Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 10
19
~1
030
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
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jp
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s.v
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t
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p
:/
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d
s.
i
a
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s
c
o
re.
c
o
m
Photovoltaic em
ulator of diffe
rent solar array configurations
u
nder partial shadin
g conditions usi
n
g
damping inje
ction
c
o
ntrolle
r
Mu
st
apha
Alao
ui
1
, Ha
tt
ab
Ma
ke
r
2
, A
z
eddin
e
Mo
u
h
sen
3
, Hicham Hih
i
4
1,
2
In
terd
is
ciplin
a
r
y Labo
ratory
of
App
l
ied
S
c
i
e
nc
es,
EN
S
A
o
f
B
e
r
r
ec
h
i
d
,
H
a
ss
a
n
F
i
rs
t
Univers
ity,
M
o
rocco
3
Labo
ra
to
ry o
f
Radiatio
n-M
a
t
t
e
r
& In
stru
men
t
ation,
F
S
T o
f
S
e
tt
at,
Hass
an
First
Un
iv
ersity
, M
o
ro
cco
4
Lab
o
ra
to
ry o
f
En
gine
ering,
S
y
s
t
ems
and
Ap
pli
cation
s
,
ENS
A
of F
ez,
S
i
d
i
M
o
ha
med
Ben
Ab
de
llah
Un
ivers
ity,
Mo
rocco
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Se
p 5
,
20
19
Rev
i
sed
D
e
c
22
, 20
19
A
c
ce
p
t
ed
Jan
8,
202
0
In th
e
las
t
d
eca
d
e
s, r
e
s
earch
ers
and
sci
e
n
t
ists
hav
e
been
trend
i
ng
to
w
a
rds
ph
otov
olta
ic
(P
V) s
o
la
r
en
ergy
res
e
arch
a
s
on
e
o
f
the
n
o
t
e
w
o
rth
y
ren
e
wable
energ
i
es.
A
s
a matter of f
a
c
t
,
th
e
n
eed
fo
r a la
b
o
ratory sy
stem
d
e
vo
ted
to
perfo
rming
m
e
a
s
u
r
em
en
ts
and
exp
e
ri
ment
ation
on
PV
sy
stem
s is b
e
ing
in
cre
a
sed.
Th
e
PV
array
emu
l
a
t
o
r
is
des
i
g
n
ed
to a
cco
mplish
th
is
tas
k
by
re
p
r
od
uc
i
n
g
a
c
c
u
r
a
t
el
y t
h
e
el
ectri
ca
l b
e
h
a
vi
or o
f
rea
l
PV
sourc
e
s
.
T
h
e
pres
ent p
a
p
e
r
p
r
op
oses
thu
s
a n
e
w
co
ntrol
and
d
e
sign
o
f
P
V
arr
a
y
em
u
l
ators
.
It
i
s
ba
se
d
e
s
se
n
tia
ll
y
on
a hy
br
id
Da
m
p
i
n
g
In
j
e
c
t
i
o
n
c
o
ntro
ll
er. T
h
e
p
r
op
ose
d
c
o
n
t
rol strat
e
gy
c
i
rc
u
m
v
e
nt
s
o
b
v
i
o
u
s
l
y
t
h
e e
x
istin
g P
V
e
m
ula
t
or'
s
limitations
in ter
m
s
o
f
a
ccura
cy
, sp
eed an
d
partia
l
s
h
ad
in
g
emu
l
ati
o
n
.
S
e
v
e
ra
l
resu
lts ar
e
g
i
ven
and
discu
ssed
t
o
s
h
o
w
the
efficien
cy o
f
th
e p
r
op
osed
s
y
stem
to
emu
l
at
e P
V
mo
dules
and
d
i
f
f
eren
t
P
V
array
co
nfigu
r
a
tio
ns
u
n
d
e
r u
n
iform
so
lar irr
a
di
ance
and
p
a
rtia
l sh
ad
i
n
g
con
d
i
tio
ns
.
Ke
yw
ords:
Dam
p
i
n
g i
n
je
c
t
i
on c
ont
rol
l
er
D
C
-D
C bu
ck
co
nv
ert
e
r
Hy
bri
d
r
e
fe
ren
c
ing
PV
a
r
ra
y
c
o
nfi
g
u
r
at
i
o
ns
P
V
arr
a
y
emu
l
at
o
r
PV cha
r
acter
i
stics
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Mu
st
a
pha
Al
a
oui
,
I
n
te
rd
isc
i
p
lin
ary
Labo
r
a
tory
of
A
p
p
lie
d
S
c
i
e
n
c
e
s
,
EN
SA of Berrechid, H
a
ssan Fi
r
s
t Un
iv
er
sity
,
M
o
ro
c
c
o
.
Ema
i
l
:
m
u
.a
laou
i@u
h
p
.
ac.
ma
1.
IN
TR
O
DUCTION
In
re
ce
nt
yea
r
s
,
the
i
n
te
rest
i
n
re
ne
wa
b
l
e
a
n
d
s
u
st
ai
na
bl
e
e
n
erg
y
i
s
be
in
g c
o
nsi
d
e
r
abl
y
i
n
cre
a
s
ed
,
a
growi
n
g a
w
ar
e
n
ess
o
f
t
h
e
im
pac
t
of
c
o
nve
nt
iona
l
po
wer
ge
ne
ra
t
i
o
n
re
sou
r
ces
o
n
e
nvi
ro
nme
n
t a
n
d h
u
ma
n
safe
ty
has be
en int
e
nsi
v
el
y
re
ma
rke
d
. T
h
ere
f
o
r
e
,
C
o
ntrib
u
t
i
ng
t
o
su
st
ai
nabl
e
deve
l
opme
n
t
by re
duc
i
n
g
gre
e
n
ho
use
ga
s emi
ssio
n
s
ha
s
be
c
o
me
one
of
t
h
e i
m
po
rt
a
n
t
p
r
i
o
ri
ti
es of
ma
n
y
c
ount
ri
e
s
ar
oun
d t
h
e
w
o
rl
d
[1]
.
Ph
ot
o
vol
ta
ic
sol
a
r e
n
e
r
g
y
i
s
a
g
r
ee
n
po
we
r reso
u
r
ce
wide
l
y
use
d
t
o
p
r
o
duc
e cl
ea
n el
ect
ri
ci
t
y
by u
s
i
n
g e
n
erg
y
from
t
h
e
sun
.
Ma
ny
res
e
a
r
c
h
e
r
s a
n
d
sc
ie
nti
s
t
s
ha
ve
de
v
o
t
e
d t
h
ei
r
rese
a
r
c
h
ac
ti
vi
ti
e
s
t
o
the
m
o
d
e
l
i
n
g
of
t
h
is
PV
e
n
e
r
g
y
,
i
t
s
o
p
t
i
mi
za
ti
on, i
t
s co
nt
rol a
n
d
m
a
n
y
othe
r rel
a
t
e
d fie
l
ds.
Ho
we
ver, one
o
f
t
h
e
most
maj
o
r
pro
b
l
e
ms hi
n
d
e
r
i
n
g
t
h
e pr
o
g
ress
a
nd c
o
m
p
et
it
i
v
ene
s
s
of t
h
i
s
re
ne
wabl
e
ene
r
g
y
i
s
the
i
n
t
e
rmi
t
t
e
nt
pow
e
r
pro
duct
i
o
n,
w
h
i
c
h nece
ssi
t
at
e
s
t
h
e use
o
f
sto
r
age t
e
c
hni
que
s or e
n
e
r
get
i
c
mix wi
t
h
ot
he
r
po
we
r so
urce
s. This
pro
b
l
e
m
not
o
n
l
y
i
m
pa
ct
s t
h
e
com
m
e
r
ci
al
mat
u
ri
t
y
an
d c
o
m
p
et
i
t
i
v
ene
s
s
of
the
PV s
o
l
a
r e
n
ergy
,
but
a
l
so t
h
e
re
se
arc
h
a
n
d
d
e
ve
lo
pme
n
t
o
f
P
V
e
n
e
r
g
y
sy
st
ems [1].
Ind
e
e
d
, t
h
e
i
n
te
rmit
t
e
nc
e a
n
d
we
at
he
r
de
pe
n
d
e
n
ce
o
f
PV
sol
a
r e
n
erg
y
hi
n
d
er r
e
sea
r
che
r
s
to
c
a
rr
y
out
t
h
ei
r ex
pe
ri
me
nts a
n
d me
a
s
ure
m
ent
s
on
P
V
syste
m
s
wi
t
hout
d
e
p
e
nd
ing
on
at
mo
sph
e
r
i
c co
nd
itio
n
s
o
f
te
mp
er
at
ure
a
n
d
so
lar i
r
r
a
d
i
a
n
ce [1
,
2]
.
Th
e re
al
-t
ime
expe
ri
me
n
t
a
t
i
on o
n
P
V
ene
r
g
y
o
f
t
e
n
need
s
repe
ti
t
i
ve t
e
st
s a
t
t
h
e de
sired
c
l
i
m
at
i
c
c
ondi
t
i
ons t
o
val
i
d
a
t
e
fo
r
in
s
t
a
n
ce
M
a
x
i
mu
m Po
w
e
r
Po
in
t Tr
ack
ing
(M
PPT) a
l
go
r
ithm
s
an
d
so
la
r
g
r
id
-co
nne
ct
ed
i
n
v
e
r
t
e
r
s [
1
-4
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
19
–
1
0
30
1
020
That
’s
w
h
y
,
t
h
e ne
ed
for a
P
V
em
ul
at
or s
y
st
e
m
i
s
ine
v
it
a
b
l
e
, t
h
is l
a
b
o
r
a
t
or
y
de
vic
e
h
a
s t
o
re
pr
o
d
uc
e t
h
e
el
ec
tric
al
be
ha
vi
or o
f
a
real
P
V
ge
nera
t
o
r
by
t
r
ac
kin
g
th
e
cur
r
e
n
t
-
vol
ta
ge (
I
-V
) c
h
a
r
a
c
t
e
r
i
s
ti
c
wi
tho
u
t
be
i
n
g
depe
n
d
e
n
t
o
n
wea
t
he
r c
o
n
d
i
t
i
o
n
s
. It
s
h
oul
d
rep
r
oduc
e t
h
e
same c
u
rrent
a
n
d
v
o
lt
a
g
e
of
act
ual
P
V
s
o
u
r
c
e
s at
t
h
e
de
sired
t
e
m
p
erat
ure
(T
) a
n
d ir
radi
a
n
c
e
(G
) tha
t
t
h
e use
r
wi
l
l
defi
ne
[
1
-
3
].
