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
. 64
8
~
65
6
I
S
SN
: 208
8-8
6
9
4
6
48
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
Modelin
g and Simulation
of
Cl
osed Loop Cont
roll
ed Paral
l
el
Cascaded Buck Boost Convert
er Inverter Based Solar System
T. Sun
dar
*
,
S
.
S
a
nk
ar
**
* Dept. of
EIE,
SCSVMV
University
, Kan
c
hipur
am, Tamilnadu,
India
** Dept. of
EEE, Pani
ma
la
r Instit
ut
e of
T
e
c
hnol
ogy
,
Che
n
na
i,
T
a
mi
l
n
a
du,
Indi
a
Email: sundar_1
51@
y
a
hoo
.co
.
in
, ssankarphd@
yahoo.com
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 27, 2015
Rev
i
sed
Ju
l 25
,
20
15
Accepted Aug 15, 2015
This Work deals
with design, modeling
and s
i
m
u
lation
of par
a
ll
el c
a
s
cad
ed
buck boost converter inv
e
rter based clos
ed loop controlled solar sy
stem. Two
buck boost con
v
erters ar
e cascaded in
parallel to reduce the r
i
pple in DC
output.
The DC
from the solar cell
is stepped up
using boost con
v
erter
.
Th
e
output of th
e bo
ost converter is
converted
to 50
Hz AC using single phase fu
ll
bridge inv
e
rter.
The simulation r
e
sults of open
lo
op and clos
ed lo
op s
y
stems
are com
p
ared
. This
paper has
pres
ented a s
i
m
u
link m
odel for clos
ed loo
p
controlled solar
s
y
stem. Par
a
llel cas
caded bu
ck
boost converter
is proposed
for solar
s
y
stem.
Keyword:
B
i
di
rect
i
onal
i
nve
rt
er
Buck/Boost C
o
nve
rter
DC-d
istribu
tion
ap
p
lication
s
Max
i
m
u
m
pow
er poi
nt
t
r
ac
ker
s
Sim
Powe
r
System
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
:
T. S
u
nda
r,
Research Sc
holar
Depa
rt
em
ent
of El
ect
r
oni
c a
n
d
Inst
rum
e
nt
at
ion
E
ngi
neeri
n
g
,
SCSVM
V
Uni
v
ersity,
Enat
h
u
r
,
Kanc
hi
p
u
ram
,
Tam
i
l
n
ad
u, I
ndi
a.
Em
ail: sunda
r_151@yahoo.co.in
1.
INTRODUCTION
A DC
-
D
C
co
n
v
ert
e
r i
s
a vi
t
a
l
part
o
f
al
t
e
rna
t
i
v
e and r
e
ne
w
a
bl
e ener
gy
co
nve
rsi
o
n,
po
rt
a
b
l
e
de
vi
ces,
an
d m
a
n
y
in
dustrial p
r
o
cesses. It is essen
tially u
s
ed
t
o
ac
h
i
eve a
reg
u
l
a
t
e
d
DC
vol
t
a
ge
f
r
om
an
un
re
gu
l
a
t
e
d
DC
s
o
u
r
ce
whi
c
h m
a
y
be t
h
e
out
put
of
a
rect
i
f
i
e
r o
r
a
bat
t
e
r
y
or a
sol
a
r cel
l
et
c. Ne
vert
he
l
e
ss, t
h
e
vari
at
i
o
n
i
n
the source is si
gni
ficant, m
a
inly because
of
the variation
in th
e line voltage, running
out
of a
battery etc
., but
within a speci
fied lim
i
t. Taking all these into accoun
t, the
objective is to re
gul
ate the
voltage at a desired
v
a
lu
e wh
ile d
e
liv
ering
to
a wid
e
ly v
a
ryin
g
load
. A DC
-D
C
swi
t
c
hi
n
g
re
gu
l
a
t
o
r i
s
kno
w
n
t
o
be su
peri
o
r
ove
r
a
linear re
gulator m
a
inly because of its better effici
ency and higher
c
u
rre
nt-d
rivi
ng c
a
pability. There are
vari
ous t
o
p
o
l
o
gi
es i
n
t
h
e co
n
t
ext
of DC
-DC
con
v
ert
e
rs t
h
e
buc
k-
b
oost
c
o
nve
rt
er are
wi
del
y
used
. The
basi
c
ci
rcui
t
o
f
buc
k
-
b
o
o
st
co
n
v
ert
e
r i
s
s
h
o
w
n i
n
Fi
gu
re
1. T
h
e
out
put
v
o
l
t
a
ge
of a
DC
-DC
c
o
n
v
e
r
t
e
r i
s
c
o
n
t
rol
l
e
d
b
y
op
erating
it in
th
e clo
s
ed
l
o
op
, and
alterin
g
its MO
SFE
T (s
wi
t
c
h)
gat
e
si
gnal
acc
or
di
n
g
l
y
. It
i
s
ba
si
cal
l
y
g
o
v
e
rn
ed
b
y
a switch
i
ng
log
i
c, th
u
s
co
n
s
titutin
g
a set o
f
sub
s
ystem
s
d
e
p
e
n
d
i
n
g
u
pon
th
e statu
s
(on
-
o
f
f) o
f
the
switch. In the
well known pulse widt
h m
odulation (P
W
M
) technique, the
control is accom
p
lished by varying
t
h
e d
u
t
y
rat
i
o
of a
n
e
x
t
e
r
n
a
l
fi
xed
fre
q
u
e
n
cy
cl
oc
k t
h
ro
ug
h
one
o
r
m
o
re
fee
dbac
k
l
o
o
p
s,
w
h
e
n
eve
r
any
param
e
t
e
r vari
es. P
I
c
ont
r
o
l
l
ers a
r
e t
h
e
m
o
st
wi
del
y
-
u
se
d typ
e
of con
t
roller for i
n
du
strial ap
p
licatio
ns. Th
ey
are structurally sim
p
le and
exhi
bit
ro
bu
st
p
e
rf
or
m
a
n
ce ov
er a
w
i
d
e
r
a
n
g
e
of
op
er
ati
n
g cond
itio
n
s
. In
the
abse
nce of the
com
p
lete
knowledge of
the process
,
these types of controlle
rs are the
most efficient choice
s
.
