Int
ern
at
i
onal
Journ
al of
P
ow
er El
ectron
i
cs a
n
d
Drive
S
ys
te
m
(I
J
PE
D
S
)
Vo
l.
9
, No
.
2
,
J
un
e
201
8
, pp.
660
~
667
IS
S
N:
20
88
-
8
694
,
DOI: 10
.11
591/
ij
peds
.
v
9
.i
2
.
pp
66
0
-
667
660
Journ
al h
om
e
page
:
http:
//
ia
escore.c
om/j
ourn
als/i
ndex.
ph
p/IJPE
D
S
Fin
ite
-
Contr
ol
-
S
et Pr
edicti
ve Cu
rrent
Contr
ol Based
Real a
nd
Reactiv
e Po
wer Cont
ro
l
of
Grid
-
Connect
ed Hybri
d Modul
ar
Multi
level Conv
erter
Ra
s
hmi
Ranj
an Be
her
a
,
Am
arnath T
h
ak
u
r
Depa
rtment
o
f
E
EE
,
Nat
iona
l
Instit
ut
e
of
T
ec
hnol
og
y
Jam
shedpur
,
India
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
1
4,
2017
Re
vised
N
ov
27, 2
017
Accepte
d
Fe
b
07
, 201
8
Thi
s
pape
r
prop
oses
a
m
odi
ed
thre
e
-
phase
topolog
y
of
Modular
Mu
lt
il
ev
e
l
Convert
er
(MM
C)
and
i
t
s
appli
ca
t
ion
in
gr
id
c
onnec
t
ion
of
dis
tri
bute
d
dc
gene
ra
ti
ons.
This
topol
og
y
h
as
r
educ
ed
num
ber
of
sw
it
ch
count
s
compare
d
to
the
conv
ent
ion
a
l
MM
C,
el
imin
at
es
th
e
problem
of
ci
rcu
lating
cur
ren
t
and
havi
ng
high
er
e
ci
en
c
y
.
A
sing
le
dc
sourc
e
is
r
e
quire
d
to
produc
e
sinusoidal
output
s.
Th
e
nu
m
ber
of
sub
-
m
o
dule
s
(SM
s)
in
thi
s
topol
og
y
is
hal
f
of
th
e
SM
s
req
uire
d
in
ca
se
of
MM
C,
in
addi
t
ion
to
a
single
H
-
brid
e
ci
rcu
it
per
phase
.
Thi
s
pap
er
pre
sents
a
fi
nit
e
-
con
trol
-
set
pre
dic
t
ive
cur
r
ent
cont
ro
l
sche
m
e
(FCS
-
P
CC)
for
the
grid
conne
cted
dc
source
through
t
he
proposed
H
y
brid
Modular
Multi
le
v
el
Con
ver
te
r
(HM
MC).
Thi
s
cont
rol
le
r
cont
rols
th
e
desire
d
re
al
and
rea
c
ti
ve
power
demand
of
the
grid
insta
nt
aneous
l
y
.
Th
e
sim
ula
ti
on
stud
y
of
a
thr
ee
phas
e
grid
conn
ec
t
e
d
s
y
stem
h
as
be
en
done
in
Matl
ab/
Sim
uli
nk
and
the
result
s
are
provide
d
f
or
the
d
i
ere
nt
re
al
and
r
e
ac
t
ive
pow
er
d
e
m
ands,
to
v
al
id
a
te
the c
onc
ept
s.
Ke
yw
or
d:
Gr
i
d
Co
nnect
ed
Syst
em
Modula
r
M
ulti
le
vel Co
nv
e
rte
r
Pr
e
dicti
ve
Cu
rrent Co
ntr
ol
Re
al
and
Re
act
ive
Power
Con
tr
ol
Copyright
©
201
8
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed.
Corres
pond
in
g
Aut
h
or
:
Ra
sh
m
i R
anj
an
Behera
,
Nati
on
al
I
ns
ti
tute o
f
Tec
hnol
og
y J
am
sh
edpur
Dep
t.
of E
EE,
Nati
on
al
I
ns
ti
tute o
f
Tec
hnol
og
y
J
am
sh
edpur, In
dia
Em
a
il
: rash
m
iranj
a
n101
1@g
m
ai
l.co
m
1.
INTROD
U
CTION
The
m
ultilevel
vo
lt
age
sou
r
ce
conver
te
r
s
are
qu
it
e
popula
r
powe
r
el
ect
ronics
so
lut
ion
s
to
the
m
edium
to
hig
h
-
vo
lt
age
ap
plica
ti
on
s.
