TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5121 ~ 51
2
8
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.592
7
5121
Re
cei
v
ed Fe
brua
ry 19, 20
14; Re
vised
Ma
rch 15, 20
14; Accepted
March 28, 20
14
Solution Trajectories for a Single-Phase Programmed
PWM Inverter
A
y
ong Hiendro*, Sy
a
i
furrahman, De
d
i
Triy
anto, Junaidi
Dep
a
rtment of Electrical E
ngi
neer
ing, Un
iver
sitasT
anjung
pu
ra
Jala
n Jen
d
. A.
Yani, Ponti
a
n
a
k
7812
4, Indon
esia
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: a
y
ong
h2
000
@
y
ah
oo.com
A
b
st
r
a
ct
T
h
is pa
per pr
e
s
ents sol
u
tio
n
trajectori
es for
progr
a
m
med
PW
M techniq
u
e
to el
i
m
in
ate
specific
order h
a
r
m
on
i
cs in a sing
le
phase i
n
vert
er. Evolut
io
nar
y algor
ith
m
is
appl
ied to d
e
termin
e
opti
m
u
m
sw
itching a
ngl
es in or
der to
el
min
i
nat
e lo
w
order har
monics for
mo
d
u
lati
on i
ndex:
-1
M
+1
. An
imple
m
entati
o
n
usi
ng
a
DE
2-11
5 Cyc
l
o
n
e
IVE F
P
GA
dev
ice
is
al
so re
porte
d i
n
this
p
aper.
T
h
e
exper
imenta
l
r
e
sults s
how
th
at the te
c
hni
qu
e effective
l
y e
l
i
m
i
nates t
he
s
p
ecific h
a
r
m
o
n
ic
s, and
offers l
o
w
har
mo
nic disto
r
tions on the i
n
ve
rter output af
ter filtering.
Ke
y
w
ords
: F
P
GA, harmo
nic
eli
m
i
nati
on, ev
oluti
onar
y a
l
g
o
r
ithm, pro
g
ra
mme
d
PW
M, trajectory
Copy
right
©
2014 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
Pulse width modulatio
n
(PWM)
i
n
verte
r
s hav
e b
een
widely
studie
d
and
appli
e
d
in many
appli
c
ation
s
,
such as
motor drive,
uninter
rupta
b
le power supply, and rene
wable p
o
w
er
gene
ration. I
n
ord
e
r to ge
t good sin
u
so
idal output
from the PWM
inverter, it has to op
erate
on
highe
r
swit
chi
ngfreq
uen
cy.
Con
s
e
quently
, the hig
h
swi
t
ching
freq
ue
ncy g
ene
rate
s hi
gh
swit
chi
ng
stre
ss on se
micon
d
u
c
tor
device
s
an
d hen
ce, increa
se
spo
w
e
r
losse
s
in them [1].
Programme
d
PWM is
an al
ternative to tr
aditional P
W
M techni
que
s. Progra
mme
d PWM
works with lo
w switchi
ng frequ
en
cyso t
hatswitch
i
ng
losse
s
is min
i
mal. This te
chni
que
can
be
use to elimi
nate sp
ecifi
c
unde
sire
d lowe
r-
ord
e
r
harm
oni
c co
mpone
nts from output
of
singl
epha
se i
n
verters an
d to control its fundam
ental. The re
mainin
g highe
r-ord
e
r
harmoni
cs
a
r
e
then su
ppressed by u
s
ing
a sm
all L
-
C p
a
ssive filter.
The main p
r
oble
m
of the pro
g
ra
m
m
ed PWM is in solving
a set of
nonlin
ear
transce
nde
ntal equ
ations.
