I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
(
I
J
P
E
DS)
Vo
l.
1
7
,
No
.
1
,
Ma
r
ch
20
2
6
,
p
p
.
3
1
7
~
3
34
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
7
.
i
1
.
p
p
3
1
7
-
3
34
317
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
G
rid
-
tied
photo
v
o
ltaic sy
stem MP
PT alg
o
rithms pe
rforma
nce:
co
mpa
ra
tive a
na
ly
sis
L
o
uis
Nica
s
e
Ng
uef
a
ck
,
K
a
y
o
de
T
im
o
t
hy
Ak
ind
ej
i,
Aba
y
o
m
i A
.
Adebiy
i
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
P
o
w
e
r
En
g
i
n
e
e
r
i
n
g
,
F
a
c
u
l
t
y
o
f
E
n
g
i
n
e
e
r
i
n
g
a
n
d
t
h
e
B
u
i
l
t
E
n
v
i
r
o
n
me
n
t
,
D
u
r
b
a
n
U
n
i
v
e
r
s
i
t
y
o
f
T
e
c
h
n
o
l
o
g
y
,
D
u
r
b
a
n
,
S
o
u
t
h
A
f
r
i
c
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
an
2
3
,
2
0
2
5
R
ev
is
ed
Dec
2
3
,
2
0
2
5
Acc
ep
ted
J
an
2
3
,
2
0
2
6
Be
twe
e
n
2
0
1
5
a
n
d
2
0
2
4
,
g
l
o
b
a
l
so
lar
p
h
o
t
o
v
o
lt
a
ic
(P
V)
c
a
p
a
c
it
y
ro
se
sig
n
ifi
c
a
n
t
ly
fro
m
2
2
3
.
2
0
4
G
W
to
1
6
2
4
G
W,
c
o
n
tri
b
u
ti
n
g
t
o
t
h
e
re
d
u
c
ti
o
n
o
f
g
re
e
n
h
o
u
se
g
a
s
e
m
issio
n
s
a
ss
o
c
iate
d
with
fo
ss
il
-
f
u
e
l
-
b
a
se
d
p
o
we
r
g
e
n
e
ra
ti
o
n
.
S
o
lar
P
V
is
re
c
o
g
n
i
z
e
d
fo
r
it
s
e
n
v
ir
o
n
m
e
n
tal
b
e
n
e
f
it
s
a
n
d
is
in
c
re
a
sin
g
ly
se
e
n
a
s
a
v
iab
le
a
lt
e
rn
a
ti
v
e
f
o
r
a
l
o
n
g
-
term
su
sta
in
a
b
le
e
n
e
rg
y
su
p
p
l
y
.
Ho
we
v
e
r,
th
e
p
o
we
r
o
u
t
p
u
t
o
f
P
V
sy
ste
m
s
is
h
ig
h
l
y
d
e
p
e
n
d
e
n
t
o
n
a
tmo
sp
h
e
ric
c
o
n
d
it
i
o
n
s,
p
a
rti
c
u
la
rly
so
lar
irra
d
iatio
n
a
n
d
tem
p
e
ra
tu
re
,
wh
ich
c
a
n
c
a
u
se
flu
c
tu
a
ti
o
n
s
a
n
d
re
d
u
c
e
o
v
e
ra
ll
e
fficie
n
c
y
.
To
a
d
d
re
ss
th
is,
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
(M
P
P
T)
tec
h
n
i
q
u
e
s
a
re
e
m
p
lo
y
e
d
t
o
o
p
ti
m
ize
e
n
e
rg
y
e
x
trac
ti
o
n
u
n
d
e
r
v
a
ry
in
g
e
n
v
iro
n
m
e
n
tal
c
o
n
d
it
i
o
n
s.
T
h
is
stu
d
y
p
re
se
n
ts
a
c
o
m
p
a
ra
ti
v
e
a
n
a
ly
sis
o
f
fo
u
r
M
P
P
T
a
l
g
o
ri
th
m
s
,
p
e
rtu
r
b
-
a
n
d
-
o
b
se
rv
e
(P
&
O),
in
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
(In
C),
fu
z
z
y
l
o
g
ic
c
o
n
tro
l
(F
LC),
a
n
d
a
rti
f
icia
l
n
e
u
ra
l
n
e
tw
o
rk
(AN
N)
fo
r
g
r
id
-
ti
e
d
P
V
sy
st
e
m
s
u
sin
g
M
ATLAB/S
imu
li
n
k
.
Eac
h
a
lg
o
rit
h
m
wa
s
e
v
a
lu
a
ted
u
n
d
e
r
d
y
n
a
m
ic
c
o
n
d
i
ti
o
n
s
to
d
e
term
in
e
it
s
trac
k
in
g
e
fficie
n
c
y
a
n
d
re
sp
o
n
siv
e
n
e
ss
.
Th
e
re
su
lt
s
sh
o
w
t
h
a
t
wh
il
e
c
o
n
v
e
n
ti
o
n
a
l
m
e
th
o
d
s li
k
e
P
&
O
a
n
d
In
C
a
r
e
sim
p
ler,
th
e
y
a
re
les
s
e
ffe
c
ti
v
e
u
n
d
e
r
ra
p
i
d
ly
c
h
a
n
g
i
n
g
c
o
n
d
it
io
n
s.
F
LC
d
e
m
o
n
stra
tes
fa
ste
r
c
o
n
v
e
rg
e
n
c
e
b
u
t
re
q
u
ires
g
re
a
ter
c
o
m
p
u
tatio
n
a
l
re
so
u
r
c
e
s.
Th
e
in
telli
g
e
n
t
c
o
n
tro
ll
e
rs
d
e
m
o
n
stra
t
e
d
su
p
e
ri
o
r
p
e
rfo
rm
a
n
c
e
:
F
LC
a
c
h
iev
e
d
t
h
e
h
ig
h
e
st
p
o
we
r
o
u
t
p
u
t
o
f
1
.
0
1
9
×
1
0
⁶
W
wi
th
a
c
o
rre
sp
o
n
d
in
g
v
o
lt
a
g
e
o
f
1
.
4
2
2
×
1
0
⁴
V,
w
h
il
e
th
e
AN
N
a
lg
o
rit
h
m
fo
ll
o
we
d
c
l
o
se
ly
with
9
.
6
5
0
×
1
0
⁵
W
a
n
d
1
.
2
0
0
×
1
0
⁴
V,
re
sp
e
c
ti
v
e
l
y
.
Th
e
c
o
m
p
a
r
a
ti
v
e
in
si
g
h
ts
g
a
in
e
d
fro
m
th
is
a
n
a
ly
sis
o
ffe
r
p
ra
c
ti
c
a
l
g
u
i
d
a
n
c
e
fo
r
se
lec
ti
n
g
M
P
P
T
c
o
n
tr
o
ll
e
r
s
in
re
a
l
-
wo
rld
s
o
lar en
e
rg
y
a
p
p
li
c
a
ti
o
n
s.
K
ey
w
o
r
d
s
:
Ar
tific
ial
n
eu
r
al
n
etwo
r
k
Fu
zz
y
lo
g
ic
co
n
tr
o
ller
I
n
cr
em
en
tal
c
o
n
d
u
ctan
ce
Ma
x
im
u
m
p
o
wer
p
o
i
n
t
Per
tu
r
b
atio
n
a
n
d
o
b
s
er
v
atio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ab
ay
o
m
i A
.
Ad
e
b
iy
i
Dep
ar
tm
en
t o
f
E
lectr
ical
Po
wer
E
n
g
in
ee
r
in
g
,
Facu
lty
o
f
E
n
g
in
ee
r
in
g
a
n
d
th
e
B
u
ilt E
n
v
ir
o
n
m
en
t
Du
r
b
an
Un
i
v
er
s
ity
o
f
T
ec
h
n
o
l
o
g
y
Du
r
b
an
,
So
u
th
Af
r
ica
E
m
ail:
ab
ay
o
m
ia@
d
u
t.a
c.
za
1.
I
NT
RO
D
UCT
I
O
N
Ph
o
to
v
o
ltaic
(
PV)
ce
lls
ar
e
d
ev
ices
th
at
d
etec
t
elec
tr
o
m
a
g
n
etic
r
ad
iatio
n
a
n
d
d
is
s
ip
ate
cu
r
r
en
t
o
r
v
o
ltag
e,
o
r
b
o
th
,
in
r
esp
o
n
s
e
t
o
th
e
c
o
n
ce
n
tr
atio
n
o
f
s
o
lar
i
n
s
o
latio
n
.
I
ts
ap
p
licatio
n
h
as
g
o
n
e
ex
p
o
n
e
n
tial,
as
p
r
esen
ted
in
Fig
u
r
e
1
.
T
h
e
ap
p
r
o
ac
h
to
h
ar
n
ess
in
g
th
e
m
ax
im
u
m
p
o
te
n
tial
o
f
s
o
lar
en
er
g
y
is
ter
m
ed
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
.
An
MPPT
is
a
ty
p
e
o
f
elec
tr
o
n
ic
DC
to
DC
r
eg
u
lato
r
th
at
m
ax
im
izes
co
m
p
atib
ilit
y
ac
r
o
s
s
th
e
lo
ad
an
d
th
e
s
o
lar
PV
ar
r
ay
.
T
h
e
m
ai
n
ap
p
licatio
n
a
n
d
m
er
its
o
f
MPPT
in
s
o
lar
p
o
wer
s
y
s
tem
g
en
er
atio
n
ar
e
to
m
ax
im
ize
th
e
ca
p
ab
ilit
y
an
d
en
er
g
y
o
f
s
o
lar
ce
lls
[
1
]
.
E
s
ca
latin
g
g
l
o
b
al
en
er
g
y
n
ee
d
s
ar
e
d
r
iv
in
g
a
r
ap
id
r
is
e
in
th
e
c
o
n
s
u
m
p
tio
n
o
f
f
o
s
s
il
f
u
els,
r
esu
ltin
g
in
d
etr
im
e
n
tal
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
317
-
3
34
318
en
v
ir
o
n
m
en
tal
ef
f
ec
ts
lik
e
g
lo
b
al
war
m
in
g
,
ac
id
r
ain
,
a
n
d
o
zo
n
e
lay
er
d
ep
letio
n
[
1
]
.
T
o
s
af
eg
u
ar
d
th
e
E
ar
th
'
s
ec
o
lo
g
ical
b
alan
ce
,
it
is
im
p
er
ativ
e
to
d
iv
e
r
s
if
y
en
er
g
y
r
eso
u
r
ce
s
an
d
m
itig
ate
th
e
ad
v
er
s
e
im
p
ac
ts
ass
o
ciate
d
with
f
o
s
s
il f
u
el
tech
n
o
lo
g
ies.
Mo
r
eo
v
er
,
th
e
im
p
e
n
d
in
g
ch
al
len
g
es o
f
s
o
ar
in
g
f
u
el
c
o
s
ts
an
d
d
im
in
is
h
in
g
f
o
s
s
il
f
u
el
r
eser
v
es
m
ay
h
av
e
a
d
v
er
s
e
ec
o
n
o
m
ic
an
d
p
o
liti
ca
l
co
n
s
eq
u
en
ce
s
f
o
r
n
u
m
er
o
u
s
n
atio
n
s
in
th
e
co
m
in
g
y
ea
r
s
.
T
o
e
n
s
u
r
e
s
u
s
tain
ab
le
d
ev
elo
p
m
e
n
t,
en
h
an
cin
g
en
e
r
g
y
ef
f
icien
cy
a
n
d
m
a
x
im
izin
g
th
e
u
tili
za
tio
n
o
f
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
(
R
E
S)
ar
e
o
f
p
ar
a
m
o
u
n
t
im
p
o
r
ta
n
ce
[
1
]
-
[
4
]
.
On
e
p
o
ten
tial
s
o
lu
tio
n
t
o
ad
d
r
ess
th
is
cr
is
is
is
th
e
u
tili
za
tio
n
o
f
R
E
S.
Am
o
n
g
s
t
th
ese,
s
o
lar
en
er
g
y
h
o
ld
s
g
r
ea
t
p
r
o
m
is
e
an
d
is
ex
p
ec
ted
to
witn
ess
s
ig
n
if
ican
t
g
r
o
wth
in
its
m
ar
k
et
s
h
ar
e.