Power- Mana
gem
e
nt strategies for a gri
d
connected
P
V
-FC
hy
bri
d
sy
st
em
[1]
.
Opt
i
m
i
zed wi
nd
energy
har
v
est
i
n
g sy
st
em
usi
ng resi
st
ance em
ul
at
or an
d act
i
v
e rect
i
f
i
e
r fo
r w
i
rel
e
ss senso
r
no
des [
2
]
.
A hy
b
r
i
d
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
:
64
8 – 656
64
9
cascade c
o
nve
r
ter topol
ogy
with series
-connecte
d
symm
etrical and asy
mme
trical diode-clam
p
ed H-Bridge
cells [3
].
An efficien
t
h
i
gh
-step
-
up
in
terleav
ed
DC
-DC co
nv
erter
with
a
c
o
mmon active cla
m
p [4].
Transform
e
rless gri
d
connect
ed pow
er c
o
n
v
erter
fo
r P
V
sy
stem
[5,
6]. Adaptive
fuzzy controlled wind
ener
gy
sy
st
em
[8]
.
Di
st
ri
but
i
on v
o
l
t
a
ge c
ont
rol
f
o
r
DC
m
i
crogri
d
us
i
ng st
o
r
e
d
en
ergy
[
9
]
.
Pre
d
i
c
t
i
v
e
cont
rol
l
e
d
bi
-
d
i
r
ect
i
onal
i
n
ve
rt
er f
o
r m
i
crog
ri
d a
ppl
i
cat
i
o
n
s
[
10]
. C
h
arac
t
e
ri
zat
i
on a
n
d
t
e
st
i
ng
of a
t
o
ol
f
o
r
ph
ot
o
v
o
l
t
a
i
c
p
a
nel
m
odel
i
n
g
[1
1]
.
An
al
y
s
i
s
an
d si
m
u
lati
o
n
of ch
aracteristics and
m
a
x
i
m
u
m
p
o
w
er po
in
t
t
r
acki
n
g f
o
r p
hot
ov
ol
t
a
i
c
sy
st
em
s [12]
. C
o
m
p
ari
s
on
o
f
ph
ot
o
v
o
l
t
a
i
c
array
m
a
xim
u
m
po
wer
p
o
i
n
t
t
r
acki
n
g
t
echni
q
u
es
[1
3
]
. New
Ap
p
r
oa
ch t
o
P
h
ot
o
vol
t
a
i
c
Array
s
M
a
xi
m
u
m
Power
Poi
n
t
T
r
acki
n
g
[1
4]
. M
o
del
i
n
g an
d
Co
n
t
ro
l fo
r a Bid
i
rectio
n
a
l
Bu
ck–
Bo
ost Cascad
e Inv
e
rter [1
5
]
. A
Mu
ltilev
e
l In
verter fo
r Ph
o
t
o
v
o
ltaic
Sy
st
em
s wi
t
h
Fuzzy
L
ogi
c C
ont
rol
[
1
6]
. A
Di
rect
DC
-
lin
k Bo
o
s
t
Vo
ltag
e
PID-lik
e Fu
zzyCo
n
t
ro
l Strat
e
g
y
in
Z-S
o
u
r
ce
In
ver
t
er [
17]
.
A M
a
xi
m
u
m
Power
Poi
n
t
T
r
ac
ki
n
g
of
P
V
Sy
st
em
by
Scal
i
n
g F
u
zzy
C
ont
r
o
l
[
1
8]
.
A
cl
osed
-Lo
o
p
M
a
xi
m
u
m
po
wer
poi
nt
Trac
ker
fo
r Su
b
wa
t
t
Phot
o
v
o
l
t
a
i
c
Panel
s
[
1
9]
. Gr
i
d
- C
o
nnect
e
d
B
oost
-
Half-B
ridg
e Ph
o
t
o
v
o
ltaic Mi
cro
inv
e
rter Syste
m
Usin
g
Rep
e
titiv
e Cu
rren
t Con
t
ro
l an
d
Max
i
m
u
m
p
o
wer
poi
nt tracking
[20]. Stability
of a boo
st converter
fed from
a photovolta
ic
source
[21]. Unifie
d Approach to
Reliability Assessm
ent of Multiphase
DC-DC Conve
rters i
n
Photovoltaic
Energy Conversio
n System
s
[22].
