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201
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s
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it
ca
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ef
f
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[
1
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.
Gen
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la
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A
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P
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DC
-
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[
3
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4
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.
A
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[
5
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.
T
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(
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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694
I
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P
o
w
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&
Dr
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S
y
s
t
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
1755
–
1
7
6
4
1756
be
im
p
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[
6
]
.
O
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I
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V
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-
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o
w
er
g
e
n
er
atio
n
o
f
P
V
s
y
s
te
m
s
,
t
h
e
MP
P
T
n
o
w
co
m
e
s
i
n
b
o
th
g
r
id
-
co
n
n
ec
ted
an
d
s
ta
n
d
alo
n
e
p
o
w
er
g
en
er
atio
n
s
y
s
te
m
s
.
T
h
is
m
a
k
es
s
u
p
p
l
y
i
n
g
s
tead
y
p
o
w
er
to
a
s
p
ec
if
ic
lo
ad
d
if
f
icu
lt.
I
n
cl
u
d
i
n
g
t
h
e
MP
PT
te
ch
n
o
lo
g
y
to
th
e
P
V
s
y
s
te
m
d
esig
n
in
g
co
n
s
id
er
s
a
g
o
o
d
w
a
y
to
en
ab
le
t
h
e
tr
an
s
f
er
o
f
m
o
s
t
s
tab
l
e
a
n
d
h
i
g
h
es
t
p
o
s
s
ib
le
p
o
w
er
f
r
o
m
s
o
u
r
ce
to
lo
ad
.
T
h
e
r
ea
s
o
n
b
eh
in
d
th
i
s
is
t
h
e
co
n
ti
n
u
o
u
s
v
ar
iatio
n
in
t
h
e
p
o
w
er
w
h
ic
h
th
e
s
e
p
an
els
g
en
er
ate,
d
ep
en
d
in
g
o
n
w
ea
t
h
er
r
elate
d
f
ac
to
r
s
lik
e
te
m
p
er
at
u
r
e
an
d
ir
r
ad
ian
ce
;
th
e
ef
f
icie
n
c
y
w
it
h
w
h
ic
h
p
o
w
er
is
co
n
v
er
te
d
lo
o
k
s
v
er
y
lo
w
,
w
it
h
j
u
s
t
n
o
t
m
o
r
e
th
a
n
1
5
% o
f
th
e
to
tal
co
n
v
er
ti
n
g
en
er
g
y
f
r
o
m
s
u
n
li
g
h
t b
ec
o
m
i
n
g
elec
tr
ic
it
y
[
7
]
.
T
h
u
s
,
th
e
in
cl
u
s
io
n
o
f
MP
PT
in
P
V
s
y
s
te
m
s
to
co
n
f
ir
m
th
at
a
s
o
lar
p
an
els
g
en
er
ate
th
e
m
a
x
i
m
u
m
p
o
w
er
a
m
o
u
n
t.
A
n
o
n
li
n
ea
r
co
r
r
elatio
n
is
d
e
m
o
n
s
tr
ated
b
y
th
e
c
h
ar
ac
ter
is
t
ics
o
f
P
V
p
an
el
(
I
-
V
&
P
-
V)
b
et
w
ee
n
ir
r
ad
ian
ce
s
&
te
m
p
er
atu
r
e.
No
n
eth
ele
s
s
,
a
s
p
ec
ial
p
o
in
t
w
h
er
e
th
e
w
h
o
le
s
y
s
te
m
ca
n
f
u
n
ctio
n
w
it
h
h
ig
h
ef
f
icie
n
c
y
ca
n
b
e
f
o
u
n
d
i
n
t
h
e
c
h
ar
ac
ter
is
tic
cu
r
v
e
i
s
p
r
esen
ted
i
n
Fig
u
r
e
1
.
T
h
is
u
n
i
q
u
e
f
ac
t
i
s
d
en
o
ted
to
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
MP
P
,
w
h
ic
h
ca
n
b
e
co
n
s
id
er
ed
to
en
s
u
r
e
th
at
th
e
P
V
s
y
s
te
m
i
s
f
u
n
ctio
n
i
n
g
at
i
t
in
th
e
p
r
o
d
u
ctio
n
o
f
th
e
m
a
x
i
m
u
m
a
m
o
u
n
t
o
f
p
o
w
er
,
ca
lc
u
latio
n
s
,
m
o
n
i
to
r
in
g
an
d
co
n
tr
o
l
tech
n
iq
u
es
ar
e
r
eq
u
ir
ed
[
8
]
.
Fig
u
r
e
1
.
C
h
ar
ac
ter
is
t
ic
I
-
V
a
n
d
P
-
V
cu
r
v
es o
f
a
s
o
lar
p
an
el
T
h
e
o
u
tp
u
t
o
f
p
o
w
er
v
ar
ies
j
u
s
t
as
t
h
er
e
is
a
v
ar
iatio
n
in
t
h
e
s
o
lar
r
ad
iatio
n
.
Fig
u
r
e
1
e
x
p
lain
s
th
e
m
ax
i
m
u
m
p
o
w
er
tr
ac
k
i
n
g
p
r
i
n
cip
les,
w
h
er
e
th
e
s
lo
p
p
y
li
n
e
I
/R
c
co
n
n
o
te
s
a
co
n
s
tan
t
l
o
ad
R
c.
