Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 2,
May 2016, pp
. 285 ~ 296
DOI: 10.115
9
1
/ijeecs.v2.i2.pp28
5-2
9
6
285
Re
cei
v
ed
De
cem
ber 2
3
, 2015; Re
vi
sed
April 11, 201
6; Acce
pted
April 28, 201
6
Model Predictive Current Control of Grid Connected PV
Systems
RS Rav
i
Sankar*, SV Jay
a
Kum
a
r, K
K
Deepika
Department of EEE, Vignan’s
Inst
itute of Information T
e
chnology
, Vis
a
khapatnam, India, 530046
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: sat
y
a
_
ravi
20
01@
ya
ho
o.co
m
A
b
st
r
a
ct
This paper
deals with the design
and simulation of an
efficient s
o
lar
photov
oltaic
system
with
a
m
a
x
i
m
u
m
power point tracking system
(MP
PT). Maxim
u
m power point (
M
PP)
is obtained by
using
Pertur
b
a
n
d
Ob
se
rve (P&O) a
l
go
ri
thm
.
Th
e ou
tp
u
t
fro
m
so
l
a
r pa
ne
l
i
s
fe
d to
the D
C
-
DC
(Boo
st) co
n
v
e
r
te
r wh
i
c
h
steps up the o
u
tput voltag
e. It is
then fed to a 3-phas
e inv
e
rter. T
he in
ve
rter used is a 3-ph
ase tw
o-le
vel
inverter
im
plem
ented wi
th a
Model Predictive Control strategy. Mo
del
of the
system
is
c
onsidered in or
der
to predict th
e control var
i
a
b
l
e
s. Optimu
m s
w
itching st
ate
is selecte
d
by
mi
ni
mi
z
i
ng th
e
cost function
for
each
sa
mp
li
ng
per
iod. T
h
is
is
ach
i
eve
d
thr
o
ugh
mod
e
l
lin
g
and
MAT
L
AB
simulati
on
of v
a
rio
u
s stag
es t
hat
constitute the overall system
.
Ke
y
w
ords
: Model pr
edictiv
e control, th
ree
phase voltage so
urce inv
e
rter, PV system
, Matlab/Sim
u
link
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Gro
w
ing inte
rest in integra
t
ion of rene
w
able ene
rgy
system
s ha
s dra
w
n researche
r
s to
explore
different VSI cont
rol te
chniq
u
e
s
. P
hotovolta
ic (PV) and
wind
ha
s se
en trem
end
o
u
s
gro
w
th world
w
ide. PV pa
nels
can
be
use
d
eithe
r
o
ffline or onlin
e. In offline appli
c
ation
s
, PV
panel
s suppl
y local loa
d
s
whi
c
h can b
e
resi
dential o
r
co
mmercial.
In online ap
plicatio
ns, th
ese
module
s
not
only su
pply l
o
cal l
oad
s, b
u
t also
are
conne
cted to
the utility grid.
In this
ca
se,
the
system
woul
d be called
“gri
d-con
n
e
c
ted PV sy
ste
m
. Recently, grid-co
nne
ct
ed PV syste
m
installatio
n
is incre
a
si
ng tremend
ou
sly in m
any cou
n
t
ries. Since the output of PV panels a
r
e
dire
ct cu
rrent
(in the ca
se
of
grid-con
n
e
cted PV sy
stem
s), the
i
n
terface is typically a DC-AC
conve
r
ter
(in
v
erter) which
inverts th
e
DC
output
cu
rre
nt that co
mes from the
PV array
s
in
to a
synchro
n
ized
sin
u
soidal
waveform.In g
eneral,
PV T
h
ree
ph
ase i
n
verter (TPI)
come
s with
DC-
DC
co
nverte
r (no
r
mally, a
versio
n of Bo
ost), maximu
m power
poin
t
tracking
(M
PPT) co
ntrol
and
voltage so
urce inverter (VS
I
) packed a
s
a singl
e unit.
