I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
s
(
I
J
P
E
DS
)
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
,
p
p
.
1
8
1
3
~
1
8
2
2
I
SS
N:
2088
-
8694
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v
1
2
.
i3
.
pp
1
8
1
3
-
1
8
2
2
1813
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Co
m
pa
riso
n of
P
V panels
MP
PT
t
echniques a
pp
lied
t
o
so
la
r
w
a
ter
pu
m
ping
sy
ste
m
I
s
la
m
K
.
Abd
ul
-
Ra
zz
a
q
1
,
M
o
ha
m
ed
M
.
F
a
hi
m
Sa
k
r
2
,
Ya
s
ir
G
.
Ra
s
hid
3
1,
2
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
P
o
w
e
r
En
g
in
e
e
rin
g
,
C
o
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Ca
iro
U
n
iv
e
rsity
,
G
iza
,
Eg
y
p
t
3
De
p
a
rtme
n
t
o
f
El
e
c
tro
n
ic E
n
g
in
e
e
rin
g
,
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Di
y
a
la Un
iv
e
rsit
y
,
Di
y
a
la,
Ira
q
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
A
p
r
1
3
,
20
21
R
ev
i
s
ed
Ju
l
1
,
2
0
21
A
cc
ep
ted
J
u
l 1
2
,
2
0
21
T
h
is
p
a
p
e
r
d
e
a
ls
w
it
h
a
n
a
d
v
a
n
c
e
d
d
e
sig
n
f
o
r
a
p
u
m
p
p
o
we
re
d
b
y
so
lar
e
n
e
rg
y
to
su
p
p
ly
a
g
ricu
lt
u
ra
l
lan
d
s
w
it
h
wa
ter
a
n
d
a
lso
th
e
m
a
x
i
m
u
m
p
o
we
r
p
o
i
n
t
is
u
se
d
t
o
e
x
trac
t
th
e
m
a
x
i
m
u
m
v
a
lu
e
o
f
th
e
e
n
e
rg
y
a
v
a
il
a
b
l
e
in
sid
e
t
h
e
so
lar
p
a
n
e
ls
a
n
d
c
o
m
p
a
rin
g
b
e
tw
e
e
n
tec
h
n
iq
u
e
s
M
P
P
T
su
c
h
a
s
In
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
,
p
e
rtu
rb
&
o
b
se
r
v
e
,
f
ra
c
ti
o
n
a
l
sh
o
rt
c
u
rre
n
t
c
ircu
it
,
a
n
d
f
ra
c
ti
o
n
a
l
o
p
e
n
v
o
lt
a
g
e
c
ircu
it
to
f
in
d
th
e
b
e
st
tec
h
n
iq
u
e
a
m
o
n
g
t
h
e
se
.
T
h
e
so
lar
sy
ste
m
is
d
e
sig
n
e
d
w
it
h
m
a
in
p
a
rts:
p
h
o
t
o
v
o
lt
a
ic
(
P
V
)
p
a
n
e
l,
d
irec
t
c
u
rre
n
t
/d
irec
t
c
u
rre
n
t
(DC/DC)
c
o
n
v
e
rter,
in
v
e
rter,
f
il
ter,
a
n
d
i
n
a
d
d
it
i
o
n
,
t
h
e
b
a
tt
e
ry
is
u
se
d
to
sa
v
e
e
n
e
r
g
y
in
th
e
e
v
e
n
t
th
a
t
th
e
re
is
a
n
in
c
re
a
se
d
d
e
m
a
n
d
f
o
r
e
n
e
rg
y
a
n
d
n
o
t
to
p
ro
v
id
e
so
l
a
r
ra
d
iatio
n
,
a
s
we
ll
a
s
sa
v
in
g
e
n
e
rg
y
in
th
e
c
a
se
o
f
g
e
n
e
ra
ti
o
n
m
o
re
th
a
n
d
e
m
a
n
d
.
T
h
is
w
o
rk
w
a
s
d
o
n
e
u
sin
g
th
e
m
a
tri
x
lab
o
ra
to
ry
(
M
AT
LAB
)
s
i
m
u
li
n
k
p
ro
g
ra
m
.
K
ey
w
o
r
d
s
:
Fra
ctio
n
al
o
p
en
v
o
lta
g
e
cir
cu
i
t
Fra
ctio
n
al
s
h
o
r
t c
u
r
r
en
t c
ir
c
u
it
I
n
cr
e
m
e
n
tal
co
n
d
u
c
tan
ce
P
er
tu
r
b
an
d
o
b
s
er
v
e
So
lar
w
ater
p
u
m
p
in
g
s
y
s
te
m
Ma
x
i
m
u
m
p
o
w
er
p
o
in
t tr
ac
k
er
s
T
h
is
is
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
:
Yasir
G.
R
as
h
id
Dep
ar
t
m
en
t o
f
E
lectr
o
n
ic
E
n
g
in
ee
r
in
g
C
o
lleg
e
o
f
E
n
g
in
ee
r
i
n
g
,
Un
i
v
e
r
s
it
y
o
f
D
i
y
ala
B
aq
u
b
ah
,
3
2
0
0
1
Diy
ala,
I
r
aq
E
m
ail
:
y
as
s
er
g
h
az
ee
_
en
g
e@
u
o
d
iy
ala.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
So
lar
en
er
g
y
i
s
o
n
e
o
f
t
h
e
av
ailab
le
r
en
e
w
ab
le
e
n
er
g
y
r
es
o
u
r
ce
s
th
at
ca
n
p
r
o
v
id
e
u
s
with
s
tead
y
,
r
eliab
le
p
o
w
er
[
1
]
.
H
o
w
ev
er
,
b
ec
au
s
e
s
u
n
lig
h
t
d
o
es
n
o
t
n
ee
d
an
y
k
in
d
o
f
f
u
el,
s
o
lar
e
n
er
g
y
ca
n
b
e
u
s
ed
d
ir
ec
tl
y
to
cr
ea
te
elec
tr
icit
y
.
No
g
ases
o
r
p
o
is
o
n
s
ar
e
e
m
it
t
ed
in
to
th
e
air
.
So
lar
p
o
w
er
s
y
s
te
m
s
n
ee
d
m
i
n
i
m
al
m
ai
n
ten
a
n
ce
.
So
lar
m
o
d
u
les
h
av
e
a
s
er
v
ice
l
if
e
o
f
2
5
y
ea
r
s
w
it
h
o
u
t
lu
b
r
icatio
n
o
r
m
ain
te
n
an
ce
.
U
s
in
g
s
o
lar
en
er
g
y
d
o
es
h
a
v
e
o
n
e
d
r
a
w
b
a
ck
,
h
o
w
e
v
er
:
I
t
is
e
x
p
en
s
iv
e.
As
lo
n
g
as
t
h
e
s
u
n
d
o
esn
'
t
s
h
in
e
f
o
r
2
4
h
o
u
r
s
a
d
ay
,
t
h
e
s
o
lu
tio
n
i
n
v
o
l
v
es
t
h
e
co
m
b
i
n
atio
n
o
f
a
p
h
o
to
v
o
ltai
c
s
y
s
te
m
a
n
d
a
b
atter
y
.
I
t
is
u
s
ef
u
l
i
n
n
ea
r
l
y
a
n
y
p
lace
,
p
ar
ticu
lar
l
y
i
f
t
h
er
e
i
s
s
u
n
li
g
h
t
an
d
ac
ce
s
s
to
clea
n
w
ater
.
W
h
e
n
a
u
s
er
o
f
a
s
o
la
r
w
ater
ap
p
licatio
n
o
p
en
s
a
f
a
u
ce
t,
w
ater
is
a
p
p
li
ed
to
th
e
tan
k
f
r
o
m
ab
o
v
e
[
2
]
-
[
4
]
.
Fig
u
r
e
1
d
ep
icts
t
h
e
d
ail
y
s
u
p
p
l
y
o
f
s
o
lar
w
ater
.
P
V
s
y
s
te
m
s
f
r
a
m
e
w
o
r
k
s
ar
e
b
ein
g
u
s
ed
m
o
r
e
to
in
cr
ea
s
e
th
eir
e
n
er
g
y
-
e
f
f
icie
n
c
y
b
y
u
s
i
n
g
P
V
s
y
s
te
m
s
.