T
h
e
d
ir
ec
t
co
n
n
ec
tio
n
o
f
t
h
is
lo
ad
ac
r
o
s
s
P
V
ce
ll
w
il
l
r
esu
l
t
in
i
t
o
p
er
atin
g
a
p
o
w
er
P
a
w
h
ich
i
s
n
o
t
th
e
s
a
m
e
as
t
h
e
m
ax
i
m
u
m
P
b
,
d
esp
ite
th
e
av
ai
lab
ilit
y
o
f
t
h
e
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
th
e
ar
r
a
y
.
So
,
an
i
n
tr
o
d
u
ctio
n
to
th
e
D
C
-
DC
co
n
v
er
ter
o
r
a
p
o
w
er
co
n
d
itio
n
er
is
co
n
ce
r
n
in
g
t
h
e
s
o
l
ar
P
V
m
o
d
u
le
i
n
ad
d
itio
n
to
t
h
e
lo
ad
.
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h
e
lo
ad
is
ad
ap
ted
to
th
e
P
V
ar
r
ay
th
r
o
u
g
h
th
e
u
s
e
o
f
th
i
s
co
n
v
er
ter
in
o
r
d
er
to
en
ab
le
th
e
tr
a
n
s
f
o
r
m
atio
n
o
f
th
e
ch
ar
ac
ter
is
tic
s
alo
n
g
t
h
e
lo
cu
s
o
f
m
a
x
i
m
u
m
p
o
i
n
ts
,
t
h
er
eb
y
l
ea
d
in
g
to
t
h
e
tr
an
s
f
o
r
m
atio
n
o
f
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
t
h
e
ar
r
a
y
.
T
h
is
c
h
a
n
g
e
is
m
ad
e
to
th
e
d
u
t
y
c
y
cle
o
f
“
D”
t
ill
t
h
e
ti
m
e
w
h
e
n
t
h
e
p
ea
k
p
o
w
er
p
o
in
t
is
ac
h
iev
ed
[
9
-
1
0
]
.
T
h
e
MPPT
ca
n
b
e
r
eg
ar
d
e
d
as
an
elec
tr
o
n
ic
d
ev
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w
h
ic
h
ca
n
b
e
u
s
ed
to
ex
tr
ac
t
th
e
m
a
x
i
m
u
m
p
o
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tial
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o
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o
m
a
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o
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el.
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h
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u
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o
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t
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ter
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atch
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Desp
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Me
c
h
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ical
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ac
k
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g
s
y
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te
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a
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d
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e
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eth
er
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m
an
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tech
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h
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v
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ap
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ith
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ize
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licatio
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ar
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tu
r
b
an
d
o
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&
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,
an
d
in
cr
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ce
(
I
NC
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.
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w
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co
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p
ar
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an
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te
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r
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u
e
d
s
tan
d
ar
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co
n
ce
r
n
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r
ad
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ith
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h
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c
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,
o
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tp
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t p
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MP
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.
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I
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Dr
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P
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i
n
g
to
t
h
e
v
ar
iat
i
o
n
in
t
h
e
MP
P
o
f
a
s
o
lar
p
an
el
ca
u
s
ed
b
y
te
m
p
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r
e
an
d
ir
r
ad
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n
,
MP
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al
g
o
r
ith
m
s
b
ec
o
m
e
cr
u
cial
i
n
P
V
ap
p
licatio
n
s
.
T
h
is
is
b
ec
au
s
e
MP
P
T
alg
o
r
ith
m
s
e
n
h
a
n
ce
t
h
e
g
e
n
er
atio
n
o
f
m
a
x
i
m
u
m
p
o
w
er
f
r
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m
a
s
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lar
ar
r
a
y
[
1
1
]
.
Var
io
u
s
m
et
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o
d
s
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f
i
n
d
in
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h
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d
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m
e
n
tatio
n
.
Ho
w
e
v
er
,
th
e
y
also
h
av
e
t
h
eir
li
m
ita
tio
n
s
.
T
h
e
o
th
er
tech
n
iq
u
es
w
h
ich
h
a
v
e
b
ee
n
d
ev
elo
p
ed
ac
co
r
d
in
g
to
d
i
f
f
er
en
t
p
r
in
cip
les
i
n
clu
d
e
n
e
u
r
al
n
et
w
o
r
k
,
cu
r
r
en
t
s
w
ee
p
tech
n
iq
u
e,
f
u
zz
y
lo
g
ic
co
n
tr
o
l,
an
d
f
r
ac
tio
n
al
o
p
en
cir
cu
it
o
p
en
v
o
lta
g
e
o
r
s
h
o
r
t
cir
cu
it c
u
r
r
e
n
t,
an
d
th
i
s
tec
h
n
i
q
u
e
is
ab
le
to
p
r
o
v
id
e
an
esti
m
ated
MPP
.