In t
h
e
li
t
e
ra
tur
e
, man
y
resea
r
ch
st
u
d
i
e
s h
a
v
e
be
en
pe
rfor
me
d
re
ga
rdi
n
g
P
V
s
o
urc
e
e
m
ul
a
t
o
r
s, t
h
ey
a
r
e
in
mo
st
case
b
a
sed
on
the
sw
itc
h
e
d
-
mod
e
po
we
r
sup
p
ly
(SM
PS)
si
nc
e
SM
PS
ar
e
mor
e
eff
i
ci
en
t
th
an
li
n
e
a
r
r
e
g
u
l
a
t
ors
[5
-7]
.
Th
e
ma
jo
r
i
ty of
pr
opo
sed
PV
e
m
u
l
a
t
o
r
s suf
f
e
r
fr
om in
a
ccur
a
c
y
a
n
d in
st
a
b
il
ity
i
n
so
me
parti
c
ul
a
r
z
o
ne
s
of t
h
e
I-V
c
h
ara
c
t
e
ri
st
i
c
o
f
t
h
e
PV
m
o
dule
due
t
o
i
t
s n
onl
i
n
earit
y
,
e
s
peci
al
l
y
o
n
t
h
e
c
o
n
s
t
a
nt
current
a
n
d c
onst
a
nt
vol
ta
ge
z
o
n
e
s [2]. Se
v
e
ra
l c
o
ntr
o
l st
ra
te
gie
s
o
f
t
h
e
P
V
em
ul
at
o
r
h
a
ve
been
p
r
op
ose
d
to
ove
rc
ome
t
h
e
s
e
p
r
o
b
le
ms,
suc
h
as
pe
rt
urb a
n
d
o
b
se
rve
me
th
od
(P
&O),
Hi
l
l
C
l
i
m
bi
ng t
e
c
hni
qu
e
(
H
C),
R
e
si
sta
n
ce
Com
p
a
r
is
on
M
e
th
od
[
8
-1
0
]
.
How
e
v
e
r
,
a
l
l th
e
s
e
me
tho
d
s r
e
qu
ir
e an
it
er
at
ive
pro
c
e
s
s to
r
eac
h
th
e
ope
ra
t
i
n
g
poi
n
t
of t
h
e
s
y
ste
m
, t
h
e
i
t
e
r
at
i
o
n ste
p
is
hi
g
h
l
y
li
n
k
ed
t
o
t
h
e a
ccu
racy
a
n
d the
d
y
n
amic
of t
h
e
syste
m
,
s
o
wh
en
t
h
e it
erat
i
o
n
st
ep
is
s
m
al
l
,
t
h
e syst
em
get
s
a
g
ood
acc
u
r
ac
y
a
n
d
l
e
ss
o
s
ci
l
l
a
t
i
on, but
a
p
o
o
r
dy
namic
resp
o
n
se i
s
o
b
se
rve
d
,
a
nd whe
n
th
e
it
erat
ion st
ep
i
s
i
n
crea
se
d
,
t
h
e d
y
n
amic
res
p
o
n
se i
s
i
m
pro
v
ed a
t
t
h
e e
xpe
n
s
e o
f
acc
urac
y [2
].
The
p
r
op
ose
d
c
o
nt
rol
st
ra
te
gy
d
o
es n
o
t
re
qui
re a
n
y it
e
r
at
i
v
e a
l
go
rit
h
m an
d
e
n
su
r
e
s bo
th
go
od
ac
cur
a
c
y
an
d
h
i
g
h
dyn
a
m
ic
p
e
rfor
m
an
c
e
s.
F
u
rt
hermo
r
e
,
t
h
e c
o
m
m
erc
i
a
l
P
V
em
ul
at
o
r
s uti
l
iz
ing
pro
g
ra
mma
b
le
pow
er s
u
p
p
l
y
ha
ve a
po
o
r
d
y
n
a
mi
c
r
e
sp
on
se
wh
ic
h
c
a
n
af
f
e
c
t
t
h
e ef
ficie
n
c
y
o
f
th
e
e
m
u
l
at
ion
,
espe
c
i
a
lly
w
i
t
h
so
me
alg
o
ri
th
ms
lik
e
MPP
T
t
h
at
ne
ed
ra
pid
em
ul
a
t
ion
[2,
11
].
Mo
re
ove
r,
t
h
e
n
e
e
d
fo
r P
V
em
ula
t
ion
i
s
not
c
o
n
f
ine
d
t
o
PV
modul
es
, but
t
h
e
re
sea
r
c
h
e
r
s
u
s
u
a
l
l
y
ne
e
d
t
o
e
m
u
l
a
t
e
diffe
r
e
n
t
P
V
a
rra
y
c
o
nfi
g
u
r
at
i
ons suc
h
as
seri
es
c
o
nf
igu
r
at
ion,
p
a
r
a
l
l
el
conf
igu
r
a
tion
,
to
ta
l-
cro
ss-t
i
ed
con
f
i
g
ur
at
ion
…
und
e
r
un
ifo
r
m
c
l
i
m
a
tic
c
o
nd
i
tion
s
and
parti
a
l
l
y
sha
d
e
d
c
o
n
d
it
i
ons [12]
. Acc
o
rdi
ng t
o
t
h
e l
i
t
e
r
at
ure
revi
ew
,
t
h
e e
m
ul
at
i
on o
f
P
V
a
r
ra
y
c
o
n
f
i
gurat
i
o
n
s
un
de
r
di
ffe
re
n
t
sc
ena
r
i
o
s
of
pa
rt
ia
l
sha
d
i
n
g c
ondi
t
i
ons
i
s
bei
n
g
ra
re
ly
de
vel
o
pe
d
[2
,
1
2
]. T
h
e
r
efor
e, t
h
e
pro
pose
d
pape
r
de
al
s
wi
t
h
a
l
l
the
s
e li
mit
a
t
i
ons b
y
de
si
g
n
ing a
ne
w P
V
sou
r
ce
e
m
ul
a
t
or base
d
o
n
a
ro
b
u
st
cont
rol
st
rat
e
gy
of D
a
m
p
in
g
Inj
ect
i
o
n whi
c
h ta
kes
i
n
t
o
co
nsi
d
e
r
a
t
ion
the
n
onl
ine
a
r
i
t
y o
f
P
V
c
h
arac
te
ri
st
i
c
s
and
pr
od
uces,
as a re
sul
t
,
si
m
i
l
a
r
o
u
t
p
ut
s as a
n
a
c
t
u
al
PV
a
r
ra
y
.
Th
e
d
e
v
e
l
o
p
e
d PV
ar
ray emula
t
o
r
is
a
b
le to tr
ack
fa
ith
fu
ll
y
th
e curr
en
t a
n
d
v
o
l
ta
g
e
o
f
P
V
s
ourc
e
s
wi
th
h
i
gh
dy
n
a
mi
c re
sp
o
n
se
and
go
o
d
ac
cura
c
y
for a
n
y o
p
erat
in
g
p
o
i
n
t
in t
h
e
I-V c
u
rve a
n
d
at
any
envi
ro
nme
n
t
a
l
co
n
d
i
t
i
ons. T
h
e
p
r
o
p
o
s
e
d
P
V
s
y
st
em
is
b
a
sed e
s
se
nt
ia
ll
y
o
n
the
one
di
ode
t
w
o resi
sta
n
ces
(1
D-
2R) P
V
mo
de
l i
m
pl
e
m
e
n
t
e
d i
n
t
h
e L
o
o
k
-U
p-Ta
b
l
e
(LU
T
),
b
e
side
t
h
e
DC
-DC
b
u
ck
c
o
n
v
erte
r
fo
r t
h
e
po
we
r part
. T
h
e
em
ul
at
ion
al
gori
t
hm
b
a
sed
on
hy
bri
d
refe
renc
in
g
a
n
d da
mpin
g
i
n
j
ect
i
o
n
c
o
nt
rol
det
e
r
m
i
n
es
th
e
op
e
r
ati
n
g
po
in
t
of
th
e sy
st
e
m
a
n
d
de
liv
e
rs, a
s
a
r
e
su
l
t
,
t
h
e
requ
ir
e
d
con
t
ro
l sig
n
a
l to
th
e
po
w
e
r
co
nv
e
r
t
e
r
in
ord
e
r
t
o
tr
ack
a
c
c
u
r
a
t
e
l
y
t
h
e I
-
V
c
h
ar
ac
te
risti
c
cu
r
v
e.
2.
P
R
OPO
S
ED S
Y
S
TEM D
E
S
C
R
I
P
T
ION
The
prop
ose
d
syst
em i
s
c
o
mp
ose
d
e
s
se
nti
a
ll
y of t
h
ree
parts
w
h
ic
h
are
:
t
h
e p
o
w
e
r
e
l
e
c
t
r
o
n
i
c
c
o
nv
ert
e
r
,
th
e
re
f
e
r
e
n
ce
g
e
n
e
ra
to
r an
d th
e co
n
t
r
o
lle
r
. Th
e
p
o
w
e
r
c
o
nv
er
te
r t
r
an
sm
its t
h
e
pow
er to
th
e lo
a
d
, i
t
c
a
n
b
e
e
ith
er
a
b
u
c
k-
c
onv
er
te
r,
boo
st
co
nv
er
t
e
r
,
SEPI
C c
onv
e
r
te
r.
