ISSN: 1693-6
930
¢
23
MATLAB/SIMULINK BASED ANALYSIS OF
VOLTAGE SOURCE I
N
VERTER WITH SPACE VECTOR
MODULATION
Au
zani Jidin
1
, Tole Sutikno
2
1
Depa
rtment
of Power Ele
c
troni
cs and
Driv
e
s
, Faculty of Electrical
Enginee
ring
Universiti Teknikal Mel
a
ka Malaysia
(U
T
e
M), 754
50 Ayer Keroh, M
e
laka, Malaysia
2
Depa
rtment
of Electrical Engine
erin
g, Faculty of Indu
strial Te
ch
nol
ogy
Universita
s Ahmad Dahla
n
(UAD),
Yogyaka
r
ta 551
64,
Indone
sia
e-mail: au
za
n
i
@iee
e.org
1
, tole@ee.ua
d.ac.id
2
Abs
t
rak
Modula
s
i
ve
ctor rua
ng (sp
ace
ve
ctor m
odulatio
n, SVM) adal
ah te
kni
k
m
odula
s
i terbai
k
untuk
kem
udi
beban tig
a fasa
sep
erti
m
otor induksi
3 fasa. Pad
a pape
r ini, strategi m
odul
asi
lebar pul
sa
d
enga
n SVM
dianali
s
is
se
cara
deta
il. Strategi m
odula
s
i ini
m
enggu
nakan
kal
k
ul
asi
wa
ktu switchi
ng untuk m
en
ghitung wakt
u dari t
egan
g
an ve
ktor dite
rap
k
an p
ada
beba
n tiga fasa
seim
bang. P
r
insi
p da
ri strategi m
odu
lasi
vekt
or ruang ditu
nju
k
kan d
enga
n
m
engguna
kan
Matlab/Sim
ulink. Ha
sil
sim
ulasi m
enunj
ukkan b
ah
w
a
algoritm
a ini
adalah fle
ksibel dan
co
cok
digun
akan un
tuk ke
ndali
ve
ctor lanj
ut. Strategi sw
itchi
ng ini m
em
i
nim
alkan disto
r
si beb
an seb
aik
m
em
i
nim
alkan kerugia
n akibat jum
l
ah kom
utasi dari i
nve
rter.
Kata kunci
:
m
odulasi vect
or ru
ang, in
ve
rter, disto
r
si h
arm
onik, kom
utasi vetor
A
b
st
r
a
ct
Space
vecto
r
m
odulation
(SVM) is the
best m
odul
ation te
chni
que
to dri
v
e
3-ph
ase
loa
d
su
ch a
s
3-p
h
ase ind
uctio
n
m
otor. In
this paper,
the p
ulse wi
dth m
odulatio
n stra
tegy with SVM is
anal
yzed in d
etail. The m
odulation
strat
egy
uses
sw
it
chin
g tim
e
cal
c
ulato
r
to cal
c
ulate th
e timing
of voltage
ve
ctor ap
plied t
o the three
-
p
hase bal
an
ce
d-loa
d. The prin
ciple of the sp
ace ve
ctor
m
odulation st
rateg
y
i
s
pe
rform
ed u
s
ing
Matlab/Sim
ulink.
Th
e sim
u
l
a
tion result i
n
dicate
s that t
h
is
algorithm
is flexibl
e and su
itable to use for ad
van
c
e
vector
cont
rol. The strateg
y
of the switchi
ng
m
i
nim
i
zes the
disto
r
tion
of l
oad
cu
rrent a
s
well
as lo
ss due
to m
i
nim
i
ze
num
ber of
com
m
utations
in the inve
rter.
Key
words
:
space ve
ctor
m
odulation, inve
rter, ha
rm
onics di
stortio
n
, vecto
r
com
m
u
tations.
