Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
10
,
No.
4
,
A
ugus
t
2020
,
pp.
4400
~
44
15
IS
S
N:
20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v
10
i
4
.
pp4400
-
44
15
4400
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om/i
nd
ex
.ph
p/IJ
ECE
Integr
al slid
ing
-
mode c
on
tro
ll
er
for maxi
mu
m power poin
t
tracking
in the
grid
-
conn
ec
t
ed ph
otovolt
aic s
ystem
s
Nour
-
Ed
dine
Tariba
, Naim
a
Ik
ken,
Ahm
ed H
ad
d
ou,
A
bdelha
di Bou
knadel
,
Hafsa E
l
O
m
ar
i,
Ham
id El
O
mari
La
bora
tor
y
of
R
ene
wabl
e Ene
rg
y
,
Env
ironment a
nd
Deve
lopmen
t
(L
ERE
D).
Fac
ulty
of
Scie
n
ce and T
e
chnol
og
y
,
Univer
sit
y
Hass
an
1
st
,
Moroc
co
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ma
r 19,
2019
Re
vised A
ug 11, 2
019
Accepte
d Aug
29
, 20
19
The
output
pow
er
gene
r
at
ed
in
the
photovol
t
aic
m
odule
s
d
epe
nds
both
on
the
solar
r
adi
a
tion
and
the
te
m
per
at
ur
e
of
th
e
solar
cells.
To
m
axi
m
iz
e
the
eff
i
ci
en
c
y
of
the
s
y
stem,
it
i
s
req
uire
d
to
moni
tor
the
m
axim
um
power
point
of
the
pho
t
ovolt
aic
s
y
s
te
m
.
For
thi
s
purpose,
m
onit
or
ing
th
e
m
axi
m
um
power
point
(MP
PT)
of
phot
ovolt
aic
s
y
st
ems
should
be
as
quic
k
an
d
ac
cur
atel
y
as
p
oss
ibl
e
for
inc
r
ea
sing
en
erg
y
p
roduc
ti
on
,
whic
h
ult
imat
e
l
y
inc
re
ase
s
the
cos
t
-
eff
i
ci
en
c
y
of
th
e
photovoltaic
s
y
stem.
Thi
s
pap
er
proposes
a
new
appr
oa
ch
for
MP
PT)
usi
ng
the
concept
of
the
integr
al
s
li
ding
m
ode
cont
roller
(ISM
C)
to
ensure
fast
and
pre
ci
se
m
onit
oring
of
the
pea
k
power.
The
per
form
ance
of
the
ISM
C
is
signifi
ca
nt
l
y
i
nflue
nc
ed
b
y
th
e
choi
c
e
of
the
slid
ing
surfa
ce
.
To
assess
th
e
reliab
i
li
t
y
ISM
C
cont
rol,
the
result
s
hav
e
bee
n
compar
ed
with
those
of
a
PI
cont
roller.
Th
e
result
s
obt
ai
n
e
d
are
used
to
eva
lu
at
e
th
e
pe
rform
anc
e
of
th
e
ISM
C
strat
egy
under
diff
erent
cl
imat
ic
condi
ti
ons
.
Fina
lly
,
th
e
eff
ec
t
iveness
of
the
proposed
soluti
on
is
conf
irmed
using
sim
ula
ti
ons
in
P
SIM
to
ols
and
expe
ri
m
ent
al
result
s
were
used
to
eva
lu
at
e
th
e effect
iv
ene
ss
of the
proposed
appr
o
a
ch.
Ke
yw
or
d
s
:
DC/DC c
onve
r
te
r
Photo
vo
lt
ai
c s
yst
e
m
s
MPPT
Sli
din
g m
od
e c
on
t
ro
l
Copyright
©
202
0
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Nour
-
E
ddine T
ariba,
Lab
or
at
ory
of
Re
new
a
ble E
ne
rg
y,
Envi
r
on
m
ent an
d De
ve
lop
m
ent (
LER
ED),
Facu
lt
y o
f
Scie
nce a
nd Tec
hnology,
Un
i
ver
sit
y Ha
s
san 1
st
,
BP 577,
2600,
Sett
at
-
Mor
occ
o
.
Em
a
il
:
No
ured
din
eTa
riba
@gm
ai
l.co
m
1.
INTROD
U
CTION
The
MPPT
m
et
ho
d
f
or
phot
ovoltai
c
syst
e
m
s
intends
to
identify
the
operati
ng
po
i
nt
w
here
the
product
of
outp
ut
vo
lt
ag
e
an
d
c
urre
nt
is
m
os
t
sign
ifi
cant.
T
he
or
et
ic
al
ly
,
the
G
PV
pro
duces
m
axi
m
u
m
powe
r
w
hen
t
he
re
is
a
m
at
chi
ng
im
ped
ance
betwee
n
G
PV
and
l
oad.
The
r
efore,
the
M
P
P
T
process
gu
a
r
antees
that
the
outp
ut
im
ped
ance
a
nd
t
he
loa
d
im
p
edan
ce
of
the
GPV
cel
ls
a
re
gr
a
dual
ly
harm
on
iz
ed.
As
c
lim
a
ti
c
factors i
nf
l
uence t
he
outp
ut im
ped
ance of th
e GPV
, MPP c
an
be
ac
hie
ve
d
if the l
oad
im
ped
a
nce is a
dju
ste
d i
n
real
-
ti
m
e
to
m
on
it
or
the
outp
ut
i
m
ped
an
ce
of
the
GPV.
And
f
or
bette
r
unde
rst
and
i
ng,
the
eq
uiv
al
ent
i
m
ped
ance
R
opt
of
GPV
is
de
fine
d
as
the
r
at
io
betwee
n
the
MPP
vo
lt
ag
e
VMPP
a
nd
t
he
MPP
c
urrent
IMPP
,
(i.e.
Ro
pt=
U
MPP/
IMPP
).
T
he
sta
te
of
the
env
i
ronm
ent
changes
,
an
d
so
Rop
t.
N
eve
rth
el
ess,
so
m
e
pr
ob
le
m
s
of loa
d
a
dap
ta
t
ion
e
xist as
des
cribe
d
in
[1,
2]
.
The
m
os
t
popula
r
MPP
T
al
gorithm
s
are
the
I
nc
rem
enta
l
Condu
ct
a
nce
IN
CC
wh
ic
h
is
base
d
on
the
analy
sis
of
the
cond
uctanc
e
var
ia
ti
on
a
nd
it
s
influ
ence
on
the
operati
ng
po
int
an
d
the
p
ert
urb
an
d
ob
serve
(P
&
O)
wh
ic
h
is
con
sist
to
disturb
the
PV
volt
age
w
it
h
ste
ps
iz
e
volt
age
an
d
an
al
yz
ing
the
re
su
lt
ing
powe
r
[3
-
4].
