Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
No.
3
,
Septem
be
r 2020
, pp.
1536
~
1546
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v11.i
3
.
pp
1536
-
1546
1536
Journ
al
h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Grid con
necte
d photo
volt
aic syst
em
eff
i
ciency a
nd qualit
y
improve
ment usi
ng
f
uzzy
-
In
C
ond
MPPT
Amara
Yasmi
ne
1
, Bra
da
i
R
af
ik
2
,
Bo
uken
ou
i
Ra
c
hid
3
, Mel
li
t
A
del
4
1
Set
L
abor
at
o
ry, Elec
tron
ic
s Dep
art
m
ent
,
Bli
da
1
Univer
sity
,
Alge
ria
2
LATSILa
bora
t
ory,
E
lectr
oni
cs
Depa
rtment, Bli
da1Unive
rsity
,
Alger
ia
3
Rene
wab
le E
n
erg
ie
s d
epa
r
tm
e
nt,
Fa
cul
ty
of Te
chnol
ogy,
Bli
d
a 1 Unive
rsity
,
Al
ger
ia
4
Rene
wab
le E
n
erg
y
L
abor
a
tory,
Jijel Uni
ve
rsity
,
Alger
i
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
hist
or
y:
Re
cei
ved
Ja
n
5
, 20
20
Re
vised
A
pr
3
,
20
20
Accepte
d
A
pr
23
, 20
20
Maxim
um
Pow
er
Point
Tr
ac
ki
ng
(MP
PT)
tec
hnique
s
ar
e
d
e
vel
oped
to
har
vest
and
supply
m
axi
mu
m
p
ower
to
th
e
lo
ad
.
Thi
s
d
epe
nds
o
n
the
power
gene
ra
te
d
and
the
MP
PT
ac
cur
ac
y
.
Und
er
qui
ck
-
cha
ng
ing
wea
the
r
condi
ti
ons
,
In
cr
em
en
ta
l
Condu
ct
an
ce
(InCond
)
and
nu
me
rou
s
diffe
ren
t
al
gorit
h
ms
m
ay
fai
l
to
track
th
e
exa
c
t
Maxi
mum
Pow
er
Point
(
MP
P)
which
ma
y
result
in
sig
nifi
c
ant
power
l
oss
.
Fuzzy
Log
i
c
(FL)
b
ase
d
M
PP
T
is
qui
ck
and
accura
t
e
i
n
tr
a
cki
ng
the
MP
P,
but
th
e
high
co
mplex
it
y
and
th
e
im
plementat
ion
diffi
cu
lt
y
are
th
ei
r
main
d
isadvantage
s.
A
nov
el
FL
-
InCond
MP
PT
im
prove
d
technique
is
de
vel
oped
base
d
o
n
the
fe
at
ur
es
of
InCond
and
FL
technique
s
t
o
over
co
me
thei
r
dra
wbac
ks
.
Th
e
newly
dev
el
op
ed
appr
o
ac
h
ca
n
aut
om
at
i
call
y
adj
ust
the
var
i
at
ion
of
th
e
duty
cycle
fo
r
tr
ac
k
i
ng
the
MP
P
with
a
cc
ur
ac
y
.
The
ob
ta
in
ed
r
esult
s
ar
e
com
par
e
d
with
conve
n
tional
Per
turb
and
observe
(P
&O)
and
InCon
d
MP
PTs
for
gri
d
-
conne
c
te
d
mo
de
under
f
ast
wea
the
r
cond
it
i
ons.
It
is
de
monstra
t
ed
th
at
the
dev
el
ope
d
metho
d
outpe
rform
s
the
afo
r
em
en
ti
on
e
d
MP
PT
techni
ques
in
t
erm
s
of
tr
ac
king
response,
eff
icie
ncy
and
th
e
d
el
i
ver
ed curre
n
t
qu
al
it
y
.
Ke
yw
or
d
s
:
Eff
ic
ie
nc
y
FL
Gr
i
d
c
onnected
In
C
ond
M
PP
T
Photo
vo
lt
ai
c s
ys
te
m
Qu
al
it
y
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Ama
ra
Yasmin
e,
Set Lab
or
at
ory
, Elect
ronics
D
epar
tme
nt,
Bl
ida 1
U
niv
er
sit
y,
09000 B
li
da,
A
lgeria.
Emai
l:
amara
-
yasmi
ne@ou
tl
ook.fr
1.
INTROD
U
CTION
Re
new
a
ble
e
ne
rgy
play
s
a
sig
nificant
r
ole
in
the
ac
tual
el
ect
rici
ty
pro
duct
ion
due
t
o
thei
r
env
i
ronme
nt
-
fri
end
ly
feat
ur
e
s
an
d
the
ab
s
ence
of
C
O
2
emissi
on.
In
fact,
t
her
e
a
r
e
six
widely
known
ren
e
wa
ble
e
ne
rgy
source
s
w
hich
are
so
la
r,
wi
nd,
hydraul
ic
,
bi
om
as
s
,
ge
oth
e
rmal
a
nd
marine
.
Nevert
heless,
the
m
os
t
wi
dely
e
xp
l
or
e
d
are
wind
a
nd
so
la
r
ene
r
gy
due
t
o
their
ab
unda
nce
in
la
rg
e
ge
ogra
ph
ic
al
ar
eas
o
n
earth
a
nd
the
y
are
co
min
g
cl
os
er
t
o
be
ing
c
ompeti
ti
ve
wit
h
existi
ng
f
os
sil
f
uel
an
d
nucl
ear
powe
r
gen
e
rati
on
[1]
.
Lar
ge
scal
e
in
sta
ll
at
ion
s
of
DC
micr
o
-
gri
d
us
in
g
s
olar
en
ergy
have
bee
n
reali
ze
d
in
t
he
la
s
t
few
yea
rs
[2]
.
Tha
nk
s
to
a
ph
ys
ic
al
an
d
c
he
mica
l
phen
ome
non
cal
le
d
the
Photo
volt
ai
c
(
PV
)
ef
fect,
eac
h
s
ola
r
cel
l
produces
vo
lt
age
a
nd
el
ect
ric
cu
rr
e
nt
i
n
it
s
se
mico
n
duct
or
mate
rial
(e.
g.
,
sil
ic
on
or
ger
ma
ni
um
)
upon
expos
ur
e
t
o
li
gh
t
[3]
.
T
he
pro
du
ce
d
volt
age
an
d
c
urre
nt
(I
PV
an
d
V
PV
,
resp
ect
ivel
y)
hav
e
non
-
l
inear
char
act
e
risti
cs.
Be
sides,
t
hey
are
str
ongly
in
flue
nced
by
th
e
te
mp
e
ratur
e
and
irra
diance
.
The
e
xisti
ng
DC
-
DC
conve
rters
(B
uc
k,
Bo
os
t,
B
uc
k
-
boos
t,
Ć
uk
a
nd
Sin
gle
-
E
nded
Pr
i
mar
y
I
nducto
r
Co
nv
e
rte
r
(S
E
PI
C
)
an
d
Zet
a)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Grid
co
nnect
ed photov
oltaic
syste
m
ef
fi
ci
en
c
y and
qu
alit
y imp
r
ove
men
t
usi
ng
… (
A
m
ar
a Yas
mine
)
1537
are
us
e
d
t
o
ad
apt
the
P
V
G
volt
age
t
o
the
load
.
To
fe
ed
AC
-
loa
ds
a
nd
trans
fer
the
power
to
the
distrib
ute
d
el
ect
rical
g
rid
a
DC
-
AC i
nv
e
r
te
r
(si
ng
le
-
pha
se, th
ree
-
phase
or m
ulti
l
evel)
are esse
ntial
.
To
harvest
the
maxim
um
av
ai
la
ble
powe
r
from
t
he
P
VG,
a
go
od
ch
oic
e
of
MPPT
al
gorithm
t
o
con
t
ro
l
the
el
ect
ronic
s
witc
h
of
the
DC
-
DC
co
nverter
is
ne
cessar
y
[
4]
.
T
he
DC
-
DC
co
nv
e
rter
an
d
it
s
MPP
T
con
t
ro
ll
er
act
a
s
a
matc
hing
i
mp
e
dan
ce
un
it
betwee
n
P
VG
an
d
dc
-
l
oad.
Nominal
duty
cycle
of
t
he
c
onve
rter
switc
h
is
a
dju
s
te
d
by
the
M
P
PT
c
on
t
ro
ll
er
t
o
a
n
opt
imu
m
value,
s
o
t
he
c
onve
rter's
i
nput
resist
ance
is
e
qu
al
t
o
the
so
la
r
pan
e
l's
equ
i
valent
ou
t
pu
t
resist
an
ce.
This
ens
ur
es
maxi
mum
powe
r
tra
ns
fe
r
[5]
.