Safet
y
enha
nce
d
hi
g
h
st
ep
u
p
DC
-
D
C
C
o
n
v
e
r
t
e
r f
o
r AC
P
h
ot
o
vol
t
a
i
c
M
o
dul
e A
p
pl
i
cat
i
on
[2
3]
. O
p
t
i
m
i
zat
i
on
and
desi
g
n
of
a cascade
d
DC
/
D
C
C
o
n
v
ert
e
r
Dev
o
t
e
d t
o
g
r
i
d
co
nnect
e
d
p
hot
ov
ol
t
a
i
c
Sy
st
em
[24]
. C
o
n
t
rol
l
e
r
design
for i
n
tegrate
d
P
V
-c
onverter m
odules
unde
r
partial s
h
adi
n
g conditions
[25].
Th
e abo
v
e lite
ratu
re
d
o
e
s
n
o
t
co
v
e
r m
o
d
e
llin
g
an
d
sim
u
lat
i
o
n
of clo
s
ed
lo
op
con
t
ro
lled b
u
c
k
b
o
o
s
t
con
v
e
r
t
e
r i
n
ve
rt
er ba
sed sy
st
em
. C
l
osed l
o
op
pa
ral
l
e
l
cas
caded
buck boost converter i
nve
rter system is not
repo
rted
i
n
th
e literatu
re. Th
is wo
rk
aim
s
to
d
e
v
e
lop
cl
o
s
ed
loop
sim
u
lin
k
m
o
d
e
l for
b
u
ck
b
o
o
s
t con
v
e
rter
-
inve
rter base
d solar syste
m
.
Fi
gu
re
1.
Sc
he
m
a
t
i
c
di
agram
of
n
o
n
-i
s
o
l
a
t
e
d
b
u
ck
-
b
o
o
st
c
o
nve
rt
er
2.
OPERA
T
IONA
L CIRCU
IT FO
R BUCK-BOOST
CONVERTER
Th
e
b
a
sic
p
r
incip
l
e of th
e
bu
ck–b
oo
st co
nv
erter is fairly
si
m
p
le wh
ile
in
th
e
On
-stat
e
, th
e i
n
pu
t
voltage s
o
urce
is directly connecte
d
to the
induct
o
r (L
).
This res
u
lts in accum
u
lati
ng energy in L. In this
stage, t
h
e ca
pa
citor s
u
pplies e
n
ergy to
th
e outp
u
t
l
o
ad.
Wh
il
e in
t
h
e
Off-state, th
e i
n
du
ctor is conn
ected to
the
out
put
l
o
ad
an
d ca
paci
t
o
r
,
s
o
ener
gy
i
s
t
r
a
n
sfe
rre
d
f
r
o
m
L to
C an
d R. Co
m
p
ar
ed
t
o
th
e bu
ck
an
d bo
o
s
t
conve
r
ters, t
h
e
characteristic
s of th
e buck–boost
conve
rter
are m
a
in
ly
p
o
l
arity of th
e ou
tpu
t
vo
ltag
e
is
op
p
o
si
t
e
t
o
t
h
a
t
of
t
h
e i
n
p
u
t
;
t
h
e
out
put
v
o
l
t
a
ge ca
n
vary
con
tin
uou
sly fr
om
0
to
(f
or
an
id
eal conv
er
ter)
. The
o
u
t
p
u
t
vo
ltag
e
r
a
ng
es
fo
r
a buck
an
d a
b
o
o
s
t
co
nv
er
ter
ar
e
resp
ectiv
ely 0 to
and
to
∞
.
The
bu
ck a
n
d
bo
ost
c
o
n
v
e
r
t
e
rs, t
h
e
ope
rat
i
o
n
o
f
t
h
e
b
u
c
k
-b
o
o
st
i
s
be
st
un
de
rst
o
od
i
n
t
e
rm
s of t
h
e
in
du
ctor's "reluctan
ce" to
allow rap
i
d ch
ang
e
in
cu
rren
t.
From
th
e in
itial st
ate in
wh
ich
noth
i
n
g
is ch
arg
e
d
an
d
th
e switch
is
o
p
e
n
,
th
e curren
t throug
h the in
du
ct
o
r
is
z
e
ro
.
Whe
n
t
h
e
swi
t
c
h
i
s
fi
rst
cl
ose
d
, t
h
e
bl
ocki
ng
d
i
od
e
p
r
ev
en
ts cu
rren
t fro
m
flowing
in
t
o
t
h
e ri
gh
t h
a
nd
sid
e
of t
h
e circu
it, so
it m
u
st all flo
w
t
h
rou
g
h
t
h
e
in
du
ctor.
Howev
e
r, sin
ce t
h
e in
du
ctor do
esn
'
t lik
e rap
i
d
cu
rren
t ch
an
g
e
,
it in
itial
l
y k
eep
s th
e curren
t
lo
w
b
y
d
r
op
p
i
n
g
m
o
st o
f
th
e vo
ltag
e
p
r
ov
id
ed
b
y
th
e sou
r
ce. Over ti
m
e
, th
e in
d
u
c
t
o
r allows th
e cu
rren
t to
slo
w
ly
i
n
crease
by
de
creasi
n
g i
t
s
vo
l
t
a
ge dr
op
. Al
so d
u
ri
ng t
h
i
s
t
i
m
e
, t
h
e i
ndu
ct
or st
o
r
es ene
r
gy
i
n
t
h
e f
o
r
m
of a
m
a
gnet
i
c
fi
el
d.
2.