B
o
th
alg
o
r
ith
m
s
P
&
O
an
d
I
NC
ar
e
estab
lis
h
ed
o
n
th
e
p
r
in
cip
les
o
f
h
il
l
-
cl
i
m
b
i
n
g
b
asis
,
w
h
ic
h
in
v
o
l
v
es
t
h
e
m
o
v
e
m
e
n
t
o
f
th
e
o
p
er
atio
n
p
o
in
t
o
f
th
e
P
V
ar
r
ay
i
n
th
e
d
ir
ec
tio
n
th
at
d
ir
ec
ts
f
o
r
in
cr
ea
s
i
n
g
p
o
w
er
.
T
h
e
ea
s
y
i
m
p
le
m
e
n
ta
tio
n
o
f
h
i
ll
-
c
li
m
b
i
n
g
tec
h
n
iq
u
es
a
s
w
el
l
as
its
e
f
f
icie
n
c
y
w
h
e
n
ir
r
ad
iatio
n
i
s
co
n
s
ta
n
t,
m
a
k
es
it
o
n
e
o
f
th
e
m
o
s
t
co
m
m
o
n
MP
PT
m
eth
o
d
s
[
1
2
]
.
B
o
th
ar
e
ad
v
an
tag
eo
u
s
b
ec
au
s
e
o
f
th
e
lo
w
co
m
p
u
tatio
n
al
p
o
w
er
w
h
ich
t
h
e
y
r
eq
u
ir
e
as
w
ell
t
h
eir
s
i
m
p
li
cit
y
.
T
h
e
o
p
tim
izatio
n
alg
o
r
it
h
m
P
&
O
i
s
m
ad
e
u
p
o
f
co
n
v
er
ter
i
n
p
u
t
c
u
r
r
en
t
o
r
v
o
lta
g
e
r
ef
er
e
n
ce
w
h
ich
v
ar
y
.
A
m
ea
s
u
r
e
m
e
n
t
o
f
th
e
p
o
w
er
's
a
m
o
u
n
t
w
h
ic
h
is
p
an
el
co
n
v
er
s
atio
n
h
as
b
ee
n
ta
k
e
n
.
I
f
th
e
co
n
v
er
ted
a
m
o
u
n
t
o
f
p
o
w
er
i
s
m
o
r
e
th
a
n
th
at
w
h
ic
h
w
a
s
p
r
ev
io
u
s
l
y
m
ea
s
u
r
ed
,
it
i
m
p
lies
a
p
r
o
p
o
r
tio
n
al
s
tead
y
i
n
cr
ea
s
e
in
t
h
e
v
o
ltag
e
r
ef
er
en
ce
,
b
u
t
i
f
n
o
t,
it
i
m
p
lies
a
d
ec
r
ea
s
e.
Fi
n
d
in
g
t
h
e
o
p
ti
m
u
m
MP
P
T
r
eq
u
ir
es
co
n
ti
n
u
o
u
s
l
y
tak
i
n
g
t
h
e
s
tep
s
.
I
n
s
o
m
e
s
itu
atio
n
s
,
t
h
e
MP
P
m
a
y
n
o
t
b
e
ab
le
to
f
in
d
,
p
ar
ticu
lar
l
y
u
n
d
er
p
ar
tial
s
h
ad
in
g
,
is
r
eg
ar
d
ed
as th
e
li
m
itatio
n
o
f
t
h
is
al
g
o
r
ith
m
.
T
h
e
im
p
le
m
e
n
tatio
n
o
f
th
e
al
g
o
r
ith
m
as
w
el
l
as
tak
in
g
it
as
a
r
ef
er
en
ce
p
o
in
t
is
a
g
o
o
d
id
ea
b
ec
a
u
s
e
it
is
a
n
alg
o
r
it
h
m
w
h
ich
i
s
co
m
m
o
n
l
y
u
s
ed
.
I
t's
f
lo
w
c
h
ar
t
ca
n
b
e
s
ee
n
i
n
f
i
g
u
r
e
2
,
w
h
er
e
Y(
t)
r
ep
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ts
th
e
r
ef
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ce
s
i
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t
h
at
m
ig
h
t
b
e
eith
er
v
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lta
g
e
o
r
cu
r
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en
t
s
o
la
r
P
V.
Fo
r
ac
h
iev
in
g
MP
P
is
th
e
m
a
in
p
u
r
p
o
s
i
n
g
,
th
e
s
y
s
te
m
o
p
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atin
g
p
o
in
t c
o
u
ld
b
e
c
h
an
g
ed
w
it
h
a
s
m
all
p
er
tu
r
b
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n
(
∆Y
)
i
s
ap
p
lied
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th
e
r
ef
er
en
ce
s
i
g
n
al
o
f
th
e
s
o
lar
P
V
an
d
th
en
m
ea
s
u
r
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n
g
t
h
e
o
u
tp
u
t
p
o
w
er
af
ter
ea
ch
p
er
tu
r
b
atio
n
.
A
co
m
p
ar
i
s
o
n
is
m
ad
e,
if
t
h
e
m
ea
s
u
r
ed
p
o
w
er
is
m
o
r
e
v
al
u
e
w
it
h
r
esp
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t
to
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e
p
r
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ed
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a
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t
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a
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ig
n
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p
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w
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l
co
n
ti
n
u
e
i
n
th
e
s
a
m
e
d
ir
ec
tio
n
.
