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
. 1
,
Mar
c
h
20
15
,
pp
. 10
9
~
12
0
I
S
SN
: 208
8-8
6
9
4
1
09
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
A New Control Method for Grid
-Connected PV System Based
on Qu
asi
-
Z-Source Cas
c
aded Multi
l
evel In
vert
er Usi
n
g
Evolutionary Algorithm
Hamid
Rez
a
Mohammadi, Ali
Akhavan
Department o
f
Electrical Engin
e
ering,
Univ
ers
i
t
y
of Kas
h
an,
Kas
h
an, I
r
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 27, 2014
R
e
vi
sed Dec 2,
2
0
1
4
Accepted Dec 25, 2014
In this p
a
per
,
a
new contro
l m
e
t
hod for quasi-
Z
-
s
ource cascad
ed
m
u
ltilev
e
l
inverter
based grid-connected photovolta
ic (P
V) sy
stem is proposed. The
proposed method is capable of boosting the PV array
vo
ltag
e
to a higher
level and solves
the imbalance
problem
of DC-link voltage
in
traditional
cascad
ed H-brid
ge inverters. Th
e propos
ed control s
y
stem adjusts the grid
inje
cted
curr
ent
in phas
e
with
the
grid
voltage and
achieves independen
t
maximum powe
r
point
trac
king
(MPPT) for th
e separ
a
te PV array
s
.
To
achi
e
ve
thes
e
g
o
als
,
the propo
rt
ional-in
tegr
al (P
I) contro
llers
ar
e em
plo
y
ed
for each m
odule
.
For achieving t
h
e best perform
ance
, this paper
presents an
optimum approach to d
e
sign
the contro
ller
par
a
meters using par
ticle swarm
optimization (P
SO). The pr
imar
y
d
e
sign
go
al
is to obtain good
response b
y
minimizing the integral absolute erro
r
.
Also, the transient
response is
guaranteed b
y
minimizing the
overshoot,
settling time and
ri
se time of
the
s
y
stem response. Th
e
effectiv
en
ess of
the new p
r
oposed contro
l
method has
been v
e
rified th
rough simulatio
n studi
es based
on a sev
e
n lev
e
l quasi-
Z
-
Source c
a
scad
ed
m
u
ltil
evel
inv
e
r
t
er.
Keyword:
Cascad
ed m
u
lt
ilev
e
l in
v
e
rter
Particle swarm op
ti
m
i
zatio
n
Pho
t
ov
o
ltaic syste
m
Quasi
-
Z-
so
urc
e
i
nve
rt
er
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
:
Ham
i
d Reza Mohamm
adi,
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
Uni
v
ersity
o
f
Kash
an
,
Kash
an
, I
r
a
n
.
Em
a
il: m
o
h
a
mmad
i
@k
ash
a
nu
.ac.i
r
1.
INTRODUCTION
Ph
ot
o
vol
t
a
i
c
(
P
V)
p
o
w
e
r
ge
nerat
i
o
n
has a
great
pot
e
n
t
i
a
l
t
o
serv
e as
a cl
ean an
d i
n
exha
ust
i
b
l
e
rene
wa
bl
e ene
r
gy
so
u
r
ce. H
o
we
ve
r, o
u
t
p
u
t
powe
r
o
f
t
h
e
PV arrays is greatly affecte
d
by environmental
co
nd
itio
ns su
ch
as sto
c
h
a
stic ch
ang
e
s
o
f
the tem
p
eratu
r
e
an
d so
lar irradian
ce.
In PV syste
m
s, ex
tractin
g
t
h
e
m
a
xim
u
m
pow
er o
f
t
h
e PV a
rray
an
dc
ur
ren
t
i
n
ject
i
on i
n
t
o
t
h
e gri
d
at
un
i
t
y
power
fact
or a
r
e necessa
ry
.
I
n
recent years,
applying va
rious m
u
ltilevel
inve
rter to
pol
ogies t
o
PV
syste
m
s is gett
ing m
o
re and
m
o
re
at
t
e
nt
i
on
d
u
e t
o
t
h
e
l
a
r
g
e
p
o
w
er
-scal
e a
n
d
hi
g
h
vol
t
a
ge
d
e
m
a
nds.
Am
ong
va
ri
o
u
s
t
o
p
o
l
o
gi
es, ca
sca
d
ed
H-
bri
dge (C
HB
)
i
nve
rt
er has u
n
i
que ad
va
nt
age
s
and has
been
i
d
ent
i
f
i
e
d as a sui
t
a
bl
e t
opol
ogy
f
o
r t
r
a
n
sf
o
r
m
e
r-
less, grid-connected P
V
syste
m
s [1].
Ap
pl
y
i
ng
C
H
B
i
nve
rt
er i
n
t
h
e P
V
sy
st
em
s has s
o
m
e
ad
vant
a
g
es s
u
ch
as
the inde
pe
nde
nt m
a
xim
u
m powe
r
point tra
c
king (MPPT)
of each a
rray
.
Howe
ver, the DC-link voltage in
each inverte
r
m
odule is not
constant,
beca
use P
V
array
voltage
va
ries
due t
o
the c
h
a
nge
s of environm
ental
co
nd
itio
ns su
ch
as tem
p
eratu
r
e an
d so
lar irrad
i
atio
n or
p
a
rtial
sh
ado
w
s. Th
ese cases wi
ll
cau
se
an
imb
a
lan
ce
DC-link voltage am
ong
different H-br
i
dge
m
odules.
Furt
herm
ore, in t
h
e conve
n
tional
cascade
d
m
u
ltilevel
inve
rter (CMI) based P
V
system
, each
m
odule is a buck i
nve
rter beca
us
e the first com
p
one
n
t of the
out
put
AC vo
ltag
e
, al
ways is lo
wer th
an
th
e inpu
t DC vo
ltag
e
. T
h
ere
f
o
r
e, a
n
ad
di
t
i
onal
DC
-D
C
bo
ost
co
nve
rt
er i
s
n
ecessary to
ob
tain
th
e
d
e
sired
ou
tpu
t
vo
lt
ag
e, if t
h
e
inpu
t vo
ltag
e
is lo
wer th
an
th
e
d
e
sired
ou
tpu
t
v
o
ltage
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
. 1
,
Mar
c
h
2
015
:
10
9
–
12
0
11
0
an
d also, to balan
ce th
e DC
-lin
k vo
ltag
e
s. Th
is
DC-D
C
boost
convert
e
r inc
r
eases t
h
e com
p
lexity of the
po
we
r a
n
d
co
n
t
rol circ
uit an
d
reduces t
h
e e
f
ficiency [2].
In
rece
nt years
,
the Z
-
s
o
urce i
nve
rter
(ZSI) a
n
d qu
asi
-
Z
-
s
o
u
r
ce i
n
vert
e
r
(
Q
ZSI
)
ha
ve
bee
n
em
pl
oy
ed
fo
r PV
po
we
r gene
rat
i
o
n sy
st
em
due t
o
som
e
uni
q
u
e a
dva
n
t
ages an
d feat
u
r
es. U
n
l
i
k
e q
u
a
s
i
Z-so
urce i
n
v
e
rt
er
,
ZSI
has a d
i
sco
n
tinuo
us in
put cu
r
r
e
n
t
du
r
i
ng
th
e shoo
t-
thro
ugh
state d
u
e
to
th
e b
l
o
c
k
i
ng
d
i
o
d
e
. No
w
a
d
a
ys,
q
u
a
si-Z-sou
rce cascad
ed
m
u
ltilev
e
l in
v
e
rter
(QZS-CMI) b
a
sed
PV syste
m
s were
p
r
op
o
s
ed
wh
ich
inh
e
rits the
adva
ntage
s
of traditional CMI while overcom
i
ng issues
with im
balance DC-link
voltage
s am
ong i
nde
pende
n
t
m
odules
and PV
a
rray voltage boost.