B
u
t
d
u
e
to
th
e
lo
w
m
o
d
u
le
ef
f
icie
n
c
y
,
t
h
er
e
is
s
till
a
d
ev
ice
ca
p
ac
it
y
p
r
o
b
lem
in
p
h
o
to
v
o
lta
ic
s
y
s
te
m
s
[
4
]
.
A
s
a
r
es
u
lt,
m
at
ch
in
g
th
e
m
ax
i
m
u
m
elec
tr
ical
o
u
tp
u
t
to
a
p
h
o
to
v
o
ltaic
d
e
v
i
ce
r
eq
u
ir
es
ca
r
e
f
u
l
ev
alu
a
tio
n
o
f
it
s
co
n
s
tit
u
e
n
ts
.
P
lacin
g
o
n
l
y
r
eq
u
ir
es
c
h
o
o
s
in
g
t
h
e
b
est
P
V
m
o
d
u
les
an
d
i
m
p
le
m
en
ti
n
g
a
n
ef
f
icien
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t tr
ac
k
in
g
(
MP
PT
)
alg
o
r
ith
m
.
I
n
liter
atu
r
e,
a
m
u
lti
tu
d
e
o
f
M
P
PT
s
ch
e
m
e
s
f
o
r
s
o
lar
P
V
s
y
s
te
m
s
h
a
v
e
b
ee
n
p
r
esen
ted
in
b
o
o
k
s
an
d
j
o
u
r
n
al
ar
ticles.
Ma
n
y
tec
h
n
i
q
u
es
v
ar
y
i
n
d
i
f
f
icu
lt
y
,
h
ar
d
w
ar
e,
p
o
p
u
lar
it
y
,
a
n
d
av
a
ilab
ilit
y
,
a
m
o
n
g
o
th
er
v
ar
iab
les.
An
a
p
p
r
o
ac
h
w
h
ich
h
as
f
o
u
n
d
b
r
o
ad
ac
ce
p
tan
ce
in
P
V
tr
ac
k
in
g
i
s
b
ased
o
n
th
is
tech
n
iq
u
e,
b
u
t
n
o
t
li
m
ited
to
,
p
er
tu
r
b
atio
n
&
o
b
s
er
v
atio
n
(
P
&
O)
(
w
h
ich
is
t
h
e
m
o
s
t
k
n
o
w
n
)
,
th
e
in
cr
e
m
e
n
tal
co
n
d
u
ctan
ce
(
I
N
C
)
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2021
:
181
3
–
182
2
1814
f
r
ac
tio
n
al
s
h
o
r
t
cu
r
r
e
n
t
cir
c
u
it
an
d
f
r
ac
tio
n
al
o
p
en
v
o
lt
ag
e
c
ir
cu
it
[
5
]
-
[
7
]
.
I
n
th
i
s
w
o
r
k
,
t
h
e
e
m
p
h
asi
s
w
il
l
b
e
o
n
d
esig
n
an
d
s
i
m
u
latio
n
o
f
s
o
lar
w
ater
p
u
m
p
in
g
s
y
s
te
m
s
an
d
co
m
p
ar
is
o
n
s
t
u
d
y
b
et
wee
n
w
id
el
y
ap
p
lied
MP
PT
tech
n
iq
u
es,
w
h
i
le
co
n
s
id
er
in
g
w
ea
t
h
er
co
n
d
itio
n
s
w
il
l
b
e
o
n
a
s
s
e
s
s
i
n
g
w
h
ich
m
et
h
o
d
is
t
h
e
m
o
s
t
ca
p
ab
le
o
f
s
h
i
f
ti
n
g
r
eso
u
r
ce
p
atter
n
s
i
n
s
h
o
r
t o
r
d
er
.
Fig
u
r
e
1
.
So
lar
w
ater
d
ail
y
s
u
p
p
ly
2.
P
H
O
T
O
VO
L
T
A
I
C
SY
ST
E
M
M
O
DE
L
L
I
NG
Fig
u
r
e
2
s
h
o
w
s
th
e
m
ai
n
b
lo
ck
d
iag
r
a
m
o
f
t
h
e
p
r
o
p
o
s
ed
s
tan
d
-
alo
n
e
s
y
s
te
m
.
T
h
e
f
ir
s
t
b
lo
ck
is
r
ep
r
esen
ted
b
y
p
h
o
to
v
o
lta
ic
s
o
lar
p
an
els.
T
h
e
v
o
ltag
e
an
d
cu
r
r
en
t
t
h
at
g
et
s
s
e
n
t
to
th
e
o
u
tp
u
t
o
f
th
e
MP
P
T
co
n
tr
o
ller
w
ill
b
e
m
ea
s
u
r
ed
b
y
a
s
e
n
s
i
n
g
cir
c
u
it.
A
b
o
o
s
t
co
n
v
er
ter
D
C
/D
C
p
o
w
er
ele
ctr
o
n
ic
s
w
i
tch
u
s
es
p
u
ls
e
w
id
t
h
m
o
d
u
lat
io
n
(
P
W
M)
to
v
ar
y
its
d
u
t
y
c
y
cle.
T
h
e
b
atter
y
i
s
s
t
ill
c
h
ar
g
ed
,
w
h
i
ch
m
ea
n
s
t
h
e
r
es
t
o
f
th
e
b
lo
ck
s
ar
e
r
ep
r
esen
ted
b
y
P
W
M.
T
h
e
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
w
ill
b
e
s
en
s
ed
b
y
s
e
n
s
in
g
cir
cu
it
t
h
at
to
b
e
u
s
ed
f
o
r
m
o
d
u
latio
n
i
n
d
ex
co
n
tr
o
l to
s
tab
ilize
th
e
in
v
er
ter
alt
er
n
atin
g
c
u
r
r
en
t (
AC
)
v
o
lta
g
e
lev
el
[
8
]
,
[
9
]
.
Fig
u
r
es 2
.
T
h
e
s
tan
d
-
alo
n
e
P
V
s
y
s
te
m
b
lo
ck
d
ia
g
r
a
m
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
g
ener
a
t
o
r
m
o
de
l
W
h
en
t
h
er
e
is
lo
w
elec
tr
icit
y
p
r
o
d
u
ctio
n
f
r
o
m
P
V
ce
lls
.
As
a
r
esu
lt,
t
h
e
ce
lls
s
h
o
u
ld
b
e
laid
o
u
t
in
a
p
ar
allel
-
s
er
ial
f
as
h
io
n
,
w
h
er
e
th
e
en
er
g
y
is
cr
ea
ted
in
s
e
v
er
al
m
o
d
u
les.
A
p
h
o
to
v
o
ltaic
p
a
n
el
is
co
m
p
o
s
ed
o
f
s
er
ies
a
n
d
p
ar
allel
m
o
d
u
le
s
.
T
h
e
P
V
p
an
el
d
e
s
ig
n
b
eg
i
n
s
w
i
th
s
elec
ti
n
g
C
S6
P
-
2
5
0
P
s
o
lar
ce
ll
t
y
p
e
Mo
n
o
cr
y
s
tall
in
e
Ma
x
eo
n
Gen
I
I
P
V
m
o
d
u
les.
T
ab
le
1
also
in
cl
u
d
es
a
s
u
m
m
ar
y
o
f
th
e
s
p
ec
tif
icatio
n
s
o
f
t
h
e
P
V
p
an
el
p
ar
am
eter
s
.
P
V
p
an
els
w
ill
b
e
u
s
ed
i
n
th
is
p
r
o
j
ec
t,
w
h
ic
h
w
ill
in
cl
u
d
e
8
0
p
an
el
s
(
to
tal
ca
p
ac
it
y
i
s
2
0
K
w
)
.
T
h
ese
p
an
els
ar
e
o
r
g
an
ized
in
to
ei
g
h
t
p
ar
allel
li
n
es,
ea
ch
o
f
w
h
ich
co
n
tai
n
s
te
n
s
er
iall
y
li
n
k
ed
p
an
els
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
mp
a
r
is
o
n
o
f P
V
p
a
n
els MPP
T tec
h
n
iq
u
es a
p
p
lied
to
s
o
la
r
w
a
ter p
u
mp
in
g
s
ystem
(
I
s
la
m
K
.
A
b
d
u
l
-
R
a
z
z
a
q
)
1815
[
1
0
]
.