1. CO
NTI
N
UO
US MO
DE
If th
e cu
rren
t th
rou
g
h
th
e indu
ctor
L
ne
ve
r falls to zero during a comm
utation cycle, the
conve
r
ter is
said
to op
erate
in
con
tinu
o
u
s
m
o
d
e
.
Fro
m
t=0
to
t=DT, t
h
e co
nv
erter is in
On-St
a
te, so
t
h
e switch
S
is close
d
.
The
rate of c
h
ange
in t
h
e
in
du
ctor
cu
rr
ent (
I
L
)
i
s
t
h
e
r
ef
o
r
e
gi
ve
n
by
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
i
n
g
a
n
d
Si
m
u
l
a
t
i
o
n
of
C
l
osed
Lo
o
p
C
ont
r
o
l
l
e
d P
a
r
a
l
l
e
l
C
a
scad
ed
Buck B
o
ost
…
(T. Su
nda
r)
65
0
…………
1
At th
e end
o
f
th
e
On-state, the in
crease of
I
L
is th
erefo
r
e
∆
…………
2
D
i
s
t
h
e
dut
y
c
y
cl
e. It
re
pr
ese
n
t
s
t
h
e
f
r
act
i
o
n
o
f
t
h
e
com
m
ut
at
i
on
peri
od
T
d
u
ring
wh
ich
t
h
e switch
is
ON. T
h
ere
f
ore
D
ranges between 0 (
S
is n
e
ver
o
n
)
an
d 1 (
S
is alw
a
ys on)
.
During
th
e Off-state, th
e switch
S
is o
p
e
n
,
so
th
e ind
u
c
t
o
r cu
rren
t fl
ows th
rou
g
h
the lo
ad
. If we
assu
m
e
zero
vo
ltag
e
d
r
op
in
th
e d
i
o
d
e
, an
d a cap
acit
o
r larg
e enou
gh
for its vo
ltag
e
to
rem
a
in
co
n
s
tan
t
, th
e
evol
ut
i
o
n
o
f
I
L
is
…
…
…
…
3
There
f
ore,
t
h
e
vari
at
i
o
n of
I
L
du
rin
g
t
h
e Of
f-
peri
od
is
∆
1
…………
4
As
we c
o
nside
r
that t
h
e c
o
nverter
ope
rates i
n
stea
dy-state
conditions, t
h
e
am
ount of e
n
e
r
gy st
ore
d
in
each
of its c
o
m
ponents
has
to be
the sam
e
at the
begi
nni
ng and at t
h
e
end of a
c
o
m
m
utation cycle. As
the
ener
gy
i
n
an
i
n
duct
o
r
i
s
gi
ven
by
1
2
…………
5
It is clear that
the value
of
I
L
at the end of the off state
m
u
st
b
e
th
e sam
e
with
th
e v
a
l
u
e o
f
I
L
at the
begi
nni
ng
o
f
t
h
e O
n
-st
a
t
e
, i
.
e
.
t
h
e s
u
m
of t
h
e
vari
at
i
o
ns
of
I
L
duri
ng the
on
and the
off
states m
u
st be zero
∆
∆
0
…
………
6
Sub
s
titu
tin
g
∆
and
∆
b
y
th
eir
expr
ession
s yield
s
∆
∆
1
0
…………
7
Th
is
can
b
e
written
as
1
…………
8
Th
is in ret
u
rn
yield
s
th
at
…………
9
Fro
m
th
e abov
e exp
r
essi
o
n
it can
b
e
ob
serv
ed
t
h
at th
e
p
o
l
arity o
f
th
e ou
tpu
t
v
o
ltage is always
n
e
g
a
tiv
e
(b
ecau
s
e th
e du
ty cy
cle g
o
e
s fro
m
0
to
1
)
, and
th
at its
ab
so
lu
te valu
e in
creases
with
D, th
eo
retically
u
p
to m
i
n
u
s
infin
ity wh
en
D
ap
pro
ach
es 1
.
Ap
art
fro
m
th
e
po
larity,
th
is
co
nv
erter is eith
er step-up
(a
b
o
o
s
t
con
v
e
r
t
e
r)
o
r
st
ep-
d
ow
n
(a
bu
ck c
o
n
v
e
r
t
e
r)
.
Th
us i
t
i
s
nam
e
d a
b
u
ck
–
b
o
o
st
co
nve
rt
er.
2.
2. DIS
C
O
N
TINU
OU
S M
O
DE
In s
o
m
e
cases,
t
h
e am
ount
of
ener
gy
re
qui
re
d by
t
h
e l
o
a
d
i
s
sm
al
l
enoug
h
t
o
be t
r
ans
f
er
r
e
d i
n
a t
i
m
e
sm
a
ller than the whole commutation pe
ri
od
.
In
th
is case, the cu
rren
t
th
roug
h
th
e indu
ctor falls to
zero
du
ri
n
g
part
o
f
t
h
e
per
i
od. T
h
e
onl
y
di
ffe
re
nce i
n
t
h
e p
r
i
n
ci
pl
e d
e
scri
be
d ab
o
v
e
i
s
t
h
at
t
h
e i
nduct
o
r i
s
c
o
m
p
l
e
t
e
l
y
discha
rge
d
at t
h
e end
of t
h
e
comm
utation c
y
cle alt
hough
slight; the di
fference
has a s
t
rong e
ffect
on the
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
:
64
8 – 656
65
1
o
u
t
p
u
t
v
o
ltag
e
eq
u
a
tion
.