A Boost
conv
erter is
a p
o
wer el
ect
r
oni
c
conv
e
r
ter that
gives
output
voltage g
r
eat
er tha
n
input voltage
of the PV panel. This volta
ge re
gulati
on
is attained by
PWM. MPPT is achi
eved
by
adju
s
ting the
duty cycle by usin
g Perturb
and Ob
serve
method.
2. Rese
arch
Metho
d
Single ph
ase
inverters
(u
sually few
kW) with
a
cont
rol in syn
c
h
r
o
nou
s refere
n
c
e frame
have bee
n di
scusse
d in [10], and those
with m
odel p
r
edictive control
(MPC) hav
e been repo
rt
ed
by [11]. Amo
ng all
the
co
ntrol te
chni
q
ues mod
e
l p
r
edictive
co
ntrol (MP
C
) is
one
of the m
o
st
popul
ar
cont
rol app
roa
c
h
e
s
be
ca
use it’s si
mple to i
m
pleme
n
t an
d ha
s extre
m
ely fast dyna
mic
respon
se, it
has ro
bu
st
stability cha
r
a
c
teri
stic
s.
Co
nventional
switchi
ng-ta
ble
-
ba
sed
MPC is
simple, robu
st, and exhibits excell
ent transi
ent re
spo
n
se. Th
us, it is wid
e
ly use
d
.
MPC
con
s
id
e
r
s a
mod
e
l o
f
the
system
in
ord
e
r to
predi
ct
beha
vior of th
e
system in
future. A co
st
function i
s
e
v
aluated to
choo
se t
he
op
timal switchin
g state
s
. Thi
s
pape
r p
r
e
s
e
n
ts
a simpl
e
and
easy-to
-impl
e
ment ap
pro
a
ch
of model
ing MPC b
a
sed on TPI fo
r gri
d
tied PV
sy
st
em
s.
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ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 2, May 2016 : 285 –
296
286
2.1. Mathem
atical Modeli
ng of PV pan
e
l
A PV system con
s
ist
s
of a numb
e
r of
PV module
s
con
n
e
c
ted in
seri
es o
r
pa
rallel to
cre
a
te a DC PV
array.
Fig
u
re
1 ill
ustrates
a
simpl
e
equivalent
ci
rcuit di
ag
ram
of a PV
cell.
PV
cell is a sim
p
le P-N jun
c
tio
n
diode which conv
e
r
ts so
lar ene
rgy into electri
c
al e
n
ergy. I
pv
is the
curre
n
t gene
rated by the light. D1 an
d D2 a
r
e two a
n
ti-pa
r
allel di
ode
s, R
p
is t
h
e shu
n
t
re
sist
anc
e
and R
s
i
s
the
serie
s
resi
st
ance. V and I are the
voltage an
d cu
rrent gene
rate
d by the PV
cell
respe
c
tively.
The impli
c
it V-I relation
shi
p
is given by:
p
s
D
D
pv
R
IR
V
I
I
I
I
2
1
(1)
1
)
e
xp(
1
1
1
KT
A
IR
V
q
I
I
S
o
D
(2)
Figure 1. Two
diode mod
e
l of PV cell
1
)
e
xp(
2
2
2
KT
A
IR
V
q
I
I
S
o
D
(3)
1000
refk
k
i
scr
pv
T
T
K
I
I
(4)
Her
e
λ
is the
sola
r irradiati
on, I
scr
is the
PV device sh
ort- ci
rcuit current, T
k
and T
refk
are,
respe
c
tively, the a
c
tual
an
d refere
nce t
e
mpe
r
ature.
K
i
is the
short
-
ci
rcuit curre
n
t/ temperatu
r
e
coeffici
ent (A/
K), A
1
and A
2
are
the dio
de ide
a
lity factors. q i
s
the
cha
r
ge
of th
e ele
c
tron
an
d I
o1
and I
o2
are the reverse
sat
u
ration
cu
rre
nts of D
1
and
D
2
re
sp
ectiv
e
l
y
.
