Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
6, N
o
. 3
,
Sep
t
em
b
e
r
2015
, pp
. 45
9
~
47
6
I
S
SN
: 208
8-8
6
9
4
4
59
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Finite St
at
e P
red
ictive Current an
d Comm
on M
o
de Vol
t
age
Control of a Seven-phase
Voltage Source Inverter
Atif
Iqb
a
l, Sh
aikh Moinodd
i
n*, Kh
aliqur Rahman
Department o
f
Electrical Engin
e
er
ing, Qa
tar
Univ
er
si
ty
, Doha
, Qat
a
r
*Ele
ctri
cal
Eng
i
neering
S
ect
ion,
Univers
i
t
y
P
o
l
y
t
ec
hni
c,
Aligarh
Muslim
Universit
y
, Al
igarh
,
Ind
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 16, 2015
Rev
i
sed
Au
g 5, 201
5
Accepted Aug 20, 2015
The pap
e
r illustr
a
tes finite set pr
edic
tive
current
control (FSPC) along with
common
mode
voltag
e
control of a se
ven-phase voltag
e
source inver
t
er
(VS
I). The curr
ent and
com
m
o
n m
ode
voltage (CMV) controls are don
e
considering
a f
i
n
ite se
t of
contro
l
act
i
ons. Th
e space v
ector
model
of a sev
e
n-
phase voltage so
urce
inver
t
er
pr
oduces 2
7
= 128
space voltage v
ectors, with
126 activ
e and t
w
o zero vectors. Out of 126
space vec
t
ors 112 are distin
ct
and 14 ar
e redu
ndant vectors. To control the
cur
r
ent and
the co
mmon
mode
voltag
e
, s
p
e
c
ifi
c
s
e
t of
s
p
ac
e
vectors
are
c
hos
en that
m
i
nim
i
zes
th
e
magnitude of the CMV and
makes it a dc
signal and simultaneously
tr
ack th
e
referen
ce
curren
t
. Henc
e no co
m
m
o
n m
ode current can f
l
ow. T
h
ree s
e
ts
of
s
p
ace vec
t
ors
ar
e us
ed for s
w
itching actu
a
tion
,
i
n
one cas
e onl
y 15 vectors
are used (14
active
and one zero),
in second
case 14 v
ecto
r
s are used
,
followed b
y
us
e
of 8 s
p
ace vecto
r
s
(7 large and one zero) and fin
a
ll
y 7 larg
e
vectors
are
em
plo
y
ed.
Optim
al
algorithm
is
em
plo
y
ed to
find
the
v
ecto
r
which m
i
nim
i
ze
s
the chos
en
co
s
t
function
.
Th
e
effe
ct of s
e
le
cti
ng the
cos
t
function
,
the nu
m
b
er of s
p
ace vectors
on curr
ent
tracking
and co
m
m
on
m
ode
voltag
e
is
invest
igat
ed and
repor
ted.
The dev
e
lo
ped techniqu
e
is tested fo
r
RL lo
ad using
si
m
u
lation
a
nd ex
perimental appro
aches.
Keyword:
C
o
m
m
on m
o
d
e
v
o
l
t
a
ge
Cu
rren
t con
t
ro
l
M
odel
pre
d
i
c
t
i
v
e
c
ont
rol
Mu
lti-p
h
a
se
Seve
n-
p
h
ase
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Atif Iqb
a
l
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
Qatar Un
iv
ersity,
PO
B
o
x 271
3,
D
o
h
a
, Q
a
tar
Em
a
il: at
if.iq
b
al@qu
.
ed
u.q
a
1.
INTRODUCTION
In
powe
r electronic converte
r, the c
u
rre
n
t cont
rol is
co
nsi
d
ere
d
as
one
o
f
t
h
e i
m
port
a
nt
and c
r
uci
a
l
issu
e. Man
y
literatu
res
repo
rt
ed
cu
rren
t con
t
ro
l issu
es an
d
sev
e
ral tech
n
i
qu
es are
p
r
op
osed
o
v
er t
h
e years
[1
].
Trad
ition
a
l
m
e
th
od
s of cu
rren
t co
n
t
ro
l are Hysteresis b
a
sed
con
t
ro
l also called
b
a
n
g
-ban
g
co
n
t
ro
l, carrier-
base
d sinusoi
d
al curre
nt cont
rol a
nd c
u
rre
n
t cont
rol
ba
sed on
s
p
ace vectors
approac
h
[2]. Hysteresis current
cont
rol
i
s
m
o
st
sim
p
l
e
m
e
t
hod b
u
t
i
t
gi
ves v
a
ri
abl
e
swi
t
c
hi
ng
fre
que
ncy
and i
s
di
f
f
i
c
ul
t
f
o
r
di
gi
t
a
l
real
i
zat
i
on.
Ra
m
p
com
p
arison PWM techni
que a
nd s
p
ace vector PWM
approac
h
es yield
consta
nt switching
frequency
ope
rat
i
o
n. Hy
s
t
eresi
s
cont
r
o
l
offe
r va
ri
abl
e
swi
t
c
hi
ng
fre
que
ncy
,
h
o
w
e
v
er
, i
t
can be m
odi
fi
ed t
o
generat
e
con
s
t
a
nt
swi
t
c
hi
n
g
f
r
eq
ue
nc
y
of t
h
e
i
n
ver
t
er l
e
gs [
3
]
.
A
not
her a
p
pr
oac
h
o
f
c
u
r
r
ent
c
ont
rol
cal
l
e
d
‘
m
odel
pre
d
i
c
t
i
v
e cu
rr
ent
co
nt
r
o
l
’
(
M
PC
) i
s
bec
o
m
i
ng m
o
re po
pul
a
r
f
o
r a
p
pl
i
cat
i
ons i
n
po
wer el
ect
r
oni
c
s
a
n
d
electric dri
v
es. Since
powe
r c
o
nve
r
ter
gene
rates m
a
ny sw
itching states a
n
d s
o
m
e
of
th
em
ar
e r
e
d
und
an
t and
m
a
y
not
be
us
eful
i
n
o
b
t
a
i
n
i
n
g
hi
g
h
per
f
o
r
m
a
nce dy
nam
i
cs.
Hence
,
s
o
m
e
of
t
h
e
swi
t
chi
n
g
st
at
es c
a
n
be
rejecte
d
and may not be em
p
l
oyed for controls suc
h
con
t
ro
l are called
‘fin
ite set
m
o
d
e
l
p
r
ed
ictiv
e co
ntro
l’.
Thi
s
t
ech
ni
q
u
e
has
been
em
pl
oy
ed i
n
c
o
nt
r
o
l
l
i
ng t
h
ree
-
phase powe
r elec
tronics convert
e
rs and
dri
v
es
[4-9].