Many
co
mp
utational te
chniqu
es
have bee
n deve
l
oped i
n
[2-9
] to
determi
ne op
timum swit
chi
ng angl
es i
n
orde
r to elimi
nate the spe
c
ific lo
we
r-o
rder h
a
rm
oni
cs,
but the most
of them need
very hard d
e
r
ivation to
find the nume
r
ical expre
s
sion
of the nonlin
ear
equatio
ns b
e
f
ore obtai
nin
g
the optim
um switch
i
n
g
angle
s
. In this pa
per,
an evolution
a
ry
algorith
m
i
s
appli
ed to
optimize th
e switching
pattern
for t
he P
W
M in
verter
usi
n
g
the
transce
nde
ntal equatio
ns
without any n
u
meri
cal tra
n
s
form
ation
s
.
An FPGA device is imple
m
ented to ge
nerate the op
timum PWM waveforms. T
he FGPA
as a hard-sp
eed ha
rd-wi
r
ed logic h
a
s a high co
m
putation sp
e
ed cap
ability [10, 11].
Such
comp
utation
cap
ability is
requi
re
d to convert
switch
ing an
gles
o
b
tained from
comp
utation
a
l
p
r
oc
es
se
s
in
to
PW
M w
a
vefo
r
m
s
.
The
obje
c
tive of this pa
pe
r i
s
to
rep
o
rt
sol
u
tion
s fo
r switchi
ng
a
ngle
s
p
r
obl
e
m
s i
n
a
prog
ram
m
ed
PWM inverte
r
for single
-
ph
ase ap
plications. The
solu
tion pattern
s for both po
siti
ve
and
neg
ative value
s
of
m
odulatio
n in
d
e
x (
M
) in the range of the
programmed PWM
capability
are inve
stiga
t
ed. Finally, experime
n
tal re
sult
s a
r
e pre
s
e
n
ted
to validate the theoret
ical
argu
ment
s.
2. Schemes for Program
med PWM in a T
w
o
-
Lev
e
l Single-Phas
e In
v
e
rter
The program
med PWM p
a
ttern for a
singl
e-p
h
a
s
e
inverter (a
s seen in Fig
u
re 1
)
, is
sho
w
n i
n
Fig
u
re 2. A
s
th
e pattern i
s
odd q
uarte
r-wave
symme
try, only odd
-order
ha
rmo
n
ic
comp
one
nts
exist. The Fo
urie
r se
rie
s
e
x
pansi
on of
this outp
u
t voltage wavefo
rm is written a
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5121 – 51
28
5122
,...
7
,
5
,
3
,
1
)
sin(
)
(
n
n
t
n
V
t
v
(
1
)
The mag
n
itu
de of harm
o
n
i
c com
pon
ent
s (in
c
ludi
ng the fundam
en
tal)
V
n
is then defined
by:
N
k
k
k
dc
n
n
n
V
V
1
)
cos(
)
1
(
2
1
4
(
2
)
Figure 1. Single-p
h
a
s
e Inverter
Circuit
Figure 1. Pro
g
ramm
ed PWM Waveform
for a Single-p
hase Inverter
The pro
g
ra
m
m
ed
P
W
M
t
e
ch
niqu
e con
c
erns
to elim
inate (
N
-1) harmonics
completely
from the wav
e
form thro
ug
h calculating
of
N
switchi
ng angle
s
in
the first quarter pe
riod. T
he
remai
n
ing
on
e equ
ation i
s
reserve
d
for
controlling
th
e funda
ment
al mag
n
itude
V
1
at a pa
rticular
modulatio
n in
dex value. Hence,
the eq
uation
s
for
solving the
N
swit
chin
g
an
gles
1
,
2
,…,
N
are a
rra
nge
d into:
1
)
cos(
)
1
(
2
1
4
)
(
1
1
N
k
k
k
M
f
N
k
k
k
M
f
1
3
)
3
cos(
)
1
(
2
1
3
4
)
(
N
k
k
k
M
f
1
5
)
5
cos(
)
1
(
2
1
5
4
)
(
’…
N
k
k
k
N
N
M
N
f
1
)
1
2
(
)
)
1
2
cos((
)
1
(
2
1
)
1
2
(
4
)
(
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Solution Traj
ectori
es fo
r a Single-Ph
ase
Program
m
ed PWM Inve
rte
r
(Ayong Hi
en
dro
)
5123
Whe
r
e
f
3
,
f
5
,…,
f
(2.N-1)
are the no
rmali
z
ed
magnitu
de (with respect to the
fundame
n
tal) of
harm
oni
cs to
be eliminate
d
and
M
=
V
1
/
V
dc
is the modul
ation index.
