I
n
t
e
r
n
at
ion
al
Jou
r
n
al
of
P
owe
r
E
lec
t
r
on
ics
an
d
Dr
ive
S
ys
t
e
m
s
(
I
JP
E
DS)
Vol.
13
,
No.
1
,
M
a
r
c
h
20
2
2
,
pp.
528
~
536
I
S
S
N:
2088
-
8694,
DO
I
:
10
.
11591/i
jpeds
.
v
13
.i
1
.
pp
528
-
536
528
Jou
r
n
al
h
omepage
:
ht
tp:
//
ij
pe
ds
.
iaes
c
or
e
.
c
om
T
h
e
p
e
r
f
o
r
m
a
n
c
e
s of
p
ar
t
ia
l
s
h
ad
in
g a
d
j
u
st
e
r
f
o
r
i
m
p
r
ovi
n
g
p
h
ot
ovol
t
ai
c
e
m
u
la
t
o
r
Raz
m
an
Ayop
1
,
Chee
We
i
T
an
1
,
S
ye
d
Nor
az
izul
S
ye
d
Nas
ir
1
,
M
oh
d
Z
ak
i
Da
u
d
1
,
L
au
Kwan
Yie
w
1
,
Nor
j
u
li
a
M
oh
am
ad
Nor
d
in
1
,
Abb
a
L
awan
B
u
k
a
r
2
1
S
c
hool
of
E
le
c
tr
ic
a
l
E
ngi
ne
e
r
in
g, U
ni
ve
r
s
it
i
T
e
knol
ogi
M
a
la
ys
ia
,
J
ohor
,
M
a
la
ys
i
a
2
D
e
pa
r
tm
e
nt
of
E
le
c
tr
ic
a
l
a
nd E
le
c
tr
oni
c
E
ngi
ne
e
r
in
g, F
a
c
ul
ty
of
E
ngi
ne
e
r
in
g, U
ni
ve
r
s
it
y of
M
a
id
ugur
i,
M
a
id
ugur
i
, N
ig
e
r
ia
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
S
e
p
13,
2021
R
e
vis
e
d
J
a
n
20
,
2022
Ac
c
e
pted
J
a
n
27
,
2022
A
p
h
o
t
o
v
o
l
t
a
i
c
(PV
)
emu
l
at
o
r
(PV
E
)
i
s
e
s
s
e
n
t
i
al
eq
u
i
p
men
t
f
o
r
t
h
e
re
s
earch
an
d
d
i
a
g
n
o
s
t
i
c
o
f
PV
g
en
era
t
i
o
n
.
It
i
s
a
co
n
v
e
n
i
e
n
t
,
h
i
g
h
l
y
effi
ci
e
n
t
,
an
d
low
-
co
s
t
ap
p
ro
ac
h
w
h
en
co
m
p
are
d
t
o
c
o
n
t
ro
l
l
a
b
l
e
l
i
g
h
t
s
o
u
rces
.
N
o
n
et
h
el
e
s
s
,
t
h
e
i
m
p
l
eme
n
t
a
t
i
o
n
o
f
t
h
e
p
art
i
al
s
h
ad
i
n
g
cap
ab
i
l
i
t
y
i
n
a
PV
E
i
s
h
i
g
h
l
y
l
i
m
i
t
e
d
i
n
t
erm
s
o
f
effi
ci
e
n
cy
,
co
m
p
u
t
at
i
o
n
b
u
r
n
ed
,
n
u
mb
er
o
f
p
o
w
er
co
n
v
ert
er
s
,
an
d
f
l
ex
i
b
i
l
i
t
y
t
o
ch
a
n
g
e
i
n
t
h
e
am
b
i
e
n
t
c
o
n
d
i
t
i
o
n
.
T
h
i
s
p
a
p
er
p
ro
p
o
s
es
a
p
art
i
a
l
s
h
a
d
i
n
g
ad
j
u
s
t
er
fo
r
a
PV
E
t
h
a
t
can
o
v
erco
me
t
h
e
afo
remen
t
i
o
n
e
d
l
i
m
i
t
a
t
i
o
n
s
.
T
h
e
a
d
j
u
s
t
er
i
s
a
p
p
l
i
ca
b
l
e
t
o
t
h
e
c
o
n
v
en
t
i
o
n
a
l
PV
E
s
i
n
c
e
i
t
i
s
b
as
e
d
o
n
an
a
l
g
o
ri
t
h
m
t
h
a
t
can
b
e
ad
d
e
d
t
o
t
h
e
c
o
n
t
ro
l
l
er
o
f
t
h
e
P
V
E
.
B
y
ad
d
i
n
g
t
h
e
ad
j
u
s
t
er,
t
h
e
co
n
v
e
n
t
i
o
n
al
P
V
E
can
em
u
l
at
e
p
art
i
al
s
h
a
d
i
n
g
.
T
h
e
p
ar
t
i
a
l
s
h
ad
i
n
g
ad
j
u
s
t
er
i
s
a
d
d
e
d
i
n
t
o
a
PV
E
t
h
a
t
u
s
es
t
h
e
d
i
rec
t
referen
ci
n
g
c
o
n
t
ro
l
s
t
ra
t
eg
y
w
i
t
h
t
h
e
b
u
c
k
co
n
t
r
o
l
l
er
reg
u
l
at
e
d
b
y
t
h
e
p
ro
p
o
r
t
i
o
n
a
l
-
i
n
t
e
g
ral
co
n
t
r
o
l
l
er.
T
h
e
res
u
l
t
s
s
h
o
w
t
h
at
t
h
e
PV
E
mai
n
t
a
i
n
s
i
t
s
accu
racy
a
n
d
p
ro
d
u
ce
s
a
s
t
a
b
l
e
o
u
t
p
u
t
v
o
l
t
a
g
e
an
d
cu
r
ren
t
d
u
ri
n
g
t
h
e
l
o
a
d
ch
an
g
es
w
h
en
t
h
e
ad
j
u
s
t
er
i
s
ad
d
ed
.
In
co
n
c
l
u
s
i
o
n
,
t
h
e
p
ro
p
o
s
ed
p
art
i
al
s
h
a
d
i
n
g
ad
j
u
s
t
er
ab
l
e
t
o
i
m
p
ro
v
e
t
h
e
cap
a
b
i
l
i
t
y
o
f
t
h
e
PV
E
b
y
p
ro
v
i
d
i
n
g
a
real
-
t
i
me
p
art
i
al
s
h
a
d
i
n
g
cap
ab
i
l
i
t
y
.
K
e
y
w
o
r
d
s
:
B
uc
k
c
onve
r
ter
P
a
r
ti
a
l
s
ha
ding
P
I
c
ontr
ol
ler
PV
S
ingl
e
diode
model
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
R
a
z
man
Ayop
S
c
hool
of
E
lec
tr
ica
l
E
nginee
r
ing
,
F
a
c
ult
y
of
E
ngin
e
e
r
ing,
Unive
r
s
it
i
T
e
knologi
M
a
lays
ia
81310,
UT
M
J
ohor
B
a
hr
u,
J
ohor
,
M
a
lays
ia
E
mail:
r
a
z
man.
a
yop@utm
.
my
1.
I
NT
RODU
C
T
I
ON
P
hotovol
taic
(
P
V)
e
mul
a
tor
(
P
V
E
)
ha
s
be
c
o
me
e
s
s
e
nti
a
l
e
quipm
e
nt
f
o
r
the
r
e
s
e
a
r
c
h
a
nd
de
ve
lopm
e
nt
of
the
P
V
ge
ne
r
a
ti
on
-
ba
s
e
d
s
ys
tem.
T
he
c
omm
on
c
ont
r
ol
s
tr
a
tegy
f
o
r
the
P
VE
is
th
e
dir
e
c
t
r
e
f
e
r
e
nc
ing
method.
T
he
c
ont
r
ol
s
tr
a
tegy
c
ons
is
ts
of
the
s
tanda
r
d
P
V
model
(
P
VM
)
,
pr
opo
r
ti
ona
l
-
int
e
gr
a
l
(
P
I
)
c
ontr
oll
e
r
,
a
nd
buc
k
c
onve
r
ter
.
I
t
is
a
s
im
ple
c
ontr
ol
s
tr
a
tegy
that
doe
s
not
r
e
quir
e
a
ny
a
ddit
ional
a
lgor
it
hm
to
ope
r
a
te
s
ince
the
ope
r
a
ti
ng
point
is
de
ter
mi
ne
d
by
the
tr
a
ns
ient
r
e
s
pons
e
of
t
he
P
VE
.
Ne
ve
r
thele
s
s
,
thi
s
P
VE
doe
s
not
c
ons
ider
the
pa
r
ti
a
l
s
h
a
ding
e
f
f
e
c
t.
P
a
r
ti
a
l
s
ha
ding
oc
c
ur
s
whe
n
the
P
V
modul
e
s
d
o
not
r
e
c
e
ive
s
im
il
a
r
i
r
r
a
dianc
e
.
T
his
is
due
to
s
ha
dows
c
a
s
t
by
c
louds
or
buil
dings
or
the
P
V
mo
dules
is
not
c
lea
n
ed
pr
ope
r
ly
whic
h
lea
ds
to
the
dus
t
laye
r
.
C
omput
ing
pa
r
ti
a
l
s
ha
ding
is
a
di
f
f
icu
lt
tas
k
e
s
pe
c
ially
if
it
is
im
pleme
nted
in
to
the
P
VE
.
As
a
r
e
s
ult
,
the
major
it
y
of
the
r
e
s
e
a
r
c
h
doe
s
not
include
pa
r
ti
a
l
s
ha
ding
c
a
pa
bil
it
y.
T
he
r
e
a
r
e
2
a
ppr
oa
c
he
s
that
c
a
n
be
us
e
d
to
e
mul
a
te
pa
r
t
ial
s
ha
ding
f
or
the
P
V
E
,
whic
h
a
r
e
the
ha
r
dwa
r
e
a
nd
s
of
twa
r
e
a
ppr
oa
c
he
s
.
F
o
r
the
h
a
r
dwa
r
e
a
ppr
oa
c
h,
the
a
mpl
if
ier
c
ir
c
uit
c
ombi
ne
d
with
the
P
V
c
e
ll
is
a
s
im
ple
P
VE
with
pa
r
ti
a
l
s
ha
ding
c
a
pa
bil
it
y
[
1]
.
T
his
method
a
mpl
if
ies
the
c
ur
r
e
nt
-
volt
a
ge
(
I
-
V)
c
ha
r
a
c
ter
is
ti
c
of
the
P
V
c
e
ll
,
whic
h
a
ll
ows
hig
h
-
powe
r
e
mul
a
ti
on
a
t
a
lowe
r
c
os
t.
None
thele
s
s
,
the
metho
d
is
highl
y
in
e
f
f
icie
nt
s
ince
it
ope
r
a
tes
in
the
l
inea
r
r
e
gion
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
T
he
pe
r
for
manc
e
s
of
par
ti
al
s
hading
adjus
ter
for
impr
ov
ing
photovoltai
c
e
mulator
(
R
az
man
A
y
op
)
529
a
nd
is
li
mi
ted
to
the
type
of
P
V
c
e
ll
us
e
d.
Anothe
r
method
is
to
buil
d
the
P
VE
ba
s
e
d
on
the
tr
a
ns
is
tor
[
2]
.
