TELKOM
NIKA
, Vol.14, No
.2, June 20
16
, pp. 440~4
4
8
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i1.2755
440
Re
cei
v
ed O
c
t
ober 1
3
, 201
5; Revi
se
d March 18, 201
6
;
Accepte
d
April 2, 2016
Model Predictive Optimization Control Strategy for
Three-level AF
E Converter
Xiao
y
a
n
Shi*
, Longji Zhu, Shuijuan Yu
Dep
a
rtment of automati
on,
Co
llge
ge of El
ectrical a
nd Inform
ation En
gi
neer
i
ng,
Anhu
i Univ
ersit
y
of Scie
nce a
nd T
e
c
hnol
og
y, Huain
an 2
320
01, Anhu
i, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: shixia
o
y
an
19
80@
163.com
A
b
st
r
a
ct
In view
of the fact of traditiona
l MPC pre
d
icti
o
n
for thre
e-lev
e
l AF
E converter w
i
th
nu
mer
ous
sw
itching vect
ors, time-cost
computati
on
and c
o
mpl
e
x control,
a
s
i
mplifie
d mo
de
l pred
ictive
co
nt
rol
alg
o
rith
m is pr
opos
ed i
n
this
paper. T
he
multipl
e
curre
nt pred
iction is tr
ansfor
m
e
d
into
a singl
e virtu
a
l
referenc
e vo
lta
ge v
e
ctor pr
edi
ction
accord
in
g
to the
in
v
e
rse
proce
dure
of th
e
mo
del
curre
n
t
pred
iction,
an
d
vector distrib
u
tion
meth
od is ado
pted w
h
ich
can screens
o
u
t the optimal
vector. In the
process of roll
i
n
g
opti
m
i
z
at
ion, mu
lti-ob
ject
iv
e
control is c
a
rri
ed o
u
t by a
ddi
ng n
eutral po
i
n
t
potenti
a
l bal
ance and
r
e
d
u
c
ing
sw
itching l
o
ss
es an
d
other
constrai
nt
s to
the cost fu
ncti
on. Als
o
the
c
ontrol
de
lay
of the a
l
g
o
rith
m is
compe
n
sate
d. F
i
nally, si
mu
l
a
tion ex
per
iments of th
ree-
level AF
E co
nverter un
der
steady-state
an
d
dyna
mic cond
itions ar
e provi
d
ed. T
he results
have verifi
ed c
o
rrectness a
n
d
practicab
ility o
f
the strategy.
Ke
y
w
ords
: T
h
ree-lev
e
l AF
E converter, Mod
e
l pre
d
ictive co
ntrol, Virtual ref
e
renc
e volta
g
e
,
Vector sector
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
With the
ad
vantage
s of
low volta
ge
harm
oni
c, hi
gh p
o
wer fa
ctor and
bidi
rectio
na
l
energy flow, multi-level a
c
tive front end
(AFE)
conve
r
ter ha
s b
een
widely u
s
ed
in active po
wer
filter, reactive
powe
r
com
p
ensation, and
new ene
rgy grid ge
neration and so on
[1]. The cont
rol
targets
of
th
e
multi-l
e
vel conve
r
ter a
r
e
not only
to
adju
s
t the cu
rre
nt of the
AC side rapi
dly,
sup
p
re
ss the
harmo
nics,
and adj
ust p
o
we
r facto
r
, but also th
e
probl
ems
of neutral p
o
in
t
potential flu
c
tuation a
nd
power
device lo
ss shoul
d be
con
s
id
ered.
Fo
r a
bove p
u
rp
oses,
dome
s
tic
and
foreig
n
schol
ars have
con
ducte
d in
-de
p
t
h re
sea
r
ch o
n
its
cont
rol
strategy, whi
c
h
mainly inclu
d
e
voltage ori
e
nted co
ntrol
(VOC) a
nd di
rect po
we
r co
ntrol (DPC) [2]. Howeve
r, due
to the time
-variability a
nd
nonlin
earity, i
t
is difficu
lt to
achieve th
e
best
co
ntrol
effect. In recent
years,
with t
he ra
pid d
e
v
elopment of
digita
l processors,
som
e
com
p
lex a
nd ne
w
cont
rol
strategi
es,
su
ch
as ad
aptive control,
slid
ing mo
de
co
ntrol, fu
zzy
control, p
r
e
d
ictive cont
rol e
t
c,
are well imple
m
ented [7, 8].
For
ea
sy to
und
erstand,
flexible
con
t
ro
l, go
od
d
y
namic pe
rfo
r
man
c
e
an
d
strong
robu
stne
ss
，
finite co
ntrol
set mo
del p
r
edictive
cont
rol (F
CS-MP
C
)
ha
s be
en
widely u
s
e
d
in
power ele
c
tro
n
ics and p
o
wer tran
smi
ssi
on appli
c
atio
ns, and al
so i
t
can be ea
sil
y
and effectively
integrate
d
int
o
a va
riety of
co
nstraints
whi
c
h
can achieve multi-objectiv
e
s
opti
m
ization
cont
rol
[3]. Different from the traditional lin
e
a
r contro
l
st
rategy, FCS
-
MPC algo
rith
m is ba
sed
on
accurate mat
hematical mo
del of obje
c
t
system to p
r
edic
t the future s
t
ate. At the s
a
me time, with
taking
into
m
u
lti-co
ntrol
ob
jectives, th
e
optimal
switching state ca
n
be
dete
r
mi
ned by
the
cost
function fo
r
global
rollin
g
optimizatio
n
.