The obje
c
tive
function crea
ted fo
r optimi
z
ation i
s
expressed by:
,
...
)
(
)
1
2
(
9
7
5
3
1
N
f
f
f
f
f
f
f
f
f
f
f
f
f
f
N
,
,...,
,
,
,
,
)
1
2
(
9
7
5
3
1
(
4
)
And the soluti
ons mu
st satisfy the conditi
ons:
1
<
2
< …<
N
<
9
0
º
(
5
)
With the de
sired level of accuracy
.
Once the switchin
g angle
s
1
,
2
,…,
N
a
r
e found, the
rest of an
gles are cal
c
ul
ate
d
by:
k
=180
-
(2N+1)-k
, f
o
r
k
=
N
+
1
to 2
N
,
2N+1
=180
,
k
=360
-
(4N+2)-k
, f
o
r
k
=2
N
+2 to 4
N
+1,
4N+2
=360
(
6
)
Each p
u
lse d
e
lay (PD) an
d
pulse width
(P
W) b
e
twe
e
n
two co
nsecutive swit
ching
angle
s
for the cycl
e duratio
n
T
(a
s sh
own in Fig. 2),are
spe
c
ified by:
PD
k
=
(
2k-1
)
T
/360,
PW
k
=(
2k
-
2k-1
)
T
/360
,for
k
=1 to 2
N
+1
(7)
3. Optimizati
on of S
w
i
t
hi
ng Angles
The m
a
in
proce
dures in
an evol
ution
a
ry
a
l
go
r
i
th
mfo
r
th
e o
p
t
imiz
a
t
io
n pr
oc
es
s ar
e
initialization, mutation,
cro
s
sover or re
comb
i
nation
and
sele
ctio
n. The i
n
itial popul
ation i
s
rand
omly sel
e
cted a
nd
sh
ould cover th
e entire
para
m
eter
spa
c
e.
The mutant
individual
s are
cre
a
ted
by ad
ding th
e
weig
hted differen
c
e bet
wee
n
two pa
rent i
ndiv
i
dual
s. The
n
,
the pa
ram
e
te
r
of the mutant
individual a
n
d
the pa
rent i
ndividual
a
r
e
mixed to yield the trial in
di
vidual. If the trial
individual i
s
better than t
he pa
rent in
dividual,
the
n
the trial in
dividual repl
ace
s
the
parent
individual in the next gene
ration.
The pa
ram
e
ters to
be
set for the alg
o
rit
h
m to wo
rk
consi
s
t of obje
c
tive paramet
er (
N
),
popul
ation si
ze (
NP
), mutation fac
t
or (
F
)
,
cr
os
sover
r
a
te (
CR
) an
d bou
ndari
e
s. In this
appli
c
ation, t
he o
b
je
ctive
para
m
eter sp
ecifie
s th
e
n
u
mbe
r
of
opti
m
ized
switchi
ng a
ngle
s
. T
h
e
boun
dari
e
s m
u
st sati
sfy (5) and both
F
a
nd
CR
are in
the rang
e of [0, 1].
The first ste
p
in the optimization p
r
o
c
e
s
s is
to create
an initial population of switchi
ng
angle
s
a
s
th
e ca
ndid
a
te
solutio
n
s
b
y
assi
gnin
g
rand
om valu
es to e
a
ch
boun
dary. S
u
ch
swit
chin
g a
n
g
l
e mu
st lie
in
side
the fe
asi
b
le b
oun
ds (l
owe
r
and
up
per bou
nd
s).