Gen
er
all
y
,
w
h
e
n
a
m
e
asu
r
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p
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f
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s
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a
p
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h
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ev
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d
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d
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d
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w
il
l c
o
n
ti
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e
to
ac
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iev
e
th
e
MP
P
.
Fig
u
r
e
2
.
Flo
w
c
h
ar
t o
f
co
n
v
en
tio
n
al
MP
PT
P
&
O
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
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I
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4
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Dec
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2
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1
7
6
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1758
2
.
1
I
ncre
m
e
nta
l
C
o
nd
uct
a
nc
e
T
h
e
I
NC
alg
o
r
ith
m
i
s
co
n
s
tr
u
cted
o
n
th
e
f
ac
t
co
n
ce
r
n
i
n
g
a
s
lo
p
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o
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p
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w
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r
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a
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ai
n
s
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h
o
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e
o
r
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r
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en
t
o
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th
e
P
V
m
o
d
u
le
co
n
s
id
er
s
ze
r
o
at
th
e
MP
P
,
a
m
o
v
e
m
e
n
t
o
f
p
o
s
iti
v
e
o
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n
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e
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th
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le
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t o
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it a
n
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th
e
r
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h
t i
s
n
eg
ati
v
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o
r
p
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s
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e,
as e
x
p
lai
n
in
Fig
u
r
e
3
.
W
h
en
a
co
m
p
ar
is
o
n
o
f
t
h
e
p
o
w
er
in
cr
e
m
e
n
t
ag
ai
n
s
t
th
e
v
o
ltag
e
o
r
cu
r
r
en
t
i
n
cr
e
m
e
n
t
t
h
r
o
u
g
h
t
w
o
s
u
cc
e
s
s
i
v
e
s
a
m
p
les
i
s
m
ad
e,
t
h
en
a
MP
P
v
o
ltag
e
c
h
an
g
e
m
a
y
b
e
s
p
ec
if
ied
.
T
h
e
tr
ac
k
i
n
g
o
f
th
e
MP
P
ca
n
d
o
n
e
b
y
a
co
m
p
ar
is
o
n
o
f
th
e
in
s
ta
n
t
an
eo
u
s
co
n
d
u
cta
n
ce
ter
m
(
I
/V
)
w
it
h
a
n
i
n
cr
e
m
en
ta
l
v
alu
e
(
Δ
I/
Δ
V)
a
s
il
lu
s
tr
ated
in
th
e
f
lo
w
c
h
ar
t,
f
i
g
u
r
e.
4
.
A
r
ef
er
en
ce
v
o
lta
g
e
V
ref
r
ep
r
esen
ts
a
P
V
ar
r
ay
p
o
in
t
w
h
ic
h
is
r
eq
u
ir
ed
to
co
n
tr
o
l.
T
h
e
V
ref
at
MP
P
e
q
u
als
V
mpp
,
o
n
ce
an
MP
P
is
r
ea
ch
ed
,
t
h
en
t
h
e
o
p
er
atio
n
o
f
t
h
e
P
V
ar
r
ay
i
s
m
ai
n
tai
n
ed
at
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h
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s
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o
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t if
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ch
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g
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i
n
Δ
I
h
a
s
h
a
p
p
en
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,
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p
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if
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n
g
a
v
ar
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y
o
f
at
m
o
s
p
h
er
ic
co
n
d
itio
n
[
1
3
,
1
4
]
.
Fig
u
r
e
3
.
P
V
ar
r
ay
C
h
ar
ac
ter
i
s
tic
p
o
w
er
cu
r
v
e
.
Fig
u
r
e
4
.
I
NC
alg
o
r
it
h
m
f
lo
w
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h
ar
t
2
.
2
.
So
la
r
Arr
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Fo
r
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t
o
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s
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lar
a
r
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ay
,
b
ased
o
n
t
h
e
d
io
d
e
eq
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atio
n
b
elo
w
,
a
m
o
d
el
o
f
th
e
ar
r
ay
is
en
v
elo
p
ed
:
I
d
=
I
s
at(
eq
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/k
T
-
1
)
(
1
)
w
h
er
e
I
d
in
d
icate
s
t
h
e
d
io
d
e
cu
r
r
en
t
(
A
)
,
Vd
r
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r
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ts
t
h
e
d
io
d
e
v
o
ltag
e
(
V)
.
I
n
o
r
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er
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er
f
o
r
m
th
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s
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m
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lat
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n
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s
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a
t
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ca
p
ab
le
o
f
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r
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d
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m
o
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e
th
a
n
1
0
0
W
w
a
s
m
ad
e.
T
h
e
f
ir
s
t
co
n
d
itio
n
i
s
co
n
ce
r
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ed
w
it
h
v
o
ltag
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Vo
c
(
o
p
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o
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2
V
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d
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r
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.
4
A
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e
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o
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y
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el.
T
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Vm
p
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a
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m
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is
1
7
.
5
V
w
h
er
ea
s
th
e
c
u
r
r
en
t
I
m
p
-
m
a
x
i
m
u
m
p
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w
er
-
is
7
.
7
A
.