Se
ver
al
m
ulti
le
vel
topolo
gies
are
bein
g
c
om
m
ercialize
d,
su
c
h
a
s
Neu
t
ral
Po
int
Cl
a
m
p
(N
PC),
Fly
ing
Ca
pacit
or
(F
C)
a
nd
Ca
scaded
H
-
bri
dg
e
(C
HB)
[
1]
.
These
topolog
i
e
s
hav
e
so
m
e tec
hn
ic
al
c
halle
ng
es, like
NP
C a
nd FC a
re quit
e b
ec
om
e co
m
plex
t
o
im
ple
m
ent if the
d
e
sir
ed
le
vel
of
outp
ut
vo
lt
a
ge
is
i
ncr
ease
d,
s
o
these
h
ave
le
ss
scal
abili
ty
issues.
A
nd
al
so
as
t
hey
ha
ve
si
ng
le
i
nteg
rated
structu
re,
if
the
re
will
be
so
m
e
fau
lt
s
in
the
conve
rter
swit
ches,
the
n
the
t
otal
conver
te
r
has
to
be
re
placed.
S
o
for
reli
abili
ty
a
nd
ease
of
ope
rati
on
pu
rpose,
the
m
ultilevel
top
ol
og
ie
s
ne
ed
to
be
m
or
e
scal
able
and
s
o
nee
d
to
be
m
odular.
In
so
m
e
extent
the
C
HB
to
po
l
og
y
s
olv
e
these
pro
blem
s.
But
agai
n
the
m
ult
il
evel
topolo
gy
need to
be
le
ss
com
plex
[
2,
3].
Af
te
r
the
i
nce
ption
of
M
odul
ar
Mult
il
evel
Converte
r
(M
MC
)
in
2003[
4],
this
t
opology
becam
e
a
popula
r
al
te
r
na
ti
ve
for
the
co
nv
e
ntio
nal
m
ul
ti
le
vel
conver
t
ers.
It
has
seve
ral
ad
van
ta
ges
li
ke
m
od
ular
de
sign,
easi
er
scal
ing
of
le
vels,
hig
he
r
ef
fici
enc
y
becau
se
of
le
ss
switc
hing
com
po
nen
ts
,
and
e
xcell
ent
ou
t
pu
t
wav
e
f
or
m
s
wit
h
le
ss
har
m
on
i
c
dis
tortio
ns
.
This
to
po
l
og
y
util
iz
es
the
su
bm
od
ules
(S
M
s)
f
or
the
c
reati
on
of
le
vels.
T
he
S
Ms
hav
e
seve
r
al
cong
ur
at
io
ns,
f
ro
m
wh
e
re
the
half
b
i
dg
e
-
base
d
SM
(
H
BSM
)
is
quit
e
popula
r
for
it
'
s
si
m
plicity
in
operati
on.
The
sch
em
a
ti
c
of
t
he
MM
C
an
d
a
HBS
M
is
sho
wn
in
Fig
ur
e
1(a)
a
nd
1(
b)
resp
ect
ively
[4]
-
[10].
T
he
H
BSM
is
com
po
se
d
of
tw
o
powe
r
el
ect
r
onic
s
switc
hes
a
nd
a
capaci
to
r
acros
s
them
.
Ho
wev
e
r
this
topolo
gy
req
uires
tw
o
dc
sup
plies
and
tw
o
arm
s
of
SMs
for
the
sinusoi
dal
ou
t
pu
t
wav
e
f
or
m
s
as
sh
ow
n
i
n
Fi
gu
re
1(
a
).
This
topolo
gy
al
s
o
s
uffer
s
f
r
om
the
pro
blem
of
i
nh
e
re
nt
ci
rc
ulati
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow
Ele
c
&
D
ri
Syst
IS
S
N:
20
88
-
8
694
Finit
e
-
Co
ntro
l
-
Set P
redict
iv
e Curre
nt Co
ntr
ol B
as
ed
Re
al
and React
iv
e P
ower
…
(
R
as
hmi R
an
j
an Behe
ra
)
661
current
bet
wee
n
the
arm
s
du
e
to
the
capaci
tor
i
m
balances,
wh
ic
h
require
a
separ
at
e
con
tr
ol
sche
m
e
to
m
ini
m
iz
e thr
ou
gh capacit
or
volt
age
balanci
ng
[7
]
.
To
ad
dr
e
ss
al
l
these
issues,
m
od
i
f
ie
d
hy
br
id
MM
C
top
olog
y
is
pr
opos
e
d
in
[15],
as
sho
wn
in
Fi
gure
1(
c
)
.
This
to
polog
y
util
iz
es
only
one
a
rm
of
SMs
per
ph
as
e
al
ong
with
a
H
-
br
i
dg
e
ci
rc
ui
t
acro
ss
the
lo
ad
f
or
the
ge
ne
rati
on
of
sin
us
oi
dal
outp
uts
[
15]
.