In
here
nt
l
y
, M
P
C
i
s
com
put
at
i
onal
i
n
t
e
n
s
i
v
e a
p
p
r
oa
ch
,
ho
we
ver
,
d
u
e
t
o
t
h
e a
d
vent
of
fast
di
gi
t
a
l
si
gnal
pr
ocess
o
rs
, Fi
el
d pr
og
ram
m
abl
e
gat
e
array
s
and m
i
crocont
ro
llers it is n
o
w p
r
actically realizab
le ap
p
r
oach
fo
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
45
9 – 476
46
0
com
p
lex system
s
such as power electr
onic
conve
r
ters and drives
. The m
e
thod
of con
t
ro
l is also
attractiv
e for
m
u
l
tip
h
a
se m
o
to
r driv
es an
d
literatu
re is availab
l
e o
n
u
tilizin
g
MPC fo
r
fiv
e
-ph
a
se two-lev
e
l in
v
e
rter
[10
-
11]
,
si
x
-
p
h
ase i
nve
rt
er
[
1
2
-
1
5
]
,
fi
ve-
pha
se t
h
r
ee-l
e
vel
NPC
i
nve
rt
er
[
16]
a
n
d se
ve
n-
pha
se
i
nve
rt
er
[1
7]
.
Owi
n
g
t
o
inh
e
ren
t
ad
v
a
n
t
ag
es o
f
m
u
lti-p
h
a
se m
ach
in
e, they are con
s
id
ered
m
a
in
ly in
h
i
gh
p
o
wer
dri
v
e applications
suc
h
as
s
h
ip
pr
o
pul
si
on
, el
ect
ri
c an
d
hy
b
r
i
d
vehi
cl
e
s
, ‘m
ore electric ai
rcraft’ etc
[1
8]
.
Pro
p
e
r
Pul
s
e
W
i
dt
h M
o
d
u
l
a
t
i
on co
nt
r
o
l
t
echni
que
s are n
eeded to c
o
ntrol the dri
v
e
syste
m
s that are
supplied
b
y
m
u
lti-p
h
a
se in
v
e
rters. Several PW
M
tech
n
i
q
u
e
s are
p
r
o
p
o
s
ed
and
p
r
esen
ted in
t
h
e literatu
re
fo
r
m
u
l
ti-
pha
se
vol
t
a
ge
s
o
u
r
ce i
nve
rt
ers
[
1
8
-
1
9
]
.
Th
e curren
t
co
n
t
ro
l i
n
m
u
lti-ph
ase
d
r
i
v
e
syste
m
is
an
ex
ten
s
i
o
n of t
h
ree-ph
ase dri
v
e su
ch
as
hy
st
eresi
s
c
ont
rol
,
car
ri
er-
b
as
ed c
ont
rol
,
spa
ce vect
o
r
base
d c
ont
rol
a
n
d
o
t
her
n
o
n
-
l
i
n
ear
co
nt
r
o
l
s
[
1
8]
,
[2
0]
.
Thi
s
pa
per
p
r
o
pos
es
fi
ni
t
e
set
m
odel
p
r
edi
c
t
i
ve c
u
r
r
ent
c
o
nt
r
o
l
o
f
a
se
ve
n-
p
h
ase
VS
I
f
eedi
n
g a
R
L
l
o
ad. T
h
e ai
m
of t
h
e
w
o
r
k
i
s
t
o
de
vel
o
p cu
r
r
ent
co
nt
r
o
l
ap
pr
oac
h
al
on
g
wi
t
h
com
m
on m
ode vol
t
a
ge
cont
rol
.
The c
o
mm
on m
ode voltage
can
be controlled
by pre-sele
c
tion
of a s
e
t of space
vector.
The sim
ilar approac
h
i
s
em
pl
oy
ed fo
r a
fi
ve-
p
hase
VSI
i
n
[
21]
.
T
h
e
pr
op
ose
d
a
p
p
r
oach
i
s
ext
e
nsi
o
n
of
m
e
t
h
od
ad
o
p
t
e
d
f
o
r
a fi
ve
-
pha
se
V
S
I [1
0
-
1
1
]
.
A seve
n-
pha
se
i
n
vert
er gene
rat
e
s 2
7
= 128 s
p
ace
vectors a
n
d thus there is greater
degre
e
of free
d
om
in
choosi
ng proper
space v
ect
or com
b
ination
for im
ple
m
enting
t
h
e control
algorithm
[22]. This
pape
r p
r
o
p
o
ses
an al
gori
t
h
m
based o
n
a choi
ce of 1
4
ac
tive and
one zero,
14 active, 7 active and one zero and
7 active while the total set
of vectors are 128. Reduce
d num
ber of space
vectors are use
d
since it is easier for
t
h
e real
t
i
m
e im
pl
em
ent
a
t
i
on an
d c
ont
rol
of
com
m
on
m
ode
v
o
l
t
a
ge.
2.
FINITE ST
ATE PREDICT
I
VE CU
R
R
ENT
C
O
NT
RO
L
2.1. The
Control Strategy
Th
e cu
rren
t con
t
ro
l sugg
ested in
th
is p
a
p
e
r i
s
b
a
sed
on
t
h
e
fin
ite set m
o
d
e
l p
r
ed
ictiv
e app
r
o
a
ch
. Th
e
po
we
r co
nve
rt
er y
i
el
d 2
7
= 1
28 s
w
i
t
c
hi
n
g
s
t
at
es, ho
weve
r,
for t
h
e cu
rre
n
t
cont
r
o
l
,
re
du
ced swi
t
c
hi
ng
st
at
es
are u
tilized
and
h
e
n
ce called ‘fin
ite set’ MPC. A b
l
o
c
k
d
i
agram
to
sho
w
th
e
p
r
i
n
ciple o
f
th
e propo
sed
st
rat
e
gy
i
s
depi
ct
ed i
n
Fi
g
u
re
1. T
h
e di
scret
e
l
o
ad m
o
d
e
l called
‘Pred
i
ctiv
e Mo
d
e
l’ is
u
s
ed
to
pre-calcu
late th
e
traj
ectory o
f
the lo
ad
cu
rren
t i
n
th
e n
e
x
t
samp
lin
g
in
terv
al assu
m
i
n
g
th
e k
n
o
w
n
curren
t
in
th
e p
r
esen
t sam
p
le.