1. INTRODUCT
I
ON
Due to
the g
r
owi
ng of fa
st pro
c
e
s
sor,
many
re
se
arche
s
tod
a
y show
great int
e
re
st to
develop n
e
w
or to modify
PWM control
algorith
m
to
o
b
tain goo
d pe
rforma
nces
of ac d
r
ives. Th
e
conve
n
tional
PWM metho
d
kn
own as
sinusoidal
p
ul
s
e-width
mod
ulation (SP
W
M) is
one of t
he
simple te
chni
que in voltag
e sou
r
ce inverter (VSI).
Thi
s
tech
nique a
pplie
s simpl
e control strate
gy
by compa
r
in
g
the three-ph
ase mo
dulate
d sign
als (kn
own a
s
refe
re
nce
sign
al) wi
th carrier
sign
al.
In this techni
que the switching freq
uen
cy is
dep
end
s on the carrier switchi
ng.
The amplitu
d
e
output voltag
e can b
e
vari
ed by controll
ing the modul
ation index d
e
fines a
s
in [1].
step
six
,
1
1
−
=
V
V
M
i
(1)
Traditio
nally t
he SPWM
te
chni
que
is
wi
dely u
s
ed
in
variable
spee
d drive
of in
ductio
n
machi
ne, e
s
p
ecially fo
r scalar
co
ntrol
where
the
stator voltag
e an
d freq
uen
cy can be
co
ntroll
ed
with minimu
m
online
comp
utational requ
ireme
n
t. In
addition, this techniqu
e is e
a
sy to impleme
n
t
Matlab/Sim
u
link Based An
alysis of Voltage Sou
r
ce Inve
rter
with Space….. (Auzani Jidi
n)
Evaluation Warning : The document was created with Spire.PDF for Python.
¢
ISSN: 16
93-6
930
24
even with si
mple anal
ogu
e ICs
circuits. Howeve
r, this alg
o
rithm
has the follo
wing d
r
a
w
ba
cks.
This te
ch
niqu
e is
una
ble t
o fully utilize
the av
aila
bl
e DC b
u
s su
pply voltage
to the VSI. This
techni
que
gi
ves mo
re tot
al harmoni
c
distortio
n
(T
HD), this
alg
o
rithm d
o
e
s
not sm
ooth t
h
e
prog
re
ss of future devel
op
ment of vector co
nt
rol im
plementatio
n of ac drive. These dra
w
b
a
c
ks
lead to
deve
lopment
of a
sop
h
isti
cate
d PWM
algo
rithm which i
s
Spa
c
e
Vector Mo
dulatio
n
(SVM). Thi
s
algorithm
g
i
ves 15% m
o
re vo
ltag
e output co
mp
are to the
sinusoidal P
W
M
algorithm, thereby increasi
ng the
DC bus utilization.
Furthermore,
it minimizes the THD as
well
as lo
ss du
e to minimize
numbe
r of commutation
s in the inverter. This alg
orithm ha
s b
een
modified to
i
mprove
the
a
c
d
r
ive p
e
rfo
r
mances
by
many researche
r
s a
s
in
[2-6] a
nd [7].
For
instan
ce, the
SVM ha
s wi
de p
r
o
s
pe
ct
of re
sea
r
ch
t
hat nee
d to
explore
e
s
pe
cially to imp
r
ove
dynamic p
e
rf
orma
nce in o
v
ermod
u
latio
n
rang
e and f
o
r matrix con
v
erter ap
plica
t
ions.
2.
SPACE VECTOR MODULATION
The th
ree
-
p
hase lin
e to
neut
ral
sin
e
waves re
quire
d fo
r 3
-
pha
se
loa
d
ca
n b
e
rep
r
e
s
ente
d as 12
00 p
ha
s
e-shifted vect
ors
(v
a
, v
b
and v
c
) in sp
ace as
sho
w
n i
n Figure 1. F
or a
balan
ce
d loa
d
, 3-ph
ase conne
cted
system, these ve
ctors
sum t
o
ze
ro. At any time instant the
three
-
ph
ase load voltage
s
can
be exp
r
e
s
sed by a
si
n
gle sp
ace ref
eren
c
e ve
ctor v* as sh
own
in
figure
1.