T
his
method
us
e
s
the
P
VM
e
lec
tr
ica
l
c
ir
c
uit
model
a
s
a
r
e
f
e
r
e
nc
e
a
nd
the
diode
pr
e
s
e
nted
in
the
P
VM
is
r
e
plac
e
d
with
the
tr
a
ns
is
tor
.
Although
thi
s
method
is
s
im
ple
a
nd
it
r
e
quir
e
s
a
low
c
os
t
to
bui
ld
,
it
ha
s
s
e
ve
r
a
l
li
mi
tations
.
T
his
method
r
e
quir
e
s
mul
ti
ple
powe
r
s
our
c
e
s
,
ha
s
low
e
f
f
icie
nc
y,
a
nd
ha
s
a
high
r
ipp
le
whe
n
e
mul
a
ti
ng
the
c
e
r
tain
r
e
gion
on
the
I
-
V
c
ha
r
a
c
ter
i
s
e
d
c
ur
ve
.
Anothe
r
method
us
e
d
to
e
mul
a
te
pa
r
t
ial
s
ha
ding
is
to
c
ombi
ne
s
e
ve
r
a
l
P
VE
[
3]
.
T
his
a
ppr
oa
c
h
is
s
uit
a
ble
f
or
a
s
im
ple
s
e
r
ies
c
onf
igur
a
ti
on
s
ince
th
e
digi
tal
c
ontr
oll
e
r
us
e
d
ne
e
ds
to
c
omput
e
mul
ti
ple
P
VM
in
r
e
a
l
-
ti
me,
whic
h
bur
de
n
the
digi
tal
c
ontr
oll
e
r
a
nd
may
a
f
f
e
c
t
the
pe
r
f
or
manc
e
of
the
P
VE
.
T
his
method
i
s
a
ls
o
una
ble
to
e
mul
a
te
pr
ope
r
ly
a
t
a
c
e
r
tain
r
e
gion
of
the
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
.
F
or
the
s
of
twa
r
e
a
ppr
oa
c
h,
the
c
ontr
ol
s
tr
a
tegy
is
ba
s
e
d
on
the
c
omm
on
dir
e
c
t
r
e
f
e
r
e
nc
ing
method
.
T
he
modi
f
ica
ti
on
is
done
on
the
P
VM
to
a
ll
ow
pa
r
ti
a
l
s
ha
ding
c
a
pa
bil
it
y.
I
f
the
P
VM
output
i
s
a
dde
d
togethe
r
ba
s
e
d
on
the
P
VM
input
,
thes
e
P
VM
s
a
r
e
a
ble
to
pr
oduc
e
pa
r
ti
a
l
s
ha
ding
[4
]
,
[
5]
.
T
hi
s
c
ontr
ol
s
tr
a
tegy
is
c
a
ll
e
d
the
P
VM
a
dde
r
method.
I
t
is
ne
a
r
ly
s
im
il
a
r
to
the
mul
ti
ple
P
V
E
method
with
the
a
dva
ntage
of
us
ing
only
a
s
ingl
e
powe
r
c
onve
r
ter
.
How
e
ve
r
,
the
digi
tal
c
ontr
oll
e
r
s
ti
ll
s
ne
e
d
to
c
omput
e
mul
ti
p
le
P
VM
to
e
mul
a
te
the
pa
r
ti
a
l
s
ha
ding.
T
o
r
e
duc
e
the
c
omp
utation
bur
de
n
,
the
c
omput
a
ti
on
of
the
P
VM
s
is
c
o
nduc
ted
of
f
li
ne
a
nd
the
da
ta
is
c
oll
e
c
ted
a
nd
plac
e
d
in
th
e
look
-
up
table
(
L
UT
)
f
or
the
r
e
a
l
-
ti
me
ope
r
a
ti
on
[6
]
−
[
9]
.
Although
thi
s
method
s
olves
the
c
omput
a
ti
on
pr
oblem,
it
ha
s
a
f
lexibil
it
y
pr
ob
lem.
T
his
mea
ns
t
ha
t
it
is
dif
f
icult
to
c
ha
nge
the
ir
r
a
dianc
e
a
nd
tempe
r
a
tur
e
dur
ing
r
e
a
l
-
ti
me
ope
r
a
ti
o
n
s
ince
the
I
-
V
c
ur
ve
is
g
e
ne
r
a
ted
e
xter
na
ll
y
dur
ing
the
of
f
li
ne
pe
r
iod
.
T
he
li
ter
a
tur
e
s
hows
that
e
mul
a
ti
ng
pa
r
ti
a
l
s
ha
din
g
is
a
dif
f
icult
tas
k.
W
he
n
it
c
omes
to
P
VE
with
the
pa
r
ti
a
l
s
ha
ding
c
a
pa
bil
it
y,
R
e
c
e
ntl
y,
the
s
ingl
e
-
ba
s
e
d
P
VM
with
pa
r
ti
a
l
s
ha
ding
c
a
pa
bil
it
y
is
de
ve
loped,
whic
h
s
igni
f
ica
ntl
y
r
e
duc
e
the
pr
oc
e
s
s
ing
bur
d
e
n
[
10]
.
T
he
r
e
f
o
r
e
,
thi
s
model
is
s
uit
a
ble
to
s
olve
the
li
mi
tation
f
a
c
e
d
by
the
P
VM
a
dde
r
method
.
T
his
p
a
pe
r
pr
e
s
e
nts
a
ne
w
method
f
or
the
P
VE
with
the
a
bil
it
y
to
pr
oduc
e
pa
r
ti
a
l
s
ha
ding
ba
s
e
d
on
the
s
of
twa
r
e
a
ppr
oa
c
h.
I
t
us
e
s
a
ne
w
a
djus
ter
that
c
a
n
pr
oduc
e
pa
r
ti
a
l
s
ha
ding
by
only
a
djus
ti
ng
the
input
of
the
s
tanda
r
d
P
VM
.
T
his
P
VM
is
ba
s
e
d
on
the
s
ingl
e
diode
model
with
a
s
e
r
ies
r
e
s
is
tor
or
1D1R
model.
T
he
c
omm
on
di
r
e
c
t
r
e
f
e
r
e
nc
ing
method
is
c
hos
e
n
a
s
the
c
ontr
ol
s
tr
a
tegy.
T
he
c
onti
nuous
c
ur
r
e
nt
mode
buc
k
c
onve
r
ter
is
s
e
lec
ted
f
or
the
P
VE
a
nd
c
ontr
ol
led
us
ing
the
c
omm
on
P
I
c
ontr
oll
e
r
.
T
he
P
VE
is
s
im
ulate
d
us
ing
the
M
AT
L
AB
/S
im
uli
nk
s
im
ulation
platf
or
m.
T
he
ne
x
t
s
e
c
ti
on
dis
c
us
s
e
s
the
c
ontr
ol
s
tr
a
tegy
us
e
d
in
the
P
VE
.
T
he
n,
the
de
s
ign
of
the
M
P
P
T
c
onve
r
te
r
is
s
hown
in
the
f
oll
owing
s
e
c
ti
on.
T
he
r
e
s
ult
s
a
nd
dis
c
us
s
ion
a
r
e
c
ove
r
e
d
in
the
ne
xt
s
e
c
ti
on.
T
he
pa
pe
r
e
nds
with
a
c
onc
lus
ion.
2.
P
ROP
OS
E
D
P
HO
T
OVOL
T
AI
C
E
M
UL
A
T
OR
T
he
P
VM
us
e
d
f
o
r
the
P
VE
is
a
s
im
pli
f
ied
ve
r
s
ion
of
the
P
VM
a
dde
r
method.
I
ns
tea
d
of
us
ing
mul
ti
ple
s
tanda
r
d
P
VM
,
the
ir
r
a
dianc
e
(
G
)
,
modul
e
tempe
r
a
tur
e
(
T
)
,
a
nd
P
V
volt
a
ge
(
V
pv
)
a
r
e
a
djus
ted
s
o
that
only
one
s
tanda
r
d
P
VM
a
ble
to
be
r
e
pr
e
s
e
nted
a
s
mul
ti
ple
s
tanda
r
d
P
VM
f
or
the
pa
r
ti
a
l
s
ha
ding.
T
he
a
djus
tm
e
nt
a
lgor
it
hm
is
c
a
ll
e
d
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
,
a
s
s
hown
in
F
igur
e
1
.
Dur
ing
the
pa
r
ti
a
l
s
ha
ding,
ther
e
a
r
e
mul
ti
ple
G
a
nd
T
inpu
ts
f
or
the
P
VM
(
G
v
e
c
a
nd
T
v
e
c
)
.
T
he
V
pv
input
f
or
the
P
VM
is
highe
r
than
the
ope
n
-
c
ir
c
uit
volt
a
ge
,
V
oc
,
of
a
s
ingl
e
P
V
modul
e
s
ince
it
is
V
pv
in
s
e
r
ies
(
V
p
v
_
s
r
)
.
T
he
f
unc
ti
on
of
th
e
pa
r
ti
a
l
s
ha
ding
a
djus
ter
is
to
s
e
lec
t
a
s
uit
a
ble
G
a
nd
T
(
G
i
a
nd
T
i
)
f
or
the
one
s
tanda
r
d
P
VM
.
T
he
n
,
the
V
pv
is
r
e
duc
e
d
to
f
or
the
us
e
of
the
one
P
VM
(
V
pv
ne
e
ds
to
be
e
q
ua
l
to
or
lowe
r
than
V
oc
f
or
a
va
li
d
P
VM
)
.
T
he
ne
w
V
pv
is
c
a
ll
e
d
a
djus
ted
V
pv
,
V
pv
_
a
d
j
.
T
he
f
inal
ou
tput
f
or
the
P
VM
is
the
s
e
r
ies
P
V
c
ur
r
e
nt
,
I
p
v
_
s
r
.
T
he
I
p
v
_
s
r
be
c
omes
the
r
e
f
e
r
e
nc
e
c
ur
r
e
nt,
I
r
e
f
,
f
o
r
the
P
I
c
ontr
ol
ler
.
T
he
I
r
e
f
is
c
ompa
r
e
d
with
the
output
c
ur
r
e
nt,
I
o
,
f
r
om
the
buc
k
c
onve
r
te
r
to
obta
in
the
e
r
r
o
r
f
or
the
P
I
c
ontr
ol
ler
.
T
he
P
I
c
ontr
oll
e
r
us
e
s
the
e
r
r
or
to
p
r
oduc
e
the
c
or
r
e
s
ponding
duty
c
yc
le,
d
.
T
he
puls
e
width
modul
a
ti
on,
P
W
M
,
us
e
the
d
a
nd
pr
oduc
e
the
s
witching
p
u
ls
e
,
sp
,
f
or
the
buc
k
c
onve
r
ter
.
T
he
buc
k
c
onve
r
ter
pr
oduc
e
s
the
I
o
a
c
c
or
ding
to
th
e
I
r
e
f
.
T
he
c
or
r
e
s
ponding
output
volt
a
ge
,
V
o
,
f
r
om
the
buc
k
c
onve
r
ter
is
s
e
nt
to
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
to
be
c
ome
V
p
v
_
s
r
.
P
a
r
t
i
a
l
S
h
a
d
i
n
g
A
d
j
u
s
t
e
r
S
t
a
n
d
a
r
d
P
V
M
o
d
el
P
I
C
o
n
t
r
o
l
l
er
P
W
M
B
u
c
k
C
o
n
v
er
t
e
r
G
v
e
c
T
v
e
c
G
i
T
i
V
p
v
_a
d
j
I
p
v
_s
r
=
I
r
e
f
V
p
v
_s
r
=
V
o
I
o
d
sp
V
o
I
o
-
+
V
o
I
o
F
igur
e
1
.