The
res
ult
for
these
al
go
rit
hm
s
is
the
volt
age
VMPP
(
resp
IM
PP)
w
it
ch
cor
re
spo
nds
to
the
m
axi
m
u
m
powe
r.
T
he
m
os
t
sig
nifican
t
con
ce
r
n
f
or
a
ll
these
MPPT
s
is
the
de
gr
e
e
of
de
pende
nc
y
of
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
I
nte
gr
al
sli
ding
-
mode
control
le
r for ma
xi
mum po
we
r
point
tracki
ng
…
(
No
ur
-
Ed
din
e
T
ar
iba
)
4401
the
MPPTs
m
on
it
ori
ng
res
ponse
on
the
siz
e
of
the
distu
rb
a
nce.
F
urt
he
rm
or
e,
the
trac
king
sig
nal
osc
il
la
te
s
appr
ox
im
at
ely
arou
nd
it
s
re
fe
ren
ce
point,
an
d
this
eve
n
un
der
ste
ady
-
sta
t
e
co
nd
it
io
ns
[
5
]
.
It
is
c
ru
ci
al
t
o
us
e
a
seco
nd
lo
op,
ge
ner
al
ly
a
P
I
co
ntr
oller
to
keep
the
MPP
trackin
g
acc
ur
acy
[6
]
.
The
se
co
ntr
ol
la
ws
m
ay
be
insuffici
ent
be
cause
they
are
no
t
reli
able,
pa
rtic
ularly
wh
e
n
the
req
ui
rem
e
nts
on
dynam
i
c
char
act
erist
ic
s
an
d
accuracy
a
re
ve
ry
stric
t.O
n
the
oth
e
r
ha
nd,
it
'
s
i
m
po
rtant
to
li
nea
rize
t
he
syst
em
m
od
el
ar
ound
a
s
pecific
op
e
rati
ng
po
i
nt
,
wh
ic
h
is
usu
al
ly
the
PPM
at
a
par
ti
cular
conditi
on.
Sin
ce
the
PV
m
od
ule
an
d
the
DC/DC
conve
rter
a
re
non
-
li
near
by
t
heir
natu
re,
ho
wev
e
r,
the
pe
r
for
m
ance
an
d
sta
bili
ty
of
the
li
near
co
ntr
oller
ar
e
lim
it
ed
in the vic
init
y of
the PPM
. Th
is c
onstrai
nt affect
s syst
e
m
p
erfor
m
a
nce sin
ce t
he
operati
ng
po
i
nt v
ari
e
s
with
unex
pect
ed
an
d
inevit
able
env
i
ronm
ental
disturba
nces.
T
o
so
lv
e
this
issue,
the
w
orkin
g
m
et
ho
d
descr
i
bed
in
t
he
li
te
ratur
e
[
7
,
8]
us
es
a
sli
di
ng
re
gu
la
to
r
(
SMC
)
to
c
ontr
ol
the
in
duct
an
ce
or
capaci
to
r
input
current
of
the
boos
t
co
nv
e
r
te
r
associat
ed
with
the
GPV
m
od
ule,
th
us
ens
uri
ng
th
e
ov
e
rall
sta
bili
ty
of
the
syst
em
at
al
l
op
e
rati
ng
points.
T
he
so
l
ution
pr
opos
e
d
i
n
this
pa
per
co
nsi
der
s
m
ulti
ple
casca
de
c
on
tr
ollers
as
fo
ll
ows:
Th
e
P&O
MPPT
al
gorithm
is
us
ed
with
PI
c
ontrolle
r
to
pro
vi
de
the
ref
e
re
nc
e
to
the
SMC
wh
ic
h
gen
e
rate
the
MOSFET
act
ivati
on
sig
nal.
Howe
ver,
the
desig
n
of
t
hes
e
three
c
ontrol
le
rs
is
do
ne
se
par
at
el
y,
wh
ic
h
com
plicates
the
per
fect
con
tr
ol
of
the
syst
e
m
.
In
corr
ect
cho
ic
e
of
P
&O
ste
p
siz
e
and
e
xecu
ti
on
pe
rio
d
m
ay
resu
lt
in
unsta
ble
syst
e
m
op
er
at
ion.
A
nd
c
an
not
gu
a
ra
ntee
the
sam
e
per
form
ance
ov
e
r
the
entire
op
e
rati
ng
rang
e,
as
t
he
PI
c
on
t
ro
ll
er
re
qu
i
res
a
li
near
iz
e
d
m
od
el
of
th
e
syst
em
aro
und
the
PPM.
I
n
fact,
inco
rr
ect
desig
n of any s
uc
h PI
c
ontrolle
r
has t
he p
otentia
l t
o
m
ake th
e
P
&O u
ns
ta
ble.
Ba
sed
on
these
pr
e
vious
w
ork
s
and
c
onside
r
at
ion
s,
a
nd
t
o
r
e
m
edy
undesir
able
eff
ect
s
on
t
he
ou
t
put
powe
r
of
the
GPV
an
d
to
e
xt
ract
it
s
m
axi
m
u
m
po
we
r
a
n
ada
ptati
on
st
age
bet
ween
t
he
G
PV
a
nd
t
he
load
is
us
e
d,
w
hich
is
us
ually
a
DC
-
DC
co
nverter
,
The
input
of
the
DC/DC
conve
rter
pa
rt
is
fo
rm
ed
by
the
PV
gen
e
rato
r
a
nd the
ou
t
pu
t i
s c
onnecte
d
to
v
a
r
i
able loa
d.
A
c
ontr
ol syst
em
ch
ang
e
s the
duty
cyc
le
an
d
im
plici
tly
the
in
pu
t
im
ped
ance
of
the
c
onve
rter
un
ti
l
th
e
syst
em
reaches
the
M
PP
F
igure
1.
T
he
S
MC
com
bin
ed
with
IN
CC
ai
m
ed
at
pe
rfor
m
ing
a
f
ast
MPPT
a
ct
ion
on
P
V
syst
e
m
s
us
ing
a
cas
cade
c
ontrol.
T
his
a
ppr
oach
a
vo
i
ds
the
us
e
of
li
ne
arized
m
od
el
s
to
pro
vid
e
global
sta
bili
ty
in
al
l
the
op
erati
on
range.
In
s
uch
a
way,a
c
om
pact
desig
n
is
achiv
ed
al
so
re
duce
s
the
syst
e
m
c
os
t
an
d
com
plexity
.
The
sli
di
ng
m
od
e
co
ntro
l
has
widely
pro
ved
it
s
eff
ect
ivene
ss
thr
oug
h
re
porte
d
the
or
et
ic
al
stud
ie
s.
T
he
pr
i
ncipal
ob
j
e
ct
ive
consi
sts
that
the
dy
na
m
ic
of
the
syst
e
m
un
der
co
ntr
ol
is
fo
rce
d
to
f
ollo
w
exactl
y
the
require
d
res
pons
e.