Refere
nces
[3]-[4] prese
n
t the
vari
ous
m
u
lti-
carrier bi
pola
r
PW
M
t
echni
q
u
es f
o
r
QZS-C
M
I a
n
d [
5
]
foc
u
sed
on t
h
e p
a
ram
e
t
e
r desi
g
n
o
f
t
h
e QZS-C
M
I. The
pha
se shi
f
t
e
d
si
nus
oi
dal
p
u
l
s
e wi
dt
h m
odul
at
i
on (P
S-S
P
W
M
)
i
s
use
d
i
n
[
6
]
as a
m
o
dul
at
i
o
n sche
m
e
, but
PV sy
st
em
has
neve
r
bee
n
m
odel
e
d i
n
det
a
i
l
t
o
de
si
g
n
t
h
e
c
ont
rol
l
e
rs
.
In
t
h
i
s
pa
per
a ne
w c
o
nt
rol
m
e
t
hod
f
o
r a
QZ
S-C
M
I
ba
sed
PV
sy
st
em
i
s
pr
op
ose
d
. T
h
e c
ont
ro
l
ob
ject
i
v
es a
r
e
i
nde
pen
d
e
n
t
D
C
-l
i
nk
vol
t
a
ge
cont
rol
,
i
nde
p
e
nde
nt
M
PPT
cont
rol
a
nd c
u
rre
nt
i
n
je
ct
i
on
t
o
t
h
e
gri
d
at
uni
t
y
p
o
we
r fact
or
. T
h
e p
r
o
p
o
rt
i
o
na
l
-
i
n
t
e
gral
(PI
)
cont
rol
l
e
rs a
r
e
em
pl
oy
ed t
o
c
ont
rol
eac
h QZ
S-C
M
I
m
odul
e. T
o
ac
hi
eve
a
hi
g
h
a
n
d
fast
pe
rf
o
r
m
a
nce, t
h
i
s
pa
per
p
r
ese
n
t
s
a
n
opt
i
m
u
m
appr
oac
h
t
o
desi
gn
P
I
param
e
t
e
rs usi
ng
pa
rt
i
c
l
e
sw
arm
opt
im
i
z
at
ion
(P
SO
) an
d
al
so t
h
e P
S
-S
P
W
M
m
odul
at
i
on
schem
e
i
s
used f
o
r
t
h
e si
ngl
e
pha
s
e
QZS
-
C
M
I. T
h
i
s
pa
per i
s
o
r
gani
ze
d as
fo
llo
ws: Section
2 co
n
s
ists an
overv
iew of th
e syste
m
wi
t
h
p
r
op
ose
d
cont
rol
st
rat
e
g
y
;
Sect
i
on 3
fo
cuses
on t
h
e sy
st
em
m
odel
i
n
g
and
gri
d
-c
o
n
n
ect
ed co
nt
r
o
l
;
desi
g
n
of t
h
e P
I
para
m
e
t
e
rs usi
n
g P
S
O i
s
pre
s
ent
e
d i
n
sect
i
o
n
4;
t
h
e PS
-SP
W
M
m
odul
at
i
on sc
hem
e
i
s
presen
t
e
d
i
n
sectio
n
5
;
th
e effectiv
en
ess of th
e
p
r
op
o
s
ed strateg
y
is
v
e
rified
b
y
sim
u
lat
i
o
n and
co
m
p
ariso
n
th
e
resu
lts with
t
h
e re
fere
nce
[
2
]
i
n
sect
i
o
n
6;
an
d
fi
nal
l
y
, a
concl
u
si
o
n
i
s
m
a
de i
n
sect
i
o
n
7.
2.
QZS-
C
M
I AND
ITS CON
T
R
O
L STRA
TEGY
The Q
Z
S-C
M
I
based
g
r
i
d
-c
o
nnect
e
d
P
V
s
y
st
em
wi
t
h
t
h
e pr
op
ose
d
c
o
nt
r
o
l
st
rat
e
gy
i
s
sho
w
n i
n
Fi
gu
re
1.
C
o
m
p
ari
n
g
t
o
t
h
e c
o
n
v
e
n
t
i
onal
C
M
I m
odul
e,
an
i
n
duct
o
r
-
capa
c
i
t
o
r i
m
pedanc
e net
w
o
r
k
i
s
i
n
cl
ud
e
d
in the input stage of
each m
odule. T
h
isstruc
t
ureis use
d
to
synt
hesize DC
voltage s
o
urc
e
s to ge
nerate
2
n
+
1
staircase output wave
form
where
,
n
i
s
t
h
e
n
u
m
b
er o
f
i
nde
pen
d
e
n
t
P
V
a
r
ray
.
T
h
e i
ndi
vi
dual
PV
s
o
u
r
c
e
i
s
a
n
array
c
o
m
pose
d
of
i
d
e
n
t
i
cal
PV
panel
s
i
n
se
r
i
es an
d
paral
l
e
l
.
Fi
gu
re
1.
(a
)
q
Z
S-C
M
I
base
d
g
r
i
d
-t
i
e
P
V
p
o
w
er
sy
st
em
and
(b
)
dc
-l
i
n
k
p
eak
vol
t
a
g
e
c
o
nt
r
o
l
*
1
ˆ
DC
V
*
ˆ
D
Cn
V
t
PI
n
*
PV
k
k1
V
n
PV
k
k1
V
*
s
ˆ
i
*
s
i
PR
s
i
*
PV
2
V
PV
2
V
2
PI
PL
L
0
si
n(
t
)
*
PV
n
V
PV
n
V
n
PI
mn
V
m2
V
n
k2
m3
V
m(
n
1
)
V
m1
V
PI
*
ˆ
D
Ck
V
ˆ
D
Ck
V
*
2
L
k
i
2
L
k
i
P
1
1
Ck
k
V
D
1
Ck
V
m2
V
mn
V
()
inv
Gs
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A New Con
t
ro
l
Metho
d fo
r
G
r
id
-
C
onn
ected
PV S
y
stem
Ba
sed
o
n
…
(H
am
i
d
Reza
Moha
mm
ad
i)
11
1
2.1.
Quasi-Z
-
s
o
urce inver
t
er
oper
ation
Fi
gu
re
2.
Eq
ui
val
e
nt
ci
rc
ui
t
o
f
t
h
e
qZ
SI;
(a)
no
n
-
sh
o
o
t
-
t
h
ro
ug
h st
at
e a
n
d (
b
)
sh
o
o
t
-
t
h
ro
u
g
h
st
at
e
The
QZS
-
C
M
I
com
b
i
n
es t
h
e
QZS
net
w
o
r
k
i
n
t
o
eac
h C
M
I
m
odul
e. T
h
e
Q
Z
SI ca
n
be
o
p
e
r
at
ed i
n
t
w
o
m
o
d
e
s, i.e., the no
n-
sh
oo
t-
t
h
r
oug
h and
t
h
e
sh
oo
t-
t
h
rou
g
h
[
6
].