T
he
block
diagr
a
m
of
the
pr
opos
e
d
P
V
E
with
pa
r
ti
a
l
s
ha
ding
c
a
pa
bil
it
y
by
a
dding
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
528
-
53
6
530
2
.
1.
P
h
ot
ovolt
a
ic
m
od
e
l
T
he
P
VM
c
ons
is
t
s
of
two
c
omponents
,
whic
h
a
r
e
t
he
s
tanda
r
d
P
VM
a
nd
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
.
T
he
pur
pos
e
of
the
s
tanda
r
d
P
VM
is
to
c
omput
e
a
s
tanda
r
d
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
without
pa
r
ti
a
l
s
ha
ding.
W
hil
e
the
f
unc
ti
on
o
f
the
pa
r
ti
a
l
s
ha
ding
a
djus
te
r
is
to
r
e
c
e
ive
mul
ti
ple
i
r
r
a
dianc
e
a
nd
tempe
r
a
tu
r
e
input
,
s
e
lec
t
one
ir
r
a
dianc
e
a
nd
one
tempe
r
a
tur
e
,
a
nd
s
e
nt
it
to
a
s
ingl
e
s
tanda
r
d
P
VM
.
T
he
s
e
lec
ti
on
a
l
lows
the
pr
oduc
ti
on
of
the
pa
r
t
ial
s
ha
ding
c
ha
r
a
c
ter
is
ti
c
.
2
.
1
.
1.
S
t
an
d
ar
d
p
h
ot
ovol
t
aic
m
o
d
e
l
T
he
mathe
matica
l
c
ha
r
a
c
ter
is
ti
c
e
qua
ti
on
f
or
th
e
s
tanda
r
d
P
VM
is
pr
e
s
e
nted
u
s
ing
(
1)
,
whic
h
c
a
lcula
te
the
photovol
taic
c
ur
r
e
nt,
I
pv
[
11
]
,
[
12]
.
I
t
is
ba
s
e
d
on
the
s
ingl
e
diode
model
with
a
s
e
r
ies
r
e
s
is
tor
,
whic
h
is
wide
ly
us
e
d
in
the
P
VE
a
ppli
c
a
ti
on
due
to
the
low
c
omput
a
ti
on
bur
de
n
[
13
]
−
[
15]
.
C
omm
only,
the
pa
r
a
ll
e
l
r
e
s
is
tor
,
R
p
,
is
c
ons
ider
e
d
in
the
s
ingl
e
di
ode
P
VM
.
None
thele
s
s
,
it
is
not
a
ppli
c
a
ble
f
or
th
e
pa
r
ti
a
l
s
ha
ding
a
djus
ter
[
10]
.
T
he
Ame
r
is
c
o
80J
-
B
P
V
modul
e
is
c
hos
e
n
f
or
the
s
im
ulation,
i
n
whic
h
the
n
umber
of
P
V
c
e
ll
s
in
a
modul
e
,
n
s
,
is
72
[
16]
.
T
he
K
tv
a
nd
tempe
r
a
tur
e
c
oe
f
f
icie
nt
s
hor
t
c
ir
c
uit
c
u
r
r
e
nt,
K
ti
,
a
r
e
-
0.
16
V/
°C
a
nd
0.
002
A/
°C
,
r
e
s
pe
c
ti
ve
ly.
T
h
e
P
V
modul
e
ha
s
the
maximum
powe
r
point
volt
a
ge
a
nd
c
ur
r
e
nt
a
t
the
S
T
C
(
V
mp
_
s
t
c
a
nd
I
mp
_
s
t
c
)
a
t
35
.
8
V
a
nd
2.
23
A
,
r
e
s
pe
c
ti
ve
ly.
T
he
ope
n
-
c
ir
c
uit
volt
a
ge
a
nd
s
hor
t
c
ir
c
uit
c
ur
r
e
nt
a
t
the
S
T
C
(
V
o
c
_
s
t
c
a
nd
I
s
c
_
s
t
c
)
a
r
e
44.
4
V
a
nd
2
.
32
V
,
r
e
s
pe
c
ti
ve
ly.
=
ℎ
−
[
(
+
)
−
1
]
(
1)
W
he
r
e
I
ph
is
the
photo
-
ge
ne
r
a
ti
on
c
ur
r
e
nt
,
V
pv
is
t
he
P
V
volt
a
ge
,
I
s
is
the
s
a
tur
a
ted
c
ur
r
e
nt,
V
t
is
the
ther
mal
volt
a
ge
,
a
nd
A
is
the
idea
li
ty
f
a
c
tor
.
2
.
1
.
2
.
P
ar
t
ial
s
h
ad
i
n
g
ad
j
u
s
t
e
r
T
he
pa
r
ti
a
l
s
ha
ding
a
djus
ter
is
a
n
e
s
s
e
nti
a
l
pa
r
t
of
the
P
VE
to
pr
oduc
e
pa
r
t
ial
s
ha
ding.
T
he
a
lgo
r
it
hm
s
tar
ts
by
loading
the
pa
r
a
mete
r
s
of
the
P
V
modul
e
a
nd
c
ons
tants
,
a
s
pr
e
s
e
nt
e
d
in
F
igur
e
2
.
T
he
I
ph
f
or
the
f
ir
s
t
G
a
nd
T
(
G
1
a
nd
T
1
)
is
c
a
lcula
ted.
T
he
n
,
the
V
t
a
nd
I
s
a
r
e
e
va
luate
d,
r
e
s
pe
c
ti
ve
ly.
T
he
n,
the
I
ph
f
or
the
f
oll
owing
G
a
nd
T
a
r
e
c
a
lcula
ted
unti
l
the
n
s
is
a
c
hieve
d.
At
the
s
a
me
ti
me,
the
c
r
it
ica
l
P
V
volt
a
ge
,
V
p
v
_
c
r
i
,
is
de
ter
mi
ne
d
us
ing
(
2)
a
nd
(
3)
.
T
he
n,
the
s
um
of
P
V
volt
a
ge
,
V
p
v
_
s
u
m
,
is
c
a
lcula
ted
us
ing
(
4)
.
T
he
V
p
v
_
c
r
i
is
c
ompar
e
d
with
the
V
p
v
_
s
r
.
I
f
the
V
p
v
_
s
r
is
s
maller
th
a
n
V
p
v
_
s
u
m
,
the
V
p
v
_
s
u
m
is
upda
ted
by
s
ubtr
a
c
ted
wi
t
h
V
p
v
_
c
r
i
a
nd
the
V
p
v
_
a
d
j
is
c
a
lcula
ted
us
ing
(
5)
.
T
his
c
ondit
i
on
oc
c
ur
s
whe
n
the
ope
r
a
ti
ng
point
of
the
P
VE
is
lo
c
a
ted
on
the
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
f
or
the
highes
t
G
.
_
(
)
=
(
(
)
)
−
ℎ
(
(
)
,
(
)
)
(
2)
=
[
ℎ
(
(
)
,
(
)
)
−
ℎ
(
(
+
1
)
,
(
+
1
)
)
(
(
)
)
+
1
]
(
3)
_
=
∑
[
_
(
)
]
=
1
+
(
−
1
)
_
_
(
4)
_
=
_
−
_
(
5)
S
t
a
r
t
L
oa
d pa
r
a
m
e
t
e
r
s
a
nd c
ons
t
a
nt
s
i
=1
I
ph
(
G
(
i
)
, T
(
i
)
)
V
t
(
T
(
i
))
I
s
(
T
(
i
))
i
<
N
I
ph
(
G
(
i
+1)
, T
(
i
+1)
)
V
pv
_c
r
i
(
i
)
V
pv
_s
um
E
nd
V
pv
_s
r
<
V
pv
_s
um
V
pv
_a
dj
i
<
=
N
V
pv
_s
um
=
V
pv
_s
um
–
V
pv
_c
r
i
(
G
(
i
)
, T
(
i
)
)
I
pv
=
f
(
V
p
v
_
a
d
j
, G
(
i
)
, T
(
i
)
)
j
=
j
+
1
I
pv
=
0
j
=
1
j
<
=
J
Y
e
s
Y
e
s
Y
e
s
No
No
No
P
a
r
t
i
a
l
S
ha
di
ng A
dj
us
t
e
r
No
Y
e
s
S
t
a
nda
r
d P
V
M
ode
l
I
pv
_s
r
=
I
pv
F
igur
e
2
.
T
he
f
lowc
ha
r
t
of
the
P
VM
with
the
pa
r
ti
a
l
s
ha
ding
c
a
pa
bil
it
y
ba
s
e
d
on
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
method
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
T
he
pe
r
for
manc
e
s
of
par
ti
al
s
hading
adjus
ter
for
impr
ov
ing
photovoltai
c
e
mulator
(
R
az
man
A
y
op
)
531
I
f
the
V
p
v
_
s
r
is
e
qua
l
to
or
la
r
ge
r
than
V
p
v
_
c
r
i
,
the
ope
r
a
ti
ng
point
o
f
the
P
VE
is
loca
ted
on
the
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
f
or
the
s
e
c
ond
-
highes
t
a
n
d
lo
we
r
G
.
I
n
thi
s
c
ondit
ion,
the
a
lgo
r
it
hm
c
he
c
ks
whe
ther
the
c
ur
r
e
nt
pa
r
ti
a
l
s
ha
ding
a
djus
ted,
i
,
is
e
qua
l
to
or
lo
we
r
than
the
N
.
I
f
the
c
ondit
ion
is
not
tr
ue
,
th
is
mea
ns
that
the
c
omput
a
ti
on
is
a
lr
e
a
dy
a
t
the
lowe
s
t
G
a
nd
the
V
p
v
_
a
d
j
is
c
a
lcula
ted
us
ing
(
5)
.
I
f
the
c
ondit
ion
is
t
r
ue
,
thi
s
mea
ns
that
the
c
omput
a
ti
on
is
be
twe
e
n
the
highes
t
G
a
nd
the
lowe
s
t
G
.
F
or
thi
s
c
ondit
ion
,
the
c
ompu
tation
is
r
e
pe
a
ted
unti
l
the
V
p
v
_
s
r
is
s
maller
than
V
p
v
_
c
r
i
.
Af
ter
the
c
omput
a
ti
on
of
the
pa
r
ti
a
l
s
h
a
ding
a
djus
ter
is
c
ompl
e
ted,
the
V
p
v
_
a
d
j
,
G
i
,
a
nd
T
i
a
r
e
pr
oduc
e
d
a
nd
us
e
d
by
the
s
tanda
r
d
P
VM
.
S
ince
the
s
tanda
r
d
P
VM
is
ba
s
e
d
on
a
n
im
pli
c
it
e
qua
ti
on,
the
it
e
r
a
ti
on
method
s
uc
h
a
s
the
Ne
wton
-
R
a
phs
on
me
thod
is
ne
e
de
d.
Us
ing
the
Ne
wton
-
R
a
phs
on
meth
od,
(
1)
i
s
it
e
r
a
ted
unti
l
the
number
of
it
e
r
a
t
ions
f
or
the
s
tan
da
r
d
P
VM
,
J
,
is
a
c
hieve
d.