PV
ce
lls
ar
e
a
v
iab
le
m
eth
o
d
f
o
r
h
a
r
n
ess
in
g
s
o
lar
en
er
g
y
.
H
o
wev
er
,
a
ch
allen
g
e
with
th
e
s
o
lar
s
y
s
tem
is
its
in
ter
m
itten
t
n
atu
r
e,
as
th
e
tim
es
o
f
m
a
x
im
u
m
s
o
lar
in
s
o
latio
n
r
ar
ely
alig
n
with
en
er
g
y
d
em
an
d
.
Hen
ce
,
it
is
lo
g
ical
to
s
to
r
e
th
e
PV
en
er
g
y
g
en
e
r
ated
d
u
r
in
g
p
er
i
o
d
s
o
f
h
ig
h
s
u
n
lig
h
t
n
o
t
o
n
ly
to
s
u
s
tain
p
o
wer
s
u
p
p
ly
d
u
r
i
n
g
lo
w
-
in
s
o
l
atio
n
tim
es
o
r
clo
u
d
y
p
er
io
d
s
b
u
t
also
to
en
s
u
r
e
a
co
n
tin
u
o
u
s
elec
tr
ic
p
o
wer
o
u
tp
u
t
[
5
]
.
T
h
e
g
l
o
b
al
PV
r
o
o
f
t
o
p
an
d
u
tili
ty
-
s
ca
le
s
eg
m
en
ts
'
g
r
o
wth
is
d
ep
icted
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Glo
b
al
PV r
o
o
f
t
o
p
a
n
d
u
tili
ty
-
s
ca
le
s
eg
m
en
ts
g
r
o
w
th
[
2
]
On
e
o
f
th
e
p
r
im
a
r
y
c
h
allen
g
es
f
ac
in
g
PV
s
y
s
tem
s
is
o
p
er
atin
g
at
m
ax
i
m
u
m
p
o
wer
u
n
d
er
all
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
in
clu
d
in
g
tem
p
er
at
u
r
e
f
lu
ctu
atio
n
s
,
s
h
if
tin
g
s
u
n
lig
h
t,
s
h
ad
e
co
n
d
itio
n
s
,
an
d
m
o
d
u
le
ag
ein
g
.
T
o
ad
d
r
ess
th
ese
is
s
u
es,
an
ef
f
icien
t
alg
o
r
ith
m
ca
ll
ed
m
ax
im
u
m
p
o
we
r
p
o
i
n
t
tr
a
ck
in
g
(
MPPT)
h
as
b
ee
n
d
e
v
elo
p
e
d
[
6
]
,
wh
ich
wi
ll
in
cr
ea
s
e
s
y
s
tem
ef
f
icien
cy
an
d
lo
wer
co
s
ts
[
7
]
.
Ma
n
y
r
e
s
ea
r
ch
s
tu
d
ies
o
f
f
e
r
v
ar
io
u
s
m
eth
o
d
s
to
attain
MPPT.
As
th
ey
ar
e
s
im
p
le
to
u
s
e
an
d
r
ea
s
o
n
ab
ly
p
r
iced
,
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
,
an
d
in
cr
em
e
n
tal
co
n
d
u
ctan
ce
(
I
n
C
)
ar
e
a
f
ew
o
f
th
e
tr
ad
itio
n
al
MPPT
m
eth
o
d
s
th
at
h
av
e
b
ee
n
ex
ten
s
iv
ely
u
tili
ze
d
f
o
r
tr
ac
k
in
g
th
e
MPP [
8
]
.
Ad
d
itio
n
ally
,
o
s
cillatio
n
s
n
ea
r
MPP
ar
e
ca
u
s
ed
b
y
a
s
p
ec
if
i
c
p
r
ed
ilectio
n
.
T
h
e
p
o
o
r
tr
ac
k
in
g
s
p
ee
d
an
d
s
tr
o
n
g
o
s
cillatio
n
s
n
ea
r
MPP
ar
e
p
r
o
b
lem
s
with
th
es
e
m
eth
o
d
s
[
9
]
.
Nu
m
er
o
u
s
r
e
s
ea
r
ch
s
tu
d
ies
h
av
e
s
o
u
g
h
t
t
o
r
eso
lv
e
th
is
is
s
u
e
b
y
in
tr
o
d
u
cin
g
a
r
tific
ial
in
tellig
en
ce
m
et
h
o
d
o
lo
g
ies
a
n
d
o
p
ti
m
izatio
n
s
tr
ateg
ies,
s
u
ch
as
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
(
FLC)
[
1
0
]
-
[
1
7
]
.
W
h
ile
th
e
C
h
im
p
o
p
tim
izatio
n
alg
o
r
ith
m
d
o
es
n
o
t
r
eq
u
ir
e
a
m
ath
em
atica
l
m
o
d
el
o
r
tech
n
i
ca
l
k
n
o
wled
g
e
o
f
t
h
e
ex
ac
t
m
o
d
e
o
f
o
p
er
atio
n
,
it
ca
n
d
ea
l
with
th
e
n
o
n
lin
ea
r
p
r
o
p
er
ties
[
1
8
]
.
I
n
s
ev
er
al
a
p
p
licatio
n
s
,
ar
tific
ial
n
eu
r
al
n
etw
o
r
k
(
ANN)
tech
n
iq
u
es
ar
e
wid
ely
u
s
ed
to
h
a
n
d
le
n
o
n
lin
ea
r
ity
[
1
9
]
.
A
d
d
itio
n
all
y
,
th
e
b
est
MPPT
s
o
lu
tio
n
is
ex
p
lo
r
ed
b
y
th
e
ap
p
licatio
n
o
f
m
ac
h
in
e
lear
n
in
g
(
ML
)
[
2
0
]
.
T
h
eir
ef
f
ec
tiv
e
n
ess
is
lar
g
ely
r
elian
t
o
n
th
o
r
o
u
g
h
tr
ain
in
g
,
wh
ich
ty
p
ically
r
e
q
u
ir
es
a
s
ig
n
if
ican
t
am
o
u
n
t
o
f
p
r
o
ce
s
s
in
g
p
o
wer
a
n
d
tim
e
to
c
o
m
p
lete
[
2
1
]
.
R
ec
en
t
r
esear
ch
h
as
s
h
o
w
n
a
p
ar
ticu
lar
in
ter
est
in
b
io
-
i
n
s
p
ir
ed
MPPT
alg
o
r
ith
m
s
,
wh
ich
h
av
e
p
r
o
d
u
ce
d
s
u
p
er
i
o
r
o
u
tco
m
es
th
an
ev
o
l
u
tio
n
ar
y
MPPT
co
n
tr
o
ller
s
in
ter
m
s
o
f
in
cr
ea
s
ed
p
r
ec
is
io
n
an
d
s
p
ee
d
.
Fo
r
g
lo
b
al
p
o
in
t
tr
ac
k
in
g
,
th
is
s
tu
d
y
u
s
ed
ar
tific
ial
n
eu
r
al
n
etwo
r
k
s
an
d
f
u
zz
y
lo
g
ic
co
n
tr
o
l.
T
h
ese
m
eth
o
d
s
tr
ac
k
ed
th
e
g
lo
b
al
p
o
in
t
s
atis
f
ac
to
r
ily
in
b
o
th
s
tan
d
ar
d
s
u
n
r
ad
iatio
n
an
d
p
ar
tially
s
h
ad
ed
co
n
d
itio
n
s
.
Ho
wev
er
,
th
ese
m
eth
o
d
s
n
ee
d
in
tr
icate
ca
lcu
latio
n
s
.
T
h
is
wo
r
k
p
r
o
p
o
s
es
a
co
m
p
r
e
h
en
s
iv
e
co
m
p
ar
ativ
e
a
n
aly
s
is
o
f
MPPT
alg
o
r
ith
m
s
with
in
a
g
r
id
-
tied
p
h
o
to
v
o
ltaic
s
y
s
tem
co
n
tex
t.
Un
lik
e
p
r
ev
i
o
u
s
s
tu
d
ies
th
at
f
o
cu
s
o
n
ly
o
n
s
tan
d
alo
n
e
PV
s
y
s
tem
s
o
r
s
im
p
lifie
d
ir
r
ad
ian
ce
p
r
o
f
iles
,
th
is
s
tu
d
y
ev
alu
ates
th
e
alg
o
r
ith
m
s
'
tr
ac
k
in
g
b
e
h
av
io
r
u
n
d
er
r
ea
lis
tic
g
r
id
-
tied
co
n
s
tr
ain
ts
.
T
h
e
s
p
ec
if
ic
g
o
als
in
clu
d
e:
i
)
I
m
p
lem
en
tin
g
f
o
u
r
wid
el
y
u
s
ed
MPPT
tech
n
iq
u
es
(
Per
t
u
r
b
a
n
d
Ob
s
er
v
e,
in
cr
em
en
tal
co
n
d
u
ctan
ce
,
f
u
z
zy
lo
g
ic,
an
d
th
e
ar
tific
ial
n
eu
r
al
n
etwo
r
k
)
u
n
d
er
id
e
n
tical
test
co
n
d
itio
n
s
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Gri
d
-
tied
p
h
o
to
v
o
lta
ic
s
ystem
MPP
T a
lg
o
r
ith
ms p
erfo
r
ma
n
ce
…
(
Lo
u
is
N
ica
s
e
N
g
u
efa
ck
)
319
ii
)
A
s
s
e
s
s
in
g
th
eir
tr
ac
k
in
g
ef
f
icien
cy
,
co
n
v
er
g
e
n
ce
tim
e,
v
o
ltag
e
r
ip
p
le,
an
d
o
u
tp
u
t
p
o
wer
s
tab
ilit
y
;
an
d
iii
)
A
n
aly
zin
g
th
eir
s
u
itab
ilit
y
f
o
r
in
teg
r
atio
n
with
g
r
id
-
tied
in
v
er
ter
s
y
s
tem
s
.
T
h
e
s
tu
d
y
in
tr
o
d
u
ce
s
a
u
n
if
ie
d
test
in
g
f
r
am
ewo
r
k
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
,
wh
ich
allo
w
s
d
ir
ec
t
an
d
f
air
co
m
p
a
r
is
o
n
.
Fin
d
in
g
s
s
h
o
w
th
at
wh
ile
P&
O
is
s
im
p
le,
it
s
u
f
f
er
s
u
n
d
er
r
ap
id
ly
ch
an
g
in
g
c
o
n
d
itio
n
s
,
wh
e
r
ea
s
f
u
zz
y
l
o
g
i
c
-
co
n
tr
o
lled
MPPT
o
f
f
er
s
f
aster
co
n
v
er
g
e
n
ce
b
u
t
is
co
m
p
u
tatio
n
ally
in
ten
s
iv
e,
p
r
o
v
id
in
g
ac
tio
n
ab
le
in
s
ig
h
ts
f
o
r
r
ea
l
-
wo
r
ld
MPPT
co
n
tr
o
ller
d
ep
l
o
y
m
en
t.
T
h
is
wo
r
k
is
s
tr
u
ctu
r
ed
in
to
f
iv
e
m
ain
s
ec
tio
n
s
f
o
r
clar
ity
an
d
f
lo
w
: i)
Sectio
n
1
in
tr
o
d
u
ce
s
th
e
s
tu
d
y
,
o
u
tlin
in
g
th
e
p
r
o
b
lem
,
o
b
jec
tiv
es,
an
d
s
ig
n
if
ican
ce
o
f
th
e
r
esear
ch
;
ii)
Sectio
n
2
co
v
er
s
th
e
elec
tr
ical
m
o
d
ellin
g
an
d
ch
ar
ac
ter
is
tics
o
f
th
e
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
te
m
,
ex
p
lain
in
g
th
e
m
eth
o
d
o
lo
g
y
u
s
ed
in
th
e
s
tu
d
y
;
iii)
I
n
s
ec
tio
n
3
,
th
e
p
r
o
p
o
s
ed
MPPT
alg
o
r
ith
m
s
ar
e
d
escr
ib
ed
in
d
etail,
h
ig
h
lig
h
tin
g
th
eir
wo
r
k
in
g
p
r
in
ci
p
les
an
d
r
elev
an
ce
;
iv
)
Sectio
n
4
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
,
in
clu
d
in
g
a
th
o
r
o
u
g
h
a
n
aly
s
is
an
d
c
o
m
p
ar
is
o
n
o
f
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
es
;
an
d
v)
Fin
ally
,
s
ec
tio
n
5
co
n
clu
d
es
th
e
p
a
p
er
b
y
s
u
m
m
ar
izin
g
th
e
k
ey
f
i
n
d
in
g
s
a
n
d
th
eir
im
p
licatio
n
s
.