T
he
be
nefi
t
of
su
ch
co
nt
ro
l
an
d
wh
at
m
akes
it
so
i
nteresti
ng
is
it
s
rob
us
tn
ess
agai
ns
t
sys
tem
dist
ur
ba
nc
es
an
d
un
ce
rta
inti
es
[9
,
10
]
.
In
t
his
pap
e
r,
t
he
inte
rest
was
fo
c
use
d
on
t
he
us
e
of
a
n
inte
gr
al
P
W
M
-
base
d
S
MC
in
the
P
V
syst
e
m
to
m
a
xim
iz
e
the en
e
r
gy g
e
ne
rated
by the
GPV a
nd to
im
pr
ov
e
the
sta
bili
ty
o
f
the syste
m
[11
]
.
Figure
1. Ci
rcui
ta
l schem
e o
f
the sli
di
ng m
od
e co
ntr
oller (S
MC
)
lo
op
The
sli
di
ng
m
od
e
co
ntr
ol
is
app
li
ed
to
fo
ll
ow
t
he
m
axi
m
um
po
we
r
of
t
he
photov
oltai
c
syst
e
m
[1
2].
Am
on
g
t
he
a
dvanta
ges
of
thi
s
co
ntr
ol
a
re
hi
gh
preci
sio
n,
good
sta
bili
ty
,
sim
plicity
,
inv
aria
nce,
r
obust
ness
,
et
c.
[13,
14]
,
m
aking
it
par
t
ic
ularly
su
it
able
fo
r
syst
em
s
with
i
m
pr
eci
se
m
o
dels.
Of
te
n,
it
is
pr
efer
a
ble
to
sp
eci
fy
t
he
dynam
ic
s
of
the
syst
e
m
du
ri
ng
the
c
onverge
nc
e
m
od
e.
In
th
is
case,
t
he
c
ontr
oller
str
uctu
re
has
two
pa
rts,
on
e
represe
nting
th
e
dynam
ic
s
durin
g
the
sli
ding
m
od
e
an
d
t
he
oth
e
r
re
present
ing
t
he
dynam
i
cs
of
the
disc
onti
nu
ou
s
syst
em
durin
g
the
co
nve
rg
e
nce
m
od
e.
The
pa
pe
r
is
org
a
nized
as
f
ollows:
Sect
ion
s
2.1
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S
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t J
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p
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ol.
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, No
.
4
,
A
ugus
t
2020
:
4400
-
441
5
4402
and
2.2
int
rod
uces
a
n
ove
rv
i
ew
of
the
phot
ovoltai
c
ge
nerat
or
a
nd
t
he
I
NC
C
MPPT
al
gorithm
,
resp
e
ct
ively
.
The
n
Sect
io
n
2.3
intr
oduc
es
the
no
n
-
li
ne
ar
m
at
he
m
a
tical
m
o
del
representin
g
the
GPV
an
d
the
boost
conve
rter.
Sect
ion
2.4
presen
ts
the
pr
opos
e
d
sli
di
ng
surfa
ce
an
d
inte
gr
al
sli
ding
m
od
e
con
t
ro
ll
er
struc
tur
e
,
and
der
i
vation
of
the
e
xisten
ce
conditi
on
s
.
Nu
m
erical
si
m
ulati
on
s
us
in
g
PSI
M
un
der
va
rio
us
co
nd
it
io
ns
are
pr
ese
nted
i
n
sect
ion
3.
Ex
pe
rim
ental
resu
lt
s
are
represe
nt
ed
in
4
il
lustrate
the
validi
ty
and
eff
ic
ie
ncy
of
the
pro
posed
i
nteg
ral
sli
din
g
m
od
e
con
tr
ollers
com
par
e
d
to
the
PI
strat
e
gy
.
Finall
y,
concl
us
io
ns
are
gi
ven
i
n
the last
secti
on
.
2.
PHOTO
VOL
TAIC S
YS
TE
M
2.1
.
Genera
t
or
p
h
oto
vo
lt
aic G
P
V
In
li
te
ratur
e,
s
ever
al
m
at
hem
at
ic
al
m
od
el
s
descr
i
be
t
he
operati
on
a
nd
be
hav
i
or
of
t
he
photov
oltai
c
gen
e
rato
r.
T
he
se
m
od
el
s
dif
f
er
in
the
cal
cul
at
ion
p
ro
c
ed
ure,
accura
cy
an
d
the
num
ber
of
pa
ram
et
ers
inv
ol
ved
in
the
cal
cula
ti
on
of
the
c
urren
t
-
volt
age
char
act
e
risti
cs
[15].
O
ne
diode
m
od
el
is
the
m
os
t
po
pula
r
.
Its
equ
i
valent
ci
rcu
it
is
a
p
-
n
jun
ct
io
n
an
d
wh
e
n
it
'
s
illum
inate
d
it
has
the
par
ti
cular
it
y
of
be
ing
a
ble
to
functi
on
as
a
gen
e
rato
r,
pro
du
ci
ng
a
s
hort
-
ci
rcu
it
c
urren
t
pro
portio
nal
to
the
il
lum
inati
on
.
T
he
e
quivale
nt
el
ect
rical
desig
n
of
a
ju
nctio
n
is
sho
wn
in
t
he
F
ig
ur
e
2
,
w
he
re
the
R
sh
an
d
R
s
are
respec
ti
vely
the
par
al
l
el
and
series re
sist
or
s
wh
ic
h
represe
nt
the los
se
s
[16].
The
e
nergy
s
ource
ge
nerat
es
the
s
hort
ci
r
cuit
cu
rr
e
nt
I
ph
,
w
hich
is
m
ai
nly
dep
e
ndent
on
s
ola
r
rad
ia
ti
on.
A
di
od
e
c
onduct
s
t
he
rev
e
rse
sat
urat
ion
cu
rr
e
nt
I
d.
The
c
urren
t
I
pv
sup
plyi
ng
the
l
oad
is
def
i
ned
by
the
di
ff
e
ren
ce
betwee
n
Id
an
d
I
ph
,
I
Rsh
.
T
he
cha
racteri
sti
c
I
pv
(V
pv
)
of
thi
s
m
od
el
is
g
i
ve
n
by
the
f
ollow
i
ng
equ
at
io
ns
:
I
pv
=
I
ph
−
I
d
−
I
R
sh
(1)
The o
utput cu
r
ren
t
-
volt
age
(I
-
V)
cha
racteri
st
ic
s can be calc
ulate
d by usi
ng
the
fo
ll
owin
g equ
at
io
n:
I
PV
=
N
P
I
SC
−
N
P
(
E
V
PV
N
S
V
T
Α
+
R
S
I
PV
N
S
V
T
Α
−
1
)
−
V
PV
R
SH
−
R
s
R
SH
I
PV
(2)
I
sc
:
sh
ort
-
c
irc
ui
t
cur
re
nt
of
P
V
cel
l,
R
sh
:
Sh
unt
Re
sist
or
,
R
s
:
resist
or
se
ries,
I
d
is
the
re
verse
sat
ur
at
io
n
c
urren
t
of
the
di
od
e
.