M
a
ny
MPPT
al
gorithms
ha
ve
been
stu
died
a
nd
de
velo
pe
d
in
t
he
li
te
r
at
ur
e
;
the
y
ca
n
be
eval
uate
d
acc
ordin
g
to
man
y
performa
nce
i
nd
ic
es
s
uch
as
the
num
ber
of
the
us
e
d
sens
or
s
,
respo
ns
e
ti
me,
c
omplexit
y,
de
pe
nd
e
nce
on
the
PV
s
ys
te
m
paramet
ers,
t
he
te
chn
i
qu
e
of
im
plementat
io
n
a
nd
c
os
t
[6]
.
MPPT
al
gorit
hms
are
cl
assifi
e
d
into
two
mai
n
cat
e
gories:
direct
methods
that
do
not
require
knowle
dge
of
t
he
PVG
par
am
et
ers
s
uc
h
as
P
erturb
and
O
bs
er
ve
(
P&O),
Hill
-
Cl
imbin
g
(
HC)
,
I
ncr
e
mental
Co
nductance
(
I
nC
ond
)
,
F
uzzy
Lo
gic
(F
L
)
an
d
Ne
ur
a
l
netw
orks.
H
oweve
r,
i
nd
ir
ec
t
methods
de
pend
on
t
he
PVG
pa
ramet
ers
an
d
nee
d
to
isolat
e
th
e
PVG
per
i
od
ic
al
ly
t
o
measu
re
the
var
ia
ti
ons
of
i
ts
par
a
mete
rs
su
c
h
as
f
racti
onal
ope
n
-
ci
rc
ui
t
vo
lt
age,
fr
ac
ti
on
al
sh
ort
ci
rc
uit
current,
fix
ed
volt
age,
a
nd
c
urren
t
m
et
hods.
It
is
w
or
t
h
me
ntion
i
ng
that
di
rect
M
P
PT
m
et
hods
are
widely
exp
lore
d
a
nd ad
a
pt
ed
as
rev
ie
we
d
in
[6
,
7]
.
P&O, H
C, a
nd
I
nC
ond
meth
ods ar
e mai
nly
a
dopted
i
n
ma
ny r
esea
rch
pa
pe
rs
due to thei
r
algo
rith
m’s
simpli
ci
ty,
w
hich
ca
n
be
easi
l
y
im
pleme
nted
,
as
w
el
l
as
t
he
ir
high
e
ff
ic
ie
nc
y
c
ompa
red
t
o
t
he
a
f
or
e
men
ti
on
ed
ind
irect
MPPT
te
ch
niques.
T
he
pr
i
nciple
of
the
P
&O
is
base
d
on
mea
su
ri
ng
the
vo
l
ta
ge
a
nd
c
urre
nt
of
the
PVG
it
erati
vely,
to
cal
c
ulate
the
inst
antaneous
P
V
power.
If
t
he
ne
w
cal
culat
ed
powe
r
val
ue
is
gr
eat
e
r
than
the
pre
vio
us
on
e
,
t
he
volt
age
is
per
tu
rb
e
d
posit
ively
an
d
the
ne
w
powe
r
val
ue
will
be
rec
orde
d
f
or
th
e
new
it
erati
on.
Othe
rw
ise
,
t
he
vo
lt
age
sho
uld
be
dec
reme
nted
a
nd
t
he
old
powe
r
val
ue
will
be
ke
pt.
T
he
op
e
rati
on
c
on
t
inu
es
unti
l
the
instanta
neous
powe
r
reac
he
s
the
M
P
P
[8
,
9]
.
P
&O
an
d
HC
hav
e
the
same
fun
dame
ntal
pri
nciple.
T
heir
main
dif
fer
e
nc
e
li
es
in
the
strat
egy
e
mp
l
oyed
for
co
ntr
ol
li
ng
the
el
ect
ronic
switc
h of t
he D
C
-
DC c
onve
rter. Hence
, P&O
g
e
ner
at
es t
he
appr
opriat
e duty c
ycle by
mea
ns
of
a
P
rop
or
t
ion
al
In
te
gr
al
(
PI)
c
on
t
ro
ll
er,
w
herea
s,
HC
c
on
t
rol
s
the
DC
-
DC
conve
rter
by
in
vo
l
ving
a
di
rec
t
per
tu
rb
at
i
on
on
t
he
du
t
y
c
ycle.
It
s
hould
be
menti
on
e
d
that
t
he
di
rect
duty
cy
cl
e
co
ntr
ol
strat
e
gy
us
ed
by
H
C
has
th
e
be
ne
fit
of
avo
i
ding a
PI c
on
t
ro
ll
er a
nd t
he
tria
l
-
e
rror a
ppr
oach f
or tu
ning it
s
gains (
Kp and
Ki)
.
The
aut
hor
in
[
10
]
te
ste
d
P
&
O,
HC
,
In
C
ond
a
nd
FL
Con
t
ro
ll
er
(
FLC
)
unde
r
dif
fere
nt
le
vels
of
irrad
ia
nce
to
com
par
e
thei
r
meas
ur
e
d
po
wer
wav
e
f
or
m
s.
FL
M
PPT
dem
onstrat
es
a
fast
respo
nse
ti
me
com
par
e
d
to
t
he
othe
r
in
vest
igate
d
MPPTs
.
H
oweve
r,
the
al
gorithm’s
c
omplexit
y
of
P
&O,
HC
a
nd
I
nCon
d
are
lo
we
r.
I
n
I
nCond
M
P
PT,
t
he
c
onduct
ance
an
d
t
he
i
ncr
eme
nta
l
co
nductance
are
cal
culat
ed
by
the
meas
ured
PV
c
urre
nt
a
nd
vo
lt
a
ge.
Th
en,
t
heir
val
ue
s
are
co
mp
a
r
ed
t
o
ma
ke
th
e
rig
ht
decisi
on
for
increme
ntin
g
or
dec
reme
nting
the
volt
age
re
f
ere
nce.
Th
e
main
obje
ct
ive
of
I
nCon
d
M
PP
T
is
t
o
a
chie
ve
the
op
ti
mal
c
onditi
on
of
M
PP
at
w
hic
h
t
he
instanta
neous
c
onduct
ance
is
e
qual
to
the
inc
re
mental
cond
uctance
[
11]
.
It
is
imp
or
t
ant
to
point
ou
t
that
in
P&
O,
HC
a
nd
I
nCon
d
M
PP
Ts,
us
i
ng
s
mall
per
t
urb
at
ion
ste
p
siz
e
incre
ases
the
ste
ad
y
sta
te
trackin
g
accurac
y.
H
owever,
the
al
go
r
it
hm
ma
y
fail
to
achie
ve
the
exac
t
M
PP
unde
r
f
ast
tran
sie
nt
var
ia
ti
ons
of
irrad
ia
nce.
O
n
the
co
ntra
ry,
us
i
ng
la
r
ge
per
t
urbati
on
l
eads
to
consi
der
a
ble
powe
r
rip
ples
in
ste
ad
y
-
sta
te
co
nd
it
io
ns
,
re
du
ci
ng
the
tracki
ng
e
ff
i
ci
ency
an
d
af
fecti
ng
the
sta
bili
ty
of
PV
s
ys
te
ms.
The
a
utho
r
in
[12]
pr
opos
e
d
a
va
riable
ste
p
siz
e
I
nCon
d
M
PP
T
to
ov
e
r
come
dr
a
w
back
s
of
us
in
g
a
fi
xe
d
ste
p
siz
e.
Simulat
io
n
res
ults
show
t
ha
t
thi
s
M
PPT
sti
ll
pr
esents
a
poor
performa
nce
unde
r
lo
w
i
rr
a
diance
le
vel.
A
n
ada
ptive
I
nC
ond
base
d
on
a
n
e
nh
a
nce
d
ste
p
m
odel
an
d
c
on
t
ro
l
strat
egy
to
trac
k
t
he
M
P
P
i
n
a
n
a
da
ptive w
a
y
has
b
een
p
r
opos
e
d
in
[13]
. I
ts
main
d
ra
w
ba
ck
is
the
di
ff
ic
ulty o
f
set
ti
ng
ma
ny
i
niti
al
par
amet
ers
inclu
ding
t
he
er
ror
per
mi
tt
ed
facto
r
an
d
preci
se
di
re
ct
ion
co
ntr
ol
-
s
cal
ing
factors (
N
1
a
nd
N2).
To
this,
the trial
-
er
r
or
a
ppr
oach is t
he on
l
y path t
o
t
une the
se r
a
ndom pa
ramete
rs.
As
disc
us
se
d
in
[
14]
,
a
we
ll
-
desig
ned
F
LC
can
offer
a
rob
us
t
c
ontrol
of
nonlin
ear
s
ys
te
ms
.
The
co
nce
ptio
n
phase
of
FL
C
f
or
c
on
t
ro
ll
ing
nonlinea
r
s
ys
te
m
does
not
re
qu
i
re
know
le
dg
e
of
the
s
yst
em’s
mathemat
ic
al
model.