2.
M
E
T
H
O
D
T
h
is
s
tu
d
y
ap
p
r
aises
th
e
ap
p
r
o
p
r
iate
liter
atu
r
e
o
n
s
tate
-
of
-
t
h
e
-
ar
t
PV
tech
n
o
lo
g
y
an
d
o
t
h
er
r
elate
d
I
E
E
E
s
tan
d
ar
d
s
in
t
h
e
d
esig
n
o
f
p
o
wer
s
y
s
tem
s
.
A
test
s
y
s
t
em
was
u
s
ed
,
an
d
it
was
m
o
d
elled
an
d
s
im
u
lated
in
MA
T
L
AB
/Si
m
u
lin
k
s
o
f
twar
e.
T
h
e
ap
p
r
o
ac
h
in
clu
d
es
th
e
m
o
d
ellin
g
o
f
2
5
p
an
els
in
s
er
ies
an
d
2
0
p
ar
allel
m
o
d
u
les,
r
esp
ec
tiv
ely
,
with
a
to
tal
o
f
7
7
5
k
W
r
e
q
u
ir
ed
,
a
n
d
th
e
m
ath
em
atica
l
m
o
d
ellin
g
o
f
th
e
PV
s
y
s
tem
u
s
in
g
s
ev
er
al
MPPT
alg
o
r
it
h
m
s
to
s
u
p
p
o
r
t
th
e
r
esear
ch
o
b
jectiv
es.
Mo
r
eo
v
e
r
,
a
s
en
s
itiv
ity
s
tu
d
y
was
p
er
f
o
r
m
ed
t
o
d
i
f
f
er
en
tiate
th
e
wo
r
th
o
f
ea
ch
MPPT
a
lg
o
r
ith
m
,
r
esp
ec
tiv
ely
,
to
b
e
im
p
lem
en
ted
in
MA
T
L
AB
/S
im
u
lin
k
s
o
f
twar
e.
T
h
e
f
ea
tu
r
es
o
f
s
em
ico
n
d
u
cto
r
p
-
n
d
i
o
d
es
an
d
s
o
lar
ce
lls
ar
e
v
er
y
s
im
ilar
.
On
e
p
o
p
u
lar
m
o
d
el
u
s
ed
to
r
ep
r
esen
t
th
e
eq
u
iv
ale
n
t
elec
tr
ical
c
ir
cu
it
o
f
a
s
o
lar
ce
ll
is
a
s
in
g
le
-
d
io
d
e
m
o
d
el,
as
s
h
o
wn
in
Fig
u
r
e
2
[
1
]
.
Fig
u
r
e
2
.
E
q
u
iv
alen
t so
lar
ce
ll c
ir
cu
it o
f
a
s
in
g
le
-
d
io
d
e
m
o
d
e
l [
1
]
I
n
th
e
co
n
tex
t
o
f
th
e
PV
ce
ll,
th
e
o
u
tp
u
t
cu
r
r
e
n
t
an
d
o
u
tp
u
t
v
o
ltag
e
ar
e
d
e
n
o
ted
as
I
an
d
V,
r
esp
ec
tiv
ely
.
T
h
e
d
io
d
e'
s
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t
is
r
ep
r
esen
ted
b
y
I
O
,
w
h
ile
th
e
d
io
d
e
id
ea
lity
f
ac
to
r
is
d
en
o
ted
as a
.
A
d
d
itio
n
ally
,
t
h
e
s
y
m
b
o
ls
R
P
an
d
R
S
d
en
o
te
p
ar
allel
an
d
s
er
ies r
esis
tan
ce
,
r
esp
ec
tiv
ely
.
=
ℎ
−
[
(
+
×
×
ℎ
)
−
1
]
−
+
×
(
1
)
ℎ
=
[
_
+
(
−
)
]
(
2
)
W
h
er
e
th
e
s
h
o
r
t
-
cir
cu
it
cu
r
r
en
t
at
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC)
is
r
ep
r
esen
ted
b
y
I
s
c_
ST
C
.
T
h
e
ce
ll
tem
p
er
atu
r
e
at
STC is
in
d
icate
d
b
y
T
STC
(
2
5
°C
)
,
G
(
W
/m
2
)
r
ep
r
esen
tin
g
th
e
in
s
o
latio
n
in
ci
d
en
t o
n
t
h
e
PV c
ell
s
u
r
f
ac
e.
T
h
e
in
s
o
latio
n
le
v
el
at
STC
i
s
d
en
o
ted
b
y
G
STC
(
1
0
0
0
W
/m
2
)
,
an
d
th
e
s
h
o
r
t
cir
cu
it
cu
r
r
en
t
co
ef
f
icien
t,
o
r
K
a
,
is
u
s
u
ally
g
iv
en
b
y
th
e
ce
ll
m
a
n
u
f
ac
t
u
r
er
.
Mo
r
eo
v
e
r
,
(
2
)
e
x
p
lain
s
h
o
w
tem
p
er
atu
r
e
af
f
ec
ts
th
e
s
atu
r
atio
n
c
u
r
r
e
n
t
I
O
[
3
]
.
T
h
e
o
p
e
n
cir
c
u
it
v
o
ltag
e
u
n
d
er
s
tan
d
ar
d
test
cir
cu
m
s
tan
ce
s
(
STC)
is
r
ep
r
esen
ted
b
y
V
OC_STC
in
th
e
co
n
te
x
t p
r
o
v
id
ed
.
=
+
(
−
)
[
(
+
(
−
)
)
/
×
ℎ
]
−
1
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
317
-
3
34
320
Nu
m
er
o
u
s
DC
-
DC
co
n
v
er
ter
s
wer
e
in
v
en
ted
,
in
clu
d
i
n
g
b
u
ck
,
c
u
k
,
an
d
b
o
o
s
t
co
n
v
er
ter
s
.
C
o
n
s
id
er
in
g
its
o
u
ts
tan
d
in
g
ef
f
icien
cy
,
th
e
b
o
o
s
t
co
n
v
e
r
ter
i
s
th
e
m
o
s
t
p
o
p
u
lar
c
h
o
ice
a
m
o
n
g
t
h
ese
f
o
r
PV
-
g
en
er
ated
s
y
s
tem
s
[
1
]
.
T
h
e
p
r
im
ar
y
ca
u
s
e
is
th
at,
as
a
lo
s
s
p
o
wer
eq
u
atio
n
s
h
o
ws,
it
ca
n
p
r
o
v
id
e
an
d
co
n
tr
o
l
an
o
u
tp
u
t
v
o
ltag
e
th
at
is
h
ig
h
er
th
an
th
e
in
p
u
t
v
o
ltag
e
w
h
ile
m
ain
tain
in
g
a
lo
w
o
u
tp
u
t
c
u
r
r
en
t.
T
h
e
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
'
s
k
ey
co
m
p
o
n
en
t
is
a
tr
an
s
is
to
r
th
at
co
n
t
r
o
ls
th
e
am
p
lifie
d
p
r
o
ce
s
s
in
g
v
ia
a
co
n
tr
o
ller
.
T
r
an
s
is
to
r
s
s
u
ch
as
th
e
in
s
u
lated
g
ate
b
ip
o
lar
tr
an
s
is
to
r
(
I
G
B
T
)
,
b
ip
o
lar
ju
n
ctio
n
tr
a
n
s
is
to
r
(
B
J
T
)
,
a
n
d
m
etal
o
x
id
e
s
em
ico
n
d
u
cto
r
f
ield
ef
f
ec
t
tr
an
s
i
s
to
r
(
MO
SF
E
T
)
ar
e
f
r
eq
u
en
tly
u
tili
ze
d
in
DC
-
DC
co
n
v
er
ter
s
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
is
co
n
tin
u
o
u
s
ly
h
ig
h
er
th
an
t
h
e
in
p
u
t
v
o
ltag
e
d
u
e
to
th
e
b
o
o
s
t
co
n
v
er
te
r
.
T
h
e
cir
cu
it
to
p
o
lo
g
y
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
is
s
h
o
w
n
in
Fig
u
r
e
3
.
T
ab
les
1
an
d
2
p
r
esen
t
th
e
co
n
v
er
ter
p
ar
am
et
er
s
an
d
n
etwo
r
k
an
d
in
v
er
ter
p
a
r
am
eter
s
u
s
ed
in
t
h
is
s
tu
d
y
.
Fig
u
r
e
3
.
B
o
o
s
t c
o
n
v
er
ter
ci
r
c
u
it to
p
o
lo
g
y
[
1
]
T
a
b
l
e
1
.
B
o
o
s
t
c
o
n
v
e
r
t
e
r
p
a
r
a
m
e
t
e
r
s
D
e
scri
p
t
i
o
n
V
a
l
u
e
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
(
H
z
)
5
0
0
0
I
n
d
u
c
t
o
r
r
e
si
s
t
a
n
c
e
0
.
1
Ω
I
n
d
u
c
t
a
n
c
e
1
0
0
e
-
3
H
C
a
p
a
c
i
t
o
r
r
e
s
i
st
a
n
c
e
0
.
1
Ω
C
a
p
a
c
i
t
a
n
c
e
5
0
e
-
6
F
Lo
a
d
1
5
0
Ω
T
ab
le
2
.
E
x
is
tin
g
n
etwo
r
k
an
d
in
v
er
ter
p
ar
am
eter
s
D
e
scri
p
t
i
o
n
V
a
l
u
e
D
e
scri
p
t
i
o
n
V
a
l
u
e
B
r
e
a
k
e
r
r
e
si
s
t
a
n
c
e
(
O
h
m)
0
.
0
1
S
o
u
r
c
e
i
n
d
u
c
t
a
n
c
e
(
H
)
1
6
.
5
8
e
-
3
S
n
u
b
b
e
r
r
e
s
i
st
a
n
c
e
(
O
h
m)
1e
6
B
a
se
v
o
l
t
a
g
e
(
V
r
ms)
P
h
-
Ph
2
5
e
3
S
n
u
b
b
e
r
c
a
p
a
c
i
t
a
n
c
e
C
s (F
)
I
n
f
N
o
mi
n
a
l
p
h
a
se
-
to
-
p
h
a
se
v
o
l
t
a
g
e
V
n
(
V
r
ms)
3
8
0
P
h
a
se
-
to
-
p
h
a
se
v
o
l
t
a
g
e
(
V
r
ms)
3
8
0
N
o
mi
n
a
l
f
r
e
q
u
e
n
c
y
f
n
(
H
Z)
50
F
r
e
q
u
e
n
c
y
(
H
Z)
50
A
c
t
i
v
e
p
o
w
e
r
P
(
W
)
1
0
e
3
S
o
u
r
c
e
r
e
s
i
st
a
n
c
e
(
O
h
m)
0
.
8
9
2
9
W
h
en
th
e
s
witch
S
is
tu
r
n
ed
o
n
,
th
e
d
io
d
e
D
b
ec
o
m
es
r
e
v
er
s
e
-
b
iased
,
m
ea
n
in
g
it
n
o
l
o
n
g
e
r
co
n
d
u
cts
cu
r
r
en
t.
As
a
r
esu
lt,
th
e
in
d
u
ct
o
r
L
is
ef
f
ec
tiv
el
y
d
is
co
n
n
ec
ted
f
r
o
m
th
e
o
u
tp
u
t
s
id
e
an
d
in
s
tead
b
ec
o
m
es
p
a
r
t
o
f
a
cl
o
s
ed
lo
o
p
with
th
e
v
o
lta
g
e
s
o
u
r
ce
.