Fig
u
r
e
3
s
h
o
w
s
s
o
lar
ce
l
ls
eq
u
i
v
ale
n
t
cir
c
u
it
i
n
-
s
er
ies
an
d
-
p
ar
allel
i
s
s
h
o
w
n
i
n
a
n
d
th
e
f
o
r
m
u
la
f
o
r
th
eir
an
d
[
1
1
]
,
[
1
2
]
:
[
(
)
]
(
)
(
1
)
w
h
er
e
,
is
lig
h
t
-
g
en
er
ated
c
u
r
r
en
t;
ce
ll
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t;
A
is
id
ea
lit
y
f
ac
to
r
(
=1
)
;
T
is
ce
ll
te
m
p
er
at
u
r
e
(
in
C
elsi
u
s
)
;
K
is
B
o
ltz
m
an
n
’
s
c
o
n
s
ta
n
t
(
=
1
.
3
8
0
5
×
1
0
−
23
N
m
/K)
;
q
is
elec
tr
o
n
i
c
ch
ar
g
e
(
=1
.
6
×1
0
−
19
C
)
;
an
d
is
th
e
s
er
ies
a
n
d
p
ar
allel
r
esis
t
an
ce
r
esp
ec
tiv
e
l
y
,
is
th
e
s
o
lar
s
h
o
r
t
-
cir
cu
it
c
u
r
r
en
t.
T
o
lear
n
m
o
r
e
ab
o
u
t
th
e
d
i
f
f
er
e
n
ce
s
in
t
h
e
i
m
p
ac
t
o
f
d
i
f
f
er
en
t
ir
r
ad
iatio
n
lev
els
o
n
t
h
e
P
-
V
an
d
I
-
V
ch
ar
ac
ter
i
s
tics
,
s
ee
Fi
g
u
r
e
4
an
d
Fi
g
u
r
e
5.
T
ab
le
1
.
Sp
icef
icatio
n
s
o
f
C
S6
P
-
2
5
0
M
P
V
m
o
d
el
[
1
3
]
P
r
o
p
e
r
t
y
V
a
l
u
e
M
a
x
i
m
u
m
P
o
w
e
r
(
P
max
)
(
W
)
2
5
0
W
V
o
l
t
a
g
e
a
t
P
max
(
V
)
3
0
.
4
V
C
u
r
r
e
n
t
a
t
P
max
(
A
)
8
.
2
2
A
O
p
e
n
-
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
V
o
c
)
(
V
)
3
7
.
5
V
S
h
o
r
t
-
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
I
sc) (
A
)
8
.
7
4
A
T
e
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
P
o
w
e
r
(
%/
K
)
-
0
.
4
5
T
e
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
V
o
c
(
%/
K
)
-
0
.
3
5
T
e
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
i
S
C
(
%/
K
)
-
0
.
0
6
C
e
l
l
t
y
p
e
(
e
)
M
o
n
o
c
r
y
st
a
l
l
i
n
e
M
o
d
u
l
e
e
f
f
i
c
i
e
n
c
y
1
5
.
5
4
%
D
i
me
n
si
o
n
s
(
mm
)
1
6
3
8
(
h
)
x
9
8
2
(
w
)
4
0
(
d
)
W
e
i
g
h
t
2
0
k
g
Fig
u
r
e
3
.
So
lar
p
an
el
elec
tr
icall
y
eq
u
i
v
ale
n
t
cir
cu
it [
1
2
]
Fig
u
r
e
4
.
A
t T
=2
5
°C
,
th
e
P
-
V
ch
ar
ac
ter
is
tics
f
o
r
v
ar
io
u
s
s
o
lar
ir
r
ad
ian
ce
(
G)
v
alu
es a
r
e
s
h
o
w
n
Fig
u
r
e
5
.
A
t T
=2
5
°C
,
th
e
I
-
V
ch
ar
ac
ter
is
tic
s
f
o
r
v
ar
io
u
s
s
o
lar
ir
r
ad
ian
ce
(
G)
v
alu
es a
r
e
s
h
o
w
n
2
.
2
.
B
o
o
s
t
c
o
nv
er
t
er
m
o
del
B
y
i
n
t
e
r
p
o
s
i
n
g
a
p
o
w
e
r
c
o
n
v
e
r
t
e
r
(
D
C
-
D
C
c
o
n
v
e
r
t
e
r
)
b
e
t
w
e
e
n
t
h
e
p
h
o
t
o
v
o
l
t
a
i
c
g
e
n
e
r
a
t
o
r
a
n
d
t
h
e
l
o
a
d
(
b
a
t
t
e
r
y
)
,
t
h
e
M
P
P
T
c
a
n
b
e
a
c
h
i
e
v
e
d
.
B
y
a
c
t
i
n
g
o
n
t
h
e
c
o
n
v
e
r
t
e
r
d
u
t
y
c
y
c
l
e
(
D
)
,
t
h
e
o
p
e
r
a
t
i
o
n
p
o
i
n
t
c
a
n
b
e
g
u
a
r
a
n
t
e
e
d
t
o
b
e
t
h
e
M
P
P
T
.
I
t
u
s
e
s
s
t
e
p
-
u
p
m
e
t
h
o
d
o
l
o
g
y
.
T
h
e
v
o
l
t
a
g
e
t
h
e
s
e
n
s
o
r
p
r
o
d
u
c
e
s
i
s
l
a
r
g
e
r
t
h
a
n
t
h
e
v
o
l
t
a
g
e
t
h
a
t
i
s
f
e
d
i
n
t
o
i
t
.
T
h
e
c
i
r
c
u
i
t
s
h
o
w
n
i
n
F
i
g
u
r
e
6
h
a
s
a
n
i
n
d
u
c
t
o
r
,
a
c
a
p
a
c
i
t
o
r
,
a
s
w
i
t
c
h
,
a
n
d
a
d
i
o
d
e
[
1
4
]
.
W
h
e
n
t
h
e
s
w
i
t
c
h
i
s
c
l
o
s
e
d
,
t
h
e
d
i
o
d
e
t
e
n
d
s
t
o
b
e
r
e
v
e
r
s
e
b
i
a
s
e
d
a
n
d
t
h
e
c
u
r
r
e
n
t
i
n
c
r
e
a
s
e
s
t
h
r
o
u
g
h
t
h
e
i
n
d
u
c
t
o
r
.
W
h
e
n
t
h
e
s
w
i
t
c
h
i
s
s
w
i
t
c
h
e
d
o
f
f
,
t
h
e
d
i
o
d
e
t
e
n
d
s
t
o
b
e
f
o
r
w
a
r
d
b
i
a
s
e
d
,
t
h
e
i
n
d
u
c
t
i
v
e
v
o
l
t
a
g
e
s
t
o
r
e
d
i
n
t
h
e
c
a
p
a
c
i
t
o
r
i
s
d
i
s
c
h
a
r
g
e
d
,
a
n
d
t
h
e
c
u
r
r
e
n
t
i
s
a
l
l
o
w
e
d
t
o
f
l
o
w
t
h
r
o
u
g
h
t
h
e
i
n
d
u
c
t
a
n
c
e
.
O
n
c
e
t
h
e
v
o
l
t
a
g
e
h
a
s
b
e
e
n
i
n
c
r
e
a
s
e
d
,
i
t
i
s
r
o
u
t
e
d
t
o
t
h
e
l
o
a
d
.
T
h
e
d
u
t
y
c
y
c
l
e
i
s
c
a
l
c
u
l
a
t
e
d
u
s
i
n
g
t
h
e
v
a
l
u
e
s
o
f
t
h
e
i
n
p
u
t
a
n
d
o
u
t
p
u
t
v
o
l
t
a
g
e
s
s
p
e
c
i
f
i
e
d
i
n
t
h
e
(
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2021
:
181
3
–
182
2
1816
(
2
)
Fig
u
r
e
6
.
T
h
e
b
o
o
s
t c
o
n
v
er
ter
cir
cu
it
2
.
3
.
M
P
P
T
t
ec
hn
iqu
es
T
h
e
MP
PT
c
o
n
tr
o
l
is
a
k
e
y
c
o
m
p
o
n
en
t
o
f
t
h
e
P
V
s
y
s
te
m
.
I
t
is
cr
itical
to
o
p
ti
m
al
s
y
s
te
m
o
p
er
atio
n
.
T
h
is
co
n
tr
o
l
ap
p
r
o
ac
h
is
d
er
iv
ed
f
r
o
m
t
h
e
p
r
in
cip
le
o
f
o
p
ti
m
al
v
ar
iatio
n
o
f
t
h
e
c
y
cl
ic
r
atio
D,
an
d
w
e
w
ill
p
r
esen
t
a
n
d
ex
p
lai
n
later
t
h
e
m
o
s
t
p
o
p
u
lar
co
n
tr
o
l
tech
n
iq
u
es.