I
t
can
b
e
calcu
lated as f
o
llow
s
,
b
e
cau
se th
e inducto
r
cur
r
e
n
t
at th
e b
e
g
i
nn
ing
o
f
th
e
cycle is zero, its m
a
xim
u
m
value
at (t=DT)
is
…
…
…
…
10
Du
rin
g
t
h
e
of
f-
peri
od
,
I
L
falls
to
zero
after
δ
.T
0
…………
1
1
Usi
n
g t
h
e t
w
o
pre
v
i
o
us e
q
uat
i
ons
,
δ
is
…………
1
2
The loa
d
curre
nt
is equal to the avera
g
e
diode c
u
rrent
.Th
e
d
i
od
e curren
t is equ
a
l to
th
e ind
u
c
t
o
r
cu
rren
t du
ri
n
g
th
e
off-stat
e. Th
erefore, th
e
ou
tpu
t
curren
t
can
b
e
written
as
2
…
………
1
3
R
e
pl
aci
ng
and
δ
by t
h
eir
res
p
ective expre
ssions
yields
2
…………
1
4
Th
erefo
r
e,
th
e o
u
t
p
u
t
vo
ltag
e
g
a
in
can
b
e
written
as
2
…………
1
5
Co
m
p
ared
to
th
e exp
r
essi
on
o
f
th
e ou
tpu
t
vo
ltag
e
g
a
in
for th
e co
n
tinu
ous
m
o
d
e
, th
is ex
pressi
o
n
is
m
u
ch
m
o
re com
p
li
cat
ed. Furt
herm
ore, i
n
di
s
c
ont
i
n
u
o
u
s
o
p
e
r
at
i
o
n
,
t
h
e o
u
t
p
ut
vol
t
a
ge
not
onl
y
de
pen
d
s
o
n
t
h
e
d
u
t
y cycle,
bu
t also
on
th
e indu
ctor
v
a
lu
e, the in
pu
t
v
o
ltag
e
and
th
e ou
tpu
t
curren
t
.
The co
n
v
ert
e
r
ope
rat
e
s i
n
d
i
scont
i
n
u
ous
m
ode when l
o
w cu
rre
nt
i
s
draw
n by
t
h
e l
o
ad
, an
d i
n
cont
i
n
u
o
u
s
m
o
de at
hi
g
h
er l
o
ad c
u
r
r
e
n
t
l
e
vel
s
. T
h
e l
i
m
i
t bet
w
ee
n di
sc
ont
i
n
u
o
u
s
an
d
cont
i
n
u
ous m
ode
s i
s
reache
d
when the inductor
c
u
rrent
falls to ze
ro e
x
actly at
the
end
of the c
o
mmutation cycle.
In this
case, the
out
put
c
u
rrent
(o
u
t
pu
t cu
rren
t at
th
e limit b
e
tween co
n
tinuo
u
s
and
di
sco
n
t
i
n
uo
us m
odes)
i
s
gi
ve
n by
:
2
1
…
………
1
6
R
e
pl
aci
ng
by
t
h
e e
x
p
r
essi
on
gi
ve
n i
n
t
h
e
di
s
c
ont
i
n
u
o
u
s
m
ode sect
i
o
n y
i
el
ds
2
1
…………
1
7
As
i
s
t
h
e c
u
rr
ent
at
t
h
e
l
i
m
it
bet
w
een
c
ont
i
n
u
o
u
s
a
n
d
di
s
c
ont
i
n
u
o
u
s
m
odes
o
f
o
p
erat
i
ons
,
i
t
sat
i
s
fi
es t
h
e ex
pressi
o
n
s o
f
b
o
t
h
m
odes. T
h
eref
ore
,
usi
ng
t
h
e ex
pressi
on
of t
h
e
o
u
t
p
ut
v
o
l
t
a
ge i
n
c
ont
i
n
u
o
u
s
m
o
d
e
, th
e
p
r
evio
u
s
exp
r
ession
can
b
e
written
as:
2
…………
1
8
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
i
n
g
a
n
d
Si
m
u
l
a
t
i
o
n
of
C
l
osed
Lo
o
p
C
ont
r
o
l
l
e
d P
a
r
a
l
l
e
l
C
a
scad
ed
Buck B
o
ost
…
(T. Su
nda
r)
65
2
Let
'
s now
i
n
t
r
o
duce
t
w
o m
o
re n
o
t
a
t
i
ons
, t
h
e
no
rm
al
i
zed vol
t
a
ge,
defi
ned
b
y
|
|
. It c
o
r
r
es
ponds
to
th
e g
a
i
n
in
v
o
ltag
e
of th
e
co
nv
erter, th
e
n
o
rm
alized
cu
rren
t,
d
e
fi
n
e
d
by
|
|
. The term
is eq
ual
to the m
a
xim
u
m increase of t
h
e induct
o
r c
u
rrent during a cycle; i.e., the in
crease of
t
h
e inductor
curre
nt
with
a duty cycle D=1.
So, in
steady state oper
at
io
n
o
f
th
e conv
erter, th
is m
ean
s th
at
|
|
eq
ual
s
0 fo
r n
o
out
put
current, and
1
for the m
a
xim
u
m
cu
rren
t
the co
nv
erter can
deliv
er.