A
s
com
par
ed
t
o
t
he
MM
C
this
HMMC
is
ha
vi
ng
half
of
the
SMs
with
one
H
-
bri
dg
e
,
so
le
ss
sw
it
ching
com
ponen
ts
.
The
co
m
par
ison
of
num
ber
of
switc
hes
an
d
SMs
with
th
e
MM
C
is
giv
en
in
Table
1.
D
ue
to
le
ss
s
witc
h
co
unts
this
topolo
gy
is
m
o
re
ef
fici
ent
an
d
hav
i
ng
le
ss
c
om
plex
ci
rcu
it
ry.
T
his
desig
n
is
h
a
vin
g
le
ss
e
nergy
stori
ng
com
po
ne
nts,
w
hich
m
akes
this
m
or
e
com
pact
an
d
le
ss
e
r
cost.
I
n
this
pa
per
on
e
of
it
’s
app
li
cat
io
n
are
a
of
gri
d
c
onne
ct
ed
dc
s
ources
,
su
it
ably
for
r
enew
a
ble
distri
bu
te
d
gen
e
rati
ons
(DGs) has
b
e
en
inv
e
sti
gated.
The
c
on
t
ro
l
of
gr
i
d
co
nnect
ed
co
nverte
rs
is
a
ver
y
m
uch
chall
eng
i
ng
ta
sk
beca
us
e
of
f
r
equ
e
nt
loa
d
var
ia
ti
ons,
w
hich
need
s
to
s
uppo
rt
fr
e
que
nt
real
an
d
reacti
ve
power
dem
and
by
t
he
gri
d.
T
he
refor
e
th
e
D
Gs
hav
e
t
o
pr
ov
i
de
require
d
real
and
reacti
ve
powe
r
to
sta
bili
ze
the
gri
d
pow
er
.
Va
rio
us
c
on
t
ro
l
sc
hem
es
for
this
pur
po
se
ha
ve
be
en
publishe
d
base
d
on
pro
portio
nal
plu
s
in
te
gr
al
(
PI)
c
ontrolle
rs
.
As
this
ap
plica
ti
on
is
Mult
i
Inp
ut
Mult
i
Ou
tp
ut
(MIMO
)
kind
of
syst
e
m
,
therefore
m
ul
ti
ple
PI
co
ntr
ollers
nee
d
to
be
ap
plied
for
the
desir
e
d
c
on
tr
ol
act
ion
.
T
he
pro
blem
with
these
P
I
co
ntr
ollers
is
that
these
ha
ve
t
o
be
pro
per
ly
tun
e
d,
oth
e
rw
ise
t
hey
can
a
dv
e
rsely
aff
ect
the
syst
em
.
Hen
ce
thes
e
kind
of
syst
em
s
need
a
sim
pler
c
on
t
ro
l
sc
hem
es.
Var
i
ou
s
ad
va
nc
ed
c
on
t
ro
l
the
or
ie
s
ha
ve
bee
n
e
vo
l
vi
ng
s
pe
ci
al
ly
fo
r
the
powe
r
el
ect
r
on
i
cs
(P
E
s)
a
ppli
cat
ion
s.
The
m
od
el
predict
ive
co
ntr
oller
w
hich
ar
e
us
ually
pr
e
f
err
e
d
earli
er
f
or
the
c
hem
ical
ind
us
t
ries,
are
no
w
beco
m
ing
popula
r
i
n
a
pp
li
cat
ion
s
of
P
Es,
be
cause
of
it
’s
s
i
m
pler
desig
n,
and
easi
er
im
ple
m
en
ta
ti
on
be
caus
e
of ev
olu
ti
on
of f
ast
er
m
ic
ro
process
or
s
for fa
ste
r
com
pu
ta
ti
on
s
[6],
[9
]
-
[
14]
.
This pape
r
pre
sents f
i
nite co
nt
ro
l set
s (FC
S)
base
d
pre
dicti
ve
curre
nt contr
ol tech
nique [1
1]
-
[
14]
f
or
the
gri
d
co
nne
ct
ed
dc
s
ource
thr
ough
HMM
C.
This
te
c
hniqu
e
i
s
use
d
to
fin
d
the
best
s
witc
hing
se
que
nce
for
the
switc
hes
of
HMMC
fro
m
the
finite
switc
hing
sta
te
s,
thr
ough
m
ini
m
iz
ing
a
cost
functi
on
de
riv
ed
f
ro
m
error
betwe
en
the
re
fer
e
nce
a
nd
m
easur
ed
gri
d
c
urren
t
.
I
n
this
w
ork,
sepa
rate
predict
ive
con
t
ro
ll
ers
are
u
s
e
d
for
in
div
i
du
al
ph
a
ses.
