Int
ern
at
i
onal
Journ
al
of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
N
o.
4
,
Decem
be
r 202
0
,
pp.
1799
~
1804
IS
S
N:
20
88
-
8694
,
DOI:
10
.11
591/
ij
peds
.
v11.i
4
.
pp
1
799
-
1804
1799
Journ
al
h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Coast
f
unctio
n
p
aram
eters
o
ptim
izat
i
on
f
or
DC
batter
y
s
ourc
e
i
nverter
feeding
t
hree
-
phase
i
nduct
ive
loa
d
Riyadh
G.
O
mar
Depa
rt
m
ent
of
E
le
c
tri
c
al
Engi
n
eering,
Co
ll
eg
e
of
Engi
ne
eri
ng,
Mustansi
riya
h
U
niv
e
rsity,
Ir
a
q
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
hist
or
y:
Re
cei
ved
Feb
28
,
2020
Re
vised
A
pr
2
6
,
20
20
Accepte
d
J
un
10
,
20
20
The
com
mon
ly
r
epor
te
d
measure
s
of
the
pre
d
ic
t
i
ve
a
cc
ur
ac
y
are
eva
lu
at
ed
in
thi
s
pap
er.
Abs
olut
e
,
squar
ed,
per
ce
n
ta
g
e,
and
integra
l
err
ors
me
thods
are
im
plemented,
to
red
u
ce
the
obj
ec
t
ive
func
t
ion,
which
em
p
loyed
in
mode
l
pre
dictive
cont
r
ol.
The
s
e
me
th
ods
are
usua
ll
y
inv
esti
ga
te
d
fo
r
dc
sourc
e
inve
rt
er,
whi
ch
cont
rol
le
d
by
fini
te
set
mode
l
pre
dictiv
e
cur
r
ent
con
trol
sys
te
m,
with
th
r
ee
-
phase
induc
t
i
on
mo
t
or
loa
d
.
I
n
th
is
p
ape
r
,
the
ev
al
u
at
ion
inc
lud
es
diff
erent
aspe
ct
s,
a
cc
ur
ac
y,
co
mplexit
y
,
sys
te
m
har
monics
content
,
and
execut
ion
time.
A
v
it
a
l
cr
it
e
rion
in
th
is
proc
ess
is
the
per
for
ma
nc
e
of
th
e
inve
rt
er,
and
th
e
ma
t
chi
ng
b
et
we
en
the
ref
ere
nc
e
and
th
e
m
ea
s
ur
ed
machin
e
cur
ren
ts.
The
ev
al
ua
ti
on
show
s
t
hat
for
one
t
erm
obje
c
ti
ve
fun
ct
io
n,
absolute
and
squar
e
err
o
rs
give
simi
la
r
result
s
with
les
s
exe
cution
time
for
th
e
absolut
e
err
or
,
b
ut
if
multi
te
r
ms
obje
c
ti
ve
func
ti
o
n
the square e
rro
r
is bett
er.
Ke
yw
or
d
s
:
Ab
s
olu
te
er
ror (AE
)
Cost
-
f
unct
ion
Finit
e co
ntr
ol s
et
(
FCS
)
per
ce
ntage
er
r
or (
P
E)
Square
er
ror (S
E)
This
is
an
open
acc
ess
arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Ri
yadh Gh
a
ne
m Omar
,
Dep
a
rtme
nt of
Ele
crical
Engineeri
ng,
M
ust
ansiri
yah
Un
i
ver
sit
y, Ba
ghda
d,
Ir
a
q.
Emai
l:
d
yala
1968@
gm
ai
l.co
m
1.
INTROD
U
CTION
The
first
t
houg
ht o
f
Mo
del
P
r
edict
ive
C
on
tr
ol
(
M
PC
)
a
nd
R
retreat
ing
H
ori
zo
n
C
on
tr
ol (R
EC)
ca
n
be
fo
ll
owe
d
bac
k
to
the
19
60
s
wh
e
n
it
was
ut
il
iz
ed
as
an
inten
d
to
ma
na
ge
m
ulti
var
ia
bl
e
comp
el
le
d
c
on
t
ro
l
issues
.
The
ch
emic
al
an
d
oil
industr
ys,
w
e
re
pioneers
in
the
a
ppr
opriat
ion
of
MPC
,
wh
il
e
the
pri
nc
ipal
at
te
mp
t
to
ap
pl
y
it
to
an
el
ect
rical
dr
i
ve
f
ra
mew
ork
was
made
ov
e
r
tw
o
decad
e
s
la
te
r
[1
-
6].
Since
f
or
a
tw
o
le
vel
volt
age
s
ource
i
nv
e
rter
(
VSI
)
,
t
her
e
ar
e
ei
ght
mi
xes
of
in
ver
te
r
e
xpresses,
the
w
or
ding
of
fi
nite
c
on
t
ro
l
set
(F
CS)
is
gi
ven
.