I
n
the
e
nd,
the
I
pv
be
c
o
mes
the
I
p
v
_
s
r
.
2
.
2.
B
u
c
k
c
on
ve
r
t
e
r
T
he
P
VE
r
e
quir
e
s
a
powe
r
c
onve
r
ter
to
wor
k
.
T
h
e
powe
r
c
onve
r
ter
us
e
d
f
o
r
the
P
VE
is
c
omm
only
the
buc
k
c
onve
r
ter
due
to
the
low
pa
s
s
ive
c
omponents
r
e
quir
e
ment
a
nd
high
-
powe
r
e
f
f
icie
nc
y
[6
]
,
[
17
]
,
[
18
]
.
T
he
e
quivale
nt
c
ir
c
uit
o
f
the
buc
k
c
onve
r
ter
p
r
o
vided
in
F
igu
r
e
3
c
ontains
pa
r
a
s
it
ic
r
e
s
is
tor
s
f
or
a
mor
e
r
e
a
li
s
ti
c
s
im
ulation.
T
he
r
e
a
r
e
two
pa
r
ts
in
de
s
ign
ing
the
buc
k
c
onve
r
ter
,
whic
h
is
the
de
s
ign
of
the
pa
s
s
ive
e
leme
nt
a
nd
the
c
ontr
oll
e
r
f
o
r
the
buc
k
c
onve
r
ter
.
V
i
L
C
R
o
+
V
o
-
I
o
sp
r
L
r
C
F
igur
e
3
.
T
he
topol
ogy
o
f
the
buc
k
c
onve
r
ter
with
pa
r
a
s
it
ic
r
e
s
is
tor
s
T
he
de
s
ign
of
the
buc
k
c
onve
r
ter
f
or
the
P
VE
is
ba
s
e
d
on
the
c
onve
nti
ona
l
buc
k
c
onve
r
ter
[
19
]
,
[
20]
.
T
he
f
ir
s
t
pa
r
a
mete
r
c
a
lcula
ted
is
the
inpu
t
vo
lt
a
ge
,
V
i
us
ing
(
6
)
.
T
he
V
i
is
a
f
f
e
c
ted
by
the
maxi
mum
V
oc
,
V
oc
_
m
a
x
,
a
nd
maximum
d
,
d
m
a
x
.
B
a
s
e
d
on
the
s
im
ulation
of
the
P
VM
,
the
V
oc
_
m
a
x
is
195
.
6
V.
W
hil
e
th
e
d
m
a
x
is
s
e
t
to
0.
9.
T
he
c
a
lcula
ted
V
i
is
217.
3
V.
S
ince
t
he
c
a
lcula
ti
on
doe
s
not
c
on
s
ider
the
nonidea
li
ty
f
a
c
tor
,
a
higher
volt
a
ge
ne
e
ds
to
be
c
hos
e
n,
whic
h
is
250
V.
i
=
_
(
6)
T
he
inducta
nc
e
,
L
,
de
s
ign
is
i
mpor
tant
to
mainta
in
c
onti
nuous
c
ur
r
e
nt
ope
r
a
ti
on.
T
his
is
e
s
s
e
nti
a
l
e
s
pe
c
ially
f
or
the
P
I
c
ont
r
oll
e
r
de
s
ign
s
ince
a
dif
f
e
r
e
nt
c
ontr
oll
e
r
is
ne
e
de
d
if
the
buc
k
c
onve
r
te
r
op
e
r
a
tes
in
the
dis
c
onti
nuous
c
ur
r
e
nt
mode
.
T
he
V
o
_
m
a
x
a
nd
t
he
maximum
out
put
r
e
s
is
tanc
e
,
R
o
_
m
a
x
,
ba
lanc
e
ne
e
ds
to
be
c
ons
ider
e
d
in
the
de
s
ign.
I
n
the
idea
l
c
ondit
ion
,
th
e
R
o
_
m
a
x
is
in
f
ini
ty.
None
thele
s
s
,
the
buc
k
c
onve
r
te
r
c
a
nnot
be
c
ontr
oll
e
d
whe
n
the
R
o
_
m
a
x
is
inf
ini
ty
[
19
]
.
T
he
r
e
f
or
e
,
a
c
e
r
tain
li
m
it
is
c
hos
e
n,
whic
h
is
700
Ω
.
T
h
is
R
o
_
m
a
x
is
c
hos
e
n
be
c
a
u
s
e
it
c
ove
r
s
the
mos
t
a
r
e
a
in
the
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
.
B
a
s
e
d
on
the
R
o
_
m
a
x
,
th
e
output
volt
a
ge
c
or
r
e
s
ponding
to
R
o
_
m
a
x
,
V
o_
R
o
_
m
a
x
,
is
obt
a
ined
f
r
om
the
P
VM
.
Us
ing
(
7)
,
the
r
e
quir
e
d
L
is
3
mH,
whic
h
the
s
witching
f
r
e
que
nc
y,
f
s
,
is
20
kHz
.
T
h
e
c
or
r
e
s
ponding
i
nter
na
l
r
e
s
is
tanc
e
of
the
inductor
,
r
L
,
is
0.
9
Ω.
=
(
1
−
_
_
)
_
2
(
7)
T
he
c
a
pa
c
it
a
nc
e
,
C
,
is
de
s
igned
to
ope
r
a
te
the
buc
k
c
onve
r
ter
a
t
the
de
s
ir
e
d
r
ippl
e
f
a
c
tor
.
T
he
c
hos
e
n
output
volt
a
ge
r
ippl
e
f
a
c
tor
,
γ
Vo
,
f
or
the
P
VE
is
0
.
5%
[
21
]
.
B
a
s
e
d
on
(
8)
,
the
C
r
e
qui
r
e
d
is
36
µ
F
,
whic
h
mi
nim
um
D
,
d
m
i
n
,
is
0.
01
.
T
he
c
or
r
e
s
pondin
g
i
nter
na
l
r
e
s
is
tanc
e
of
the
c
a
pa
c
it
or
,
r
C
,
is
0.
3
Ω
.
=
1
−
8
2
(
8)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
528
-
53
6
532
T
o
de
s
ign
the
P
I
c
ont
r
oll
e
r
,
the
tr
a
ns
f
e
r
f
unc
ti
on
of
the
powe
r
c
onve
r
te
r
is
ne
e
de
d.
T
he
t
r
a
ns
f
e
r
f
unc
ti
on
of
the
buc
k
c
onve
r
ter
,
G
b
(
s
)
,
is
ne
e
de
d,
a
s
pr
ovided
in
(
9
)
[
18
]
,
[
22]
.
T
he
G
b
(
s
)
ha
s
the
I
o
a
s
of
the
output
s
ince
the
c
ur
r
e
nt
-
c
ontr
oll
e
d
di
r
e
c
t
r
e
f
e
r
e
nc
ing
method
is
us
e
d
f
o
r
thi
s
P
VE
.
F
o
r
the
tr
a
ns
f
e
r
f
unc
ti
on
of
the
P
I
c
ontr
oll
e
r
,
G
c
(
s
)
,
it
c
a
n
be
pr
e
s
e
nted
a
s
(
10)
.
Us
ing
the
a
utom
a
ti
c
tuni
ng
f
unc
ti
on
p
r
ovide
d
by
the
M
AT
L
AB
/S
im
uli
nk,
the
pr
op
o
r
ti
ona
l
a
nd
int
e
gr
a
l
ga
ins
(
K
p
a
nd
K
i
)
a
r
e
0
.
0001
a
nd
39,
r
e
s
pe
c
ti
ve
ly.
(
)
=
̂
(
)
̂
(
)
=
1
2
+
1
+
1
(
9)
(
)
=
̂
(
)
̂
(
)
=
+
⁄
(
10)
3.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
T
he
r
e
is
f
ive
pe
r
f
or
manc
e
a
na
lys
is
c
onduc
ted
f
or
the
p
r
opos
e
d
P
VE
.
T
his
pe
r
f
or
manc
e
a
na
lys
is
is
c
onduc
ted
to
e
ns
ur
e
the
dir
e
c
t
r
e
f
e
r
e
nc
ing
meth
od
c
ontr
ol
s
tr
a
tegy
a
ble
to
c
ope
with
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
modi
f
ica
ti
on
.
T
he
a
c
c
ur
a
c
y,
load,
i
r
r
a
dia
nc
e
,
s
tabili
ty,
a
nd
e
f
f
icie
nc
y
tes
ts
a
r
e
c
onduc
ted
us
ing
a
r
e
s
is
t
ive
load.
W
hil
e
the
c
ompatibi
li
ty
tes
t
is
c
onduc
ted
us
ing
the
M
P
P
T
c
onve
r
ter
a
s
the
load
f
or
the
P
VE
,
whic
h
the
r
e
s
is
ti
ve
load
is
r
e
moved
f
r
o
m
the
s
im
ul
a
ti
on.
3.
1.
Ac
c
u
r
ac
y
t
e
s
t
T
he
a
c
c
ur
a
c
y
is
a
n
e
s
s
e
nti
a
l
a
s
pe
c
t
whe
n
it
c
omes
to
P
V
E
.
T
he
P
VE
is
c
ons
ider
e
d
a
c
c
ur
a
te
if
the
ope
r
a
ti
ng
point
s
f
a
ll
on
the
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
of
the
P
V.
T
hr
e
e
types
of
a
c
c
ur
a
c
y
tes
t
s
c
a
n
be
c
onduc
ted
on
the
P
VE
.
T
he
s
e
c
a
n
be
e
it
he
r
by
c
ompar
ing
the
V
o
a
nd
I
o
o
f
the
P
V
E
with
the
V
pv
a
nd
I
pv
o
f
the
P
VM
[
23
]
,
[
24]
,
P
V
modul
e
[
25
]
,
o
r
both
P
VM
a
nd
P
V
modu
le
[
11]
.
T
he
c
ompar
is
on
with
the
P
V
modul
e
e
va
luate
s
the
a
c
c
ur
a
c
y
of
the
c
ontr
ol
s
tr
a
tegy
a
nd
P
VM
us
e
d
in
the
P
VE
.
W
hil
e
the
c
ompar
is
on
with
the
P
VM
only
e
va
luate
s
the
a
c
c
ur
a
c
y
of
the
c
ontr
ol
s
tr
a
tegy
us
e
d
in
the
P
VE
.
S
ince
the
pa
pe
r
f
oc
us
e
d
on
the
a
c
c
ur
a
c
y
of
the
c
ontr
ol
s
tr
a
tegy
a
nd
not
the
a
c
c
ur
a
c
y
of
the
P
VM
,
the
V
o
a
nd
I
o
of
the
P
VE
a
r
e
c
ompar
e
d
with
the
V
pv
a
nd
I
pv
of
the
P
VM
.
T
h
e
c
o
mp
a
r
is
on
o
f
t
he
I
-
V
c
ha
r
a
c
te
r
is
t
ic
c
u
r
ve
s
pr
od
uc
e
d
b
y
t
he
P
V
E
a
n
d
P
VM
a
r
e
s
ho
wn
i
n
F
ig
u
r
e
4
.
T
he
r
e
s
ult
s
hows
that
the
V
o
a
nd
I
o
pr
oduc
e
d
by
th
e
P
VE
is
on
the
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
of
P
V.
T
his
s
how
that
the
pr
opos
e
d
P
VE
ha
s
high
a
c
c
ur
a
c
y.