V
T
is
the
therm
al
vo
lt
age;
it
dep
e
nd
s
e
xclu
sively
on
the
tem
per
at
ure.
N
s
nu
m
ber
of
ser
ie
s
cel
l,
N
p
num
ber
of
par
al
le
l
cel
l.
To
sim
plify
the
pr
e
vious
m
od
e
l,
an
e
qu
i
valen
t
Thev
e
nin
ci
rc
uit
can
be
de
ri
ved
by
us
in
g
li
nea
rizat
ion
[
17
]
, a
s s
how
n
i
n
Fi
gure
3.
Figure
2. P
V
c
el
l
e
qu
iv
al
ent
c
ircuit
Figure
3. The
ve
nin
m
od
el
of
PV
Wh
e
re
R
eq
=
−
1
g
(
g
=
d
i
pv
d
v
pv
|
i
pv
=
I
mp
v
pv
=
V
mp
is
the
der
i
vative
of
t
he
no
n
-
li
nea
r
functi
on
i
pv
vs
vpv
at
t
he
operati
ng
MPP
point
a
nd
V
eq
=
V
mp
−
I
mp
g
is
t
he
e
quivale
nt
T
he
ven
i
n
vo
lt
age
.
T
he
SC
HO
T
T
POLY
240
poly
cryst
a
ll
ine
photov
oltai
c
m
od
ule
is
us
e
d
to
a
naly
ze
and
validat
e
the
MPPT
al
gorit
hm
,
the
el
ect
rical
ch
aracte
ris
ti
cs
are
sh
ow
n
in
the
T
able
1
[
18]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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t J
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g
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20
88
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8708
I
nte
gr
al
sli
ding
-
mode
control
le
r for ma
xi
mum po
we
r
point
tracki
ng
…
(
No
ur
-
Ed
din
e
T
ar
iba
)
4403
Table
1.
Elec
tr
ic
al
char
act
eris
ti
cs
of
PV
m
od
ule
No
min
a
l P
o
wer
[W
p
]
Pmpp
≥2
4
0
Vo
ltag
e at
No
m
in
al Power [V]
V
m
p
p
3
0
.4
Cu
rr
en
t a
t No
m
in
a
l Power [
A]
I
m
p
p
Op
en
-
Circu
it Volt
ag
e [
V]
Vo
c
Sh
o
rt
-
Circu
it Cu
rr
en
t [
A]
Isc
7
.90
3
7
.3
8
.47
STC (
1
0
0
0
W
/
m
2
,
AM
1
.5 c
ell te
m
p
e
rature
2
5
°C
2.2.
Increme
n
ta
l c
on
d
uct
an
ce
de
sign
The
I
ncr
em
ental
Con
duct
anc
e
Algorithm
(I
NCC
)
ta
kes
it
s
b
ase
on
the
fa
ct
that
the
m
axi
m
u
m
po
we
r
po
i
nt
(MPP
)
is
on
ly
reac
he
d
if
dP
PV
dV
PV
is
zer
o,
if
t
he
de
rivati
ve
is
neg
at
ive
t
he
operati
on
po
i
nt
is
on
t
he
ri
gh
t
of
the
m
axi
m
u
m
,
w
hen
it
is
posit
ive
the
op
e
r
at
ion
po
i
nt
is
on
the
rig
ht
[1
9,
20
].
T
he
M
PP
ca
n
t
her
e
fore
be
m
ai
ntained
by
com
par
ing
the
instanta
neous
cond
uctance
(
Gci
=
I/V
)
with
the
inc
rem
ent
of
the
c
on
duct
ance
(∆G
ci
=
∆I/∆
V)
,
as
s
how
n
i
n
the
fl
ow
c
hart
in
Fig
ure
4.
V
ref
c
orres
pond
s
to
the
re
fer
e
nce
vo
lt
age
f
or
w
hic
h
the
PV
pa
nel
is
fo
rc
ed
to
sta
r
t
op
e
rat
ing
.
I
n
the
MPP,
V
r
ef
=
V
MPP
.
O
nc
e
wer
eac
h
the
MPP,
we
m
a
i
ntain
the
co
rr
es
pond
ing
operati
ng
po
i
nt
.
Howe
ve
r
if
a
c
ha
ng
e
in
I
pv
is
note
d,
wic
h
is
relat
ed
to
a
cha
ng
e
in
the
atm
os
pher
ic
conditi
on
s
and
t
her
e
fore
a
change
of
t
he
ope
rat
in
g
po
i
nt
co
rr
es
po
nd
i
ng
t
o
the
MPP.
The
al
gorithm
var
ie
s
V
ref
upwa
rd
s
or
dow
nwar
ds
de
pe
nd
i
ng
on
the
new
MPP.
T
he
increm
ent
’s
siz
e
determ
ines
how
quic
kly
the
MPP
can
be
t
r
acked.
A
quic
k
trac
king
ca
n
be
ob
ta
ine
d
with
a
la
r
ger
i
ncre
m
ent,
bu
t
t
he
syst
em
cou
l
d
no
t
operate
ex
act
ly
at
the
MPP
a
nd
osc
il
la
te
s
aro
un
d
it
.
As
wi
th
the
P
&O
m
et
hod,
we
have
to
m
ake
a
ch
oice
betwee
n
high
sp
ee
d
a
nd
hi
gh
pr
eci
si
on,
th
eref
or
e
we
ha
ve
t
o
fi
nd
the
bes
t
com
pr
om
ise
between
t
hese
t
wo
va
riables.
We
ca
n
im
pr
ove
this
m
et
hod
by
nee
rin
g
the
op
e
rati
ng
point
to
the
MPP
i
n
the
first
ste
p,
a
nd
us
in
g
afte
rward
s
the
sec
on
d
c
on
tr
oller
t
o
accur
at
el
y
track
the
MPP.
Othe
rs
m
et
ho
d
a
re
c
om
m
on
ly
us
ed
i
n
the
li
te
rat
ur
e,
it
con
sist
of
usi
ng
a
co
ntr
oller
to
kee
p
the
V
pv
volt
age
op
erate
at
Vm
pp
and e
nsure
the sta
bili
ty
o
f
syst
em
[
21
,
2
2
].
Figure
4. Flo
w
char
te
of
inc
re
m
ental
co
nd
uctance alg
ori
thm
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In
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ol.
10
, No
.
4
,
A
ugus
t
2020
:
4400
-
441
5
4404
2.3
.
Boo
s
t
c
onvert
er
Desp
it
e
the
ch
oice
of
the
MP
PT
al
gorithm
,
a
DCDC
co
nv
e
rter
is
necessa
r
y
to
interface
the
GPV
a
nd
the
loa
d
to
le
ad
the
G
PV
to
the
MPPT
.