More
ove
r
,
the
a
dv
a
nce
ment
of
the
in
ver
te
r
sta
te
s
is
performe
d
uti
li
zi
ng
the
retre
at
ing
horizo
n
c
on
tr
ol
method
,
t
he
c
enter
of
m
odel
pr
e
dicti
ve
co
nt
ro
l.
T
he
idea
of
M
PC
de
pends
on
t
he
est
imat
ion
of
thin
gs
t
o
c
om
e
c
onduct
of
the
s
ys
te
m
,
to
us
e
t
his
da
ta
to
fi
nd
ou
t
ideal
qua
ntit
ie
s
for
t
he
in
ci
ti
ng
var
ia
bles
[
7
-
10
].
E
xec
ution
of
this
met
hod
c
an
be
is
olate
d
i
nto
t
hr
ee
pri
nc
ipal
ste
ps
:
est
i
mati
on
of
the
f
act
or
s
that
can
not
be
est
imat
ed,
pr
e
dicti
on
of
things
to
co
me
c
on
du
ct
of
the
syst
em,
an
d
s
ys
te
m
ou
t
pu
t
s
op
ti
miza
ti
on.
Pr
esci
ent
c
on
t
ro
l
ha
s
man
y
favor
a
ble
ci
rc
um
sta
nces
that
ma
ke
it
a
ge
nu
i
ne
ch
oice
if
high
powe
rful
c
on
t
r
ol
of
el
ect
rical
dri
ves
is
requ
ired.
T
he
i
dea
is
strai
ghtf
orw
ard
an
d
exec
ut
e,
al
so
ma
ny
s
ys
te
m
con
strai
nts
ca
n
be
ad
de
d,
m
ul
ti
var
ia
ble
case
s
can
be
c
onsi
der
e
d
,
a
nd
no
nl
inearit
y
can
be
inco
rpor
at
e
d
[11]
.
This
c
on
tr
ol
st
rateg
y
re
quires
bunc
hes
of
e
sti
mati
on
s
c
on
t
r
ast
ed
with
co
nventio
nal
met
hods
.
Desp
it
e
th
at
the
pr
esci
e
nt
c
ontr
ol
plo
t
de
pe
nds
on
f
urt
her
de
velo
ped
c
ontro
l
hypothe
sis,
the
subse
qu
e
nt
con
t
ro
l
pro
ced
ur
e
is
no
t
a
ny
more
mind
-
boggli
ng
than
a
tra
diti
onal
plan
de
pe
ndent
on
PI
c
on
trolle
rs
a
nd
s
pa
ce
vecto
r
m
odulati
on
(S
V
M).
Bot
h
c
on
t
ro
l
pla
ns
n
e
ed
a
m
od
el
of
t
he
in
ver
te
r
a
nd
the
vo
lt
a
ge
ve
ct
or
s
that
it
cre
at
es.
In
t
he
old
style
plo
t,
i
nformat
ion
on
the
volt
age
vectors
is
ut
il
iz
ed
fo
r
e
xec
ution
of
the
m
odulato
r.
T
hes
e
volt
age
vect
or
s
a
r
e
the
li
mit
ed
ar
rangeme
nt
(f
i
nite)
of
po
te
nt
ia
l
incit
at
ion
s
in
predict
ive
co
ntr
ol
st
rategy.
T
o
al
te
r
t
he
P
I
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
Int
J
P
ow
Ele
c
&
D
ri S
ys
t,
Vol.
11
,
N
o.
4
,
D
ecembe
r
2020
:
1799
–
1804
1800
con
t
ro
ll
e
rs
,
li
ne
ar
eq
uatio
ns
r
epr
ese
ntin
g
th
e
load
m
od
el
i
s
re
qu
ire
d.
T
he
co
ntro
ll
er
in
the
ne
w
str
at
egy
will
com
pu
te
t
he
volt
age
vecto
r
ne
xt
predict
io
ns.
This
ca
n
be
accom
plishe
d
by
us
i
ng
a
dis
crete
-
ti
me
ve
rs
ion
of
the
load
model
.
The
pr
e
sentat
ion
of
t
he
PI
c
on
t
r
ollers
reli
es
upon
the
s
uitable
cha
ng
e
of
their
pa
ramete
rs
kp
and
ki
[
12].
T
his
ca
n
be
a
voided
i
n
the
ne
w
c
on
t
ro
l
st
rategy
since
no
pa
rameter
’s
a
dj
us
tme
nt
is
nee
ded.
A
cost ca
pacit
y must
be
c
har
a
c
te
rized, w
hich on acc
ou
nt of c
urren
t c
ontr
ol is ex
tre
mely
ba
sic
.