The
pre
-
calcul
a
ted curre
nt sa
m
p
le is then fe
d to t
h
e
optim
izer along w
ith the comm
anded c
u
rrent
(obt
ained
fro
m
th
e ex
tern
al u
s
er con
t
ro
lled
loo
p
). Th
e op
timizer calcu
lates th
e co
st fun
c
tion
for all th
e p
o
ssib
l
e
switch
i
ng
co
m
b
in
ation
s
of the in
v
e
rter (no
t
e th
at s
m
al
ler set o
f
v
ect
o
r
s
are cho
s
en). Th
u
s
, it g
e
n
e
rates th
e
opt
i
m
al
swi
t
c
hi
ng
st
at
e co
rre
spo
n
d
i
n
g t
o
t
h
e gl
obal
m
i
ni
m
u
m
cost
fu
n
c
t
i
on i
n
eac
h
sam
p
l
i
ng i
n
t
e
r
v
al
a
n
d
passes i
t
on t
o
t
h
e gat
e
dri
v
e of t
h
e i
n
vert
e
r
.
Thi
s
i
s
how t
h
e opt
i
m
al
curre
nt
cont
rol
sol
u
t
i
on i
s
obt
ai
n
e
d
.
The
tech
n
i
qu
e
of
m
o
d
e
l p
r
ed
ictiv
e co
n
t
ro
l con
cep
t is d
i
fferen
t fro
m
th
e
trad
itio
n
a
l
pu
lse wid
t
h
m
o
du
latio
n
m
e
thod.
In tra
d
itional P
W
M
the sym
m
e
tr
ical switching patterns are
ge
nerate
d a
nd it is
ens
u
re
d that e
ach leg
changes
the
state at-least twice in the
same switchi
ng
interv
al.
Th
is ensu
re con
s
tan
t
switch
i
ng
frequ
en
cy
sp
ectru
m
o
f
th
e lo
ad
cu
rren
t. Co
n
t
rary to
th
is, in
th
e m
o
d
e
l p
r
ed
ictiv
e co
n
t
ro
l app
r
o
a
ch
th
ere is n
o
fix
e
d
swi
t
c
hi
n
g
pat
t
ern a
nd
hence
t
h
e spect
r
u
m
sho
w
s va
ri
abl
e
swi
t
c
hi
n
g
f
r
eq
uency
.
Ho
we
v
e
r, M
P
C
app
r
o
ach i
s
v
e
ry
p
o
werfu
l b
e
ing
sim
p
le a
n
d
i
n
tu
itiv
e. Th
e con
t
ro
ller can
in
co
rpo
r
ate
m
a
n
y
d
e
sired
co
n
t
ro
l feat
u
r
es and
can m
e
t
several
cont
rol
o
b
j
ect
i
v
es by
sim
p
l
e
m
odi
fi
cat
i
on of t
h
e c
o
st
funct
i
o
n. T
h
e cost
fu
nct
i
on ca
n
i
n
co
rp
orat
e
ot
her c
o
nt
r
o
l
fea
t
ures s
u
c
h
as r
e
duce
d
s
w
i
t
c
hi
ng l
o
sses
,
l
o
w
e
r swi
t
c
h
st
res
s
, n
u
m
b
er o
f
s
w
i
t
c
h
comm
utation e
t
c.
A seve
n-phase
voltage s
o
urc
e
inve
rte
r
yield large
num
b
er of s
p
ace
vectors
(126 active
and
2 zero),
sev
e
ral
po
ssib
l
e so
l
u
tio
n
s
could
ex
ist t
o
im
p
l
e
m
en
t
m
o
d
e
l
pred
ictiv
e con
t
ro
l. Man
y
con
t
ro
l obj
ectiv
es can
b
e
met with
flex
ib
le con
t
ro
l. Nev
e
rt
h
e
less, in
t
h
is p
a
p
e
r
t
h
ree
di
ffe
re
nt
sol
u
t
i
ons a
r
e i
n
vest
i
g
at
ed an
d
rep
o
rt
e
d
.
Howev
e
r, th
ere still rem
a
in
man
y
m
o
re to
ex
p
l
o
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Finite State
Predictive Curre
nt and C
o
mmon M
o
de
Voltage Control
of a
S
even-phase …
(Atif Iqbal)
46
1
k
i
s
k
i
*
s
1
k
i
s
Fi
gu
re
1.
M
o
d
e
l
pre
d
i
c
t
i
v
e c
ont
rol
bl
oc
ks
s
c
hem
a
t
i
c
2.
2.
T
h
e Cos
t
Functi
on
Th
e cho
i
ce of th
e co
st fun
c
tio
n
is th
e m
o
st i
m
p
o
r
tan
t
an
d
cru
c
ial step
of th
e m
o
d
e
l p
r
ed
ictive
co
n
t
ro
l. An
in
t
e
llig
en
t ch
o
i
ce lead
s to
th
e o
p
t
i
m
al so
lu
tio
n o
f
th
e con
t
ro
l o
b
j
ectiv
es. Thu
s
, th
e cost fun
c
tio
n
sh
ou
l
d
in
clud
e all th
e p
a
rameters to
b
e
op
t
i
m
i
zed
with
in
th
e i
m
p
o
s
ed
co
n
s
t
r
ain
s
. In
t
h
e curren
t
contro
l th
e
m
o
st
im
port
a
nt
va
ri
abl
e
i
s
t
h
e
cu
rre
nt
t
r
ac
ki
ng
er
ro
r.
Th
us
t
h
e m
o
st
sim
p
l
e
an
d st
rai
g
ht
f
o
r
w
ar
d c
h
oi
ce
i
s
t
h
e
abs
o
lute val
u
e
of t
h
e c
u
rrent
error. T
h
e ot
her c
h
oices co
ul
d
be s
qua
re
of t
h
e c
u
r
r
ent
err
o
r
,
i
n
t
e
g
r
al
of t
h
e
current error, the rate of change of e
r
r
o
r etc.
In this pape
r,
squ
a
re o
f
th
e absol
u
te error is
chose
n
. Specifically
in a seven-pha
se drive syste
m
there ex
ist three
ort
h
ogona
l subs
paces na
mely
α
-
β
and
x
1
-y
1
and
x
2
-y
2
. Thus
i
n
case of a
seve
n-phase
dri
v
e syste
m
the curre
nt errors in
all th
e th
ree
p
l
an
es h
a
ve to
be
co
nsi
d
e
r
ed f
o
r de
vi
si
n
g
a cost
fu
nct
i
o
n.