T
h
er
e
ar
e
a
n
u
m
b
er
o
f
co
m
m
o
n
a
n
d
p
r
ac
tica
l
m
o
d
el
s
f
o
r
esti
m
ati
n
g
h
o
w
m
u
c
h
a
P
V
p
o
w
er
w
i
ll
i
n
cr
ea
s
e
w
it
h
alt
itu
d
e,
i
n
cl
u
d
in
g
p
er
tu
r
b
&
o
b
s
er
v
e,
in
cr
e
m
e
n
tal
co
n
d
u
cta
n
ce
,
an
d
f
r
ac
tio
n
al
s
h
o
r
t c
u
r
r
en
t c
ir
cu
it
an
d
f
r
ac
tio
n
al
o
p
en
v
o
ltag
e
cir
c
u
it [
1
5
]
,
[
1
6
]
.
2
.
3
.
1
.
P
er
t
urb a
nd
o
bs
er
v
e
(
P
&O
)
t
ec
hn
iqu
e
T
h
i
s
t
e
c
h
n
i
q
u
e
i
s
w
i
d
e
l
y
u
s
e
d
f
o
r
t
r
a
c
k
i
n
g
t
h
e
m
a
x
i
m
u
m
p
o
w
e
r
d
u
e
t
o
i
t
s
s
im
p
l
e
d
e
s
i
g
n
.
T
h
i
s
m
e
t
h
o
d
a
d
j
u
s
t
s
t
h
e
P
V
m
o
d
u
l
e
v
o
l
t
a
g
e
a
n
d
c
o
m
p
a
r
e
s
t
h
e
n
ew
p
o
w
e
r
o
u
t
p
u
t
w
i
t
h
t
h
a
t
o
f
t
h
e
p
r
e
v
i
o
u
s
p
e
r
t
u
r
b
a
t
i
o
n
c
y
c
l
e
i
n
o
r
d
e
r
t
o
s
e
e
i
f
i
t
h
a
s
r
e
t
u
r
n
e
d
t
o
n
o
r
m
a
l
.
O
n
t
h
e
s
am
e
p
r
i
n
c
i
p
l
e
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
7
,
t
h
e
P
V
m
o
d
u
l
e
v
o
l
t
a
g
e
s
h
i
f
t
s
t
h
e
c
o
n
t
r
o
l
s
y
s
t
e
m
i
n
t
h
i
s
d
i
r
e
c
t
i
o
n
i
f
t
h
e
P
V
o
u
t
p
u
t
v
o
l
t
a
g
e
r
i
s
e
s
,
a
n
d
t
h
e
p
o
w
e
r
i
s
l
i
m
i
t
e
d
i
f
i
t
d
o
e
s
n
'
t
[
1
7
]
,
[
1
8
]
.
Fig
u
r
e
7
.
T
h
e
f
lo
w
c
h
ar
t o
f
th
e
P
&
O
t
ec
hn
i
qu
e
2
.
3
.
2
.
I
ncre
m
ent
a
l
c
o
nd
uct
a
nce
(
I
C)
M
P
P
T
t
ec
hn
iqu
e
I
n
c
r
em
en
t
al
c
o
n
d
u
ct
an
c
e
t
e
ch
n
i
q
u
e
em
p
l
o
y
s
an
a
r
r
ay
te
r
m
in
a
l
v
o
lt
ag
e
th
a
t
is
b
a
s
e
d
o
n
th
e
M
PP
T
v
o
l
t
ag
e
.
H
e
r
e
is
th
e
d
ia
g
r
am
f
o
r
t
h
is
t
ec
h
n
i
q
u
e
in
F
ig
u
r
e
8
.
T
h
e
g
en
e
r
al
f
o
r
m
o
f
th
is
te
c
h
n
i
q
u
e
i
s
th
i
s
[
1
9
]
,
[
2
0
]
.
at
MP
PT
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
mp
a
r
is
o
n
o
f P
V
p
a
n
els MPP
T tec
h
n
iq
u
es a
p
p
lied
to
s
o
la
r
w
a
ter p
u
mp
in
g
s
ystem
(
I
s
la
m
K
.
A
b
d
u
l
-
R
a
z
z
a
q
)
1817
at
th
e
lef
t o
f
MP
PT
(
4
)
at
th
e
r
ig
h
t o
f
MP
P
T
(
5
)
=
(
6
)
Fig
u
r
e
8
.
T
h
e
f
lo
w
c
h
ar
t o
f
th
e
I
NC
tech
n
iq
u
e
T
h
e
d
P
/
d
V
is
d
ef
in
ed
as
t
h
e
id
en
ti
f
ier
f
ac
to
r
f
o
r
t
h
e
MP
PT
.
T
h
e
I
NC
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
to
ef
f
ec
ti
v
el
y
tr
ac
k
th
e
MP
P
T
o
f
a
p
h
o
to
v
o
ltaic
p
an
el
b
y
u
ti
lizi
n
g
t
h
is
f
ac
to
r
.
T
h
e
d
ef
in
itio
n
s
ar
e
tak
e
n
in
to
ac
co
u
n
t
w
h
e
n
tr
ac
k
in
g
t
h
e
MP
PT
.
at
MP
P
T
(
8
)
at
th
e
lef
t o
f
MP
PT
(
9
)
at
th
e
r
ig
h
t o
f
MP
P
T
(
1
0
)
2
.
3
.
3
.
T
ec
hn
iqu
e
f
ra
ct
io
na
l o
pen c
ircuit
v
o
lt
a
g
e
(
F
VO
C)
t
ec
hn
iqu
e
T
h
is
tech
n
iq
u
e
i
s
b
ased
o
n
t
h
e
n
ea
r
l
y
lin
ea
r
r
elatio
n
s
h
ip
b
et
w
ee
n
t
h
e
o
p
en
cir
c
u
it
v
o
ltag
e
VOC
a
n
d
th
e
p
h
o
to
v
o
ltaic
p
a
n
el
'
s
o
p
ti
m
al
v
o
ltag
e
V
MP
P
[
2
1
]
-
[
2
3
]
.
T
h
e
r
elatio
n
s
h
ip
b
et
w
ee
n
V
OC
a
n
d
V
MPP
is
g
i
v
en
b
y
th
e
(
1
1
)
.
(
1
1
)
w
h
er
e
Kv
t
h
e
co
ef
f
icie
n
t
o
f
b
et
w
ee
n
b
et
w
ee
n
0
.
7
1
an
d
0
.
8
v
ar
ies.
T
h
e
f
lo
w
c
h
ar
t
in
F
i
g
u
re
9
illu
s
tr
ate
s
th
e
FVOC
tec
h
n
iq
u
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2021
:
181
3
–
182
2
1818
Fig
u
r
e
9
.
Flo
w
c
h
ar
t o
f
FVO
C
tech
n
iq
u
e
2
.
3
.
4
.
F
ra
c
t
io
na
l
s
ho
rt
circ
uit
curr
ent
(
F
SCC)
t
ec
hn
iqu
e
T
h
is
tech
n
iq
u
e
is
li
n
ea
r
in
r
esp
o
n
s
e
an
d
th
er
e
is
al
m
o
s
t
a
d
ir
ec
t
co
r
r
elatio
n
b
etw
ee
n
th
e
o
p
tim
u
m
I
MPP
an
d
th
e
s
h
o
r
t
cir
cu
it
c
u
r
r
en
t
I
SC
c
h
a
n
g
e
o
f
th
e
P
V
i
n
d
if
f
er
e
n
t
at
m
o
s
p
h
er
ic
co
n
d
iti
o
n
s
[
2
4
]
,
[
2
5
]
.
T
h
e
r
elatio
n
b
et
w
ee
n
I
MPP
a
n
d
I
s
c
is
g
i
v
en
b
y
th
e
(
1
2
)
:
(
1
2
)
w
h
er
e
is
t
h
e
co
ef
f
icien
t o
f
b
et
w
ee
n
0
.
7
8
an
d
0
.
9
2
v
ar
ies.
T
h
e
f
lo
w
ch
ar
t i
n
Fi
g
u
r
e
1
0
illu
s
tr
ates th
e
F
SC
C
tech
n
iq
u
e.
Fig
u
r
e
1
0
.