In
tri
gu
e
a
ddit
ion
al
ly
has
e
xpan
de
d
in
fi
guri
ng
ou
t
w
hi
ch
mathe
mati
cal
meth
od
w
il
l
produce
increasin
gly
e
xa
ct
an
d
exact
predict
io
ns
of
th
e
var
ia
bles
unde
r
c
ontr
ol
[13
,
14].
Our
m
otiv
at
ion
in
this
no
te
is
to
i
nv
est
igate
and
decip
her
a
ccessi
ble
factu
al
p
rop
or
ti
ons
of
the
normal
error
relat
ed
with
a
l
ot
of
model
-
delivere
d
pr
e
di
ct
ion
s.
I
n
this
work
an
exa
minati
on
of
the
overall
ca
pacit
ie
s
of
1
-
a
ver
a
ge
model
perfor
manc
e
error,
2
-
the
square
e
rro
r
(
SE),
3
-
the
abs
olu
t
e
per
ce
nta
ge
e
rror
(
AP
E
),
a
nd
4
-
t
he
a
bs
ol
ut
e
error
(AE)
.
Every
on
e
of
these
measu
res
re
pr
esents
the
e
rro
r
val
ue
in
m
odel
va
riables
f
or
eac
h
pr
e
dic
ti
on
.
T
hese
m
easur
e
s
add
it
io
nally
ha
ve
bee
n
util
iz
ed
t
o
a
ppear
the
di
ff
e
ren
c
e
bet
ween
th
e
est
imat
es
t
o
fin
d
w
hich
on
e
is
t
he
mo
st
reli
able.
Figurin
g
o
f
A
E
is
gen
e
rall
y
basic.
It
incl
udes
add
i
ng
the
amo
un
ts
of
t
he
abso
l
ute
erro
r
s
to
get
the
total
er
ror
val
ue
.
C
ompu
ti
ng
t
he
SE
is
ac
hie
ved
by
s
ummi
ng
eac
h
squa
re
er
ror.
E
ve
ry
e
rror
value
im
pa
ct
s
the
aggre
gate
in
re
la
ti
on
to
it
s
square
,
instea
d
of
it
s
amo
unt
.
E
norm
ous
mist
a
kes,
as
a
res
ult,
aff
ect
t
he
ag
gregat
e
sq
ua
re
er
r
or
th
an
do
the
li
tt
le
r
erro
rs.
T
his
impli
es
that
the
com
plete
sq
ua
re
erro
r
will
de
velo
p
as
the
over
al
l
error
is
th
ough
t
inside
a d
imi
nish
i
ng
num
be
r
of p
r
ogres
siv
el
y
hu
ge
in
div
i
du
al
e
rro
rs.
T
he
abs
olu
te
p
erc
entage
error
(
APE)
is
one
of
the
m
ost
broa
dly
util
iz
ed
pro
portio
ns
of
c
on
je
ct
ure
preci
sio
n,
bec
ause
of
it
s
poi
nts
of
interest
of
scal
e
-
in
dep
e
ndenc
y
a
nd
i
nter
op
e
rab
il
it
y.
I
n
a
dd
it
ion
,
t
he
i
nteg
ral
f
or
th
e
a
bsolute
e
rro
r
(IA
E)
ca
n
be
a
pp
li
ed
to
c
ompu
te
t
he
c
ost
functi
on,
t
his
functi
on
re
pres
ents
the
sy
ste
m
necessit
ie
s
by
add
i
ng
ma
ny
s
mall
par
ts
incl
ud
i
ng
with
it
.
These
par
ts
are
c
ontr
olled
va
riables
ref
e
ren
ce
fo
ll
owin
g
pa
rt
that
can
be
mo
t
or
t
orq
ue
,
sp
ee
d
or
loa
d
current
a
nd
vo
lt
age.
As
a
n
e
xa
mp
le
,
for
one
var
ia
ble
the
va
rio
us
meth
ods
of
c
os
t
f
unct
ion
(
G)
evaluati
on a
re:
=
|
(
+
1
)
−
(
+
1
)
|
(
1)
Wh
e
re,
y
reference
is
the
ref
e
ren
c
e
va
riable
will
no
t
to
be
c
on
tr
olled
w
hile,
y
predicted
is
the
pr
e
dicte
d
value
for
th
e
same
var
ia
ble.
The
tw
o
par
ts
are
cal
c
ulate
d
at
the
i
ns
ta
nt
of
(
k+1)
a
fter
discreti
zi
ng
th
e
sy
ste
m
m
ode
l.
The
M
SE
and
I
AE a
re show
n
in
e
qu
at
io
ns (
2) an
d (4).