It
inte
grat
es
only
t
he
exp
e
rts’
e
xperi
ence
int
o
the
desig
n
process
to
co
nv
e
rt
li
nguisti
c
values
into
a
c
on
t
ro
l
si
gn
al
by
mea
ns
of
t
hree
main
sta
ges
:
Fu
zzi
ficat
io
n,
infe
ren
c
e
a
nd
defuzzifi
cat
io
n.
FLC
has
been
hybri
diz
ed
with
va
ri
ou
s
Soft
Co
mputi
ng
(S
C
)
te
chn
i
qu
e
s
su
c
h
a
s
Genet
ic
Algo
rithm
(
G
A),
Pa
rtic
le
Sw
ar
m
O
ptimi
zat
ion
(PSO
),
Ar
ti
fici
al
Neur
al
Netw
ork
(ANN)
an
d
A
nt
Colo
ny
Op
ti
mi
zat
ion
(FLC
)
to
t
rack
the
M
PP
.
H
oweve
r,
hybr
i
d
FLC
-
SC
te
c
hniq
ues
ha
ve
hi
gh
c
omplexit
y,
as
the
y
nee
d
to
pr
ocess
th
e
th
ree
sta
ges
of
F
LC
as
well
as
to
te
st
a
popula
ti
on
of
duty
c
yc
le
s
or
volt
ag
es
by
SC
te
ch
niques.
This
makes
the
Hyb
rid
F
LC
-
SC
MPPT
s
the
m
os
t
cu
mb
e
rsome
an
d
co
mp
le
x
al
gorith
ms.
T
o
ge
t
rid
of
the
above
-
mentio
ned
dra
wb
ac
ks
an
d
t
o
im
pro
ve
the
P
V
s
ys
te
m
e
ff
ic
ie
ncy
,
FLC
ha
s
bee
n
hybri
di
zed
with
c
onve
ntion
al
M
PP
Ts.
A
n
int
el
li
gen
t
f
uzzy
discrete
pro
por
ti
on
al
-
inte
gr
al
-
der
i
vative
(
FL
-
DP
I
D
)
M
PPT
for
batte
ry
c
ha
rg
i
ng
con
t
ro
l
is
pro
pose
d
in
[15
]
f
or
en
ha
ncin
g
ba
tt
ery
li
fe
ti
me
and
re
du
ci
ng
powe
r
lo
ss.
T
he
co
nt
ro
ll
er
al
gorith
m
is
bas
ed
on
r
egu
la
ti
ng
the
powe
r
delive
r
ed
to
the
batte
ry
by
c
onsid
erin
g
t
he
tran
sit
ion
res
ponse
a
nd
the
rip
ples
in
the
ou
t
pu
t
vol
ta
ge
a
nd
c
urre
nt.
Nine
f
uzz
y
r
ules
ha
ve
be
en
us
e
d
t
o
a
c
hieve
bette
r
tr
ackin
g
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
3
,
Se
ptembe
r
2020
:
15
36
–
15
46
1538
performa
nce
c
ompare
d
to
co
nv
e
nt
io
nal
P&
O
an
d
In
C
ond.
To
s
urm
ount
the
dr
a
wb
ac
ks
of
us
in
g
a
fixe
d
ste
p
siz
e
HC meth
ods,
a hybrid
FL
-
HC
MPPT
co
ntr
ol
te
ch
nique
is propose
d
i
n
[16]
. FL
-
HC M
PP
T v
aries
the
ste
p
siz
e
to
im
prove
the
respo
ns
e
ti
me
unde
r
fa
st
va
riat
ion
s
of
i
rr
a
diance.
H
oweve
r,
os
ci
ll
at
ion
s
ar
ound
th
e
M
P
P
are
t
he
main
li
mit
s
of
t
his
MPPT.
A
n
amel
i
or
at
io
n
of
P
&
O
us
in
g
FLC
is
prese
nted
in
[
17]
.
L
ow
os
ci
ll
at
ion
s
and
hi
gh
ef
fici
ency
in
t
rack
i
ng
the
MPP
a
re
achieve
d
us
i
ng
the
pro
pose
d
strat
eg
y
c
omp
ared
to
c
onve
nt
ion
al
P&O.
Howe
ve
r,
t
he
ste
a
dy
-
st
at
e
os
ci
ll
at
ion
s
co
uld
not
be
c
omplet
el
y
el
im
inate
d.
Mo
reov
er,
H
ybrid
FL
-
P&O
M
PP
T
s
uffe
rs
f
rom
slo
w
r
esp
on
se
ti
me,
w
hich
ca
us
es
sig
nificant
powe
r
loss
unde
r
fast
var
ia
ti
on
s
of
irrad
ia
nce.
H
ybri
d
M
PPT
s
base
d
on
In
C
ond
a
nd
FLC
to
trac
k
the
M
PP
are
pro
po
s
ed
i
n
[18
-
20]
.
The
e
valuati
on
of
the
se
MPP
Ts
de
pends
on
the
typ
e o
f
me
mb
e
rsh
i
p
f
unct
ion
s
,
the
num
be
r
of
f
uzzy
rules,
an
d
the
trac
king
pe
rformance
un
der
dif
fer
e
nt
operati
ng
c
ondi
ti
on
s.
A
hybri
d
I
nC
ond
-
FLC
co
ntro
l
te
c
hniqu
e
is
pro
po
se
d
i
n
[
18]
.
The
rati
o
of
de
rivati
ve
powe
r
a
nd
volt
ag
e,
as
wel
l
as
the
va
riat
ion
of
this
rat
io
ar
e
cal
culat
ed
a
nd
em
ploye
d
a
s
the
FLC
i
nput
s.
T
he
FLC
outp
ut
is
passe
d
t
hro
ugh
a
P
I
c
ontr
ol
to
re
gu
la
te
the
s
witc
hing
conve
rter
duty
c
ycle.
The
MPPT
sho
ws
im
pro
ved
e
ff
ic
ie
ncy
a
nd
reli
ab
il
it
y
in
t
rack
i
ng
t
he
M
PP
.
H
ow
e
ve
r,
us
i
ng
49
fu
z
zy
r
ules
i
n
a
dd
it
ion
t
o
a
P
I
co
ntr
oller
i
ncr
eas
es
the
c
omplex
it
y
of
the
c
on
tr
ol
a
nd
slow
s
it
s r
es
po
ns
e ti
me.
A
co
m
bin
at
io
n
of
FL
(
9
fu
zz
y
ru
le
)
and
I
nCon
d
has
been
ex
pe
rimental
ly
te
ste
d
in
[19
]
.
The
al
go
rithm
may
fail
to
ac
hieve
t
he
acc
urat
e
MPP
f
or
s
om
e
operati
ng
conditi
ons.
T
he
pro
po
s
ed
MPPT
in
[20]
em
ploys
FLC
with
25
r
ules
wh
ic
h
are
desig
ne
d
by
c
onside
rin
g
t
he
i
ncr
e
mental
c
onduct
ance
pr
i
nc
iple
to
gen
e
rate
the
a
ppr
opriat
e
du
t
y
cycle
f
or
a
buck
-
boos
t
co
nverter
.
N
o
co
m
par
is
on
with
th
e
existi
ng
M
P
PTs
has
been
done
to
s
how
the
trac
kin
g
e
f
fici
enc
y
of
this
M
PP
T.
T
hu
s
,
t
he
majo
r
dr
a
w
back
of
th
ese
met
hods
is
their
dev
el
opment
a
nd
a
ppli
cat
ions
for
only
sta
nd
al
on
e
sy
ste
ms
with
out
con
si
der
i
ng
t
he
gr
i
d
an
d
ac
loads
.
Accor
dingly,
many r
esea
rches
ce
ntered on ele
ct
rici
ty
tran
sfer
f
rom
t
he
P
V
s
ys
te
m
to
g
r
id
ei
the
r
by
im
pro
ving
the
inv
e
rter
t
opol
og
ie
s
or
c
ontr
ollers’
sc
he
mes.
I
n
lo
w
volt
age
a
pp
li
cat
ion
s
,
the
us
e
of
a
si
ng
le
-
ph
ase
H
-
br
i
dg
e
ci
rcu
it
is
adequate
t
o
co
ordi
nate
the
P
V
s
ys
te
m
to
the
util
it
y
gr
i
d.
T
he
in
ver
te
r
is
ca
pa
ble
of
trans
ferrin
g
D
C
mea
sured
vo
lt
age
and
c
urre
nt
to
desi
red
A
C
wav
e
forms
r
especti
ng
the
s
ta
bili
ty
marg
i
ns
and
gu
a
ra
ntee
high
powe
r
qual
it
y
[21]
.