B
u
ck
c
o
nv
ert
e
r t
o
pol
og
y
ha
s
bee
n
c
hose
n
i
n
t
h
i
s
a
p
pl
i
cat
i
o
n
si
nce
it
e
n
sures
wi
de
c
o
v
e
rage
of t
h
e
PV
cha
r
act
eris
t
i
c
c
u
rves
fro
m
t
h
e
sh
ort
c
i
r
c
ui
t to
t
h
e
ope
n
ci
rc
uit
o
p
era
t
ing p
o
i
n
t
s
[13
-
1
5
].
Be
si
de
s,
i
t
has
a
si
mp
le
st
ru
c
t
ure
w
i
t
h
f
e
w
e
r co
mp
on
en
ts,
th
e
cur
r
e
n
t
an
d v
o
lta
g
e
r
i
pp
le
s c
a
n
b
e
w
e
ll-
a
d
j
u
ste
d
by c
hoo
sing
th
e
ri
g
h
t val
u
es
of i
n
d
u
ct
anc
e
L a
n
d
capa
c
i
t
a
nce
C
[16
-
19].
The
c
u
rre
n
t a
n
d v
o
lt
age
of t
h
e loa
d
a
r
e se
ns
ed an
d
del
i
ve
re
d t
o
t
h
e sec
o
n
d
part
whi
c
h
c
o
nsi
s
t
s
o
f
t
h
e
r
e
f
e
r
e
n
c
e
g
e
n
e
r
a
to
r. Th
e la
te
st co
n
t
ai
ns
LU
T wh
er
e
t
h
e
PV
ch
a
r
ac
ter
i
sti
c
s ar
e
i
m
p
l
e
m
e
n
t
e
d
.
LU
T
t
e
ch
niq
u
e
ha
s
bee
n
wi
de
l
y
use
d
i
n
l
i
t
e
r
at
ure
for P
V
e
m
ula
t
o
r
a
p
pli
c
a
t
ions
d
u
e
t
o
it
s sim
p
l
i
c
i
t
y
and
s
p
ee
d
[2
,
20
]. T
h
e
n
u
m
b
er
o
f
dat
a
po
i
n
t
s
of
the
L
U
T i
s
c
h
ose
n
t
o
ha
ve
a
n
ac
c
u
rat
e
op
e
r
a
t
i
n
g
poi
nt
lo
c
a
liz
a
tio
n
w
ith
ou
t
a
f
f
e
ct
ing
th
e
me
mor
y
of th
e
pro
c
e
s
so
r
[1
,
2
,
21-
23
].
A
f
t
e
r ge
nera
ti
ng t
h
e
vol
t
a
g
e
a
n
d
cu
rre
n
t
re
f
e
re
nces
,
whi
c
h
cor
r
es
po
n
d
t
o
the
o
p
e
r
a
t
ing
poi
nt
o
f
t
h
e
sy
st
em
, th
e
Damp
i
n
g
I
n
je
ct
io
n
(
D
I
)
con
t
rol
l
e
r
t
a
k
e
s ov
e
r
in
o
r
d
e
r
to
trac
k
a
c
c
u
r
a
t
e
ly
th
e
r
e
f
e
re
nc
e;
if
th
e
o
p
e
r
a
ti
ng
po
in
t b
e
l
o
n
g
s to
th
e c
o
nsta
n
t
c
u
r
r
en
t z
o
n
e
(C
CZ)
,
t
h
e f
i
r
s
t
d
a
mpin
g
in
je
c
t
ion
co
n
t
r
o
ll
er
(
D
I1) w
i
l
l
t
r
ac
k the
cu
rre
n
t
re
fere
nce,
whereas
i
f
t
h
e
ope
rat
i
n
g
poi
nt
i
s
at
t
h
e co
nst
a
nt
v
o
l
t
a
g
e z
o
n
e
(C
VZ
), t
h
e
s
econ
d
dam
p
i
ng i
n
je
ct
i
on c
ont
rol
l
er
(D
I2)
wil
l
ta
ke
ove
r i
n
o
r
de
r t
o
t
r
ac
k
t
h
e
v
o
lt
a
g
e
refe
re
nc
e.
Thi
s
c
o
ntr
o
l st
rat
e
g
y
i
s
wel
l
-
det
a
i
l
e
d i
n
t
h
e
ne
xt
s
e
c
t
ion.
T
h
e
DI
c
o
ntr
o
ll
e
r
ge
n
e
rat
e
s,
a
s
a
re
s
u
l
t
,
t
h
e
dut
y
c
y
cl
e d
w
h
i
c
h
wi
l
l
be
use
d
b
y
t
h
e
P
u
lse Widt
h
Mo
d
u
l
a
t
i
on (P
W
M
)
t
e
c
hni
que
t
o
d
e
l
i
ver t
h
e c
o
nt
rol
si
g
n
al
u
of the
p
o
w
e
r
c
o
nv
erte
r
t
r
ansi
sto
r
as
show
n i
n
F
i
gu
re
1.
The
si
mula
ti
o
n
pa
rame
te
rs of
t
h
e PV em
ul
at
or
wit
h
the
c
h
a
r
a
c
t
e
ri
st
ic
s
o
f
t
h
e
PV mo
dul
es
to
em
ul
at
e
are prese
n
t
e
d
in Ta
bl
es
1
a
n
d
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Ph
ot
o
v
ol
tai
c
e
m
ul
at
or of
di
ff
e
r
e
n
t s
o
lar
arr
a
y
c
onf
i
g
ur
ati
o
ns un
der
p
a
rt
i
a
l
…
(
M
ust
a
p
h
a
A
l
ao
ui
)
1
021
Fi
gu
re
1.
O
v
er
a
l
l str
u
ct
u
r
e
of
t
h
e
p
r
op
ose
d
P
V
em
ul
at
o
r
Tabl
e 1. PV
E
m
ul
at
o
r
Pa
ram
e
t
e
r
s
Variab
le
Va
lu
e
I
nput volta
g
e V
s
150 V
Ca
pac
itor
C
10
µF
I
nduct
o
r L
5 m
H
Sw
itc
hing f
r
e
quenc
y
f
Contr
o
ller
gai
n
R1
C
o
n
t
ro
l
l
e
r
g
ai
n R
2
50 KH
z
100
0
0.
0
1
Tab
l
e
2
.
Datash
eet P
a
r
a
meters
of
th
e M
ono
ALLM
AX PLU
S
and
M
ono
REN
OGY
P
V
M
odu
les
V
a
ria
b
le
Mono A
LLMA
X
PL
US
PV
m
odule
Mono RE
N
O
GY P
V
m
odule
Pea
k
ra
te
d po
w
e
r
Ope
n
cir
c
ui
t volta
g
e V
oc
335 W
46.
1V
50 W
22.
6 V
Shor
t ci
rc
uit curr
e
n
t I
sc
9.
41A
2.
92
A
Maxim
u
m
pow
e
r
p
o
int
vol
tage
V
m
pp
37.
8 V
18.
5 V
Ma
x
i
mu
m
p
o
w
er
p
o
i
n
t cu
rr
en
t
I
m
pp
8.
87 A
2.
71 A
T
e
m
p
e
r
at
ure
coe
ffic
i
ent
of
I
sc
:
k
i
0.
053 A/
°C
0.
05 A
/
°C
T
e
m
p
e
r
atur
e
c
o
ef
fici
ent of
V
oc
:
k
v
-0.
31 V
/
°C
-0.
31 V
/
°C
T
e
m
p
e
r
at
ure
coe
ffic
i
ent of
pow
er
:
k
p
-
0
.
41 %/°C
-
0
.
42 %/°
C
N
u
m
b
er
of Cell
s i
n
ser
i
e
s
Ns
72
36
T
h
e
L
and
C
va
lu
e
s
a
r
e
cho
s
e
n
t
o
op
er
a
t
e
in
t
h
e
con
tin
uou
s co
ndu
c
tio
n
m
o
d
e
,
t
h
e
c
o
n
t
r
o
ll
er
g
a
i
n
s
a
r
e sel
e
c
t
ed t
o
ens
u
r
e
t
h
e
de
si
r
e
d
d
y
n
amic
a
n
d
st
at
i
c
per
f
or
manc
es
, t
h
e
y
c
a
n
be
t
u
ne
d t
o
c
h
an
ge
t
h
e
dy
n
a
mi
c
be
ha
vi
o
r
o
f
t
h
e
PV
e
m
u
l
a
t
or
. F
u
rt
her
m
o
r
e
,
we
ha
ve
c
hos
en
t
w
o t
y
pes
o
f
P
V
m
o
d
u
l
e
s
fr
om t
w
o
P
V
c
o
n
s
t
r
uc
t
o
r
s
i
n
or
der t
o
t
e
st
di
ffe
rent
po
wer
s
,
t
h
e pa
ra
met
e
rs
are
t
a
ke
n
f
r
o
m t
h
e te
ch
ni
cal
d
a
t
a
shee
ts.
T
h
e
fi
rst
o
n
e
MON
O
ALLM
AX mo
du
l
e
is u
s
ed
to
v
a
li
d
a
t
e
th
e
e
m
u
l
at
ion
of
PV
modu
l
e
s,
w
h
ile
t
h
e
se
con
d
one
MO
N
O
R
E
NO
GY
is u
s
e
d
f
o
r
t
h
e em
ula
t
ion
of
P
V
a
r
ra
ys
u
nde
r
par
t
i
a
l
l
y
s
h
ade
d
c
ondi
t
i
ons.
3.
PROP
OSE
D
C
O
NT
R
O
L S
T
RAT
EG
Y
OF THE
P
V
E
M
UL
A
T
O
R
In t
h
i
s
part
,
a
new
c
o
nt
rol
str
a
t
e
gy
of
the
P
V
ar
r
a
y em
ul
at
or i
s
p
r
e
s
e
n
te
d
,
i
t
i
s
based e
s
se
nti
a
ll
y o
n
t
h
e
passi
vit
y
da
mpi
n
g i
n
j
e
c
t
i
on c
o
ntr
o
l,
whi
c
h
use
s
a
n
ene
r
get
i
c
app
r
oa
c
h
a
n
d e
n
s
u
re
s a
go
o
d
d
yna
mi
c
r
e
sp
o
n
se
c
o
m
p
ari
n
g t
o
c
o
nve
nt
i
onal
li
nea
r
c
o
m
p
en
sat
o
r
s
s
u
ch
a
s
p
r
op
o
r
t
i
ona
l i
n
t
e
gra
t
or
(PI
) c
ont
rol
l
e
r
[1
7]
.