=
(
(
+
1
)
−
(
+
1
)
)
2
(
2)
=
|
(
+
1
)
−
(
+
1
)
|
/
|
(
+
1
)
|
(
3)
=
∫
|
(
)
−
(
)
|
0
(
4)
Com
par
in
g
e
quat
ions
1
a
nd
2,
the
la
st
one
pro
du
ces
la
rg
e
cost
f
un
c
ti
on
for
e
rror
values
m
ore
than
(
1)
w
hile
giv
e
a
small
re
su
lt
s
f
or
er
rors
le
ss
than
(
1).
I
n
power
el
ect
r
on
ic
s
,
the
first
on
e
will
af
fect
on
th
e
beh
a
vior
of
t
he
co
ntr
oller
se
ns
it
ivit
y
a
nd
mu
c
h
faster
on
e
is
need
e
d
wi
th
high
s
witc
hi
ng
f
re
qu
e
ncies
.
Wh
il
e
the
sec
ond
will
re
duce
t
he
se
nsi
ti
vity
f
or
sma
ll
changes
bu
t
with
le
ss
re
fe
r
ence
t
rack
i
ng
po
s
sibil
it
ie
s.
F
or
the
(A
P
E)
as
in
e
quat
ion
(
3)
t
he
huge
detrime
nt
that
it
produce
s
intermi
nab
le
or
uncl
ear
qu
al
it
ie
s
fo
r
ze
ro
or
nea
r
zero val
ues.
2.
GENER
AL
D
ESCRIPT
IO
N
O
F
DC
B
A
TT
ERY
S
OURCE
IN
VER
TE
R
WITH
T
HREE
-
P
HAS
E
INDU
CTIVE
LOAD
The
sta
nd
a
r
d
f
orm
of
t
he
D
C
batte
ry
s
our
ce
inv
e
rter
is
exh
i
bited
i
n
F
igure
1
[15
-
25
],
w
hich
is
famil
ia
r
powe
r
el
ect
ronics
ha
rdw
are
util
iz
ed
f
or
dr
i
ving
t
hree
-
phase
in
du
c
ti
ve
loa
d.
T
his
de
vice
e
mp
l
oys
six
IG
BT
s
witc
hes
(S
1
-
S
6
)
an
d
re
pr
ese
ntin
g
the
load
with
L
(i
nducta
nce),
R
(resi
sta
nce)
,
a
nd
e
(b
ac
k
e.
m.f)
.
The
ph
a
se
vo
lt
ages
VaN,
VbN, an
d VcN
are
the i
nv
e
rter
outp
ut
vo
lt
age
s.
The
real t
ime
model cu
rr
e
nt i
n vecto
r
f
orm c
an be
ob
ta
in
ed
from:
=
∗
+
+
(
5)
No
te
that
for
recreati
on
a
nd
exp
l
or
at
ory
outc
om
e
s,
the
i
nductive
lo
ad
back
-
em
f
is
th
ought
to
be
const
ant
sin
usoidal
wa
ve
for
m.
T
he
disc
rete
form
of
the
pr
e
dicte
d
loa
d
current
der
i
ved
from
e
qu
at
io
n
(5)
f
or
(k
+
1) insta
nt is:
Evaluation Warning : The document was created with Spire.PDF for Python.
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Coa
st f
un
ct
io
n
pa
r
amet
ers
opti
miza
ti
on for
dc b
attery
sourc
e invert
er fee
din
g …
(Ri
ya
dh
G.
O
ma
r
)
1801
(
+
1
)
=
(
1
−
∗
)
(
)
+
(
(
)
−
.
.
̂
(
)
)
(
6)
The
e
valuate
d moto
r bac
k
e.
m.f
.
.
̂
(
)
can
be
f
ou
nd from t
he
pr
evio
us
i
ns
ta
nt
of ti
me as:
.
.
̂
(
−
1
)
=
(
−
1
)
−
(
)
−
(
−
)
(
−
1
)
(
7)
Wh
e
re,
T
s
is
t
he
sam
pling
ti
me,
a
nd
v(k
)
r
epr
ese
nts
the
volt
age
vect
or
a
t
ti
me
(
k)
w
hich
has
se
ve
n
values
f
or
t
his
ty
pe
of
i
nv
e
rter.
Each
value
is
te
ste
d
to
c
al
culat
e
the
pr
edict
ed
c
urre
nt
at
ti
me
(
k+1)
.
T
he
vo
lt
age
vect
or
that
pro
du
ce
le
ast
cost
func
ti
on
(less
e
rro
r)
;
will
be
sel
ect
ed
as
a
swi
tc
hin
g
c
omma
nd
t
o
inv
e
rter s
witc
he
s.
E
N
V
aN
V
bN
V
cN
n
L
R
e
S
1
S
3
S
5
S
4
S
6
S
2
V
nN
Figure
1.
To
po
logy
of the
DC
b
at
te
r
y
s
ource
inv
e
rter
.