C
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n
ce
r
n
in
g
a
f
u
ll
s
o
lar
il
lu
m
i
n
atio
n
,
a
n
o
u
tp
u
t
p
o
w
er
o
f
1
3
5
W
ca
n
b
e
o
b
tain
ed
f
r
o
m
th
e
s
o
lar
ar
r
ay
b
y
p
lu
g
g
i
n
g
t
h
ese
v
alu
e
s
i
n
to
P
=
I
V.
Fig
u
r
e
5
s
h
o
w
s
t
h
at
v
ar
y
i
n
g
t
h
e
P
V
s
o
lar
ar
r
ay
i
n
cid
en
t
ill
u
m
i
n
atio
n
alo
n
g
s
id
e
t
h
e
o
u
tp
u
t
i
m
p
ed
an
ce
,
i
m
p
l
ies
t
h
at
th
e
e
x
tr
ac
tio
n
o
f
P
o
w
e
r
v
er
s
u
s
Vo
ltag
e
an
d
C
u
r
r
en
t
v
er
s
u
s
Vo
lt
ag
e
g
r
ap
h
s
ca
n
b
e
p
er
f
o
r
m
ed
s
o
as
to
ac
h
ie
v
e
t
h
e
MP
P
o
f
th
e
s
o
lar
ar
r
ay
.
T
h
e
MP
P
is
th
e
p
o
w
er
p
ea
k
v
er
s
u
s
Vo
ltag
e
g
r
ap
h
.
I
f
th
e
i
n
cid
en
t
ill
u
m
i
n
atio
n
o
f
t
h
e
P
V
s
o
lar
ar
r
a
y
i
s
v
ar
y
i
n
g
in
ad
d
itio
n
to
th
e
o
u
tp
u
t
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g
r
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o
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er
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t a
g
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in
s
t V
o
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n
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x
tr
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ted
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o
r
f
in
d
i
n
g
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e
s
o
lar
ar
r
ay
MP
P
,
as
s
h
o
w
n
in
f
i
g
u
r
e
5
.
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:
2088
-
8
694
Tit
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o
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crip
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r
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u
r
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h
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r
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h
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io
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co
m
m
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l
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r
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y
a
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le
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io
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o
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el
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esid
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o
u
b
le
-
d
io
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e
m
o
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el
[
1
5
]
.
T
h
e
P
V
p
an
el
co
n
s
is
t
s
o
f
a
P
V
s
et
ce
ll
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h
ich
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r
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g
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d
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d
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ate
a
n
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al
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ax
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m
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tr
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s
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en
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ic
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m
ico
n
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ct
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r
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h
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izi
n
g
th
e
ce
lls
.
A
P
V
ce
ll
m
a
y
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e
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eg
ar
d
ed
lik
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e
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er
ato
r
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at
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r
o
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ce
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a
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cu
r
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p
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ep
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ter
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al
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r
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ir
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tio
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r
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k
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n
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te
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er
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r
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r
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y
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h
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d
io
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e
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o
d
el
r
ep
r
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ts
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e
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V
ce
lls
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Fig
.
6
-
a)
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d
th
e
d
o
u
b
le
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d
io
d
e
m
o
d
el
(
Fig
.
6
-
b
)
r
e
p
r
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ts
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e
d
if
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er
e
n
t p
ar
a
m
eter
s
o
f
th
e
m
o
d
el
[
1
6
]
.
Fig
u
r
e
6
(
a)
P
V
ce
ll E
q
u
iv
alen
t c
ir
cu
it
(
b
)
P
V
p
an
els d
o
u
b
le
-
d
io
d
e
m
o
d
el
T
h
e
cu
r
r
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eq
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atio
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io
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o
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el
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cell
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ph
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D
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SH
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r
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p
p
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ll
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ph
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ph
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sat
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(
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∗
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h
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m
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o
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th
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el
ce
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ig
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sh
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ph
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elate
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V
ce
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an
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.
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.
I
d1
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[
(
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fo
r
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I
s
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(
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w
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er
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s
i is t
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io
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er
s
e
s
atu
r
atio
n
c
u
r
r
en
t,
a
n
d
V
t=k/
Tq
is
th
e
p
an
el
t
h
er
m
al
v
o
lta
g
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.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
1755
–
1
7
6
4
1760
3
.
1
.
M
P
P
T
O
pera
t
ing
Z
o
ne
f
o
r
DC
–
DC
Co
nv
er
t
er
T
o
po
lo
g
y
T
h
e
s
o
lar
P
V'
s
MP
P
T
o
p
er
ati
n
g
zo
n
e
r
elies
o
n
t
h
e
to
p
o
lo
g
y
o
f
D
C
–
DC
co
n
v
er
ter
,
a
n
d
th
e
r
esis
ti
v
e
lo
ad
v
alu
e
is
r
estricte
d
t
h
er
eb
y
m
a
k
in
g
th
e
MP
PT
ef
f
ec
ti
v
e
.
T
h
e
i
m
p
le
m
en
tatio
n
o
f
t
h
e
MP
PT
is
ca
r
r
ied
o
u
t
u
n
d
er
th
e
co
n
v
er
ter
co
n
tr
o
l,
i.e
.
it
ca
u
s
es
v
ar
iatio
n
in
t
h
e
d
u
t
y
c
y
cle
(
d
)
.