Be
sid
e
s, du
e to
th
e
non
li
n
e
a
r
i
t
y
o
f
th
e
PV c
h
a
r
a
c
t
e
r
i
s
tic
s,
it is r
e
q
u
i
r
e
d
th
e
u
s
e
of
a sp
e
c
i
f
i
c
non
li
n
e
a
r
con
t
ro
l
str
a
t
e
g
y
a
b
l
e
to
p
r
od
uc
e a stab
l
e
and
ac
c
u
r
a
te PV
e
m
u
l
at
o
r
ou
tpu
t
s
i
r
r
e
sp
e
c
tiv
e of th
e op
er
at
in
g po
i
n
t
posi
t
i
o
n
,
unli
k
e
di
re
ct
re
f
e
r
e
nci
n
g
met
h
o
d
w
h
ic
h
s
u
f
f
e
r
s
fr
om
i
n
acc
u
r
ac
y i
n
so
me
pa
rt
i
c
ul
ar
I
-
V
cu
rv
e
ar
ea
s [2,
2
4
]
.
Th
e
pr
opo
se
d co
n
t
r
o
l str
a
te
gy
con
s
ist
s
o
f
a h
y
b
ri
d
re
f
e
r
e
nci
n
g
me
thod
dep
e
nd
ing
on
t
h
e
po
sit
i
o
n
o
f
t
h
e o
p
era
t
i
n
g poi
nt o
f
t
h
e
P
V
e
m
ul
at
or
as depi
c
t
e
d
i
n
Fi
gu
re
2. Wh
en t
h
e ope
ra
ti
n
g
poi
nt is
a
t
t
h
e c
onst
a
nt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
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6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
19
–
1
0
30
1
022
current
re
gi
o
n
,
t
h
e PV mo
dul
e
c
u
rre
n
t is ap
pro
x
i
m
at
el
y
c
o
n
s
ta
n
t
n
e
a
r
t
o
t
h
e
shor
t
c
i
rc
uit
c
u
r
r
en
t
Isc
,
w
h
ile
t
h
e P
V
mod
u
l
e
v
o
l
t
a
ge
i
s
h
i
gh
l
y
va
ri
a
b
l
e
. The
r
e
f
o
r
e,
a
da
mpi
n
g
i
n
je
ct
ion c
o
ntr
o
ll
er
base
d
o
n
c
u
rre
n
t
r
e
f
e
r
e
n
c
i
n
g
is
re
co
m
m
end
e
d
to
gu
ara
n
t
y
a
st
a
b
le
c
u
rr
en
t
loo
p
as
we
ll
a
s
an
a
c
c
ur
a
t
e
PV
em
u
l
a
t
or
ou
tp
uts.
On
t
h
e ot
he
r ha
n
d
,
i
f
t
h
e
o
p
era
t
i
ng
poi
nt
i
s
at
the
co
nst
a
nt
vol
t
a
ge
z
o
ne,
t
h
e P
V
mo
dul
e vol
t
a
ge
i
s
al
most
con
s
t
a
nt
nea
r
t
o
t
h
e
o
p
en
-c
ir
cui
t
vol
t
a
ge V
o
c
.
T
h
er
efore
,
a da
mpi
n
g in
j
e
c
t
i
on co
nt
rol
l
e
r ba
se
d on
v
o
l
t
age
re
fe
re
nci
n
g
i
s
suit
abl
e
t
o
ha
v
e
a
st
abl
e
re
fe
r
e
nce
v
o
l
t
a
g
e
a
nd the
r
e
b
y
a
n
ac
cura
t
e
P
V
e
m
ul
at
i
o
n
.
In or
der to
l
o
cat
e t
h
e p
o
si
t
i
on o
f
the
ope
rat
i
ng
p
o
int
,
a
com
p
aris
on
be
t
w
e
e
n
an
d
is
r
e
qu
i
r
ed
,
w
i
th
V
l
o
a
d
a
n
d
Il
oa
d are
res
p
e
c
t
i
v
el
y
t
h
e
l
o
a
d
vol
t
a
ge
a
n
d
c
u
rrent
, an
d V
m
pp
an
d Imp
p
are
res
p
ec
ti
vel
y
the
ma
xi
mum
p
o
w
e
r
poi
nt
vol
ta
ge
a
n
d
c
u
rrent
. We
c
a
n
al
so
c
o
mp
a
r
e
∆
to
∆
,
wh
er
e
∆
an
d
∆
are
re
spe
c
t
i
ve
ly t
h
e
P
V
vo
lt
ag
e
a
n
d
cu
rr
e
n
t
v
a
r
i
a
tio
n
s
if
th
e PV c
h
ar
a
c
t
e
r
i
st
ic
pr
es
en
t
s
mo
re
tha
n
o
n
e
m
a
x
i
mu
m po
w
e
r po
int
.
It i
s
w
o
rt
h
y
to
not
e t
h
at
the
re
fe
re
nc
es a
r
e
ge
nerat
e
d fr
om t
h
e L
U
T.
The
d
a
t
a
poi
nts
of t
h
e LUT
are
ca
lc
ula
t
e
d
offl
i
n
e usi
n
g
t
h
e 1D
2R
ma
the
m
a
t
ic
mo
de
l o
f
t
h
e
P
V
pa
nel
whe
r
e t
h
e
c
u
rre
nt
a
n
d
v
o
l
t
a
g
e
a
r
e
l
i
nke
d
ac
c
o
rdi
n
g
t
o
t
h
e
fol
l
o
w
in
g e
quat
i
o
n:
ℎ
∗
∗
1
∗
(1)
Wit
h
Ire
f i
s
t
h
e P
V
c
u
rre
n
t
r
e
fe
re
nc
e, V
o
i
s
the
o
u
t
put
vol
t
a
ge
, Ip
h i
s
t
h
e
p
hot
oel
ect
ri
c
c
u
rre
n
t,
Is
is
t
h
e
di
ode
sat
u
rat
i
on c
u
rre
nt
,
Vt
i
s
t
h
e
ju
nc
ti
on
t
h
e
r
mal
v
o
l
t
a
g
e,
A
is
t
h
e
di
o
d
e i
d
eal
i
t
y
fac
t
or
, R
s
a
n
d
Rp a
r
e
re
spe
c
t
i
v
el
y t
h
e
PV
mo
d
u
le
s
e
ri
es a
n
d s
h
unt
resi
st
a
n
ces
. T
h
e
vol
t
a
ge
re
fe
re
nce
i
s
c
o
mp
u
t
ed
usi
n
g
t
h
e
reve
rse
I
-
V
LU
T,
wh
ich
i
s
th
e V
-
I
LU
T.
Fi
gu
re
2. Co
nt
rol
st
ra
te
g
y
o
f
d
a
mpin
g i
n
j
e
c
t
i
o
n
in
funct
i
o
n of the
o
p
erat
i
n
g
poi
n
t
loc
a
t
i
o
n
Let
’
s fi
nd t
h
e
e
x
p
r
essi
ons o
f
DI1
a
n
d
D
I
2.
Eul
e
r
Lag
r
a
n
g
e
a
v
e
r
a
g
e
d
st
at
e mo
del
of the
buc
k
c
o
nve
rt
er is de
fi
ne
d as
[
2
5
]
:
0
0
0
1
1
1/
0
(2
)
W
ith
x
is th
e
st
a
t
e
v
e
c
t
or
o
f
the
sy
s
t
em
1
2
A
n
d
E is
th
e
inp
u
t
vo
lt
ag
e
:
E=V
s
I
t
ca
n
b
e
al
so
w
r
itt
en
a
s
:
ℜ
(3)
Whe
r
e:
L0
0C
D
i
a
g
ona
l mat
r
i
x
c
ont
a
i
ni
ng
t
h
e st
ora
g
e el
e
m
ent
s
of t
h
e sy
st
em;
0
5
10
15
20
25
30
35
40
45
50
0
1
2
3
4
5
6
7
8
9
10
V
o
l
t
ag
e (
V
)
Cu
r
r
e
n
t
(
A
)
C
ont
r
o
l
La
w
D
I
2
R=
Rm
p
p
Mp
p
C
o
n
s
t
a
n
t
e V
o
l
t
ag
e Z
o
n
e
C
o
nt
r
o
l
La
w
D
I
1
C
o
n
s
t
a
nt
e
C
u
r
r
e
nt
Z
o
ne
R <
R
m
p
p
R >
=
R
m
p
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Pho
t
o
v
o
l
ta
i
c
e
m
u
l
a
t
o
r
o
f
d
iffe
re
n
t
so
la
r a
rra
y
c
o
n
f
igu
r
a
t
i
o
n
s
u
n
d
e
r
pa
rt
i
a
l
…
(Mu
s
ta
pha
Ala
o
u
i
)
1
023
0
1
10
An
ti
symme
tric
m
a
tr
ix rep
r
e
s
e
n
t
i
ng
the
in
te
rcon
n
e
ctio
n
b
e
tw
e
e
n th
e sy
s
t
em
com
p
o
n
e
n
t
s
;
ℜ
00
01
/
R
Sy
mme
t
r
ic
de
f
i
n
i
t
e
p
o
s
iti
ve
ma
tr
i
x
re
pr
e
s
en
ti
ng
th
e d
i
ss
ip
at
iv
e
e
l
eme
n
ts o
f
th
e
system
;
0
C
o
n
t
a
i
ns
the
e
x
o
g
e
n
o
u
s
an
d c
ont
rol i
n
p
u
t
s
of
t
h
e syst
em
.