T
h
is
ca
u
s
es
th
e
cu
r
r
en
t
th
r
o
u
g
h
th
e
in
d
u
cto
r
t
o
in
cr
ea
s
e
lin
ea
r
ly
d
u
e
to
th
e
ap
p
lied
in
p
u
t
v
o
ltag
e,
s
in
ce
th
e
in
d
u
cto
r
r
esis
ts
ch
an
g
es
in
cu
r
r
e
n
t
b
y
s
to
r
in
g
e
n
er
g
y
in
its
m
ag
n
etic
f
ield
.
Du
r
in
g
th
is
in
ter
v
al,
t
h
e
o
u
tp
u
t
s
tag
e
is
is
o
lated
f
r
o
m
t
h
e
in
p
u
t,
an
d
th
e
lo
ad
r
ec
eiv
es
p
o
wer
s
o
lely
f
r
o
m
th
e
d
is
ch
ar
g
e
o
f
th
e
o
u
tp
u
t
ca
p
ac
ito
r
C
,
wh
ich
tem
p
o
r
ar
ily
m
ain
tain
s
th
e
o
u
tp
u
t
v
o
ltag
e
a
n
d
s
u
p
p
lies
cu
r
r
en
t
to
th
e
lo
ad
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
b
eh
a
v
io
r
o
f
t
h
e
in
d
u
cto
r
c
u
r
r
en
t
i
n
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
,
wh
er
e
th
e
cu
r
r
e
n
t
f
l
o
win
g
t
h
r
o
u
g
h
t
h
e
in
d
u
cto
r
r
em
ai
n
s
n
o
n
z
er
o
th
r
o
u
g
h
o
u
t
th
e
en
tire
s
witch
in
g
c
y
cle.
I
n
th
is
m
o
d
e,
th
e
in
d
u
cto
r
cu
r
r
en
t
r
e
m
ain
s
p
o
s
itiv
e
(
i.e
.
,
(
)
>
0
)
at
all
tim
es,
en
s
u
r
in
g
co
n
tin
u
o
u
s
en
er
g
y
tr
a
n
s
f
er
an
d
im
p
r
o
v
ed
ef
f
icien
cy
in
p
o
wer
d
eliv
er
y
.
Un
d
er
s
tead
y
-
s
ta
te
co
n
d
itio
n
s
in
C
C
M,
th
e
d
u
ty
cy
cle
D,
wh
ich
is
th
e
r
atio
o
f
th
e
s
witch
-
o
n
tim
e
to
th
e
to
tal
s
witch
in
g
p
e
r
io
d
,
ca
n
b
e
ca
lcu
lated
u
s
in
g
(
4
)
.
=
1
−
(
4
)
W
h
er
e:
V
d
is
th
e
in
p
u
t v
o
ltag
e
,
Vo
is
th
e
co
n
v
er
ter
'
s
o
u
tp
u
t v
o
ltag
e,
an
d
D
is
th
e
d
u
ty
r
atio
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
V
O
o
f
th
e
co
n
v
er
ter
in
c
r
ea
s
es
p
r
o
p
o
r
tio
n
ally
with
th
e
d
u
ty
r
atio
D
,
as
in
d
icate
d
b
y
(
4
)
.
T
h
is
r
elatio
n
s
h
ip
s
h
o
ws
th
at
b
y
ad
ju
s
tin
g
th
e
am
o
u
n
t
o
f
tim
e
th
e
s
witch
r
em
ain
s
o
n
d
u
r
in
g
ea
ch
s
witch
in
g
cy
cle,
th
e
av
er
a
g
e
v
o
ltag
e
d
eliv
er
e
d
to
th
e
l
o
ad
ca
n
b
e
ef
f
ec
tiv
ely
co
n
tr
o
lled
.
As
th
e
d
u
ty
r
atio
in
cr
ea
s
es,
th
e
co
n
v
er
ter
tr
an
s
f
er
s
m
o
r
e
en
er
g
y
to
th
e
o
u
tp
u
t
,
r
esu
ltin
g
in
a
h
ig
h
er
o
u
tp
u
t
v
o
ltag
e.
Ho
wev
er
,
ch
an
g
in
g
th
e
d
u
ty
r
atio
n
o
t
o
n
ly
af
f
ec
ts
th
e
o
u
tp
u
t
v
o
ltag
e
b
u
t
also
in
f
lu
e
n
ce
s
th
e
b
e
h
av
io
u
r
o
f
b
o
t
h
th
e
in
p
u
t
an
d
o
u
tp
u
t
cu
r
r
e
n
ts
o
f
th
e
c
o
n
v
er
ter
.
T
h
ese
v
a
r
iatio
n
s
ca
n
im
p
ac
t
th
e
o
v
er
all
s
tab
ilit
y
a
n
d
ef
f
icien
c
y
o
f
th
e
s
y
s
tem
,
esp
ec
ially
in
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
,
wh
er
e
th
e
in
d
u
cto
r
c
u
r
r
en
t n
e
v
er
d
r
o
p
s
to
ze
r
o
.
T
o
en
s
u
r
e
s
m
o
o
th
a
n
d
s
tab
le
o
p
e
r
atio
n
in
th
is
m
o
d
e,
it
is
ess
en
tial
to
p
r
o
p
er
ly
d
esig
n
th
e
p
ass
iv
e
co
m
p
o
n
e
n
ts
,
n
am
ely
,
th
e
i
n
d
u
cto
r
an
d
ca
p
a
cito
r
u
s
ed
in
th
e
co
n
v
er
ter
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Gri
d
-
tied
p
h
o
to
v
o
lta
ic
s
ystem
MPP
T a
lg
o
r
ith
ms p
erfo
r
ma
n
ce
…
(
Lo
u
is
N
ica
s
e
N
g
u
efa
ck
)
321
T
h
e
(
5
)
is
u
s
ed
to
ca
lcu
late
t
h
e
v
alu
e
o
f
t
h
e
in
d
u
cto
r
L
r
e
q
u
ir
ed
to
lim
it
th
e
cu
r
r
en
t
r
i
p
p
le
Δ
I
L
an
d
m
ain
tain
co
n
tin
u
o
u
s
co
n
d
u
cti
o
n
(
5
)
.
=
2
∆
(
5
)
Her
e,
V
d
is
th
e
in
p
u
t
v
o
ltag
e,
D
is
th
e
d
u
ty
r
atio
,
Δ
I
L
is
th
e
p
ea
k
-
to
-
p
ea
k
in
d
u
cto
r
cu
r
r
en
t
r
ip
p
le,
an
d
f
p
is
th
e
s
witch
in
g
f
r
eq
u
en
cy
.
T
h
e
(
6
)
p
r
o
v
id
es
th
e
r
eq
u
i
r
ed
v
alu
e
f
o
r
th
e
o
u
tp
u
t
ca
p
ac
ito
r
C
,
wh
ich
s
m
o
o
th
s
t
h
e
o
u
tp
u
t
v
o
ltag
e
an
d
r
ed
u
ce
s
th
e
v
o
ltag
e
r
ip
p
le
Δ
V
O
(
6
)
.
=
∆
(
6
)
W
h
er
e
I
O
is
th
e
o
u
tp
u
t
cu
r
r
en
t
,
Δ
V
O
is
th
e
allo
wab
le
o
u
tp
u
t
v
o
ltag
e
r
i
p
p
le,
a
n
d
f
p
is
th
e
s
witch
in
g
f
r
e
q
u
en
c
y
.
T
h
e
p
r
o
p
er
s
elec
tio
n
o
f
t
h
ese
co
m
p
o
n
en
ts
is
cr
u
cial
f
o
r
ac
h
iev
in
g
t
h
e
d
esire
d
p
er
f
o
r
m
an
ce
,
m
in
im
izin
g
lo
s
s
es,
an
d
en
s
u
r
in
g
th
e
r
eliab
le
o
p
er
atio
n
o
f
th
e
co
n
v
er
ter
i
n
C
C
M.
Fig
u
r
e
4
.
B
o
o
s
t c
o
n
v
er
ter
v
o
lt
ag
e
an
d
c
u
r
r
e
n
t w
av
ef
o
r
m
in
c
o
n
tin
u
o
u
s
co
n
d
u
ctio
n
o
p
er
atio
n
[
1
]
3.
M
AXI
M
U
M
P
O
WE
R
P
O
I
N
T
T
RA
CK
I
NG
(
M
P
P
T
)
I
n
th
e
ev
er
-
ad
v
an
cin
g
f
ield
o
f
s
o
lar
en
er
g
y
tech
n
o
lo
g
y
,
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
p
lay
s
a
v
ital
r
o
le
in
en
h
a
n
cin
g
th
e
ef
f
icien
c
y
a
n
d
p
er
f
o
r
m
a
n
ce
o
f
PV
s
y
s
tem
s
.
As
s
o
lar
p
an
els
ar
e
s
u
b
ject
to
co
n
s
tan
tly
ch
an
g
in
g
e
n
v
ir
o
n
m
en
tal
f
ac
to
r
s
,
s
u
ch
as
ir
r
a
d
ian
ce
,
tem
p
er
at
u
r
e,
a
n
d
s
h
a
d
in
g
,
th
e
elec
tr
ical
ch
ar
ac
ter
is
tics
o
f
th
ese
p
an
els f
lu
ctu
ate.
MPPT
is
a
p
o
wer
el
ec
tr
o
n
ic
d
ev
ice
i
n
teg
r
ated
with
in
tellig
en
t
co
n
tr
o
l
alg
o
r
ith
m
s
th
at
d
y
n
am
ically
tr
ac
k
an
d
o
p
er
ate
th
e
PV
s
y
s
tem
at
its
o
p
tim
al
p
o
in
t,
k
n
o
w
n
as
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t
(
MPP)
.
T
h
is
ca
p
ab
ilit
y
en
s
u
r
es
th
at,
r
eg
ar
d
less
o
f
v
a
r
y
in
g
co
n
d
itio
n
s
,
th
e
m
ax
im
u
m
p
o
s
s
ib
le
p
o
wer
is
ex
tr
ac
ted
f
r
o
m
t
h
e
s
o
lar
ar
r
ay
a
n
d
d
eliv
e
r
ed
to
th
e
l
o
ad
with
th
e
h
ig
h
est p
o
s
s
ib
le
ef
f
icien
cy
[
1
]
.
T
r
ad
itio
n
ally
,
MPPT
m
eth
o
d
s
h
av
e
r
elied
o
n
alg
o
r
ith
m
ic
tec
h
n
iq
u
es d
esig
n
ed
t
o
ad
j
u
s
t
th
e
o
p
er
atin
g
v
o
ltag
e
o
r
c
u
r
r
en
t
o
f
th
e
PV
m
o
d
u
les
in
r
esp
o
n
s
e
to
o
b
s
er
v
ed
ch
an
g
es
in
p
o
wer
o
u
tp
u
t.
Am
o
n
g
th
ese,
th
e
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P&
O)
m
eth
o
d
an
d
th
e
in
cr
em
en
tal
co
n
d
u
cta
n
ce
(
I
n
C
)
tech
n
iq
u
e
h
av
e
b
ee
n
th
e
m
o
s
t
wid
ely
ad
o
p
ted
.
T
h
e
P&
O
m
e
th
o
d
o
p
er
ates
b
y
in
cr
em
e
n
tally
ad
ju
s
tin
g
th
e
v
o
ltag
e
a
n
d
o
b
s
er
v
in
g
th
e
ch
a
n
g
e
in
p
o
wer
;
if
th
e
p
o
wer
in
cr
e
ases
,
th
e
alg
o
r
ith
m
co
n
tin
u
es
in
th
e
s
am
e
d
ir
ec
tio
n
;
o
th
e
r
wis
e,
it
r
ev
er
s
es.
I
n
co
n
tr
ast,
th
e
I
n
C
m
eth
o
d
d
ete
r
m
in
es
th
e
MPP
b
ased
o
n
th
e
s
lo
p
e
o
f
th
e
p
o
wer
-
v
o
ltag
e
cu
r
v
e,
o
f
f
e
r
in
g
f
aster
an
d
m
o
r
e
p
r
ec
is
e
tr
ac
k
in
g
u
n
d
er
r
ap
id
ly
ch
a
n
g
in
g
co
n
d
itio
n
s
.