Usi
n
g
t
h
ese no
t
a
t
i
ons, we ha
v
e
i
n
co
nt
i
n
uo
us
m
ode
|
|
;
in
d
i
scon
tin
uou
s m
o
d
e
,
|
|
|
|
;
The cu
rre
nt
a
t
t
h
e l
i
m
i
t
bet
w
een c
ont
i
n
u
ous a
n
d di
sc
o
n
t
i
n
u
o
u
s m
ode i
s
1
.
There
f
ore
t
h
e
l
o
c
u
s
of
t
h
e
l
i
m
it
bet
w
een
c
ont
i
n
u
ous
a
n
d
di
scont
i
n
u
o
u
s
m
ode
s
i
s
gi
ve
n
b
y
|
|
1
1
.
3.
TWO-ST
AGE PV INVERTER SYST
E
M
WITH BOOST-T
Y
PE
MPPTs
No
wa
day
s
, a c
o
n
v
e
n
t
i
onal
t
w
o-st
a
g
e co
n
f
i
g
urat
i
o
n i
s
usua
l
l
y
adopt
e
d
i
n
t
h
e PV i
n
vert
e
r
sy
st
em
s.
Each
MPPT is
realized
with a b
o
o
s
t
co
nv
er
te
r
to
s
t
ep
up
the
P
V
-
a
rr
a
y
vo
ltage close t
o
the specifie
d
DC
-link
v
o
ltag
e
, as show
n in
Fi
g
u
r
e
2. Th
e boo
st con
v
e
r
t
er
is
op
erated in
by-pass
m
ode whe
n
t
h
e PV-array vol
t
age is
higher tha
n
the DC-link
volt
a
ge, Ho
weve
r, since the characteristics of
PV arrays are
different from each
othe
r, the i
nve
rter ope
r
ated i
n
by-pass m
o
de canno
t trac
k
each individua
l
m
a
xim
u
m
power
poi
nt accurately,
and t
h
e i
n
vert
er su
ffe
rs f
r
o
m
as hi
gh
-v
ol
t
a
ge st
ress as
th
e op
en
vo
ltag
e
of th
e arrays. To
release th
is
li
mitatio
n
,
an
MPPT to
po
logy, w
h
ich
co
m
b
in
es bu
ck
an
d
b
o
o
s
t conv
er
ter
s
is p
r
o
p
o
s
ed
in
th
is stud
y, in w
h
ich
t
h
e c
ont
r
o
l
al
g
o
ri
t
h
m
fo
r t
r
ac
ki
n
g
m
a
xim
u
m
p
o
we
r
p
o
i
n
t
s
i
s
base
d
o
n
a
pe
rt
ur
bat
i
o
n a
n
d
obs
er
vat
i
o
n
m
e
t
h
o
d
.
Th
e MPPT
will switch
op
erat
io
n
m
o
d
e
s b
e
t
w
een
bu
ck
and
boo
st wh
en
t
h
e ou
tpu
t
vo
ltag
e
of a PV array is
cl
ose t
o
t
h
e
DC
-
bus
v
o
l
t
a
g
e
. The
desi
gn
ed co
nt
r
o
l
l
e
r
can s
w
i
t
c
h co
nt
r
o
l
l
a
ws t
o
achi
e
ve sm
oot
h m
ode
tran
sitio
n and
fu
lfill on
lin
e co
nfigu
r
ation
ch
eck fo
r t
h
e
M
PPTs, wh
ich
can
b
e
eith
er sep
a
rate o
r
in
p
a
rallel
co
nn
ection
,
to d
r
aw th
e m
a
x
i
m
u
m
p
o
w
er fro
m
th
e PV
arrays m
o
re effectiv
ely. Ad
d
ition
a
lly, a u
n
i
form
cu
rren
t co
n
t
ro
l
sch
e
m
e
is
in
tro
d
u
c
ed
to
th
e
co
n
t
ro
ller to
e
qual
l
y
di
st
ri
b
u
t
e
t
h
e PV a
rray
out
put
c
u
r
r
ent
t
o
t
h
e
two
MPPTs i
n
p
a
rallel op
eratio
n.
Fi
gu
re
2.
C
o
nv
ent
i
onal
t
w
o-st
age P
V
i
nve
rt
e
r
sy
st
em
wi
t
h
B
oost
-
t
y
pe M
P
PTs
To
r
e
du
ce leakag
e
g
r
ou
nd
cu
rr
en
t cir
c
u
l
ating th
rou
g
h
PV arr
a
ys and
gr
ound
, sev
e
r
a
l tr
an
sf
or
m
e
r
l
ess
i
nve
rt
er t
o
pol
ogi
es
were
p
r
op
ose
d
. E
v
e
n
t
h
o
u
g
h
t
h
ey
can achie
ve
high efficienc
y
, they require
m
o
re
com
pone
nt
s t
h
an t
h
e c
o
n
v
e
n
t
i
onal
f
u
l
l
-
b
r
i
d
ge t
o
pol
ogy
.
Th
us, i
n
t
h
i
s
st
udy
, t
h
e bi
di
rect
i
onal
f
u
l
l
-
bri
d
g
e
i
nve
rt
er i
s
o
p
e
r
at
ed wi
t
h
bi
p
o
l
a
r m
odul
at
i
o
n t
o
a
voi
d l
eak
age g
r
o
u
nd c
u
r
r
ent
a
nd t
o
sav
e
po
wer c
o
m
pone
nt
s
wh
ile still su
stain
i
n
g
co
m
p
arativ
ely h
i
g
h
efficien
cy to
th
ose in
. No
te th
at a fu
ll-b
r
i
d
g
e
i
n
v
e
rter op
erated
wit
h
bi
p
o
l
a
r m
odul
a
t
i
on can achi
e
v
e
onl
y
l
o
w f
r
e
que
ncy
com
m
o
n
-
m
ode v
o
l
t
a
ge (
V
C M
= (
V
dc
−
V
s
)
/
2), res
u
l
t
i
ng
in
low
le
a
k
ag
e
g
r
ou
nd
cu
rr
en
t.