Co
n
s
i
d
e
r
in
g t
h
e
fo
llo
w
i
n
g
d
e
sir
e
d
H
a
mil
t
onia
n
s
t
or
ag
e func
ti
o
n
:
(4)
W
ith
is the
e
rror an
d x
d
i
s
t
h
e
de
sire
d va
lu
e
o
f
x.
The desi
re
d da
mpin
g
ℜ
of
t
h
e
clo
s
e
d
-
l
oo
p
is:
ℜ
ℜ
ℜ
(5)
W
ith
ℜ
i
s
t
h
e
re
qui
re
d
da
mpi
n
g t
o
be
i
n
je
ct
ed
so t
h
at
ℜ
c
a
n
b
e
sym
m
et
ri
c d
e
fi
n
i
te
p
o
s
itiv
e
.
The
d
yna
mic
o
f
t
h
e
e
r
ro
r ass
o
ci
at
ed wi
t
h
t
h
e st
ora
g
e fu
nct
i
o
n
i
s
de
fi
ne
d
as
:
ℜ
(6)
In
orde
r t
o
hav
e
a pa
ssi
ve
a
n
d
st
abl
e
cl
ose
d
-l
oo
p, we
c
a
n
ch
oos
e
0
[
25]
The
c
o
nt
rol
l
a
w
dy
namic
i
s
t
h
en
ex
p
r
e
s
se
d
as:
ℜ
ℜ
(7)
Let’
s choose
ℜ
to
be as:
ℜ
10
0
2
(8)
R
1
an
d R
2
ar
e tw
o
po
sit
i
v
e
r
e
a
l
n
u
mb
er
s.
Thus:
ℜ
10
0
2
1/
(9)
Th
e
r
efo
r
e:
1
2
1
1
1
2
1
2
2
2
0
(10
)
For
the
c
o
nsta
nt c
u
r
rent
reg
i
o
n:
Let
’
s
fi
x
x1
d =
Ire
f
=
ct
e
Then from (10):
2
1
1
2
2
2
2
0
(11
)
Usi
ng
(1
1) a
n
d
(2):
2
1
1
2
(12
)
S
u
b
s
tit
u
tin
g
2
e
xpressi
o
n
i
n
(1
1), w
e
fi
nd:
2
2
2
2
2
0
(13
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
19
–
1
0
30
1
024
That
yi
el
ds rep
l
aci
ng
x2d
b
y
i
t
s ex
pressi
on
from (11
)
:
2
2
2
1
2
1
(14
)
F
i
n
a
lly
,
th
e
c
o
n
t
ro
l l
a
w
D
I
1
i
s
ex
p
r
esse
d a
s
:
DI1
:
∗
(15
)
For
the
c
o
n
s
ta
n
t
vol
ta
ge re
gi
on
:
x2
d =
V
r
ef
=
c
t
e
Then:
1
1
1
1
1
2
2
0
(16
)
Usi
ng
(1
6) a
n
d
(2):
1
2
2
(17
)
S
u
b
s
tit
u
tin
g the
ex
pre
ssi
on
in
(
1
6
)
, w
e
fi
nd:
1
2
1
1
1
(18
)
Then:
1
2
1
1
2
2
(19
)
F
i
n
a
lly
,
th
e
c
o
n
t
ro
l l
a
w
D
I
2
i
s
wri
tte
n
a
s
:
DI2
:
(20
)
It
is i
m
p
o
rt
a
n
t
t
o
n
o
t
e
t
h
at
t
o
a
v
oi
d
e
x
c
e
s
si
ve s
w
i
t
c
hi
n
g
bet
w
ee
n
c
ont
rol
l
e
r
s
whe
n
R
is
ne
ar
to
Rmp
p
, a
n
ove
rl
ap i
s
ma
de ar
ou
nd t
h
e
M
P
P
(
∆
R=
2
Ω
)
so
t
h
e
sy
s
t
em
i
n
th
e
M
P
P
ar
ea
can
b
e
co
n
t
ro
ll
ed
b
o
t
h
by
t
h
e
D
I
1
or DI
2. Thi
s
f
r
eq
ue
nt t
r
ansi
ti
o
n
ma
y be
d
u
e
t
o
n
o
i
s
e
o
r
me
a
s
u
r
eme
n
t
errors
i
n
pra
c
t
i
ce.
4.
SIM
U
LAT
I
ON
RE
SUL
T
S
AN
D DIS
C
US
S
I
ON
4
.
1
.
D
y
na
mic
perfo
r
ma
nces st
udy
4.1.
1.
P
V
m
o
d
u
l
e
emu
l
ator
un
der
d
y
n
a
m
i
c l
o
a
d
i
n
g
In
t
h
i
s
pa
rt,
i
n
order
t
o
ve
ri
fy i
f
t
h
e p
r
o
p
o
se
d
syst
em remai
n
s
st
abl
e
an
d ac
cura
te
un
der
c
h
an
gi
n
g
t
h
e
re
si
st
ive
l
o
ad
from
an
I-V c
u
rve
re
gi
o
n
t
o
a
n
othe
r, we
have
subj
ec
t
e
d
t
h
e
P
V
e
m
ul
a
t
or t
o
a
rapi
d
l
o
ad
varia
t
i
o
n p
r
ofi
l
e
w
h
i
c
h
inc
l
u
d
e
s t
h
e
c
onsta
nt
curre
nt
z
o
ne,
t
h
e c
o
nst
a
nt
v
o
lt
age
z
one
a
n
d t
h
e
MP
P
z
o
ne
as
depi
ct
ed
in
Fi
g
u
re
3
.
A
s
s
h
ow
n i
n
t
h
e a
b
o
v
e
fi
g
u
r
e
, it
i
s
ob
vio
u
s
t
h
at
t
h
e
p
r
op
o
s
ed
P
V
sy
ste
m
mai
n
t
a
i
n
s
it
s
st
abi
l
i
t
y an
d
ac
cura
c
y
e
v
e
n
un
de
r
va
ryi
ng
t
h
e re
sist
i
v
e
lo
a
d
from
a
n
I-V
re
gi
o
n
to
a
not
her
,
t
h
e
P
V
e
m
ul
at
or t
r
ac
ks
r
a
pi
dly
t
h
e
P
V
m
o
dul
e
c
u
rre
nt an
d
v
o
l
t
a
ge
, w
h
ic
h
proo
fs t
h
e
rob
u
st
ness of
t
h
e
p
r
o
pose
d
c
o
n
t
rol
st
ra
t
e
gy
.
M
o
r
e
o
v
e
r
,
t
h
e sta
tic
e
r
r
o
r
is neg
l
ig
ib
le
ar
ound
1
%
and
th
e cu
rre
n
t
and
v
o
lt
a
g
e ri
pp
le
s a
r
e to
o
sma
l
l.
In
dee
d
, f
o
r R
>
=
R
mp
p, the
c
u
rre
n
t
a
n
d
v
o
lt
age
ri
p
p
l
e
s fa
ct
or i
s
a
ppro
x
im
at
el
y 0.
2%,
a
n
d for R
<
R
m
pp, t
h
e
current
ri
ppl
e
fact
or i
n
c
r
e
a
se
s
sl
i
ght
l
y
t
o
1
,
2
%
be
ca
use
of the
out
put
c
u
rre
n
t
inc
r
ea
s
e
.
Ove
r
al
l,
t
h
e
P
V
emul
at
o
r
out
pu
t
ri
p
p
l
e
s re
mai
n
s
m
al
l
fo
r al
l
t
h
e
ope
ra
ti
n
g
poi
nt
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Pho
t
o
v
o
l
ta
i
c
e
m
u
l
a
t
o
r
o
f
d
iffe
re
n
t
so
la
r a
rra
y
c
o
n
f
igu
r
a
t
i
o
n
s
u
n
d
e
r
pa
rt
i
a
l
…
(Mu
s
ta
pha
Ala
o
u
i
)
1
025
Fi
gu
re
3. P
V
e
m
ula
t
or out
put
s u
nde
r c
h
a
ngi
ng
t
h
e
resi
st
ive
l
o
ad
fro
m
I-
V c
u
rve z
o
ne t
o
a
not
he
r
4.1.
2.
P
V
m
o
dul
e
emul
ator
fee
d
i
n
g re
si
s
t
i
v
e lo
ad a
t
di
ff
ere
nt
I
-
V cur
v
e zone
s
The
d
y
n
a
m
i
c
p
e
rf
ormance
s
of t
h
e
p
r
o
p
o
se
d P
V
mod
u
l
e
e
m
ul
at
or are
e
v
al
uat
e
d
in
t
h
is
pa
rt
. We
ha
ve
cho
s
en t
h
re
e
re
si
st
ance
l
o
a
d
s
,
e
ach
o
n
e c
o
rre
sp
on
ds t
o
one
I-
V c
u
rve
z
o
n
e
. Th
e o
p
e
r
at
in
g
poi
nt
s c
o
rre
spo
n
d
t
o
t
h
e
i
n
te
rsec
ti
on
be
twe
e
n
t
h
e
resi
sta
n
ce
charact
e
r
i
s
t
i
c
wit
h
t
h
e
I-V
c
h
ara
c
t
e
rist
i
c
o
f
the
PV
mod
u
l
e
.
A
com
p
ari
s
on
i
s
done
be
tw
ee
n t
h
e
c
u
rre
n
t a
n
d
volt
a
g
e
o
f
t
h
e
PV e
m
ul
at
o
r
w
i
t
h
the
P
V
mo
d
u
l
e
’s
o
n
es as s
h
o
w
n
in
Fi
gur
e 4
.
F
i
g
u
r
e
4
.
Dyn
a
mi
c r
e
sp
on
se
of
th
e PV
mod
u
l
e
emu
l
ato
r
a
t
th
e thr
e
e
I-V
c
h
a
r
ac
te
ri
stic
regio
n
s
0
0.
0
1
0.
02
0.
0
3
0.
04
0.
0
5
0.
06
0.
07
0.
08
0.
09
0.
1
0
10
20
30
ti
m
e
(
s
)
R
e
s
i
s
t
anc
e (
O
hm)
0
0.
0
1
0.
02
0.
0
3
0.
04
0.
0
5
0.
06
0.