Desp
ite
th
eir
ef
f
ec
tiv
en
ess
,
th
ese
m
eth
o
d
s
o
f
ten
s
tr
u
g
g
le
with
tr
ac
k
in
g
d
elay
s
,
o
s
cillatio
n
s
ar
o
u
n
d
th
e
MPP,
an
d
s
u
b
o
p
tim
al
p
er
f
o
r
m
a
n
ce
d
u
r
in
g
tr
a
n
s
ien
t
en
v
ir
o
n
m
en
tal
ev
en
ts
lik
e
f
a
s
t
clo
u
d
m
o
v
em
e
n
t
o
r
p
a
r
tial
s
h
ad
in
g
.
T
o
o
v
er
co
m
e
th
ese
lim
itatio
n
s
,
th
is
r
esear
ch
an
d
d
e
v
elo
p
m
e
n
t
in
MPPT
h
av
e
s
h
if
ted
to
war
d
in
tellig
en
t,
ad
ap
tiv
e
tech
n
iq
u
es
r
o
o
ted
in
ar
tific
ial
in
tellig
en
ce
an
d
s
o
f
t
co
m
p
u
tin
g
.
A
r
tific
ial
n
eu
r
al
n
etwo
r
k
s
(
ANNs)
an
d
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
(
FLCs
)
ar
e
co
n
s
id
er
ed
at
th
e
f
o
r
ef
r
o
n
t
o
f
th
is
in
n
o
v
atio
n
.
ANN
-
b
ased
MPPT
s
y
s
tem
s
ar
e
ca
p
ab
le
o
f
lear
n
in
g
f
r
o
m
h
is
to
r
ical
an
d
r
ea
l
-
tim
e
d
ata,
a
llo
win
g
th
em
to
p
r
ed
ict
an
d
r
e
s
p
o
n
d
t
o
ch
a
n
g
in
g
c
o
n
d
itio
n
s
with
a
h
ig
h
d
eg
r
e
e
o
f
ac
cu
r
ac
y
.
Me
an
wh
ile,
f
u
zz
y
lo
g
ic
p
r
o
v
id
es
a
r
u
le
-
b
ased
y
et
f
lex
ib
le
ap
p
r
o
ac
h
to
h
an
d
le
u
n
ce
r
tain
ties
in
in
p
u
t
p
ar
am
eter
s
,
em
u
latin
g
h
u
m
an
r
ea
s
o
n
in
g
to
m
ak
e
d
e
cisi
o
n
s
wh
er
e
p
r
ec
is
e
m
ath
em
atica
l
m
o
d
els
ar
e
in
s
u
f
f
icien
t.
T
h
ese
in
tellig
en
t
m
eth
o
d
s
o
f
f
e
r
im
p
r
o
v
ed
tr
ac
k
in
g
s
p
ee
d
,
r
ed
u
ce
d
o
s
cillatio
n
s
ar
o
u
n
d
th
e
MPP,
an
d
b
etter
a
d
ap
tab
ilit
y
in
c
o
m
p
lex
s
ce
n
ar
io
s
,
m
ak
i
n
g
th
em
h
ig
h
ly
ef
f
ec
tiv
e
in
m
o
d
er
n
PV
ap
p
licatio
n
s
[
2
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
317
-
3
34
322
Ho
wev
er
,
th
e
ad
v
an
ce
m
e
n
t
in
MPPT
s
tr
ateg
ies
also
in
tr
o
d
u
ce
s
n
ew
ch
allen
g
es.
T
h
e
s
elec
tio
n
o
f
an
MPPT
tech
n
iq
u
e
m
u
s
t
co
n
s
id
er
m
u
ltip
le
p
r
ac
tical
f
ac
to
r
s
s
u
ch
as
c
o
m
p
u
tatio
n
al
c
o
m
p
le
x
ity
,
r
esp
o
n
s
e
tim
e,
im
p
lem
en
tatio
n
co
s
t,
an
d
h
a
r
d
war
e
co
m
p
atib
ilit
y
.
W
h
ile
tr
ad
itio
n
al
m
eth
o
d
s
ar
e
s
im
p
ler
an
d
ea
s
ier
to
im
p
lem
en
t
o
n
l
o
w
-
co
s
t
m
icr
o
co
n
tr
o
ller
s
,
i
n
tellig
en
t
alg
o
r
it
h
m
s
o
f
ten
r
e
q
u
ir
e
m
o
r
e
s
o
p
h
i
s
ticated
p
r
o
ce
s
s
o
r
s
an
d
g
r
ea
ter
m
em
o
r
y
,
wh
ich
c
an
in
cr
ea
s
e
th
e
o
v
er
all
s
y
s
tem
co
s
t.
C
o
n
s
eq
u
e
n
tly
,
th
e
c
h
o
ic
e
b
etwe
en
class
ical
an
d
ad
v
a
n
ce
d
MPPT
m
eth
o
d
s
d
ep
en
d
s
lar
g
el
y
o
n
t
h
e
s
p
ec
if
ic
r
eq
u
ir
em
en
ts
o
f
t
h
e
PV
ap
p
licatio
n
,
wh
eth
er
it
p
r
io
r
itizes
co
s
t
-
ef
f
ec
tiv
en
ess
,
p
r
ec
is
io
n
,
o
r
s
ca
lab
ilit
y
.
L
o
o
k
in
g
ah
ea
d
,
th
e
f
u
t
u
r
e
o
f
MPPT
lies
in
th
e
d
ev
elo
p
m
e
n
t
o
f
h
y
b
r
id
an
d
s
elf
-
ad
ap
tiv
e
s
y
s
tem
s
th
at
co
m
b
in
e
th
e
s
tr
en
g
th
s
o
f
m
u
ltip
le
tech
n
iq
u
es.
I
n
teg
r
atio
n
with
I
o
T
p
latf
o
r
m
s
,
r
ea
l
-
tim
e
wea
th
e
r
d
ata,
an
d
e
d
g
e
co
m
p
u
tin
g
is
ex
p
e
cted
to
en
h
a
n
ce
th
e
p
r
ed
ictiv
e
ca
p
ab
ilit
ies o
f
MPPT
s
y
s
tem
s
,
tr
an
s
f
o
r
m
in
g
th
em
f
r
o
m
r
ea
ctiv
e
co
n
tr
o
ller
s
in
to
p
r
o
ac
tiv
e
d
ec
is
io
n
-
m
ak
er
s
.
As
s
o
lar
en
er
g
y
c
o
n
t
in
u
es
to
s
ca
le
g
lo
b
ally
,
MPPT
will
r
em
ain
a
c
r
u
cial
en
a
b
ler
,
ev
o
l
v
in
g
f
r
o
m
a
m
er
e
ef
f
icien
cy
to
o
l in
t
o
a
b
as
is
o
f
s
m
ar
t,
r
esp
o
n
s
iv
e,
a
n
d
h
ig
h
-
p
er
f
o
r
m
i
n
g
e
n
er
g
y
s
y
s
tem
s
[
2
3
]
,
[
2
4
]
.
3
.
1
.
P
er
t
urba
t
io
n a
nd
o
bs
er
v
a
t
io
n M
P
P
T
T
h
e
p
er
tu
r
b
atio
n
an
d
o
b
s
er
v
at
io
n
(
P&
O)
m
eth
o
d
r
e
m
ain
s
o
n
e
o
f
th
e
m
o
s
t
f
o
u
n
d
atio
n
al
a
n
d
wid
ely
im
p
lem
en
ted
s
tr
ateg
ies
in
th
e
d
o
m
ain
o
f
MPPT.
I
ts
co
n
tin
u
ed
p
o
p
u
lar
ity
in
b
o
t
h
ac
ad
em
ic
r
esear
ch
an
d
co
m
m
er
cial
ap
p
licatio
n
s
s
tem
s
f
r
o
m
a
co
m
b
in
atio
n
o
f
tech
n
ical
s
im
p
licity
,
co
s
t
-
ef
f
ec
tiv
en
ess
,
an
d
ea
s
e
o
f
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
.
Des
p
ite
th
e
em
er
g
en
ce
o
f
m
o
r
e
a
d
v
an
ce
d
an
d
in
tellig
en
t
tr
ac
k
in
g
alg
o
r
ith
m
s
,
P&
O
s
till
h
o
ld
s
a
ce
n
tr
al
p
o
s
itio
n
i
n
MPPT
liter
atu
r
e
an
d
s
er
v
es
as
a
b
en
ch
m
a
r
k
f
o
r
ev
alu
atin
g
n
ewe
r
tec
h
n
iq
u
es.
At
th
e
co
r
e
o
f
th
e
P&
O
m
eth
o
d
lies
a
d
ec
ep
tiv
ely
s
im
p
le
lo
g
ic:
Per
tu
r
b
t
h
e
o
p
er
atin
g
v
o
ltag
e
o
r
cu
r
r
en
t o
f
th
e
PV
s
y
s
tem
s
lig
h
tly
an
d
o
b
s
er
v
e
th
e
ef
f
ec
t
o
n
o
u
tp
u
t
p
o
wer
.
I
f
th
e
p
o
wer
in
cr
ea
s
es,
th
e
p
er
tu
r
b
atio
n
co
n
tin
u
es
in
th
e
s
am
e
d
ir
ec
tio
n
;
i
f
it
d
ec
r
ea
s
es,
th
e
d
ir
ec
tio
n
is
r
ev
er
s
ed
.
T
h
is
tr
ial
-
an
d
-
er
r
o
r
ap
p
r
o
ac
h
en
ab
les
th
e
alg
o
r
ith
m
to
g
r
a
d
u
ally
co
n
v
er
g
e
o
n
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
,
wh
er
e
th
e
o
u
tp
u
t
p
o
wer
is
at
it
s
p
ea
k
f
o
r
th
e
g
iv
en
en
v
ir
o
n
m
e
n
tal
c
o
n
d
itio
n
s
.
T
h
is
alg
o
r
ith
m
ca
n
b
e
v
is
u
alize
d
th
r
o
u
g
h
a
c
o
n
tr
o
l
lo
o
p
th
at
o
p
er
ates
co
n
tin
u
o
u
s
ly
,
m
ea
s
u
r
in
g
th
e
cu
r
r
e
n
t
a
n
d
v
o
ltag
e
o
u
t
p
u
t
o
f
th
e
PV
m
o
d
u
le
an
d
m
ak
in
g
i
n
cr
em
en
tal
ad
ju
s
tm
en
ts
to
th
e
d
u
ty
cy
cle
o
f
th
e
ass
o
ciate
d
DC
-
DC
co
n
v
er
ter
.
A
ty
p
ical
f
lo
wc
h
ar
t o
f
t
h
is
d
ec
is
io
n
-
m
ak
in
g
p
r
o
ce
s
s
,
s
u
ch
as
th
e
o
n
e
s
h
o
wn
in
Fig
u
r
e
5
,
h
ig
h
lig
h
ts
its
s
tr
aig
h
tf
o
r
war
d
lo
g
ic
s
tr
u
ct
u
r
e.
Sin
ce
it
d
o
es
n
o
t
r
ely
o
n
co
m
p
le
x
m
ath
em
atica
l m
o
d
els o
r
ex
ten
s
iv
e
d
atasets
,
P&
O
is
h
ig
h
ly
ad
ap
tab
le
an
d
c
an
b
e
d
ep
lo
y
e
d
o
n
in
ex
p
en
s
iv
e
m
icr
o
co
n
tr
o
ller
s
with
lim
ited
p
r
o
ce
s
s
in
g
p
o
we
r
[
2
5
]
.
Fig
u
r
e
5
.
P&
O
alg
o
r
ith
m
f
l
o
wch
ar
t [
1
]
Ho
wev
er
,
th
e
s
im
p
licity
o
f
t
h
e
P&
O
m
eth
o
d
is
b
o
th
its
s
tr
en
g
th
an
d
its
lim
itatio
n
.
Un
d
er
s
tead
y
-
s
tate
co
n
d
itio
n
s
,
it
p
er
f
o
r
m
s
well
an
d
m
ai
n
tain
s
th
e
o
p
e
r
atin
g
p
o
in
t
clo
s
e
to
th
e
M
PP
.