In
space ve
ctor
modulatio
n
st
rategy
, the
m
o
tor frequ
en
cy and
the
mo
tor voltag
e
ca
n
be cont
rolled
by controlli
ng
the amplitude and the fre
quen
cy of v*.
This PWM control strateg
y
o
f
the inverte
r
can be
applie
d to the vario
u
s te
chni
que
of ac moto
r
drive such a
s
scalar
co
ntrol,
field oriente
d
control and di
rect torque
co
ntrol.
Figure 1. Three-p
h
a
s
e voltage vecto
r
s a
nd the
resultant sp
a
c
e refe
re
nce vector
Figure 2 Th
e vector
of three
-
pha
se
stato
r
cur
re
n
t
s
In this
se
ctio
n the ma
nipu
lation of spa
c
e ve
cto
r
is
di
scusse
d. To
unde
rsta
nd e
asily the
manipul
ation
of spa
c
e vect
or, the three
-
pha
se stat
o
r
curre
nt of the inductio
n mo
tor are u
s
e
d as
s
h
ow
n in
F
i
gu
r
e
2
.
T
h
e ind
u
c
tion
mo
tor
is co
ns
id
ere
d
Y
c
o
nn
ectio
n
a
n
d
i
a
, i
b
and i
c
are t
h
e
pha
se
stator
curre
n
t. Each coil
of the
stator
pro
du
c
es a
si
nu
soid
ally distri
bute
d mmf. The
s
e
pha
se stato
r
curre
nts vect
or ca
n be ad
d
ed vectori
ally and give
s eq
uation 2.
()
c
b
a
s
i
i
i
i
+
+
=
3
2
(2)
whe
r
e i
s
is
an
insta
n
tane
ou
s q
uantity an
d it
is not a
p
hasor
qua
ntity. The i
s
can
be written as a
compl
e
x num
ber,
=
s
i
(3)
θ
j
s
e
i
i
a
i
b
i
c
i
a
i
b
i
c
v
a
v
b
v
c
12
0
0
12
0
0
12
0
0
v
*
TELKOM
NIKA
Vol. 7, No. 1, April 2009 : 23 - 30
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOMNI
KA
ISSN:
1693-6930
■
25
Matlab/Sim
u
link Based An
alysis of Voltage Sou
r
ce Inve
rter
with Space….. (Auzani Jidi
n)
and in ste
ady
state, the i
s
is expre
s
sed
as
t
j
s
e
i
ω
=
s
i
(4)
By using Eule
r theorem the
three-pha
se
st
ator p
hase curre
n
ts are expre
s
sed a
s
a
j
a
i
e
i
=
=
0
0
a
i
b
i
b
j
b
ai
e
i
=
=
0
120
c
i
c
j
c
i
a
e
i
2
0
240
=
=
(5)
By substitutin
g
equatio
n (4
) into equatio
n (1), the follo
wing e
quatio
n is obtain
e
d
()
c
b
a
i
a
ai
i
2
3
2
+
+
=
s
i
(6)
To d
e
termin
e
the
re
sultant
vector or spa
c
e
r
e
fer
e
nc
e
ve
c
t
o
r
o
f
th
e th
r
e
e-
ph
as
e
vo
lta
g
e
s
and
curre
n
ts,
it is impo
rta
n
t to tran
sform the th
re
e-pha
se ve
ctors to d-q axis.
This p
r
o
c
e
s
s is
popul
arly kn
o
w
n a
s
Park Tran
sform
ation
. The recta
ng
ular coo
r
dinat
e in Figure 3 (a)
sho
w
s ho
w
the compl
e
x vectors can b
e
transf
o
rme
d
into real an
d imagina
ry compon
ents.