Figu
r
e
2 sh
ow
s th
e
Q
Z
SI
eq
u
i
v
a
len
t
ci
r
c
u
its
o
p
e
rating
in
t
h
e two
m
o
d
e
s an
d d
e
fin
e
s t
h
e
p
o
l
arities o
f
al
l v
o
ltag
e
s and
cu
rren
ts. If th
e switch
i
ng
p
e
rio
d
is
T
s
, th
e shoo
t-
thr
oug
h p
e
r
i
od
is
T
sh
and
no
n-
sho
o
t
-
t
h
r
ou
gh
p
e
r
i
od
is
T
nsh
, where:
T
s
T
sh
T
nsh
(1
)
There
f
ore,
t
h
e
sho
o
t
-
t
h
r
o
ug
h
dut
y
rat
i
o i
s
D=
T
sh
/T
s
.W
h
e
n th
e
k
th
m
odul
e
i
s
i
n
no
n-
sh
o
o
t
-
t
h
ro
u
g
h
st
at
e, t
h
e
po
we
r i
s
t
r
an
s
m
i
t
t
e
d fr
om
t
h
eDC
si
de t
o
t
h
eAC
si
de a
n
d
i
nve
rt
er
ope
rat
e
s as a t
r
a
d
i
t
i
onal
C
M
I.
In
st
eady
st
at
e,
t
h
e
f
o
l
l
o
wi
n
g
rel
a
t
i
ons can be obt
ai
ne
d.
1
ˆˆ
,
12
D
C
k
P
Vk
k
P
Vk
H
k
k
D
C
k
k
VV
B
V
V
S
V
D
(
2
)
Whi
l
e
a sh
oot
-
t
hr
ou
g
h
m
ode, t
h
ere i
s
no
p
o
we
r t
r
an
sm
i
s
si
on
, beca
use t
h
e DC
-l
i
n
k
vo
l
t
a
ge i
s
zero. I
n
t
h
i
s
m
ode, there
are:
ˆ
0,
0
DCk
H
k
VV
(
3
)
Fo
r th
e QZS-C
M
I, th
e syn
t
h
e
sized
v
o
ltag
e
is:
11
ˆ
nn
H
Hk
k
D
C
k
kk
VV
S
V
(
4
)
In t
h
e a
b
ove e
quat
i
o
ns
,
ˆ
D
Ck
V
is th
e
k
th
m
odul
e
D
C
-l
i
nk peak v
o
l
t
a
ge;
V
PVk
is t
h
e ou
tpu
t
vo
ltag
e
of
th
e
k
th
PV arra
y;
D
k
and
B
k
are th
e
shoo
t-throug
h
du
ty ratio
an
d boo
st facto
r
o
f
th
e
k
th
m
odul
e, res
p
ec
t
i
v
el
y
;
V
Hk
is th
e
o
u
t
pu
t vo
ltag
e
of the
k
th
m
odul
e a
n
d
S
k
{-1,
0,
1}
i
s
t
h
e s
w
i
t
c
hi
n
g
f
unct
i
o
n
of
t
h
e
k
th
m
odul
e.
2.
2. Pri
n
ci
pl
e of
C
o
n
t
rol
Str
a
te
g
y
Each QZ
S-C
M
I
m
odul
e has t
w
o i
n
de
pen
d
e
n
t
cont
r
o
l
com
m
a
nds:
sh
oot
-t
hr
o
u
g
h
d
u
t
y
rat
i
o
D
n
and
m
odul
at
i
on si
g
n
al
V
m
.
D
n
is used
to
ad
ju
st the DC-link
vo
ltag
e
to a
desire
d re
fere
nce
value.
While,
V
n
is
u
s
ed
to
co
n
t
ro
l th
e g
r
i
d
in
j
ected
po
wer.
T
h
e m
a
in goals of the
cont
rol syst
em
of QZS
-
C
M
I
base
d gri
d
-c
o
n
n
ect
ed
PV system
are: 1)
Inde
pe
nde
nt M
PPT
for e
ach m
odule t
o
ens
u
re t
h
e m
a
xim
u
m
powe
r
extraction from
each
PV array; 2
)
Cu
rren
t inj
ection
in
to
th
e grid
at u
n
ity
powe
r
fact
or a
nd
3) B
a
l
a
nce DC
-l
i
n
k
peak v
o
l
t
a
ge f
o
r al
l
QZS
-
CM
I m
o
d
u
les.
For ac
hie
v
ing
these goals, the PI
controllers are em
ployed. T
h
e tota
l PV array vo
ltage lo
op
adju
sts
th
e su
m
o
f
n
PV array vo
ltages u
s
ing
a PI co
n
t
ro
ller, PI
t
.
Each PV array
voltage re
fere
nce is calculated by its
M
PPT bl
o
c
k
.
Al
so, t
h
e cu
rre
nt
l
o
o
p
achi
e
ve
s a si
nus
oi
dal
gri
d
-i
n
j
ect
e
d
cur
r
ent
i
n
pha
se
wi
t
h
t
h
e g
r
i
d
vol
t
a
ge
.
A pr
o
p
o
r
t
i
o
nal
-res
o
nant
(PR
)
cont
r
o
l
l
e
r m
a
kes t
h
e act
ual
gri
d
cu
rre
nt
t
o
t
r
ack t
h
e de
si
red g
r
i
d
i
n
je
ct
ed
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
. 1
,
Mar
c
h
2
015
:
10
9
–
12
0
11
2
cu
rr
en
t [7
].
The
n
-
1
i
nde
pe
nd
ent
PV ar
ray
v
o
l
t
a
ge l
o
ops c
ont
rol
t
h
e ot
he
r
n
-
1
P
V
array
vol
t
a
ges t
o
ac
hi
ev
e
th
eir own
MPPTs th
ro
ugh
th
e
n
-
1
P
I
co
nt
r
o
l
l
e
rs,
nam
e
d as PI
2
to
PI
n
, res
p
ectively. Also,
as show
n in Fi
gure
1
(b
), DC
-l
i
nk
p
eak v
o
l
t
a
ge i
s
cont
rol
l
e
d i
n
t
e
rm
s of i
t
s
shoo
t
-
t
h
r
o
u
g
h
d
u
t
y
rat
i
o
f
o
r eac
h QZS
-
C
M
I m
odul
e.
A
PI co
n
t
ro
ller is u
s
ed
fo
r t
h
e DC-lin
k
v
o
ltage
lo
op
to
m
a
k
e
th
e DC
-lin
k
p
e
ak
vo
ltag
e
tracks its referen
ce
v
a
lu
e.
A
pr
op
o
r
t
i
onal
co
nt
rol
l
e
r
(P
)
i
s
use
d
t
o
i
m
pr
ove
t
h
e
dy
nam
i
c of t
h
e r
e
sp
o
n
se.
Fi
nal
l
y
, t
h
e i
nde
pe
nde
nt
sho
o
t
-
th
ro
ugh
du
ty ratio
D
k
and m
odul
at
i
o
n si
g
n
al
V
mk
are co
m
b
i
n
ed i
n
t
o
t
h
e P
S
-SP
W
M
m
odul
at
i
on sc
hem
e
for
k
th
m
odul
e t
o
ac
hi
eve t
h
e
de
si
re
d
g
o
al
s.
3.
SYSTE
M
MO
DELING
The
bl
oc
k
di
a
g
ram
of t
h
e
Q
Z
S-C
M
I
base
d
g
r
i
d
-c
o
nnect
e
d
P
V
sy
st
em
is sh
o
w
n
i
n
Fi
gu
re
3.