Howeve
r, nume
r
ou
s switchi
ng
ve
ctors,
time
-co
s
t
comp
utation and compl
e
x
co
st
functio
n
s which
lim
i
t
the application of FCS
-
MPC. In [13] a
simplified
mo
del p
r
edi
ctive
algo
rithm i
s
presented
which
can
effectively red
u
ce the
ope
rati
on
time and im
prove the
efficien
cy. But part of t
he
control pe
rfo
r
man
c
e i
s
af
fected. In [9] a
satisfa
c
to
ry p
r
edi
ctive cont
rol
strate
gy i
s
u
s
e
d
to
rea
lize th
e multi
p
le target
sat
i
sfactio
n
cont
rol
among th
e NPC three
-
eve
l
rectifier, n
e
u
tral poi
nt po
tential balan
ce, current tra
cki
ng an
d lo
w
swit
chin
g fre
quen
cy ope
ra
tion throug
h fuzzy deci
s
io
n
.
In [12] multiple virtual voltage vecto
r
s
are
con
s
tru
c
ted t
hat borrowe
d from discrete
voltage spa
c
e ve
ctor modulation
(DSVM) id
ea.
Although the
effect of tracki
ng control
is impr
oved
obviously, but the numb
e
r of MPC rolling
optimizatio
n i
s
in
crea
sed,
whi
c
h h
a
s
brou
ght a
ve
ry se
riou
s
challen
ge to t
he a
c
tual di
gital
system impl
e
m
entation [4-6].
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Model Pre
d
ict
i
ve Optim
i
zati
on Co
ntrol Strateg
y
for Th
ree-le
vel AFE
Con
v
e
r
ter (Xi
aoyan Shi)
441
To si
mplify the predi
ctio
n process
a
nd redu
ce
the
comp
utation time
，
the
pape
r
discu
s
ses th
e voltage
p
r
edictio
n
cont
rol m
odel
of
the
neutral
point
cl
amp
ed
(NP
C
) A
F
E
conve
r
ter
ba
sed
on F
C
S-MPC. First, a
c
cordi
ng to
t
he inve
rse proce
dure of th
e mod
e
l current
predi
ction th
e
single vi
rtual
referen
c
e vo
ltage vect
o
r
i
s
obtai
ned. T
hen the
co
st function
of the
output voltag
e is expre
s
se
d by
the equivalent transfo
rmation a
nd some co
nst
r
ai
nt conditio
n
s
are
introdu
ce
d to the co
st funct
i
on to reali
z
e
multi-obj
ect control. Finally
, the optimal swit
chin
g stat
e
is dete
r
mine
d
and taken a
s
the outp
u
t of the cont
rol
l
er. For th
e control d
e
lay of algorithm,
the
compensation scheme is
also pr
esented. In order to verify the
correctness and feasi
b
ility of
the
algorith
m
, the three
-
level
AFE converter sim
u
latio
n
experim
ent
al platform i
s
built ba
se
d
on
Matlab/sim
u
li
nk. Th
e resul
t
s indi
cate th
at the
propo
sed st
rategy h
a
s a
go
od
static an
d dyna
mic
perfo
rman
ce.
2. Traditiona
l Curren
t
Mo
del Predictiv
e
Con
t
rol of
Three
-lev
el
AFE Conv
erter
For imp
r
ovin
g the voltage
level, redu
ci
ng the
volum
e
of the whol
e system eff
e
ctively,
sup
p
re
ssing
the ha
rmo
n
ic p
o
llution,
the NP
C
multi-level A
F
E conve
r
te
r can m
eet
the
developm
ent requi
rem
ents of smart gri
d
in the
future. The traditi
onal mod
e
l p
r
edi
ctive cont
rol
strategy u
s
e
d
discrete m
a
thematics
model to
cal
c
ulate
cu
rre
n
t
predi
ctive value und
er
the
different state
s
of the switch and ma
ke t
he switch
con
d
ition sel
e
cte
d
throu
gh cost function wh
en
the cu
rre
nt predictive value
and the co
m
m
and
current
value is clo
s
est [10, 11]. Therefore, a
key
part of the model predi
ctive contro
l stra
tegy is to establish disc
rete mathematics model of the
system a
nd e
v
aluate the sw
itch
state co
ntrol beh
avio
r by the cost functio
n
.
2.1. Mathem
atics Mod
e
l of Thre
e
-lev
el AFE Conv
erter
The NP
C thre
e-level AFE converte
r topol
ogy stru
cture is sh
own in Figure 1.
Figure 1. The
three-l
e
vel AFE conve
r
ter
circuit topolo
g
y
,,
abc
ee
e
are power gri
d
voltage,
,,
ab
c
ii
i
are AC
sid
e
current,
dc
i
is DC
side cu
rrent;
L
and
R
are A
C
si
de in
du
ctan
ce a
nd
equivalent
re
sista
n
ce;
12
,
CC
are the two
capa
cito
r
cap
a
cita
nce
value corre
s
pondi
ng to th
e DC
side.