3.
AS
SES
SME
N
T MO
DEL
P
RECISIO
N A
ND R
ES
ULT
S
The
sim
ulati
on
pr
ocess
f
or
t
he
in
ver
te
r
mod
el
is
ca
rr
ie
d
out
us
in
g
M
at
la
b
/Si
mu
li
nk.
Finit
e
(
MPC
)
current
c
on
t
ro
l
al
gorithm
is
a
pp
li
ed
t
o
traci
ng
t
he
phase
c
urren
t
ref
e
ren
c
es.
The
model
par
a
mete
rs
use
d
are
(R=
10Ω
,
L=
10m
H,
e
.m.f=
100V,
an
d
T
s
=25
µse
c.)
.
F
or
(A
E
)
a
ppr
oach,
fi
gures
(2)
de
monstrate
t
he
erro
r
betwee
n
the
re
fer
e
nce
c
ur
rent
comma
nd
an
d
it
s
relat
ive
a
ct
ual
one,
wh
i
le
figure
(
3)
s
hows
t
he
act
ua
l
Ø
-
a
trackin
g
it
s
re
fer
e
nce.
Fi
gur
es
(4
&
5)
ex
hib
it
s
the
ha
r
monics
co
nten
t
fo
r
a
sel
ect
e
d
wi
ndow
f
rom
the
measu
red cu
rr
e
nt and its
disto
rtion rati
o f
or (AE)
app
ro
ac
h.
Figures
(
6
-
9)
pr
ese
nts
t
he
sa
me
f
or
(S
E
)
a
ppr
oach,
t
hese
res
ults
s
how
that
the
m
od
el
in
the
t
wo
appr
oach
es
ha
ve
nea
rly
the
same
be
hav
i
or.
T
he
per
ce
ntage
er
ror
(PE)
a
ppro
ac
h
when
ap
plied
s
hows
a
sli
gh
tl
y
le
ss
e
rror
but
with
la
rg
e
r
t
otal
harmo
nic
distor
ti
on
(T
HD)
com
pa
red
wi
th
the
previ
ous
t
wo
appr
oach
es
. T
hi
s can be
noti
ced in
Fig
ures
(
10
-
13).
Fig
ure
2. Er
ror
b
et
wee
n
t
he re
fer
e
nce a
nd act
ual
current
Ø (a)
(AE)
.
Fig
ure
3
.
re
fere
nce
(r
e
d) an
d ac
tual cu
rr
e
nt
Ø
(
a)
(AE)
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S
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:
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-
8
694
Int
J
P
ow
Ele
c
&
D
ri S
ys
t,
Vol.
11
,
N
o.
4
,
D
ecembe
r
2020
:
1799
–
1804
1802
Fig
ure
4
.
Sele
c
te
d
cu
rr
e
nt
window
for o
ne
cycle (
AE
).
Fig
ure
5
.
Ha
rm
on
ic
s
content
f
or the selec
te
d cur
ren
t
Figure
6. Er
ror
b
et
wee
n
t
he re
fer
e
nce a
nd act
ual
current
Ø (a)
(SE).
Figure
7. Re
fere
nce
(r
e
d) an
d ac
tual cu
rr
e
nt
Ø
(
a)
(S
E
)
Figure
8. Sele
c
te
d
cu
rr
e
nt
window
for o
ne
c
yc
le
(S
E
)
Figure
9. Ha
rm
on
ic
s
content
f
or the selec
te
d cur
ren
t
Figure
10. E
rro
r betwee
n
the
re
fer
e
nce a
nd a
ct
ual
current
Ø (a)
(PE).
Figure
11. refe
ren
ce
(red
)
a
nd actual
c
urren
t
Ø
(
a)
(P
E
)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
Coa
st f
un
ct
io
n
pa
r
amet
ers
opti
miza
ti
on for
dc b
attery
sourc
e invert
er fee
din
g …
(Ri
ya
dh
G.
O
ma
r
)
1803
Figure
12.
Sele
ct
ed
cu
rr
e
nt
wi
ndow fo
r on
e
cycle (
PE)
Figure
13. Har
monics c
on
te
nt for
t
he
sel
ect
e
d
c
urren
t
4.
CONCL
US
I
O
N
The
ai
m
of
thi
s
w
ork
is
t
o
de
monstrate
a
nd
c
ompare
bet
ween
va
rio
us
cost
-
functi
on
op
ti
miza
ti
on
appr
oach
es
. The
pre
dicti
ve
c
ontr
ol
strat
e
gy
(
FCS
-
M
PC)
is
u
se
d
t
o
dr
i
ve
i
nductive
loa
d
via 3
-
Ø
batte
r
y
sou
rce
inv
e
rter.