(a) (b
)
i
ds
d-
axi
s
q-
axi
s
θ
i
qs
i
s
2
3
2
3
−
2
1
−
12
0
0
12
0
0
12
0
0
Figure 3. The
complex vect
or, (a
) in re
ctangul
ar coo
r
d
i
nates, (b
) sp
ace referen
c
e
vector
From
eq
uatio
n (4), by
ap
plying the E
ule
r Th
eo
rem, th
e real
and
im
agina
ry comp
onent
s
can
b
e
obtaine
d as
2
3
2
1
0
120
j
e
a
j
+
−
=
=
2
3
2
1
0
240
2
j
e
a
−
−
=
=
and
(7)
Separate into
real
an
d ima
ginary te
rm
s
and
hen
ce
th
e expressio
n
s
for the t
w
o
axis
curre
n
ts
in
terms of the three
-
p
ha
s
e currents
can b
e determi
ned
as
Evaluation Warning : The document was created with Spire.PDF for Python.
¢
ISSN: 16
93-6
930
26
()
qs
ds
c
b
c
b
a
ji
i
i
i
j
i
i
i
+
=
−
+
⎟
⎠
⎞
⎜
⎝
⎛
−
−
=
3
1
3
1
3
1
3
2
s
i
(8)
Therefore, th
e spa
c
e reference vector
can be
obtain
ed usi
ng Pythago
ra
s The
orem a
s
de
pi
cted
in Figure 3(b
)
.
The po
wer
ci
rcuit of the inverter consi
s
t
s
of six-IGBT
T1, T2, T3,
T4, T5,
with their
anti parallel d
i
ode
s as sho
w
n in Figu
re 4. The circuit also in
clud
ed
the brakin
g resi
stan
ce R
6
T
f
and
the braki
ng transi
s
tor T
f
. These ele
m
ent
s di
ssipate th
e en
ergy
reg
enerated
by the inve
rter. T
h
e
load i
s
con
s
i
dere
d a
s
Y-conne
cted i
n
orde
r to m
ake cle
ar
unde
rstan
ding
ab
out prin
cipl
e
of
modulatio
n techni
que.
1
v
T6)
T4,
(T1,
T6)
T3,
(T1,
T6)
T3,
(T2,
T5)
T3,
(T2,
T5)
T4,
(T2,
T5)
T4,
(T1,
T5)
T3,
(T1,
T6)
T4,
(T2,
2
v
3
v
4
v
5
v
6
v
7
v
0
v
*
v
2
40V
T
1
T
3
T
4
T
5
T
6
R
f
T
f
C
f
V
D
a
v
b
v
c
v
T
2
α
Figure 4. Power
Circuit of the Inverter
Figure 5. Space Vect
or hex
agon
Similarly, the voltage vector of the load
voltages
(va,
vb and vc), for the thre
e-pha
se bal
an
ced
load is
()
c
b
a
v
a
av
v
2
3
2
+
+
=
v
(9)
with
0
240
0
120
,
j
j
e
a
e
a
=
=
The inverte
r
bridg
e sh
own
in Figure 4, use
s
six IGBTs switch
es.
For safe ope
ration of
the VSI, whe
never
one
switch of a
half
bridg
e
i
s
tu
rn
on, the oth
er
swit
ch of th
e
same
half b
r
i
dge
must be off and vice versa
.
That is mean three ind
ep
ende
nt PWM
s
are g
ene
rat
ed for the three
half b
r
idge.
T
h
is
gives ri
se
s to
eight
di
stinct sw
itchin
g state
s
of V
S
I, where
sta
t
es 1
throug
h
6
are
called
the
active
state
s
and
state
s
0
and
7
ar
e
ca
lled the
ina
c
ti
ve state
s
. Th
e inve
rter
do
es
not gene
rate
purely
sinu
soidal voltage
s to the
loa
d, but depe
ndi
ng on
swit
chi
ng state
s
of the
transi
s
to
rs it
gene
rate
s v
o
ltage ve
ctors v
0
, v
1
,….
,
v
7
whi
c
h
are
sh
own
in
spa
c
e
vector hexa
g
on
in Figu
re
5.
As seen
in
F
i
gure
5, the
zero
voltag
e
vectors h
a
ve
ze
ro volta
g
e
amplitud
e a
n
d
locate
d at th
e ori
g
in of th
e hexag
on.