I
n
gene
ral
,
fo
r
cu
rre
nt
er
ro
r,
t
h
e c
o
st
f
u
nct
i
o
n i
s
gi
ve
n as;
1
ˆ
1
ˆ
ˆ
1
ˆ
1
ˆ
ˆ
1
ˆ
1
ˆ
ˆ
2
*
2
2
*
2
2
2
1
*
1
1
*
1
1
1
*
*
k
i
k
i
k
i
k
i
g
k
i
k
i
k
i
k
i
g
k
i
k
i
k
i
k
i
g
y
y
x
x
y
x
y
y
x
x
y
x
(1
)
The fi
nal
c
o
st
f
unct
i
o
n
ca
n be
exp
r
esse
d
as;
2
2
2
2
1
1
2
2
2
1
1
ˆ
ˆ
ˆ
y
x
y
x
y
x
y
x
g
g
g
J
(
2
)
Whe
r
e
.
de
n
o
t
e
m
odul
us
an
d
,
&
ar
e t
u
n
i
ng
p
a
r
a
m
e
ter
s
th
at of
fer
s
d
e
gr
ee
o
f
fr
eedom
to
put
e
m
phasis on
2
2
1
1
or
,
or
y
x
y
x
subs
paces
. Com
p
arative st
udie
s
are
m
a
de to e
m
phasize the
effect of
choi
ce
o
f
t
h
e
t
uni
ng
pa
ram
e
ter
on
t
h
e
per
f
o
rm
ance of t
h
e
cont
rol
l
e
r.
2.3. Seve
n-phase Vol
t
ag
e Source Inverte
r
Model
Po
wer ci
rcui
t
t
o
p
o
l
o
gy
of a
s
e
ven
-
phase
V
S
I fee
d
i
n
g a
R
L
E l
o
a
d
i
s
s
h
o
w
n i
n
Fi
g
u
re
2
.
The i
nve
rt
er
i
n
p
u
t
DC
vol
t
a
ge i
s
rega
rde
d
fu
rt
he
r o
n
as b
e
i
ng co
nst
a
nt
. The i
n
vert
er
o
u
t
p
ut
pha
se v
o
l
t
a
ges are den
o
t
ed i
n
Fi
gu
re 2 wi
t
h
l
o
we
r case sy
m
bol
(
a
, b,…
,
g)
,
wh
ile th
e l
e
g
vo
ltag
e
s h
a
v
e
sy
m
b
o
l
s in
cap
ital le
tters
(A,
B,
……., G)
.
The
m
odel of seven-phase VSI is developed i
n
space vect
or form
in [
23], assum
i
ng an ideal
com
m
ut
ati
on a
n
d
zer
o
fo
r
w
ar
d
vol
t
a
ge
d
r
op
.
A
bri
e
f
revi
e
w
i
s
p
r
ese
n
t
e
d
h
e
re.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
45
9 – 476
46
2
V
dc
v
a
v
b
V
A
V
B
a
e
b
e
v
g
V
G
g
e
n
N
Fi
gu
re
2.
P
o
we
r ci
rc
ui
t
o
f
a s
e
ven
-
phase
V
S
I
The
rel
a
t
i
ons
hi
p
bet
w
ee
n t
h
e
i
nve
rt
er
p
h
ase-t
o
-
n
e
u
t
r
al
v
o
l
t
a
ges a
n
d i
n
vert
e
r
pol
e
v
o
l
t
a
ges
i
s
o
b
t
a
i
n
ed
as;
G
F
E
D
C
B
A
a
v
v
v
v
v
v
v
v
7
/
1
7
/
6
G
F
E
D
C
A
B
b
v
v
v
v
v
v
v
v
7
/
1
7
/
6
G
F
E
D
B
A
C
c
v
v
v
v
v
v
v
v
7
/
1
7
/
6
G
F
E
C
B
A
D
d
v
v
v
v
v
v
v
v
7
/
1
7
/
6
(
3
a
)
G
F
D
C
B
A
E
e
v
v
v
v
v
v
v
v
7
/
1
7
/
6
G
E
D
C
B
A
F
f
v
v
v
v
v
v
v
v
7
/
1
7
/
6
F
E
D
C
B
A
G
g
v
v
v
v
v
v
v
v
7
/
1
7
/
6
whe
r
e t
h
e inve
rter
pole
voltages take t
h
e
values
of ± 0.5
V
dc
. T
h
e c
o
m
m
on m
ode vol
t
a
ge i
s
de
fi
ne
d as:
7
G
F
E
D
C
B
A
nN
v
v
v
v
v
v
v
V
(
3
b
)
An
d c
o
m
m
on m
ode cur
r
ent
i
s
de
fi
ne
d as
t
h
e cu
r
r
e
n
t
f
l
o
w
i
n
g thr
oug
h th
e
str
a
y cap
acitance:
dt
dV
C
i
nN
stray
nN
(
3
c
)
Hence t
h
e c
o
m
m
on
m
ode cur
r
ent
can
be
red
u
ce
d by
re
duci
ng t
h
e
rat
e
of cha
n
ge o
f
t
h
e com
m
on
m
ode vol
t
a
ge.
The com
m
on
m
ode vol
t
a
ge
can be el
im
i
n
at
ed com
p
l
e
t
e
ly
i
f
t
h
e rat
e
of cha
nge
of c
o
m
m
o
n
m
ode vol
t
a
ge i
s
m
a
de zero or i
n
ot
her w
o
rds i
f
t
h
e
com
m
on
m
ode vol
t
a
ge i
s
m
a
de dc. In t
h
i
s
pa
pe
r, t
h
e
com
m
on m
ode v
o
l
t
a
ge i
s
m
a
de
dc
by
c
h
o
o
s
i
n
g
a s
p
eci
fi
c
set
o
f
t
h
e s
p
a
ce vect
ors
as
di
scuss
e
d
i
n
t
h
e ne
xt
sect
i
on.
In ge
neral
,
a
n
n
ph
ase t
w
o
lev
e
l VSI yield
a to
tal o
f
2
n
nu
m
b
er of s
w
i
t
c
h
i
ng st
at
es. T
h
e
r
ef
ore
,
f
o
r a
seve
n-
pha
se V
S
I, t
o
t
a
l
num
ber o
f
s
w
i
t
c
hi
n
g
st
at
es are
1
2
8
,
i
n
whi
c
h t
w
o
are zer
o
vect
o
r
s an
d t
h
e rem
a
i
n
i
n
g
126
a
r
e
active vectors.
By using dec
o
upling trans
f
orm
a
ti
on m
a
trix give
n i
n
e
quation
(4b) each voltage
vector
can be dec
o
mpos
ed int
o
three ort
hogonal two dim
e
nsional subs
paces
d-
q,x
1
-y
1
and
x
2
-
y
2
(assum
i
ng i
s
ol
at
e
d
neut
ral
an
d
he
nce
no
zer
o se
que
nce c
o
m
p
o
n
ent
)
.
In ca
se
of a
se
ven
-
phase
V
S
I
,
t
o
t
a
l
swi
t
c
hi
n
g
c
o
m
b
i
n
at
i
o
n
of
1
2
8
num
bers y
i
el
d sam
e
num
ber
of
swi
t
c
hi
n
g
spac
e vol
t
a
ge vect
ors
.