Flo
w
ch
ar
t o
f
FS
C
C
tech
n
iq
u
e
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
As
ill
u
s
tr
ated
in
Fig
u
r
e
1
1
,
th
e
co
n
s
id
er
ed
p
h
o
to
v
o
ltaic
s
y
s
te
m
g
e
n
er
ates
2
0
k
W
an
d
is
d
esig
n
ed
,
s
i
m
u
lated
,
an
d
i
m
p
le
m
e
n
ted
.
T
h
is
s
y
s
te
m
is
d
iv
id
ed
in
to
s
ix
s
tag
e
s
.
T
h
e
f
ir
s
t
s
tag
e
i
s
a
p
h
o
to
v
o
ltaic
ar
r
ay
w
it
h
8
0
p
an
el
s
,
t
h
e
s
ec
o
n
d
s
ta
g
e
is
a
b
o
o
s
t
co
n
v
er
ter
DC
/D
C
,
an
d
t
h
e
i
n
v
er
ter
(
3
-
le
v
el
s
i
n
g
le
-
p
h
ase
b
r
id
g
e,
H
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
mp
a
r
is
o
n
o
f P
V
p
a
n
els MPP
T tec
h
n
iq
u
es a
p
p
lied
to
s
o
la
r
w
a
ter p
u
mp
in
g
s
ystem
(
I
s
la
m
K
.
A
b
d
u
l
-
R
a
z
z
a
q
)
1819
v
o
ltag
e
s
o
u
r
ce
)
.
T
h
e
f
o
u
r
th
s
tag
e
in
c
lu
d
es
a
p
as
s
iv
e
L
C
L
(
L
P
F)
f
ilter
co
n
n
ec
ted
to
th
e
m
ai
n
o
f
f
-
g
r
id
f
i
f
t
h
d
y
n
a
m
ic
lo
ad
cir
cu
it,
an
d
t
h
e
f
in
al
s
ta
g
e
is
a
b
atter
y
.
Fig
u
r
e
1
1
.
T
h
e
s
i
m
u
latio
n
o
f
P
V
s
y
s
te
m
T
ab
le
2
s
h
o
w
MP
P
T
co
n
tr
o
lle
r
at
f
ix
ed
te
m
p
er
atu
r
es
(
T
)
w
it
h
r
an
g
e
o
f
ir
r
ad
ian
ce
(
G)
,
w
h
i
le
T
a
b
le
3
s
h
o
w
MP
PT
c
o
n
tr
o
ller
at
d
if
f
er
en
t
te
m
p
er
atu
r
es
(
T
)
w
it
h
f
i
x
ed
ir
r
ad
ian
ce
(
G)
.
Fig
u
r
e
s
12
(
a)
-
(
d
)
an
d
Fig
u
r
e
13
(
a)
-
(
d
)
illu
s
tr
ate
th
e
s
tep
r
esp
o
n
s
e
o
f
p
o
w
er
f
o
r
v
ar
io
u
s
MP
PT
tech
n
iq
u
es
a
t
d
if
f
er
e
n
t
te
m
p
er
atu
r
es
(
T
)
25°
,
ir
r
a
d
ian
ce
(
G)
1
0
0
0
W
/
2
an
d
t
e
m
p
er
atu
r
e
(
T
)
1
5
°
,
i
r
r
ad
ian
ce
(
G)
6
0
0
W
/
2
,
r
e
s
p
ec
tiv
el
y
.
T
ab
le
4
an
d
T
a
b
le
5
s
h
o
w
co
m
p
ar
is
o
n
b
et
w
ee
n
th
e
f
o
u
r
MP
PT
te
ch
n
iq
u
es
af
ter
tak
e
1
0
(
s
ec
)
o
f
ti
m
e
o
p
er
atio
n
te
m
p
er
atu
r
e
(
T
)
2
5
°
,
ir
r
ad
i
an
ce
(
G)
1
0
0
0
W
/
2
an
d
te
m
p
er
at
u
r
e
(
T
)
1
5
°
,
I
r
r
a
d
ian
ce
(
G)
6
0
0
W
/
2
,
r
esp
ec
tiv
el
y
,
m
e
n
tio
n
o
v
er
s
h
o
o
t,
u
n
d
er
s
h
o
o
t,
r
is
e
ti
m
e
an
d
s
ettin
g
ti
m
e.
T
ab
le
2
.
M
P
PT
co
n
tr
o
ller
f
ix
e
d
(
T
=2
5
)
,
r
an
g
e
o
f
(
G=
2
0
0
,
6
0
0
,
1
0
0
0
)
G
V
-
PV
P
&
O
I
N
C
F
V
O
C
F
S
C
C
V
Er
r
o
r
V
Er
r
o
r
V
Er
r
o
r
V
Er
r
o
r
2
0
0
3
6
0
.
7
9
8
3
6
0
.
6
0
.
1
9
8
3
5
9
.
8
0
.
9
9
8
3
5
2
.
5
8
.
2
9
8
3
5
1
.
0
8
2
9
.
7
1
6
6
0
0
3
6
0
.
8
0
6
3
6
0
.
6
0
.
2
0
9
3
5
9
.
8
1
.
0
0
9
3
5
2
.
6
8
.
2
0
9
3
5
1
.
2
9
.
6
0
9
1
0
0
0
3
6
0
.
8
2
6
3
6
0
.
6
0
.
2
2
6
3
5
9
.
8
1
.
0
2
6
3
5
2
.
6
8
.
2
2
6
3
5
1
.
2
1
9
.
6
1
6
T
ab
le
3
.
M
P
PT
co
n
tr
o
ller
r
an
g
e
o
f
(
T
=1
0
,
3
0
,
5
0
)
,
f
ix
ed
(
G=
1
0
0
0
)
G
V
-
PV
P
&
O
I
N
C
F
V
O
C
F
S
C
C
V
Er
r
o
r
V
Er
r
o
r
V
Er
r
o
r
V
Er
r
o
r
10
3
6
0
.
8
2
6
3
6
0
.
6
0.
2
2
6
3
6
0
.
1
7
0.
6
5
6
35
3
.
1
6
7
.
6
6
6
3
5
1
.
93
8
.
8
9
6
30
3
6
0
.
8
26
3
6
0
.
6
0
.
2
26
3
5
9
.8
1
.
0
26
3
5
2
.
6
8
.
2
26
3
5
1
.
2
1
9
.
6
16
5
0
3
6
0
.
2
6
7
3
51
.
02
0
.
2
47
3
4
9.
6
8
1.
5
8
7
3
47
.
87
3
.
3
9
7
3
49
.
67
5
.
5
9
7
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2021
:
181
3
–
182
2
1820
(a
)
(b
)
(d
)
(d
)
F
i
g
u
r
e
1
2
.
T
h
e
r
e
s
u
l
t
o
f
p
o
w
e
r
f
r
o
m
d
i
f
f
e
r
e
n
t
t
e
c
h
n
i
q
u
e
s
i
n
t
e
m
p
e
r
a
t
u
r
e
(
T
)
2
5
°
,
(
a
)
i
r
r
a
d
i
a
n
c
e
(
G
)
1
0
0
0
W
/
2
;
(
b
)
I
N
C
c
u
r
v
e
;
(
c
)
F
O
V
C
c
u
r
v
e
;
(
d
)
F
S
C
C
c
u
r
v
e
(
a)
(
b
)
(
c
)
(
d
)
F
i
g
u
r
e
1
3
.
T
h
e
r
e
s
u
l
t
o
f
p
o
w
e
r
f
r
o
m
d
i
f
f
e
r
e
n
t
t
e
c
h
n
i
q
u
e
s
i
n
t
e
m
p
e
r
a
t
u
r
e
(
T
)
1
5
°
,
(
a
)
i
r
r
a
d
i
a
n
c
e
(
G
)
6
0
0
W
/
2
;
(
b
)
I
N
C
c
u
r
v
e
;
(
c
)
F
O
V
C
c
u
r
v
e
;
a
n
d
(
d
)
F
S
C
C
c
u
r
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
mp
a
r
is
o
n
o
f P
V
p
a
n
els MPP
T tec
h
n
iq
u
es a
p
p
lied
to
s
o
la
r
w
a
ter p
u
mp
in
g
s
ystem
(
I
s
la
m
K
.
A
b
d
u
l
-
R
a
z
z
a
q
)
1821
T
ab
le
4
.