T
he
I
-
V
c
ha
r
a
c
ter
is
ti
c
of
the
P
VE
is
in
th
e
dis
c
r
e
te
f
or
m
be
c
a
us
e
the
a
c
c
ur
a
c
y
of
the
P
VE
be
c
omes
lowe
r
if
the
va
r
i
a
ble
load
is
s
we
e
p
f
r
om
z
e
r
o
to
inf
ini
ty
.
T
his
is
d
ue
to
the
s
low
tr
a
ns
ient
r
e
s
pons
e
of
the
P
VE
.
T
he
P
V
E
r
e
qu
ir
e
s
a
c
e
r
tain
ti
me
to
a
c
hieve
a
s
tea
dy
-
s
tate
.
T
he
r
e
f
or
e
,
the
V
o
a
nd
I
o
of
the
P
VE
a
r
e
r
e
c
or
de
d
a
f
ter
the
s
tea
dy
-
s
tate
is
a
c
hieve
d
with
mul
ti
ple
f
ixed
loads
.
T
he
r
e
i
s
a
ls
o
no
s
hor
t
-
c
ir
c
uit
(
R
o
is
z
e
r
o)
a
nd
ope
n
-
c
ir
c
uit
(
R
o
is
inf
ini
ty)
tes
ts
c
onduc
ted
on
the
P
V
E
.
T
his
is
be
c
a
us
e
the
buc
k
c
onve
r
ter
c
a
nnot
wor
k
pr
ope
r
ly
dur
ing
thi
s
c
ondit
ion.
W
he
n
the
R
o
is
e
qua
l
to
z
e
r
o
,
the
V
o
ne
e
ds
to
be
z
e
r
o,
whic
h
then
pr
oduc
e
z
e
r
o
I
o
i
f
a
buc
k
c
onve
r
ter
is
us
e
d.
How
e
ve
r
,
the
I
pv
f
r
om
the
P
VM
is
not
z
e
r
o
whe
n
V
pv
e
qua
ls
to
z
e
r
o,
whic
h
mea
ns
that
the
P
VE
f
a
il
s
to
e
mul
a
te
the
s
hor
t
-
c
ir
c
uit
tes
t.
I
f
the
R
o
is
inf
ini
ty
,
the
V
o
c
a
nnot
be
r
e
gulate
d
a
nd
ope
r
a
tes
ne
a
r
to
V
i
.
A
di
f
f
e
r
e
nt
type
of
c
onve
r
ter
is
ne
e
de
d
in
or
de
r
to
op
e
r
a
te
a
t
thes
e
point
s
.
F
igur
e
4
.
T
he
c
ompar
is
on
of
the
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
of
the
P
VM
a
nd
P
V
E
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
T
he
pe
r
for
manc
e
s
of
par
ti
al
s
hading
adjus
ter
for
impr
ov
ing
photovoltai
c
e
mulator
(
R
az
man
A
y
op
)
533
3.
2
.
L
oad
t
e
s
t
T
he
load
tes
t
is
c
onduc
ted
on
the
P
VE
to
a
na
lys
e
the
t
r
a
ns
ienc
e
pe
r
f
or
manc
e
a
nd
s
tabili
ty
dur
ing
load
c
ha
nge
s
.
A
good
P
VE
c
a
n
c
ha
nge
to
a
ne
w
ope
r
a
ti
ng
poin
t
without
a
ny
os
c
il
lation
a
t
a
f
a
s
t
r
a
te.
B
y
r
e
f
e
r
r
ing
to
F
igur
e
5
(
a
)
,
the
load
s
tar
ts
a
t
30
Ω
.
A
t
0.
2
s
,
the
load
is
s
teppe
d
up
to
160
Ω
f
or
0.
2
s
.
T
he
n
the
load
is
s
teppe
d
down
ba
c
k
to
30
Ω.
T
he
wa
ve
f
or
ms
of
the
Vo
a
nd
I
o
of
the
P
VE
a
r
e
r
e
c
or
de
d
in
F
ig
ur
e
5
(
a
)
a
nd
F
igur
e
5
(
b
)
,
r
e
s
pe
c
ti
ve
ly.
T
he
pe
r
c
e
ntage
ove
r
s
hoot,
%
OS
,
o
f
the
is
obs
e
r
ve
d
a
nd
it
is
c
a
lcula
ted
us
ing
(
11)
[
26
]
.
A
P
VE
ne
e
ds
to
ha
ve
z
e
r
o
or
low
%
OS
to
a
void
da
maging
the
load
or
the
c
omponents
in
t
he
P
VE
.
Anothe
r
f
a
c
tor
that
ne
e
ds
to
be
c
ons
ider
e
d
is
th
e
s
e
tt
li
ng
ti
me,
ts
,
whic
h
is
us
e
d
to
a
na
lys
e
the
tr
a
ns
ient
pe
r
f
or
manc
e
o
f
the
P
V
E
,
whic
h
is
de
f
ined
a
s
the
ti
me
take
n
f
or
the
I
o
to
b
e
withi
n
2%
of
it
s
s
tea
dy
-
s
tate
va
lue.
%
O
S
=
(
)
−
(
)
(
)
×
100%
(
11
)
W
he
r
e
I
o
(m
a
x
)
is
the
maximum
outpu
t
c
ur
r
e
nt
ove
r
s
hoot
a
nd
I
o
(
s
s
)
is
the
s
tea
dy
-
s
tate
output
c
ur
r
e
nt.
B
a
s
e
d
on
F
igur
e
5
(
b
)
,
whe
n
the
load
is
s
teppe
d
down
f
r
om
160
Ω
to
30
Ω
,
ther
e
is
a
lar
ge
I
o
ove
r
s
hoot
oc
c
ur
.
Us
ing
(
11)
,
the
%
OS
is
147
.
7
%
.
T
he
la
r
ge
I
o
ove
r
s
hoot
is
c
a
us
e
d
by
the
C
t
ha
t
tr
y
to
maintain
V
o
a
f
ter
the
load
is
s
teppe
d
down.
T
his
ove
r
s
hoot
c
a
nnot
be
a
voided
whe
n
the
buc
k
c
on
ve
r
ter
is
us
e
d
f
or
the
P
VE
.
None
thele
s
s
,
the
C
is
only
36
µ
F
a
nd
the
I
o
s
hould
be
r
e
duc
e
d
quickly.
How
e
v
e
r
,
the
I
o
wa
ve
f
or
m
s
hows
that
it
take
s
43.
4
ms
to
a
c
hieve
a
s
tea
dy
-
s
tate
.
T
he
s
low
r
e
s
pons
e
is
due
to
the
c
on
s
tr
a
int
of
the
P
I
c
ontr
oll
e
r
.
T
o
r
e
duc
e
the
dur
a
ti
on
of
the
ov
e
r
s
hoot,
a
f
a
s
ter
a
nd
mo
r
e
r
obus
t
c
ont
r
oll
e
r
li
ke
f
u
z
z
y
logi
c
or
s
hif
t
c
ontr
oll
e
r
s
[
20]
.
T
he
r
e
s
ult
s
hows
the
t
s
dur
ing
the
be
ginni
ng
of
the
ope
r
a
ti
on
is
44.
1
ms
.
W
he
n
the
load
is
s
teppe
d
up
a
nd
down
,
the
t
s
is
80
.
5
ms
a
nd
43.
4
ms
,
r
e
s
pe
c
ti
ve
ly.
T
he
r
e
s
ult
s
s
how
that
the
t
s
is
f
a
s
ter
whe
n
the
load
is
s
teppe
d
down
c
ompar
e
d
to
whe
n
the
load
is
s
teppe
d
up.
T
he
s
low
r
e
s
pons
e
dur
ing
a
high
load
c
ondit
ion
is
due
to
the
li
mi
tation
o
f
the
P
I
c
o
ntr
oll
e
r
.
T
he
P
I
c
ontr
oll
e
r
is
de
s
igned
a
t
t
he
lowe
s
t
load
to
a
void
uns
table
output
.
I
f
the
P
I
c
ontr
oll
e
r
is
de
s
ign
ed
a
t
the
higher
load
c
ondit
ion,
the
output
be
c
omes
uns
table
whe
n
the
load
is
low
.
None
thele
s
s
,
the
P
I
c
ontr
oll
e
r
a
lone
doe
s
not
a
f
f
e
c
t
the
t
s
f
or
the
P
VE
[
20]
.
I
f
the
e
f
f
e
c
t
of
P
I
c
ontr
oll
e
r
a
lone
is
a
c
c
ounted,
the
t
s
incr
e
a
s
e
s
a
s
the
V
o
incr
e
a
s
e
s
.
B
y
r
e
f
e
r
r
ing
to
F
igu
r
e
6
,
thi
s
r
e
lations
hip
doe
s
not
a
pply.
T
his
is
be
c
a
us
e
the
c
ontr
ol
s
tr
a
tegy
us
e
d
in
the
P
VE
a
f
f
e
c
ts
the
t
s
f
o
r
t
he
P
VE
.
S
ince
the
d
ir
e
c
t
r
e
f
e
r
e
nc
ing
c
ontr
ol
s
tr
a
tegy
is
us
e
d
f
o
r
the
P
V
E
,
the
t
s
be
c
omes
higher
a
t
the
loca
l
a
nd
global
M
P
P
.
T
he
t
s
be
c
omes
lowe
r
whe
n
the
ope
r
a
ti
on
lea
ve
s
the
M
P
P
a
nd
move
to
the
c
ons
tant
vo
lt
a
ge
r
e
gion.
A
r
obus
t
P
VE
s
hould
maintain
a
c
ons
tant
t
s
a
t
the
va
r
ious
ope
r
a
ti
ng
point
.
(
a
)
(
b)
F
igur
e
5
.
T
he
ti
me
-
domain
r
e
s
pons
e
of
the
P
VE
whe
n
the
load
is
s
teppe
d
up
f
r
om
30
Ω
to
160
Ω
a
t
0
.
2
s
a
nd
s
teppe
d
down
f
r
om
160
Ω
to
30
Ω
a
t
0
.
4
s
(
a
)
outp
ut
volt
a
ge
wa
ve
f
or
m
(
b)
output
c
ur
r
e
nt
wa
ve
f
or
m
F
igur
e
6
.
T
he
s
e
tt
li
ng
ti
me
of
the
output
volt
a
ge
of
the
P
VE
a
t
va
r
ious
load
c
ondit
ion
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
528
-
53
6
534
4.
CONC
L
USI
ON
T
he
P
VM
r
e
quir
e
s
a
high
c
omput
a
ti
on
s
ince
it
is
ba
s
e
d
on
a
n
im
pli
c
it
e
qua
ti
on
that
r
e
quir
e
s
mul
ti
ple
it
e
r
a
ti
ons
.
T
o
pr
oduc
e
pa
r
ti
a
l
s
ha
ding,
s
e
ve
r
a
l
P
VM
s
ne
e
d
to
be
us
e
d,
whic
h
f
ur
the
r
incr
e
a
s
e
s
the
c
omput
a
ti
on
bur
de
n.
None
thele
s
s
,
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
a
ll
ows
pa
r
ti
a
l
s
ha
ding
c
a
pa
bil
it
y
wi
th
only
a
s
ingl
e
P
VM
.
T
his
gives
a
n
a
dva
ntage
f
or
the
P
VE
be
c
a
us
e
the
P
VE
a
ble
to
ope
r
a
te
in
r
e
a
l
ti
me
a
nd
r
e
quir
e
s
a
low
c
omp
utation
to
wor
k
p
r
ope
r
ly.