T
he
co
nt
ro
l
of
t
his
de
vi
ce
mig
ht
be
guaran
te
e
d
ei
ther
by
mea
ns
of
Direct
Power
C
ontrol
(DPC)
st
rateg
y
wh
ic
h
dep
e
nds
on
the
i
ns
ta
ntane
ous
act
iv
e
an
d
re
act
ive
powe
r
co
ntr
ol.
W
her
e
the
gates
switc
h
O
N/OFF
sta
te
is
done
util
iz
ing
a
lo
okup
ta
ble;
or
,
th
r
ough
a
n
in
direct
powe
r
meth
od
na
med
Vo
lt
age
O
rient
ed
C
on
tr
ol
(VOC).
T
his
te
ch
nique
depen
ds
on
the
cha
nge
betwee
n
sta
ti
onar
y
c
oor
din
at
e’s
α
β
and
sync
hrono
us
r
otati
on
co
ordinates
dq
a
nd
guara
ntees
high
dy
namic
and
sta
ti
c
per
f
orma
nce
via
a
n
in
ner
current
lo
op.
Detai
ls
of
t
hes
e
te
ch
niques
a
r
e
do
ne
i
n
[22
-
24]
.
T
he
VO
C
is
ad
op
te
d
t
o
a
chieve
the
pur
po
s
e
of
this
pa
per
an
d
it
s
deta
il
s
are
el
aborated
i
n
Sect
ion
3.
The
pr
e
sent
paper
pro
po
ses
a
hybr
i
d
M
PPT
te
chn
i
qu
e
that
br
i
ng
s
t
oget
he
r
the
a
dvanta
ges
of
f
uzzy
a
nd
I
nC
ond
for
imp
r
ov
i
ng
t
he
tra
ckin
g
ef
fici
en
cy
an
d
minimi
zi
ng
l
osse
s
wh
e
n
the
po
wer
tra
ns
f
err
e
d
t
o
t
he
AC
-
gr
i
d.
PV
sy
ste
m
co
m
po
sed
of
PVG,
DC
-
DC
conve
rter
c
ontrolle
d
by
H
ybr
id
FL
-
I
nCon
d
M
PP
T,
H
-
Brid
ge
DC
-
AC
in
ve
rter
as
so
ci
at
e
d
with
t
he
el
e
ct
rical
gr
i
d
th
rou
gh
a
n
L
-
filt
er
a
nd
con
t
ro
ll
ed
by
VO
C
st
rateg
y
us
in
g
the
cl
ass
ic
al
PI
te
ch
nique
is
dev
el
op
e
d
a
nd
te
ste
d
us
i
ng
MATL
AB
-
Simu
li
n
k plat
form
.
The desire
d o
bj
ect
ives to be a
chieve
d by the
dev
el
op
e
d M
P
PT ar
e:
−
Im
prov
i
ng the
respo
ns
e ti
me,
this al
lows fast
M
P
P trac
king.
−
En
han
ci
ng
t
he
powe
r
qual
it
y
by
dec
reasin
g
rip
ples
in
the
outp
ut
cu
rr
e
nt
a
nd
volt
age,
he
nce,
tra
nsfer
rin
g
maxim
um
pow
er
to
the
gr
i
d.
−
Ach
ie
ve
the
MPP
under ir
rad
i
ance
var
ia
ti
ons
.
−
M
a
ximizi
ng th
e tracki
ng ef
fici
ency
.
The
rest
of
thi
s
pa
per
is
orga
nized
as
fo
ll
ows:
fi
rstly,
the
desc
riptio
n
of
sy
ste
m
a
nd
it
s
pa
rameter
s
desig
n
a
re
give
n
in
Sect
io
n
2.
The
resea
rc
h
met
hod
is
e
xp
la
i
ne
d
i
n
Se
ct
ion
3.
The
S
imulat
ion
res
ul
ts
and
com
par
is
ons are
presente
d
in
Sect
ion
4
a
nd s
om
e c
oncl
us
i
ons a
nd futu
re
work are
g
i
ven in S
ect
io
n 5.
2.
SY
STE
M DESC
RIPTIO
N AND P
A
RAM
ET
ERS D
E
SI
GN
2.1.
System
de
scri
pt
ion
Figure
1
s
how
s
the
pr
opos
e
d
gr
i
d
-
c
onnecte
d
P
V
s
ys
te
m
.
It
include
s
a
P
V
G
c
onnecte
d
t
o
the
dc
-
li
nk
inv
e
rter
si
de
th
rou
gh
a
DC
-
D
C
boos
t
c
onve
r
te
r.
T
he
s
witc
hi
ng
de
vice
of
t
his
la
tt
er
is
c
ontr
olled
by
me
ans
of
an
im
pro
ved
f
uzzy
I
nCon
d
M
PP
T.
T
he
n,
t
he
inc
orp
or
a
ti
on
of
the
syst
em
to
t
he
gri
d
is
ens
ur
e
d
t
hro
ugh
a
n
H
-
br
i
dg
e
ci
rc
ui
t
top
ol
ogy,
w
hich
is
a
de
qu
a
te
for
lo
w
vo
lt
age
a
pp
li
cat
io
ns
.
L
-
filt
er
is
inserte
d
at
the
i
nv
e
rter
ou
t
pu
t
to
el
im
inate
the
high
-
fr
e
qu
e
nc
y
cu
rrent
rip
ples.
A
V
OC
strat
eg
y
is
util
iz
ed
t
o
con
t
ro
l
the
in
ver
te
r
switc
hes
sta
te
s
th
rou
gh
the
cl
assic
al
PI
c
on
t
ro
ll
er,
a
nd
t
o
ge
ner
at
e
the
s
witc
hin
g
si
gn
al
s
t
hro
ugh
P
ulse
Width
M
od
ulati
on techn
i
qu
e
(PW
M)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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t J
P
ow Elec
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ys
t
IS
S
N: 20
88
-
8
694
Grid
co
nnect
ed photov
oltaic
syste
m
ef
fi
ci
en
c
y and
qu
alit
y imp
r
ove
men
t
usi
ng
… (
A
m
ar
a Yas
mine
)
1539
Figure
1. G
rid connect
ed
P
V system im
plem
entat
ion
i
n M
A
TLAB/SI
MUL
INK
2.2.
Boo
s
t
c
onvert
er
pa
r
ame
ters
design
To
be
ne
fit
fro
m
the
P
VG
a
nd
extr
act
it
s
maximum
avail
a
ble
powe
r,
the
desig
n
of
the
DC
-
DC
sta
ge
is
necess
ar
y.
The
co
nverter
co
ntains
a
n
inducto
r,
capa
ci
tor
a
nd
a
powe
r
switc
h
(
M
O
SFET
or
IG
BT
)
con
t
ro
ll
ed
by
an
M
PPT
al
go
rithm.
Acc
ordi
ng
t
o
the
meas
ur
e
d
c
urren
t
a
nd
volt
age
at
the
P
VG
outp
ut
side,
the M
P
PT’s
c
ontr
ol v
aries
the
dut
y
c
ycle
of
the
DC
-
DC
co
nverter
t
o
t
rack t
he
M
P
P,
as
w
el
l
as
t
o
su
cces
sfu
ll
y
li
mit
the
high
cu
rr
e
nt
an
d
vo
lt
age
rip
ples
f
or
obta
inin
g
high
-
qual
it
y
in
the
distribu
te
d
pow
er
[18]
.
Con
se
quently
,
the
well
-
desi
gn
e
d
DC
-
DC
boos
t
c
onve
rter
is
esse
ntial
fo
r
ac
hievi
ng
this
goal
.
T
his
can
be
done
by
dete
r
minin
g
the
mi
nimum
values
of
P
V
outp
ut
capaci
t
or
C
pvmin
,
boos
t
in
du
ct
or
L
bmin
,
a
nd
boos
t
capaci
tor
C
bmin
us
i
ng the
fo
ll
owin
g rela
ti
on
s
[15
,
25]
:
=
∆
8
∆
(1)
=
2
∆
(2)
=
(
1
−
)
8
∆
(3)
wh
e
re
∆I
L
is
th
e
inducto
r
rip
pl
e
cur
re
nt
an
d
∆V
pv
is
the
volt
age
rip
ple
acr
oss
the
PVG.
D
is
the
du
t
y
cycle.
I
L
is t
he i
nducto
r
c
urrent
an
d f
is the
s
witc
hing
fr
e
quency
.
2.3.
Inv
er
ter
outp
ut
L
-
filter
des
ign
The
in
ve
rter
outp
ut
in
du
ct
or
(L
f
)
minimi
ze
s
the
cu
rr
e
nt
r
ipp
le
s
(
∆
)
cause
d
by
t
he
switc
hing
fr
e
qu
e
nc
y
(
)
of
the
in
ve
rter.