The
cl
assic
al
so
luti
on
desc
ribed
in
t
he
publishe
d
li
te
ratur
e
[
23]
consi
sts
of
a
DC/DC
co
nver
te
r
with
a
n
MPPT
co
ntr
oller
and
a
regulat
e
d
DC/AC
c
on
ver
te
r
t
o
in
j
ect
energy
into
the
netw
ork
an
d
ad
just
the
DC
bus
volt
age.
The
ove
r
al
l
syst
e
m
is
s
how
n
in
Figur
e
5.
This
so
lu
t
ion
is
widely
ad
opte
d
as
it
al
lows
sim
ultaneous
m
on
it
or
in
g
of
the
MP
P
and
po
wer
fa
ct
or
c
orrecti
on
[24].
The
DC/DC
c
onve
rter
wit
h
a
n
MPPT
co
ntr
oller
al
lows
th
e
GPV
bus
volt
age
to
be
re
gu
la
te
d
as
a
f
un
c
ti
on
of
the
MPP.
Be
sides,
the
DC/D
C
conver
te
r
se
le
ct
ed
in
this
arch
it
ect
ure
ge
ner
al
ly
us
es
a
ste
p
-
up
c
onve
r
te
r
to
adap
t
t
he
in
pu
t
vo
lt
age
to
a
high
vo
lt
a
ge
require
d
by
c
onve
ntion
al
gr
id
-
c
onnected
inv
e
rters
[
25
]
.
Th
us
,
the ef
fici
ency
and stabil
it
y of t
he photo
volt
ai
c syst
e
m
are
guara
nteed
..
Figure
6
re
pre
sen
ts
t
he
PV
s
yst
e
m
’s
el
ect
ri
cal
ci
rcu
it
without
los
ses
.
T
he
dynam
ic
equ
at
ions
ar
e
def
i
ned
to
re
present
the
syst
e
m
in
the
stat
e
sp
ace
wh
e
re
the
sta
te
var
i
ables
are
the
inducto
r
cu
rr
e
nt
and
the
vo
lt
age
at
input
capaci
tor
,
wh
il
e
the
input
of
the
c
onve
rter
is
t
he
duty
cy
c
le
,
the
Thev
e
nin
e
qu
i
va
le
nt
ci
rcu
it
m
od
el
r
epr
ese
nts
t
he
P
V
,
a
nd
the
out
pu
t
volt
age
of
the
boos
t
c
onve
rter
c
orres
pond
s
to
V
0
,
t
he
in
duct
or
current
is
iL,
and
t
he
duty
cy
cl
e
is
d
.
In
a
dd
it
io
n,
the
i
nducta
nce
of
th
e
ste
p
-
up
c
onve
rter
is
desi
gned
t
o
op
e
rate
in
c
onti
nu
ous
co
nduc
ti
on
m
od
e
C
CM
[2
6
,
2
7
]
s
ince
the
disc
onti
nuous
c
onduct
ion
m
od
e
(
DCM)
i
s
no
t
rec
omm
en
ded
for
the
s
olar
syst
em
a
nd
th
us
ca
us
e
s
a
la
rg
e
volt
age
rip
ple
an
d
os
ci
ll
at
ion
s
arou
nd
the MPP
[2
8
],
reducin
g
t
hat
way
the e
ff
ect
i
ve powe
r
in
j
ec
te
d
into
the
grid.
Figure
5. Ty
pi
cal
arch
it
ect
ure
of a
gr
i
d
c
onne
ct
ed
P
V
syst
e
m
Figure
6. The
ve
nin
m
od
el
of
GPV in
casca
de
w
it
h
boost
co
nv
e
rter
All ave
rag
i
ng
s
ta
te
equ
at
io
ns
ov
e
r
a
switc
hi
ng
per
i
od are gi
ven in t
he follo
wing set.
−
−
=
0
(3)
=
+
(4)
=
−
(
1
−
)
V
o
(5)
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In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
I
nte
gr
al
sli
ding
-
mode
control
le
r for ma
xi
mum po
we
r
point
tracki
ng
…
(
No
ur
-
Ed
din
e
T
ar
iba
)
4405
=
(
1
−
)
−
(6)
=
−
(7)
Con
tr
ol t
o i
nput
vo
lt
age
tra
ns
f
er
f
unct
ion
:
2
)
(
Ls
R
C
Ls
R
V
R
d
s
v
eq
in
eq
o
eq
pv
(8)
To
validat
e
th
e
MPPT
ap
pr
oach
we
c
onsider
a
c
omm
er
ci
al
pan
el
SC
HO
T
T
P
OLY
240
wh
ic
h
the
boost
co
nverter
f
ollow
s
the
featu
re:
Ci
n=
1000
uF
,
L=2
70uH,
C
o=10
0uF,
Vo
=
70V
with
a
s
witc
hing
fr
e
qu
e
ncy
at
50
kH
z
.
T
he
PI
co
ntr
oller
’s
de
sign
was
bas
e
d
on
pla
nt
da
m
pin
g
rati
o
a
nd
un
dam
ped
natu
ral
fr
e
qu
e
ncy.
Wefi
xed
t
he
dam
pin
g
rati
o
at
0.
7,
and
wesett
le
dt
he
ti
m
e
un
der
80
m
s
and
t
he
error
at
ste
a
dy
sta
te
unde
r
5%,
belo
ww
e
giv
e
the
P
I
c
on
tr
oler
’s
tra
ns
fe
r funct
io
n
:
(
)
=
0
.
001
+
0
.
71
(9)
2.
4
.
Sli
ding
m
od
e
controll
er desi
gn
In
rece
nt
deca
des
the
s
li
ding
m
od
e
con
t
ro
l
has
e
xp
a
nded
consi
der
a
bl
y
.
This
ph
e
nom
e
non
is
m
os
tl
y
cause
d
by
th
e
fast
an
d
finite
tim
e
con
ve
r
gen
ce
pro
pe
rty
of
e
rro
rs,
as
well
as
the
h
igh
r
obus
tne
ss
against
m
od
el
ing
errors
and
s
om
e
t
ypes
of
exte
rn
al
disturba
nces
[
2
9
,
30]
.
The
s
wi
tc
hin
g
functi
on
s
of
sta
te
var
ia
bles,
on
w
hic
h
is
base
d
t
his
non
-
li
near
co
ntr
ol,
a
re
us
e
d
t
o
c
reate
a
s
li
ding
s
urf
ace
or
hype
r
su
r
face,
in
the
pe
rs
pecti
ve
of
m
aki
ng
the
dynam
ic
s
of
syst
em
to
reach
a
gi
ven
sli
ding
surf
ace
a
nd
rem
ai
n
there
un
ti
l
equ
il
ib
rium
is
achieved
,
Fig
ur
e
7
.
This
dy
nam
ic
s
beco
m
es
then
inse
nsi
ti
ve
to
disturbance
s
m
ay
they
be
exter
nal or
para
m
et
ric
as long
as the
sli
ding
con
t
ro
l
’
s c
ondi
ti
on
s
a
re
s
ec
ure
d [31].