T
he
pa
r
ti
a
l
s
ha
ding
a
djus
ter
is
a
ne
w
c
onc
e
pt
a
nd
is
not
be
ing
tes
ted
in
the
P
VE
.
B
a
s
e
d
on
the
s
im
ulation
r
e
s
ult
s
,
thi
s
a
djus
ter
is
s
uit
a
ble
f
or
the
P
VE
.
T
he
a
c
c
ur
a
c
y
tes
t
s
hows
t
he
P
VE
c
a
n
im
it
a
te
the
I
-
V
c
ha
r
a
c
ter
is
ti
c
c
ur
ve
p
r
o
duc
e
d
by
the
P
VM
.
T
his
r
e
s
ult
not
only
s
hows
c
ombi
ning
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
with
the
P
V
E
ha
s
pr
oduc
e
d
high
a
c
c
ur
a
c
y
r
e
s
ult
s
but
a
ls
o
s
hows
it
is
s
table
dur
ing
the
s
tea
dy
s
tate
ope
r
a
ti
on
.
T
he
r
e
s
ult
s
hows
that
th
e
tr
a
ns
ient
r
e
s
pons
e
be
c
omes
s
lowe
r
a
s
the
load
in
c
r
e
a
s
e
s
.
T
he
r
e
is
a
ls
o
a
c
u
r
r
e
nt
s
pike
that
oc
c
ur
s
dur
ing
th
e
load
s
teppe
d
down
.
A
di
f
f
e
r
e
nt
powe
r
c
onve
r
ter
,
c
los
e
d
-
loop
c
ontr
oll
e
r
,
a
nd
c
ont
r
ol
s
tr
a
tegy
a
r
e
ne
e
de
d
to
im
p
r
ove
the
P
V
E
.
I
n
c
onc
lus
ion,
the
pa
r
ti
a
l
s
ha
ding
a
djus
ter
c
a
n
wor
k
with
the
P
V
E
s
ince
it
is
a
c
c
ur
a
te.
T
he
tr
a
ns
ient
r
e
s
pons
e
of
the
P
VE
r
e
quir
e
s
im
p
r
ove
ment
due
to
the
s
low
r
e
s
pons
e
a
t
a
high
load
a
nd
a
high
c
ur
r
e
nt
s
pike
whe
n
the
load
de
c
r
e
a
s
e
s
.
AC
KNOWL
E
DGE
M
E
NT
S
T
he
g
r
a
ti
tude
to
Unive
r
s
it
i
T
e
knologi
M
a
lays
ia
(
U
T
M
)
f
or
pr
ovidi
ng
f
unding
,
U
T
M
E
nc
our
a
ge
ment
R
e
s
e
a
r
c
h
(
UT
M
E
R
)
Gr
a
nt
unde
r
vote
Q.
J
130
000.
2651.
18J
39.
L
a
s
tl
y,
a
ppr
e
c
iation
to
c
oll
e
a
gue
s
that
c
ontr
ibut
e
d
to
the
c
ompl
e
ti
on
o
f
the
r
e
s
e
a
r
c
h
.
RE
F
E
RE
NC
E
S
[
1]
O
.
M
id
tg
a
r
d,
“
A
s
im
pl
e
phot
ovol
ta
ic
s
im
ul
a
to
r
f
or
te
s
ti
ng
of
pow
e
r
e
le
c
tr
oni
c
s
,
”
2007
E
ur
ope
an
C
onf
e
r
e
nc
e
on
P
ow
e
r
E
le
c
tr
oni
c
s
and A
ppl
ic
at
io
ns
, 2007, pp. 1
-
10, doi:
10.1109/E
P
E
.2007.4417450.
[
2]
A
.
Z
e
ga
oui
,
M
.
A
il
le
r
ie
,
P
.
P
e
ti
t,
a
nd
J
.
-
P
.
C
ha
r
le
s
,
“
U
ni
ve
r
s
a
l
T
r
a
ns
is
to
r
-
ba
s
e
d
ha
r
dw
a
r
e
S
I
M
ul
a
to
r
f
or
r
e
a
l
ti
me
s
im
ul
a
ti
on
of
phot
ovol
ta
ic
ge
ne
r
a
to
r
s
,
”
Sol
ar
E
ne
r
g
y
, vol
. 134, pp. 193
-
201,
2016, doi:
10.1016/j
.s
ol
e
ne
r
.2016.05.005.
[
3]
S
.
M
is
hr
a
,
S
.
R
a
ju
,
A
.
K
s
hi
r
s
a
ga
r
a
nd
N
.
M
oha
n,
“
A
n
E
x
tr
e
me
ly
L
ow
-
C
os
t
M
ul
ti
-
P
a
ne
l
P
V
E
mul
a
to
r
f
or
R
e
s
e
a
r
c
h
a
nd
E
duc
a
ti
on,
”
2018
I
E
E
E
E
ne
r
gy
C
onv
e
r
s
io
n
C
ong
r
e
s
s
and
E
x
pos
it
io
n
(
E
C
C
E
)
,
2018,
pp.
4760
-
4765,
doi
:
10.1109/E
C
C
E
.2018.8557361.
[
4]
T
.
D
.
M
a
i,
S
.
D
e
B
r
e
uc
ke
r
,
K
.
B
a
e
r
t,
a
nd
J
.
D
r
ie
s
e
n,
“
R
e
c
o
nf
ig
ur
a
bl
e
e
mul
a
to
r
f
or
phot
ovol
ta
ic
modul
e
s
unde
r
s
ta
ti
c
pa
r
ti
a
l
s
ha
di
ng c
ondi
ti
ons
,
”
Sol
ar
E
ne
r
gy
, vol
. 141, pp. 256
-
265, J
a
nu
a
r
y 2017
, doi
:
10.1016/j
.s
ol
e
ne
r
.2016.11.050
.
[
5]
R
.
K
a
dr
i,
H
.
A
ndr
e
i,
J
.
-
P
.
G
a
ube
r
t,
T
.
I
va
novi
c
i,
G
.
C
ha
mp
e
noi
s
,
a
nd
P
.
A
ndr
e
i,
“
M
ode
li
ng
of
th
e
phot
ovo
lt
a
ic
c
e
ll
c
ir
c
ui
t
pa
r
a
me
te
r
s
f
or
opt
im
um
c
onne
c
ti
on
mode
l
a
nd
r
e
a
l
-
ti
me
e
mul
a
to
r
w
it
h
pa
r
ti
a
l
s
ha
dow
c
ondi
ti
ons
,
”
E
ne
r
gy
,
vol
.
42,
no.
1,
pp. 57
-
67, 2012
, doi
:
10.1016/j
.e
ne
r
gy.2011.10.018
.
[
6]
M
.
A
la
oui
,
H
.
M
a
ke
r
,
A
.
M
ouhs
e
n,
a
nd
H
.
H
ih
i,
“
P
ho
to
vol
t
a
ic
e
mul
a
to
r
of
di
f
f
e
r
e
nt
s
ol
a
r
a
r
r
a
y
c
on
f
ig
ur
a
t
io
ns
unde
r
pa
r
ti
a
l
s
ha
di
ng c
ondi
ti
ons
us
in
g da
mpi
ng i
nj
e
c
ti
on c
ont
r
ol
le
r
,”
I
nt
e
r
nat
io
nal
J
our
nal
of
P
ow
e
r
E
le
c
tr
oni
c
s
and Dr
iv
e
Sy
s
te
m
,
vol
. 11,
no.
2,
pp. 1019
-
1030, J
une
2020
, doi
:
10.11591/i
jp
e
ds
.v11.i2.pp1019
-
1030
.
[
7]
A
.
X
e
nophontos
,
J
.
R
a
r
e
y,
A
.
T
r
ombe
tt
a
a
nd
A
.
M
.
B
a
z
z
i,
“
A
f
le
xi
bl
e
lo
w
-
c
os
t
phot
ovol
ta
ic
s
ol
a
r
p
a
ne
l
e
mul
a
ti
on
pl
a
tf
o
r
m,
”
2014 P
ow
e
r
and E
ne
r
gy
C
onf
e
r
e
nc
e
at
I
ll
in
oi
s
(
P
E
C
I
)
, 2014, p
p. 1
-
6, doi:
10.1109/P
E
C
I
.2014.6804542.
[
8]
C.
-
C
.
C
he
n,
H
.
-
C
.
C
h
a
ng,
C
.
-
C
.
K
uo,
a
nd
C
.
-
C
.
L
in
,
“
P
r
ogr
a
m
ma
bl
e
e
ne
r
gy
s
our
c
e
e
mul
a
to
r
f
or
phot
ovol
ta
ic
p
a
ne
ls
c
ons
id
e
r
in
g
pa
r
ti
a
l
s
ha
dow
e
f
f
e
c
t,
”
E
ne
r
gy
, vol
. 54, pp. 174
-
183, 2013
, doi
:
10.1016/j
.e
ne
r
gy.2013.01.060
.
[
9]
M
.
C
.
D
i
P
ia
z
z
a
a
nd
G
.
V
it
a
le
,
“
P
hot
ovol
ta
ic
f
ie
ld
e
mul
a
ti
on
i
nc
lu
di
ng
dyna
mi
c
a
nd
pa
r
ti
a
l
s
ha
dow
c
ondi
ti
ons
,
”
A
ppl
ie
d
E
ne
r
gy
,
vol
. 87,
no. 3,
pp. 814
-
823,
2010
, doi
:
10.1016/j
.a
pe
ne
r
gy.2009.09.036
.
[
10]
R
.
A
yop,
C
.
W
.
T
a
n,
M
.
S
.
A
.
M
a
hmud,
S
.
N
.
S
ye
d
N
a
s
ir
,
T
.
A
l
-
H
a
dhr
a
mi
,
a
nd
A
.
L
.
B
uka
r
,
“
A
s
im
pl
if
ie
d
a
nd
f
a
s
t
c
o
mput
in
g
phot
ovol
ta
ic
mode
l
f
or
s
tr
in
g
s
im
ul
a
ti
on unde
r
pa
r
ti
a
l
s
ha
di
ng
c
ondi
ti
on,
”
Sus
ta
in
abl
e
E
ne
r
gy
T
e
c
hnol
ogi
e
s
and A
s
s
e
s
s
m
e
nt
s
,
vol
.
42, p. 100812, 2020
, doi
:
10.1016/j
.s
e
ta
.2020.100812
.
[
11]
R
.
A
yop
a
nd
C
.
W
.
T
a
n,
“
A
n
A
da
pt
iv
e
C
ont
r
ol
le
r
f
or
P
hot
ovol
t
a
ic
E
mul
a
to
r
us
in
g
A
r
ti
f
ic
ia
l
N
e
ur
a
l
N
e
twor
k,
”
I
ndone
s
ia
n
J
our
nal
of
E
le
c
tr
ic
al
E
ngi
ne
e
r
in
g and C
om
put
e
r
Sc
ie
n
c
e
, vol
.
5,
no. 3,
pp. 556
-
563, 2017
, doi
:
10.11591/i
je
e
c
s
.v5.i
3.pp556
-
563
.
[
12]
I
.
M
ous
s
a
,
A
.
B
ou
a
ll
e
gue
a
nd
A
.