P
er
f
o
r
m
a
n
ce
co
m
p
ar
i
s
o
n
o
f
MP
P
T
tech
n
iq
u
e
s
f
o
r
P
V
at
T
=
2
5
°
,
G
=
1
0
0
0
W
/
2
M
P
P
T
T
e
c
h
i
q
u
e
s
U
n
d
e
r
sh
o
o
t
(
%)
O
v
e
r
sh
o
o
t
(
%)
S
e
t
t
l
i
n
g
t
i
me
(
se
c
)
R
i
se
t
i
me
(
se
c
)
P
&
O
5
.
8
3
0
.
8
9
2
0
.
4
3
7
6
.
8
4
3
I
N
C
1
.
8
9
1
0
.
7
5
1
8
.
4
2
5
6
.
9
5
4
F
V
O
C
6
.
9
2
5
.
8
7
9
.
8
3
5
5
.
2
1
7
F
S
S
C
7
.
3
8
5
.
4
2
9
.
6
7
2
5
.
3
7
2
T
ab
le
5
.
P
er
f
o
r
m
a
n
ce
co
m
p
ar
i
s
o
n
o
f
MP
P
T
tech
n
iq
u
e
s
f
o
r
P
V
at
T
=
1
5
°
,
G
=
6
0
0
W
/
2
M
P
P
T
T
e
c
h
i
q
u
e
s
U
n
d
e
r
sh
o
o
t
(
%)
O
v
e
r
sh
o
o
t
(
%)
S
e
t
t
l
i
n
g
t
i
me
(
se
c
)
R
i
se
t
i
me
(
se
c
)
P
&
O
4
.
2
1
2
.
5
7
2
1
.
8
4
6
8
.
4
9
2
I
N
C
1
9
.
5
7
4
.
2
8
1
1
.
4
8
7
8
.
9
2
1
F
V
O
C
1
4
.
8
3
3
.
3
7
1
6
.
4
7
5
7
.
6
4
7
F
S
S
C
1
6
.
4
8
3
.
8
2
2
2
.
7
4
9
7
.
3
8
4
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
al
s
o
in
clu
d
es
t
h
e
d
esig
n
an
d
s
i
m
u
latio
n
o
f
a
2
0
-
k
W
p
h
o
to
v
o
ltaic
-
p
o
w
er
ed
p
u
m
p
th
at
u
s
e
s
s
i
m
p
le
m
et
h
o
d
s
,
s
u
c
h
as
P
VP
.
I
n
s
u
m
m
ar
y
,
t
h
e
r
esu
lt
s
ca
n
b
e
s
tated
is
b
ein
g
a
s
:
T
h
e
b
est
o
s
cillatio
n
i
n
P
&
O
MP
PT
tech
n
iq
u
e
;
t
h
e
b
est
r
is
e
ti
m
e,
s
e
ttli
n
g
ti
m
e
in
Fra
ctio
n
al
v
o
ltag
e
c
u
r
r
en
t
c
ir
cu
it
(
o
p
en
,
s
h
o
r
t)
MP
PT
;
A
t
T
=1
5
°
,
G=
6
0
0
W/
2
th
e
I
n
cr
e
m
en
tal
co
n
d
u
cta
n
ce
MP
P
T
b
est p
er
f
o
r
m
an
ce
i
n
s
e
ttli
n
g
ti
m
e
.
RE
F
E
R
E
NC
E
S
[1
]
P
.
S
o
u
latian
t
o
rk
,
“
P
e
rf
o
rm
a
n
c
e
c
o
m
p
a
riso
n
o
f
a
t
w
o
P
V
m
o
d
u
l
e
e
x
p
e
ri
m
e
n
tal
se
tu
p
u
sin
g
a
m
o
d
i
f
ied
M
P
P
T
a
lg
o
rit
h
m
u
n
d
e
r
re
a
l
o
u
td
o
o
r
c
o
n
d
it
io
n
s,
”
S
o
la
r
En
e
rg
y
,
v
o
l.
1
6
9
,
p
p
.
4
0
1
-
4
1
0
,
J
u
ly
2
0
1
8
,
d
o
i
:
1
0
.
1
0
1
6
/
j.
so
len
e
r.
2
0
1
8
.
0
4
.
0
6
5
.
[2
]
A
.
K.
T
i
w
a
ri
e
t
a
l
.,
“
Eff
e
c
t
o
f
h
e
a
d
a
n
d
P
V
a
rra
y
c
o
n
f
i
g
u
ra
ti
o
n
s
o
n
so
lar
wa
ter
p
u
m
p
in
g
s
y
ste
m
,
”
in
M
a
ter
ia
ls
T
o
d
a
y
:
Pro
c
e
e
d
i
n
g
s
,
Oc
t
o
b
e
r
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
m
a
tp
r.
2
0
2
0
.
0
9
.
2
0
0
.
[3
]
R.
F
o
ste
r
,
a
n
d
A
.
Co
ta,
“
S
o
lar
wa
ter
p
u
m
p
in
g
a
d
v
a
n
c
e
s
a
n
d
c
o
m
p
a
ra
ti
v
e
e
c
o
n
o
m
ics
,
”
En
e
rg
y
Pro
c
e
d
ia
,
v
o
l
.
5
7
,
p
p
.
1
4
3
1
-
1
4
3
6
,
2
0
1
4
,
d
o
i:
1
0
.
1
0
1
6
/j
.
e
g
y
p
ro
.
2
0
1
4
.
1
0
.
1
3
4
.
[4
]
E.
G
u
p
ta,
“
T
h
e
im
p
a
c
t
o
f
so
lar
wa
ter
p
u
m
p
s
o
n
e
n
e
rg
y
-
wa
ter
-
f
o
o
d
n
e
x
u
s:
Ev
id
e
n
c
e
f
ro
m
Ra
j
a
sth
a
n
,
In
d
ia,
”
E
n
e
rg
y
Po
li
c
y
,
v
o
l.
1
2
9
,
p
p
.
5
9
8
-
6
0
9
,
Ju
n
i
2
0
1
9
,
d
o
i:
1
0
.
1
0
1
6
/j
.
e
n
p
o
l.
2
0
1
9
.
0
2
.
0
0
8
.
[5
]
Y.
Zh
u
,
M
.
K.
Kim
,
a
n
d
H.
W
e
n
,
“
S
im
u
latio
n
a
n
d
a
n
a
ly
sis
o
f
p
e
rtu
rb
a
ti
o
n
a
n
d
o
b
se
rv
a
ti
o
n
-
b
a
se
d
se
lf
-
a
d
a
p
tab
le
ste
p
siz
e
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
t
ra
c
k
in
g
str
a
teg
y
w
it
h
lo
w
p
o
w
e
r
lo
ss
f
o
r
p
h
o
to
v
o
l
taic
s,
”
En
e
rg
ies
,
v
o
l.
1
2
,
n
o
.
1
,
p
.
9
2
,
De
c
e
m
b
e
r
2
0
1
8
,
d
o
i:
1
0
.
3
3
9
0
/en
1
2
0
1
0
0
9
2
.
[6
]
K.
S
.
T
e
y
a
n
d
S
.
M
e
k
h
il
e
f
,
“
M
o
d
if
ied
in
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
a
lg
o
rit
h
m
f
o
r
p
h
o
to
v
o
lt
a
ic
sy
ste
m
u
n
d
e
r
p
a
rti
a
l
sh
a
d
in
g
c
o
n
d
it
io
n
s
a
n
d
lo
a
d
v
a
ri
a
ti
o
n
,
”
IE
EE
T
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l.
6
1
,
n
o
.
1
0
,
p
p
.
5
3
8
4
-
5
3
9
2
,
Oc
t.
2
0
1
4
,
d
o
i:
1
0
.
1
1
0
9
/T
IE.
2
0
1
4
.
2
3
0
4
9
2
1
.
[7
]
M
.
M
.
S
h
e
b
a
n
i,
T
.
Iq
b
a
l
,
a
n
d
J.
E
.
Qu
a
ico
e
,
“
Co
m
p
a
rin
g
b
ise
c
ti
o
n
n
u
m
e
rica
l
a
lg
o
rit
h
m
w
it
h
f
ra
c
ti
o
n
a
l
sh
o
rt
c
irc
u
i
t
c
u
rre
n
t
a
n
d
o
p
e
n
c
ircu
it
v
o
lt
a
g
e
m
e
th
o
d
s
f
o
r
M
P
P
T
p
h
o
t
o
v
o
lt
a
ic
sy
st
e
m
s,
”
in
2
0
1
6
IEE
E
El
e
c
tri
c
a
l
Po
we
r
a
n
d
En
e
rg
y
Co
n
fer
e
n
c
e
(
EP
EC)
,
2
0
1
6
,
p
p
.