Th
e
d
e
tails will b
e
ex
p
l
ain
e
d
as follo
ws.
n
*
PV
k
k1
V
n
PV
k
k1
V
PI
t
G(
s
)
*
s
i
s
i
PRi
G(
s
)
n
mk
k1
V
n
vf
k
k1
G(
s
)
n
mk
k1
V
n
k2
in
v
1
G(
s
)
m1
V
H1
V
n
k1
fs
1
Ls
r
H
V
g
V
1
DC
1
1
1D
ˆ
2V
(
1
2D
)
n
DC
n
n
1D
ˆ
2V
(
1
2D
)
n
k1
p
1
Cs
n
k1
k
1D
PV
k
i
k
D
*
s
ˆ
i
n
PV
k
k1
V
0
si
n(
t
)
PI
k
G(
s
)
*
PV
k
V
PV
k
V
mk
V
vf
k
G(
s
)
in
v
k
G(
s
)
g
V
sk
DC
k
k
ˆ
i(
1
D
)
ˆ
2V
(
1
2
D
)
Hk
V
p
1
Cs
k
1D
k
D
PV
k
i
PV
k
V
S
e
pa
ra
te
Vo
l
t
a
g
e
C
ont
r
o
l
l
e
r
,
k
2
,
3
,
.
..,
n
T
o
t
a
l
V
olt
a
ge
Co
nt
roll
e
r
G
r
i
d
Co
nne
ct
e
d
C
u
rr
ent
C
ont
r
o
l
l
e
r
Fi
gu
re
3.
B
l
oc
k
di
ag
ram
of t
h
e p
r
o
p
o
sed
co
n
t
rol
gri
d
-c
on
ne
ct
ed sy
st
em
for
t
h
e
QZS
-
C
M
I
base
d P
V
sy
st
e
m
3.
1. I
ndepe
nd
ent P
V
Voltage an
d In
jec
t
ed
Curre
nt Con
t
rol
In
the
k
th
QZS
-
C
M
I m
odul
e t
h
e c
u
r
r
ent
o
f
t
h
e i
n
d
u
ct
o
r
L
1
is:
1
PV
k
Lk
P
V
k
p
dV
ii
C
dt
(
5
)
Whe
r
e
i
L1k
is the cu
rren
t of indu
ctor
L
1
a
nd al
so,
i
PVk
is th
e cu
rren
t
o
f
k
th
PV ar
r
a
y; an
d
C
p
is th
e shu
n
t
capacito
r
with
th
e PV array. Th
e to
tal ou
tpu
t
vo
ltag
e
of th
e QZS-CM
I can
b
e
written
as:
V
s
H
gf
f
s
di
VL
r
i
dt
(
6
)
Whe
r
e
V
g
is th
e grid
vo
ltage an
d
i
s
is th
e g
r
i
d
in
jected current;
r
f
is parasitic resistanceand
L
f
is the filter
in
du
ctan
ce. Con
s
eq
u
e
n
tly, th
e tran
sfer fun
c
tio
n of
t
h
e g
r
id
in
j
ected
cu
rren
t
can
b
e
ob
tain
ed
b
y
:
()
1
()
()
()
s
f
H
gf
f
Is
Gs
Vs
V
s
L
s
r
(
7
)
To
m
a
k
e
th
e actu
a
l g
r
id
in
j
ected
cu
rren
t to
track the desire
d re
fere
nce, a PR controller
0
22
0
()
iR
PR
i
i
P
k
Gs
k
s
is
u
s
ed
, wh
er
e
ω
0
i
s
t
h
e
res
o
n
a
nt
f
r
eq
ue
ncy
i
.
e.
31
4
ra
d/
s.
In t
h
e
next
st
e
p
, a g
r
i
d
v
o
l
t
a
ge
feed
f
o
r
w
ar
d c
ont
rol
l
o
o
p
i
s
a
ppl
i
e
d
.
T
h
ere
f
ore
,
t
h
e
k
th
m
odul
e has
t
h
e
fo
llowing
m
o
du
latio
n
sign
al:
()
()
mk
mk
g
v
f
k
VV
V
s
G
s
(
8
)
In the above equation,
mk
V
is th
e
k
th
m
odul
e m
o
d
u
l
a
t
i
on
si
gn
al
;
mk
V
is o
u
t
pu
t o
f
th
e PI co
n
t
ro
l
l
er in
th
e
k
th
m
odul
e an
d
()
vf
k
Gs
is:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A New Con
t
ro
l
Metho
d fo
r
G
r
id
-
C
onn
ected
PV S
y
stem
Ba
sed
o
n
…
(H
am
i
d
Reza
Moha
mm
ad
i)
11
3
()
1
ˆ
()
,
(
)
()
()
Hk
vfk
i
n
v
k
D
C
k
in
v
k
m
k
Vs
Gs
G
s
V
nG
s
V
s
(
9
)
Du
e
to
DC-link
p
eak
vo
ltag
e
b
a
lan
ce con
t
ro
l,
th
e DC-link peak voltages
a
r
e
equal.
T
h
e
r
efore:
()
()
,
1
,
2
,
.
.
.
,
in
v
k
i
n
v
Gs
G
s
k
n
(
1
0
)
Acco
r
d
i
n
g t
o
Fi
gu
re
3, t
h
e c
l
osed
-l
o
o
p
t
r
a
n
sfer
f
unct
i
o
n
o
f
t
h
e
gri
d
i
n
jec
t
ed cu
rre
nt
c
o
n
t
rol
sy
st
em
can
b
e
written
as:
22
00
*
32
2
2
2
00
0
0
ˆ
()
()
()
()
(
)
ˆˆ
ˆ
1(
)
(
)
(
)
()
()
PR
i
f
i
n
v
s
DC
k
i
P
i
P
i
R
ic
PRi
f
i
n
v
s
f
f
DC
k
i
P
f
DCk
i
P
D
C
k
i
R
f
Gs
G
s
G
s
Is
V
k
S
k
k
G
Gs
G
s
G
s
Is
Ls
r
V
k
s
L
s
V
k
V
k
r
(1
1)
Acco
r
d
i
n
g
t
o
F
i
gu
re 2,
eac
h P
V
a
rray
vol
t
a
g
e
can be o
b
t
a
i
n
ed by
:
1
1
()
[
(
)
(
)
]
PV
k
P
V
k
L
k
p
Vs
I
s
I
s
Cs
(
1
2
)
In
t
h
e
n
o
n
-
s
h
o
o
t
-
t
h
ro
u
g
h
m
ode, t
h
e
out
put
po
we
r i
s
e
qual
t
o
i
n
put
p
o
we
r.
The
r
ef
ore:
1_
ˆ
ˆ
ˆ
2
sH
k
DC
k
D
C
k
P
V
k
L
k
n
s
h
iv
vi
v
i
(
1
3
)
In
th
e ab
ov
e eq
u
a
tion
,
ˆ
Hk
v
i
s
t
h
e out
put
pea
k
v
o
l
t
a
ge of t
h
e
k
th
m
odul
e;
DC
k
i
is the avera
g
e curre
n
t of
th
e DC-link
in th
e
k
th
m
odul
e;
1_
Lk
n
s
h
i
i
s
t
h
e aver
age cu
rre
nt
of
i
nduct
o
r
L
1
in
no
n-
sh
oo
t-
thr
oug
h
m
o
d
e
.