F
r
equ
e
ntly,
a
ri
pple
of
20
%
is
chosen
in
the
i
nv
e
rter
outp
ut
current
to
sel
e
c
t
the L
f
min
,
∆
can
be
e
xpresse
d
a
s
[
26]
,
[27]
:
∆
/
=
4
(4)
The mi
nim
um
inv
e
rter ind
uct
or (
)
can
be o
btained
a
s :
=
4
∆
(5)
It
is
im
portant
to
note
that,
the
DC
-
DC
c
onve
rter
an
d
t
he
H
-
bri
dge
i
nverter
a
re
as
sume
d
to
ha
ve
the same
sw
it
chin
g
fre
qu
e
ncy
value
(f=f
sw
)
t
o offer
a
high
dynamic
res
pons
e
of the
sy
ste
m.
3.
RESEA
R
CH MET
HO
D
The
pro
po
s
ed
gr
i
d
c
onnected
PV
sy
ste
m
c
ontr
ollers
are
de
velo
ped
withi
n
this
sect
io
n.
T
he
propose
d
FL
-
In
C
ondis
e
xp
la
ine
d
i
n
sub
-
sect
io
n
(a)
a
nd
sche
mati
zed
in
flo
wch
a
rt
of
Fig
ur
e
2.
T
he
V
OC
S
I
MULI
N
K
scheme
is g
i
ve
n by sub
-
sect
io
n (b) a
nd d
et
ai
l
ed
as
w
el
l.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
3
,
Se
ptembe
r
2020
:
15
36
–
15
46
1540
3.1.
Prop
os
ed
FL
-
InCond
MPP
T
In
ord
e
r
to
ma
ximize
po
wer
f
rom
the PVG
a
nd
en
ha
ncin
g
i
ts
eff
ic
ie
nc
y,
the d
esi
gn o
f
an
ap
propriat
e
M
PP
T
is
nece
ssary.
Accord
i
ng
l
y,
a
n
a
dv
a
nc
ed
hy
br
i
d
FL
-
I
nCon
d
MPP
T
is
pro
posed
by
c
ombi
ning
FL
an
d
In
C
ond
al
gorit
hm
s
.
T
he
fl
owchar
t
of
t
he
pr
opos
e
d
al
gorithm
is
il
lustrate
d
i
n
Fig
ur
e
2.
At
fi
rst,
the
al
gorithm
acqu
i
res
the
P
V
volt
age
a
nd
current
(V
pv
a
nd
I
pv
,
res
pecti
ve
ly),
as
well
a
s
the
loa
d
volt
age
(
V
dc
)
i
n
or
der
t
o
cal
culat
e
us
in
g
the
(
8
)
.
is
employed
a
s
a
sc
al
ing
fact
or
to
the
FLC
in
put.
It
represe
nts
the
rati
o
betwee
n
t
he
m
aximum
l
oad
volt
age
(
V
dcmax
)
an
d
ma
ximum
P
V
volt
age
(
V
mpp
).
The
vo
l
ta
ge
tra
nsfer
f
un
ct
io
n
of the
b
oo
st c
onve
rter is
writ
te
n
as
[
4]
,
[
19]
:
Figure
2. The
pro
po
se
d MP
P
T alg
or
it
hm fl
owcha
rt
=
=
1
1
−
=
(6)
wh
e
re
V
pv
,
V
dc
are
the
P
V
vo
l
ta
ge
a
nd
loa
d
vo
lt
age
,
res
pec
ti
vely
a
nd
I
pv
,
I
dc
a
re
the
P
V
cu
rr
e
nt
a
nd
load
cu
rr
e
nt,
r
especti
vely
.
D
max
is
sel
ect
ed
by
em
ployin
g
the
maxim
um
P
V
V
oltage
(V
m
pp
),
m
axim
um
powe
r
(P
mpp
)
a
nd the
r
esi
sti
ve
loa
d v
al
ue
(
)
acco
r
ding to
the
f
ollow
i
ng r
el
at
io
n
=
1
−
√
∗
(
7)
The val
ue
of
use
d
i
n
the
prop
os
e
d
met
hod
is
co
m
pute
d b
y
c
on
si
der
i
ng
(
6
)
and
(
7
)
as
fo
ll
ows
=
1
1
−
(8)
By
obta
inin
g
,
the
rati
o
of
the
ou
t
pu
t
a
nd
in
put
volt
age
of
t
he
bo
os
t
co
nve
rter
ca
n
be
e
xp
resse
d
us
in
g
a
n
a
da
ptive
value
as:
E
(
k
)
=
dV
dc
(
k
)
×
dV
pv
(
k
)
(9)
The variat
io
n
i
n
the
er
ror
E
(
k
)
can
b
e e
xpres
sed
a
s
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Grid
co
nnect
ed photov
oltaic
syste
m
ef
fi
ci
en
c
y and
qu
alit
y imp
r
ove
men
t
usi
ng
… (
A
m
ar
a Yas
mine
)
1541
dE
(
k
)
=
E
(
k
)
−
E
(
k
−
1
)
(10)
(
9
)
an
d
(
10
)
a
r
e
us
ed
as
i
nput
s
of
the
f
uzzy
sy
ste
m.
W
hen
the
value
s
of
E(k)
an
d
(
)
are
small
(i.e
the
insta
ntaneous
po
wer
is
ap
proac
hing
the
M
P
P)
,
a
s
mall
value
of
sh
oul
d
be
sel
e
ct
ed
by
the
FL
C.
Howe
ver,
in
t
he
in
the
ca
se
wh
e
re
E
(k)
a
nd
(
)
are
la
r
ge,
a
la
rg
e
valu
e
of
sh
oul
d
be
sel
ect
ed.
E(
k)
and
(
)
are
the
i
nputs
of
the
FLC
an
d
is
the
ou
t
pu
t.
T
he
input
var
ia
bl
es
are
div
i
de
d
int
o
five
membe
rs
hip
f
unct
ions:
NB
,
NS
,
ZE
,
PS
a
nd
PB.
The
refore
,
the
re
su
lt
in
g
num
bers
of
r
ul
es
are
25
proc
esse
d
by Mam
dan
i
f
uzzy in
fer
e
nce
sy
ste
m
(
with
max
-
min
).
Tab
le
1
recapitulat
es the
fu
zz
y r
ules.
Table 1
.
Fu
zzy
rules
E
dE
NB
NS
ZE
PS
PB
ZE
NB
NB
NM
NS
ZE
NS
NB
NM
NS
ZE
PS
ZE
NM
NS
ZE
PS
PM
PS
NS
ZE
PS
PM
PB
PB
ZE
PS
PM
PB
PB
The
dif
fu
zi
ficat
ion
sta
ge
us
es
seve
n
mem
be
rsh
i
p
functi
ons
(
NB:
ne
gative
big,
NS
:
ne
ga
ti
ve
small
,
NM
:
ne
gative
me
diu
m
,
ZE:
zer
o,
PS:
pos
it
ive
small
,
P
M
:
posit
ive
m
edium
PB
:
po
sit
ive
bi
g)
al
ongs
i
de
the cente
r of g
r
avity tec
hn
i
qu
e
for
calc
ulati
ng the a
ppr
opriat
e step size
,
=
∑
(
)
∑
(
)
(11)
wh
e
re
is
the
con
t
ro
l
sig
nal
pro
vid
e
d
by
the
FLC
a
nd
D
i
are
the
center
of
t
he
ma
x
-
mi
n
com
posit
ion
in
t
he
outp
ut
membe
rs
hip
f
un
ct
io
ns.
S
ha
pe
of
t
he
FLC
membe
rs
hip
f
un
ct
io
ns
are
s
how
n
i
n
Figure
3.
Fig
ure
3. M
e
m
ber
s
hip
f
unct
io
ns
: (a
) Inp
ut of
FLC:
E a
nd
dE
(b) O
utput
of FLC:
dD
The
duty
c
ycl
e
is
inc
reme
nted
or
dec
rem
ented
by
thr
ough
ca
rryin
g
ou
t
t
he
FLC
r
ules.
A
n
accurate
du
t
y
cycle
D
is
ob
t
ai
ned
by
co
m
bin
in
g
F
LC
a
nd
I
nCond
MPPT.
Var
ia
ti
ons
of
th
e
P
V
vo
lt
age
(dV
pv
)
a
nd the
PV
c
urre
nt (dI
pv
)
are
calc
ulate
d
as
foll
ows
(
)
=
(
)
−
(
−
1
)
(12)
(
)
=
(
)
−
(
−
1
)
(13)
-
If
dV
pv
is e
qu
al
to
zer
o,
the
va
riat
ion
of
P
V
c
urren
t
(dI
pv
)
is
cal
culat
ed.
If
dI
pv
is equ
al
ze
r
o,
it
mea
ns
that
the
M
PP
is
ac
hieve
d
a
nd
the
old
value
of
t
he
du
t
y
c
ycle
D(k
-
1)
is
kep
t
.