T
he
a
nalysis
is
ca
rr
i
ed
out
us
in
g
M
at
la
b/Si
m
ulink
pack
a
ge,
th
a
ap
proac
hes
unde
r
c
onside
ra
ti
on
a
r
e
abs
olu
te
,
s
qu
a
re,
a
nd
pe
rcent
age
erro
r,
whil
e
the
integral
error
is
el
imi
nated
beca
us
e
of
it
s
ne
ed
for
long
execu
ti
on
ti
me
.
The
obta
ined
resu
lt
s
s
how
th
at
fo
r
(
AE)
a
nd
(SE)
t
her
e
w
as
rapp
ro
c
hem
ent
bet
wee
n
t
he
m
in
error
am
plit
ude,
out
pu
t
c
urre
nt
ha
rm
onic
s
c
on
te
nt
a
nd
exe
cuting
ti
me,
but
in
case
of
(
AE)
a
faster
a
nd
m
or
sensiti
ve
f
or
s
mall
er
ror
c
on
trolle
r
is
needed.
F
or
the
pe
rcen
ta
ge
e
rro
r
(P
E
)
t
he
e
rro
r
amplit
ude
is
sl
igh
tl
y
more
tha
n
t
he
pr
e
vious
t
wo
c
ases
but
the
re
was
a
nota
ble
increase
i
n
harmo
nics
c
on
te
nt
(THD).
Si
nc
e
the
dev
ia
ti
ons
are
sq
ua
re
d,
the
S
E
giv
es
a
ge
ne
rall
y
high
wei
gh
t
to
huge
de
viati
on
s
.
This
i
mp
li
es
t
he
SE
sh
oul
d
be
pro
gr
essi
ve
ly
val
uab
le
w
hen
en
orm
ou
s
erro
rs
a
re
es
pecial
ly
unfort
un
at
e.
O
ne
un
mist
akab
le
fa
vora
ble
po
sit
io
n
of
SE
ov
e
r
AE
is
that
SE
kee
ps
a
wa
y
f
rom
the u
ti
li
zat
ion
o
f
ta
king
the
a
bsolute for
eac
h
er
ror,
w
hic
h
is
unwa
nted
in
ma
ny
nume
ric
al
com
puti
ng
s
te
ps
.
The
res
ul
ts
ap
pro
ved
th
e
(F
C
S
-
M
PC)
performa
nce
qual
it
y,
as can
b
e
seen
in ho
w
the
actu
al
cu
r
ren
t t
racks i
ts refe
re
nce
comma
nd.
ACKN
OWLE
DGE
MENTS
The
a
uthor
m
igh
t
wan
t
t
o
dem
onstrat
e
than
kfulnes
s
t
o
M
ust
ansiria
h
Un
i
ver
sit
y
for
helping
this w
ork.
REFERE
NCE
S
[1]
B.
R
ahi
m
a,
G
Amar
,
B.
Toufik,
C
.
Moham
ed
,
“
High
-
p
erf
orm
anc
e
ac
t
ive
pow
er
f
il
t
er
imple
m
ent
a
ti
on
base
d
o
n
pre
dictive
cur
r
en
t
con
trol
,”
In
te
rn
ati
onal
Journal
of
Pow
er
Elec
tr
onic
s
and
Dr
ive
Syste
m
(IJ
PE
DS
)
,
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.
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No.
1
,
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-
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201
9.
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Hong
Quan
g,
N.
Qu
ang,
N
.
Hien
,
N.
Binh
,
“
Min
Max
M
odel
Pred
ic
t
ive
Control
for
Polys
ole
noid
L
inea
r
Motor
,"
Int
ernati
onal
Journa
l
of
Pow
er
El
e
ct
ronics
an
d
Dr
iv
e
Syst
e
m
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P
EDS),
Vol.
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,
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-
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bindu
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.
,
A.V.Ra
vi
Teja
,
G.
Bhuvan
eswari
,
Bh
im
Singh,
“
Perform
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en
hanc
e
me
nt
in
a
mul
ti
le
ve
l
inve
r
t
er
fed
PTC
induc
t
i
on
mo
tor
drive
by
opt
im
a
l
volta
ge
v
ector
s
el
e
ct
i
on
,
”
Int
ernati
on
al
Journal
of
P
ower
E
le
c
tronics
and
Dr
iv
e
S
ystem
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PE
DS)
,
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Li
m
,
Che
e
Shen
,
e
t
a
l.
"F
CS
-
MPC
-
base
d
cur
ren
t
cont
ro
l
of
a
f
iv
e
-
phase
induc
t
io
n
mot
or
and
i
ts
com
par
ison
with
PI
-
PWM c
ontrol."
IE
EE
Tr
ansac
ti
ons on
Industri
al
E
le
c
tronic
s
,
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61
,
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,
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2014
.