Yet,
in
r
ap
id
ly
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Gri
d
-
tied
p
h
o
to
v
o
lta
ic
s
ystem
MPP
T a
lg
o
r
ith
ms p
erfo
r
ma
n
ce
…
(
Lo
u
is
N
ica
s
e
N
g
u
efa
ck
)
323
ch
an
g
in
g
en
v
ir
o
n
m
en
ts
,
s
u
c
h
as
wh
en
cl
o
u
d
s
p
ass
o
v
er
a
s
o
lar
ar
r
ay
,
it
m
a
y
s
tr
u
g
g
le
t
o
d
is
tin
g
u
is
h
wh
eth
er
ch
an
g
es
in
o
u
tp
u
t
p
o
wer
ar
e
d
u
e
to
p
er
tu
r
b
atio
n
s
o
r
ex
ter
n
al
f
ac
to
r
s
.
T
h
is
ca
n
lead
to
o
s
cillatio
n
s
ar
o
u
n
d
th
e
MPP
o
r
m
is
d
ir
ec
tio
n
in
th
e
tr
ac
k
in
g
p
r
o
ce
s
s
.
Desp
ite
th
i
s
,
its
lo
w
co
m
p
u
tatio
n
al
o
v
e
r
h
ea
d
an
d
m
in
im
al
h
ar
d
war
e
r
e
q
u
ir
em
e
n
ts
m
ak
e
it
an
attr
ac
tiv
e
s
o
lu
tio
n
f
o
r
s
m
all
to
m
ed
iu
m
-
s
ca
le
PV
s
y
s
tem
s
,
esp
ec
ially
in
co
s
t
-
s
en
s
itiv
e
ap
p
licatio
n
s
.
R
em
ar
k
ab
ly
,
th
e
p
r
in
cip
les
o
f
t
h
e
P&
O
m
eth
o
d
h
av
e
s
er
v
ed
as
th
e
b
lu
ep
r
in
t
f
o
r
m
o
r
e
s
o
p
h
is
ticated
h
y
b
r
id
a
n
d
ad
ap
tiv
e
alg
o
r
ith
m
s
.
Ma
n
y
r
e
s
ea
r
ch
er
s
h
av
e
s
o
u
g
h
t to
en
h
a
n
ce
its
p
er
f
o
r
m
a
n
ce
b
y
in
teg
r
atin
g
it
with
tech
n
i
q
u
es
s
u
ch
as
f
u
zz
y
lo
g
ic,
n
e
u
r
al
n
etwo
r
k
s
,
o
r
v
ar
ia
b
le
s
tep
-
s
ize
ad
ju
s
tm
en
ts
.
T
h
ese
im
p
r
o
v
em
e
n
ts
aim
to
r
etain
th
e
s
im
p
licity
o
f
P&
O
wh
ile
ad
d
r
ess
in
g
its
r
esp
o
n
s
iv
en
ess
an
d
s
tab
ilit
y
u
n
d
er
d
y
n
a
m
ic
co
n
d
itio
n
s
.
I
n
th
is
s
en
s
e,
th
e
P&
O
m
eth
o
d
is
n
o
t
ju
s
t
a
b
asic
MPPT
tech
n
iq
u
e
;
it
is
a
ca
taly
s
t
f
o
r
in
n
o
v
ati
o
n
,
a
p
latf
o
r
m
u
p
o
n
w
h
ich
th
e
n
e
x
t
g
e
n
er
ati
o
n
o
f
s
m
ar
t,
r
esp
o
n
s
iv
e,
an
d
ad
a
p
tiv
e
MPPT
s
tr
ateg
ies co
n
tin
u
es to
b
e
b
u
ilt [
2
6
]
.
3
.
2
.
I
ncre
m
ent
a
l
c
o
nd
uct
a
nce
M
P
P
T
T
h
e
in
cr
em
e
n
tal
co
n
d
u
ctan
c
e
(
I
n
C
)
m
eth
o
d
r
e
p
r
esen
ts
a
m
o
r
e
a
n
aly
tical
an
d
m
at
h
em
atica
lly
g
r
o
u
n
d
ed
a
p
p
r
o
ac
h
to
MPPT
in
PV
s
y
s
tem
s
.
I
ts
d
ev
elo
p
m
en
t
em
er
g
ed
as
a
r
esp
o
n
s
e
to
th
e
lim
itatio
n
s
o
f
s
im
p
ler
m
eth
o
d
s
,
s
u
ch
as
p
er
tu
r
b
atio
n
an
d
o
b
s
er
v
atio
n
(
P&
O)
,
p
ar
ticu
lar
l
y
in
ter
m
s
o
f
p
r
ec
is
io
n
a
n
d
ad
ap
tab
ilit
y
to
r
ap
id
ly
f
lu
ctu
a
tin
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
h
e
I
n
C
alg
o
r
ith
m
is
b
ased
o
n
a
cr
itical
in
s
ig
h
t
in
to
th
e
p
o
wer
-
v
o
ltag
e
(
P
–
V)
ch
ar
ac
ter
is
tics
o
f
a
p
h
o
to
v
o
ltaic
ar
r
ay
.
Sp
ec
if
ically
,
it
ex
p
l
o
its
th
e
f
ac
t
th
at
th
e
d
er
iv
ativ
e
o
f
p
o
wer
with
r
esp
ec
t
to
v
o
ltag
e
,
d
P/d
V,
e
q
u
als
ze
r
o
at
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
.
T
h
is
p
r
in
cip
le
allo
ws
th
e
MPPT
co
n
tr
o
ller
to
d
eter
m
in
e
wh
eth
e
r
th
e
s
y
s
tem
h
as
r
ea
ch
ed
th
e
MPP,
o
r
wh
eth
er
it
s
h
o
u
ld
in
cr
ea
s
e
o
r
d
ec
r
ea
s
e
th
e
o
p
er
atin
g
v
o
ltag
e
to
m
o
v
e
c
lo
s
er
to
it.
Un
lik
e
p
er
tu
r
b
atio
n
-
b
ased
tech
n
iq
u
es
th
at
r
ely
o
n
iter
ativ
e
o
b
s
er
v
a
tio
n
,
I
n
C
ca
lcu
lates
th
is
d
er
iv
ativ
e
ex
p
licitly
,
u
s
in
g
th
e
P
V
ar
r
ay
'
s
r
ea
l
-
tim
e
o
u
tp
u
t
cu
r
r
en
t
(
I
)
an
d
v
o
ltag
e
(
V)
d
ata
[
2
7
]
.
At
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t,
th
e
in
cr
e
m
en
tal
co
n
d
u
ctan
ce
(
d
I
/d
V)
a
n
d
th
e
i
n
s
tan
tan
eo
u
s
co
n
d
u
cta
n
ce
(
I
/V)
a
r
e
eq
u
al,
lead
in
g
to
t
h
e
co
n
d
itio
n
in
(
7
)
.
=
(
×
)
=
1
+
→
1
×
=
1
+
(
7
)
T
h
is
eq
u
ality
f
o
r
m
s
th
e
d
ec
is
io
n
-
m
ak
i
n
g
co
r
e
o
f
th
e
I
n
C
alg
o
r
ith
m
.
I
f
th
e
in
cr
e
m
en
tal
co
n
d
u
ctan
ce
is
g
r
ea
ter
th
an
t
h
e
n
e
g
ativ
e
o
f
th
e
in
s
tan
tan
eo
u
s
co
n
d
u
ctan
c
e,
th
e
o
p
er
atin
g
p
o
in
t
lies
to
t
h
e
lef
t
o
f
th
e
MPP,
an
d
th
e
v
o
ltag
e
m
u
s
t
b
e
i
n
cr
ea
s
ed
.
C
o
n
v
er
s
ely
,
if
th
e
i
n
cr
em
en
tal
co
n
d
u
cta
n
ce
is
less
,
th
e
o
p
er
atin
g
p
o
in
t
lies
to
th
e
r
ig
h
t
o
f
th
e
MPP,
an
d
t
h
e
v
o
ltag
e
m
u
s
t
b
e
d
ec
r
ea
s
ed
.
On
ly
wh
en
th
e
two
ar
e
eq
u
al
d
o
es
th
e
alg
o
r
ith
m
co
n
f
ir
m
th
at
th
e
MPP
h
as
b
ee
n
l
o
ca
ted
.
An
al
g
o
r
ith
m
i
c
im
p
lem
en
tatio
n
o
f
t
h
is
p
r
o
ce
s
s
,
illu
s
tr
ated
in
Fig
u
r
e
6
h
i
g
h
lig
h
ts
its
s
y
s
tem
atic
n
atu
r
e
an
d
r
esp
o
n
s
iv
e
n
ess
to
d
y
n
a
m
ic
co
n
d
itio
n
s
.
T
h
e
I
n
C
m
et
h
o
d
o
f
f
e
r
s
a
d
is
tin
ct
ad
v
an
tag
e
in
g
r
id
-
tied
s
y
s
tem
s
,
wh
er
e
p
r
ec
is
io
n
an
d
r
ea
l
-
tim
e
ad
ap
tab
ilit
y
ar
e
p
ar
a
m
o
u
n
t.
As
it
av
o
id
s
u
n
n
ec
ess
ar
y
o
s
cillatio
n
s
ar
o
u
n
d
th
e
MPP
an
d
m
ak
es
in
f
o
r
m
ed
v
o
ltag
e
ad
ju
s
tm
en
ts
b
ased
o
n
s
lo
p
e
an
aly
s
is
,
it
en
ab
les
m
o
r
e
s
tab
le
an
d
ef
f
icien
t
o
p
er
atio
n
,
p
ar
ticu
lar
ly
u
n
d
e
r
co
n
d
itio
n
s
o
f
r
ap
id
ir
r
a
d
ian
c
e
f
lu
ctu
atio
n
o
r
p
ar
tial
s
h
ad
i
n
g
,
w
h
er
e
o
th
er
m
eth
o
d
s
o
f
ten
f
alter
.
T
h
e
(
8
)
th
r
o
u
g
h
(
1
0
)
p
r
o
v
id
e
t
h
e
lo
g
i
c
f
o
u
n
d
atio
n
f
o
r
th
e
d
ir
ec
tio
n
al
d
ec
is
io
n
-
m
ak
in
g
with
in
t
h
e
I
n
C
alg
o
r
ith
m
.
B
y
ev
alu
atin
g
t
h
e
r
elatio
n
s
h
ip
b
et
wee
n
d
I
/d
V
an
d
I
/V
in
r
ea
l
tim
e,
th
e
MPPT
co
n
tr
o
ller
ca
n
ac
cu
r
ately
d
ete
r
m
in
e
wh
eth
er
to
in
cr
ea
s
e,
d
ec
r
ea
s
e,
o
r
m
ain
tain
th
e
PV
o
p
er
atin
g
v
o
ltag
e,
e
n
s
u
r
in
g
c
o
n
s
is
ten
t
an
d
ef
f
icien
t
tr
ac
k
in
g
o
f
th
e
MPP e
v
en
u
n
d
er
r
ap
id
ly
ch
an
g
in
g
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
[
2
8
]
.
=
0
>
−
1
,
(
)
(
8
)
=
0
=
−
1
,
(
)
(
9
)
=
0
<
−
1
,
(
ℎ
)
(
1
0
)
Mo
r
eo
v
er
,
d
u
e
t
o
its
d
eter
m
in
is
tic
co
n
tr
o
l
l
o
g
ic,
I
n
C
is
well
-
s
u
ited
f
o
r
in
teg
r
atio
n
in
to
d
ig
ital
co
n
tr
o
ller
s
a
n
d
m
icr
o
p
r
o
ce
s
s
o
r
s
u
s
ed
in
m
o
d
er
n
p
o
wer
elec
tr
o
n
ic
c
o
n
v
er
te
r
s
.
W
h
ile
it
m
ay
r
eq
u
ir
e
s
lig
h
tly
m
o
r
e
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
th
an
P&
O,
its
in
cr
ea
s
ed
ac
cu
r
ac
y
a
n
d
tr
ac
k
in
g
s
tab
ilit
y
m
ak
e
it
a
p
r
ef
er
r
e
d
ch
o
ice
in
m
a
n
y
h
ig
h
-
p
er
f
o
r
m
a
n
ce
g
r
id
-
tied
PV
ap
p
licatio
n
s
.