The
n
t
he
sim
ulati
on
stud
y
is
stu
died
for
diff
e
re
nt
real
a
nd
react
ive
dem
and
f
r
om
the
gr
i
d,
w
ho
se
r
e
f
eren
ces
w
e
re
pro
vid
e
d
m
anu
a
ll
y and
the
r
e
sul
ts are s
how
n.
Figure
1. Sc
he
m
at
ic
s o
f
(a
)
C
onve
ntion
al
sin
gle
-
ph
ase
MM
C t
opology
, (b
)
H
al
f
-
bri
dge
S
ub
-
Mo
dule
(S
M),
(c)
Hyb
rid
MM
C t
opology.
2.
TOPOL
OG
Y AND B
AS
I
C OPE
R
ATIO
N
The
sin
gle
-
ph
a
se
t
opology
of
HMMC
is
sh
own
in
Fig
ur
e
1(c).
Where
a
H
br
id
ge
is
co
nnect
ed
wit
h
an
arm
of
SM
s.
The
th
ree
phase
gri
d
c
onne
ct
ed
topolo
gy
is
sh
own
i
n
F
igure
2.
Each
SM
is
com
po
sed
of
a
half
br
i
dge
ci
rc
uit
with
tw
o
s
witc
hes
a
nd
a
capaci
tor
acr
oss
them
,
as
s
hown
in
Fig
ur
e
1(b
).
O
n
t
he
AC
side
a
s
sh
ow
n
in
Fi
gur
e 2
,
the t
hr
ee
phases a
re
dec
ouple
d
th
r
ough t
hr
ee
transf
or
m
ers,
T (
a
, b, c
).
The HMM
C
Table
1.
C
om
par
iso
n betwee
n co
nv
e
ntio
nal
MM
C and HM
MC
Nu
m
b
e
r
o
f
su
b
-
m
o
d
u
les
Nu
m
b
e
r
o
f
switch
e
s
Nu
m
b
e
r
o
f
vo
ltag
e so
u
rces
MMC
2
N
2x2
N
2
HMM
C
N
+1
H
-
Brig
d
e
2
N
+4
1
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
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694
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nt J
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ow
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c
&
Dr
i
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, Vol.
9
, N
o.
2
,
J
une
2018 :
660
–
667
662
pro
du
ces
outp
ut
o
n t
he AC si
de
as,
(1)
Figure
2. Sc
he
m
at
ic
d
ia
gr
am
of thr
ee
-
ph
ase
gr
i
d
-
ti
ed HM
MC
The
SM
as
sh
own
in
Fig
ure
1(b
),
is
sai
d
to
be
connecte
d
w
hen
the
up
per
switc
h
i.e.
Sn1
in
ON
an
d
lowe
r
switc
h
S
n2
is
OF
F
,
a
nd
the
SM
is
by
passe
d
w
he
n
S
n1
is
OF
F
a
nd
Sn2
is
O
N
.
Th
e
switc
hes
of
the
H
-
br
i
dg
e
a
re
s
witc
hed
at
the
li
ne
fr
e
quency
i.s
.
at
50H
z.
T
he
opposit
e
dia
gonal
s
witc
h
pa
irs
are
s
witc
he
d
O
N
and OF F
at p
osi
ti
ve
an
d neg
a
ti
ve
half
cyc
le
s for
t
he reve
rsa
l of loa
d
c
urrent
to
ge
ne
rate A
C at
load side
.
3.
PREDI
CTI
V
E CUR
RENT
CONTR
OL S
CHE
ME
The
gri
d
c
onne
ct
ed
three
-
ph
ase
HMMC
is
con
t
ro
ll
ed
by
s
epar
at
e
pr
e
dicti
ve
cu
rr
e
nt
co
ntr
ollers
pe
r
ph
a
se.
T
he
pr
i
m
ary
obj
ect
ive
of
this
c
on
tr
ol
le
r
is
to
prov
i
de
the
ade
quat
e
switc
hing
se
qu
ence
to
t
he
s
wi
tc
hes
of
HMMC
to
ge
ner
at
e
desire
real
an
d
reacti
ve
powe
r
dem
and
by
the
gri
d.
T
he
ov
e
rall
s
yst
e
m
integrated
with
pr
e
dicti
ve
c
on
t
ro
ll
er im
ple
m
e
nted pe
r ph
ase
is sh
o
w
n
i
n
Fi
gure
3.
The
c
ontrol
sc
hem
e
is
div
ide
d
int
o
th
ree
st
ages,
first
one
is
to
gen
e
rate
the
re
fer
e
nce
c
urren
t,
f
or
-
m
ula
ti
on
of c
ost
f
unct
io
n,
a
nd the
n
c
hoosi
ng the
opti
m
u
m
switc
hing se
qu
ence
with th
e
m
ini
m
u
m
err
or.