T
h
e
m
a
in
ai
m
o
f
m
ak
in
g
ad
j
u
s
t
m
en
t
s
to
th
e
d
u
t
y
c
y
cle
is
f
o
r
m
atc
h
in
g
th
e
lo
ad
i
m
p
ed
an
ce
to
t
h
e
i
n
p
u
t
i
m
p
ed
an
ce
R
i
n
w
h
ic
h
is
n
o
ticed
b
y
t
h
e
co
n
v
er
ter
.
Fi
g
u
r
e
7
s
h
o
w
s
t
h
e
s
o
lar
P
V
i
m
p
ed
an
ce
.
T
h
er
e
i
s
a
r
elatio
n
s
h
ip
b
et
w
e
e
n
t
h
e
R
in
n
o
ticed
b
y
th
e
co
n
v
er
ter
an
d
t
h
e
R
o
co
n
n
e
cted
w
it
h
co
n
v
er
ter
b
y
ch
ar
ac
ter
is
tic
eq
u
atio
n
s
.
T
h
er
e
is
v
ar
iatio
n
in
t
h
is
m
at
h
e
m
a
tical
eq
u
atio
n
,
d
ep
en
d
in
g
o
n
t
h
e
t
o
p
o
lo
g
ies o
f
co
n
v
er
ter
[
1
7
]
.
Fi
g
u
r
e
7
.
DC
–
DC
co
n
v
er
ter
d
iag
r
a
m
T
h
e
i
m
p
le
m
e
n
tatio
n
o
f
th
e
i
m
p
r
o
v
ed
MPPT
s
tr
u
ctu
r
e
i
s
p
er
f
o
r
m
ed
u
s
i
n
g
t
h
e
DC
–
D
C
b
u
c
k
co
n
v
er
ter
as
s
h
o
w
n
i
n
Fi
g
u
r
e
8
.
T
h
e
o
u
tp
u
t
v
o
lta
g
e
o
f
s
o
lar
P
V
is
d
er
iv
ed
f
r
o
m
t
h
e
b
u
c
k
co
n
v
er
ter
in
p
u
t
v
o
ltag
e.
T
h
e
r
elatio
n
s
h
ip
b
et
w
ee
n
t
h
e
(
in
p
u
t a
n
d
o
u
tp
u
t
v
o
ltag
e)
b
u
c
k
co
n
v
er
ter
is
g
i
v
e
n
b
y
eq
u
atio
n
6
.
W
h
er
e
th
e
o
u
tp
u
t v
o
lta
g
e
is
d
e
n
o
ted
b
y
Vo
,
t
h
e
d
u
t
y
c
y
cle
i
s
d
an
d
in
p
u
t v
o
lta
g
e
Vi
n
o
f
t
h
e
b
u
ck
co
n
v
er
ter
.
Fig
u
r
e
8
: B
u
ck
co
n
v
er
ter
d
iag
r
a
m
4
.
CO
M
P
ARIS
O
N
O
F
CO
NT
RO
L
A
L
G
O
RI
T
H
M
Un
d
er
s
ta
n
d
in
g
t
h
e
w
a
y
th
e
s
e
alg
o
r
ith
m
s
r
esp
o
n
d
to
v
ar
io
u
s
c
h
a
n
g
e
s
o
f
s
o
lar
ar
r
ay
ir
r
ad
ian
ce
is
p
o
s
s
ib
le
th
r
o
u
g
h
a
co
m
p
ar
is
o
n
o
f
th
e
o
u
tp
u
t
w
av
e
f
o
r
m
s
f
r
o
m
ea
ch
r
u
n
.
4
.
1
.
Ca
s
e
1
:
P
&O
a
t
Co
ns
t
a
nt
I
rr
a
dia
nce
A
f
ir
s
t
M
A
T
L
A
B
m
o
d
el
r
u
n
is
d
o
n
e
w
it
h
a
co
n
s
tan
t
i
n
p
u
t
ir
r
ad
ian
ce
b
y
t
h
e
s
o
lar
ar
r
a
y
.
A
m
ea
s
u
r
ab
le
a
m
o
u
n
t
o
f
r
ip
p
le
is
p
o
s
s
ess
ed
b
y
t
h
e
r
esp
o
n
s
e
cu
r
v
e,
w
h
ic
h
r
ep
r
esen
t
th
e
o
u
tp
u
t
v
o
ltag
e
as
p
r
esen
ted
in
Fig
u
r
e
9
.
a.
W
h
en
th
er
e
is
litt
le
in
itial
o
v
er
s
h
o
o
t
at
th
e
cu
r
r
en
t
r
esp
o
n
s
e,
th
e
P
W
M
o
f
th
e
g
ate
is
co
n
tr
o
lled
b
y
t
h
e
MP
P
T
s
o
as
to
b
r
in
g
i
t
n
ea
r
t
h
e
MP
P
as
ex
p
lain
ed
in
Fi
g
u
r
e
9
.
b
.
I
n
F
i
g
u
r
e
9
.
c
th
e
o
u
tp
u
t
p
o
w
er
s
ta
y
s
al
m
o
s
t
co
n
s
ta
n
t
f
r
o
m
3
m
s
ec
a
n
d
ab
o
v
e.