0
7
0.
08
0.
09
0.
1
0
10
20
30
40
50
ti
m
e
(
s
)
V
o
l
t
a
ge(
V
)
Vp
v
Ve
m
u
0
0.
0
1
0.
02
0.
0
3
0.
04
0.
0
5
0.
06
0.
0
7
0.
08
0.
0
9
0.
1
0
2
4
6
8
10
ti
m
e
(
s
)
C
u
rr
e
n
t
(A
)
Ip
v
Ie
m
u
0.
047
0.
048
0.
049
45.
3
5
45
.
4
45.
4
5
0
.
0898
0.
09
9.
4
9.
5
R<
R
m
p
R>
R
m
p
R>
Rm
p
R=
Rm
p
R=
R
m
p
R<
R
m
p
R<
R
m
p
0
0.
0
0
2
0.
0
0
4
0.
006
0.
0
0
8
0.
0
1
0
5
10
15
20
ti
m
e
(
s
)
V
o
l
t
ag
e(
V
)
Vp
v
Ve
m
u
0
0.
0
0
5
0.
0
1
0
10
20
30
40
ti
m
e
(
s
)
V
o
l
t
ag
e(
V
)
Vp
v
Ve
m
u
0
0.
005
0.
0
1
0
10
20
30
40
50
ti
m
e
(
s
)
V
o
l
t
ag
e(
V
)
Vp
v
Ve
m
u
0
0.
0
0
2
0.
004
0.
006
0.
0
0
8
0.
01
0
2
4
6
8
10
ti
m
e
(
s
)
C
u
r
r
ent
(
A
)
Ip
v
Ie
m
u
0
0.
005
0.
01
0
2
4
6
8
10
ti
m
e
(
s
)
C
u
r
r
ent
(
A
)
Ip
v
Ie
mu
0
0.
002
0.
004
0.
0
0
6
0.
008
0.
01
0
0.
5
1
1.
5
2
2.
5
ti
m
e
(
s
)
Cu
rr
e
n
t
(A
)
Ip
v
Ie
m
u
0
10
20
30
40
50
0
2
4
6
8
10
Vo
l
t
a
g
e
V
(
V
)
C
u
r
r
ent
(
A
)
Ip
v
=
f
(
V
)
I =
V
/
R
0
20
40
60
0
2
4
6
8
10
V
o
l
t
age V
(V
)
C
u
rr
e
n
t
(A
)
Ip
v
=
f
(
V
)
I =
V
/
R
0
10
20
30
40
50
0
2
4
6
8
10
Vo
l
t
a
g
e
V
(
V
)
C
u
r
r
ent
(
A
)
Ip
v
=
f
(
V
)
I =
V
/
R
18
.
8
1
18
.
815
18.
8
2
9.
40
4
9.
40
6
9.
40
8
5
5.
1
5.
2
x 1
0
-3
18
.
6
18
.
8
19
19
.
2
3.
4
3.
6
x 1
0
-3
9.
4
9.
45
9.
5
37
.
7
6
37.
7
8
8.
85
8.
86
8.
87
7
8
9
x 1
0
-3
37.
6
37.
7
37.
8
7
8
9
x 1
0
-3
8.
84
8.
86
8.
88
44
.
9
4
44
.
9
6
44
.
9
8
2.
24
2.
25
2.
26
4.
3
4.
4
4.
5
x 1
0
-3
44.
9
6
44.
9
8
45
45.
0
2
4.
1
4.
2
4.
3
4.
4
4.
5
x 1
0
-3
2.
24
6
2.
24
8
2.
25
2.
25
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
Int J
Pow
Elec &
Dri Syst,
Vol. 11,
No. 2,
J
u
ne
2020
:
1019
– 1030
1
026
Fi
gu
re
4 sh
ow
s t
h
e d
yna
mi
c pe
r
f
o
r
ma
nces
of
the
pr
o
p
o
se
d P
V
e
m
u
l
a
t
or
,
i
t
c
ont
ai
ns t
h
re
e c
o
l
u
m
n
s
,
an
d
e
ach
co
lumn
p
r
o
v
i
d
e
s th
e I
-
V
c
h
a
r
a
c
t
e
rist
ic
o
f
th
e
PV mod
u
le
w
i
t
h
th
e r
e
sisti
v
e lo
a
d
c
h
ara
c
t
e
r
i
st
ic
, th
e
P
V
m
o
del
v
o
l
t
a
ge
wi
t
h
t
h
e
P
V
em
ul
at
or
v
o
l
t
a
ge,
a
n
d t
h
e
PV
mo
de
l
cu
r
r
e
nt
w
i
t
h
t
h
e
P
V
em
ul
at
or
cu
rr
e
n
t
.
T
h
e op
er
a
ting
p
o
i
n
t
at
th
e con
s
ta
n
t
cur
r
e
n
t
r
e
g
i
o
n
co
rr
espo
nd
ing
t
o
R = 2
Ω
i
s
s
how
n i
n
the
f
i
r
s
t col
u
m
n
,
whi
l
e
t
h
e
se
c
o
nd
c
o
l
u
m
n
sho
w
s
a
n
o
p
era
t
in
g p
o
int
at
t
h
e Ma
xi
mu
m po
wer
re
gio
n
(
)
.
Th
e
th
ird
c
o
lum
n
inc
l
u
d
e
s an o
p
e
r
a
t
i
n
g
poi
nt
a
t
t
h
e co
nst
a
nt
vol
t
a
ge
regi
on
(R =
2
0
Ω
).
P
V
em
ula
t
or
out
p
u
ts ar
e ne
arl
y
th
e
sa
me
as
the
PV
mo
d
e
l’
s
o
n
e
s,
th
e
re
la
ti
v
e
st
at
ic
er
r
o
r
s
a
nd
a
r
e n
e
g
l
i
g
ib
le
not
e
x
cee
din
g
1
%
,
t
h
e c
u
r
r
e
nt
a
n
d
volt
a
ge
ri
p
p
l
e
s
a
r
e
ar
ou
n
d
1.
5%,
w
h
e
r
ea
s t
h
e
se
tt
l
i
ng
ti
me is t
o
o
sma
l
l
b
e
t
w
e
e
n
60
0 µs
and
1 ms,
w
h
i
l
e
t
h
e
co
mme
r
ci
al
P
V
e
m
u
l
a
t
or
s
u
s
i
ng pr
ogr
am
mab
l
e
pow
er
supp
ly
h
a
v
e
a
dy
na
mi
c
per
f
o
r
ma
nce
be
t
w
e
e
n 1
0
ms
to
10
0
ms
[2
].
T
h
e
r
e
f
or
e,
t
h
e
desi
g
n
e
d
PV
emul
at
o
r
has
a
g
o
o
d
dy
na
mi
c
per
f
o
r
ma
nce
c
o
mpa
r
ed t
o
m
o
st
of
t
h
e exi
s
ti
n
g
P
V
em
ul
at
or
s, t
h
e t
r
a
n
si
ent
dy
na
mi
c re
sp
ons
e
i
s
v
e
r
y
r
a
pi
d
a
n
d
t
h
e
a
ccur
a
c
y
i
s
ve
ry
hig
h
.
Be
si
d
e
s,
the
pr
opo
s
e
d no
nl
i
n
ea
r
p
o
we
r
devi
ce
i
s
abl
e
t
o
ma
int
a
i
n
it
s
st
abi
l
i
t
y
a
n
d a
c
c
ura
c
y
i
n
a
n
y
I-
V
c
u
r
v
e
re
g
i
on,
u
n
li
ke
e
x
i
s
t
i
ng P
V
e
m
ul
at
ors
base
d
on
co
nve
nt
i
o
nal
cont
rol
str
a
t
e
g
i
es
th
a
t
su
ff
e
r
f
r
o
m
in
s
t
ab
ilit
y
a
nd i
n
ac
cu
ra
cy
i
n
th
e
co
nsta
nt
cu
r
r
e
n
t
r
e
g
i
o
n
and
t
h
e
co
n
s
tan
t
vol
t
a
ge
re
gi
o
n
[2
].
4.
1.
3.
S
o
l
a
r
e
m
u
l
at
or
o
f
se
v
eral
P
V
arr
a
y
con
f
i
g
ur
ati
o
n
s
u
n
d
e
r
p
a
rti
a
l
l
y
shad
ed
co
n
d
i
t
i
o
ns
I
n
th
is
se
ct
io
n, se
v
e
ra
l
so
la
r
P
V
ar
ray
conf
ig
ur
a
tion
s
a
r
e
pro
p
o
s
ed
:
S
e
ries,
P
a
ra
lle
l,
S
e
ri
es-
P
a
r
a
lle
l
(
S
P
)
,
H
o
ney
-
C
o
m
b
(
H
C
)
,
Br
i
dge
-Li
n
ke
d (
B
L)
a
n
d
T
o
t
a
l
Cross
-
Ti
e
d
(
T
C
T
) c
o
n
f
ig
u
r
a
t
ions
. Ea
c
h
P
V
ar
r
a
y
co
nf
igu
r
a
tion
i
s
su
b
j
ec
ted
to
a
p
a
r
t
i
a
l
sh
a
d
i
n
g
con
d
itio
n
sce
n
a
r
io
as
illu
s
t
r
a
te
d
in
F
i
gure
5
,
wh
i
c
h
af
fec
t
s th
e
I-V
and P
-
V ch
a
r
a
c
t
e
r
is
tic
s
o
f
th
e
P
V
arr
a
y
.
Th
e ma
in ob
je
ct
iv
e of
t
h
is p
a
r
t
i
s
t
o
sho
w
t
h
e
ab
ilit
y of th
e
pr
opose
d
P
V
ar
ra
y
em
ula
t
or
t
o
t
r
a
c
k t
h
e
out
put
c
u
r
r
e
n
t
and
vol
t
a
g
e
of t
h
e
PV
a
r
r
a
y
f
o
r e
a
c
h
s
o
la
r P
V
co
nf
igu
r
a
tion
un
d
e
r
p
a
rt
ia
lly
sh
a
d
e
d
c
o
n
d
ition
s
and
p
r
o
v
i
d
e
th
e
sa
me
ou
tputs
.