A
s
suming
sym
m
etry of the
three
-
ph
ase
AC
voltage and i
gnori
ng the
asymmet
r
y of the grid si
d
e
resi
stan
ce
and the f
ilter inducta
nce, the
mathemati
c
al
model of three-level AFE
converte
r in
the
coo
r
din
a
te can be d
e
scrib
ed a
s
following:
,
,,
,
di
L
eu
R
i
dt
(1)
Whe
r
e
,,
,
,,
eiu
are t
he voltage, current and A
C
sid
e
voltag
e of three
-
lev
e
l AFE
c
o
n
v
er
te
r
.
Ass
u
ming
co
n
t
ro
l s
y
s
t
em samp
lin
g
pe
r
i
od
s
T
is small en
ough, Equ
a
tion (1
)
can
b
e
approximated
as followi
ng
by the forwa
r
d differen
c
e p
r
inci
ple.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 440 – 44
8
442
,,
,
(1
)
(
)
s
d
i
ik
ik
dt
T
(2)
Acco
rdi
ng to (1), (2), the di
screte p
r
edi
ct
ion model of the co
nverte
r is obtain
ed.
,,
,
,
(
1
)
[
()
()
]
(
1
)
(
)
ss
TR
T
ik
ek
u
k
ik
L
L
(3)
The switchi
n
g function of
converte
r circuit
(,
,
)
j
Sj
a
b
c
is used
to repre
s
e
n
t the four
swit
chin
g sta
t
e of each pha
se. Taki
n
g
a phase as an exam
ple, When
1
a
S
and
2
a
S
are
simultan
eou
sl
y condu
cting
,
1
a
S
, a point to o point level is
2
dc
U
; When
2
a
S
and
3
a
S
are
simultan
eou
sl
y cond
ucting
,
0
a
S
, a point to o point le
vel is 0. Wh
en
3
a
S
and
4
a
S
are
simultan
eou
sl
y con
d
u
c
ting,
1
a
S
, a
point to
o
point level
is
2
dc
U
. The
r
e
are th
ree level
s
i
n
t
h
e
DC
side. T
h
e
r
efore, the th
ree
-
level AF
E conve
r
ter
AC sid
e
ha
s
3
32
7
kind
s of voltage
state
combi
nation.
The A
C
si
de
voltage vecto
r
,
uu
can be get from
the DC bus
volta
ge o
f
the
thre
e-
level AFE converter a
nd the switchi
ng
state
,,
abc
SS
S
.
(2
)
6
3
()
6
dc
abc
dc
bc
U
uS
S
S
U
uS
S
(4)
2.2. Dete
rmination of
Co
st Func
tion
Curre
n
t mod
e
l predi
ctive control strate
gy by
using the finitene
ss
of powe
r
devi
c
e on
-off
state and a
c
cording to the discrete m
a
thematical
model of the controll
ed o
b
ject predi
ct the
future valu
e
of the in
put
current in
diffe
rent
sw
it
chin
g state
s
.
Ho
wever, i
n
o
r
d
e
r to
en
su
re
good
control pe
rformance and e
nhan
ce the reliability of
th
e whole
syst
em, the fluctuation of neu
tral
point potenti
a
l is a pro
b
l
e
m that can
not be i
gno
red.Fo
r thre
e
-
level AFE converte
r syst
em,
based o
n
the
predi
ction
of the future
st
ate of the 27
swit
ch o
ne b
y
one
，
the optimal switchi
n
g
state is dete
r
mined by usi
ng the
co
st functio
n
to achieve cu
rr
ent
tracking an
d
maintain the
balan
ce of n
eutral p
o
int p
o
tential. Co
n
s
ide
r
ing
th
e
existen
c
e of
midpoint p
o
tential fluctu
ating
probl
em of t
h
ree
-
level to
pology, the
predi
cted val
ue
(1
)
dc
Uk
of the neutral p
o
int
potential
deviation at
(1
)
kT
is expre
s
sed
as follo
wing:
22
2
21
()
(1
)
[
(
)
(
)
(
)
]
(
)
(
)
()
(
)
()
()
a
s
dc
a
b
c
b
d
c
c
dc
dc
d
c
ik
T
U
k
Sk
Sk
S
k
i
k
U
k
C
ik
Uk
U
k
U
k
(5)
No
wad
a
ys the AFE converters control syste
ms a
r
e g
enerally base
d
on the tech
nique of
PWM mo
dul
ation. Shorte
n the pe
riod
of the mo
d
u
l
a
tion alg
o
rith
m wo
uld in
crease the o
u
tput
voltage of the fundame
n
tal wave cont
ent and re
du
ce
the ha
rm
onic di
stortio
n
of the AC side
curre
n
t. However, the pe
ri
odic m
odul
ation of the
rel
a
tionship me
ans to in
crea
se the
swit
ch
ing
freque
ncy of
power
device
s
, whi
c
h
will directly
affect the ef
ficien
cy and
temperature
of
conve
r
ter. T
h
erefo
r
e, that i
s
ne
ede
d to
weig
h
main
control o
b
je
ctives an
d swit
chin
g freq
uen
cy.
So the co
st function d
e
term
inati
on contai
ns multiple fa
ctors.
2
*
1,
,
2
3
(
1
)
(
1)
(
1
)
(
1)
dc
s
Ji
k
i
k
U
k
f
k
(6)
Given cu
rrent
value
*
,
(1
)
ik
can b
e
obtaine
d by two orde
r tre
nd extrapol
ation.