Equation (1) i
s
modi
fi
ed fo
r PV module as:
p
s
D
p
D
p
pv
p
R
IR
V
I
N
I
N
I
N
I
2
1
(5)
p
s
s
s
o
p
s
s
o
p
pv
p
R
IR
V
kT
A
N
IR
V
q
I
N
kT
A
N
IR
V
q
I
N
I
N
I
1
exp
1
exp
2
2
1
1
(6)
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IJEECS
ISSN:
2502-4
752
Model Pre
d
ict
i
ve Current Control of Gri
d
Con
n
e
c
ted PV System
s
(RS Rav
i
Sank
ar)
287
Her
e
N
s
an
d N
p
are the
No
. of cells i
n
serie
s
an
d pa
rallel re
sp
ectiv
e
ly. The mod
u
les
are
con
fi
g
u
re
d in a No.of se
rie
s
and p
a
rall
el
stru
cture
s
wi
th any numbe
r of PV modules to pro
d
u
c
e
a
PV array.
No
w the PV array V-I rel
a
tionship is give
n by the following e
quatio
ns.
pp
ss
p
pp
ss
s
ss
pp
ss
s
o
pp
ss
pp
ss
s
o
pp
pv
pp
N
N
R
N
N
IR
V
kT
A
N
N
N
IR
V
q
I
N
kT
A
N
N
N
IR
V
q
I
N
I
N
I
1
exp
1
exp
2
2
1
1
(7)
Her
e
N
ss
an
d N
pp
are t
he num
ber
of module
s
con
n
e
c
ted in
seri
es a
n
d
parall
e
l,
respe
c
tively. In this pa
per,
stand
ard
KC2
00GT
dat
a
s
h
eet pa
ram
e
te
rs are u
s
e
d
t
o
imple
m
ent t
h
e
PV system in a SIMULINK
environ
ment.
Table 1. KC2
00GT p
a
ram
e
ter sp
ecifi
c
a
t
ions
Max
i
mum Voltag
e (V
m
)
26.3V
Curre
nt at Ma
xi
mum Po
w
e
r
(I
m
)
7.61A
Open Ci
rcuit Voltage (V
oc
)
32.9V
Short Circuit Cur
r
ent (I
sc
)
8.21A
Total No.of C
e
lls in Series (Ns
54
T
o
tal No.of Cells in Par
a
llel (
N
p
) 1
Temper
ature Co
ef
fi
cient of V
oc
(K
v
) -123
mV/
o
C
Temper
ature Co
ef
fi
cient of I
sc
(K
i
) 3.18mA/
o
C
s
a
turati
on c
u
rren
t
I
o1
= I
o2
1.045×10
−
9
A
R
p
415.405
Ω
.
R
s
0.221
By using th
e above K
C
20
0GT p
a
rameters a
PV system
is desi
gne
d usin
g
MATLAB/SIMULINK enviro
n
ment.
The
maximum po
wer point tracking
syste
m
i
s
u
s
ed to
extract
maximum po
wer f
r
om th
e PV panel.
The p
r
obl
e
m
con
s
id
ere
d
by MPPT techni
que
s i
s
to
automatically find the
voltage
or curre
n
t at wh
ich a
PV
a
rray sho
u
ld ope
ra
te
to
obtai
n the
maximum p
o
w
er outp
u
t u
nder a
given
temperature
and i
r
radian
ce. This en
su
res th
at the p
anel
delivers max
i
mum po
we
r to the
syst
em. Among
the differe
nt method
s u
s
ed to track
the
maximum p
o
w
er poi
nt, Perturb an
d O
b
se
rve meth
od
is th
e
mos
t
w
i
de
ly us
ed
me
th
od
in
PV
MPPTs and i
s
highly comp
etitive against
other MPPT method
s.
2.2. Perturb
and Obs
e
rv
e
Method
In Perturb an
d observe (P
&O) method,
the M
PPT algorithm i
s
ba
sed o
n
the calcul
ation
of the power of the PV panel
and
c
h
ange in
power, by
s
a
mpling both the
PV c
u
rrent and
voltage. The
tra
c
ker
ope
rates
by pe
ri
odically
in
cre
m
enting
or d
e
creme
n
ting
the solar a
r
ray
voltage. This
algorith
m
is summari
ze
d in
table 2.