The
sp
a
c
e v
ector hexa
go
n ha
s six
se
ctors
whi
c
h
are
divided into
six equal si
ze
d se
ctors of
600. Each
se
ctor i
s
bo
und
ed by two a
c
t
i
ve vectors. T
h
e
locu
s of the
circle i
s
p
r
oje
c
t
ed by the spa
c
e ve
ctor v* d
epen
ds o
n
v0
, v1,….,v7 .
Mathemati
c
al
ly,
it can be re
prese
n
ted by e
quation 1
0
.
∑
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
=
7
7
...
2
,
1
n
n
s
n
T
t
x
v
n
*
v
=
(10
)
whe
r
e T
s
is the sam
p
ling t
i
me.
TELKOM
NIKA
Vol. 7, No. 1, April 2009 : 23 - 30
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOMNI
KA
ISSN:
1693-6930
■
27
Matlab/Sim
u
link Based An
alysis of Voltage Sou
r
ce Inve
rter
with Space….. (Auzani Jidi
n)
The refe
ren
c
e spa
c
e ve
ctor rotate
s an
d moves through the diff
erent secto
r
s of the
compl
e
x
and v
k+1
(11
)
he
r
e k i
s
wh
ich secto
r
tha
t
the modulation vector v* lies.
In the vector modulation i
t
is con
s
ide
r
ed t
hat the referen
c
e ve
ctor v* is con
s
tant and
stationa
plan
e as sh
own i
n
figure 5 a
s
time t in
crea
ses. In e
a
ch PWM
cycle, m
odulatio
n vector
v* is sampl
e
d at the fixed input sa
mpling fre
q
u
ency 2fs. During thi
s
time, the se
ctor is
determi
ned a
nd the mod
u
lation vecto
r
v* is m
appe
d
onto two adj
ace
n
t vectors. Figure 6 sh
ows
the refe
re
nce
vecto
r
v* in
se
cto
r
1,
wit
h
the
adja
c
e
n
t vecto
r
s v1
and
v2. In
gene
ral th
e t
w
o
adja
c
ent vect
ors in all
se
ctors
can b
e expre
s
sed a
s
v
k
w
ry in
the
com
p
lex p
l
ane, d
u
rin
g
t
he
sam
p
ling
interval T
s
. A
s
d
epi
cted i
n
equatio
n 9, t
h
e
referen
c
e vol
t
age vecto
r
s
v* is eq
ual to
the time ave
r
age
of the v
o
ltage ve
ctors ap
plied to t
h
e
load d
urin
g th
e sam
pling i
n
terval Ts
(T
s=2fs,
whe
r
e f
s
is th
e switching fre
que
ncy). For exam
ple,
con
s
id
er the
v* is station
a
r
y in se
cto
r
1 at a vecto
r
angle
α
a
s
i
llustrate
d in f
i
gure
6. Usin
g
equatio
n 9, the v* can be d
e
termin
ed a
s
0
0
2
1
*
v
T
T
v
T
T
v
T
T
v
s
s
b
s
a
+
+
=
(12
)
whe
r
e t
1
t
2
a
nd t
0
are the resp
ective on
-times to gene
rate voltage vectors v
1
, v
2
a
nd v
o
.