[5]
Varga
s,
Rodr
ígu
ez
,
Amm
ann,
an
d
Wh
ee
l
er,
“Pre
dic
ti
v
e
Curre
nt
Control
of
an
In
duct
ion
Mac
h
ine
Fed
by
a
M
at
ri
x
Convert
er
with
React
iv
e
Pow
er
Contro
l”.
I
E
EE
Tr
ansacti
on
s
on
Industrial
Elec
troni
cs
,
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ol.
55
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-
Rub,
J.
Guziñski,
Z.
Krze
mi
nski
,
an
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H.
A.
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t
,
“Pre
d
ictive
c
urre
nt
con
trol
of
volt
ag
e
-
sourc
e
inve
rt
ers,
”
IEEE
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Vahe
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-
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a
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,
“
Real
-
Tim
e
Implem
ent
a
ti
o
n
of
Model
-
Pred
ic
ti
v
e
Contro
l
o
n
Seven
-
Le
v
el Packed
U
-
Cell I
nv
er
te
r
,”
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EE
E
Tr
ans.
Ind
.
E
lectron
.
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ig
uez
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or
,
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,
“
Model
Pre
dic
ti
v
e
Control:
MP
C’s
Role
in
the
Evol
u
ti
on
of
Pow
er
El
e
ct
ron
i
cs
,”
IEEE
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.
E
le
c
tron.
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.
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ol.
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,
pp
.
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–
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,
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[9]
J.
Rodrigu
ez,
an
d
P.
Cort
es,
"P
re
dic
ti
v
e
Control
of
Pow
er
Conve
rte
rs
and
E
le
c
trica
l
Driv
es",
a
Jo
hn
W
iley
&
Sons
,
Lt
d.
Publicati
on
,
first edi
t
ion, 20
12
.
[10]
T.
Geye
r
,
"Low
Compl
exity
Model
Predi
ct
iv
e
Control
in
Pow
er
Elec
tron
ic
s
a
nd
Pow
er
Sys
te
ms",
PhD
.
The
sis,
S
wiss
Feder
al
In
stit
ute of Te
chno
logy,
2005
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
Int
J
P
ow
Ele
c
&
D
ri S
ys
t,
Vol.
11
,
N
o.
4
,
D
ecembe
r
2020
:
1799
–
1804
1804
[11]
Li
upingWang,
Shan
Cha
i,
Dae
Yoo,
Lu
Gan
a
nd
Ki
Ng
,
“
PID
and
Pr
edi
c
ti
ve
Control
of
Elec
t
ric
a
l
Driv
es
and
Pow
er
Convert
er
s Us
ing
MA
TL
AB/S
IMU
LINK,
2015
John
Wi
l
e
y
&
Sons
Singap
ore
Pte
.
Lt
d
.
[12]
Bose,
Bi
ma
l
K,”
Modern
power
el
e
ct
roni
cs
and
AC dri
ves”
Pr
en
ti
c
e
Hal
l
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002.
[13]
Sungil
Kima,
H
ee
young
Ki
mb,
”
A
new
metri
c
of
absolute
per
c
ent
ag
e
err
or
for
int
er
mi
t
te
n
t
de
ma
nd
for
ec
asts”
,
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rnational
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as
ti
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l
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ot
t
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i
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a
,
“
Advant
age
s
of
the
mean
absolut
e
err
or
(MA
E)
over
the
root
me
an
square
err
or
(RMS
E)
in
asses
sing
ave
r
age m
o
del
p
erf
orm
anc
e
”,
CL
IMA
TE
R
E
SEA
RCH
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Seyed
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Moham
m
ad
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t
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Nik
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umz
i
Nik
Idr
is
,
“Ve
ct
or
Con
trol
of
Thre
e
-
Phas
e
Induc
ti
on
Motor
with
TwoStat
o
r
Phases
Open
-
Circ
ui
,
”
Int
ernati
onal
Journal
of
Powe
r
Elec
tronic
s
and
Dr
ive
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)
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Hasabe
lra
sul
,
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ashim
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“Comparison
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ca
rri
er
PW
M
Techni
ques
for
C
a
sca
ded
H
-
Bridg
e
Multi
le
v
el
Inve
r
te
r.”
In
te
rnation
al
Journal
of
Po
wer
Elec
troni
cs
and
Dr
iv
e
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PE
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R.
Gunaba
la
n
,
V.
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“S
pee
d
Sensorl
ess
Vec
tor
Con
trol
of
Induc
t
ion
Motor
Drive
wi
th
PI
an
d
Fuz
z
y
Control
le
r
,
”
In
ter
nati
onal
Journal
of
Powe
r
El
e
ct
ronics
and
Dr
i
ve
Syste
m
(IJ
PED
S)
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Yasir
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ee
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l
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i
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“T
h
ird
h
arm
oni
c
inj
e
ct
io
n
PWM
t
ec
hniq
ue
for
m
axi
m
iz
i
ng
DC
-
BUS
uti
li
z
a
ti
on
of
Fiv
e
-
Pha
se
VS
Is”,
Indon
esian
Journal
o
f
Elec
tric
al
Eng
i
nee
ring
and
Co
mputer
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ie
nc
e
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h
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Siam
i,
Mohs
en,
et
al
.