O
u
t
of t
h
ese 12
8 sp
ace
voltage vect
ors, 126
are active and two are zero
space vect
ors
and t
h
ey form
nine concentri
c
polygons
of fourteen sides
in
d-
q
pla
n
e with zero s
p
ace
vectors
at the origi
n
as
shown i
n
Fi
gure
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Finite State
Predictive Curre
nt and C
o
mmon M
o
de
Voltage Control
of a
S
even-phase …
(Atif Iqbal)
46
3
Fig
u
re 3
.
Ph
ase-to
-n
eu
tral v
o
lta
ge space
vol
t
age vect
ors
(st
a
te
s 0 a
n
d
12
8
are at
ori
g
i
n
)
i
n
d-
q
pl
ane
Howe
ver, sinc
e a seven-phas
e system
is under c
onsi
d
erati
o
n, one has to
represe
n
t the inve
rter s
p
ace vectors
in a seven-dimensional space. Such
a space
can be dec
o
m
pose
d
into three
two-dim
e
nsional sub-s
p
aces
(
d-q,
x
1
-y
1
and
x
2
-y
2
) and one single-dim
ensional sub-
s
p
ace (ze
r
o-se
quence
). Since the
load is assum
e
d to be star-
connected wit
h
isolated ne
utral poi
nt
, ze
r
o
-se
q
uence
ca
nn
ot
be ex
ci
t
e
d a
nd i
t
i
s
t
h
eref
ore
su
ffi
ci
ent
t
o
consider only t
h
ree
two-dim
e
nsional s
u
b-s
p
aces,
d-
q,x
1
-y
1
and
x
2
-y
2
. Inve
rter
volta
ge s
p
ace vect
or i
n
d-
q
sub-
space
is give
n with [20],
g
f
e
d
c
b
a
dq
v
a
v
a
v
a
v
a
v
a
av
v
v
*
2
*
3
*
3
2
7
/
2
(4a
)
whe
r
e
7
/
2
j
e
a
,
7
/
4
2
j
e
a
,
7
/
6
3
j
e
a
,
7
/
6
3
*
j
e
a
,
7
/
4
2
*
j
e
a
,
7
/
2
*
j
e
a
In
vert
e
r
vol
t
a
g
e
space
vect
o
r
s
i
n
t
h
e sec
o
nd
t
w
o
-
di
m
e
nsi
o
n
a
l
su
b-s
p
ace
(
x
1
-y
1
)
a
n
d t
h
e t
h
i
r
d t
w
o
-
di
m
e
nsi
onal
sub-s
p
ace (
x
2
-y
2
) are d
e
term
in
ed
with
,
(4
b)
The
phase
volt
a
ge s
p
ace
vect
ors
in t
h
ree
orthogonal
plan
es
,
obtaine
d
using (1),
a
r
e s
h
own in Figures
3-5.
It
can
be see
n
fr
om
Fi
gures
3
-
5 t
h
at
t
h
e
out
er m
o
st
i
.
e. fi
r
s
t
,
seco
n
d
, t
h
i
r
d,
fo
u
r
t
h
,
fi
ft
h
,
si
xt
h,
seve
nt
h
,
an
d
eighth tetra
-
de
cagons s
p
ace
vectors
of t
h
e
d
–
q
pl
a
n
e m
a
p i
n
t
o
t
h
e si
xt
h,
ei
ght
h
,
t
h
i
r
d,
s
econ
d
,
fi
ft
h, se
vent
h,
first and
fourth of t
h
e tetra-de
cagon
of the
x
1
–
y
1
pl
ane res
p
ect
i
v
el
y
;
and
seve
nt
h, f
o
u
r
t
h
,
t
h
i
r
d,
ei
ght
h, fi
ft
h,
f
i
r
s
t, six
t
h
an
d seco
nd
of
th
e tetr
a-
D
ecagon o
f
th
e
x
2
–
y
2
plane res
p
ectively. To show this
m
a
pping
same
sym
bolic repre
s
entation a
r
e used for t
h
e sa
me group
of
s
p
ace vect
ors
.
Furt
her, it is
obs
e
rve
d
from
the above
m
a
ppi
n
g
t
h
at
t
h
e
pha
se se
que
nce
a, b,
c, d,
e,
f
&
g
of
d
–
q
plane
corre
s
p
onds t
o
a,
c
,
e,
g
,
b, d,
f
of
x
1
–
y
1
pl
ane (t
hi
r
d
ha
rm
oni
c)
an
d
a,
d,
g,
c, f
,
b
,
e
of
x
2
–
y
2
plane
(fifth ha
rm
onic),
res
p
ectively.
g
f
e
d
c
b
a
y
x
g
f
e
d
c
b
a
y
x
v
a
av
v
a
v
a
v
a
v
a
v
v
v
a
v
a
av
v
a
v
a
v
a
v
v
4
5
2
6
3
2
2
5
3
6
4
2
1
1
7
/
2
7
/
2
Evaluation Warning : The document was created with Spire.PDF for Python.
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S
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94
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S
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l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
45
9 – 476
46
4
Fi
gu
re
4.
P
h
as
e-t
o
-
n
e
u
t
r
al
vo
l
t
a
ge space
vec
t
ors
for states
1-128.(states
0-
12
8 ar
e at or
ig
i
n
)
in
x
1
-y
1
pl
ane
2.4. Discrete
Load Model
The loa
d
is assum
e
d as a seven-phase RL (Resista
nce and, inductance
).
Th
e d
i
screte time
m
o
d
e
l o
f
th
e lo
ad
su
itab
l
e fo
r curren
t
pred
ictio
n
is ob
tain
ed
fro
m
[67
]
;
L
RT
k
i
k
v
L
T
k
i
s
s
1
1
ˆ
(
5
)
Where
R
and
L
are t
h
e resi
st
ance and
i
nductance of t
h
e
l
o
ad,
T
s
is th
e
sa
mp
lin
g
in
t
e
rv
al,
i
is
the loa
d
current space
vector,
v
i
s
t
h
e
i
nvert
er vo
l
t
age space vector used as a decisi
on vari
able.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Finite State
Predictive Curre
nt and C
o
mmon M
o
de
Voltage Control
of a
S
even-phase …
(Atif Iqbal)
46
5
Fi
gu
re
5.
P
h
as
e-t
o
-
n
e
u
t
r
al
vo
l
t
a
ge space
vec
t
ors
fo
r
states
1-
128
(
s
tates0
-128 are
at origi
n
) in
x
2
-y
2
pl
ane
3.
FINITE
ST
A
TE
PREDI
C
T
I
VE CO
MM
ON MO
DE V
O
LTAGE CO
NTROL
C
o
m
m
on
m
ode vol
t
a
ge ca
n be co
nt
r
o
l
l
e
d
by
pri
o
r sel
ect
i
on o
f
t
h
e s
p
a
ce vect
or
s of a
seven
-
p
h
ase
v
o
ltag
e
source in
v
e
rter
wh
en
im
p
l
e
m
en
tin
g
th
e
fin
ite
se
t
pre
d
i
c
t
i
v
e c
ont
rol
.