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ISSN: 25
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752
IJEECS
Vol.
2, No. 2, May 2016 : 285 –
296
288
Table 2. Sum
m
ary of P&O algorith
m
Chan
ge in
v
o
l
t
a
g
e
Chan
ge in
po
w
e
r
Next p
e
rtu
b
ati
o
n In d
u
t
y
c
y
cle
Positive
Positive
Incr
eased
Positive
Negative
Decreased
Negative Positive
Decreased
Negative Negative
Increased
At MPP, rate
of chang
e o
f
powe
r
is zero
. In next sampli
ng in
stant, powe
r
e
x
tracted
decrea
s
e
s
a
n
d
hen
ce the
pertu
rbatio
n reverses
as
shown in Figu
re 2. In this m
e
thod the
sta
b
le
con
d
ition is a
rrived a
r
ou
nd
the peak po
wer p
o
int. In orde
r to main
tain the powe
r
variation
sm
all
the pertu
rbati
on si
ze is re
main very sm
all.
Figure 2. PV
panel
cha
r
a
c
teristi
c
s
The algo
rith
m involves p
e
rturbation
s
on t
he duty cycle of the DC-DC p
o
wer
conve
r
ter
(D
)
, Voltage of the DC-link that is betwe
en the PV array and the po
wer
conve
r
ter
(V)
.
If
P(k
)
>
P(k
-
1),
then the direction of pe
rturbatio
n on
d
u
ty cycle is m
a
intaine
d
. And if
∆
V
<0
, the voltag
e is in
cre
a
se
d by increa
si
ng the duty cycle as
D(
k
)
=
D(
k-1
)
+C
wh
ere C
is step size
else if
∆
V >
0
, the voltage is de
cre
a
sed
by incre
a
si
ng
the duty cycle as
D(k
)
=
D(k
-
1)
-
C
.
If
P(k
)
<
P(k-1),
then the
dire
ction of
pertu
rbation
is reve
rsed.
This i
s
expl
ained in
Figure 3.
2.3. DC
-D
C Boos
t Co
nv
erter
A Boost
conv
erter is
a p
o
wer el
ect
r
oni
c
conv
e
r
ter that
gives
output
voltage g
r
eat
er tha
n
input voltage.
Whe
n
b
o
th the inp
u
t an
d
the output
qu
antities a
r
e
DC voltage
s, it
is
kno
w
n
as
a
DC-DC b
o
o
s
t conve
r
ter
or
step-up
conv
erter. Fig
u
re
4 illustrates
a
type of boost
conve
r
ter
wh
ich
con
s
i
s
ts of o
ne controll
ed
swit
ch, S (IG
B
T), one
un
controlle
d swit
ch
(diod
e
),
D and two en
e
r
gy
stora
ge devi
c
es like indu
ct
or and
cap
a
ci
tor.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Model Pre
d
ict
i
ve Current Control of Gri
d
Con
n
e
c
ted PV System
s
(RS Rav
i
Sank
ar)
289
Figure 3. Flow Ch
art for P
&
O algorithm
Figure 4. Boost conve
r
ter
circuit
Gate
sign
al f
r
om MPPT
controlle
r i
s
gi
ven to the
converte
r a
n
d
value
s
of L,
C
are
desi
gne
d by using de
sig
n
equation
s
.
Values of
L, C are vari
ed to get the requi
red o
u
tput
voltage. The
input voltage
to the d
c
-dc
boo
st convert
e
r i
s
V
s
= 1
5
2
V and
the
o
u
tput voltage
o
f
dc-dc b
o
o
s
t converte
r is V
dc
= 300V. The
capa
citan
c
e
C=15mF a
nd
indu
ctan
ce L
=
0.1m
H.