A
co
n
s
tan
t
e
f
f
icie
n
c
y
o
f
9
4
%
is
ac
h
ie
v
ed
b
y
th
e
co
n
v
er
ter
an
d
t
h
e
n
t
h
r
o
u
g
h
o
u
t
th
e
p
er
io
d
o
f
s
i
m
u
latio
n
t
h
e
s
tead
y
e
f
f
icie
n
c
y
r
e
m
ai
n
s
a
l
m
o
s
t
co
m
p
letel
y
f
lat
as p
r
esen
ted
in
F
ig
u
r
e
9
.
d
.
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:
2088
-
8
694
Tit
le
o
f m
a
n
u
s
crip
t is sh
o
r
t a
n
d
clea
r
,
imp
lies
r
esea
r
ch
r
esu
l
ts
(
F
i
r
s
t A
u
th
o
r
)
1761
Fig
u
r
e
9
: P
&
O
s
i
m
u
latio
n
r
es
u
lt a
t c
o
n
s
tan
t ir
r
ad
ian
ce
(
a)
o
u
tp
u
t v
o
ltag
e
(
b
)
cu
r
r
en
t r
esp
o
n
s
e
(
c)
o
u
tp
u
t p
o
w
er
(
d
)
ef
f
icien
c
y
4
.
2
.
Ca
s
e
2
:
P
&O
w
it
h Va
ri
a
ble Irra
dia
nce.
A
s
ec
o
n
d
ca
s
e
in
v
o
lv
e
s
s
i
m
u
l
atio
n
u
s
in
g
v
ar
iab
le
ir
r
ad
ian
ce
to
th
e
in
p
u
t
s
o
lar
ar
r
a
y
.
T
h
e
ch
an
g
es
i
n
ir
r
ad
ian
ce
ar
e
tr
ac
k
ed
b
y
b
o
th
t
h
e
s
o
u
r
ce
a
n
d
o
u
tp
u
t
v
o
lt
ag
e
as
p
r
esen
ted
in
f
ig
u
r
e
1
0
.
b
.
L
ittl
e
s
tar
t
-
u
p
o
v
er
s
h
o
o
t
o
cc
u
r
s
i
n
t
h
e
cu
r
r
e
n
t
r
esp
o
n
s
e
to
e
v
er
y
c
h
an
g
e
in
ir
r
ad
ian
ce
.
Du
r
i
n
g
th
e
o
p
e
r
atio
n
,
th
er
e
w
as
a
ten
d
en
c
y
o
f
t
h
e
s
o
u
r
ce
c
u
r
r
en
t
o
s
cillati
n
g
a
b
it
as
s
h
o
w
n
in
Fi
g
u
r
e
1
0
.
c.
I
n
co
m
p
ar
is
o
n
t
o
th
e
i
n
p
u
t
p
o
w
er
w
h
ic
h
is
s
h
o
w
n
i
n
Fig
u
r
e
1
0
.
d
,
th
e
o
u
tp
u
t
p
o
w
er
r
e
m
ain
s
r
elativ
el
y
clo
s
e
in
m
a
g
n
it
u
d
e.
Du
e
t
o
t
h
e
f
ac
t
t
h
at
th
e
av
er
a
g
e
o
f
o
v
er
0
:0
0
0
1
w
as
ac
h
ie
v
ed
b
y
th
e
in
p
u
t
an
d
o
u
tp
u
t
p
o
w
er
,
e
f
f
icien
c
y
o
f
t
h
e
co
n
v
er
ter
s
h
o
t
to
o
v
er
1
0
0
%; th
is
ca
u
s
ed
a
litt
le
s
lo
w
d
o
w
n
in
th
e
i
n
p
u
t p
o
w
er
.
I
n
g
e
n
er
al,
it c
an
b
e
s
aid
t
h
at
d
esp
ite
th
e
s
u
d
d
en
ch
an
g
es i
n
ir
r
ad
ian
c
e,
t
h
e
ef
f
i
cien
c
y
d
id
n
o
t
g
o
b
elo
w
8
0
% a
s
illu
s
tr
ated
in
F
ig
u
r
e
1
0
.
e.
Fig
u
r
e
10
.
P
&
O
s
i
m
u
latio
n
r
esu
lt a
t
v
ar
iab
le
ir
r
ad
ian
ce
(
a)
ir
r
ad
ian
ce
(
b
)
o
u
tp
u
t v
o
lta
g
e
(
c)
cu
r
r
en
t r
esp
o
n
s
e
(
d
)
o
u
t
p
u
t p
o
w
er
(
e)
ef
f
ic
ien
c
y
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.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
1755
–
1
7
6
4
1762
4
.
3
.
Ca
s
e
3
:
I
NC
w
it
h Co
ns
t
a
n
t
I
rr
a
dia
nce
T
h
e
s
i
m
u
latio
n
o
f
I
NC
al
g
o
r
ith
m
at
co
n
s
ta
n
t
i
n
p
u
t
r
ad
ian
c
e
is
u
s
ed
b
y
t
h
i
s
r
u
n
.
I
t
to
o
k
a
lo
n
g
er
p
er
io
d
o
f
ti
m
e
f
o
r
t
h
e
s
o
u
r
ce
v
o
lta
g
e
to
r
ea
c
h
a
le
v
el
th
at
is
ac
ce
p
tab
le.