Fi
gu
re
5.
The
dif
f
e
r
e
n
t
P
V
a
r
ra
y
co
nf
i
g
u
r
at
ions
u
nde
r
p
a
rt
i
a
l
sha
d
i
n
g c
o
n
d
it
i
ons
Fi
gu
re
s 6
a
nd
7
s
h
ow
f
o
r
e
a
c
h
PV
ar
ra
y c
o
n
f
i
g
urat
i
o
n
t
h
e I
-
V
a
n
d
P
-
V
cha
r
act
e
r
i
s
t
i
c
cur
v
e
i
n
t
h
e
f
i
r
s
t
a
n
d
sec
o
n
d
wa
v
e
f
o
rm
s
of
e
a
c
h
c
o
lum
n
,
an
d t
h
e
out
put
v
o
lt
age
a
n
d
c
u
r
r
e
n
t
o
f
t
h
e
P
V
a
r
ra
y e
m
ul
at
or
an
d
t
h
e P
V
a
rra
y
i
n
t
h
e
l
a
st
wa
vef
o
r
m
s
of
ea
ch
P
V
c
o
n
f
i
g
ura
t
i
o
n.
The
P
V
a
rra
y
e
m
ul
at
o
r
s
h
o
u
ld
del
i
v
e
r
t
h
e
same
o
u
t
p
u
t
curr
en
t
an
d vo
lt
ag
e
c
o
r
r
e
s
po
nd
i
n
g
to
t
h
e in
te
r
s
e
c
ti
o
n
po
i
n
t
o
f
th
e
PV
ch
ar
a
c
t
e
r
i
st
i
c
s.
As
de
sc
ri
bed
i
n
F
i
gur
es
6 a
n
d
7
,
we
ha
ve c
hos
en di
f
f
e
re
nt resi
sti
v
e l
o
a
d
val
u
e
s
fo
r
e
a
c
h
P
V
ar
r
a
y
c
o
n
f
i
g
u
r
at
i
o
n,
the
o
p
era
t
i
n
g
p
o
int
i
s
c
l
e
a
rly
sho
w
n fo
r ea
c
h
ca
se i
n
t
h
e I-
V an
d P-
V cha
r
act
erist
i
c
s. It
c
a
n be
c
oncl
ude
d
tha
t
t
h
e
de
vel
o
pe
d
PV
a
rra
y
e
m
ul
a
t
or
p
r
ovi
de
s t
h
e
same
o
u
t
put
c
u
rre
nt a
n
d
v
o
l
t
a
ge
of
t
h
e
PV
a
rra
y
f
o
r
a
ny
P
V
ar
ra
y c
o
n
f
i
g
urat
i
o
n u
nde
r
p
a
r
t
ia
l shadi
n
g
c
o
n
d
i
t
i
on
s.
T
h
e
coo
r
di
na
te
s
of
the
o
p
e
r
at
i
ng p
o
i
n
ts
ar
e
t
h
e
sam
e
a
s
t
h
e
P
V
emu
l
a
t
o
r
ou
tpu
t
s.
N
o
t
e
t
h
at
th
e
t
r
an
si
e
n
t
dy
n
a
mic
r
e
spon
s
e
i
s
v
e
ry
f
a
st si
nce
th
e
se
tt
l
i
ng ti
me i
s
ar
o
u
n
d
5
0
0
µ
s
a
n
d
ca
n
c
h
a
nge
sl
i
g
htl
y
de
pe
n
d
in
g
o
n
t
h
e
l
o
a
d
val
u
e
.
Be
side
s, si
nc
e
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Pho
t
o
v
o
l
ta
i
c
e
m
u
l
a
t
o
r
o
f
d
iffe
re
n
t
so
la
r a
rra
y
c
o
n
f
igu
r
a
t
i
o
n
s
u
n
d
e
r
pa
rt
i
a
l
…
(Mu
s
ta
pha
Ala
o
u
i
)
1
027
ac
cura
c
y
i
s
the
key
fe
at
u
r
e
th
a
t
a
ny P
V
e
m
u
l
at
or
sh
o
u
l
d
e
n
sure
t
o
mi
mic
fai
t
h
ful
l
y
the
P
V
so
u
r
c
e
be
ha
vio
r
,
t
h
e ac
c
u
ra
c
y
o
f
t
h
e
p
r
op
ose
d
P
V
arra
y em
ula
t
or i
s
ve
ry
hig
h
be
ca
use t
h
e st
at
i
c
e
rror remai
n
s
ve
ry
sma
l
l
i
rre
spe
c
t
i
v
e
of t
h
e P
V
a
rra
y
c
o
n
f
i
gurat
i
on, t
h
e
pa
rt
ia
l shad
i
ng c
o
n
d
it
i
on
a
nd
t
h
e l
o
ad
val
u
e, whi
c
h co
ns
t
i
t
u
t
e
s
an im
po
rt
ant
a
dde
d
-
va
l
u
e
of t
h
e pr
opose
d
p
o
w
er
el
e
c
t
r
o
n
i
c
syst
em
c
o
mpa
r
ed to
the
e
x
ist
i
ng P
V
em
ul
at
o
r
s.
F
i
gu
re
6.
D
y
na
mi
c res
p
o
n
se
o
f
t
h
e
P
V
ar
ra
y
emula
t
or
fo
r
se
rie
s
(a
) pa
ra
ll
el
(b) a
n
d
S
P
c
o
nfi
g
u
r
at
i
o
n
s
(c
)
Fi
g
ur
e
7
.
D
y
na
mic
res
p
on
s
e
of
th
e P
V
a
rra
y
em
u
l
a
t
or
for
HC
(
d
)
BL
(
e
)
a
n
d TC
T confi
g
urat
io
ns
(
f
)
0
1
2
3
4
5
x 1
0
-3
0
50
ti
m
e
(
s
)
V
o
l
t
age
(
V
)
Vpv
Vem
u
0
1
2
3
4
5
x 1
0
-3
0
1
2
3
ti
m
e
(
s
)
Cu
rr
e
n
t
(
A
)
Ip
v
Ie
m
u
0
50
100
0
1
2
3
V
o
l
t
a
ge V
(
V
)
Curr
e
n
t
(
A
)
Ip
v
=
f
(
V
)
I =
V
/
R
0
50
100
0
50
100
150
200
V
o
l
t
age V
(V
)
Po
w
e
r
(
W
)
Pp
v
=
f
(
V)
P =
V
2
/R
0
1
2
3
4
5
x 1
0
-3
0
10
20
30
ti
m
e
(
s
)
V
o
l
t
age
(
V
)
Vpv
Vem
u
0
1
2
3
4
5
x 1
0
-3
0
0.
5
ti
m
e
(
s
)
C
u
rren
t
(A
)
Ip
v
Ie
mu
0
5
10
15
20
0
5
10
V
o
l
t
age V
(V
)
Cu
rr
e
n
t
(
A
)
Ip
v
=
f
(
V
)
I =
V
/
R
0
5
10
15
20
0
50
100
150
V
o
l
t
age
V
(
V
)
P
o
w
e
r(W
)
Ppv
=
f
(
V)
P =
V
2
/R
0
1
2
3
4
5
x 1
0
-3
0
50
ti
m
e
(
s
)
V
o
l
t
ag
e(V
)
Vpv
Vem
u
0
1
2
3
4
5
x 1
0
-3
0
5
ti
m
e
(
s
)
Curr
e
n
t
(A
)
Ip
v
Ie
m
u
0
20
40
60
80
0
2
4
6
8
10
V
o
l
t
age V
(
V
)
C
u
rrent
(A
)
Ip
v
=
f
(
V
)
I =
V
/
R
0
20
40
60
80
0
10
0
20
0
30
0
V
o
l
t
age V
(
V
)
Po
w
e
r
(
W
)
Ppv
=
f
(
V)
P =
V
2
/R
66
.
9
67
67
.
1
2.
22
2.
23
2.
24
66
68
140
150
160
3.
9
3.
95
x 1
0
-3
67
67
.
2
2.
3
2.
35
x 1
0
-3
2.
2
3
2.
23
5
2.
2
4
21
.
6
21
.
6
5
0.
4
0.
4
5
2
1
.
626
21
.
6
265
9.
35
9.35
5
9.
36
Ppv
=
f
(
V)
P =
V
2
/R
5
10
15
x 1
0
-4
21
.
5
22
5
10
x 1
0
-4
0.43
0.
43
5
0.44
49
50
4.
8
5
5.
2
49
50
51
240
250
260
7.
5
8
x 1
0
-4
49
.
9
50
50
.
1
1.
2
1.25
x 1
0
-3
4.
98
5
5.
02
(
a
)
S
e
r
i
e
s
C
o
nf
i
gur
at
i
o
n
(b
)
P
a
r
a
ll
e
l
C
o
n
f
ig
u
r
a
t
io
n
(
c
)
S
P
C
o
n
f
ig
u
r
a
t
io
n
0
1
2
3
4
5
x 1
0
-3
0
5
10
ti
m
e
(
s
)
Vol
t
age
(V)
Vp
v
Ve
m
u
0
1
2
3
4
5
x 1
0
-3
0
5
10
ti
m
e
(
s
)
Cur
r
ent
(
A
)
Ip
v
Ie
m
u
0
20
40
60
80
0
5
10
Vo
l
t
ag
e V (V)
Cur
r
ent
(
A
)
Ip
v
=
f
(
V
)
I =
V
/
R
0
20
40
60
80
0
10
0
20
0
30
0
V
o
l
t
a
ge V (V
)
P
o
w
e
r(W
)
Pp
v
=
f
(
V
)
P =
V
2
/R
0
1
2
3
4
5
x 1
0
-3
0
10
20
30
40
ti
m
e
(
s
)
Vol
t
age(
V)
Vpv
Vem
u
0
1
2
3
4
5
x 1
0
-3
0
2
4
6
8
ti
m
e
(
s
)
Cur
r
ent
(
A
)
Ip
v
Ie
m
u
0
20
40
60
80
0
5
10
Vol
t
age
V
(
V
)
C
u
rre
n
t
(A
)
Ip
v
=
f
(
V
)
I =
V
/
R
0
20
40
60
80
0
100
200
300
Vol
t
a
ge V (
V
)
P
o
w
e
r(W
)
0
1
2
3
4
5
x 1
0
-3
0
50
100
ti
m
e
(
s
)
Vol
t
ag
e(V)
Vpv
Vem
u
0
1
2
3
4
5
x 1
0
-3
0
1
2
ti
m
e
(
s
)
Cur
r
ent
(
A
)
Ip
v
Ie
m
u
0
20
40
60
80
0
5
10
Vo
l
t
ag
e V
(
V
)
Cur
r
ent
(
A
)
Ip
v
=
f
(
V
)
I =
V
/
R
0
20
40
60
80
0
100
200
300
Vo
l
t
ag
e V (V)
Po
w
e
r
(
W
)
Pp
v
=
f
(
V)
P =
V
2
/R
8
9
10
9.05
9.1
9.15
9.2
9
10
70
80
90
1
1.1
1.