he times a
b
o
ve must fulfill the following
equation:
(13
)
on
s
id
erin
g that v0=0, equ
ation (12
)
giv
e
s,
,
T
s
c
T
t
t
t
=
+
+
2
1
C
2
1
*
v
T
v
T
T
v
b
s
a
=
(14)
he equ
ation
(13
)
is verifie
d
as seen in f
i
gure 6 that
(15
)
rom fig
u
re
6, the amplit
ude of volta
ge vect
o
r
s Ua
a
nd Ub is
obtai
ned
by
applying
the
T
s
+
T
2
1
*
U
U
v
+
=
F
trigono
metri
c
relation
s
α
α
sin
3
1
cos
*
*
1
v
v
U
−
=
(16
)
α
sin
3
2
*
2
v
U
=
(17
)
hese co
mpo
nent vectors
U1 an
d U2 a
r
e used to
ca
lculate the a
m
ount of time that v1 and v2
T
vectors are a
pplied d
u
rin
g
PW
M cycl
e. Con
s
id
erin
g that
D
V
v
v
3
2
2
1
=
=
(18
)
usin
g equ
atio
ns (1
2) to (17
)
, the on-time
s t1, t2 and to are obtain
ed
s
T
1
t
s
T
t
0
s
T
t
2
t
1
s
T
s
T
t
2
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¢
ISSN: 16
93-6
930
28
s
D
a
T
V
v
t
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
α
α
sin
3
1
cos
2
3
*
=
1
t
(19
)
()
s
D
b
T
V
v
t
α
sin
3
*
=
=
2
t
(20
)
2
1
0
t
t
T
t
s
−
−
=
(21
)
It can
be
cle
a
r
ly se
en f
r
om
equ
ation
s
(1
8) to
(2
0), th
a
t
the on
-time
s
t1, t2 an
d to
depe
nd
on th
e
magnitud
e
an
d angle of the
refere
nce vector v* and o
n
the sampli
n
g
time Ts.
In [1], the op
timization
of the switchi
n
g
seq
uen
ce
s i
s
p
r
op
osed
by locatin
g
t
he zero
voltage vecto
r
v7 as the la
st vector in th
e sw
it
chin
g seque
nce with
in a sam
pling
interval and
by
locatin
g vo
as the
last
vector i
n the
reversio
n of
swit
chin
g seque
nce wit
h re
sp
ect to
the
seq
uen
ce of
the previou
s
sam
pling i
nterval.
The optimal vecto
r
comm
utatio
n and switch
ing
sequences is
illustra
ted in Figure 7.
(a)
1
v
2
v
7
v
2
v
1
v
0
v
2
t
1
t
0
t
2
t
1
t
0
t
T1
T3
T5
(b)
Figure 6. Vector v* in
se
ct
or 1
Figure 7. Optimal vector
(a) Optimal vect
or co
mmutati
on.
(b) O
p
timal switchi
ng sequ
ences.
From figu
re
7, it can be
seen th
at the ch
ang
e from one ve
ctor to anoth
e
r
is obtai
ned
by
swit
chin
g the
tran
si
stor i
n
one
ph
ase. In th
is way, the nu
mbe
r
of
com
m
ut
ations an
d t
he
swit
chin
g losse
s
in the po
wer
semi
co
n
ducto
rs
can b
e minimized.
3.
THE SPACE
VECTO
R MO
DUL
AT
OR
In this
se
ctio
n, the d
e
scri
p
tion of th
e
spac
e ve
ctor
modulato
r
i
s
discu
s
sed. T
he
spa
c
e
vector m
odul
ator is
co
nst
r
ucte
d u
s
ing
Matlab/
Simu
link. The
sp
ace ve
ctor
modulato
r
(S
VM)
contai
ns
six blocks, sho
w
n
in the followin
g
figure. The
s
e blocks are
descri
bed b
e
l
o
w.
The thre
e-ph
ase g
ene
rato
r is u
s
ed to
prod
uce thre
e sine
wave
s with variabl
e
freque
ncy a
nd
amplitude. T
he thre
e sig
n
als a
r
e out o
f
phase
with
each other
b
y
120 deg
re
es. The inve
rte
r
deman
ded
freque
ncy
and
voltage
are
t
w
o
of the
blo
c
k inp
u
ts. T
h
e d
c
voltag
e
to the inve
rte
r
i
s
measured fro
m
the DC bu
s voltage me
asu
r
em
ent. This mea
s
u
r
e i
s
used to co
mpute the voltage
vector ap
plie
d to the motor. The thre
e to two
tran
sfo
r
mation
s con
v
erts voltage
s from the three-
pha
se to the two-p
h
a
s
e sy
stem u
s
ing P
a
rk’
s
T
r
an
sformation The
o
rem.