To
m
a
in
tain
th
e
DC-b
us
v
o
ltag
e
fo
r th
e
g
r
i
d
-co
n
n
ected in
v
e
rter, th
e
co
n
t
ro
ls, su
ch as rob
u
st,
adaptive
,
a
nd
fuzzy, we
re a
d
opte
d
.
When a
d
opting these
co
n
t
ro
ls
for the stu
d
i
ed
DC
-d
istribu
tio
n syste
m
, a
h
eav
y step-lo
a
d
ch
an
ge at th
e DC-bu
s
side will cau
se h
i
gh DC-bu
s
v
o
ltag
e
v
a
riatio
n
and
flu
c
t
u
atio
n, an
d
th
e
sy
st
em
m
i
ght
run a
b
n
o
r
m
a
ll
y
or d
r
op i
n
t
o
u
n
d
er o
r
o
v
er
vol
t
a
ge pr
ot
ect
i
o
n
.
B
u
l
k
y
DC
-
b
u
s
capaci
t
o
rs ca
n be
ad
op
ted
to
in
crease th
e h
o
l
d-u
p
tim
e
an
d
sup
p
ress th
e fl
u
c
tu
atio
n
of th
e DC-b
u
s
v
o
ltage, b
u
t
it will
in
crease
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e
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64
8 – 656
65
3
the size and c
o
st of t
h
e syste
m
s
i
gni
fican
tly. Add
itio
n
a
lly, ev
en
thou
gh
t
h
er
e a
r
e a
p
proaches t
o
achie
ve fa
st
DC-b
u
s
vo
ltage d
y
n
a
m
i
cs, the syste
m
s with
lo
ad
con
n
ected to
th
e DC
bu
s
h
a
v
e
no
t
b
een
stu
d
i
ed
yet.
4.
SIMULATION RESULTS
Ope
n
l
o
o
p
sy
st
em
wi
t
h
st
ep
chan
ge i
n
i
n
so
l
a
t
i
on i
s
s
h
o
w
n i
n
Fi
g
u
r
e
3.
Tw
o
buc
k
b
o
o
s
t
co
nve
rt
e
r
s
are connected
in pa
rallel to
increase t
h
e
power
rating. T
h
e step cha
n
ge
in
in
pu
t
d
u
e
t
o
in
crease i
n
the so
lar
ener
gy
i
s
sh
o
w
n i
n
Fi
gu
re
4a. T
h
e
o
u
t
p
ut
vol
t
a
ge o
f
bo
ost
co
n
v
ert
e
r
i
s
sh
ow
n i
n
Fi
gu
re
4b
. T
h
e
vol
t
a
g
e
in
cr
eases fr
o
m
32
0V
t
o
39
0V. Th
e
A
C
o
u
t
pu
t vo
ltag
e
and
lo
ad
cur
r
e
n
t
are show
n in
Figu
r
e
4
c
and
Figu
r
e
4d
respectively. It
can
be
seen that the steady
state
err
o
r
i
n
t
h
e
out
put
v
o
l
t
a
ge
and
cu
rre
nt
i
s
hi
g
h
er
.
Fi
gu
re
3.
O
p
e
n
l
o
o
p
sy
st
em
Fi
gu
re
4a.
I
n
p
u
t
Vol
t
a
ge
Fi
gu
re 4
b
. O
u
t
put
V
o
l
t
a
ge of
B
oost
C
o
nve
rt
er
Fi
gu
re 4c.
O
u
t
put
V
o
l
t
a
ge of
In
vert
e
r
Fi
gu
re 4
d
. O
u
t
put
C
u
r
r
e
n
t
o
f
In
vert
e
r
Fig
u
r
e
4
.
Sim
u
latio
n
r
e
su
lts
of
th
e op
en
loop of
two
bu
ck bo
o
s
t
conv
er
ter
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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8-8
6
9
4
Mo
del
i
n
g
a
n
d
Si
m
u
l
a
t
i
o
n
of
C
l
osed
Lo
o
p
C
ont
r
o
l
l
e
d P
a
r
a
l
l
e
l
C
a
scad
ed
Buck B
o
ost
…
(T. Su
nda
r)
65
4
Th
e
Sim
u
lin
k
d
i
agr
a
m
o
f
closed
l
o
op
system
is sh
own
in Figu
r
e
5. Th
e D
C
ou
tpu
t
voltag
e
of
the
b
o
o
s
t con
v
e
rter is sen
s
ed
and
it is co
m
p
ared
with
t
h
e
r
e
f
e
r
e
n
ce
vo
ltage. Th
e er
ro
r is pr
o
c
essed
u
s
in
g a
PI
cont
rol
l
e
r. T
h
e out
p
u
t
of t
h
e PI cont
rol
l
e
r
i
s
used t
o
up
dat
e
t
h
e pul
se
wi
dt
h ap
pl
i
e
d
t
o
t
h
e buc
k bo
os
t
co
nv
erter. Th
e step
ch
ang
e
in
inp
u
t
v
o
ltag
e
is sh
own
in
Fi
g
u
re
6
a
. Th
e in
pu
t vo
ltag
e
i
n
creases fro
m
1
0
V
t
o
1
4
V. Th
e
o
u
t
pu
t of t
h
e
bo
o
s
t
co
nv
erter is
sho
w
n
i
n
Fi
gu
re
6
b
. Th
e
ou
tpu
t
d
e
creases and
settles at 2
40V. The
out
put
vol
t
a
ge
and c
u
rre
nt
wa
vef
o
rm
s are sh
ow
n i
n
Fi
g
u
re
6c an
d Fi
gu
re
4d
res
p
ect
i
v
el
y
.