K
he
dh
e
r
,
“
D
e
ve
lo
pme
nt
of
a
lo
w
c
os
t
P
V
s
im
ul
a
to
r
ba
s
e
d
on
F
P
G
A
te
c
hnol
ogy,
”
2017
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on Gr
e
e
n E
ne
r
gy
C
on
v
e
r
s
io
n Sy
s
te
m
s
(
G
E
C
S)
, 2017, pp. 1
-
6, doi:
10.1109/
G
E
C
S
.2017.8066243.
[
13]
U
.
K
.
S
hi
nde
,
S
.
G
.
K
a
dw
a
ne
,
R
.
K
.
K
e
s
hr
i
a
nd
S
.
P
.
G
a
w
a
nd
e
,
“
D
ua
l
M
ode
C
ont
r
ol
le
r
-
B
a
s
e
d
S
ol
a
r
P
hot
ovol
ta
ic
S
im
ul
a
to
r
f
or
T
r
ue
P
V
C
h
a
r
a
c
te
r
is
ti
c
s
,
”
in
C
anadian
J
ou
r
nal
of
E
le
c
tr
i
c
al
and
C
om
put
e
r
E
ngi
ne
e
r
in
g
,
vol
.
40,
no.
3,
pp.
237
-
245,
S
um
me
r
2017, doi:
10.1109/C
J
E
C
E
.2017.2708721.
[
14]
Y
.
-
T
.
S
e
o,
J
.
-
Y
.
P
a
r
k
a
nd
S
.
-
J
.
C
hoi
,
“
A
r
a
pi
d
I
-
V
c
ur
ve
g
e
ne
r
a
ti
on
f
or
P
V
mode
l
-
ba
s
e
d
s
ol
a
r
a
r
r
a
y
s
im
ul
a
to
r
s
,
”
2016
I
E
E
E
E
ne
r
gy
C
onv
e
r
s
io
n C
ong
r
e
s
s
and E
x
pos
it
io
n (
E
C
C
E
)
, 2016, pp. 1
-
5, doi:
10.1109/E
C
C
E
.2016.7854764.
[
15]
B
.
D
.
P
a
te
l
a
nd A
.
R
a
n
a
,
“
A
pol
e
-
pl
a
c
e
me
nt
a
ppr
oa
c
h
f
or
buc
k
c
onve
r
te
r
ba
s
e
d
P
V
a
r
r
a
y
E
mul
a
to
r
,
”
2016
I
E
E
E
1s
t
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on
P
ow
e
r
E
le
c
tr
oni
c
s
,
I
nt
e
ll
ig
e
nt
C
ont
r
ol
and
E
ne
r
gy
S
y
s
te
m
s
(
I
C
P
E
I
C
E
S)
,
2016,
pp.
1
-
5,
doi
:
10.1109/I
C
P
E
I
C
E
S
.2016.7853397.
[
16]
A
me
r
e
s
c
o S
ol
a
r
,
“
A
me
r
e
s
c
o S
ol
a
r
80W
(
24V
)
P
hot
ovol
ta
ic
M
odul
e
s
-
80J
-
B
(
24V
)
,
”
e
d:
A
me
r
e
s
c
o I
nc
., 2014.
[
17]
D
.
S
ubhi
a
nd
R
.
T
ha
bi
t,
“
A
N
e
w
L
ow
C
o
s
t
S
ol
a
r
A
r
r
a
y
E
mul
a
to
r
B
a
s
e
d
on
F
uz
z
y
a
nd
32
-
B
it
M
ic
r
oc
ont
r
ol
le
r
,
”
I
nt
e
r
nat
i
onal
J
our
nal
of
Sc
ie
nc
e
and E
ngi
ne
e
r
in
g I
nv
e
s
ti
gat
io
ns
, vol
. 9,
no. 1
01,
20
20.
[
18]
M
.
A
la
oui
,
H
.
M
a
ke
r
,
A
.
M
ouhs
e
n,
a
nd
H
.
H
ih
i,
“
R
e
a
l
-
ti
me
e
mul
a
ti
on
of
phot
ovol
ta
ic
e
ne
r
gy
us
in
g
a
da
pt
iv
e
s
ta
te
f
e
e
dba
c
k
c
ont
r
ol
,
”
SN
A
ppl
ie
d Sc
ie
nc
e
s
, vol
. 2, p. 492, 2020
, doi
:
10.100
7/
s
42452
-
020
-
2294
-
2
.
[
19]
D
. W
. H
a
r
t,
P
ow
e
r
E
le
c
tr
oni
c
s
,
N
e
w
D
e
lh
i
:
T
a
ta
M
c
G
r
a
w
-
H
il
l
, 2011.
[
20]
R
. A
yop, C
. W
. T
a
n, a
nd A
. L
. B
uka
r
,
“
S
im
pl
e
a
nd f
a
s
t
c
omput
a
ti
on photovol
ta
ic
e
mul
a
to
r
us
in
g s
hi
f
t
c
ont
r
ol
le
r
,
”
I
E
T
R
e
ne
w
abl
e
P
ow
e
r
G
e
ne
r
at
io
n
, vol
. 14,
no. 11,
pp. 2017
-
2026, 2020
, doi
:
10.1049/i
e
t
-
r
pg.2019.1504.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
T
he
pe
r
for
manc
e
s
of
par
ti
al
s
hading
adjus
ter
for
impr
ov
ing
photovoltai
c
e
mulator
(
R
az
man
A
y
op
)
535
[
21]
S
.
M
.
A
z
ha
r
uddi
n
e
t
al
.
,
“
A
N
e
a
r
A
c
c
ur
a
te
S
ol
a
r
P
V
E
mul
a
to
r
U
s
in
g
dS
P
A
C
E
C
ont
r
ol
le
r
f
or
R
e
a
l
-
ti
me
C
ont
r
ol
,
”
in
E
ne
r
gy
P
r
oc
e
di
a
,
vol
. 61,
pp. 2640
-
2648
, 2014, doi:
10.1016/j
.e
gypr
o.
2014.12.266
.
[
22]
S
. E
.
I
. R
e
ma
c
he
, A
. Y
. C
h
e
r
if
, a
nd K
.
B
a
r
r
a
,
“
O
pt
im
a
l
c
a
s
c
a
de
d pr
e
di
c
ti
ve
c
ont
r
ol
f
or
photovol
ta
ic
s
ys
te
ms
:
a
ppl
ic
a
ti
on ba
s
e
d
on
pr
e
di
c
ti
ve
e
mul
a
to
r
,
”
I
E
T
R
e
ne
w
abl
e
P
ow
e
r
G
e
ne
r
at
io
n
, vol
. 1
3,
no. 15,
pp. 2740
-
2751, 2019
, doi
:
10.1049/i
e
t
-
r
pg.2019.0068
.
[
23]
R
.
A
yop,
C
.
W
.
T
a
n,
a
nd
C
.
S
.
L
im
,
“
T
he
R
e
s
is
ta
nc
e
C
ompa
r
is
on
M
e
th
od
us
in
g
I
nt
e
gr
a
l
C
ont
r
ol
le
r
f
or
P
hot
ovol
ta
ic
E
mul
a
t
or
,
”
I
nt
e
r
nat
io
nal
J
our
nal
of
P
ow
e
r
E
le
c
tr
oni
c
s
and Dr
iv
e
Sy
s
te
m
s
,
vol
. 9,
no. 2,
2018
, doi
:
10.11591/i
jp
e
ds
.v9.i
2.pp820
-
828.
[
24]
I
.
M
ous
s
a
,
A
.
K
he
dhe
r
,
a
nd
A
.
B
oua
ll
e
gu
e
,
“
D
e
s
ig
n
of
a
L
ow
-
C
os
t
P
V
E
mul
a
to
r
A
ppl
ie
d
f
o
r
P
V
E
C
S
,
”
E
le
c
tr
oni
c
s
,
vol
.
8,
no.
2,
p. 232, 2019
, doi
:
10.3390/e
le
c
tr
oni
c
s
8020232
.
[
25]
Y
.
M
a
ll
a
l,
L
.
E
l
B
a
hi
r
,
a
nd
T
.
H
a
s
s
boun,
“
H
ig
h
-
P
e
r
f
or
ma
nc
e
E
mul
a
to
r
f
or
F
ix
e
d
P
hot
ovol
ta
ic
P
a
ne
ls
,
”
I
nt
e
r
nat
io
nal
J
ou
r
na
l
of
P
hot
oe
ne
r
gy
, vol
. 2019,
p. 3951841,
2019
, doi
:
10.1155/2019/
3951841
.
[
26]
N
. S
. N
is
e
, C
ont
r
ol
S
ys
te
ms
E
ngi
ne
e
r
in
g vol. 7t
h E
di
ti
on
,
N
e
w
J
e
r
s
e
y, U
ni
te
d S
ta
te
s
:
J
ohn W
il
e
y & S
ons
, I
nc
., 2015.
B
I
OG
RA
P
HI
E
S
OF
AU
T
HO
RS
R
a
z
m
a
n
A
y
o
p
recei
v
e
d
t
h
e
b
ac
h
el
o
r’s
d
e
g
ree
i
n
el
e
ct
ri
ca
l
en
g
i
n
eer
i
n
g
w
i
t
h
firs
t
-
cl
as
s
h
o
n
o
u
r
s
,
t
h
e
ma
s
t
er’
s
d
e
g
ree
i
n
el
ec
t
ri
cal
e
n
g
i
n
eeri
n
g
w
i
t
h
s
p
ec
i
al
i
zat
i
o
n
i
n
p
o
w
er
s
y
s
t
em,
an
d
t
h
e
Ph
D
d
e
g
ree
i
n
el
ec
t
ri
c
al
en
g
i
n
eeri
n
g
fro
m
U
n
i
v
ers
i
t
i
T
ek
n
o
l
o
g
i
Mal
a
y
s
i
a
(U
T
M),
J
o
h
o
r,
Mal
ay
s
i
a,
i
n
2
0
1
3
,
2
0
1
5
,
a
n
d
2
0
1
8
,
res
p
ect
i
v
el
y
.
H
e
i
s
a
Sen
i
o
r
L
ect
u
rer
w
i
t
h
U
T
M
an
d
a
memb
er
o
f
Po
w
er
E
l
ect
r
o
n
i
cs
a
n
d
D
r
i
v
e
s
Res
earch
G
ro
u
p
,
Sch
o
o
l
o
f
E
l
ect
r
i
ca
l
E
n
g
i
n
eeri
n
g
,
Facu
l
t
y
o
f
E
n
g
i
n
eer
i
n
g
,
U
T
M.
H
i
s
res
ear
ch
i
n
t
eres
t
s
i
n
cl
u
d
e
re
n
ew
a
b
l
e
e
n
erg
y
an
d
p
o
w
er
e
l
ect
r
o
n
i
cs
.
H
e
ca
n
b
e
co
n
t
ac
t
ed
at
ema
i
l
:
raz
man
.
ay
o
p
@
u
t
m.
m
y
.
C
hee
Wei
Ta
n
recei
v
ed
h
i
s
B.
E
n
g
.
d
eg
r
ee
i
n
el
ect
ri
cal
en
g
i
n
eer
i
n
g
(fi
rs
t
cl
as
s
h
o
n
o
r
s
)
fro
m
U
n
i
v
ers
i
t
i
T
e
k
n
o
l
o
g
i
Mal
a
y
s
i
a
(U
T
M),
i
n
2
0
0
3
an
d
a
Ph
.