Figure
3. O
veral
l gr
id
con
nec
te
d
HMMC
sy
stem
w
it
h
pred
ic
ti
ve
curre
nt c
on
t
ro
l sc
hem
e.
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Finit
e
-
Co
ntro
l
-
Set P
redict
iv
e Curre
nt Co
ntr
ol B
as
ed
Re
al
and React
iv
e P
ower
…
(
R
as
hmi R
an
j
an Behe
ra
)
663
3.1.
Ref
ere
nce
Cur
rent
Gener
ati
on
This contr
ol sch
em
e is
ap
plied for
in
div
i
du
a
l ph
ases se
par
a
te
ly
. S
o
the r
ef
eren
ce c
urren
t
is gen
er
at
e
d
for
each
ph
a
se
.
In
eac
h
phas
e,
the
first
ste
p
is
to
der
ive
th
e
or
th
ogonal
sign
al
s
by
sensi
ng
t
he
phase
c
urrent
per
sam
ple
time
Ts
.
Be
cause
for
the
co
ntr
oller,
two
or
t
hogonal
sig
nals
f
r
om
a
s
ing
le
sign
al
is
necessa
ry
to
con
t
ro
l
the
rea
l
and
reacti
ve
powe
r
sepa
rate
ly
.
Ther
e
fore
a
n
sig
nal
ort
hogonal
to
t
he
act
ual
phase
v
olta
ge
is
gen
e
rated
.
As
sh
ow
n
i
n
Fi
gur
e
4,
vαn
a
nd
vβ
n
are
the
sig
nals
or
t
hogona
l
to
eac
h
oth
e
r,
w
her
e
the
first
one
i
s
the
act
ual
volt
age
pe
r
phase
and
t
he
seco
nd
one
is
pha
se
sh
ifte
d
by
π/
2.
The
nota
ti
on
n
is
us
e
d
for
the
diff
e
re
nt
ph
a
s
es
a,
b,
c.
N
ow
t
he
se
signa
l
wh
ic
h
are
in
sta
ti
on
ary
r
efere
nce
f
ram
e,
conve
rted
into
th
e
synch
ron
ous (d
− q)
ref
e
ren
ce
fr
am
e u
sin
g
f
ol
lowing e
quat
io
ns
[11].
(2)
Now
from
these
vo
lt
age
sig
na
ls
in
d−
q
ref
e
r
ence
fr
am
e
an
d
util
iz
ing
the
ref
e
ren
ce
real
and
reacti
ve
powe
r,
t
he
r
e
fe
ren
ce
curre
nt s
ign
al
s i
n d−
q r
efere
nce fr
am
e are calc
ulate
d usin
g,
(3)
The
n
the
desir
ed
ref
e
re
nce
current
to
m
at
c
h
up
with
the
real
and
react
ive
powe
r
de
m
and
by
the
gr
i
d,
is
gen
e
rated
b
y,
(4)
Figure
4. Flo
w
char
t
of pre
dicti
ve
cu
rr
e
nt c
o
nt
ro
l al
gorit
hm
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i
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o.
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,
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une
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–
667
664
3.2.
Formul
at
i
on
of Cos
t
F
unct
i
on
In
t
his
sta
ge,
th
e
gr
i
d
pa
ram
eter
s
are obtai
n
e
d
in
a d
isc
rete sam
ple
t
i
m
e
Ts
.
The
a
ct
ual
gri
d
cu
rrent
is
discreti
zed
,
w
hich
will
furth
er
us
e
d
f
or
th
e
fu
tu
re
predi
ct
ion
from
the
m
easur
ed
gri
d
cu
rr
e
nt
and
vo
lt
age
values
at sam
ple tim
e k
, u
si
ng the
forwa
rd
-
Euler
a
ppr
oxim
at
ion
as:
(5)
The
fu
t
ur
e
gri
d
c
urren
t
pr
e
di
ct
ion
is
done
by
cal
culat
ing
t
he
gr
id
cu
rr
e
nt
for
eac
h
possible
volt
age
sta
te
s.
These
volt
age stat
es a
r
e cal
culat
ed fr
om
the d
if
fe
re
nt sw
it
c
hing
c
om
bin
at
ion
s,
as
sh
ow
n
in
Ta
ble 2
.
Table
2.