1
-
5
,
d
o
i:
1
0
.
1
1
0
9
/E
P
EC.
2
0
1
6
.
7
7
7
1
6
8
9
.
[8
]
G
.
B.
In
g
a
le,
S
.
P
a
d
h
e
e
,
a
n
d
U.
C.
P
a
ti
,
“
De
sig
n
o
f
sta
n
d
a
lo
n
e
P
V
s
y
ste
m
f
o
r
DC
-
m
icro
g
rid
,
”
in
2
0
1
6
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
En
e
rg
y
Ef
fi
c
ien
t
T
e
c
h
n
o
lo
g
ies
fo
r
S
u
sta
i
n
a
b
il
it
y
(
ICEE
T
S
)
,
2
0
1
6
,
p
p
.
7
7
5
-
7
8
0
,
d
o
i
:
1
0
.
1
1
0
9
/IC
EE
T
S
.
2
0
1
6
.
7
5
8
3
8
5
2
.
[9
]
S
.
Ob
u
k
h
o
v
,
A
.
Ib
ra
h
im
,
A
.
A
.
Zak
i
Dia
b
,
A
.
S
.
A
l
-
S
u
m
a
it
i,
a
n
d
R.
A
b
o
e
lsa
u
d
,
“
Op
ti
m
a
l
p
e
rf
o
r
m
a
n
c
e
o
f
d
y
n
a
m
ic
p
a
rti
c
le
s
w
a
r
m
o
p
ti
m
iza
ti
o
n
b
a
se
d
m
a
x
i
m
u
m
p
o
w
e
r
trac
k
e
rs
f
o
r
sta
n
d
-
a
lo
n
e
P
V
s
y
ste
m
u
n
d
e
r
p
a
rti
a
l
sh
a
d
in
g
c
o
n
d
i
ti
o
n
s,
”
IEE
E
Acc
e
ss
,
v
o
l.
8
,
p
p
.
2
0
7
7
0
-
2
0
7
8
5
,
2
0
2
0
,
d
o
i:
1
0
.
1
1
0
9
/A
CCES
S
.
2
0
2
0
.
2
9
6
6
4
3
0
.
[1
0
]
Z.
M
.
A
li
,
N.
V
.
Qu
y
n
h
,
S
.
Da
d
f
a
r,
a
n
d
H.
Na
k
a
m
u
ra
,
“
V
a
riab
le
s
tep
siz
e
p
e
rtu
rb
a
n
d
o
b
se
rv
e
M
P
P
T
c
o
n
tro
ll
e
r
b
y
a
p
p
ly
in
g
θ
-
m
o
d
if
ied
k
ril
l
h
e
rd
a
lg
o
rit
h
m
-
slid
in
g
m
o
d
e
c
o
n
tr
o
ll
e
r
u
n
d
e
r
p
a
rti
a
l
ly
sh
a
d
e
d
c
o
n
d
it
i
o
n
s,
”
J
o
u
r
n
a
l
o
f
Clea
n
e
r P
ro
d
u
c
ti
o
n
,
v
o
l.
2
7
1
,
p
.
1
2
2
2
4
3
,
Oc
t
o
b
e
r
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
jcle
p
ro
.
2
0
2
0
.
1
2
2
2
4
3
.
[1
1
]
M
.
A
.
Ha
sa
n
,
a
n
d
S
.
K.
P
a
rid
a
,
“
A
n
o
v
e
rv
ie
w
o
f
so
lar
p
h
o
t
o
v
o
lt
a
ic
p
a
n
e
l
m
o
d
e
li
n
g
b
a
se
d
o
n
a
n
a
ly
ti
c
a
l
a
n
d
e
x
p
e
ri
m
e
n
tal
v
ie
w
p
o
in
t,
”
Ren
e
wa
b
le
a
n
d
S
u
sta
in
a
b
le
En
e
rg
y
Rev
iews
,
v
o
l.
6
0
,
p
p
.
7
5
-
8
3
,
Ju
ly
2
0
1
6
,
d
o
i
:
1
0
.
1
0
1
6
/
j.
rse
r.
2
0
1
6
.
0
1
.
0
8
7
.
[1
2
]
K.
J.
S
i
n
g
h
,
K.
L
.
R.
K
h
o
,
S
.
J.
S
in
g
h
,
Y.
C
.
De
v
i,
N.
B.
S
i
n
g
h
,
a
n
d
S
.
K.
S
a
rk
a
r,
“
A
rti
f
icia
l
n
e
u
ra
l
n
e
tw
o
rk
a
p
p
ro
a
c
h
f
o
r
m
o
re
a
c
c
u
ra
te
so
lar
c
e
ll
e
lec
tri
c
a
l
c
ircu
it
m
o
d
e
l,
”
In
t
e
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
o
n
C
o
mp
u
ta
t
i
o
n
a
l
S
c
i
e
n
c
e
&
Ap
p
li
c
a
ti
o
n
s
,
v
o
l
.
4
,
p
p
.
1
0
1
-
1
1
6
,
2
0
1
4
,
d
o
i:
1
0
.
5
1
2
1
/IJCS
A
.
2
0
1
4
.
4
3
1
0
.
[1
3
]
Ca
n
a
d
ian
S
o
lar,
“
Da
tas
h
e
e
t:
CS
6
P
-
2
5
0
M
,
”
2
0
1
2
.
[
On
li
n
e
].
Av
a
il
a
b
le:
h
tt
p
s:/
/se
las
e
n
e
rg
y
.
g
r/t
e
c
h
n
ica
l%
2
0
d
a
ta/s
o
lar
-
p
a
n
e
ls/Can
a
d
ian
%
2
0
S
o
lar/C
S
6
P
/CS
6
P
-
2
5
5
M
%
2
0
m
o
n
o
.
p
d
f
.
[1
4
]
H.
A
.
A
tt
ia
,
a
n
d
F
.
d
e
lAm
a
G
o
n
z
a
lo
,
“
S
tan
d
-
a
lo
n
e
P
V
sy
ste
m
w
it
h
M
P
P
T
f
u
n
c
ti
o
n
b
a
se
d
o
n
f
u
z
z
y
l
o
g
ic
c
o
n
tr
o
l
f
o
r
re
m
o
te
b
u
il
d
in
g
a
p
p
li
c
a
ti
o
n
s,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
I
J
PE
DS
)
,
v
o
l.
1
0
,
n
o
.
2
,
p
p
.
8
4
2
-
8
5
1
,
J
u
n
e
2
0
1
9
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
p
e
d
s
.
v
1
0
.
i
2
.
p
p
8
4
2
-
8
5
1
.
[1
5
]
M
.
A
.
Isla
m
,
A
.
M
e
ra
b
e
t,
R.
Be
g
u
e
n
a
n
e
,
H.
Ib
ra
h
im
,
a
n
d
H.
A
h
m
e
d
,
“
S
im
u
latio
n
b
a
se
d
stu
d
y
o
f
m
a
x
i
m
u
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
a
n
d
f
re
q
u
e
n
c
y
re
g
u
latio
n
f
o
r
sta
n
d
-
a
l
o
n
e
s
o
lar p
h
o
to
v
o
lt
a
ic
sy
ste
m
s,
”
in
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Ren
e
wa
b
le
E
n
e
rg
ies
a
n
d
Po
we
r
Qu
a
li
ty
(
ICRE
PQ’1
4
)
,
v
o
l.
1
,
n
o
.
1
2
,
A
p
ril
2
0
1
4
,
p
p
.
1
-
6
,
d
o
i:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2021
:
181
3
–
182
2
1822
1
0
.
2
4
0
8
4
/rep
q
j1
2
.
3
7
8
.
[1
6
]
Z.
M
a
ss
a
q
,
A
.
A
b
o
u
n
a
d
a
,
a
n
d
R.
M
o
h
a
m
e
d
,
“
Ro
b
u
st n
o
n
-
li
n
e
a
r
c
o
n
tro
l
o
f
a
h
y
b
rid
wa
ter p
u
m
p
in
g
s
y
ste
m
b
a
s
e
d
o
n
in
d
u
c
ti
o
n
m
o
to
r,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
,
v
o
l.
1
1
,
n
o
.
4
,
p
p
.
1
9
9
5
-
2
0
0
6
,
De
c
e
m
b
e
r
2
0
2
0
,
d
o
i:
1
0
.