,
"A
Com
puta
ti
on
al
ly
Eff
i
ci
en
t
Lookup
T
abl
e
Based
FC
S
-
MP
C
for
PM
SM
Drive
s
Fed
b
y
Matri
x
Conv
ert
e
rs
,
"
IEEE
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ansacti
ons on
Industrial
E
lectronic
s
.
Vol.
pp
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1
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17.
[20]
M.
Reya
sudin
Basir
Khan,
Jag
ade
esh
Pasupule
ti
,
Jabb
ar
Al
-
Fa
tt
ah
,
Mehrda
d
Ta
hm
ase
bi
,
"En
erg
y
ma
n
ageme
n
t
sys
te
m
for
PV
-
Bat
t
ery
microgrid
base
d
on
mod
el
pre
dictive
cont
r
ol",
Indone
sian
Journal
of
El
e
ctr
ic
al
Eng
ineerin
g
and
Computer
S
ci
en
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hu
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esh
Sai
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av,
C.
R
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asa
n
,
“
Synthesis
of
mode
l
pre
d
ictive
con
trol
l
er
for
a
n
ide
nti
f
ie
d
mod
el
of
MIM
O
proc
e
ss
,
”
Indon
esian
Journal
o
f
Elec
t
rical
Engi
n
ee
rin
g
and
Computer
Sci
en
ce
,
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941~
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49,
Februa
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20
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[22]
Omar
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Riy
adh
G.,
and
R
abee'H.
The
j
el
.
"F
inite
C
ontrol
Set
Mode
l
Predic
t
ive
Curr
ent
Control
FC
S
-
MP
C
Based
on
Cost
Functi
on
Optim
izati
o
n,
with
Curr
ent
L
imit
Constr
ai
nts
fo
r
Four
-
Le
g
VS
I
,
"
Iraqi
Journal
for
Elec
tric
al
&
El
e
ct
ronic
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n
ee
ring
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12.
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o.
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2016.
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H.
Young,
M.
Pere
z
,
and
Jos
e
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odrigue
z
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ly
sis
of
Finit
e
-
Control
-
Set
Model
Predic
ti
v
e
Curr
e
nt
Control
with
Model
Para
me
t
e
r
Mismat
c
h
in
a
Thre
e
-
Phase
Inv
ert
er
”
IE
EE
Trans
ac
ti
ons
on
Ind
ustria
l
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tron
i
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[24]
C.
Gar
ci
a
,
J.
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z
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va,
C.
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ja
s,
P.
Za
nch
et
t
a,
and
H.
Abu
-
Rub,
“Full
Predi
ct
iv
e
C
asc
ade
d
Spe
ed
a
nd
Curre
nt
Con
trol
of
an Induction
Mac
hine”,
IEEE
Tr
ansacti
ons on
Ene
rgy
Conv
ersion
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31
,
Iss
ue:
3,
Sep
t. 2016
.
[25]
Riya
dh
G.
Omar
,
“FCS
-
MP
C
strat
egy
for a
f
ive
-
phase
vol
ta
ge
so
urc
e inve
r
te
r
using m
ax
im
um
l
o
a
d
cur
ren
t
constra
in
t”
.
IE
E
E,
2018
1st I
n
te
r
nati
onal
S
cientif
ic
Con
fe
renc
e
o
f
Engi
n
ee
ring
Scienc
es
-
3rd S
ci
e
nti
fic
Con
fe
renc
e
of
Eng
ine
ering
S
ci
en
ce (ISCE
S)
,
Ira
q,
2018.
BIOGR
AP
HI
ES OF
A
UTH
ORS
Dr
.
Ri
ya
dh
G.
Oma
r
is
a
le
ct
ur
er
i
n
the
Ele
ct
ric
al
Eng
i
neer
i
ng
de
pa
rtment,
M
ust
ansiri
yah
U
niv
e
rsity,
B
aghda
d
-
Ir
a
q,
f
or
18
years
i
n
powe
r
s
ys
te
m
anal
ys
is
&
powe
r
el
ect
r
onic
s.
He
is
a
m
embe
r
i
n
th
e
e
le
ct
rical
eng
i
ne
erin
g
De
par
t
ment
c
ouncil.
He has
man
y p
ub
li
cat
io
ns
mai
nly
i
n powe
r
el
ect
ronics an
d p
red
ic
ti
ve
c
ontr
ol.
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