Equ
a
tio
n
(1
3) can
b
e
rewritten
u
s
ing
(2)
as
fo
llo
ws:
1_
ˆ
ˆ
ˆ
2(
1
2
)
sH
k
Lk
n
s
h
DC
k
k
iv
i
vD
(
1
4
)
Al
so,
i
n
t
h
e s
h
oot
-t
hr
o
u
g
h
m
ode
, t
h
e
ave
r
a
g
e cu
rre
nt
o
f
t
h
e
i
n
d
u
ct
o
r
L
1
is:
1_
Lk
s
h
P
V
k
ii
(
1
5
)
There
f
ore, the
avera
g
e c
u
rrent o
f
th
e i
n
du
ctor
L
1
i
n
the
one
switching cycl
e
can
b
e
ob
tained
as
fo
llo
ws:
11
_
1
_
ˆ
ˆ
(1
)
(1
)
ˆ
2(
1
2
)
s
kH
k
Lk
k
L
k
s
h
k
L
k
n
s
h
k
P
V
k
DC
k
k
iD
v
iD
i
D
i
D
i
vD
(
1
6
)
In
ad
d
ition
,
a PI con
t
ro
ller
()
I
t
PI
t
P
t
k
Gs
k
s
is u
s
ed
to
track th
e to
tal referen
ce vo
ltag
e
co
m
i
n
g
fr
om
M
PPT. T
h
e
bl
oc
k
di
ag
r
a
m
of t
h
e t
o
t
a
l
PV
ar
ray
vol
t
a
ge l
o
o
p
i
s
sh
o
w
n
i
n
Fi
g
u
re
4
.
Al
s
o
,
f
o
r
m
odul
es
2
to
n
a
PI controller
()
I
k
PI
k
P
k
k
Gs
k
s
is app
lied
to sep
a
rate
PV
v
o
lta
ge to ach
i
ev
e th
eir ow
n MPPTs.The
b
l
o
c
k
d
i
agr
a
m
o
f
th
e sep
a
r
a
te
PV
ar
r
a
y
vo
ltag
e
loop
is show
n in
Figu
r
e
5.
3.
2.
I
ndepe
nd
ent DC-link Voltage
Con
t
rol
Th
e ind
e
p
e
nd
en
t DC-link
v
o
l
tag
e
con
t
ro
l sch
e
m
e
is sh
o
w
n in
Figu
re
1
(b). Th
is con
t
ro
l lo
op
, ad
ju
st
DC
-l
i
n
k pea
k
vol
t
a
ge
usi
ng t
h
e capaci
t
o
r-
C
1
vol
t
a
ge a
n
d t
h
e i
n
duct
o
r
-
L
2
current
for eac
h QZ
S-CMI m
o
dule.
Refere
nce [8]
prese
n
ts the
k
th
QZS-C
M
I m
odul
e
’
s t
r
a
n
sfe
r
fu
nct
i
o
n f
r
om
t
h
e sh
o
o
t
-
t
h
ro
ug
h
d
u
t
y
rat
i
o
t
o
t
h
e
DC
-l
i
n
k peak vol
t
a
ge
,
G
Vdk
(
s
) an
d
fr
om
t
h
e sh
oot
-t
hr
o
u
g
h
d
u
t
y
rat
i
o
t
o
t
h
e i
n
duct
o
r
-
L
2
curre
n
t,
G
iLd
k
(
s
) as
fo
llows:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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94
I
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PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
10
9
–
12
0
11
4
12
22
ˆ
()
(
1
2
)
(
)
12
()
()
(
1
2
)
s
k
ck
ck
k
Vd
k
k
L
is
D
V
V
D
Gs
LC
s
R
r
C
s
D
(
1
7
)
2
12
12
22
ˆ
()
(
)
(
)
(
)
(1
2
)
()
()
[
(
)
(
1
2
)
]
s
ck
ck
c
k
c
k
k
iL
d
K
k
i
LC
V
V
s
R
r
V
V
C
s
L
s
R
r
D
Gs
Ls
R
r
LCs
R
r
C
s
D
(1
8)
Whe
r
e,
L
is th
e ind
u
c
t
o
r and
C
is the capacitor
of the
im
pedance
network.
R
is the
series resistance of
capacitors
and
r
is th
e p
a
rasitic resistan
ce o
f
i
n
du
ctors;
V
ck1
and
V
ck
2
are capacit
o
r
C
1
a
nd
C
2
vol
t
a
ges,
respectively.
A p
r
op
ortion
a
l g
a
in
K
dPk
i
s
em
pl
oy
ed for t
h
e i
nduct
o
r c
u
r
r
e
nt
l
o
o
p
t
o
i
m
p
r
o
v
e t
h
e dy
na
m
i
c respon
se.
As s
h
o
w
n i
n
F
i
gu
re 6
,
A
PI
cont
ro
ller
with th
e tran
sf
er
fun
c
tio
n of
()
Vd
I
k
Vi
P
I
k
V
d
P
k
k
Gs
k
s
is cascade
d
to
th
e ind
u
c
t
o
r curren
t
loo
p
to
con
t
ro
l th
e
DC-li
n
k p
e
ak
vo
ltage.
n
k
k1
DCk
k
1D
1
ˆ
2
V(
1
2
D
)
p
1
Cs
k
1D
ic
G(
s
)
PI
t
G(
s
)
p
vk
i
n
PV
k
k1
V(
s
)
n
*
PV
k
k1
V(
s
)
n
k1
Fi
gu
re
4.
B
l
oc
k
di
ag
ram
of t
h
e t
o
t
a
l
PV
v
o
l
t
age l
o
o
p
sk
DC
k
k
ˆ
i(
1
D
)
ˆ
2V
(
1
2
D
)
p
1
Cs
k
1D
inv
k
G(
s
)
PI
k
G(
s
)
pv
k
i
PV
k
V(
s
)
*
PV
k
V(
s
)
Fig
u
r
e
5
.
Blo
c
k
d
i
agr
a
m
o
f
the sep
a
r
a
te PV
v
o
ltag
e
loop
dP
k
K
vi
P
I
k
G(
s
)
k
d(
s
)
*
DCk
V(
s
)
iL
dk
G(
s
)
DC
k
V(
s
)
Vd
k
G(
s
)
Fi
gu
re
6.
B
l
oc
k
di
ag
ram
of t
h
e DC
-l
i
n
k
pea
k
v
o
l
t
a
ge c
ont
ro
l
of
t
h
e
k
th
m
odul
e
4.
DESIGN OF PI
CONT
ROLLERS
USING
PARTICL
E
SWARM
OPTIMIZ
A
TION
Th
e PI con
t
ro
l
l
er is a well-kn
own
m
e
th
od
for in
du
st
rial co
n
t
ro
l processes. Th
is is du
e to
itsro
bu
st
p
e
rf
or
m
a
n
ce an
d sim
p
le str
u
ctu
r
e i
n
a w
i
de r
a
n
g
e
of
oper
a
tin
g cond
itio
n
s
. Tun
i
ng
of
su
ch a con
t
ro
ller
requires s
p
ecification of two
p
a
ram
e
ters: p
r
opo
rtion
a
l g
a
i
n
K
p
and
in
teg
r
al gain
K
i
[9
].
In
th
e past,
th
is
pr
o
b
l
e
m
has been h
a
n
d
l
e
d
b
y
a t
r
i
a
l
and e
r
r
o
r t
e
c
hni
que
.
In t
h
i
s
pa
pe
r,
t
h
e p
r
o
b
l
e
m
of t
h
e P
I
pa
ra
m
e
t
e
rs
t
uni
n
g
i
s
f
o
rm
ul
at
ed as a
n
opt
i
m
i
zati
on p
r
o
b
l
e
m
.