**
*
*
,,
,
,
(1
)
3
(
)
3
(
1
)
(
2
)
ik
i
k
ik
i
k
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Model Pre
d
ict
i
ve Optim
i
zati
on Co
ntrol Strateg
y
for Th
ree-le
vel AFE
Con
v
e
r
ter (Xi
aoyan Shi)
443
(1
)
s
fk
is th
e
avera
ge n
u
mbe
r
of ci
rcuit switch
es
at the
(1
)
kT
. The switching loss is
relevant to
switchi
ng volt
age
and
cu
rrent. It is n
o
t
a sim
p
le li
ne
ar
relation
shi
p
with
switch
ing
freque
ncy. In
gene
ral, the
avera
ge
swi
t
ching f
r
eq
ue
ncy is smalle
r, lower
switching lo
sse
s
,
so
algorith
m
sel
e
ction ave
r
ag
e swit
chin
g freque
nc
y is u
s
ed as o
ne of the optimization index.
,,
(1
)
(
)
(1
)
12
ii
s
abc
Sk
S
k
fk
(8)
In the
co
st fu
ntion
12
3
,,
den
ote
re
sp
ectively
curre
n
t e
rro
r
，
the mi
dpoi
nt unb
alan
ce
voltage and
averag
e swit
chin
g freq
uen
cy weig
hts.
By weighting
coefficient
s to adju
s
t the value
of the fun
c
tion
can flexi
b
ly and
co
n
v
eniently
opti
m
ize th
e ov
erall
perfo
rm
ance of the
AFE
conve
r
ter, wh
ich it is very d
i
fficult for
the conve
n
tional
control metho
d
s to do this.
3. Three-lev
e
l AFE Conv
e
r
ter Voltage
Predictiv
e
Control
Model p
r
edi
ct
ive control al
gorithm l
oop
s once in
ea
ch
control cy
cle
.
The ru
nning
time of
the algo
rithm
sho
u
ld
be
sh
ort en
oug
h to
obtain
a hig
her
sam
p
ling
freque
ncy,
so
the complexi
ty
of the algorit
hm need
s to
be re
duced. In ord
e
r to
sel
e
ct the optim
al swit
chin
g state from the 27
swit
chin
g
states
and
ma
ke
the
cu
rre
nt value
of the fu
ture
,
(1
)
ik
as
c
l
os
e a
s
p
o
ss
ib
le to
the
curre
n
t refe
re
nce val
ue
*
,
()
ik
, a simplified
predictive
control al
go
rithm i
s
propo
se
d b
y
inverse
thinkin
g
. Accordin
g to the mathemati
c
al
model of
the AFE converter, assum
p
tin
g
the existen
c
e
of voltage vector
*
,
()
uk
which can ma
ke
,
()
ik
equal to
*
,
()
ik
, then
*
,
()
uk
is cal
c
ul
ated
by
Equation (9).
*
,,
*
,,
,
()
()
()
()
()
L
ik
ik
uk
e
k
R
i
k
L
T
(9)
Whe
r
e
*
,
()
uk
is cal
l
ed 'virtual ref
e
ren
c
e voltag
e
vector'. Fo
r the FCS-MP
C algo
rithm,
only outputin
g a voltage
vector e
a
ch control pe
rio
d
, the neare
s
t voltage ve
ctor to
*
,
()
uk
is
optimal voltage vector
OPT
u
. The final co
st function
J
is selected as following:
2
*
1,
,
2
3
(1
)
(
1
)
(1
)
(
1
)
dc
s
Ju
k
u
k
U
k
f
k
(10)
In the pre
s
e
n
t
ed algo
rithm
,
the 26 time
s current p
r
e
d
iction
pro
c
e
ss i
s
simplifi
ed a
s
a
singl
e virtual
referen
c
e voltage vect
or p
r
edictio
n,
then
the cal
c
ulati
on is g
r
e
a
tly redu
ce
d. Based
on the FCS
-
MPC sin
g
le p
r
edi
ction met
hod, usi
ng
th
e vector di
stri
bution meth
o
d
can
determ
i
ne
the optimal switchi
ng stat
e. The
sp
ace
voltage vectors
of all the
swit
chin
g stat
es of the three-
level AFE converter a
r
e shown in Figure 2. The th
re
e-ph
ase brid
g
e
arm switch
state '1', '0' a
nd '-
1' re
spe
c
tivel
y
are expre
ssed by t
he symbol '+', '0', '-'. The thr
ee l
e
vel spa
c
e v
e
ctors a
r
e div
i
ded
into 6 large
sectors, which
the swit
ch sta
t
e of each ve
ctor i
s
adja
c
e
n
t.
For exa
m
ple,
whe
n
*
,
()
uk
in the third
sector
III, compar
ed to other volt
age vectors,
01
2
5
61
61
7
1
8
,,
,
,
,
,
,
uu
u
u
uu
u
u
are mo
re
cl
ose to
*
,
()
uk
, then the curre
n
t con
s
trai
nts a
r
e rel
a
tively
small. In ord
e
r to comp
are the value of t
he neutra
l point potential of each voltage vecto
r
, a
voltage ve
cto
r
i
s
ta
ken
a
s
the
referen
c
e vecto
r
and
co
mpa
r
ed
to
the se
ctors whi
c
h have
t
h
e
same mi
dpoi
nt potential constraint valu
e. If the vect
or in the
current con
s
traint
value is g
r
e
a
ter
than the ref
e
ren
c
e ve
cto
r
, then these vect
ors would be excl
uded from t
he scope of
th
e
can
d
idate ve
ctor.