As
a
r
esu
lt,
th
e
in
cr
em
en
tal
c
o
n
d
u
ctan
ce
m
eth
o
d
is
n
o
t
ju
s
t
an
alter
n
ativ
e
to
s
im
p
ler
MPPT
alg
o
r
ith
m
s
,
it
is
a
s
o
p
h
is
ticated
s
tr
ateg
y
t
h
at
e
m
b
o
d
ies
th
e
b
alan
ce
b
etwe
en
m
ath
em
atica
l
r
ig
o
r
,
alg
o
r
ith
m
ic
p
r
ec
is
io
n
,
an
d
p
r
ac
tical
p
er
f
o
r
m
an
ce
,
a
n
d
co
n
t
in
u
es
to
s
er
v
e
as
a
b
en
ch
m
ar
k
in
co
m
p
ar
ativ
e
s
tu
d
ies
o
f
MPPT
m
eth
o
d
s
f
o
r
g
r
id
-
tied
p
h
o
to
v
o
ltaic
s
y
s
tem
s
[
2
9
]
.
T
h
is
m
eth
o
d
m
ea
s
u
r
es
th
e
PV
ar
r
ay
'
s
o
p
er
atin
g
v
o
ltag
e
(
V)
a
n
d
c
u
r
r
e
n
t
(
I
)
u
s
in
g
two
s
en
s
o
r
s
.
T
h
e
(
1
1
)
a
n
d
(
1
2
)
ca
n
b
e
u
s
ed
to
d
ig
itally
c
o
m
p
u
te
th
e
in
cr
em
en
tal
ch
an
g
es
(
d
V
a
n
d
d
I
)
o
f
th
e
PV
a
r
r
ay
'
s
o
u
t
p
u
t
cu
r
r
en
t
(
I
)
an
d
v
o
ltag
e
(
V)
b
y
s
am
p
lin
g
th
ese
v
alu
es a
t su
cc
ess
iv
e
tim
e
in
ter
v
als (
k
-
1
)
an
d
(
k
)
[
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
317
-
3
34
324
(
)
=
(
)
−
(
−
1
)
(
1
1
)
(
)
=
(
)
−
(
−
1
)
(
1
2
)
Fig
u
r
e
6
.
I
n
C
MPPT
f
lo
wch
ar
t [
1
]
3
.
3
.
Art
if
ici
a
l
neura
l net
wo
rk
co
nt
ro
lled M
P
P
T
As
th
e
d
em
a
n
d
f
o
r
s
m
ar
ter
,
m
o
r
e
r
esp
o
n
s
iv
e,
an
d
ad
a
p
tiv
e
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
in
cr
ea
s
es,
Ar
tific
ial
n
eu
r
al
n
etwo
r
k
s
(
ANNs)
h
av
e
em
er
g
ed
as
a
tr
an
s
f
o
r
m
ativ
e
ap
p
r
o
ac
h
in
t
h
e
d
ev
elo
p
m
e
n
t
o
f
m
ax
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
i
n
g
(
MPPT)
alg
o
r
ith
m
s
.
R
ep
r
e
s
en
tin
g
a
b
r
an
c
h
o
f
ar
tific
ial
in
tellig
en
ce
,
ANN
-
b
ased
MPPT
s
tr
ateg
ies
o
f
f
er
d
is
tin
ct
ad
v
a
n
tag
es
o
v
er
tr
a
d
itio
n
al
tech
n
i
q
u
es,
p
a
r
ticu
la
r
ly
in
d
y
n
am
ic
an
d
u
n
p
r
e
d
ictab
le
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
.
C
o
n
v
en
tio
n
al
MPPT
alg
o
r
ith
m
s
,
s
u
ch
as
p
er
tu
r
b
atio
n
an
d
o
b
s
er
v
atio
n
(
P&
O)
a
n
d
in
cr
e
m
en
tal
co
n
d
u
cta
n
ce
(
I
n
C
)
,
wh
ile
ef
f
ec
tiv
e
in
s
tead
y
-
s
tate
co
n
d
itio
n
s
,
o
f
te
n
s
u
f
f
er
f
r
o
m
d
elay
e
d
c
o
n
v
er
g
e
n
ce
an
d
s
u
b
o
p
tim
al
p
er
f
o
r
m
a
n
ce
u
n
d
er
r
ap
id
v
a
r
iatio
n
s
in
s
o
lar
ir
r
ad
ian
ce
an
d
tem
p
er
atu
r
e.
T
h
ese
s
h
o
r
tco
m
i
n
g
s
ca
n
r
esu
lt in
o
s
cillatio
n
s
n
ea
r
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
MPP)
o
r
f
ailu
r
e
t
o
tr
ac
k
it
alto
g
eth
er
.
I
n
co
n
tr
ast,
ANN
-
b
ased
MPPT
o
v
er
co
m
es
th
ese
lim
itatio
n
s
th
r
o
u
g
h
a
d
ata
-
d
r
iv
e
n
,
ad
ap
tiv
e
lear
n
i
n
g
ap
p
r
o
ac
h
ca
p
ab
le
o
f
g
en
er
alizin
g
co
m
p
le
x
,
n
o
n
lin
ea
r
r
elatio
n
s
h
ip
s
b
et
wee
n
en
v
ir
o
n
m
en
tal
v
ar
iab
les
an
d
th
e
s
y
s
tem
’
s
p
o
wer
o
u
tp
u
t.
T
h
e
co
r
e
s
tr
u
ctu
r
e
o
f
a
n
ANN
-
co
n
tr
o
lled
MPPT
s
y
s
tem
i
s
illu
s
tr
ated
in
Fig
u
r
e
7
.
T
h
is
c
o
n
f
ig
u
r
atio
n
ty
p
ically
em
p
l
o
y
s
s
o
lar
ir
r
ad
ian
ce
an
d
ce
ll
te
m
p
er
atu
r
e
as
in
p
u
t
v
ar
iab
les
to
th
e
n
eu
r
al
n
etwo
r
k
.
T
h
e
n
etwo
r
k
is
tr
ain
ed
to
m
ap
th
ese
in
p
u
ts
to
a
co
r
r
esp
o
n
d
in
g
d
u
ty
r
atio
f
o
r
th
e
DC
-
DC
co
n
v
er
ter
,
w
h
ich
ad
ju
s
ts
th
e
o
p
er
atin
g
p
o
in
t
o
f
th
e
p
h
o
to
v
o
ltaic
(
PV)
ar
r
ay
to
m
atch
th
e
MPP
in
r
ea
l
tim
e.
T
h
is
tr
ain
in
g
p
r
o
ce
s
s
u
tili
ze
s
s
u
p
er
v
is
ed
lear
n
in
g
tech
n
iq
u
es,
wh
e
r
ein
th
e
AN
N
is
p
r
esen
ted
with
m
u
ltip
le
s
ce
n
ar
io
s
o
f
s
o
lar
an
d
th
er
m
al
co
n
d
itio
n
s
,
an
d
th
e
co
r
r
esp
o
n
d
in
g
o
p
tim
al
d
u
ty
r
a
tio
s
ar
e
d
eter
m
in
ed
u
s
in
g
k
n
o
wn
MPP d
ata
[
3
0
]
.
On
e
o
f
th
e
m
o
s
t
ef
f
ec
tiv
e
t
r
ain
in
g
alg
o
r
ith
m
s
f
o
r
th
is
a
p
p
licatio
n
is
th
e
L
ev
e
n
b
er
g
-
Ma
r
q
u
ar
d
t
b
ac
k
p
r
o
p
ag
atio
n
alg
o
r
ith
m
,
k
n
o
wn
f
o
r
its
f
ast
co
n
v
er
g
en
c
e
an
d
h
ig
h
ac
cu
r
ac
y
in
f
u
n
ct
io
n
ap
p
r
o
x
im
ati
o
n
.
Du
r
in
g
tr
ain
i
n
g
,
t
h
e
ANN
o
p
ti
m
izes
its
in
ter
n
al
p
ar
am
eter
s
k
n
o
wn
as
weig
h
ts
th
r
o
u
g
h
iter
ativ
e
m
in
im
izatio
n
o
f
th
e
m
ea
n
s
q
u
a
r
ed
e
r
r
o
r
(
MSE
)
b
etwe
en
t
h
e
p
r
ed
icted
o
u
tp
u
t
(
a
)
an
d
th
e
ac
tu
al
t
ar
g
et
o
u
tp
u
t
(
t
)
,
as
d
escr
ib
ed
in
(
1
3
)
.
=
1
∑
(
−
)
2
=
1
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Gri
d
-
tied
p
h
o
to
v
o
lta
ic
s
ystem
MPP
T a
lg
o
r
ith
ms p
erfo
r
ma
n
ce
…
(
Lo
u
is
N
ica
s
e
N
g
u
efa
ck
)
325
W
h
er
e
N
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
tr
ain
in
g
s
am
p
les,
t
v
is
th
e
d
esire
d
o
u
tp
u
t
f
o
r
th
e
v
th
s
a
m
p
le,
an
d
a
v
is
th
e
p
r
ed
icted
o
u
tp
u
t.
T
h
e
tr
ain
i
n
g
g
o
al
is
to
m
in
im
ize
th
is
er
r
o
r
ac
r
o
s
s
th
e
d
ataset,
th
er
eb
y
en
ab
lin
g
th
e
ANN
to
lear
n
th
e
o
p
tim
al
d
u
ty
r
atio
f
o
r
an
y
g
iv
en
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
.
Fig
u
r
e
7
.
ANN
-
co
n
tr
o
lled
MP
PT
s
tr
u
ctu
r
e
[
9
]
T
h
e
p
r
ac
tical
r
ea
lizatio
n
o
f
ANN
-
b
ased
MPPT
h
as
b
ee
n
ex
p
lo
r
ed
ac
r
o
s
s
v
ar
io
u
s
co
n
v
er
te
r
to
p
o
lo
g
ies,
in
clu
d
in
g
B
o
o
s
t
an
d
C
UK
co
n
v
er
ter
s
,
wh
er
e
t
h
e
ANN
s
er
v
es
as
an
in
telli
g
en
t
co
n
tr
o
ller
th
at
co
n
tin
u
o
u
s
ly
ad
ju
s
ts
th
e
o
p
er
atin
g
p
o
in
t
o
f
th
e
P
V
s
y
s
tem
.
T
h
e
s
im
u
latio
n
en
v
ir
o
n
m
en
t
o
f
MA
T
L
AB
/S
im
u
lin
k
was
u
s
ed
to
v
alid
ate
th
e
m
o
d
el,
co
n
f
ir
m
in
g
its
s
u
p
er
i
o
r
ity
in
b
o
t
h
r
esp
o
n
s
e
tim
e
an
d
tr
ac
k
in
g
ac
cu
r
ac
y
.
Of
p
ar
ticu
l
ar
in
ter
est
is
th
e
u
s
e
o
f
f
ee
d
-
f
o
r
war
d
m
u
lti
-
lay
er
n
eu
r
al
n
etwo
r
k
s
,
wh
ich
c
o
n
s
is
t
o
f
in
p
u
t,
h
id
d
e
n
,
an
d
o
u
tp
u
t
lay
er
s
ar
r
an
g
e
d
in
a
f
o
r
war
d
-
o
n
ly
to
p
o
l
o
g
y
.
T
h
ese
ar
ch
itect
u
r
es
ar
e
ca
p
ab
le
o
f
ap
p
r
o
x
im
atin
g
h
i
g
h
ly
n
o
n
lin
ea
r
f
u
n
ctio
n
s
an
d
ca
n
g
en
e
r
alize
well
to
u
n
s
ee
n
d
ata,
m
ak
in
g
th
e
m
h
ig
h
ly
s
u
itab
le
f
o
r
r
ea
l
-
wo
r
l
d
s
o
lar
en
er
g
y
s
y
s
tem
s
th
at
en
co
u
n
te
r
v
ar
y
in
g
o
p
e
r
atio
n
al
co
n
d
itio
n
s
th
r
o
u
g
h
o
u
t
th
e
d
ay
.