They
are i
n
pha
s
e
sin
ce th
e lo
ad
i
s
a resistiv
e lo
ad
.
Fi
gu
re 5.
Si
m
u
l
i
nk
M
odel
of
C
l
osed Lo
o
p
S
y
st
em
Fi
gu
re
6a.
I
n
p
u
t
Vol
t
a
ge
Fi
gu
re 6
b
. O
u
t
put
V
o
l
t
a
ge of
t
h
e
B
o
ost
C
o
n
v
ert
e
r
Fi
gu
re 6c.
O
u
t
put
V
o
l
t
a
ge of
t
h
e
I
n
vert
er
Fi
gu
re 6
d
. O
u
t
put
C
u
r
r
e
n
t
o
f
t
h
e
I
n
vert
er
Fi
gu
re
6.
Si
m
u
l
a
t
i
on res
u
l
t
s
o
f
t
h
e
cl
ose
d
l
o
o
p
of
t
w
o
buc
k
bo
ost
c
o
nve
rt
ers
5.
CO
NCL
USI
O
N
Closed l
o
op c
ont
rolled
pa
rallel cascaded
buc
k
boos
t c
o
nve
rter i
nve
rte
r
system
is s
u
ccess
f
ully
m
odel
l
e
d and sim
u
l
a
t
e
d usi
n
g sim
power s
y
st
em
. The resul
t
s
of o
p
e
n
l
o
o
p
an
d cl
ose
d
l
o
o
p
sy
st
em
s are
p
r
e
s
en
te
d.
Th
e c
l
o
s
ed
loop
s
y
s
t
e
m
is
capabl
e
of
reducing t
h
e stea
dy stat
e error.
Th
e simu
latio
n resu
lts
are i
n
line with the predications
. The
closed
sy
st
em
has ad
va
nt
ages
l
i
k
e im
prove
d response and reduce
d
steady
state
Evaluation Warning : The document was created with Spire.PDF for Python.
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S
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:
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94
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J
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S
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l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
64
8 – 656
65
5
erro
r. Th
e
d
i
sad
v
a
n
t
ag
e
of this syste
m
is th
at it h
a
s
li
mite
d
vo
ltag
e
trackin
g
rang
e. Th
e co
n
t
ri
bu
tio
n
of th
is
work is to
propos
e a parallel cascad
ed
bu
ck
bo
ost con
v
e
rter
to
i
m
p
r
ov
e th
e n
pow
er
r
a
tin
g
and
r
e
du
ce th
e
in
v
e
rter inpu
t cu
rren
t
ripp
le.
Th
e scop
e of th
is work
is th
e si
m
u
latio
n
o
f
clo
s
ed
loo
p
con
t
ro
lled
con
v
e
rter-inv
erter syste
m
with
PI
co
n
t
ro
ller. Th
e clo
s
ed
loop
si
m
u
la
tio
n
using fu
zzy con
t
ro
ller
will b
e
d
o
n
e
in
fu
t
u
re.
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I
J
PED
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S
SN
:
208
8-8
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9
4
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del
i
n
g
a
n
d
Si
m
u
l
a
t
i
o
n
of
C
l
osed
Lo
o
p
C
ont
r
o
l
l
e
d P
a
r
a
l
l
e
l
C
a
scad
ed
Buck B
o
ost
…
(T. Su
nda
r)
65
6
BIOGRAP
HI
ES OF
AUTH
ORS
T.
Sundar
is
a Res
earch S
c
ho
la
r in the D
e
pt.
of
EIE, S
C
S
V
M
V
Univers
i
t
y
, K
a
n
c
hipuram
. He
is
doing research
in the field of
PV sy
stem usi
ng Advanced
Instrumentation S
y
stem. He is
a
res
earch
s
c
hol
ar
in S
C
S
V
M
V
Univers
i
t
y
.
His
are
a
of in
ter
e
st is
PV S
y
stem
s and
th
e
i
r Contro
l.
S.
San
k
ar
obtained his B.E Degree in Electr
i
cal & El
ectronics Engineer
ing at Sri Venkateswar
a
College
of Eng
i
neer
ing, from
M
a
dras
Univers
i
t
y
and
M
.
E (
P
ower S
y
s
t
em
) Degree
from
Annam
a
lai Univ
ersit
y
Chid
am
ba
ram
.
He h
a
s do
ne his Ph.D
in the ar
ea of FACTS controllers.
His
res
ear
ch in
t
e
res
t
s
ar
e
in th
e
are
a
of
F
A
CTS and PV s
y
s
t
ems. He h
a
s publis
hed pap
e
rs on
IPFC and Converter.
Evaluation Warning : The document was created with Spire.PDF for Python.