I
n
a s
e
ven
-
phase
V
S
I, t
h
e
pos
si
bl
e s
w
i
t
c
h
i
ng c
o
m
b
i
n
at
i
o
ns a
r
e
(t
o
p
s
w
i
t
c
hes):
1-
ON
, 6-
OF
F,
2-
ON
, 5-
OF
F,
3-
ON
, 4-
OF
F,
4-
ON
, 5-
OF
F,
5-
ON
, 2-
OF
F, and
6-
ON
, 1-
OF
F.
Each s
w
itching c
o
m
b
ination produce
s
di
fferent s
p
ace
ve
ctors a
n
d also
diffe
re
nt
com
m
on
m
ode vol
t
ages as
listed
in
Tab
l
e
1
.
It
i
s
ob
ser
v
ed
fr
om
Tabl
e 1,
t
h
at
t
h
e com
m
on m
ode
vol
t
a
ge m
a
gni
t
ude
vari
es
wi
t
h
t
h
e choi
ce
o
f
space vectors. The
c
o
mm
on m
ode
voltage magnitude
a
n
d
di
ffere
n
t s
w
itch c
o
m
b
inations are
gi
ven in
Table
2.
Using
zero swi
t
ch
in
g states (all u
p
p
e
r switches ON
o
r
all
lower switch
e
s ON) p
r
od
u
c
ed
eith
er
zero
commo
n
m
ode vol
t
a
ge
or
hi
g
h
est
com
m
on
m
ode v
o
l
t
a
ge. I
n
a
l
l
com
m
on
m
ode v
o
l
t
a
ge re
d
u
ct
i
on t
echni
que
s ge
n
e
ral
l
y
,
use
of
zer
o
vec
t
or i
s
av
oi
de
d.
In
o
r
de
r t
o
m
a
int
a
i
n
t
h
e c
o
m
m
on
m
ode
v
o
l
t
a
ge c
o
nst
a
nt
s
o
t
h
at
com
m
on m
ode
current rem
a
ins zero the set of ve
ctor
s t
h
at
can be use
d
can be ch
ose
n
from
Tabl
e 2. In o
r
der t
o
o
b
t
a
i
n
maxim
u
m
output
voltage it is m
a
ndatory to use la
rge le
ngths
s
p
ace vectors
.
Howe
ver,
if 14 largest
vectors
are u
s
ed
th
e commo
n
m
o
d
e
vo
ltag
e
will v
a
ry b
e
tween
4
/
7V
dc
an
d 3/
7V
dc
. He
nce any
o
n
e
set
of se
ven l
a
rgest
len
g
t
h v
ect
o
r
s
can
b
e
u
s
ed
to
i
m
p
l
e
m
en
t fin
ite set p
r
ed
ictive con
t
ro
l.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
45
9 – 476
46
6
Tabl
e
1.
Swi
t
c
hi
n
g
c
o
m
b
i
n
at
i
ons
a
n
d
com
m
o
n
m
ode v
o
l
t
a
ges i
n
a se
ve
n-
pha
se
VSI
Vector
Nu
m
b
er
Switching co
m
b
in
ation
Co
m
m
on
m
ode vo
ltage
1
s
t
La
rge Vecto
r
s (
7
cos(3
/7) )
-1
V
DC
0.
6420V
DC
97,
112,
56,
28,
14
,
7,
67,
{1100
001},
{11
1
0
000},
{011
100
0},
{0011
100},
{00
0
1
110},
{000
011
1},
{1000
011}
(3
/7
)V
dc
113,
120,
60,
30,
1
5
,
71,
99
{1110
001},
{11
1
1
000},
{011
110
0},
{0011
110},
{00
0
1
111},
{100
011
1},
{1100
011}
(4
/7
)V
dc
2
nd
Larg
e
Vecto
r
s
(
4
/7
)co
s
(
/7)V
DC
0.
5148V
DC
115,
121,
12
4,
62,
31,
79,
103
{1110
011},
{11
1
1
001},
{111
110
0},
{0111
110},
{00
1
1
111},
{100
111
1},
{1100
111}
(5
/7
)V
dc
96,
48,
24,
12,
6,
3,
65
{1100
000},
{01
1
0
000}
,
{001
100
0},
{0001
100},
{00
0
0
110},
{000
001
1},
{1000
001}
(2
/7
)V
dc
3
rd
Large Vectors
(
4
/7)V
DC
0.
4041V
DC
81,
104,
52,
26,
13
,
70,
35,
49,
88,
44.
22,
11,
69,
98
{
10
10
00
1
},{
1
1010
00
}, {
01
10
10
0
},{
00
11
01
0
}, {
00
011
01
},{
10
00
1
1
0
},
{
01
00
01
1
},{
0
1100
01
}, {
10
11
00
0
},{
01
01
10
0
}, {
00
101
10
},{
00
01
0
1
1
},
{
10
00
10
1
},{
1
1000
10
}
(3
/7
)V
dc
114,
57,
92,
46,
23
,
75,
101,
10
5,
116,
58,
29,
78,
39,
83
{
11
10
01
0
},{
0
1110
01
}, {
10
11
10
0
},{
01
01
11
0
}, {
00
101
11
},{
10
01
0
1
1
},
{
11
00
10
1
},{
1
1010
01
}, {
11
10
10
0
},{
01
11
01
0
}, {
00
111
01
},{
10
01
1
1
0
},
{
01
00
11
1
},{
1
0100
11
}
(4
/7
)V
dc
4
th
La
rg
e Ve
cto
r
s (
4
/7
)co
s
(2
/7)V
DC
0.
3563V
DC
33,
80,
40,
20,
10,
5,
66
{0100
001},
{10
1
0
000},
{010
100
0},
{0010
100},
{00
0
1
010},
{
00
001
01},
{1000
010}
(2
/7
)V
dc
117,
122,
61,
94,
4
7
,
87,
107
{1110
101},
{11
1
1
010},
{011
110
1},
{1011
110},
{01
0
1
111},
{101
011
1},
{1101
011}
(5
/7
)V
dc
5
th
La
rge Ve
ctors (
2
/7)V
DC
0.
2857V
DC
64,
32,
16,
8,
4,
2,
1
{1000
000},
{01
0
0
000}
,
{001
000
0},
{0001
000},
{00
0
0
100},
{000
001
0},
{0000
001}
(1
/7
)V
dc
123,
125,
12
6,
63,
95,
111,
119
{1111
011},
{11
1
1
101},
{111
111
0},
{0111
111},
{10
1
1
111},
{110
111
1},
{1110
111}
(6
/7
)V
dc
6
th
La
rge Ve
ctors (
7
cos(2
/7))
-1
V
DC
0.