If
dI
pv
is
high
er
or
lo
wer
t
ha
n
zero, the
duty
cycle D
is inc
r
emented
or
dec
reme
nted, res
pe
ct
ively, b
y
a s
te
p
siz
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
3
,
Se
ptembe
r
2020
:
15
36
–
15
46
1542
-
If
dV
pv
is
dif
f
eren
t
f
rom
zer
o,
the
in
sta
ntan
eous
c
onduct
a
nce
(
(
)
(
)
)
a
nd
the
i
ncr
e
mental
co
nductance
(
(
)
(
)
)
are
cal
culat
e
d
a
nd
co
mp
a
re
d.
If
no
c
ha
nge
is
detect
ed
,
D(k
-
1)
is
kep
t.
H
ow
e
ver,
if
(
(
)
(
)
)
>
-
(
(
)
(
)
)
the
du
t
y
c
ycle is i
ncr
e
me
nted by a ste
p
siz
e
(dD).
Othe
rw
is
e,
the
duty c
ycl
e is dec
reme
nt
ed.
3.2.
Inv
er
ter
Cont
rol
The
volt
age
or
ie
nted
c
ontr
ol
or
V
OC
is
a
n
ind
irect
strat
eg
y
of
c
ontrolli
ng
t
he
act
i
ve
a
nd
reacti
ve
powe
r
durin
g
t
he
in
co
rpo
rati
on
of
m
ic
r
o
-
gri
ds
to
the
el
ect
rical
gr
i
d.
It
a
ims
at
ori
entin
g
the
c
urren
t
vecto
r
reg
a
rd
i
ng
the
l
ine
vo
lt
ag
e
ve
ct
or
thr
ough
a
ct
ive
an
d
react
ive
c
urren
t
c
ontr
ol[23
].
The
pr
i
ncipal
funct
ion
of
this
meth
od
is
to
minimi
ze
t
he
erro
r
be
twee
n
I
d
,Iq
(d
i
rect
an
d
qu
a
drat
u
r
e
pa
rts
of
th
e
measu
red
gri
d
current
and
t
ran
s
f
or
me
d
us
i
ng
Par
k
T
ran
s
f
or
mati
on
)
and
t
heir
re
fe
ren
ce
values
I
d
-
ref
,
I
qr
e
fr
es
pecti
vely
.
The
valu
e
of
Idref
is
obta
ined
th
r
ough
an
oute
r
PI
c
ontr
oller
lo
op
wh
ic
h
al
so
sta
bili
zes
the
inve
rter
DC
-
side
vo
lt
age
.
I
qref
is
ke
pt
equ
al
t
o
zer
o
(Iqr
e
f=0)
to
co
m
pensat
e
an
y
inj
ect
ed
reacti
ve
powe
r
to
th
e
s
ys
te
m
a
nd
gua
ran
te
e
un
it
power
fa
ct
or
.
These
er
rors
are
fe
d
t
o
P
I
co
ntr
ollers
in
a
n
Inner
Current
C
on
t
ro
l
lo
ops
ca
pa
ble
of
regulat
ing
the
outp
ut
H
-
br
i
dg
e
c
urren
t.
Finall
y,
V
da
nd
Vq
vo
lt
age
s
are
ge
ne
rated
a
nd
c
onve
rted
t
o
modu
la
ti
ng
si
gn
al
s
e
mp
l
oye
d
by
t
he
P
W
M
in
ve
rter
pulse
gen
e
rato
r.
The
a
dvanta
ge
of
this
met
hod
are
the
high
abili
ty
of
minimi
zi
ng
t
he
TH
D
a
nd
e
nsuri
ng
sa
ti
sfactory
dyna
mic
a
nd
sta
ti
c
pe
r
forma
nces
[
24].
T
he
c
ontr
oller
descr
i
bed
a
bove
is
dep
ic
te
d
i
n
Fig
ur
e
4,
w
hi
le
the
P
I
c
ontr
ol
tra
ns
f
er
f
unct
ion
is
do
ne
i
n
(
14
)
,
wh
e
rein
K
p
a
nd K
i a
re th
e
proporti
onal
and i
nteg
ral g
ai
ns
r
especti
vely
.
Figure
4. V
OC
H
-
bri
dge in
ve
rter c
on
t
ro
l
(
)
=
+
(14)
The deri
ved tra
ns
fe
rs funct
io
n o
f
the
d
-
q cu
rrents lo
ops a
re
done
a
s:
I
d
(
s
)
I
dr
ef
(
s
)
=
I
q
(
s
)
I
qr
ef
(
s
)
=
k
P
+
k
i
s
L
f
s
2
+
(
k
P
+
r
)
s
+
k
i
(15)
wh
e
re
r
is t
he
i
nv
e
rter
outp
ut i
nducto
r's resi
s
ta
nce .
The
sta
nd
a
r
d
s
econd
orde
r
tra
ns
fe
r funct
io
n
i
s d
e
fine
d
as
(
s
)
=
k
p
ω
n
2
s
2
+
2ζ
ω
n
2
s
+
ω
n
2
(16)
wh
e
re
=
√
,
ζ
=
+
2
√
ω
n
and ζ a
re
na
tural fre
qu
e
nc
y an
d
dam
ping
rati
o of
t
he
s
yst
em r
es
pecti
vel
y.
Com
par
in
g
(
15
)
a
nd
(
16
)
,
w
e
get the c
urre
nt
con
t
ro
l
gains
a
s
k
P
=
2
ω
n
L
f
−
r
(17)
Evaluation Warning : The document was created with Spire.PDF for Python.
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t J
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ow Elec
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ys
t
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S
N: 20
88
-
8
694
Grid
co
nnect
ed photov
oltaic
syste
m
ef
fi
ci
en
c
y and
qu
alit
y imp
r
ove
men
t
usi
ng
… (
A
m
ar
a Yas
mine
)
1543
k
i
=
L
f
ω
n
(18)
Obviousl
y,
the
desi
gn
of
gains
de
fine
d
by
the
e
qu
at
i
on
s
mu
st
guara
nte
e
the
sta
bili
ty
mar
gin
s
an
d
the dy
namic
pe
rformance
.
4.
RESU
LT
S
A
ND AN
ALYSIS
This
sect
io
n
is
de
vo
te
d
t
o
e
va
luati
ng
the
pe
rformance
of
t
he
pro
po
se
d
MPPT.
To
this
e
nd,
a
nalyse
s
of
ma
ny
performa
nce
i
nd
ic
e
s
at
diff
e
re
nt
op
e
rati
ng
c
ondi
ti
on
s,
as
well
as
c
ompa
risons
with
co
nve
ntion
a
l
P&O
a
nd
I
nC
ond
for
gri
d
-
c
onnected
m
ode
are
car
ried
out
.
Firstl
y,
the
pro
po
se
d
M
P
PT
is
eval
uated
un
der
sta
nd
a
rd
te
st
c
onditi
on
(S
TC;
1
kW/
m²
at
25
°C)
.
S
eco
ndly
,
te
sts
unde
r
fa
st
va
ry
i
ng
ir
ra
diance
co
ndit
ion
s
a
re
carried
out.
Finall
y,
a
co
mpa
rison
to
co
nv
entional
P&
O,
In
C
ond
is
pe
rformed
t
o
va
li
date
the
pr
opos
ed
te
chn
iq
ue.
The
M
at
la
b
-
Simul
ink
s
of
t
war
e
pa
ckag
e
has
be
en
em
ployed
f
or
im
pleme
nting
t
he
P
V
sy
st
em,
as
sh
ow
n
in
Fi
gur
e 1
.
T
he
sim
ul
at
ion
par
a
mete
rs
a
re
pr
ese
nte
d
in
Ta
ble 2.
Table
2
. T
he
impleme
nted
syst
em
Para
mete
r
set
ti
ngs
Sy
m
b
o
l
Para
m
eter
Valu
e
PV
Mod
u
le
PMPP
Maximu
m
po
wer
3
3
4
.905 W
VMPP
Vo
ltag
e at
P
m
ax
4
1
.5 V
IM
PP
Cu
rr
en
t at
P
m
ax
8
.07
A
DC
-
DC
Co
n
v
erter
CPV
PV capacito
r
110
f
Lb
Bo
o
st in
d
u
ctan
ce
3
m
H
Cd
c
DC
-
Link
Cap
acito
r
3300
f
fsw
Switch
in
g
f
requ
en
cy
2
0
KHz
AC sid
e
Lf
Filter
in
d
u
cto
r
3
m
H
rf
Filer
resisto
r
0
.01
o
h
m
Vg
Grid v
o
ltag
e
220V
fsw
Switch
in
g
f
requ
en
cy
2
0
KHz
4.1.
Te
st
un
der ST
C
(
1kW/
m²
at
25°C)
Figure
5
s
how
s
the
measu
re
d
cu
rr
e
nt,
vo
lt
a
ge
a
nd
po
wer
I
pv
,
V
pv
an
d
P
pv
,
res
pecti
vely
unde
r
STC
.