The
blo
c
k of
vector sele
ction i
s
u
s
e
d
to
find
the
secto
r
of th
e t
w
o-a
x
is pla
ne i
n
which
the
voltage vect
or lies. Th
e two-axi
s
plan
e is divided
into six different secto
r
s spa
c
ed by
60
degree
s.
TELKOM
NIKA
Vol. 7, No. 1, April 2009 : 23 - 30
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOMNI
KA
ISSN:
1693-6930
■
29
Matlab/Sim
u
link Based An
alysis of Voltage Sou
r
ce Inve
rter
with Space….. (Auzani Jidi
n)
Figure 8. Block di
agram of
spa
c
e vecto
r
modulato
r
The ramp
ge
n
swit
chin
g fre
quen
cy.
his ramp i
s
use
d as a ti
me ba
se for t
he switchi
ng
seq
uen
ce. T
he switchi
ng
time cal
c
ulat
or is
se
d
to
cal
c
ul
ate the
timing
of the
voltag
e vect
o
r
appli
ed to
the m
otor
(the
thre
e-pha
se
re
sistiv
e-
indu
ctiv
Simulation re
sults
we
re
pe
rforme
d u
s
in
g Simulin
k bl
ock a
s
sho
w
n in Fig
ure
8. The d
c
us V
D
i
s
eq
ual to 22
0V, is conn
ecte
d t
o
the inp
u
t of
the inverte
r
.
For the
linea
r ope
rating
ra
nge
nd
ary o
f
the
hexagon
. Therefore the maximum a
m
plitude of the
desi
r
ed
erato
r
i
s
u
s
e
d to produ
ce
a unita
ry ram
p at the P
W
M
T
u
e loa
d
is represen
ted as th
ree
-
pha
se ind
u
cti
on moto
r). T
he blo
c
k inpu
t is the se
cto
r
in
whi
c
h th
e vol
t
age ve
ctor li
es. T
he l
ogi
c gate
s
re
ceiv
e the
timing
seq
uen
ce
fro
m
the
switchi
ng
time calculat
or
and
the
ra
mp fro
m
the
ramp
ge
nerator. Thi
s
blo
c
k co
mpa
r
e
s
th
e ramp
and
t
he
gate timing si
gnal
s to activate the inverter switch
es at
the prope
r time.
4. SIMULATIO
N
RESULTS
b
the v* must not exceed
s the bou
v* is
cal
c
ulate
d
as
2
2
*
2
2
⎞
⎛
⎞
⎜
⎛
=
D
V
v
max
6
3
⎟
⎠
⎜
⎝
−
⎟
⎠
⎝
D
V
(22
)
Figure 9 Pha
s
e voltage a
n
d
pha
se curre
n
t
Figure 10 Sp
ace Ve
ctor pl
ane (a
) voltag
e (b)
cu
rre
nt
a
m
litude
using e
quat
ion (21
)
with
a fundamen
tal
eque
ncy of 250
Hz. The t
hree
-
p
ha
s
e voltage and th
e three
-
pha
se curre
nt can
be transfo
rm
ed
into spa
Figure 9, sho
w
s th
e ph
ase voltage
amplitude of
v* is set to the maximum a
n
d
pha
se
cu
rrent of the three-p
h
a
s
e lo
a
d
, whe
n
p
fr
c
e ve
ctor pla
ne a
s
sho
w
n in fig
ure 10.
It ca
n observed t
hat from the Figure 10(a)
the
locu
s of the referen
c
e ve
ctor with a max
i
mum
radi
us t
ouch the bou
ndary of the hexago
n. Figure
10(b
)
sh
ows
that the lo
cu
s of
t
he
sp
ace vecto
r
cu
rrent ha
s l
e
ss
ripple
an
d ex
hibit a ve
ry l
o
w
Evaluation Warning : The document was created with Spire.PDF for Python.
¢
ISSN: 16
93-6
930
30
distortio
n du
e to switchi
n
g freque
ncy
of 5 kHz.