Can
d
ida
t
e vectors
co
rrespon
ding
to
each
se
ctor
are li
st on
Ta
ble 1.
With th
e
decrea
s
e
of the candid
a
te
vect
ors, the
hexagon
sh
ado
w re
gion
is
form
ed a
can
d
idate ve
ctor
region. In s
e
c
t
or III, if
()
(
)
0
,
()
()
0
,
()
()
0
dc
a
d
c
b
d
c
c
Uk
i
k
Uk
i
k
Uk
i
k
, the num
ber
o
f
candid
a
te
v
e
ct
or
s is r
e
d
u
ce
d t
o
7.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 440 – 44
8
444
*
u
，
Figure 2. Voltage vecto
r
s d
i
stributio
n
Table 1. Sele
ction of ca
ndi
dat
e v
e
ct
or
s f
o
r ea
ch s
e
ct
o
r
Sector
Ι
Ⅱ
Ⅲ
Ⅳ
Ⅴ
Ⅵ
()
()
0
dc
a
Uk
i
k
3
u
9
u
3
u
9
u
3
u
9
u
()
()
0
dc
a
Uk
i
k
4
u
10
u
4
u
10
u
4
u
10
u
()
()
0
dc
b
Uk
i
k
13
u
7
u
7
u
13
u
13
u
7
u
()
()
0
dc
b
Uk
i
k
()
()
0
dc
c
Uk
i
k
()
()
0
dc
c
Uk
i
k
14
u
5
u
6
u
8
u
5
u
6
u
8
u
5
u
6
u
14
u
11
u
12
u
14
u
11
u
12
u
8
u
11
u
12
u
S
a
m
p
li
n
g
a
n
d
ge
tt
i
n
g th
e kth ti
m
e
s
,
∗
，
,
，
,
P
r
e
d
icti
n
g
,
∗
1
，
a
c
c
or
di
n
g
ex
p
re
ss
io
n
(
7
)
an
d
(
9
)
J
udg
i
n
g
se
c
t
or a
n
d g
e
t
t
i
ng
S(
N
)
P
r
e
d
ic
ting
i
α,
β
k
1
，
∆
1
acco
r
d
i
n
g exp
r
essi
o
n
(
7
)
an
d
(9
)
i=
N
?
P
r
e
d
ic
ting
i
α,
β
k
1
，
∆
1
acco
r
d
i
n
g exp
r
essi
o
n
(
7
)
an
d
(9
)
1
,
∗
1
,
1
2
2
|
1
|
|
1
|
,i=1
,…N
if
J<
=J
=i
fo
r
i=
1
:
N
Ou
t
p
ut
Figure 3. The
flow cha
r
t of FCS-MP
C al
gorithm
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Model Pre
d
ict
i
ve Optim
i
zati
on Co
ntrol Strateg
y
for Th
ree-le
vel AFE
Con
v
e
r
ter (Xi
aoyan Shi)
445
Searchin
g th
e discrete vol
t
age vecto
r
n
ear
OPT
u
. can d
e
termin
e the fi
nal MPC
syst
em
optimal swit
ching state.
Th
e
flow ch
art
o
f
FCS-MP
C a
l
gorithm i
s
sh
own i
n
Fig
u
re
3.
i
is
defined
as th
e lo
op
variable,
OP
J
is
the value of
the optimal c
o
s
t
func
tion.
()
OP
Si
is output optimal
swit
chin
g
sig
nal. Th
e al
go
rithm i
s
put in
the timin
g
int
e
rrupt
routin
e
s
.
When
the
timer i
n
terrupt
is
trigge
red, th
e
switchi
ng
sig
nals for th
e fi
rst
cycle
be
gi
n to affe
ct th
e a
c
tual h
a
rd
ware
circuit,
an
d
voltage and
current sam
p
li
ng start u
p
.
Before th
e
rol
ling o
p
timizati
on the
optim
a
l
voltage ve
ct
or
OPT
u
. of the
sy
stem is obtai
n
e
d
by the Equ
a
tion (9).
The
d
e
termin
ed
discrete
voltage
vector is put i
n
[]
SN
.
N
is the
nu
mber of
FCS-MP
C
rolling o
p
timi
zation. T
a
ki
ng into
a
ccount voltage
sp
ace vector di
strib
u
tion
cha
r
a
c
teri
stics of th
e th
re
e-level to
pol
ogy, the valu
e of
N
can
be 4, 5,
and 7.
Then rolling
optimizatio
n only need
s to be ca
rri
ed out 7 time
s, whi
c
h greatly enhan
ce th
e system onl
in
e
sea
r
ching effi
cien
cy.
4. Contr
o
l Dela
y
and Co
mpensa
tion Scheme
Ideally,
AD sampling, algo
rithm calculat
ion,
co
ntrol
si
gnal a
c
tion
of
MPC
cont
rol
system
sho
u
ld be
co
mpleted at the sa
me time. But actual
digital pro
c
e
ssi
ng sy
stem
has
con
s
um
ed
certai
n p
r
og
ram execution
time, so the
cont
rol
sign
al is b
oun
d to delay a
pe
riod of time
after
output. In th
e
de
sign
p
r
o
c
ess of
the A
F
E co
nverte
r co
ntroll
er,
control
delay
effect is a
n
i
s
sue
that shoul
d n
o
t be ignored.