S
hort
t
ran
sie
nt
ti
me
has
bee
n
obta
ined
by
the
pro
pose
d
M
PP
T,
w
hich
is
ar
ound
30
ms
.
Th
rou
ghout
this
op
e
rati
on
c
ondi
ti
on
,
the
insta
ntane
ous
P
V
powe
r,
P
pv
has
been
mainta
in
ed
at
334
W,
wh
ic
h
is
the
de
sire
d
maxim
um
po
wer
t
hat
must
be
ob
ta
ine
d
at
STC
(F
ig
ur
e
5.
c
)
.
As
ca
n
be
see
n
f
rom
Fig
ur
e
5.
a
.
and
b,
the
insta
ntane
ous
volt
age
(V
pv
)
a
nd
cu
rr
e
nt
(I
pv
)
are
a
rou
nd
their
maxim
um
value
s,
w
hich
are
41.5
V
,
8.0
7
A
,
resp
ect
ivel
y.
F
igure
6.(a)
s
ho
ws
the
volt
age
at
t
he
i
nv
e
rter
DC
-
side
an
d
it
s
ref
e
re
nce
(
V
dc
a
nd
V
dc_ref
)
un
der
STC.
It
ca
n
be
note
d
that
t
he
dc
volt
age
ha
s
bee
n
bo
os
te
d
to
t
he
desire
d
le
vel,
w
hich
is
40
0V.
T
he
re
fore,
the
pro
posed
M
PP
T
is
capa
ble
of
re
gula
ti
ng
t
he
volt
age
and
minimi
zi
ng
l
os
s.
He
nc
e,
the
in
ver
te
r
ou
t
pu
t
current
wa
veform
is
purel
y
sinu
s
oid
al
an
d
al
so
well
s
yn
chr
oniz
ed
with
the
gri
d
volt
age
as
s
how
n
i
n
t
he
Figure
6.
(
b).
this
permi
ts
the
trans
fer
of
maxim
um
power
t
o
the
gr
i
d
an
d
e
nsures
un
it
po
wer
f
act
or
.
Additi
on
al
l
y,
the
anal
ys
is
of
the
T
H
D
us
i
ng
MATL
AB/SI
M
UL
I
NK
P
OWER
G
UI
f
or
both
vo
lt
age
a
nd
current
gi
ves
va
lue
s
of
0.0
2%
an
d
1.1
6%
res
pecti
vely
w
hic
h
c
onf
orms
t
o
that
gi
ven
by
I
EEE
519
-
s
tan
da
rd
.
The
act
ive
po
wer ex
ported
by th
e
in
ver
te
r
i
s equal t
o DC
-
powe
r
w
hile t
he
r
eact
ive
pow
er r
e
sts eq
ual t
o
ze
ro.
Figure
5 .P
V
outp
ut(a) cu
rr
e
nt
, (b)vo
lt
age
and(c)
Powe
r
at
STC
(25°
C
&
1 kW
/m²
)
Figure
6. (a
) D
C
-
li
nk
V
oltage
, (b) PCC
Vo
lt
age a
nd
current
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
3
,
Se
ptembe
r
2020
:
15
36
–
15
46
1544
4.2.
Te
st
un
der
va
ry
ing irradi
ance
En
vironm
e
ntal
co
nd
it
io
ns
a
re
ti
me
varyin
g.
Ther
e
f
or
e,
che
ckin
g
the
abili
ty
of
the
pro
pose
d
M
PPT
in
tracki
ng
the
M
PP
unde
r
fa
st
var
ia
ti
on
s
of
irrad
ia
nce
is
ne
cessar
y.
T
his
has
bee
n
acc
ompli
sh
e
d
by
va
ry
i
ng
the
ir
rad
ia
nce
ma
ny
ti
mes
within
a
few
seco
nd
s
.
F
ou
r
le
ve
ls
ar
e
c
on
si
der
e
d
in
this
te
st,
w
hic
h
a
re
1kW/m²,
0W/
m
²,
0.5kW/m²
,
0.9kW/m².
MPPs,
co
rresp
on
ding
t
o
t
he
af
or
e
mentio
ne
d
irrad
ia
nce
le
ve
ls
are:
334.5
3W,
0W,
166.2
W
a
nd
301.7
1W,
re
spe
ct
ively.
As
c
an
be
see
n
f
rom
Fig
ur
e
7,
th
anks
to
t
he
pr
opos
e
d
M
PP
T,
t
he
ou
t
pu
t
PV
volt
ag
e
(
V
pv
)
a
nd
cu
rr
e
nt
(
I
pv
)
a
re
kep
t
a
r
ound
th
ei
r
ma
ximum
values
V
m
pp
an
d
I
mpp
,
resp
ect
ivel
y.
T
his
mea
ns
that
the
insta
ntane
ous
powe
r
of
th
e
P
VG
achie
ve
s
the
MPP
(the
re
d
das
hed
li
ne
)
fo
r
each
le
vel
of
ir
rad
ia
nce
(F
ig
ure
7c).
High
pe
rformance
a
nd
sta
bili
ty
are
s
how
n
in
t
he
DC
-
li
nk
volt
age
w
hich
is
kep
t
ar
ound
it
s
ref
e
ren
c
e
(400V
)
un
de
r
irra
diance
var
ia
ti
ons
ap
pl
ie
d
to
the
P
V
syst
em
Fig
ur
e
8.
Fu
rt
hermo
re,
t
he
i
nv
e
rter
ou
tpu
t
c
urre
nt
ke
eps
a
si
nu
s
oi
dal
wa
ve
f
or
m
with
var
ia
ble
am
plit
ud
e
Fi
gure
9
sta
ying
in
phas
e
with
the
gr
id
vo
lt
age
.
Small
THD
value
s
are
sho
wn
i
n
bo
th
curre
nt
an
d
vo
lt
age
a
nd
th
e
FFT
analysis
giv
e
s
values
of
1.16% an
d 0.0
1% r
especti
vely
.
Figure
7. P
V
outp
ut (
a
),
c
urre
nt
(
b) volt
age
a
nd (
c
)
Power u
nder
fa
st varyin
g
i
rr
a
di
ance con
diti
on
Figure
8.DC
-
li
nk volt
age
(
V
dc
) under
f
ast
va
r
ia
ti
on
s
of
irra
diance
Figure
9. PCC
Vo
lt
age
and c
urre
nt un
der fast
v
a
riat
ion
s
of ir
rad
ia
nce
4.3.
Co
m
pa
ri
s
on
with
conve
nt
i
onal P&O
an
d InCond
MP
PTs
In
t
his
s
ub
-
se
ct
ion
,
f
ur
the
r
assessme
nts
of
performa
nce
unde
r
fast
va
riat
ion
s
of
ir
r
adiance
an
d
te
mp
erat
ur
e
a
r
e
carrie
d
out.
To
this
e
nd,
t
wo
well
-
know
n
M
PPT
meth
od
s
,
namely
c
onve
ntion
al
P
&O
[13]
and
I
nCon
d
[
28]
are
em
ploy
ed
in
the
pr
es
ent
co
mp
a
rison.
Re
s
ults
sho
wing
wav
e
for
ms
of
th
e
P
V
outp
ut
powe
r
obta
ine
d
by
t
he
pro
posed
M
PP
T,
P
&O
a
nd
I
n
-
C
ond
are
de
picte
d
in
Fig
ur
e
10
.
Table
3
repre
sents
a
com
par
is
on
in
te
rms
of
c
onve
rg
e
nce
ti
me,
st
eady
-
sta
te
er
ror,
a
ver
a
ge
pow
er
at
1k
W/m
²,
trackin
g
e
ff
ic
ie
ncy,
gr
i
d
c
urren
t
T
HD
an
d
the
e
rror
bet
ween
P
PV
an
d
P
g
bet
we
en
t
he
pro
po
se
d
M
P
PT,
P&
O
an
d
In
C
ond.
As
ca
n
be
see
n
f
rom
Table
3,
the
nu
merical
va
lues
of
co
nve
rg
e
nce
ti
me
de
monstrate
th
e
su
pe
rio
r
tra
ckin
g
performa
nce
of
th
e
pro
po
se
d
MPPT
(
20
m
s).
W
herea
s,
P
&O
an
d
I
nCond
ta
ke
a
rou
nd
40.
2m
s
an
d
38.9ms,
resp
ect
ivel
y,
t
o
re
ach
the
M
PP
.
P
&O
presents
pow
er
rip
ple
ar
ound
the
M
PP
an
d
c
on
s
eq
ue
ntly,
l
ow
e
r
eff
ic
ie
nc
y
in
tracki
ng
t
he
MPP
(a
r
ound
97.
04%),
Com
pa
red
t
o
98.3%
for
In
C
ond.