The pr
o
b
l
e
m
form
ul
at
i
on em
pl
o
y
s
fo
ur
per
f
o
r
m
ance
in
d
e
x
e
s, i.e., t
h
e ov
ersho
o
t
, t
h
e settlin
g
ti
m
e
, th
e rise tim
e
a
n
d
t
h
e in
teg
r
al
ab
so
lu
te error
o
f
t
h
e step resp
on
se
as t
h
e ob
ject
i
v
e fu
nct
i
on t
o
t
uni
ng t
h
e P
I
p
a
ram
e
t
e
rs for get
t
i
ng a wel
l
per
f
o
r
m
a
nce unde
r a gi
ve
n p
l
ant
.
I
n
th
is stu
d
y
, t
h
e
p
r
im
ary d
e
sig
n
g
o
a
l is to
ob
t
a
in
go
od
resp
on
se
b
y
min
i
m
i
zin
g
the in
tegral ab
so
l
u
te erro
r. At
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A New Con
t
ro
l
Metho
d fo
r
G
r
id
-
C
onn
ected
PV S
y
stem
Ba
sed
o
n
…
(H
am
i
d
Reza
Moha
mm
ad
i)
11
5
th
e sam
e
ti
m
e
,
th
e tran
sien
t
resp
on
se is
g
u
a
ran
t
eed b
y
m
i
n
i
mizin
g
th
e
ov
ershoo
t, t
h
e sett
lin
g
tim
e an
d
t
h
e
rise
t
i
m
e
of t
h
e st
e
p
res
p
o
n
se
.F
urt
h
erm
o
re,
we e
m
pl
oy
a so
lu
tio
n algo
rith
m
based
on
p
a
rticle swarm
o
p
t
i
m
izatio
n
.
The
PSO
i
s
a
st
ochast
i
c
opt
i
m
i
zat
i
on t
echn
i
que,
w
h
i
c
h
u
s
es swa
r
m
i
ng b
e
havi
ors
o
b
se
r
v
ed
i
n
fl
oc
k
o
f
b
i
rd
s. In
fact, th
e PSO
was in
sp
ired
b
y
th
e so
ci
ol
ogi
cal
beha
vi
o
r
associ
at
ed
with swarm
s
. PSO was
devel
ope
d
by
J
a
m
e
s Ken
n
e
d
y
an
d R
u
ssel
l
E
b
er
hart
i
n
1
9
9
5
as
a
new
he
u
r
i
s
t
i
c
m
e
t
hod
[
10]
.
It
uses
a
n
u
m
b
er
o
f
p
a
rticles th
at co
n
s
titu
te a
swarm
m
o
v
i
ng
aroun
d
i
n
o
n
e
N
-dim
ensional
searc
h
s
p
ace l
o
oking
for t
h
e
best
p
o
s
ition
.
Th
e in
d
i
v
i
du
als in
th
e swarm
are
called
p
a
rticle
s. Each
p
a
rticle in
th
e PSO al
g
o
rith
m
is a
p
o
t
en
tial
sol
u
t
i
o
n
fo
r t
h
e o
p
t
i
m
i
zat
i
onpr
o
b
l
e
m
and k
eep t
r
ac
k
o
f
i
t
s
co
-o
r
d
i
n
at
es
i
n
t
h
e
p
r
o
b
l
e
m
space
an
d t
r
i
e
s t
o
search t
h
e be
st position through flying in
a
m
u
ltidi
m
ensional space,
which a
r
e a
ssoc
i
ated with the
best
so
lu
tion
(called
b
e
st fitn
ess)
it h
a
s ach
iev
e
d
so
far th
at called
“
pbest
”
.
An
ot
he
r “be
s
t
”
val
u
e cal
l
e
d “
gbe
st
”
th
at is track
e
d
b
y
th
e
g
l
ob
al
version
o
f
th
e particle sw
arm
o
p
tim
izer is the ov
erall
b
e
st
v
a
lu
e and
its l
o
cation
obt
ai
ne
d
so
fa
r
by
eac
h
part
i
c
l
e
.
The t
r
a
n
si
ent
resp
o
n
se i
s
ve
ry
im
port
a
nt
, t
h
ere
f
o
r
e
bot
h
t
h
e am
pl
i
t
ude and t
i
m
e durat
i
on
of t
h
e
tran
sien
t respon
se m
u
st b
e
k
e
p
t
with
in
to
lerab
l
e li
m
i
t
s
. H
e
nce, f
o
ur i
n
d
e
xes o
f
the tra
n
sient res
p
ons
e are
u
tilized
to
ch
aracterize th
e
p
e
rform
a
n
ce o
f
PI con
t
ro
l systems.
4.
1. Resp
on
se Par
a
meters
Overs
h
oot:
W
i
t
h
the ass
u
m
p
tion of
y
as
the step res
p
onse,
y
max
i
s
t
h
e
m
a
xim
u
m
v
al
ue and
y
ss
is the
steady-state
val
u
e o
f
y
. th
ere
f
or
e
th
e ov
er
sh
oo
t
(
f
O
) is eq
ual to
:
ma
x
Os
s
f
yy
(
1
9
)
Rise Time
:
The
rise tim
e
(
f
RT
) i
s
defi
ned
as t
h
e t
i
m
e requi
re
d f
o
r
t
h
e st
ep re
sp
o
n
se t
o
ri
se f
r
om
10%
t
o
9
0
%
o
f
its fin
a
l v
a
l
u
e.
Hen
ce:
90
%
1
0
%
RT
y
y
ft
t
(
2
0
)
S
e
ttlin
g
Ti
me:
Th
e settlin
g
ti
me (
f
ST
) i
s
def
i
ned as t
h
e t
i
m
e requi
r
e
d
f
o
r t
h
e st
ep
res
p
o
n
se t
o
dec
r
e
a
se an
d st
ay
with
in
a 5%
o
f
its fin
a
l
v
a
lu
e.
ST
st
f
t
(
2
1
)
I
n
teg
r
a
l
A
b
so
lu
te
E
r
ro
r:
The i
n
tegral absolute e
r
ror (
f
IA
E
) can b
e
written
as:
0
|(
)
|
IA
E
f
et
d
t
(
2
2
)
4.
2. Ob
jecti
v
e
Functi
on
Th
e ob
j
ectiv
e
fu
n
c
tion
(
f
Totel
)
fo
r op
tim
a
l
d
e
sig
n
of
PI
con
t
roller
s
can
b
e
fo
rm
u
l
a
t
ed
as fo
llo
w
s:
To
t
a
l
O
R
T
S
T
I
A
E
f
ff
f
f
(
2
3
)
To a
ppl
y
P
S
O
fo
r t
u
ni
n
g
t
h
e
PI c
ont
rol
l
e
rs
,
t
h
e cl
ose
d
-l
oo
p t
r
a
n
sfe
r
fu
nc
t
i
on
of t
h
e t
o
t
a
l
PV
v
o
l
t
a
ge
l
o
o
p
, se
parat
e
PV
vol
t
a
ge l
o
o
p
an
d
DC
-l
i
n
k
peak
v
o
l
t
a
ge i
s
necessa
ry
. T
h
ese cl
ose
d
-l
o
op t
r
ans
f
er
f
u
n
c
t
i
ons
are
cal
cul
a
t
e
d
usi
n
g bl
oc
k di
a
g
ram
of Fi
g
u
re
4
–
6
,
respect
i
v
el
y
.
