizin
g the Optim
i
zation Algorithm
in Ca
scade
d
H-Bridge Multile
vel Inverte
r
(M.Sure
s
h Ku
m
a
r)
463
In the Figu
re
6 sh
own that
the ha
rmoni
c
orde
rs for th
e
given outp
ut
pha
se voltag
e of 11
level CHBML
I using PSO algorith
m
.
In the Figure 7 sho
w
n that th
e output pulse voltage of 11
level CHBM
L
I for the given Modulatio
n Index
= 0.3 an
d Load Pha
s
e
Angle=120 d
egre
e
.
Figure 6. Harmonic
Ord
e
r
Vs Magnitu
de
Phase O
u
tpu
t
Voltage
Figure 7. Output Phase Vo
ltage of
MI=0.
3
at Load Ph
ase Angl
e=1
20de
gre
e
In the Figure
8 sho
w
n th
at the harmoni
c orde
r for the
given output
phase voltag
e of 11
level CHBML
I using PSO algorith
m
.
In the Figure.9 sho
w
n that th
e output pulse voltage of 11
level CHBM
L
I for the given Modulatio
n I
ndex= 0.5 an
d Load Pha
s
e
Angle=120 d
egre
e
.
Figure 8. Harmonic
Ord
e
r
Vs Magnitu
de
Phase O
u
tpu
t
Voltage
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TELKOM
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KA
Vol. 13, No. 3, March 2
015 : 458 – 4
6
6
464
Figure 9. Output Phase Vo
ltage of MI
=0.
3
at Load Ph
ase Angl
e=1
20 deg
ree
Table 2. THD and Output
Voltage Valu
e at Variou
s Modulatio
n Index
Modulation Index
RMS output volta
ge
(V
oRM
S
)
RMS value of ou
tput voltage
fundamental com
ponent
% V
oT
HD
0.2 40.8855
16.7162
22.2
0.3 50.2887
25.2896
17.8
0.4 58.1488
33.8128
13.9
0.5 65.1517
42.4474
11.4
0.6 71.1688
50.6500
9.80
0.7 76.7500
58.9139
8.30
0.8 82.1900
67.5671
6.98
0.9 87.4450
76.4662
5.57
In Figu
re 1
0
sho
w
s the
co
mpari
s
o
n
of
THD value
wi
th variou
s m
o
dulation i
nde
x. In this
part h
a
s
not
iced
THD v
a
lue i
s
com
e
in 5 %
at modul
ation
index=0.9. In com
pare
wi
th
conve
n
tional
method
(T
HD=27%
) T
H
D
value i
s
very
low in p
r
o
p
o
s
ed
metho
d
(THD=5.5%
)
.
In
prop
osed met
hod lo
wer o
r
d
e
r ha
rmoni
cs also elimi
nate
d
and THD value is mini
mi
zed.
Figure 10. V
oT
HD Vs
Modulat
ion Index
Figure 11. V
oT
HD Vs
Modulat
ion Index v
s
V
oR
M
S
In Figure
11
sho
w
n that th
e com
pari
s
o
n
betwee
n
RM
S output voltage an
d THD voltage
and MI. It shows that maximum RMS o
u
tput
voltage=87.4
45V ca
n be attained
at V
0T
HD
=5.57%
at MI=
0
.9.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Utilizin
g the Optim
i
zation Algorithm
in Ca
scade
d
H-Bridge Multile
vel Inverte
r
(M.Sure
s
h Ku
m
a
r)
465
In Figure 12
sho
w
n that
the com
p
a
r
is
on
betwee
n
RMS volt
age of fund
amental
comp
one
net
and T
H
D vol
t
age an
d MI. It sho
w
s th
a
t
maximum
RMS voltage
of fundam
e
n
tal
comp
one
nt=7
6.462V ca
n b
e
attained at V
0T
HD
=5.57%
at MI =0.9
Figure 12. V
oT
HD Vs
Modulat
ion Index v
s
V
oR
M
S
7. Conclusio
n
In this pape
r, PSO algorithm can p
r
o
g
rammed in S
H
EPWM met
hod to solve
the non-
linear
pro
b
le
m is inve
stigated. The
prop
osed m
e
thod to sol
v
e non-li
nea
r tran
scen
de
ntal
equatio
n to fi
nd optim
um
swit
chin
g an
gle for
CHB
M
LI. At the instant, PSO
algorith
m
ca
n be
use
d
to elimi
nate sp
ecifi
c
numbe
r of h
a
rmo
n
ics, re
duce the min
i
mum
THD a
nd improves
the
power qu
ality of the system. These co
mputational
result
s validate that the PSO algorithm
can
effectively attain the glob
al solutio
n
a
nd also co
ntribute bette
r THD results co
mpa
r
e
with
conve
n
tional method.
Ackn
o
w
l
e
dg
ements
The autho
rs want to than
k AICTE New
Delhi fo
r the
sup
port given
to this work throu
gh
the re
sea
r
ch
work an
d
awa
r
de
d the
“Ca
r
ee
r A
w
ard for Yo
ung Te
achers”
Dr.K.Ram
ani
(
F.No.1
1.8/AICTE/RIF
D
/CAYT/POL-I/2013-14
).
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