The i
n
itializati
o
n
is assig
ned b
y
:
i,j
(0)
=
mi
n
j
+
rand
j
(
ma
x
j
–
mi
n
j
)
,
(
8
)
i
=
1
,2,…,
NP
,
j
=
1
,2,…,
N
Whe
r
e
i,j
(0)
is the initial
p
opulatio
n (g
e
neratio
n
G
=0
) of candi
dat
e sol
u
tion
s,
mi
n
j
and
ma
x
j
are
the lower a
n
d
uppe
r bo
und
s of
j
th
de
cisi
on switching
angle
s
, an
d
rand
j
is
a rand
om value
within
[0,1] generat
ed acco
rdin
g to a uniform p
r
oba
bility distribution.
Evaluating th
e fitness valu
e of ea
ch
swi
t
chi
ng
angle
of the pop
ula
t
ion is
carried
out by
usin
g (4
).The
best switchi
n
g angle
bestj
(0)
and the be
st value
f
best
(0)
are then
sele
cted by usin
g:
f
best
(0)
=
f
(
best
j
(0
)
),
bestj
(0)
i,j
(0)
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5121 – 51
28
5124
Mutation or
differential o
perato
r
creat
es a mutant
switching a
ngle by pert
u
rbin
g a
rand
omly
sel
e
cted
switchi
ng a
ngle
wit
h
the
differe
nce
of the
two
other ran
domly sele
cted
swit
chin
g a
n
g
l
es. All of th
e
s
e
switchi
ng
angle
s
m
u
st
be different from ea
ch
othe
r. To
co
ntrol
the
pertu
rbatio
n and imp
r
ove
conve
r
ge
nce, the differ
ence betwe
en two swit
chin
g a
ngle
s
is ampli
f
ied
by a mutation
factor
F
, a consta
nt in the
ran
ge of [0,
1]. For e
a
ch
pare
n
t (ta
r
get
) switching
a
ngle
i,j
(G),
a mutant switchi
ng an
gle
v
i,j
(G)
is produ
ced u
s
in
g
one of the followin
g
mutation variant:
v
i,j
(
G
+1)
=
ra,j
(
G
)
+
F
(
rb,j
(
G
)
–
rc,j
(
G
)
)+
F
(
rd,j
(
G
)
–
re,j
(
G
)
)
(
1
0
)
Whe
r
e th
e i
ndices
ra
,
rb
,
rc
,
rd
,
re
{1,2,…,
NP
}
are
ran
domly
cho
s
e
n
mut
ually exclu
s
i
v
e
integers an
d must be diffe
rent from ea
ch other
an
d all are differen
t
from the base index
i
. The
angle
s
ra,j
(G)
,
rb,j
(G)
and
rc,j
(G)
are the sh
uffled in
dividual
s fro
m
the pop
ul
ation
i,j
(G)
, while
G
=
0
,1,2,…,
G
ma
x
denotes the sub
s
eq
u
ent gene
ratio
n
cr
eated for each ite
r
atio
n (ge
neration
)
.
The angl
e
bestj
(
G
) is the
best swit
chi
ng angle
with the best fitness in the populatio
n
a
t
gene
ration
G.