*
i
(
k-
1)
Tk
T
(
k+
1)
T
(
k+
2
)
T
u
(
k-
1)
...
i
*
i
(
k-
1)
Tk
T
(
k+
1)
T
(
k+
2
)
T
u
(
k-
1)
i
u
(
k
)
i
(
k+
1)
u
(
k-
1)
u
(
k
)
i
(
k+
1)
(a)
Ide
a
l
cu
r
r
en
t
pr
ed
i
c
ti
n
g
pr
ocess
(b
)
A
c
t
u
al
cu
r
r
en
t
pr
ed
i
c
ti
n
g
pr
oces
s
*
i
u
(
k-
1)
i
u
(
k
)
i
(
k+
1)
(
k-
1)
Tk
T
(
k+
1)
T
(
c
)
Cu
r
r
en
t
pr
ed
i
c
t
i
o
n
p
r
o
c
es
s
w
i
t
h
de
l
a
y
co
mp
en
s
a
t
i
on
Figure 4. Current predi
ctio
n pro
c
e
s
s
Figure 4(a), (b) illu
strate t
he
cu
rrent predictio
n pr
ocess for the id
eal situatio
n
and the
actual situati
on
ba
sed on MPC.
The
co
ntrol del
ay co
mpen
sation
st
rategy ope
ra
tes a
s
sh
own
in
Figure
4
(
c). The
g
r
id sid
e
cu
rre
nt
,
(1
)
ik
is p
r
edi
cted from
Equation
(4
). Then the
cu
rre
nt is
use
d
as the
starting
current of the system,
and the model p
r
edictio
n pro
c
ess is p
r
oje
c
ted
forward.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 440 – 44
8
446
,,
**
,,
(
2
)
(
1
)
(1
)
[
(1
)
(
1
)
]
ss
RT
T
ik
i
k
e
k
u
k
L
L
(11)
The treatme
nt of neutral
point poten
tial is
con
s
i
s
tent with th
e grid si
de
curre
n
t.
Acco
rdi
ng to the Equation
(7) the midp
oi
nt potential
(2
)
dc
uk
T
is obtain
ed.
222
()
(
2
)
[
()
()
(
)
]
(
)
(
1
)
()
a
s
dc
a
b
c
b
dc
c
ik
T
U
k
Sk
Sk
Sk
i
k
U
k
C
ik
(12)
The optimal
swit
chin
g sta
t
e of the rolling
optimization mome
nt is dete
r
mine
d
by the
state of the
(2
)
kT
,
and is kept to the
(1
)
kT
. In essence the del
ay compe
n
sa
tion belong
s to
multi-ste
p
pre
d
iction. Ba
se
d on di
screte
pr
edi
ct mo
del
of system in
a sam
p
ling
p
e
riod
s
T
, multi-
step predi
ctio
n are carried
out to comp
ensate and
correct the infl
uen
ce of the
control d
e
lay
cau
s
e
d
by the optimal switchin
g state.
To su
m up, t
he structu
r
e
of the co
ntrol
sy
stem b
a
se
d on F
C
S-M
P
C algo
rithm
is shown
in Figure 5. The DC bu
s voltage is adj
usted by t
he PI
controlle
r, an
d the cu
rre
nt referen
c
e val
u
e
is gen
erate
d
. Acco
rdin
g to the model
predictive control theory, the voltage
,
()
uk
is predi
cte
d
whi
c
h i
s
n
e
e
ded to t
r
a
c
k
the refe
re
nce
cu
rrent in t
he
coo
r
di
na
te. Then
opti
m
al voltage
vector is take
n a
s
the
out
put of the
co
ntro
lle
r d
e
termined
by the
se
cto
r
of th
e voltage
,
()
uk
loc
a
tion.
/
ab
c
,
e
,
i
P
e
,
P
i
,
)
1
(
,
k
u
)
(
*
k
u
,
e
1
Pa
r
k
C
N
S
)
1
(
*
,
k
i
)
(
,
k
u
Figure 5. The
stru
cture of the co
ntrol sy
stem ba
sed o
n
FCS-MP
C
5. Simulation and Analy
s
is
In orde
r to
verify the correctn
ess o
f
the pro
p
o
s
ed F
C
S-MP
C control
al
gorithm,
Simulation st
udy of contro
l system in Figure 5
is p
r
e
s
ente
d
based
on Matlab/Simulink. Syste
m
simulatio
n
pa
ramete
rs a
r
e
listed in Tabl
e 2.
Table 2. System simul
a
tio
n
para
m
eters
List
Parameters
Value
1 Grid
sidevoltagefrequenc
y
f
/Hz
50Hz
2
Electricity
grid line voltage
e
ab
/V
90V
3
DC side capacitor C/
μ
F
2500
μ
F
4 Line
inductance
L
/mH
1.5mH
5 Load
resistance
R
/
Ω
8
Ω
6
Sampling freque
ncy /kHz
10kHz
Figure 6 an
d
Figure
7 are
the steady
-state
current simulation wa
veform
and a
phase
curre
n
t spe
c
trum analysi
s
resp
ectively of th
ree-l
e
vel AFE conve
r
ter
based on the
FCS-MP
C.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Model Pre
d
ict
i
ve Optim
i
zati
on Co
ntrol Strateg
y
for Th
ree-le
vel AFE
Con
v
e
r
ter (Xi
aoyan Shi)
447
Figure 6. Steady state cu
rrent waveform
Fi
gure 7. A phase cu
rrent spe
c
tru
m
ana
lysis
The result in
Figure 6 i
n
dicate
s in
put
cu
rre
nt
of t
he sy
stem i
s
stable.