Figure
7. Illust
rati
on of slidi
ng s
urface c
onve
rg
e
nce
Our
fo
c
us
in
t
his
sect
io
n
is
t
he
a
pp
li
cat
io
n
of
SM
C
c
on
t
rol
to
a
boos
t
co
nv
e
rter
operati
ng
in
CC
M.
The
s
olu
ti
on
pr
opos
e
d
in
this
work
is
to
c
ons
ider
tw
o
casca
de
co
ntr
ollers
as
fo
ll
o
ws:
the
IN
CC
co
ntr
ol
wh
ic
h
is
desig
ned
t
o
prov
i
de
a
re
f
eren
ce
w
hich
is
propor
ti
on
al
to
the
opti
m
a
l
power
P
MPP
of
th
e
phot
ov
oltaic
gen
e
rato
r
,
as
well
as
the
SMC
con
tr
oller
wh
ic
h
is
in
c
harge
of
th
G
PV
volt
age
re
gu
la
ti
on
.
T
he
con
t
ro
ll
er
unde
r
stu
dy
is
a
seco
nd
-
ord
er
pro
portio
nal
-
integ
ral
-
der
i
va
ti
ve
(PID
)
S
M
vo
lt
age
-
m
od
e
c
on
tr
oller.
It
ta
kes
into
acco
unt
a
n
ad
diti
onal
vo
lt
age
error
i
ntegr
al
te
rm
in
the
con
t
ro
l
al
go
r
it
h
m
to
reduce
the
ste
ady
-
sta
t
e
error
of
the
pr
act
ic
a
l
SM
-
co
ntro
ll
e
d
syst
em
.
T
he
app
li
cat
ions
of
this
syst
em
com
m
on
ly
kn
own
as
inte
gral
SM
con
t
ro
l
has
at
tr
act
ed
m
any recen
t i
nterests s
uc
h
as their
us
e
in pow
e
r
co
nv
erters
[3
2
,
3
3
].
The
co
ntr
ol v
a
riable
x for the
P
ID S
MC
can
be
e
nunciat
ed
i
n
the
f
or
m
belo
w
:
x
=
[
x
1
x
2
x
3
]
=
[
V
ref
−
β
V
PV
d
dx
(
V
ref
−
β
V
PV
)
∫
(
V
ref
−
β
V
PV
)
]
(10)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
4400
-
441
5
4406
w
he
re
x
1
,
x
2
,
a
nd
x
3
are
res
pecti
vel
y
the
volt
age
e
rror,
t
he
volt
ag
e
er
ror
dy
nam
i
cs
(
or
t
he
rate
of
var
ia
ti
on
of
vo
lt
age
e
rro
r)
,
and
t
he
integ
ra
l
of
volt
age
e
r
ror.
Nex
t
ste
p
is
su
bs
ti
tu
ti
on
of
th
e
co
nvert
er
be
ha
vio
ral
m
od
el
s
unde
r
CC
M
i
nto
(
10),
an
d
tim
e
diff
ere
ntiat
ion
of
this
la
st
equ
at
io
n
pro
duce
the
sta
te
-
sp
ace
des
cri
ptions
require
d for th
e co
ntr
oller
de
sign o
f
the
GP
V
a
nd bo
os
t c
onve
rters
.
[
x
̇
1
x
̇
2
x
̇
3
]
=
[
0
1
0
−
1
Ci
n
.
L
−
1
Req
.
C
i
n
0
1
0
0
]
.
[
x
1
x
2
x
3
]
+
[
0
−
β
.
Vb
C
in
.
L
0
]
.
U
+
[
0
Vre
f
Cin
.
L
]
(11)
The
sta
nd
a
r
d
f
or
m
o
f
t
he
sta
t
e sp
ace
equati
on
giv
es:
x
̇
=
Ax
+
Bv
+
D
(12)
Af
te
r
the
sta
te
-
sp
ace
descr
i
ption
s
are
obta
ine
d
,
desig
ning
t
he
co
ntro
ll
er
is
the
nex
t
s
te
p
.
F
or
syst
em
s
li
ke
those
, it i
s
reco
m
m
end
ed
to h
a
ve
a
g
e
ne
r
al
SM contr
ol law that a
dopts
a
s
witc
hi
ng fu
nction s
uch as
:
u
=
{
1
whe
n
S
>
0
0
whe
n
S
<
0
(13)
w
he
re
S
, t
hat c
an be e
xpresse
d by the e
quat
ion bell
ow,
r
e
presents
the
insta
ntane
ous stat
e
trajecto
r
y:
S
=
α
1
x
1
+
α
2
x
2
+
α
3
x
3
=
J
T
x
(14)
W
it
h
J
T
=
[
α
1
α
2
α
3
]
;
α
1
,
α
2
,
α
3
re
pr
e
sen
ti
ng
the
sli
ding
co
e
ff
ic
ie
nts.
2.4
.1
.
Deriv
ati
on
of e
xistenc
e condi
tio
ns
The
ne
xt
im
p
or
ta
nt
issue
of
sli
ding
m
od
e
co
ntr
ol
a
fter
switc
hing
s
urf
ace
desi
g
n
is
gu
a
ra
nteei
ng
the
existe
nce
of
a
sli
di
ng
m
od
e
.
A
s
uitabl
e
co
nd
it
io
n
e
xi
sts
in
the
li
te
ratur
e;
it
is
ca
ll
ed
the
reac
ha
bili
t
y
conditi
on a
nd is writ
te
n
as
fo
l
lows
[
3
4
].
li
m
S
→
0
S
S
̇
<
0
(15)
Must be
sati
sfi
ed.
This ca
n be
expres
sed
as
{
S
̇
S
→
0
+
=
J
T
Ax
+
J
T
B
v
S
→
0
+
+
J
T
D
<
0
S
̇
S
→
0
−
=
J
T
Ax
+
J
T
B
v
S
→
0
−
+
J
T
D
>
0
(16)
0
<
C
in
L
(
α
3
α
2
−
1
C
in
L
)
(
V
ref
−
β
V
PV
)
−
β
L
(
α
2
α
1
−
1
C
in
L
)
(
i
PV
−
i
L
)
<
β
V
o
−
V
ref
(17)
This
c
on
t
ro
ll
er
’s
der
i
vation
proces
s
ca
n
be
su
m
m
arized
in
two
ste
ps.
Fi
rstly
,
the
form
ulati
on
of
the
eq
uiv
al
e
nt
co
ntro
l
sig
na
l
u
eq
wh
ic
h
is
a
sm
oo
th
f
unct
ion
of
the
dis
crete
in
pu
t
functi
on
u,
us
in
g
the
in
var
ia
nce
conditi
ons
by
set
ti
ng
the
tim
e
dif
fer
e
ntiat
ion
of
(
16)
as
S
̇
=
0
.