Followi
ng th
e
mutation
op
eration,
cro
s
sover i
s
a
ppl
ied to
the
p
opulatio
n. Crossover
operator is u
s
ed
to in
crea
se th
e dive
rsity of
the mu
tant switchi
n
g an
gle
s
. It gene
rate
s a
trial
swit
chin
g an
gle
t
i,j
(
G
+1)
. Th
e trial switchi
ng an
gle i
s
a
combi
nation
of
v
i,j
(
G
+1)
and
i,j
(
G
)
based
on
binomial
sch
e
me. In the
b
i
nomial
sche
me, if t
he
ran
dom n
u
mb
er
is le
ss o
r
e
q
u
a
l than
CR
, t
h
e
para
m
eter
wil
l
come from
v
i,j
(
G
+1)
, otherwise the pa
ra
meter
come
s from
i,j
(
G
)
. If
CR
=1, it me
ans
that
t
i,j
(
G
+1
)
will be composed entirely of
v
i,
j
(
G
+1)
. The binomial cro
s
sover ca
n be exp
r
esse
d as:
otherwise
)
(
or
)
(
if
)
(
1)
(
1)
(
G
i,j
rand
j
G
i,j
G
i,j
α
j
j
CR
rand
v
t
(
1
1
)
Whe
r
e
i=
1,2,
…,
NP
,
j
=1,
2
,
…
,
N
, and
j
r
and
is a ran
domly ch
ose
n
index
{1,2,…,
N
} tha
t
guarantee
s
t
i,j
(
G
+1) to get
at least one p
a
ram
e
ter fro
m
v
i,j
(
G
+1)
.
Finally,
t
i,j
(G+1)
yielded from
the cro
s
sover ope
ration i
s
accepte
d
for t
he next ge
ne
ration if
and only if it has a
n
equ
al
or lo
wer valu
e of
the obje
c
tive function than that of its pare
n
t
i,j
(
G
)
. I
t
can b
e
expre
s
sed a
s
follo
ws:
otherwise
)
(
)
(
if
)
(
)
(
1)
(
1)
(
1)
(
G
i,j
G
i,j
G
i,j
G
i,j
G
i,j
α
α
f
α
f
t
α
(
1
2
)
The be
st switchin
g angle
a
nd value of the curre
n
t gen
eration a
r
e al
so sele
cted in
here a
s
:
f
best
(
G
+1)
=
f
(
bes
tj
(
G
+1)
),
be
stj
(
G
+1)
i,j
(
G
+1)
(
1
3
)
The mutation
, crossove
r a
nd sele
ction
pro
c
e
s
ses a
r
e repe
ated to
create a ne
w next generat
ion
until
f
best
(
G
+1)
meets
its
crit
erion
and result
s in
bestj
(
G
+1)
as the satisfied switchi
ng angl
e.
Figure 3. Swithing Angle
s
Solution Traj
ectori
es fo
r N=3
-1
-0
.
9
-0
.
8
-0
.
7
-0
.6
-0
.5
-0
.
4
-0
.
3
-0
.
2
-0
.
1
10
20
30
40
50
60
70
80
90
M
a
n
g
l
e (deg
ree)
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
10
20
30
40
50
60
70
80
90
M
a
n
g
l
e (deg
ree)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Solution Traj
ectori
es fo
r a Single-Ph
ase
Program
m
ed PWM Inve
rte
r
(Ayong Hi
en
dro
)
5125
Figure 3 illust
rates switchi
n
g pa
tterns of
the single-phase i
n
verter for index modulation:
-1
M
+1 a
s
results of the
af
orem
ention
ed optimization.
4. Field Programmable G
a
te Arra
y
(FPGA) Imple
m
enta
tion
The imple
m
e
n
tation syste
m
of prog
ra
mm
ed PWM
is usi
ng the
DE2-115
Cyclone IVE
FPGA device
.
The pul
se g
enerator
dev
elopme
n
t di
a
g
ram i
s
sho
w
n as i
n
Figu
re
4. The
DE2-115
board in
clud
es a
n
oscilla
tor that pro
d
u
ce
s 50
MH
zclo
ck
sign
al. The timer/
counter i
s
u
s
ed to
cou
n
t again
s
t clock pul
se frequ
en
cy of
50Hz or
20
m
s
. The ROM l
ookup table (LUT
) stores t
he
PWM sig
nal
pattern. The
PWM sig
nal i
s
then compa
r
ed with the
counter o
u
tput
.Theco
m
pa
ra
tor
is an XNO
R
gate that gen
erate
s
HIG
H
pulse output
i
f
both inputs
are the same
. The toggle flip
-
flop (T
-FF)
co
nstru
c
t
s
a flip
-flop an
d it to
ggle
s
from
on
e state to the
next (HIG
H t
o
LO
W o
r
LO
W
to HIGH) at every clock
cycl
e in orde
r to generate PWM.