2
x 1
0
-3
9.14
9.16
9.18
1.5
1.6
1.7
x 1
0
-3
9.
1
4
9.
1
6
9.
1
8
32
34
36
38
8.2
8.4
8.6
34
36
38
29
0
29
5
30
0
Pp
v
=
f
(
V)
P =
V
2
/R
82
83
14
5
15
0
15
5
82
84
1.6
1.8
2
2.
04
2.
06
2.
08
x 1
0
-3
82
.
4
82
.
6
82
.
8
1.
25
1.
3
1.
35
x 1
0
-3
1.
83
1.
83
5
1.
84
2.
3
2.
4
2.
5
x 1
0
-3
35
.
6
35
.
8
36
2.
4
2.
4
5
2.
5
x 1
0
-3
8.
2
8.
4
8.
6
(e
)
B
L
C
o
n
f
ig
u
r
a
t
io
n
(f
)
T
C
T
C
o
n
f
i
g
u
r
a
t
i
o
n
(
d
)
H
C
C
o
n
f
ig
u
r
a
t
io
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
19
–
1
0
30
1
028
4.2.
S
t
a
t
i
c
pe
r
f
or
m
a
nc
e
stu
d
y
Thi
s
pa
rt
at
t
e
mpts t
o
i
n
vest
i
g
at
e t
h
e
st
a
t
i
c
pe
rforma
n
c
e
s
of t
h
e
p
r
op
os
e
d
P
V
arra
y e
m
ula
t
o
r
. The
r
e
s
i
sta
n
c
e
l
o
a
d
h
a
d
b
een
v
a
ri
ed
in
or
d
e
r
to
sw
eep
al
l th
e I-
V ch
a
r
a
c
t
e
r
i
st
ic
c
u
rv
e
f
r
o
m
t
h
e c
o
n
s
tan
t
cu
rr
e
n
t
re
gi
on
t
o
the
c
onst
a
nt
v
o
l
t
ag
e
regi
on
o
f
t
h
e
P
V
so
urce
. F
o
r e
a
c
h
resi
st
a
n
ce
val
u
e,
t
h
e
PV
e
m
ula
t
o
r
c
u
rrent
and
vol
ta
ge
ha
d
bee
n
mea
s
ur
ed a
n
d c
o
m
p
a
r
e
d
to
t
h
e
P
V
sou
r
c
e
o
n
es
u
nde
r di
ffe
r
e
n
t
sola
r irra
di
an
c
e
an
d
t
e
mpera
t
ure
va
l
u
es. T
h
e
first
Fig
u
re
8
s
h
o
w
s t
h
e
I-V
c
u
rves
whi
l
e
the
PV em
ul
at
or
i
s
mi
mi
cki
n
g
the
P
V
modul
e
un
de
r
di
ffe
re
nt
we
at
her c
o
n
d
it
i
ons
, w
h
e
r
ea
s
the
s
econ
d
F
i
g
u
re
9
p
r
e
s
e
n
ts t
h
e
I-V c
u
rves
i
n
t
h
e c
a
se
of em
ula
t
i
ng P
V
a
rra
y
c
onfig
urat
i
ons
u
nde
r
part
i
a
l
l
y s
h
a
d
e
d
c
o
n
d
i
t
i
o
n
s
.
A
cco
rdi
n
g t
o
F
i
gu
re
s
8
a
n
d
9,
t
h
e
sta
t
i
c
pe
rformanc
e
s
of
t
h
e p
r
op
ose
d
ci
rc
ui
t
mee
t
t
h
e
P
V
e
m
ula
t
io
n
re
qui
re
me
nt
s
i
n
t
e
rms
o
f
acc
urac
y a
n
d
t
h
e
abi
l
i
t
y t
o
em
ul
a
t
e
t
h
e
w
hol
e
I-V
c
h
a
r
a
c
t
e
ri
s
t
ic
s of
di
ffe
re
n
t
P
V
arra
y co
n
f
i
g
ura
t
i
ons
unde
r
p
a
rt
i
a
l
l
y
sha
d
ed
con
d
i
t
i
o
n
s
.
As
hig
h
l
i
ghte
d
in
t
h
e fi
g
u
re
s bel
o
w
,
t
h
e st
at
i
c
err
o
r i
s
v
e
ry
sma
ll
n
o
t
e
x
ce
ed
in
g
1
%,
wh
i
c
h
e
m
ph
a
s
i
z
e
s
th
e goo
d
ac
cu
r
a
c
y
of the
PV
emu
l
a
t
or
. Th
e
r
efor
e
,
t
h
e
u
s
e
r
ca
n
c
h
o
o
se
t
h
e
way
t
o
c
o
nne
ct
t
h
e P
V
mod
u
l
e
s, t
h
e
de
si
re
d we
at
he
r pa
ra
me
te
rs a
nd t
h
e
gi
v
e
n
part
i
a
l
s
h
ade
d
con
d
i
t
i
on
s, s
o
t
h
e p
r
o
p
o
sed s
y
st
em aft
e
r ge
t
t
i
ng t
h
e re
q
u
ired i
n
format
i
on c
a
n
pro
v
i
d
e
t
h
e same P
V
arra
y
beha
vi
o
r
at
a
n
y
t
i
m
e
wi
t
h
out
needi
n
g
t
o
buy
re
al
P
V
pa
ne
ls o
r
to
ha
ve a
la
rge
are
a
for
PV
mo
d
u
l
e
s.
Fi
gu
re
8.
C
o
mpa
r
i
s
on
bet
w
ee
n I-
V
c
u
rves o
f
t
h
e P
V
e
m
ula
t
or
a
nd t
h
e
P
V
mo
dul
e u
nde
r di
ffe
r
e
n
t sola
r
i
r
r
a
d
i
an
ce
s a
nd a
m
b
i
en
t te
mpe
r
a
t
u
r
e
F
i
gu
re
9.
C
o
mpa
r
i
s
on
bet
w
ee
n I-
V
c
u
rves o
f
t
h
e P
V
e
m
ula
t
or
a
nd t
h
e
P
V
a
rra
y for di
ffe
rent
P
V
a
r
ra
y
c
o
n
f
i
g
urat
i
o
ns un
de
r part
i
a
l
s
h
a
d
i
n
g
co
n
d
it
i
ons
0
5
10
15
20
25
30
35
40
45
50
0
2
4
6
8
10
V
o
l
t
ag
e V
(V
)
C
u
rr
e
n
t
(A)
T
=
2
5
°
C
,
G
=
100
0W
/
m
2
T
=
2
5
°
C
,
G
=
800
W
/
m
2
T
=
2
5
°
C
,
G
=
600
W
/
m
2
T
=
2
5
°
C
,
G
=
400
W
/
m
2
T
=
2
5
°
C
,
G
=
200
W
/
m
2
F
r
om
t
h
e P
V
em
ul
a
t
or
0
5
10
15
20
25
30
35
40
45
50
0
2
4
6
8
10
12
14
V
o
l
t
ag
e V
(V
)
C
u
rre
n
t
(
A
)
G
=
10
00
W
/
m
2
, T
=
2
5
°
C
G
=
10
00
W
/
m
2
, T
=
5
0
°
C
G
=
10
00
W
/
m
2
, T
=
7
5
°
C
F
r
om
t
h
e P
V
em
ul
a
t
o
r
28
29
30
9.
38
9.
4
9.
42
9.
44
9.
46
9.
48
43
.
8
43
.
9
4.
15
4.
2
4.
25
4.
3
0
50
100
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
V
o
l
t
ag
e V
(
V
)
C
u
r
r
ent
(
A
)
20
40
60
80
0
2
4
6
8
10
12
V
o
l
t
ag
e V
(
V
)
Cu
r
r
e
n
t
(
A
)
20
40
60
80
2
4
6
8
10
12
Vo
l
t
a
g
e
V (
V
)
Cu
r
r
e
n
t
(
A
)
20
40
60
80
0
2
4
6
8
10
12
14
16
Vo
l
t
a
g
e
V (
V
)
Cu
r
r
e
n
t
(
A
)
20
40
60
80
0
5
10
15
V
o
l
t
ag
e V
(
V
)
C
u
r
r
ent
(
A
)
5
10
15
20
0
5
10
15
Vo
l
t
a
g
e
V (
V
)
C
u
r
r
ent
(
A
)
55
60
65
2.
3
2.
4
2.
5
(
a
)
S
e
r
i
e
s
C
onf
i
gur
at
i
o
n
(
c
)
S
P
C
onf
i
gur
at
i
o
n
(d
) H
C
C
o
n
f
ig
u
r
a
t
io
n
(
e
)
B
L
C
onf
i
gur
at
i
o
n
(
b
)
P
a
r
a
l
l
el
C
o
nf
i
g
u
r
at
i
o
n
f
r
om
t
h
e P
V
em
u
l
a
t
or
(
f
)
TC
T C
o
n
f
i
gur
a
t
i
o
n
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