1
1
5
9
1
/i
jp
e
d
s.v
1
1
.
i4
.
p
p
1
9
9
5
-
2
0
0
6
.
[1
7
]
A
.
A
.
A
b
d
u
lraz
z
a
q
,
a
n
d
A
.
H.
A
li
,
“
Eff
i
c
ien
c
y
p
e
r
f
o
rm
a
n
c
e
s
o
f
Tw
o
M
P
P
T
a
lg
o
rit
h
m
s
f
o
r
P
V
sy
ste
m
w
it
h
d
if
fe
re
n
t
so
lar
p
a
n
e
ls
ir
ra
d
ian
c
e
s,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
I
J
PE
DS
)
,
v
o
l.
9
,
n
o
.
4
,
p
p
.
1
7
5
5
-
1
7
6
4
,
De
c
e
m
b
e
r
2
0
1
8
,
d
o
i:
1
0
.
1
1
5
9
1
/i
j
p
e
d
s.v
9
.
i
4
.
p
p
1
7
5
5
-
1
7
6
4
.
[1
8
]
M
.
W
.
Ra
h
m
a
n
,
C.
Ba
th
i
n
a
,
V
.
Ka
rth
ik
e
y
a
n
,
a
n
d
R.
P
ra
sa
n
th
,
“
Co
m
p
a
ra
ti
v
e
a
n
a
l
y
sis
o
f
d
e
v
e
lo
p
e
d
in
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
(IC)
a
n
d
p
e
rt
u
rb
&
o
b
se
rv
e
(
P
&
O)
M
P
P
T
a
lg
o
rit
h
m
f
o
r
p
h
o
t
o
v
o
lt
a
ic
a
p
p
li
c
a
ti
o
n
s,
”
in
2
0
1
6
1
0
t
h
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
In
telli
g
e
n
t
S
y
ste
ms
a
n
d
Co
n
tr
o
l
(
IS
CO)
,
2
0
1
6
,
p
p
.
1
-
6
,
d
o
i
:
1
0
.
1
1
0
9
/I
S
CO.2
0
1
6
.
7
7
2
6
9
9
1
.
[1
9
]
M
.
Na
id
j
i,
M
.
B
o
u
d
o
u
r,
a
n
d
F
.
A
c
h
o
u
ri,
“
M
o
d
e
li
n
g
a
n
d
c
o
n
t
ro
l
o
f
p
h
o
to
v
o
lt
a
ic
sy
st
e
m
s
in
teg
ra
te
d
t
o
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s,
”
in
2
0
1
8
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
El
e
c
trica
l
S
c
ien
c
e
s
a
n
d
T
e
c
h
n
o
lo
g
ies
in
M
a
g
h
re
b
(
CIS
T
EM
)
,
2
0
1
8
,
p
p
.
1
-
6
,
d
o
i:
1
0
.
1
1
0
9
/CI
S
T
EM
.
2
0
1
8
.
8
6
1
3
3
2
4
.
[2
0
]
M
.
A
.
El
g
e
n
d
y
,
D.
J.
A
tk
in
so
n
,
a
n
d
B
.
Zah
a
w
i,
“
Ex
p
e
rim
e
n
ta
l
in
v
e
stig
a
ti
o
n
o
f
th
e
in
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
a
lg
o
rit
h
m
a
t
h
ig
h
p
e
rtu
r
b
a
ti
o
n
ra
tes
,
”
IET
Ren
e
wa
b
le
Po
we
r
Ge
n
e
ra
ti
o
n
,
v
o
l.
1
0
,
n
o
.
2
,
p
p
.
1
3
3
-
1
3
9
,
S
e
p
tem
b
e
r
2
0
1
5
,
d
o
i:
1
0
.
1
0
4
9
/
iet
-
rp
g
.
2
0
1
5
.
0
1
3
2
.
[2
1
]
H.
A
b
id
,
F
.
T
a
d
e
o
,
A
.
T
o
u
m
i,
a
n
d
M
.
Ch
a
a
b
a
n
e
,
“
M
P
P
T
o
f
a
p
h
o
t
o
v
o
lt
a
ic
p
a
n
e
l
b
a
se
d
o
n
T
a
k
a
g
i
-
S
u
g
e
n
o
a
n
d
f
ra
c
ti
o
n
a
l
a
lg
o
rit
h
m
s,
”
In
ter
n
a
ti
o
n
a
l
Rev
iew o
f
A
u
to
m
a
ti
c
Co
n
tro
l
,
v
o
l.
7
,
n
o
.
3
,
p
p
.
2
4
5
-
2
5
3
,
M
a
y
2
0
1
4
.
[2
2
]
K.
R.
B
h
a
ra
th
a
n
d
E
.
S
u
re
s
h
,
“
De
sig
n
a
n
d
im
p
lem
e
n
tatio
n
o
f
i
m
p
ro
v
e
d
f
ra
c
ti
o
n
a
l
o
p
e
n
c
ircu
it
v
o
lt
a
g
e
b
a
se
d
m
a
x
i
m
u
m
p
o
we
r
p
o
in
t
trac
k
in
g
a
lg
o
rit
h
m
f
o
r
p
h
o
t
o
v
o
lt
a
ic
a
p
p
li
c
a
ti
o
n
s,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ren
e
wa
b
le
En
e
rg
y
Res
e
a
rc
h
(
IJ
RE
R)
,
v
o
l.
7
,
n
o
.
3
,
p
p
.
1
1
0
8
-
1
1
1
3
,
2
0
1
7
.
[2
3
]
S
.
Ba
ro
i,
P
.
C.
S
a
rk
e
r,
a
n
d
S
.
Ba
ro
i,
“
A
n
i
m
p
ro
v
e
d
M
P
P
T
tec
h
n
i
q
u
e
-
a
lt
e
rn
a
ti
v
e
to
f
ra
c
ti
o
n
a
l
o
p
e
n
c
ircu
it
v
o
lt
a
g
e
m
e
th
o
d,
”
in
2
0
1
7
2
n
d
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
El
e
c
trica
l
&
El
e
c
tro
n
ic
En
g
i
n
e
e
rin
g
(
ICEE
E)
,
2
0
1
7
,
p
p
.
1
-
4
,
d
o
i:
1
0
.
1
1
0
9
/CE
EE
.
2
0
1
7
.
8
4
1
2
9
0
9
.
[2
4
]
H.
A
.
S
h
e
r,
A
.
F
.
M
u
rtaz
a
,
A
.
No
m
a
n
,
K.
E.
A
d
d
o
w
e
e
sh
,
K.
Al
-
Ha
d
d
a
d
,
a
n
d
M
.
Ch
iab
e
rg
e
,
“
A
n
e
w
se
n
so
rles
s
h
y
b
rid
M
P
P
T
a
lg
o
rit
h
m
b
a
se
d
o
n
f
ra
c
ti
o
n
a
l
sh
o
rt
-
c
ircu
it
c
u
rre
n
t
m
e
a
su
re
m
e
n
t
a
n
d
P
&
O
M
P
P
T
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
u
sta
i
n
a
b
le E
n
e
rg
y
,
v
o
l.
6
,
n
o
.
4
,
p
p
.
1
4
2
6
-
1
4
3
4
,
Oc
t.
2
0
1
5
,
d
o
i:
1
0
.
1
1
0
9
/T
S
T
E.
2
0
1
5
.
2
4
3
8
7
8
1
.
[2
5
]
H.
A
.
S
h
e
r,
A
.
F
.
M
u
rtaz
a
,
A
.
No
m
a
n
,
K.
E.
A
d
d
o
w
e
e
sh
,
a
n
d
M
.
C
h
iab
e
rg
e
,
“
A
n
in
telli
g
e
n
t
c
o
n
tro
l
stra
teg
y
o
f
f
ra
c
ti
o
n
a
l
sh
o
rt
c
ircu
it
c
u
rre
n
t
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
tec
h
n
iq
u
e
f
o
r
p
h
o
to
v
o
l
taic
a
p
p
li
c
a
t
io
n
s,
”
J
o
u
rn
a
l
o
f
Ren
e
wa
b
le A
n
d
S
u
sta
i
n
a
b
le E
n
e
rg
y
,
v
o
l.
7
,
n
o
.
1
,
p
.
1
3
1
1
4
,
Ja
n
u
a
r
y
2
0
1
5
,
d
o
i
:
1
0
.
1
0
6
3
/
1
.
4
9
0
6
9
8
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.