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
. 1
,
Mar
c
h
2
015
:
10
9
–
12
0
11
6
32
2
2
12
3
00
0
0
12
3
54
2
3
12
3
0
12
3
11
1
()
()
(
)
2
(
12
)
2
(
1
2
)
2
(
12
)
11
1
ˆ
()
(
(
)
)
2(
1
2
)
2
(
1
2
)
2(
1
2
)
((
P
t
i
P
I
t
iP
P
t
iP
iR
I
t
i
P
i
R
PVk
PVk
Pf
P
D
C
i
P
f
Pf
P
t
i
P
P
DD
D
kk
s
k
k
s
k
k
k
s
k
k
k
V
DD
D
DD
D
V
CL
s
C
V
k
r
s
CL
k
k
s
DD
D
C
22
2
12
3
00
0
12
3
2
12
3
00
12
3
2
12
3
00
12
3
11
1
ˆˆ
)(
)
)
2
(
12
)
2
(
1
2
)
2
(
12
)
11
1
()
(
)
2(
1
2
)
2
(
1
2
)
2(
1
2
)
11
1
()
(
)
2(
1
2
)
2
(
1
2
)
2(
1
2
)
DC
i
P
DC
i
R
f
I
t
i
P
P
t
iP
iR
It
iP
i
R
DD
D
Vk
Vk
r
k
k
s
DD
D
DD
D
kk
k
s
DD
D
DD
D
kk
k
DD
D
(2
4)
2
11
()
(
)
12
2
1
2
2
11
()
()
12
2
1
2
2
ks
ks
Pk
Ik
PV
k
k
k
ks
k
s
PV
k
PP
k
I
k
kk
Di
D
i
ks
k
VD
D
Di
Di
V
Cs
k
s
k
DD
(
2
5
)
()
()
k
DC
k
ds
Vs
(
2
6
)
25
4
2
3
2
2
26
5
4
2
2
3
2
2
ˆ
((
)
)
(
(
)
(
1
2
)
)
(
)
(
)
12
ˆˆ
()
(
)
(
(
1
2
)
(
)
)
(
(
)
)
(
)
(
1
s
Vd
Pk
d
P
k
V
d
P
k
V
d
I
k
d
Pk
d
P
k
V
d
P
k
k
d
P
k
d
Pk
Vd
Pk
k
d
P
k
D
Ck
k
d
P
k
D
C
k
d
Pk
Vd
I
k
i
k
L
C
s
k
k
LC
R
r
LC
s
k
k
L
C
s
k
k
R
r
D
s
L
k
s
k
k
R
r
D
LC
s
L
C
R
r
s
L
C
k
V
s
L
D
R
r
s
k
R
r
C
V
s
R
r
s
k
k
2
2)
k
D
5.
THE PS-SPWM FOR QZ
S-CMI
The m
odul
at
i
o
n t
echni
que a
p
pl
i
e
d i
n
t
h
e pr
op
ose
d
sy
st
em
i
s
a phase shi
f
t
e
d si
n
u
soi
d
al
pul
se wi
dt
h
m
odul
at
i
on t
h
at
show
n i
n
F
i
gu
re 7. T
h
e sho
o
t
-
t
h
r
o
u
g
h
st
at
es are i
n
sert
ed wi
t
h
t
h
e sim
p
l
e
boost
c
ont
ro
l
m
e
t
hod.
I
n
t
h
i
s
co
nt
r
o
l
m
e
t
hod, t
w
o
st
rai
ght
l
i
n
es,
whi
c
h a
r
e de
n
o
t
e
d a
s
1
-
D
n
and
D
n
-
1
,
envel
o
p
s
e
qual
t
o
or
great
er
t
h
a
n
t
h
e pea
k
val
u
e
o
f
t
h
e si
nus
oi
dal
refe
rence
si
g
n
a
l
s are
use
d
t
o
c
ont
rol
s
h
oot
-t
h
r
o
u
g
h
d
u
t
y
rat
i
o
.
Fi
gu
re
7.
M
o
d
u
l
a
t
i
on
schem
e
f
o
r t
h
e
pr
o
pos
ed sy
st
em
If t
h
e tria
ngula
r
carrier signal is sm
aller than
D
n
-
1
or
bi
gg
er t
h
a
n
1
-
D
n
the two switch
e
s of
o
n
e
leg i
n
H-
bri
dge m
o
d
u
l
e
are t
u
r
n
ed
on
si
m
u
l
t
a
neousl
y
[6]
.
In
PS
-SP
W
M sc
he
m
e
s, the num
b
er of triangular carrier
wav
e
s is eq
u
a
l
to
m
-1
, whe
r
e
m
is th
e lev
e
l
nu
m
b
er. Also
, th
e requ
ired
phase shifts
am
ong different ca
rriers
is
gi
ve
n as:
36
0
1
m
(
2
7
)
There
f
ore, in t
h
is case (
m
=
7
)
t
r
i
a
ngul
a
r
carr
i
ers of di
ffe
ren
t
H-b
r
i
d
ge m
o
dul
es are s
h
i
f
t
e
d 6
0
º wi
t
h
res
p
ect
t
o
each othe
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A New Con
t
ro
l
Metho
d fo
r
G
r
id
-
C
onn
ected
PV S
y
stem
Ba
sed
o
n
…
(H
am
i
d
Reza
Moha
mm
ad
i)
11
7
6.
SIMULATION RESULTS
The
pe
rform
a
nce eval
uation of t
h
e
propos
ed contro
l strategy was carried
ou
t b
y
d
i
fferen
t
si
m
u
latio
n
in
PSCAD/EMTDC. Th
e param
e
ters o
f
t
h
e QZS-CMI
ar
e sh
ow
n i
n
Tabl
e 1. Al
s
o
t
h
e PSO al
go
ri
t
h
m
i
s
pr
o
g
ram
m
ed in M
A
TL
AB
t
o
obt
ai
n t
h
e
bes
t
param
e
t
e
rs for t
h
e PR
an
d P
I
co
nt
rol
l
e
r
s
.
As m
e
nt
i
oned
earl
i
e
r,
t
h
e cl
osed
-l
o
o
p
t
r
ans
f
er f
u
nc
t
i
on of t
h
e t
o
t
a
l
PV vol
t
a
ge c
ont
rol
l
o
o
p
, t
h
e separat
e
PV
vol
t
a
ge c
ont
rol
l
oop
an
d th
e DC
-lin
k p
e
ak
vo
ltag
e
co
n
t
ro
l l
o
op
are
u
s
ed
for
o
p
tim
iza
tio
n
prob
lem
.
Th
e resu
lts of t
h
e PSO
al
go
ri
t
h
m
are sho
w
n i
n
Tabl
e 2. The e
ffect
i
v
eness o
f
t
h
e pr
op
ose
d
m
e
t
hod
i
s
show
n by
com
p
ari
ng t
h
e r
e
sul
t
s
of t
h
e
new
pr
o
pos
ed m
e
t
hod
fo
r pa
ram
e
t
e
r tuni
ng
of P
I
co
nt
r
o
l
l
e
rs wi
t
h
t
h
e res
u
l
t
s
of
[
2
]
i
n
Tabl
e 3
.
In t
h
i
s
tab
l
e, th
e
ov
ersh
oo
t, t
h
e settlin
g
tim
e an
d
t
h
e rise ti
m
e
o
f
th
e step
respon
se
for th
ese clo
s
ed-loo
p tran
sfer
fun
c
tion
s
are
p
r
esen
ted.As sh
own
in
t
h
istab
l
e, th
e
ov
ersh
oo
t, t
h
e settlin
g ti
m
e
an
d
t
h
e rise tim
e o
f
step
r
e
spon
se
f
o
r
al
l th
e clo
s
ed-
l
oo
p tr
an
sf
er
f
unctio
n
s
ob
tain
ed u
s
i
n
g PSO al
go
rith
m
is sm
a
l
l
e
r th
an
t
h
e
resu
lts of
[2]
.