I
n
tr
i
n
s
ically
,
ANN
-
co
n
tr
o
lled
MPPT
r
ep
r
esen
ts
a
p
ar
ad
ig
m
s
h
if
t
in
PV
en
er
g
y
o
p
tim
izatio
n
m
o
v
in
g
f
r
o
m
r
u
le
-
b
ased
lo
g
ic
to
in
tell
ig
en
t,
s
elf
-
ad
ap
tiv
e
s
y
s
tem
s
.
B
y
lear
n
in
g
f
r
o
m
d
ata
an
d
c
o
n
tin
u
o
u
s
ly
ev
o
lv
in
g
,
ANN
-
d
r
iv
en
co
n
tr
o
ller
s
n
o
t
o
n
ly
en
h
an
ce
e
n
er
g
y
h
ar
v
esti
n
g
ef
f
icien
c
y
b
u
t
also
p
av
e
th
e
way
f
o
r
n
e
x
t
-
g
en
er
atio
n
s
m
ar
t
PV
g
r
id
s
c
ap
ab
le
o
f
o
p
e
r
atin
g
a
u
to
n
o
m
o
u
s
ly
an
d
o
p
tim
ally
u
n
d
er
d
iv
er
s
e
an
d
d
y
n
am
ic
co
n
d
itio
n
s
[
3
1
]
.
3
.
4
.
F
uzzy
lo
g
ic
co
n
t
r
o
ller
M
P
P
T
T
h
e
em
er
g
e
n
ce
o
f
f
u
zz
y
lo
g
ic
as
a
r
o
b
u
s
t
m
eth
o
d
f
o
r
h
a
n
d
l
in
g
u
n
ce
r
tain
t
y
in
co
m
p
lex
s
y
s
tem
s
ca
n
b
e
cr
ed
ited
to
L
o
tf
i
Z
a
d
eh
,
w
h
o
s
e
p
io
n
ee
r
in
g
wo
r
k
laid
t
h
e
f
o
u
n
d
atio
n
f
o
r
f
u
zz
y
s
et
th
eo
r
y
.
I
n
th
e
r
ea
lm
o
f
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
,
th
is
ap
p
r
o
ac
h
h
as
tr
an
s
lated
i
n
to
th
e
d
ev
elo
p
m
en
t
o
f
th
e
f
u
z
zy
lo
g
ic
c
o
n
tr
o
ller
(
FLC)
,
a
n
o
n
lin
ea
r
,
r
u
le
-
b
ase
d
co
n
tr
o
l
m
eth
o
d
th
at
e
f
f
ec
ti
v
ely
in
teg
r
ates
ex
p
er
t
k
n
o
wl
ed
g
e
an
d
h
e
u
r
is
tic
d
ec
is
io
n
-
m
ak
in
g
in
to
th
e
co
n
tr
o
l
alg
o
r
ith
m
.
U
n
lik
e
tr
ad
itio
n
al
MPPT
tech
n
iq
u
es
th
at
r
ely
h
ea
v
ily
o
n
lin
ea
r
m
o
d
els
an
d
m
ath
em
atica
l
p
r
ec
is
io
n
,
FLCs
th
r
iv
e
in
u
n
ce
r
tain
,
n
o
n
lin
ea
r
,
an
d
r
a
p
id
ly
ch
an
g
in
g
en
v
ir
o
n
m
e
n
ts
,
m
ak
in
g
th
em
p
ar
ticu
lar
ly
well
-
s
u
ited
f
o
r
s
o
lar
p
o
wer
ap
p
licatio
n
s
.
At
its
co
r
e
,
th
e
FLC
f
o
r
MPPT
co
m
p
r
is
es
f
o
u
r
m
ain
c
o
m
p
o
n
en
ts
: f
u
zz
if
i
ca
tio
n
,
f
u
zz
y
r
u
le
b
ase,
in
f
er
e
n
ce
m
ec
h
an
is
m
,
an
d
d
ef
u
zz
if
i
ca
tio
n
.
E
ac
h
p
lay
s
a
cr
itical
r
o
le
i
n
e
n
ab
lin
g
th
e
co
n
tr
o
ller
t
o
d
y
n
am
ically
d
eter
m
in
e
th
e
o
p
tim
al
d
u
ty
c
y
cle
a
d
ju
s
tm
en
t
f
o
r
a
DC
-
DC
co
n
v
er
ter
,
th
u
s
allo
win
g
th
e
PV
s
y
s
tem
to
o
p
er
ate
at
o
r
n
ea
r
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
u
n
d
e
r
v
ar
y
in
g
s
o
lar
an
d
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
[
2
3
]
.
a)
Fu
zz
if
icatio
n
T
h
e
f
u
zz
if
icatio
n
p
r
o
ce
s
s
tr
an
s
lates
cr
is
p
n
u
m
er
ical
in
p
u
t
s
in
to
lin
g
u
is
tic
f
u
zz
y
v
ar
iab
les.
I
n
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
,
th
e
two
p
r
im
ar
y
in
p
u
ts
ar
e
th
e
er
r
o
r
(
e)
an
d
th
e
ch
an
g
e
in
er
r
o
r
(
ce
)
,
ca
lcu
lated
at
ea
ch
s
am
p
lin
g
in
s
tan
t (
k
)
.
T
h
ese
ar
e
d
ef
in
ed
m
ath
em
atica
lly
in
(
1
4
)
an
d
(
1
5
)
.
(
)
=
(
)
−
(
−
1
)
(
)
−
(
−
1
)
(
1
4
)
(
)
=
(
)
−
(
−
1
)
(
1
5
)
Her
e,
P
(
k)
r
e
p
r
esen
ts
th
e
in
s
tan
tan
eo
u
s
p
o
wer
o
f
th
e
PV
a
r
r
ay
,
an
d
I
(
k
)
its
co
r
r
esp
o
n
d
i
n
g
c
u
r
r
en
t.
T
h
ese
in
p
u
ts
ar
e
th
en
m
ap
p
e
d
to
lin
g
u
is
tic
s
u
b
s
ets
,
n
eg
ativ
e
b
ig
(
NB
)
,
n
eg
ativ
e
s
m
all
(
NS)
,
z
er
o
(
Z
0
)
,
p
o
s
itiv
e
s
m
all
(
PS
)
,
an
d
p
o
s
itiv
e
b
ig
(
PB
)
,
th
r
o
u
g
h
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
s
.
T
h
ese
f
u
n
ctio
n
s
g
r
ap
h
ically
d
ef
in
e
th
e
d
e
g
r
ee
o
f
b
elo
n
g
in
g
f
o
r
ea
ch
in
p
u
t
v
ar
iab
le
to
its
c
o
r
r
esp
o
n
d
in
g
f
u
zz
y
s
et,
en
a
b
lin
g
th
e
co
n
tr
o
ller
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
317
-
3
34
326
in
ter
p
r
et
th
e
in
p
u
ts
in
q
u
alitat
iv
e
ter
m
s
.
Fig
u
r
e
8
illu
s
tr
ates
th
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
th
e
in
p
u
t
v
a
r
iab
les
an
d
th
e
o
u
tp
u
t
(
d
u
ty
cy
cle
ch
a
n
g
e,
∆D
)
.
(
a)
(
b
)
(
c)
Fig
u
r
e
8
.
Def
in
e
d
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
:
(
a
)
co
n
v
er
ter
in
p
u
t
cu
r
r
en
t,
(
b
)
c
o
n
v
e
r
ter
in
p
u
t v
o
ltag
e,
an
d
(
c)
f
u
zz
y
co
n
t
r
o
ller
o
u
tp
u
t d
u
t
y
cy
cle
b)
Fu
zz
y
r
u
le
b
ase
T
h
e
f
u
zz
y
r
u
le
b
ase
ac
ts
as
th
e
b
r
ain
o
f
th
e
co
n
tr
o
ller
,
co
m
p
r
is
in
g
a
co
llectio
n
o
f
I
F
-
T
HE
N
r
u
les th
at
en
ca
p
s
u
late
ex
p
e
r
t
k
n
o
wled
g
e
an
d
i
n
tu
itiv
e
co
n
tr
o
l
r
esp
o
n
s
es.
T
h
ese
r
u
les
r
elate
th
e
f
u
zz
y
in
p
u
ts
to
co
r
r
esp
o
n
d
in
g
f
u
zz
y
o
u
t
p
u
ts
an
d
allo
w
th
e
s
y
s
tem
to
r
ea
ct
in
tellig
en
tly
to
v
ar
y
in
g
co
n
d
itio
n
s
.
T
h
e
f
u
zz
y
lo
g
ic
s
y
s
tem
is
th
u
s
ca
p
ab
le
o
f
m
im
ick
in
g
h
u
m
an
-
lik
e
d
ec
is
io
n
-
m
ak
in
g
,
a
d
ju
s
tin
g
th
e
c
o
n
v
e
r
ter
b
eh
av
io
r
b
ased
o
n
p
r
io
r
e
x
p
er
ien
ce
a
n
d
s
y
s
tem
k
n
o
wled
g
e
[
2
3
]
.
c)
I
n
f
er
en
ce
m
ec
h
an
is
m
I
n
f
er
en
ce
is
th
e
r
ea
s
o
n
in
g
en
g
in
e
o
f
th
e
FLC.
I
t
in
ter
p
r
ets
th
e
r
u
le
b
ase
b
y
ev
alu
atin
g
th
e
f
u
zz
y
in
p
u
ts
an
d
d
eter
m
in
in
g
h
o
w
e
ac
h
r
u
le
s
h
o
u
ld
b
e
ap
p
lied
.
T
h
e
o
u
tp
u
t
f
u
zz
y
s
ets
ar
e
co
m
b
in
ed
u
s
in
g
m
eth
o
d
s
s
u
ch
as
Ma
m
d
an
i
o
r
T
a
k
ag
i
-
Su
g
en
o
-
Kan
g
(
T
SK)
i
n
f
er
en
c
e.
Ma
m
d
an
i
i
n
f
er
en
ce
,
f
o
r
ex
am
p
le,
is
k
n
o
wn
f
o
r
its
in
tu
itiv
e
an
d
in
ter
p
r
etab
le
r
u
le
r
ep
r
esen
tatio
n
,
wh
ile
T
SK
is
co
m
p
u
tatio
n
ally
m
o
r
e
ef
f
icien
t
f
o
r
r
ea
l
-
tim
e
ap
p
licatio
n
s
.
T
h
e
s
elec
ted
in
f
er
en
ce
m
eth
o
d
s
y
n
th
esizes
th
e
v
ar
io
u
s
r
u
le
o
u
tco
m
es
i
n
to
a
co
m
p
o
s
ite
f
u
zz
y
o
u
tp
u
t r
e
p
r
esen
tin
g
t
h
e
o
v
e
r
all
co
n
tr
o
l a
ctio
n
[
2
3
]
.
d)
Def
u
zz
if
icatio
n
T
h
e
f
in
al
s
tag
e
i
n
th
e
f
u
zz
y
co
n
tr
o
l
lo
o
p
is
d
e
f
u
zz
if
icatio
n
,
wh
ich
c
o
n
v
e
r
ts
th
e
ag
g
r
eg
ated
f
u
zz
y
o
u
tp
u
t
b
ac
k
in
to
a
cr
is
p
co
n
t
r
o
l
s
ig
n
al
th
at
ca
n
b
e
im
p
lem
en
ted
b
y
th
e
DC
-
DC
co
n
v
er
t
er
.
Am
o
n
g
v
a
r
io
u
s
d
ef
u
zz
if
icatio
n
m
eth
o
d
s
,
th
e
c
en
ter
o
f
g
r
av
ity
(
C
OG)
an
d
ce
n
ter
o
f
a
r
ea
(
C
OA)
ar
e
m
o
s
t
c
o
m
m
o
n
l
y
u
s
ed
d
u
e
to
th
eir
b
alan
ce
d
r
ep
r
esen
tatio
n
o
f
f
u
zz
y
s
ets.
I
n
th
is
s
tu
d
y
,
th
e
o
u
tp
u
t (
∆D
(
k
)
is
co
m
p
u
ted
u
s
in
g
th
e
weig
h
ted
av
er
ag
e
o
f
th
e
m
e
m
b
er
s
h
ip
v
a
lu
es,
as sh
o
wn
in
(
1
6
)
an
d
(
1
7
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.