2291V
DC
51,
89,
108,
54,
27
,
77,
102
{0110
011},
{10
1
1
001},
{110
110
0},
{0110
110},
{00
1
1
011},
{100
110
1},
{1100
110}
(4
/7
)V
dc
100,
50,
25,
76,
38
,
19,
73
{1100
100},
{01
1
0
010}
,
{001
100
1},
{1001
100},
{01
0
0
110},
{001
001
1},
{1001
001}
(3
/7
)V
dc
7
th
La
rge Ve
ctors (
7
cos(
/7))
-1
V
DC
0
.
1586V
DC
82,
41,
84,
42,
21,
74,
37
{1010
010},
{01
0
1
001},
{101
010
0},
{0101
010},
{00
1
0
101},
{100
101
0},
{0100
101}
(3
/7
)V
dc
106,
53,
90,
45,
86
,
43,
85
{1101
010},
{01
1
0
101}
,
{101
101
0},
{0101
101},
{10
1
0
110},
{010
101
1},
{1010
101}
(4
/7
)V
dc
S
m
allest
Vectors
(4/7)cos(3
/7)V
DC
0.
1272V
DC
109,
118,
59,
93,
1
10,
55,
91
{1101
101},
{11
1
0
110},
{011
101
1},
{1011
101},
{11
0
1
110},
{011
011
1},
{1011
011}
(5
/7
)V
dc
17,
72,
36,
18,
9,
68,
34
{0010
001},
{10
0
1
000}
,
{010
010
0},
{0010
010},
{00
0
1
001},
{100
010
0},
{0100
010}
(2
/7
)V
dc
Zero
Ve
cto
r
s
0 {0000
000}
(
0
)
V
dc
127
{1111
111}
(
1
)
V
dc
Tabl
e 2.
C
o
m
m
on
m
ode vol
t
a
ges fo
r di
f
f
ere
n
t
swi
t
c
hi
n
g
st
at
es
Co
m
m
on m
ode
vo
ltage m
a
gnitude
Switch co
m
b
inatio
n (Upper switch
position)
Nu
m
b
e
r
of
space v
ectors
1/7V
dc
1
(ON)
-6
(O
FF)
7
2/7V
dc
2
(ON)
-5
(O
FF)
2
1
3/7V
dc
3
(ON)
-4
(O
FF)
3
5
4/7V
dc
4
(ON)
-3
(O
FF)
3
5
5/7V
dc
5
(ON)
-2
(O
FF)
2
1
6/7V
dc
6
(ON)
-1
(O
FF)
7
Whe
n
7 larges
t vectors
will be used
to im
ple
m
ent FSPC, the dc link volta
ge will not be
utilized fully. There
will b
e
a reductio
n
in
t
h
e
o
u
tp
u
t
v
o
ltag
e
m
a
g
n
itud
e
and
hen
ce th
e
resu
ltin
g
cu
rren
t th
ro
ugh
th
e l
o
ad. Th
e
dr
o
p
i
n
t
h
e
o
u
t
put
v
o
l
t
a
ge m
a
gni
t
u
de ca
n
be
fo
u
n
d
usi
n
g
Fi
gu
re
6.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Finite State
Predictive Curre
nt and C
o
mmon M
o
de
Voltage Control
of a
S
even-phase …
(Atif Iqbal)
46
7
Fi
gu
re
6.
Loc
u
s o
f
t
h
e
o
u
t
p
ut
vol
t
a
ge
i
n
a se
ven
-
phase
V
S
I
The m
a
xim
u
m
out
put
vol
t
a
ge
whe
n
14 l
a
rge
s
t
l
e
ngt
h
vect
o
r
s are
use
d
i
s
s
a
m
e
as t
h
e rad
i
us o
f
t
h
e i
n
scr
i
be
d
circle. Th
e redu
ctio
n in
t
h
e
ou
tpu
t
vo
ltag
e
mag
n
itu
d
e
can
th
u
s
b
e
calcu
lated
as:
dc
dc
dc
out
V
V
V
V
V
V
0475
.
0
5785
.
0
626
.
0
2
4
.
51
cos
2
7
.
25
cos
(
6
)
In
th
is section
,
it is ex
p
l
ain
e
d
th
e resu
l
t
s o
f
research an
d
at th
e sam
e
ti
me
is
g
i
v
e
n
the
com
p
rehe
nsi
v
e
di
scus
si
o
n
. R
e
sul
t
s
can
be
pr
esent
e
d i
n
fi
gu
res,
gra
p
hs, t
a
b
l
es and
ot
hers t
h
at
m
a
ke t
h
e r
eade
r
un
de
rst
a
n
d
eas
i
l
y
[2]
,
[
5
]
.
T
h
e di
sc
ussi
o
n
ca
n
be m
a
de i
n
s
e
veral
s
u
b-c
h
a
p
t
e
rs.
4.
SIMULATION RESULTS
Si
m
u
latio
n
is
carried ou
t fo
r two
po
ssib
l
e
so
lu
tion
s
i
n
Matlab
/
Si
m
u
lin
k en
v
i
ron
m
en
t, n
e
v
e
rth
e
less,
m
a
ny
m
o
re ca
n
be e
v
al
uat
e
d.
Fol
l
o
wi
n
g
ca
s
e
s are c
o
nsi
d
e
r
ed:
14 large s
p
ace
vectors a
n
d one
zero s
p
ace
ve
ctor
(0000000)
14 large s
p
ace
vectors
only
7 large s
p
ace
vectors a
n
d
one
zero space
ve
ctor (0000000)
7 large s
p
ace
vectors
only
Inv
e
stig
ation
i
s
don
e at
first
u
s
i
n
g ou
ter larg
e
vect
ors
set
(14 active
ve
ct
ors and one zero
vect
or)
fr
om
Tabl
e 2. The t
uni
ng
p
a
ram
e
t
e
rs are
set
such t
h
at
x
1
-
y
1
and
x
2
-
y
2
plane vectors
are eliminated and
si
nus
oi
dal
c
u
r
r
e
nt
i
s
p
r
o
d
u
ce
d. C
o
m
m
on
m
ode
v
o
l
t
a
ge
va
ri
es bet
w
een z
e
ro
, 3/
7V
dc
a
n
d 4/
7
V
dc
. F
u
rt
her t
o
obt
ai
n
com
m
on m
ode
vol
t
a
g
e
bet
w
ee
n
t
w
o
l
e
vel
s
i
.
e.