Wav
e
form i
s
almost si
nu
soidal and the
unit powe
r
factor
c
an b
e
realized. Th
e curre
n
t sp
ectru
m
analy
s
is
sho
w
s that the total ha
rmonic conten
t of A phase
cu
rre
nt is
2.96% in Fig
u
re 7. The
cu
rrent
harm
oni
c co
n
t
ent is lowe
r, and the control effect is go
od.
To furth
e
r an
alysis the vali
dity of the F
C
S-MPC
pro
p
o
s
ed
in thi
s
pa
per, dyn
a
mi
c
curre
n
t
cha
nge
d pro
c
e
ss i
s
co
nd
ucted. When
refere
nce
current value
is ri
sed fro
m
10 A to 12A at
0.03s, th
e out
put current a
r
e dem
on
strat
ed in
Figu
re
8(a
)
. Refere
n
c
e
cu
rrent val
ue i
s
de
crea
sed
from 10 A to 8A in Figure
8(b
)
. The cu
rrent step ti
m
e
is about 0.
2ms. The
n
it can b
e
found
tha
t
the respon
se
spe
ed is relat
i
vely fast.
(
a
)
R
e
fe
re
nc
e c
u
rr
e
n
t
s
t
ep
r
i
s
e
(
b
)
R
e
fe
re
nc
e c
u
rr
e
n
t
s
t
ep
fa
ll
Figure 8. Dyn
a
mic si
mulati
on re
sult
s
with referen
c
e current ch
ang
ed
The sa
mplin
g perio
d
s
T
is
100
s
, AD samplin
g time of digital processin
g
system i
s
about
5
s
, predi
ctive co
ntrol
rolling o
p
timization time i
s
about
40
s
, the total c
ont
rol delay is
about
45
d
ts
. Con
s
ide
r
ing th
e
large
propo
rtion of
d
t
in sampling
peri
od
s
T
, the delay
comp
en
satio
n
strategy is
need
ed to overcome t
he p
r
oble
m
that the AD sam
p
l
i
ng point is n
o
t
matche
d with
the switchi
n
g state actio
n
time.
In Figure 9 the st
eady-state waveform with
and
without control delay com
pen
sation a
r
e illustrate
d.
As finding in
the figure, the output cu
rrent
ripple i
s
sm
aller
with tim
e
delay
com
pen
sation
of MPC sy
ste
m
unde
r the
same
samp
ling
freque
ncy an
d given cu
rre
n
t situation, whch h
a
s mo
re
excellent current tra
cki
ng
accuracy.
(a) Simul
a
tio
n
results with
out delay
comp
en
sat
i
o
n
(b) Simul
a
tio
n
res
u
lts
with delay
com
p
e
n
satio
n
Figure 9. Simulation re
sult
s for FCS
-
MP
C witho
u
t and
with delay co
mpen
sation
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
-1
5
-1
0
-5
0
5
10
15
t/
s
i/
A
ig
a
ig
c
ig
b
0
0.
0
1
0.
0
2
0.
03
0.
0
4
0.
0
5
0.
0
6
-1
5
-1
0
-5
0
5
10
15
t/s
i/
A
ig
a
ig
b
ig
c
0
0.
01
0.
02
0.
03
0.
0
4
0.
05
0.
06
-1
5
-1
0
-5
0
5
10
15
t/s
i/
A
ig
a
ig
b
ig
c
0
0.
005
0.
0
1
0.
0
1
5
0.
02
0.
025
0.
0
3
-1
5
-1
0
-5
0
5
10
15
i/A
t/s
0
0.
005
0.01
0.
0
1
5
0.
0
2
0.02
5
0.
03
-1
5
-1
0
-5
0
5
10
15
t/s
i/A
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 440 – 44
8
448
6. Conclusio
n
As an
advan
ced
co
nverte
r control
tech
nology,
F
C
S-MPC control
strategy i
s
a
pplied to
the control
of
three
-
level A
F
E co
nverte
r
in this
pa
per.
For th
e p
r
obl
ems
existing
i
n
the t
r
adition
al
model cu
rren
t
predi
ction, a
sim
p
lified model
volt
a
g
e
predi
ction
control al
gori
t
hm is
pro
p
o
s
ed.
The virtual v
o
ltage p
r
edi
ction and volt
age ve
ctor
di
vision meth
o
d
is int
r
od
uced to sele
ct the
optimal voltage vecto
r
. It
has ove
r
com
ed effectivel
y the defects
of low efficie
n
cy of traditi
onal
MPC algo
rith
m. Finally, the simul
a
tion
results
sho
w
that the pro
posed st
rate
gy have a g
ood
static
and
dy
namic pe
rformance,
which
ha
s p
r
ovid
ed
a
simplifie
d
method
for th
e de
sig
n
of
m
u
lti-
lev
e
l conv
e
r
t
e
r MP
C
sy
st
e
m
.