Figure 4. Block
Diag
ram o
f
Pulse Gene
rator Devel
o
p
m
ent
In this pap
er,
the optimal
swit
chin
g an
gles at
M
=-1 and
N
=3
are
use
d
to be th
e FPGA
impleme
n
tation. The
switching a
ngle
s
f
o
r
M
=-1 an
d
N
=3 (as
sh
o
w
n in
Figu
re
3) i
s
presente
d
as
in
Tabl
e
1.
P
u
lse delay (PD) and pul
se
width
(PW) of
the
PWM
can be obtai
ned
by usi
n
g
(7)
andthe results are p
r
e
s
e
n
ted in Table 2.
The re
su
lts a
r
e co
nverte
d into microsecond (m
s) u
n
it.
Table 1. Opti
mal Switchi
n
g Angles
M=-1
1
24.9940
˚
2
35.5260
˚
2
89.1520
˚
Table 2. PD a
nd PW for P
W
M
M=-1
S1 & S2
S3 & S4
PD (ms)
PW(ms)
PD(ms)
PW(ms)
1.3886
0.5851
0.0000
1.3886
4.9529
0.0942
1.9737
2.9792
8.0263
0.5851
5.0471
2.9792
10.0000
1.3886
8.6114
1.3886
11.9737
2.9792
11.3886
0.5851
15.0471
2.9792
14.9529
0.0942
18.6114
1.3886
18.0263
0.5851
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5121 – 51
28
5126
Pulse g
ene
ra
tor for S1
an
d S2 (a
s
see
n
in Figu
re
1) can
be
cal
c
u
l
ated into bit
cou
n
t as
in Table 3. P
u
lse g
ene
rato
r for S3 an
d S4 is the in
verse
of it is for S1 and S2. Simulation results
of the pulse
generators
are
sho
w
n i
n
Figure 5. The sim
u
lati
on re
sult
s match expe
rim
ental
results a
s
se
en in Figu
re 6
.
Table 3. Pulse Gene
rato
r Con
s
tru
c
tion
for S1 and S2
t (ms)
t (ms)
count
bit count
0.0000
0.0000
0
000000000
0000
0000000
1.3886
1.3886
69430
000100001
1110
0110110
0.5851
1.9737
98685
000110000
0010
1111101
2.9792
4.9529
247645
001111000
1110
1011101
0.0942
5.0471
252355
001111011
0011
1000011
2.9792
8.0263
401315
011000011
1111
0100011
0.5851
8.6114
430570
011010010
0011
1101010
1.3886
10.0000
500000
011110100
0010
0100000
1.3886
11.3886
569430
100010110
0000
1010110
0.5851
11.9737
598685
100100100
0101
0011101
2.9792
14.9529
747645
101101101
0000
1111101
0.0942
15.0471
752355
101101111
0101
1100011
2.9792
18.0263
901315
110111000
0001
1000011
0.5851
18.6114
930570
111000110
0110
0001010
1.3886
20.0000
1000000
111101000
0100
1000000
Figure 5. Simulation Results of Pulse G
e
nerat
o
r
s for S1, S2 (PG-1
)
and S3, S4 (PG-2
)
Figure 6. Experime
n
tal Re
sults of Pul
s
e
Generators
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Solution Traj
ectori
es fo
r a Single-Ph
ase
Program
m
ed PWM Inve
rte
r
(Ayong Hi
en
dro
)
5127
5. Results a
nd Analy
s
is
The exp
e
rim
ents
are
carried out
with
the followi
ng
paramete
r
s:
V
dc
=10V,
L
=50m
H,
C
=30
F,
R
=100
, a
nd
f
1
=50Hz. T
h
e afform
enti
oned
evoluti
onary
algo
rithm ha
s
be
en
su
ccessfullyi
m
pleme
n
ted i
n
the
DE2
-
1
1
5
Cycl
one IV
E FPGA device. The i
n
vert
er is
ope
rate
d in
a sin
g
le-pha
semode
and i
s
mo
dulated
to gene
rate
a
norm
a
lized f
undam
entalv
o
ltage
V
1
= 0.73
with a funda
mental freq
u
ency
f
1
= 50
Hz. Th
e wav
e
formh
a
s th
reeswitching a
ngle
s
(N
=
3)
in e
a
c
h
quarte
r p
e
ri
o
d
. As the
re
sult, two ha
rm
onics a
r
e
eli
m
inated.Thi
s
is evide
n
t fro
m
the me
asu
r
ed
spe
c
tru
m
a
s
sho
w
n i
n
Fig
u
re
7, wh
eret
he third an
d fifth harmo
nics a
r
e n
o
tpre
sent. Even-o
r
d
e
r
harm
oni
cs na
turally do
not
exist. As
sh
o
w
n i
n
Fig
u
re
7, AC
output
voltage of th
e
inverte
r
with
out
filter givesth
e
THD of
68.2
%
, but the 3
rd
and
5
th
ha
rmonics have been
elimin
ated compl
e
tel
y
.
The voltag
e
THD i
s
d
e
cre
a
se
d to
15.0
%
whe
n
a filter
of
L
=50m
H,
C
=3
0
F is inserted into the
inverter. The
highe
r order
harm
oni
cs a
r
e redu
ce
d as
see
n
in Figu
re 8.
.
Figure 7. AC Output Voltag
e of the Pr
ogrammed P
W
M
Inverter with
out Filter
Figure 8. AC Output Voltag
e of the Pr
ogrammed P
W
M
Inverter with
out Filter
L
=5
0mH an
d
C
=30
F
6. Conclusio
n
Optimum
switchi
ng
pat
terns in
a
sin
g
le-pha
se p
r
og
ramm
ed P
W
M i
n
verter i
s
investigate
d
u
s
ing a
n
evo
l