D
.
d
eg
ree
i
n
e
l
ect
r
i
ca
l
en
g
i
n
eer
i
n
g
fro
m
Imp
eri
a
l
Co
l
l
eg
e
L
o
n
d
o
n
,
L
o
n
d
o
n
,
U
.
K
.
,
i
n
2
0
0
8
.
H
e
i
s
cu
rre
n
t
l
y
an
as
s
o
ci
a
t
e
p
ro
fes
s
o
r
at
U
n
i
v
er
s
i
t
i
T
e
k
n
o
l
o
g
i
Mal
ay
s
i
a
an
d
a
memb
er
o
f
t
h
e
Po
w
er
E
l
ect
ro
n
i
c
s
an
d
D
r
i
v
e
s
Res
earch
G
ro
u
p
,
Sch
o
o
l
o
f
E
l
ect
r
i
cal
E
n
g
i
n
eer
i
n
g
,
Facu
l
t
y
o
f
E
n
g
i
n
eer
i
n
g
.
H
i
s
res
earch
i
n
t
ere
s
t
s
i
n
c
l
u
d
e
t
h
e
ap
p
l
i
cat
i
o
n
o
f
p
o
w
er
el
ec
t
ro
n
i
cs
i
n
ren
ew
a
b
l
e
/
al
t
ern
a
t
i
v
e
en
erg
y
s
y
s
t
ems
,
co
n
t
r
o
l
o
f
p
o
w
er
el
ec
t
ro
n
i
c
s
an
d
en
er
g
y
man
a
g
emen
t
s
y
s
t
em
i
n
mi
cr
o
g
r
i
d
s
.
H
e
can
b
e
co
n
t
act
e
d
at
emai
l
:
c
h
eew
e
i
@
u
t
m.
m
y
.
Sy
ed
N
o
ra
z
i
zul
Sy
ed
N
a
s
i
r
recei
v
ed
t
h
e
B.
E
n
g
.
(H
o
n
s
)
d
e
g
ree
i
n
el
ect
r
i
cal
en
g
i
n
eer
i
n
g
i
n
2
0
0
8
,
M.
E
n
g
.
d
eg
ree
i
n
el
ect
r
i
cal
(p
o
w
er
)
en
g
i
n
eeri
n
g
i
n
2
0
1
4
an
d
Ph
D
d
eg
re
e
i
n
el
ect
r
i
cal
(p
o
w
er)
en
g
i
n
eeri
n
g
i
n
2
0
1
9
fro
m
U
n
i
v
ers
i
t
i
T
e
k
n
o
l
o
g
i
Mal
ay
s
i
a
(U
T
M),
J
o
h
o
r
Bah
ru
,
Mal
ay
s
i
a.
H
e
w
o
r
k
s
as
e
l
ect
r
i
cal
en
g
i
n
eer
i
n
h
i
g
h
v
o
l
t
ag
e
p
r
o
t
ec
t
i
o
n
s
i
n
ce
2
0
0
8
u
n
t
i
l
2
0
1
9
at
T
en
ag
a
N
a
s
i
o
n
a
l
Berh
ad
.
H
e
i
s
cu
rre
n
t
l
y
s
e
n
i
o
r
l
ect
u
rer
i
n
Sch
o
o
l
o
f
E
l
ect
r
i
ca
l
E
n
g
i
n
eeri
n
g
at
U
n
i
v
ers
i
t
i
T
ek
n
o
l
o
g
i
Mal
ay
s
i
a
(U
T
M).
H
i
s
cu
rr
en
t
res
earch
i
n
t
ere
s
t
s
i
n
c
l
u
d
e
p
o
w
er
s
y
s
t
em
o
p
t
i
m
i
zat
i
o
n
,
p
o
w
er
s
y
s
t
em
s
t
a
b
i
l
i
t
y
,
p
o
w
er
s
y
s
t
em
p
r
o
t
ec
t
i
o
n
an
d
h
armo
n
i
c
mi
t
i
g
a
t
i
o
n
an
d
t
h
ei
r
co
n
t
r
o
l
me
t
h
o
d
s
.
H
e
can
b
e
c
o
n
t
act
e
d
at
emai
l
:
s
y
ed
n
o
raz
i
zu
l
@
u
t
m.
m
y
.
M
o
hd
Za
ki
D
a
ud
i
s
a
L
ect
u
rer
at
Sch
o
o
l
o
f
E
l
ec
t
r
i
cal
E
n
g
i
n
eer
i
n
g
,
Facu
l
t
y
o
f
E
n
g
i
n
eeri
n
g
,
U
n
i
v
ers
i
t
i
T
ek
n
o
l
o
g
i
Ma
l
ay
s
i
a
s
i
n
ce
1
9
9
7
.
H
e
recei
v
e
d
h
i
s
B
E
n
g
i
n
E
l
ec
t
ri
ca
l
E
n
g
i
n
eeri
n
g
fr
o
m
U
n
i
v
ers
i
t
y
o
f
S
o
u
t
h
am
p
t
o
n
,
U
K
i
n
1
9
9
5
an
d
MSc
i
n
E
l
ect
r
i
c
Po
w
er
fro
m
U
n
i
v
er
s
i
t
y
o
f
N
ew
c
a
s
t
l
e
u
p
o
n
T
y
n
e
i
n
1
9
9
7
.
Cu
rren
t
l
y
h
e
i
s
emb
ark
i
n
g
a
Ph
D
i
n
E
l
ect
r
i
ca
l
E
n
g
i
n
eeri
n
g
.
H
i
s
cu
rre
n
t
res
earc
h
i
n
t
eres
t
i
n
cl
u
d
e
s
h
armo
n
i
cs
i
n
p
o
w
er
el
ect
r
o
n
i
cs
-
b
a
s
ed
p
o
w
er
s
y
t
em,
es
t
i
mat
i
o
n
t
ec
h
n
i
q
u
es
i
n
e
l
ect
r
i
c
d
ri
v
es
,
mo
d
e
l
l
i
n
g
o
f
el
ec
t
ro
ma
g
n
e
t
i
c
p
ro
ce
s
s
e
s
us
i
n
g
s
o
f
t
co
m
p
u
t
i
n
g
t
ech
n
i
q
u
e
s
,
ren
ew
a
b
l
e
e
n
erg
y
a
n
d
en
g
i
n
eeri
n
g
e
d
u
ca
t
i
o
n
.
H
e
ca
n
b
e
co
n
t
act
e
d
at
emai
l
:
md
za
k
i
@
u
t
m.
my
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
528
-
53
6
536
La
u
Kw
a
n
Y
i
ew
recei
v
ed
h
i
s
B.
E
n
g
.
d
e
g
ree
i
n
el
ec
t
ri
cal
en
g
i
n
eeri
n
g
(fi
r
s
t
cl
a
s
s
h
o
n
o
r
s
)
an
d
M.
E
n
g
.
d
e
g
ree
i
n
el
ect
r
i
cal
p
o
w
er
en
g
i
n
eeri
n
g
fro
m
U
n
i
v
er
s
i
t
i
T
e
k
n
o
l
o
g
i
Mal
ay
s
i
a
i
n
2
0
0
7
an
d
2
0
1
0
,
res
p
ect
i
v
e
l
y
.
In
2
0
1
3
,
h
e
recei
v
e
d
h
i
s
Ph
.
D
.
d
eg
ree
i
n
el
ec
t
ro
n
i
c
s
an
d
el
ect
r
i
cal
en
g
i
n
eeri
n
g
fro
m
t
h
e
U
n
i
v
ers
i
t
y
o
f
So
u
t
h
am
p
t
o
n
,
U
K
.
H
e
i
s
cu
rren
t
l
y
an
as
s
o
ci
a
t
e
p
ro
fe
s
s
o
r
at
t
h
e
In
s
t
i
t
u
t
e
o
f
H
i
g
h
V
o
l
t
a
g
e
an
d
H
i
g
h
Cu
rre
n
t
,
U
n
i
v
ers
i
t
i
T
e
k
n
o
l
o
g
i
Mal
ay
s
i
a.
H
i
s
res
earch
i
n
t
ere
s
t
s
i
n
c
l
u
d
e
h
i
g
h
v
o
l
t
ag
e
en
g
i
n
eer
i
n
g
,
d
i
el
ec
t
ri
c
mat
er
i
al
s
,
an
d
ren
ew
a
b
l
e
en
er
g
y
s
y
s
t
em
s
.
H
e
can
b
e
c
o
n
t
act
e
d
at
emai
l
:
k
w
a
n
y
i
ew
@
u
t
m
.
my
.
N
o
rju
l
i
a
M
o
ha
m
a
d
N
o
rd
i
n
recei
v
e
d
h
er
d
e
g
re
e
i
n
b
ach
e
l
o
r
o
f
e
l
ect
r
i
cal
en
g
i
n
eer
i
n
g
fro
m
t
h
e
U
n
i
v
er
s
i
t
i
T
e
k
n
o
l
o
g
i
Mal
a
y
s
i
a
(U
T
M)
i
n
2
0
0
6
an
d
t
h
e
Mas
t
er
i
n
E
n
g
i
n
eeri
n
g
Sci
e
n
ce
fro
m
t
h
e
U
n
i
v
er
s
i
t
y
o
f
N
e
w
So
u
t
h
W
al
es
i
n
2
0
0
8
.
Sh
e
t
h
en
recei
v
ed
h
e
r
Ph
.
D
i
n
el
ec
t
ri
ca
l
en
g
i
n
eer
i
n
g
fro
m
U
T
M
i
n
2
0
1
6
.
Cu
r
ren
t
l
y
,
s
h
e
i
s
a
Sen
i
o
r
L
ect
u
rer
at
t
h
e
Facu
l
t
y
o
f
E
n
g
i
n
eeri
n
g
,
U
n
i
v
ers
i
t
i
T
e
k
n
o
l
o
g
i
Mal
a
y
s
i
a
(U
T
M).
H
er
cu
rren
t
res
earch
i
n
t
eres
t
s
are
i
n
A
C
mo
t
o
r
d
ri
v
es
/
el
ec
t
ri
ca
l
d
r
i
v
e
s
,
p
o
w
er
el
ec
t
r
o
n
i
cs
ap
p
l
i
cat
i
o
n
s
,
el
e
ct
r
i
cal
mach
i
n
e
s
an
d
ren
e
w
ab
l
e
en
er
g
y
co
n
v
ers
i
o
n
.
Sh
e
can
b
e
co
n
t
ac
t
ed
at
emai
l
:
n
o
rj
u
l
i
a@
u
t
m.
my
.
A
bba
La
w
a
n
Buka
r
i
s
a
l
ect
u
rer
a
t
t
h
e
D
e
p
art
me
n
t
o
f
E
l
ect
r
i
cal
a
n
d
E
l
ec
t
ro
n
i
c
E
n
g
i
n
eeri
n
g
,
U
n
i
v
er
s
i
t
y
o
f
Mai
d
u
g
u
ri
.
H
i
s
res
earch
i
n
t
eres
t
i
n
c
l
u
d
es
ren
e
w
ab
l
e
en
erg
y
t
ech
n
o
l
o
g
i
e
s
,
en
erg
y
man
a
g
emen
t
o
p
t
i
m
i
zat
i
o
n
.
H
e
can
b
e
c
o
n
t
act
e
d
at
emai
l
:
ab
b
a
l
aw
a
n
9
@
g
ma
i
l
.
co
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.