Seco
ndly
,
the
translat
io
n
of
the
eq
uiv
al
e
nt
con
t
ro
l
functi
on to
the i
ns
ta
nt
aneous
duty
r
at
io d of t
he pu
ls
e
-
wi
dth
m
odulator
u
̃
eq
=
−
[
J
T
B
]
−
1
J
T
[
Ax
+
D
]
(18)
w
he
re
0
<
u
̃
eq
<
1
Since
u
=
1
−
u
̃
, which
a
lso a
pp
li
es
u
eq
=
1
−
u
̃
eq
, th
e
contr
ol law ca
n be
wr
it
te
n
as:
0
<
u
eq
=
β
V
o
+
C
in
L
(
α
3
α
2
−
1
C
in
L
)
(
V
r
ef
−
β
V
PV
)
−
β
L
(
α
2
α
1
−
1
C
in
L
)
(
i
PV
−
i
L
)
+
V
r
ef
β
V
o
<
1
(19)
Finall
y,
tra
ns
la
ti
ng
t
he
e
quiva
le
nt
co
ntr
ol
f
unct
ion
(19)
to
the
du
ty
rati
o
d,
w
he
re
0
<
=
v
c
<
1
,
giv
es
t
he
f
ollow
i
ng
relat
ionships
f
or
the
con
t
ro
l
sig
nal
v
c
an
d
ram
p
sign
al
v
̂
ramp
=
1
for
the
pract
ic
al
i
m
ple
m
entat
io
n of t
he P
W
M
-
ba
se
d
SM c
ontrolle
r:
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
I
nte
gr
al
sli
ding
-
mode
control
le
r for ma
xi
mum po
we
r
point
tracki
ng
…
(
No
ur
-
Ed
din
e
T
ar
iba
)
4407
v
c
=
u
eq
=
Kp1
(
V
ref
−
β
V
PV
)
−
Kp2
(
i
PV
−
i
L
)
+
β
V
o
+
V
r
ef
β
V
o
(20)
a
nd
v
̂
ramp
=
1
w
ith
Kp1
=
C
in
L
(
α
3
α
2
−
1
C
in
L
)
β
V
o
and
Kp2
=
β
L
(
α
2
α
1
−
1
C
in
L
)
β
V
o
In
e
qual
it
y
(1
5)
do
es
n’
t
re
veal
an
y
detai
ls
abo
ut
the
ch
oice
of
SMC
coeff
ic
ie
nt,
bu
t
only
pr
ovides
gen
e
ral
in
f
orm
at
ion
ab
out
SMC
existe
nc
e.
T
he
c
ho
ic
e
of
sli
ding
c
oe
ff
ic
ie
nts
acc
ordi
ng
to
t
he
desire
d
dynam
ic
pr
ope
rtie
s
is
la
r
gely
detai
le
d
in
pr
evio
us
li
te
rature
[3
4
]
,
usi
ng
Ack
e
rm
ann
'
s
fo
rm
ula
fo
r
the
design
of
sta
ti
c
co
ntr
ollers.
In
this
way,
the
sta
bili
ty
con
diti
on
of
the
syst
em
is
autom
at
ic
ally
sat
isfie
d.
In
a
ddit
io
n,
the
re
so
l
ution
of
eq
uatio
n
S
=0,
w
hich
is
pro
portion
al
to
th
e
SMC
c
oe
ff
ic
ie
nts,
res
ul
ts
in
a
sec
on
d
-
orde
r
syst
e
m
w
it
h
th
re
e
po
s
sible re
sp
onse
ty
pes:u
nd
e
r
-
dam
pin
g,
crit
ic
al
d
am
pin
g,
a
nd
ov
e
r
-
da
m
pin
g.
α
1
α
2
=
10
T
s
(21)
a
nd the
desire
d dam
pin
g rati
on ca
n be set
us
i
ng
α
3
α
2
=
25
ε
2
T
s
2
(22)
w
he
re
ε
=
√
[
ln
(
M
p
100
)
]
2
π
2
+
[
ln
(
M
p
100
)
]
2
(23)
3.
SIMULATI
O
N RESULTS
AND DIS
C
USSION
The
pur
pose
of
this
par
a
gr
a
ph
is
to
pr
esent
t
he
sim
ulatio
n
r
esults
of
the
sli
ding
m
od
e
cont
ro
l
(S
MC
)
te
chn
iq
ue
an
d
to
c
om
par
e
it
with
t
he
IN
C
C
asscociat
d
with
cl
assic
al
PI
c
on
t
ro
ll
er
.
The
sim
ulati
on
was
perf
orm
ed
us
i
ng
PS
IM
s
of
t
war
e
a
s
s
how
n
in
t
he
Fi
gur
e
8
.
It
c
on
sist
s
of
va
ryi
ng
t
he
th
ree
par
a
m
et
ers
influ
e
ncin
g
t
he
PV
c
onve
rsion
c
hains,
nam
el
y
cl
i
m
at
ic
con
diti
on
s
G,
te
m
per
at
ur
e
T
an
d
load
R
.
T
he
r
esults
ob
ta
ine
d
are
presente
d
in
Figures
9
a
nd
10
for
durati
on
of
1
sec
ond.
Fo
r
th
e
te
st
of
each
par
am
eter
,
tw
o
par
am
et
ers
are
kep
t
co
ns
ta
nt
and
the
t
hird
par
am
et
er
is
var
ie
d
by
a
s
udde
n
cha
nge
twic
e
0.
3s
an
d
0.6
s
(step
pro
file
).
Each
fig
ur
e
sh
ows
a
com
par
iso
n
of
P
V
powe
r
betwee
n
the
IN
CC
+
SMC
and
I
N
CC
+PI
m
et
ho
ds.
A
z
oom
is
m
ade
in
two
places,
the
first
at
the
sta
rt
of
t
he
pro
file
to
il
lustrate
the
res
pons
e
ti
m
e
and
the sec
ond
t
o
s
how
t
he oscil
la
ti
on
s a
rou
nd th
e PPM.
Figure
8. Ci
rcui
ta
l schem
e fo
r
sim
ulatio
n of
SMC
loop
i
n
P
SI
M
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
4400
-
441
5
4408
Seve
ral
te
sts
ha
ve
been
pe
rfo
rm
ed
to
evalua
te
the
pe
rfor
m
ance
of
SMC
f
or
M
PP
m
on
it
or
i
ng.
First
,
the
co
ntr
ol
of
t
he
SMC
is
te
st
ed
by
va
ryi
ng
the
irra
diance
wh
il
e
fi
xing
th
e
load
t
o
100Ω
an
d
te
m
per
at
ur
e
at
25°C.
The
c
orrespo
nd
i
ng
si
m
ula
ti
on
s
com
par
e
d
with
P
I
con
t
ro
ll
er
re
sul
ts
are
sh
own
in
Figure
9
.