Table 1. QZS
-
CM
I
Param
e
ters
QZ
S-CMI
Para
meters
Value
QZ
S inductance,
L
1
and
L
2
1.
8
m
H
QZS c
a
pacitance,
C
1
and
C
2
3300
µF
PV ar
ra
y parall
el c
a
pacitance,
C
p
1100
µF
Filter inductance,
L
f
1m
H
Car
r
i
er
fr
equency
,
f
c
5kHz
Gr
id voltage
220V/50Hz
Tabl
e
2. T
h
e
P
a
ram
e
t
e
rs of t
h
e C
o
nt
rol
Sy
st
em
by
Ps
o
Al
g
o
ri
t
h
m
Para
m
e
ters
Value
Para
m
e
ters
Value
k
i
P
0.
0049
1
k
iR
-
0
.
01673
k
Pt
1.
1511
k
I
t
1.
5348
k
P
k
0.
0263
k
Ik
0.
0017
k
dPk
0.
0073
k
VdPk
0.
0313
k
VdIk
2.
8122
Table
3. T
r
a
n
sfer Functions
C
h
aracteristics
Tra
n
sfer fu
nctio
n
s
Ov
ersho
o
t
(
%
)
Settling
ti
me
(sec)
Rise ti
me
(sec
)
using PSO
data
using [
2
]
data
using PSO
data
using [
2
]
data
using PSO
data
using [
2
]
data
T
o
tal PV voltage loop
8.
62
56.
1
0.
362
2.
84
0.
0395
0.
177
Separ
a
te PV voltage loop
12.
9
33.
3
0.
438
0.
511
0.
0578
0.
0651
DC-
link peak voltage loop
≈
0
≈
0
0.
243
1.
38
0.
13
0.
779
The P
-
V
cha
r
a
c
t
e
ri
st
i
c
of t
h
e
PV a
rray
i
s
s
h
o
w
n i
n
Fi
g
u
r
e
8. T
h
e m
easure
d
vol
t
a
ge
a
nd c
u
rre
nt
o
f
each PV array are use
d
to c
a
lculate the MPPT searc
h
al
gorithm
for the PV
voltage
refere
nce at the
MPP.
Inc
r
em
ent
a
l
cond
uct
a
nce
al
g
o
r
i
t
h
m
i
s
used
f
o
r
t
r
acki
n
g
t
h
e
m
a
xim
u
m
pow
er
poi
nt
o
f
a
P
V
a
rray
i
n
t
h
i
s
pape
r
[1
1]
.
Fi
gu
re
8.
P
V
a
rray
po
we
r-
vol
t
a
ge cha
r
act
eri
s
t
i
c
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
. 1
,
Mar
c
h
2
015
:
10
9
–
12
0
11
8
A
t
f
i
rst, all mo
du
les ar
e
wor
k
i
n
g at 100
0
W
/
m
2
an
d
25
ºC con
d
ition and
all th
e i
n
itial v
o
ltag
e
refe
rences
o
f
M
PPT al
g
o
r
i
t
h
m
are gi
ve
n
at
12
0
V.
T
h
e
pea
k
val
u
e
o
f
DC
-l
i
n
k
vol
t
a
ge
of
al
lm
od
ul
es i
s
cont
rol
l
e
d at
1
4
5
V
.
Aft
e
r 1 s
econ
d
, t
h
e t
h
i
r
d m
odul
e’s i
r
r
a
di
at
i
on dec
r
ea
ses t
o
70
0
W
/
m
2
. Hence, accordi
ng
t
o
Fi
g
u
r
e
8, t
h
e
refe
rence
o
f
M
PPT
de
cre
a
ses t
o
a
b
out
11
9.
3
V.
It
s
h
oul
d
be
not
e
d
t
h
at
, t
h
e
c
h
a
nge
o
f
te
m
p
erature mostly affect
s t
h
e v
o
l
t
a
ge
of
m
a
xim
u
m
power
poi
nt
, so
t
h
at
, t
e
m
p
erat
ure
ri
si
ng ca
u
s
es t
h
e
v
o
ltag
e
of m
a
x
i
m
u
m
p
o
w
er
po
in
t to dro
p
.
Wh
ile th
e ch
an
g
e
of so
lar irrad
i
atio
n
aff
ects t
h
e
curre
nt injection.
The t
o
t
a
l
P
V
v
o
l
t
a
ge (s
um
of
al
l
t
h
ree PV a
r
ray
v
o
l
t
a
ges) a
nd
ot
he
r P
V
ar
ray
v
o
l
t
a
ges ar
e sh
ow
n i
n
Figure 9(a)-(d), res
p
ectively. It can
be seen that during the change
in the MPPT reference value due to
chan
ge
of
en
vi
ro
nm
ent
a
l
con
d
i
t
i
on,
t
h
e
pr
o
pos
ed c
o
nt
r
o
l
m
e
t
hod
ha
ve e
x
cel
l
e
nt
t
r
ac
ki
ng
pe
rf
orm
a
nce aft
e
r
a
very
s
h
o
r
t
t
r
a
n
si
ent
.
It
can
be see
n
i
n
Fi
g
u
re
9(
d
)
t
h
at
,
aft
e
r a cha
n
ge
i
n
t
h
e en
vi
r
o
nm
ent
a
l
condi
t
i
on
of
m
odul
e 3,
t
h
e
co
nt
rol
l
e
r
o
f
t
h
i
s
m
odul
e t
r
acks t
h
e
ne
w
refe
rence
.
Whi
l
e, m
odul
e 2
have
n
o
t
a
ny
t
r
ansi
en
t
because no c
h
a
nge
is ha
ppeni
ng i
n
its condition. As
s
hown
in Figure
9(b-d), P
V
a
rray
vol
tage of m
odule
1 is
di
ffe
re
nt
wi
t
h
respect
t
o
m
o
d
u
l
e
s 2
an
d
3.
Thi
s
i
s
due
t
o
t
h
e fact
t
h
at
t
h
e m
odul
at
i
on
s
i
gnal
gene
rat
i
o
n
of
m
odul
e 1 i
s
di
f
f
ere
n
t
f
r
om
ot
h
e
r m
odul
es.
(a)
(b
)
(c)
(d
)
Fi
gu
re
9.
Si
m
u
l
a
t
i
on res
u
l
t
s
(
a
) T
o
t
a
l
PV
ar
r
a
y
vol
t
a
ge;
(
b
)
PV a
rray
v
o
l
t
a
ge
of
m
odul
e
1
;
(c)
PV
ar
ray
vol
t
a
ge
o
f
m
o
d
u
l
e
2;
(
d
)
PV
a
rray
vol
t
a
ge
o
f
m
odul
e 3
Fi
gu
re 1
0
. In
ve
rt
er out
put
v
o
l
t
a
ge
Fi
gu
re 1
1
. Gri
d
vol
t
a
ge
an
d
c
u
r
r
ent
The i
nve
rt
er
o
u
t
p
ut
v
o
l
t
a
ge i
s
sh
o
w
n
i
n
Fi
gu
re
10
.
It
can
be i
ndi
cat
ed
t
h
at
t
h
e s
o
l
a
r
i
r
radi
at
i
o
n
o
r
te
m
p
er
atu
r
e
do
es no
t af
fect th
e sev
e
n
-
level stair
case o
u
tp
u
t
vo
ltag
e
of
th
e inv
e
r
t
er
d
u
e
t
o
sho
o
t
-
t
h
r
ough
Evaluation Warning : The document was created with Spire.PDF for Python.