Sw
it
c
hing se
quences
for
dif
fer
e
nt
volt
age stat
es
Switch
es
Vo
ltag
e States
S
11
S
12
S
21
S
22
S
31
S
31
S
31
S
31
S
31
S
31
+
V
dc
0
1
0
1
0
1
1
1
0
0
+2
V
dc
/3
1
0
0
1
0
1
1
1
0
0
+
V
dc
/3
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
-
V
dc
/3
1
0
1
0
0
1
0
0
1
1
-
2
V
dc
/3
1
0
0
1
0
1
0
0
1
1
-
V
dc
/3
0
1
0
1
0
1
0
0
1
1
Now
the
pre
dicte
d
fu
t
ur
e
c
urren
t
val
ues
at
k
+
1
instant
f
or
eac
h
switc
hi
ng
sta
te
s
can
be
cal
culat
ed
from
each
volt
age levels
as:
(7)
Wh
e
re
ig
n
(
k
+
1)
an
d
ig
n
(
k)
are
t
he
fu
t
ure
and
m
easur
e
d
gri
d
cu
rr
e
nt
values
re
sp
ect
i
vely
,
von
(
k)
and
vgn
(
k)
ar
e
the
m
easur
e
d
inv
e
rter
ou
t
put
and
gr
i
d
vo
lt
ages
resp
ect
i
vely
.
Rf
n
an
d
Lf
n
bei
ng
t
he
gr
id
filt
ers,
w
he
re
n
de
note
s
the
ph
a
ses
(a
,
b,
c
).
T
he
n
the
cost
f
unc
ti
on
wh
ic
h
e
valuat
es
the
er
ror
be
tween
ref
e
ren
ce
curre
nt and
predict
e
d
c
urren
t
valu
e
s can
b
e
prese
nt
ed
as:
(8)
This
co
st
funct
ion
will
decid
e
the
best
s
witc
hing
se
qu
e
nc
e
wh
ic
h
will
be
pr
ov
i
ded
t
o
the
HMMC
switc
hes f
or
s
witc
hing.
3.3.
Choo
sin
g Op
t
im
um Sw
itchi
ng
Seque
nce
Af
te
r
t
he
c
os
t
functi
on
cal
cul
at
ion
f
or
each
vo
lt
age
le
vels,
the
ob
j
ect
ive
is
to
ch
oose
th
e
op
ti
m
u
m
switc
hing
seq
ue
nce.
T
his
is
do
ne
by
choosi
ng
the
cost
f
un
c
ti
on
with
m
ini
m
u
m
value.
It
m
eans,
ch
oo
si
ng
th
e
vo
lt
age
le
vel
t
o
gen
e
rate
the
cur
ren
t,
w
hich
will
be
the
m
os
t
cl
os
er
t
o
the
ref
e
re
nce
c
urr
ent
at
k
+
1
ins
ta
nce.
T
he w
ho
le
pro
cess is s
umm
arized
as
flo
wchart i
n
t
he
Fi
gur
e 4
.
4.
SIMULATI
O
N RESULTS
In
this
pa
per
a
6kW
at
ts
thre
e
-
phase
syst
em
is
si
m
ulate
d
in
the
Ma
tl
ab/
Si
m
ulink
en
vir
on
m
ent.
Th
e
real
an
d
reacti
ve
powe
r
re
fere
nces
a
re
pro
vi
ded
m
anu
al
ly
for
eac
h
ph
a
se
.
Va
rio
us
pa
ra
m
et
ers
ta
ken
f
or
t
he
si
m
ulati
on
stu
dies
are
gi
ven
in
Table
4.
Th
e
syst
e
m
is
stud
ie
d
f
or
dif
fer
e
nt
values
of
re
al
and
reacti
ve
powe
r
dem
and
s
by th
e grid.
The
gr
i
d
phase
volt
age
is
kept
at
230
V
olts
RM
S
as
sho
w
n
in
Fig
ur
e
5(a
).
T
he
c
hanges
in
the
real
and reacti
ve
po
wer re
fer
e
nces
are
done
i
n diffe
ren
t t
im
es as sh
ow
n
in
Ta
ble
3.
In
it
ia
ll
y
the
HMMC
has
to
gi
ve
3k
W
at
ts
of
real
po
wer
t
o
the
gri
d
un
ti
l
t
=
0.
5
Sec.
T
he
reac
ti
ve
powe
r
is
m
a
intai
ned
at
0
V
a
rs,
s
o
the
gr
i
d
current
has
to
be
in
ph
ase
wi
th
the
gri
d
vo
l
ta
ge
an
d
the
outp
ut
powe
r
fact
or
i
s
m
ai
ntained
at
un
it
y.
T
he
n
at
t
=
0.5
Sec
the
re
al
pow
er
a
nd
reacti
ve
powe
r
ref
e
re
nce
is
Evaluation Warning : The document was created with Spire.PDF for Python.