Wh
il
e
the
pr
opose
d
method p
rese
nt
s
a
hig
h
tra
cki
ng
e
ff
ic
ie
nc
y
of
99.
07%
.T
he
powe
r
trans
mit
te
d
from
t
he
P
VG
t
o
the
gri
d
unde
r
the
co
ntr
ol
of
the
pro
posed
M
PP
T
has
a
l
ow
po
we
r
loss
(aroun
d
4
W)
du
e
t
o
the
c
ontr
ol
of
both
t
he
P
V
vo
lt
age
(
V
pv
)
a
nd
t
he
in
ver
te
r
dc
-
si
de
volt
ag
e
(V
dc
)
,
w
hile
the
powe
r
los
s
us
in
g
P
&O
a
nd
I
nCond
is
high
(
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Grid
co
nnect
ed photov
oltaic
syste
m
ef
fi
ci
en
c
y and
qu
alit
y imp
r
ove
men
t
usi
ng
… (
A
m
ar
a Yas
mine
)
1545
6.57W
a
nd
8.4
2
W
res
pecti
ve
ly
).
T
his
le
ad
s
to
a
low
T
H
D
in
c
urren
t
de
li
ver
ed
at
PC
C
1.
16%
c
omp
ared
t
o
1.43% a
nd 2.03%
us
in
g
I
nCond a
nd
P&
O ,
resp
ect
ivel
y.
Figure
10. PV
powe
r
e
xtracte
d by P&
O,
I
nC
ond
a
nd the
pr
opos
e
d MP
PT
unde
r
fa
st va
riat
ion
s
of irra
di
ance
Table
3.
P&
O,
In
C
ond
a
nd th
e pro
posed
M
P
PT
Pe
rformanc
es
MPPT
M
eth
o
d
s
Tr
(m
s
)
Stead
y
-
state
err
o
r
(
W
)
Av
erage po
wer at
1
0
0
0
w/m
²
Ef
fic
ien
cy
(
%)
Grid cu
rr
en
t T
H
D
(%)
|
−
|
(W)
P&
O
4
0
.2
9
.90
5
0
325W
9
7
.04
2
.03
8
.42
InC
o
n
d
3
8
.9
5
.69
2
4
3
2
9
.2116
W
9
8
.3
1
.43
6
.57
Prop
o
sed
m
eth
o
d
20
3
.11
0
6
3
3
1
.7904
W
9
9
.07
1
.16
4
.31
5.
CONCL
US
I
O
N
In
this
pa
per
a
n
imp
rove
ment
of
the
PV
s
ys
t
em
eff
ic
ie
nc
y
and
of
t
he
qual
it
y
of
the
pow
er
delive
red
thr
ough
a
ne
wly
pro
po
se
d
FL
-
In
C
ond
M
PP
T
that
use
s
an
a
utom
at
ic
tun
in
g
-
c
ontr
oller
of
ste
p
siz
e,
inv
est
igati
ng
the
featu
res
of
bo
t
h
I
nCond
a
nd
F
L
c
o
ntr
ollers.
I
n
fact,
the
imp
r
ov
e
d
FL
-
In
C
ond
met
hod
al
l
ow
s
the
minimi
zat
ion
of
powe
r
lo
ss
betwee
n
the
PVG
side
a
nd
gr
id
side
(
4.3
1
w)
c
ompare
d
t
o
6.5
7W
an
d
8.4
2W
us
in
g
In
C
ond
an
d
P
&O
re
sp
ect
ively
,
off
ers
bette
r
dyna
mic
an
d
ste
a
dy
-
sta
te
pe
rfo
rma
nces,
mini
mize
s
distor
ti
ons
in
c
urren
t
th
rou
gh
the
T
HD
im
pro
veme
nt.
S
o,
high
powe
r
qu
al
it
y,
ef
fici
enc
y,
an
d
reli
abili
ty
a
re
ob
ta
ine
d
c
omp
ared
t
o
e
xisti
ng
M
PPT
te
ch
ni
qu
es
.
M
oreo
ve
r,
resu
lt
s
unde
r
sta
ndar
d
a
nd
dy
namic
c
onditi
on
s
ver
if
y
the
feas
ibil
it
y,
e
ff
ect
iv
eness
a
nd
a
cc
uracy
of
the
pla
nn
e
d
c
on
tr
ol,
wh
e
re
a
fast
c
onve
rg
e
nce
s
pe
ed
is
achieve
d
us
i
ng
the
p
r
opos
e
d met
hod
c
ompa
red
to
I
nC
ond and
P
&O wit
h on
l
y
20ms
,
c
ompa
red
to
3
8.9
ms
a
nd
40.2
s
,
res
pecti
vely.
I
n
our
f
ut
ur
e
resear
ch
,
we
inte
nd
to
e
xp
e
rime
ntall
y
validat
io
n
of
t
h
e
pro
po
se
d
m
et
hod,
integrate
it
to
la
rg
e
scal
e
a
nd
hybri
d
gri
d
-
co
nn
ect
e
d
micr
o
-
gr
i
d
s
ys
te
ms
in
cl
ud
in
g
li
near
and
non
-
li
near
loads
by k
ee
ping it
s
eff
ic
ie
nc
y
a
nd
powe
r qu
al
it
y con
ti
nu
ously at
max
im
um l
ev
el
.
REFERE
NCE
S
[1]
REN21
MEMBERS
,
“R
ENEWA
BLE
S 2019
G
LOBAL
STATUS
REPOR
T,
”
20
19.
[2]
K.
Kac
hh
iya
,
M.
Lokha
nd
e,
and
M.
Patel,
"M
ATLAB/Sim
uli
nk
mode
l
of
sol
ar
P
V
modul
e
and
MP
PT
al
gorit
hm
,
"
in
Nati
ona
l
Con
f
ere
nce on Re
ce
n
t
Tr
ends
in Engi
nee
ring
&
Te
chn
ology
,
2011.
[3]
R.
Boukenou
i,
R.
Bouhed
ir,
A.
Mellit,
and
S.
Sagla
m
,
"Exp
erime
nt
al
assess
m
e
nt
of
Poly
C
-
Si,
CIGS
and
Cd
T
e
Photovolt
aic
t
e
chnol
ogi
es
und
er
re
al
work
in
g
condi
t
ions,"
in
2019
In
te
rn
ati
onal
Con
fe
re
nce
on
Wireless
Technol
ogi
es,
E
mbedde
d
and
Int
el
li
g
ent Sy
stems
(WITS)
,
pp.
1
-
4,
2019.
[4]
M.
A.
En
any,
M.
A.
Fara
h
at,
and
A.
Nasr,
"M
odel
ing
and
e
val
ua
ti
on
of
main
ma
x
im
um
po
wer
point
tracki
ng
al
gorit
h
ms f
or
p
hotovol
taics
sys
t
em
s,"
Re
newab
l
e
and
Susta
inable
En
ergy
Revie
w
s,
vol. 58, pp. 15
78
-
1586,
2016
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[5]
R.
Boukenoui,
H.
Salhi,
R.
Bra
dai
,
and
A
.
Mel
l
it
,
“A
new
int
e
lligent
MP
PT
m
ethod
for
stand
-
alone
photovolta
ic
sys
te
ms
oper
at
i
ng
under
f
ast
tr
ansie
nt
va
riation
s
of
shading
pa
t
te
rns,”
So
l.
En
e
rgy
,
vo
l.
124
,
p
p.
124
–
142
,
Feb
.
2016.
[6]
M.
A.
Ena
ny
,
M.
A.
Far
ahat,
and
A.
Nasr,
“
Modeli
ng
and
e
val
ua
ti
on
of
m
a
in
m
axi
mu
m
po
wer
point
tr
ac
ki
ng
al
gorit
h
ms
for
photovol
taics
sy
stem
s,”
R
ene
wa
ble
and
Sustain
able
Ene
rgy
Revie
ws
,
vol
.
58
.
El
sevi
er
L
td,
pp
.
1578
–
1586,
01
-
May
-
2016.
[7]
M.
A.
Abdourra
zi
q
and
M.
Maa
roufi,
"Expe
r
im
e
nta
l
Veri
f
icati
on
of
the
Main
M
PP
T
Techni
ques
for
Photovolt
aic
Sys
te
m",
Int
ern
ati
onal
Journal
of
Pow
er
Elec
tronic
s
and
Dr
i
ve
Syste
ms
(I
JP
E
DS)
,
Vol.
8,
No.
1,
pp.
384
–
39
1
,
Marc
h
2017
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[8]
Z.
Salam,
J.
Ah
me
d,
a
nd
B
.
S.
Merugu,
"
The
a
ppli
c
at
ion
of
sof
t
com
put
ing
me
t
hods
for
MP
PT
of
PV
sys
te
m
:
A
te
chno
logi
c
al a
n
d
stat
us r
eview,"
Applied Ene
rgy
,
vol. 107, pp. 13
5
-
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2013
.
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