2.4. Three-P
h
ase Grid
-Connec
t
ed In
v
e
rters
Figure 5 sho
w
s a three p
hase brid
ge i
n
verter
whi
c
h
con
s
ist
s
of six controlle
d swit
che
s
(IGBT). To m
a
intain
con
s
t
ant DC inp
u
t cap
a
cito
r filter is
con
n
e
c
te
d between th
e PV and inv
e
rter
circuit. Termi
nals A, B, C are co
nne
cted
to three pha
se load or to th
e grid.
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ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 2, May 2016 : 285 –
296
290
Figure 5. Three-p
h
a
s
e g
r
id
-co
nne
cted
schem
e
The input d
c
in Figure 5.1 is obtain
ed from a sol
a
r a
r
ray. The swit
chin
g state
s
of the conve
r
ter
are dete
r
min
ed as follo
ws:
on
is
and
off
is
if
off
is
and
on
is
if
,
0
,
1
4
1
4
1
S
S
S
S
S
a
(7)
on
is
and
off
is
if
off
is
and
on
is
if
,
0
,
1
5
2
5
2
S
S
S
S
S
b
(8)
on
is
and
off
is
if
off
is
and
on
is
if
,
0
,
1
6
3
6
3
S
S
S
S
S
c
(9)
Whe
r
e gatin
g
signal
s S
a
, S
b
, and S
c
And can be exp
r
e
s
sed in ph
asor form by
c
b
a
S
a
aS
S
S
2
3
2
(10
)
Whe
r
e,
3
2
j
e
a
,
The output
-voltage spa
c
e
vectors gen
erat
ed by the inverter a
r
e def
ined by
cN
bN
aN
i
V
a
aV
V
V
2
3
2
(11
)
whe
r
e
V
aN
, V
bN
,
a
n
d
V
cN
are
th
e p
h
a
s
e vo
ltages of th
e
inverte
r
, wit
h
re
sp
ect to
the
negative term
inal of the dc link
N.
Figure 6. Possible voltag
e vect
ors gen
erated by the inverter
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IJEECS
ISSN:
2502-4
752
Model Pre
d
ict
i
ve Current Control of Gri
d
Con
n
e
c
ted PV System
s
(RS Rav
i
Sank
ar)
291
Then, the loa
d
voltage vector
V
i
can be
related to the
swit
chin
g stat
e vector
S
by
S
V
V
dc
i
(12
)
Whe
r
e V
dc
is
the dc-lin
k vo
ltage. Co
nsid
ering
all the
p
o
ssible
com
b
i
nation
s
of the
gating si
gnal
s
S
a
, S
b
, and S
c
, eight switching
state
s
a
nd, con
s
eq
ue
nt
ly, eight vol
t
age ve
ctors
are
obtain
ed,
as
sho
w
n in Ta
b
l
e 4, using (1
2). He
re, vari
able
s
S
a
, S
b
, and
S
c
represent the switch
ing state
s
of the
a, b, and c le
gs of the inve
rter. Note that
V
0
= V
7
.
Table 4. Swit
chin
g se
que
n
c
e of thre
e ph
ase inve
rter
S
w
itching sta
t
e
s
Ou
tpu
t
v
o
lta
g
e
S
a
S
b
S
c
V
i
0 0
0
0
1 0
0
2
3
1 1
0
3
√
3
3
0 1
0
3
√
3
3
0 1
1
2
3
0 0
1
3
√
3
3
1 0
1
3
√
3
3
1 1
1
0
2.5. Model Predictiv
e
Control
The propo
se
d strate
gy predict
s
the be
havior of the
variable
s
for
each switchi
n
g state.
These state
s
are discrete
and a discrete-time mo
d
e
l of the system is use
d
to predict the
behavio
r of VSI system.
An objective
function
i
s
defined to min
i
mize the error between t
h
e
output cu
rre
nts
a
nd refe
rence cu
rre
nts, by
cho
o
si
ng the
optim
um
swit
ching
state
for
ea
ch
sampli
ng pe
ri
od.