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ri
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Finit
e
-
Co
ntro
l
-
Set P
redict
iv
e Curre
nt Co
ntr
ol B
as
ed
Re
al
and React
iv
e P
ower
…
(
R
as
hmi R
an
j
an Behe
ra
)
665
increase
d
t
o
6
kW
at
ts
a
nd
3
kV
ars
res
pe
ct
ively
.
Fig
ure
5(b
),
(c),
a
nd
(d)
s
hows
th
e
phase
volt
ag
es
an
d
currents
f
or
phases
(a,
b,
c)
.
Fr
om
the
Figu
r
e
6,
it
can
be
seen
that
the
resp
onse
of
the
c
on
t
ro
ll
er
is
qu
i
te
fast
enou
gh to
t
rac
k
the
r
e
fer
e
nce
pow
e
rs.
Table
3.
C
ha
nges in
real an
d r
eact
i
ve
pow
er
ref
e
ren
ces
p
e
r ph
a
se
Ti
m
e
(
Se
c)
Real Po
wer
(
W
atts
)
Reactiv
e Power
(
V
ars)
0
1000
0
0
.5
2000
1000
0
.55
2000
-
1000
0
.6
1000
1000
(a)
(b)
(c)
(d)
Figure
5. (a
)
T
hr
ee
-
phase
grid
vo
lt
age
s, (b
) Phase
-
a
gr
i
d v
oltage a
nd c
urr
ent,
(c)
Ph
a
se
-
b gr
i
d vo
lt
age
and
current,
(d) P
ha
se
-
c
gr
i
d vo
lt
age a
nd curre
nt
.
The
res
pons
e
of r
eal
and r
eact
ive p
owe
r
cha
nges after c
hang
ing
the r
e
fer
e
nc
e p
ower
dem
a
nd
s ca
n
be
seen i
n
the
Fig
ur
e
7. T
he refe
ren
ce
po
wer
a
r
e cha
ng
e
d
at
ti
m
es t = 0
.
55 S
ec an
d 0.6
Sec
.
Figure
6. Cha
nges i
n
the
r
eal
and reacti
ve
po
wer dem
and
s
by
the grid
.
Durin
g
this
ti
m
e
per
iod
t
he
real
power
dem
and
is
ke
pt
at
6
kW
at
ts
and
the
reacti
ve
powe
r
is
change
d
from
3
kV
a
rs
t
o
−3
kV
ars
at
tim
e
t
=
0.
55
Sec.
With
sli
gh
t
distu
rb
a
nc
es
the
real
power
is
m
ai
ntained
co
ns
ta
nt
e
ven
c
ha
ng
i
ng
t
he
rea
ct
ive
powe
r
de
m
and
at
t
=
0.55
Sec,
wh
ic
h
can
be
cl
early
seen
i
n
the
Fig
ur
e
6.
T
hen
at
la
st
the
powe
r
re
fer
e
nc
es
are
ke
pt
at
3
kW
at
ts
a
nd
3
kV
a
rs
at
tim
e
t
=
0.
6
Sec
f
or
real
and
reacti
ve
powe
rs
res
pec
ti
vely
.
These
resu
lt
sho
ws
t
he
ef
fecti
vene
ss
an
d
the
re
sp
onse
of
t
he
FCS
-
Pr
e
dicti
ve
cu
rrent co
ntr
ol sc
hem
e. Th
e
HM
MC
p
r
ov
i
des
t
he desire
d
real
and reacti
ve p
ower
dem
and
e
d by the
gr
i
d wit
hout m
uch d
el
ay
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
I
nt J
P
ow
Ele
c
&
Dr
i
Syst
, Vol.
9
, N
o.
2
,
J
une
2018 :
660
–
667
666
The
n
the
w
hole
syst
e
m
is
s
i
m
ula
te
d
for
gri
d
vol
ta
ge
s
well
and
sa
g
co
nd
it
ion
s.
I
n
this
case
kee
pi
ng
the
reacti
ve
powe
r
dem
and
at
0V
ars
,
the
real
powe
r
dem
and
is
ke
pt
at
6kW
at
ts.
The
gri
d
volt
age
is
increase
d
by
20%
of
it
s
RMS
value
as
s
hown
in
Fi
gure
7(a).
T
he
co
rr
e
s
pondin
g
gri
d
c
urren
t
is
increa
sed
t
o
m
at
ch
up
th
e
r
eal
power
s
up
ply
by
the
H
MM
C
to
the
gri
d
as
s
how
n
i
n
Fig
ure
7(b
).
The
real
a
nd
r
eact
ive
powe
r
is
bein
g plott
ed
i
n
Fi
gu
re
7(
c
).