Referen
ces
[1]
Z
a
ragoz
a J Po
u J, Ceba
llos
S, et al. A compreh
ensiv
e stu
d
y
of a h
y
bri
d
modu
latio
n
tec
hni
que for the
neutra
l-po
int-cl
ampe
d conv
erter.
IEEE Transactions on Industrial Electronic
s
. 2009; 56(
2): 294-
304.
[2]
Kadri
R, Ga
ub
ert J P, C
ham
pen
ois G. A
n
i
m
prove
d
ma
xi
mum p
o
w
e
r
p
o
int track
i
ng
fo
r ph
otovolt
a
i
c
grid-co
n
n
e
cted
inverter
bas
ed
o
n
volt
ag
e-orie
nted c
o
ntrol.
IEEE Transactions
on Industrial
Electron
ics
. 20
11; 58(1): 6
6
-7
5.
[3]
Lee JH. Mo
de
l
predictiv
e co
ntrol revi
e
w
of th
e three d
e
ca
de
s of devel
opm
ent.
Internatio
n
a
l Jour
na
l of
Contro
l, Automation a
nd Syst
ems
. 2
011; 9(
3
)
: 415-42
4.
[4]
Atif Iqbal,
Sha
i
kh Mo
ino
d
d
i
ne
, Khal
iqur
R
a
h
m
an. F
i
n
i
te St
ate Mo
del
Pre
d
ictive
Curr
ent
an
d C
o
mmo
n
Mode V
o
lta
ge
Contro
l for a
Seven
p
h
a
se V
S
I.
Internation
a
l Jo
urna
l of
Pow
e
r Electro
n
ics a
nd Dr
ive
System
s.
20
15
; 6(3):
459-4
7
6
.
[5]
Gu Xin, Z
h
ang
Ce, Ge
ng Qi
a
ng, Sh
i T
i
ngn
a
.
Simplif
i
ed m
o
del c
u
rre
nt pre
d
ictive c
ontro
l
of three-
leve
l
rectifier.
Advan
c
ed T
e
chn
o
l
o
g
y
of Electrical
Engi
neer
in
g an
d Energy
. 2
014
; 33(2): 12-17.
[6]
M Elsisi, MA
S Abo
e
l
e
la,
M Solim
an,
W
Manso
u
r.
Mode
l Pre
d
icti
ve C
ontrol
of
T
w
o-Are
a
L
o
a
d
F
r
eque
nc
y C
o
ntrol B
a
sed
Imperia
list C
o
mpetitive
Alg
o
r
ithm.
T
E
LKOMNIKA Indo
ne
sian J
our
nal
o
f
Electrical E
ngi
neer
ing.
2
015;
16(1): 75-
82.
[7]
Cao
Xi
ao
do
ng,
T
an Guojun, W
ang Co
ng
ga
ng.
Mod
e
l pr
ed
ictive virtua
l vol
t
age vector c
o
ntrol for three-
phas
e PW
M rectifiers
. Procee
din
g
s of the C
SEE. 2014; 33(
18): 292
6-2
935
.
[8]
Vargas
R, C
o
r
t
es P, Amman
n
U,
et al. Pr
edi
ctiv
e co
ntro
l of
a thre
e-p
hase
ne
utral-
p
o
int-cl
ampe
d
inverter.
IEEE Transactio
n
s o
n
Industria
l Ele
c
tronics
. 200
7; 54(5): 26
97-
27
05.
[9]
Liu P
u
, W
ang
Yue, Co
ng W
u
l
ong, et
al.
Res
earch
es o
n
opt
imi
z
e
d
mod
e
l p
r
edictiv
e contro
l for mod
u
l
a
r
mu
lti-lev
e
l co
n
v
erters
. Procee
din
g
s of the C
SEE. 2014; 34(
36): 638
0-6
388
.
[10]
W
ang Yi
nso
n
g
,
W
ang Sh
u
y
u
an.
Multi-ste
p
Predictiv
e co
ntrol for o
u
tput c
u
rrent of thr
e
e
-
phas
e gri
d
-
conn
ected i
n
ve
rters.
Sm
art Grid
. 201
5; 3(3): 223-
228.
[11]
Vazqu
e
z S,
Le
on JI, F
r
a
nqu
e
l
o
LG, et a
l
.
M
ode
l pr
ed
ictive
contro
l w
i
th c
onstant sw
itch
i
ng fre
q
u
ency
usin
g a
discr
ete sp
ace v
e
ctor
mod
u
lation wit
h
virtual state
vectors
. IEEE International
Conference
on
Industria
l T
e
chnol
og
y. 20
09: 1-6.
[12]
Malino
w
ski M,
Kazmierk
o
w
ski MP
. A com
par
ative stu
d
y
of c
ontrol
tech
niq
u
e
s for PW
M r
e
ctifiers i
n
ac
adj
ustabl
e spe
ed driv
es.
IEEE Transactions
on Power Elec
tronics
. 200
3; 18(6): 13
90-
13
96.
[13]
Xi
a C
h
a
ngl
ia
n
g
, Liu
T
ao, Shi
T
i
ngna, So
ng
Z
hanfen
g. A si
mplifie
d fin
i
te c
ontrol s
e
t mo
d
e
l pr
ed
ictive
control for po
wer converters.
IEEE Transactions on Industrial Informatics
. 201
4; 10(2): 99
1-10
02.
Evaluation Warning : The document was created with Spire.PDF for Python.