In addition, Fig
ure 11
sho
w
s the spe
c
tru
m
o
f
pha
se current
harmo
nics a
nd gives the
THD 5.
71%.
Figure 11 Sp
ectru
m
of pha
se current ha
rmoni
cs
5. CO
NCL
USIO
N
Space Ve
ctor Modulation
only requi
re
s one refe
ren
c
e spa
c
e ve
ctor to gene
rat
e
three
-
ha
se si
ne
waves. The
am
plitude an
d freque
ncy of lo
ad voltage
ca
n be varie
d b
y
controlli
ng the
r. T
h
is alg
o
rithm
is pop
ular
ly u
s
ed in a
c
d
r
i
v
e applicatio
ns. Furth
erm
ore,
this alg
].
J
.
Holt
z
,
“
P
ulse Wid
t
h
Modulatio
n
- A Surv
e
y
”,
IEEE Transac
tions
on Indus
t
rial
Electro
n
ics, vol. 38,
no. 5,
pp. 410-420,
1992.
.J. Ke
rkm
a
n, and T.A.
Lipo, “
Simpl
e An
aly
t
ical and G
raphi
cal Tools
fo
r
-120
2, 1989.
3, 19
9
3
.
pt/Oct, 1992.
, Instrum
entation a
nd
Automation
[7].
p
referen
c
e sp
ace ve
cto
o
rithm
is flexible
a
nd suitable
to use fo
r ad
vance ve
cto
r
cont
rol. Th
e
strate
gy of the
swit
chin
g mi
nimize
s the
distortio
n of l
oad
curr
ent
as
well a
s
lo
ss
due to mi
nimize
numb
er of
comm
utation
s
in the invert
er.
REFERE
NC
ES
[1
[2].
A.M. Hava, R
Carrier
Bas
ed PWM Me
thods
”, in IEEE-PESC Conf. Records, St. Louis, Missouri, pp.
1462
-14
71, 1
997.
[3].
S. Ogawa
w
a
r
, H. Aka
g
i, and A. Na
ba
e, “
A
Nov
e
l
PWM Scheme of Voltage Source
In
v
e
rter Bas
e
d on Spa
c
e
Vector
Theo
r
y
”, in Europe
an Po
wer El
e
c
troni
cs
Conf.
,
Aache
en,
Germ
any, pp. 1197
[4].
J. Holtz, W. L
o
tzkat, and A.M. Khambad
kon
e
, “
On Co
ntinuous
Co
ntrol of PWM In
v
e
rters
in O
v
ermodulation Ran
ge Including The Six-Step
”, IEEE Trans
a
c
t
ion on Power
Electro
n
ics, vol.8, no.4, pp.546-55
[5].
T.G. Hab
e
tle
r
, F. Profum
o, M. Pastorelli, and M.
Tolbe
r
t, “
Dir
ect T
orque
Con
t
rol of
Induction
M
achines
Using Spa
ce
Vector
Mod
ulation
”, IE
EE Trans
.
On Indus
t
ry
Applicatio
ns,
vol.28, no.5, pp.104
5-1
0
5
3
, Se
[6].
A.M. Khamba
dko
ne a
nd
J. Holtz,
“
Cu
rr
ent
Con
t
rol in Ov
ermodulation Range
for Spa
ce
Vector
Mod
ulation
Bas
e
d Vec
t
or
Con
t
rolled I
nduction
M
otor
Driv
es
”, in IEEE
Internation
al Confe
r
en
ce o
n
Indu
strial
E
l
ectro
n
ics, Co
ntrol
(IECO
N
200
0
)
, pp.1334
-1
3
39, Oct 200
0.
A.M.
Hawa,
“
Carrier Ba
se
d
PWM-VSI Ov
ermodulation
Stra
tegi
es
”, Ph.D. Thes
is
, UW-
Madison, 199
7.
TELKOM
NIKA
Vol. 7, No. 1, April 2009 : 23 - 30
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