(a)
(b)
(c)
Figure
7. (a
) G
rid v
oltage,
(
b) G
ri
d
c
urre
nt,
(
c) Real
and
rea
ct
ive pow
e
r
s
upply
by H
MM
C t
o
the
grid,
dur
i
ng
swell
con
diti
on
It
can
be
obser
ved
from
the
Figure
8(c)
that
the
volt
age
sw
el
l
caused
a
sli
gh
t
inc
rem
ent
in
the
real
powe
r
as
trans
ie
nt,
but
in
ve
r
y
le
ss
tim
e
i
t
c
a
m
e
to
ref
ere
nc
e
value
due
t
o
the
fast
re
spon
s
e
of
the
co
ntr
oller.
The
n
t
he
syst
em
is
si
m
ula
te
d
for
the
sa
g
c
onditi
on
i
n
the
gr
id
volt
age
as
show
n
in
F
igure
8(a)
.
Th
e
gr
i
d
vo
lt
age
is
dec
r
eased
by
20%
of
it
s
RM
S
value,
an
d
the
c
orrespo
nd
i
ng
gr
i
d
cu
rr
e
nt
an
d
the
real
an
d
rea
ct
ive
powe
r
s
upply c
an be see
n
i
n
F
igure
8(b) an
d (c) re
s
pecti
vel
y.
(a)
(b)
(c)
Figure
8. (a
) G
rid v
oltage,
(
b) G
ri
d
c
urre
nt,
(
c) Real
and
rea
ct
ive pow
e
r
s
upply
by H
MM
C t
o
the
grid,
dur
i
ng
sag
c
onditi
on.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow
Ele
c
&
D
ri
Syst
IS
S
N:
20
88
-
8
694
Finit
e
-
Co
ntro
l
-
Set P
redict
iv
e Curre
nt Co
ntr
ol B
as
ed
Re
al
and React
iv
e P
ower
…
(
R
as
hmi R
an
j
an Behe
ra
)
667
5.
C
O
N
CLUS
I
ON
This
pap
e
r
pr
e
sents
the
gri
d
app
li
cat
io
n
of
a
ne
w
to
polo
gy
nam
ed
as
H
ybrid
Mo
du
la
r
Mul
ti
le
vel
Converte
r
(HM
MC
).
This
topolo
gy
has
r
edu
ce
d
num
ber
of
s
witc
h
co
un
ts
tha
n
the
conve
ntion
al
MM
C.
Ther
e
f
or
e
it
is
m
or
e
eff
ic
ie
nt
and
has
le
ss
co
m
plexiti
es
in
ci
rcu
it
desig
n.
A
6
kW
att
gr
i
d
co
nnect
ed
sy
stem
is
si
m
ulate
d
for
var
i
ou
s
real
a
nd
reacti
ve
po
wer
dem
and
s.
The
Finit
e
-
C
on
t
ro
l
-
Set
(
FCS)
P
re
dicti
ve
Con
tr
ol
schem
e,
wh
ic
h
is
gr
owin
g
it
’s
popula
rity
in
the
power
el
e
ct
ronics
ap
plica
ti
on
s
is
bein
g
e
m
plo
ye
d
here.
This
con
t
ro
l sc
hem
e
is q
uite ea
sie
r i
n
i
m
ple
m
entation
tha
n
the c
onve
ntio
nal PI
c
on
t
ro
ll
ers
beca
us
e of the e
voluti
on
of
fast
m
ic
ro
-
con
t
ro
ll
ers
.
F
r
om
the
si
m
ula
ti
on
re
su
lt
s
it
can
be
see
n
th
at
the
co
ntr
ol
act
ion
is
ver
y
m
uch
eff
ect
ive
and is
h
a
ving
ver
y
fa
st res
pons
e ti
m
e to trac
k
t
he r
efere
nce
real a
nd r
eact
ive
po
wer
s
.
Table
4.
Var
i
ous
par
am
et
e
rs
ta
ken f
or sim
ul
at
ion
st
ud
y
Para
m
eters
Sy
m
b
o
ls
Valu
es
Fu
n
d
a
m
en
tal
Grid
Frequ
en
cy
Grid Ph
ase Vol
tag
e
DC Inp
u
t Filter
Ind
u
ctan
ce Filter
Res
istan
ce
Sa
m
p
lin
g
T
i
m
e
Si
m
u
latio
n
T
i
m
e
Nu
m
b
e
r
o
f
Sub
-
M
o
d
u
les Per
-
Ph
ase
Su
b
-
Mod
u
le Cap
acitance
f
vg
n
Vdc
Lfn
Rf
n
Ts
t
N
CS
M
5
0
Hz
2
3
0
V
(RMS)
4
0
0
V
1
0
m
H
0
.01
Ω
5
µ
s
1
s
3
4700
µ
F
REFERE
NCE
S
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el
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