utionary alg
o
rithm. Field
prog
ramm
a
b
le gate array is use
d
to
impleme
n
t the switchi
ng p
a
ttern. Experi
m
ental resu
lts sho
w
that t
he optim
um
swit
chin
g an
g
l
es
eliminate all l
o
w o
r
de
r h
a
rmonics
of the AC o
u
tput
voltage of in
verter. Applyi
ng an
L-C fil
t
er
redu
ce
s the h
i
gher o
r
d
e
r h
a
rmo
n
ics,
an
d hen
ce mini
mize
s the voltage THD.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5121 – 51
28
5128
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ces
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ZA, Chaudhry
SK.
Quality Asses
s
me
nt of a S
i
ngl
e-ph
ase Re
sona
nt
Inverte
r
.
Internatio
nal
Journ
a
l of Pow
e
r Electron
ics and Dr
ive System (IJPEDS)
. 201
2; 2(4): 364
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aufiq JA, Mell
itt B, Goodman
CJ.
Novel Algorithm
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ene
ra
ti
ng
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a
r
Op
ti
ma
l PWM W
a
vefor
m
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r
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ives
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ings B o
n
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w
e
r Applic
atio
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a
y
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. Solvi
n
g
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ine
a
r Eq
uatio
n of Har
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onic El
imin
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o
w
e
r C
ontrol
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ift F, Kamb
e
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w
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a
lsh D
o
ma
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ch
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qu
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a
rmonic El
imin
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t
ion a
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o
ltag
e Co
ntrol i
n
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i
dth M
odu
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J
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ft RG.Inverter Harmonic
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atio
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w
s
k
i
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y D
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y GV,
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nt
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on
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o
lbert LM, M
c
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e
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u
Z
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el
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erter Us
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ltant
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heor
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u
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a
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onics
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e Har
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r
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erenc
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W
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u
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o
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igur
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l
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e
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