T
he
lo
w
trackin
g
sp
ee
d
of
t
he
c
onve
nt
ion
al
I
NCC
a
lgorit
hm
are
c
onfirm
ed
by
t
he
res
ults
with
PI
co
ntr
oller
unde
r
irrad
ia
ti
on
cha
ng
e
s
(a
bout
0.32
m
s)
with
sig
nificant
P
V
vol
ta
ge
fluctu
at
io
n
ar
ound
the
re
fer
e
nce
volt
ag
e
VMP
in
ste
ady
-
sta
te
.
In
th
e
oppos
it
e,
by
us
ing
t
he
sli
ding
co
nt
ro
l
schem
e
as
propose
d
(a
bout
0.1
6m
s)
a
hig
h
trackin
g
pe
rfo
r
m
ance
was
ex
hib
it
ed
.
Also,
wh
e
n
the
ir
rad
i
at
ion
cha
nges
without
over
shoo
ts
a
n
instant
aneous
eff
ect
on
the
P
V
vo
lt
a
ge
is
di
sp
la
ye
d
with
le
ss
fl
uctuati
on
a
rou
nd
V
MP
P
,
as
sho
wn
in
Fig
ure
9
(
b
)
(
blu
e
c
urve).
More
ov
e
r,
Fig
ur
e
9
(
a
)
c
om
par
e
s
the
pro
po
sed
c
on
t
ro
l
sc
hem
e
and
the
conve
ntion
al
I
NCC+
PI
MP
P
T
an
d
it
sh
ows
the
im
pr
ovem
ent
in
the
e
xtracted
P
V
powe
r
us
in
g
the
P
I
c
on
t
r
oller
.
T
he
res
ul
ts
al
so
c
onfir
m
that
the
opti
m
al
c
urren
t
is
sig
nificantl
y
aff
ect
ed
by
the
sudd
e
n
c
ha
ng
e
in
il
lum
inati
o
n
Fi
gure
9(
c
),
w
hile
the opti
m
al
v
oltage is
le
ss
a
ff
e
ct
ed
Fig
ure
9(b
).
(a)
(b)
(c)
(d)
Figure
9. Com
par
is
on b
et
wee
n
SMC
a
nd P
I c
on
t
ro
ll
er
un
de
r variat
ion
of i
r
rad
ia
nce (6
50W
/m
2
to
1000
W
/m
2)
; (a
)
G
PV p
ower
c
har
act
erist
ic
s,
(b) GP
V v
oltag
e, (
c
) GP
V
c
urren
t,
(d
)
Induct
ance c
urren
t
A
sec
ond
te
st
is
do
ne
for
the
PV
syst
e
m
under
a
c
onsta
nt
irrad
ia
ti
on
of
1000
W/m
2.
Bu
t
this
tim
e,
the
te
m
per
at
ure
an
d
t
he
loa
d
are
c
hange
d
from
10
0Ω
to
50
Ω
an
d
t
o
25Ω
Fig
ur
e
10
pr
esents
the
sim
ulati
on
resu
lt
s
with
th
ese
co
nd
it
io
ns
.
This
ti
m
e
the
differe
nce
in
respo
ns
e
ti
m
e
is
alm
os
t
the
sa
m
e,
it
is
abo
ut
0.
16
m
s.
Also
,
the
SMC
correct
s
a
li
tt
le
the
traj
ect
or
y
of
t
he
PPM
du
rin
g
th
e
transie
nt
re
gim
es.
In
ste
ad
y
sta
te
,
IN
CC
+P
I
os
ci
ll
at
e
aro
und
the
PPM
between
240W
an
d
23
9.82
vs
240W
and
238.9
9W.
Fr
om
these
resu
lt
s
,
it
can
be
sai
d
that
the
sli
din
g
m
od
e
c
on
t
ro
l
reac
hes
st
eady
sta
te
in
a
ver
y
s
hort
tim
e
in
the
order
of
m
illi
secon
ds.
And
it
is
no
t
i
nf
l
uen
ce
d
by
changin
g
weath
er
co
nd
it
io
ns
or
a
sudd
e
n
c
ha
ng
e
i
n
the
loa
d,
it
is
faster t
han the
PI
c
ontrolle
r
a
nd w
it
ho
ut osc
il
la
ti
ng
arou
nt
the PPM
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
I
nte
gr
al
sli
ding
-
mode
control
le
r for ma
xi
mum po
we
r
point
tracki
ng
…
(
No
ur
-
Ed
din
e
T
ar
iba
)
4409
(a)
(b)
(c)
(d)
Figure
10. C
om
par
ison
betw
een S
MC
a
nd
PI
c
ontrolle
r
und
e
r variat
io
n of t
he
l
oad an
d co
ns
ta
nt ir
ra
diati
on
;
(a)
GPV
powe
r
ch
a
racteri
sti
cs, (b) G
PV v
oltage,
(c) G
PV c
urren
t,
(
b) In
duct
ance c
urren
t
4.
E
X
PERI
MEN
TAL TE
ST
The
B
oo
st
c
onve
rter
is
us
e
d
as
a
n
a
da
ptive
sta
ge
bet
w
een
GPV
an
d
load,
an
d
is
use
d
to
bo
os
t
the
low
PV
outp
ut
volt
age
to
a
high
-
volt
age
DC
bus
ne
eded
f
or
in
ve
rter.
T
he
phot
ovoltai
c
curre
nt
an
d
the
in
du
ct
or
c
urre
nt
are
se
ns
e
d
by
a
Hall
ef
fe
ct
current
se
nsor
ACS
711
(
-
12.
5A
t
o
+
1
2.5
A)
,
the
GPV
volt
age
and
outp
ut
vol
ta
ge
of
the
bo
os
t
co
nverter
a
re
sen
sed
by
r
esi
stor
dev
i
der.
The
f
our
sig
nals
ar
e
i
nterf
a
ced
by
STM3
2F407
V
G
Disc
ov
e
ry
bo
a
r
d
thr
ough
the
AD
C
c
ha
nn
el
s
for
the
con
tr
ol
of
th
e
DC
-
DC
c
on
ver
te
r
.
The
STM3
2F4
07V
G
co
ntro
ls
the
har
dwa
re
par
t
by
us
in
g
on
e
P
W
M
outp
ut
for
switc
hing
the
MO
SFET
transisto
r
(S
C
H20
80KE
)
.
Th
e Figu
r
e 1
1
s
how
n
the expe
rim
ental
b
loc
.
The
strat
egy of co
nt
ro
l i
s i
m
pl
e
m
ente
d
in
tw
o
lo
op
c
ontr
ol,
on
e
is
sl
ow
f
or
the
I
ncre
m
ental
cond
uc
ta
nce
Al
gorithm
(5
00
Hz)
a
nd
the
ot
her
is
f
ast
for
SMC
and PI
volt
age c
on
t
ro
l l
oop wit
h
a
h
i
gh
fr
e
qu
e
ncy P
WM
50 kHz.
Figure
11. E
xp
erim
enta
l sy
stem
b
loc
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