3/
7
V
dc
an
d
4/
7V
dc
, zero
vector i
s
not em
ployed a
nd
only
14 large
s
p
ace
vectors a
r
e chosen. T
h
e t
h
ird case is
c
o
nside
r
ed
whe
n
only 8
s
p
ace vectors (7
large active
space vect
or a
nd
one zero vector) a
r
e use
d
suc
h
th
at common
m
ode voltage va
ries betwee
n 0 is 3/7V
dc
.
Furt
her
t
o
o
b
t
a
i
n
c
onst
a
nt
c
o
m
m
on m
ode v
o
l
t
a
ge
o
n
l
y
7
l
a
r
g
e act
i
v
e space
vect
o
r
s a
r
e c
h
osen
.
The
fu
n
d
am
ent
a
l
freque
ncy
o
f
t
h
e
si
nus
oi
dal
re
f
e
rence c
u
r
r
e
n
t
i
s
chose
n
as 3
0
Hz
. The l
o
a
d
pa
ram
e
t
e
rs are
R =
75
Ω
,
L =
3
3
m
H
and
E =
0
,
an
d t
h
e
dc l
i
n
k
vol
t
a
ge i
s
ke
pt
at
V
dc
= 60
0
V. The
se
ven
-
pha
se refe
renc
e
cu
rre
nt
am
pl
i
t
ude i
s
at
fi
rst
ke
pt
at
3
.
0 A a
n
d t
h
e
n
i
s
st
eppe
d
u
p
t
o
4.
0 A
an
d f
u
rt
her
red
u
ce
d t
o
2.
0 A
.
T
h
e sa
m
p
li
ng
t
i
m
e
of al
gori
t
hm
i
s
kept
at
20 µ Sec
.
The
opt
i
m
i
z
at
i
on al
go
ri
t
h
m
i
s
im
pl
em
ent
e
d u
s
i
ng
‘s’ f
u
nct
i
on
of t
h
e
Matlab
/
Si
m
u
li
n
k
.
Case
1: Usi
n
g
14 Large
s
t space vecto
rs
and
one
zer
o
vector with µ=1,
1
,
1
Th
e sim
u
lat
i
o
n
is carried
out with
fo
urteen
activ
e a
nd one zero
vector while th
e cos
t
funct
i
o
n m
i
nim
i
zes
current
tracki
n
g e
r
ror in a
ll
th
e
t
h
ree
orthog
on
al p
l
an
es. Th
is
is ach
ieved
b
y
k
eep
i
n
g th
e
tun
i
ng
p
a
ra
m
e
ters
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
45
9 – 476
46
8
1
,
1
,
1
.
Th
is resu
lts in
a con
t
ro
l actio
n
i
n
all p
l
an
es. Th
e sam
p
lin
g
ti
m
e
o
f
th
e alg
o
rith
m
is
k
e
pt
at 2
0
µsec,
which
is reason
able fo
r processor h
a
nd
lin
g. The resu
lting
wa
v
e
fo
rm
s are sho
w
n
in Figu
re
8
for
pha
se ‘a
’ act
ua
l and re
fere
nce
curre
n
t, the
transform
e
d currents (
d-
q
,
x
1
-
y
1
and
x
2
-
y
2
), t
h
e
spectrum
of
phase
‘a’ c
u
r
r
ent
a
n
d com
m
on m
ode v
o
l
t
a
ge
. Th
e vect
o
r
s t
h
at
are use
d
fo
r i
m
pl
em
ent
i
ng t
h
e m
odel
pre
d
i
c
t
i
v
e
co
n
t
ro
l is elabo
r
ated
in Figu
re 7
,
wh
ere th
e
v
e
c
t
or
s
in a
ll th
r
e
e p
l
an
e
s
ar
e d
e
p
i
c
t
e
d
.
Figure
7. Fourteen large
vector
s a
n
d one ze
ro and thei
r m
a
pping
Th
e actu
a
l curren
t fo
llows well th
e refern
ce cu
rren
t with fast d
y
n
a
m
i
cs
. Th
e To
tal h
a
rm
o
n
i
c d
i
sto
r
tio
n
is
6.
52
% con
s
i
d
e
r
i
n
g t
h
e com
put
at
i
on u
p
t
o
5
0
th
harm
oni
cs.
The v
o
l
t
a
ge ve
ct
ors o
f
d-
q
plane is dom
inant and
th
e o
t
h
e
r two
p
l
an
es are k
illed
in
order to
o
b
t
ain
si
n
u
so
i
d
al ou
tpu
t
cu
rren
t
s. Co
mm
o
n
m
o
d
e
vo
ltag
e
v
a
ries
bet
w
ee
n ze
ro
,
3/
7
V
dc
, 4/7V
dc
. Th
e d
v
/d
t
is larg
e eith
er
3
/
7
V
dc
or
4/
7V
dc
.
Case
2: Usi
n
g
14 Large
s
t space vectors with µ=1,
1
,
1
Th
e sim
u
latio
n
is carried
ou
t with
fou
r
teen
larg
est
lengt
hs active s
p
ac
e vector
s wh
ile th
e co
st fu
nction
minimizes current tracki
n
g error in a
ll th
e th
ree
ortho
gon
al p
l
an
es. Th
is
is ach
iev
e
d
b
y
k
e
ep
ing
th
e t
u
n
i
ng
param
e
ters
1
,
1
,
1
.
Th
is resu
lts i
n
a con
t
ro
l actio
n in all p
l
anes. Th
e sam
p
lin
g
tim
e o
f
t
h
e
alg
o
rith
m
is k
e
p
t
sam
e
at 2
0
µsec as in
th
e
p
r
ev
iou
s
case.
Th
e
resu
lting
wav
e
fo
rm
s are sho
w
n
in Figure 9 fo
r
pha
se ‘a
’ act
ua
l and re
fere
nce
curre
n
t, the
transform
e
d currents (
d-
q
,
x
1
-
y
1
and
x
2
-
y
2
), t
h
e
spectrum
of
phase
‘a’ c
u
rre
nt
an
d
com
m
on
m
ode
v
o
l
t
a
ge.
Fi
gu
re
8a.
Act
u
al
an
d
re
fe
re
nce phase
‘a’ curre
nt
-
500
0
50
0
-
400
-
200
0
200
400
dq [
V
]
dq
[
V
]
-
100
0
10
0
-1
0
0
-5
0
0
50
10
0
x
1
y
1
[V
]
x
1
y
1
[V]
-2
0
0
-1
0
0
0
100
200
-2
0
0
-1
0
0
0
10
0
20
0
x
2
y
2
[V
]
x
2
y
2
[V]
0
0.05
0.1
0.
15
-4
-2
0
2
4
C
u
rren
t
(I
a
) at
30 H
z
Ti
m
e
(s
)
C
u
rr
ent
(A
)
Evaluation Warning : The document was created with Spire.PDF for Python.