MPC is impl
e
m
ented in
αβ
refere
nce fra
m
e with 6 no
nze
r
o voltage
vectors and
2 ze
ro
voltage vecto
r
s. In addition
, load dynami
cs a
r
e mo
del
ed as:
e
(13
)
Whe
r
e R L and
e
are loa
d
resi
stan
ce, in
ducta
nce and
back emf re
spectively,
is the load cu
rre
n
t
and
is the VSI generate
d
voltage vecto
r
.
Usi
ng Eule
r-F
orward equ
ation, the
load current is ap
proximated by:
≅
1
(14
)
Usi
ng (1
3) a
n
d
(14
)
, we ca
n approximat
e
1
1
(15
)
Whe
r
e
k=t (p
rese
nt) and
k+1=t+1(futu
re/
p
redi
cted
) val
ue.
In ea
ch
swit
ching
state, lo
ad
current i
s
estimate
d u
s
ing
Equatio
n (1
5). T
he
obje
c
tive
function i
s
ev
aluated to
cal
c
ulate th
e opt
imal val
ue of
the load
cu
rrent, for every
swit
chin
g sta
t
e.
The optimal l
oad current i
s
applied
duri
n
g the nex
t sa
mpling p
e
rio
d
.
VSI MPC control sy
stem i
s
illustrated in Figure. 7.
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02-4
752
IJEECS
Vol.
2, No. 2, May 2016 : 285 –
296
292
Figure 7. VSI
MPC co
ntrol
block dia
g
ra
m
All the variabl
es are initialized. Usi
ng fro
m
(13), the b
a
ck-e
mf can
be cal
c
ul
ated
as :
1
1
1
(16
)
The
ba
ck-em
f
e(k),
ne
ded
in (15),
is e
s
tima
ted usi
ng an extrapol
ation of its past values.
Figure 8 o
u
tlines
step
by step implem
en
tation pr
o
c
e
s
s of Mo
del Predictive
Cont
rol of VSI. Th
e
obje
c
tive function here i
s
gi
ven by the equation:
∗
|
∗
|
(17
)
Figure 8. Flow ch
art for M
P
C cont
rol of VSI
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IJEECS
ISSN:
2502-4
752
Model Pre
d
ict
i
ve Current Control of Gri
d
Con
n
e
c
ted PV System
s
(RS Rav
i
Sank
ar)
293
Obje
ctive fun
c
tion,
g
given
by (1
7) i
s
u
s
ed to mi
nimize the e
r
ror
be
tween t
he e
s
t
i
mated
output and referen
c
e
current and the optimal
g
(k+1) is sel
e
cted for swit
ching state is applied
across VSI in the next sampling p
e
ri
od. Note that
in each
sam
p
ling pe
riod
8 predi
ction
s
are
made a
nd 8
obje
c
tive function
s are evaluated b
e
fore
sele
cting th
e cont
rol a
c
tion, S(k) for t
h
e
next samplin
g perio
d.
3. Results a
nd Analy
s
is
Simulation
s
of a thre
e p
hase voltage
inverter wit
h
RL
loa
d
were
ca
rri
ed o
u
t usin
g
MATLAB/SIMULINK an
d the model is
sh
own in Fig
u
re
9.
Figure 9. Simulink mo
del o
f
MPCC VSI
Table 5. Simulink Pa
ramet
e
rs
Parameters
Val
ues
Suppl
y
voltage
300V
Resistance 0.36ohm
Inductance 4.7mh
Sampling time
50e-6
Reference C
u
rr
e
n
t
10A
Figure 10. Switchi
ng state
s
of
grid
con
n
e
cted inve
rter
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ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 2, May 2016 : 285 –
296
294
Figure 11. Th
ree ph
ase voltage
of grid conne
cted inv
e
rter
Figure 12. Th
e grid conn
ected invert
er
current wavefo
rm for 10
amp
s
Figure 13. Cu
rre
nt
for 10amps
Figure 14. Cu
rre
nt
for 10 a
m
ps
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