T
h
e
tr
ac
k
in
g
o
f
t
h
e
MP
P
b
y
t
h
e
alg
o
r
ith
m
b
e
g
i
n
s
,
b
u
t
d
o
es
n
o
t
ev
en
tu
al
l
y
r
ea
c
h
th
e
MP
P
b
ec
au
s
e
o
f
t
h
e
s
h
o
r
t
d
u
r
atio
n
o
f
t
h
e
r
u
n
.
E
v
e
n
th
o
u
g
h
,
Fi
g
u
r
e
7
.
a
s
h
o
w
s
t
h
at
th
e
tr
ac
k
i
n
g
is
m
o
v
i
n
g
in
t
h
e
r
ig
h
t d
ir
ec
tio
n
ev
e
n
i
t e
v
en
t
u
all
y
r
ea
ch
e
s
t
h
e
MP
P
w
it
h
i
n
t
h
e
n
e
x
t
f
e
w
a
lg
o
r
it
h
m
r
ep
etitio
n
s
,
it
en
d
ed
u
p
n
o
t
d
o
in
g
s
o
.
Fig
u
r
e
7
.
b
s
h
o
w
s
th
at
w
h
ile
MP
P
is
b
ein
g
tr
ac
k
ed
,
th
e
in
d
u
cto
r
cu
r
r
en
t
p
o
s
s
ess
es
f
o
u
r
j
u
m
p
s
i
n
D.
I
t
o
n
l
y
tak
e
s
t
h
is
alg
o
r
it
h
m
f
e
w
iter
atio
n
s
b
ef
o
r
e
it
co
n
v
er
g
e
s
to
th
e
MP
P
w
h
e
n
t
h
e
f
in
al
o
u
tp
u
t
p
o
w
er
is
clo
s
e
to
1
2
0
W
as
illu
s
tr
ated
i
n
Fi
g
u
r
e
7
.
c.
Fig
u
r
e
7
.
d
s
h
o
w
s
t
h
at
t
h
e
e
f
f
icie
n
c
y
f
o
r
a
l
m
o
s
t t
h
r
o
u
g
h
o
u
t th
e
d
u
r
atio
n
o
f
th
e
r
u
n
w
as 9
7
%.
Fig
u
r
e
11
: I
NC
alg
o
r
ith
m
s
i
m
u
latio
n
r
es
u
lt a
t c
o
n
s
ta
n
t ir
r
ad
ian
ce
(
a)
o
u
tp
u
t v
o
ltag
e
(
b
)
cu
r
r
en
t r
esp
o
n
s
e
(
c)
o
u
tp
u
t p
o
w
er
(
d
)
ef
f
icien
c
y
4
.
4
.
Ca
s
e
4
:
I
NC
w
it
h Va
ria
ble Irra
dia
nce.
T
h
e
f
in
al
s
i
m
u
latio
n
o
f
I
NC
alg
o
r
ith
m
d
ea
ls
w
i
th
v
ar
iab
l
e
ir
r
ad
ian
ce
ap
p
lied
to
th
e
s
o
lar
ar
r
ay
.
Fig
u
r
e
1
2
.
a
illu
s
tr
ates
t
h
at
th
e
r
esp
o
n
s
e
o
f
th
e
s
o
u
r
ce
a
n
d
o
u
t
p
u
t
v
o
lta
g
e
i
s
r
estricte
d
s
u
b
s
e
q
u
en
t
f
o
r
ch
a
n
g
in
g
in
t
h
e
ir
r
ad
ian
ce
.
T
h
e
c
u
r
r
en
t r
esp
o
n
s
e
i
s
s
h
o
w
n
i
n
f
ig
u
r
e
1
2
.
b
,
a
ch
an
g
e
a
s
s
ta
ir
s
tep
o
cc
u
r
s
in
t
h
e
f
ig
u
r
e
a
f
ter
8
m
s
ec
.
T
h
e
tr
ac
k
in
g
o
f
t
h
e
MP
P
b
y
th
e
p
o
w
er
o
u
tp
u
t
was
q
u
ite
s
u
cc
es
s
f
u
l
a
s
s
ee
n
i
n
Fi
g
u
r
e
1
2
.
c.
T
h
e
o
cc
u
r
r
en
ce
o
f
t
h
e
lar
g
e
s
t o
s
cil
latio
n
w
as
w
h
e
n
t
h
e
e
f
f
icien
c
y
w
a
s
ca
lc
u
lated
.
Fo
r
th
e
ca
p
ac
ito
r
an
d
in
d
u
cto
r
to
g
et
b
ac
k
to
a
lo
w
er
le
v
el
o
f
o
u
tp
u
t
p
o
w
er
,
m
o
r
e
ti
m
e
i
s
r
eq
u
ir
ed
.
Mo
r
e
s
o
,
th
i
s
al
s
o
ca
u
s
ed
an
i
n
cr
ea
s
e
i
n
t
h
e
ef
f
icien
c
y
o
f
t
h
e
co
n
v
er
ter
s
u
b
s
eq
u
en
t to
th
e
i
n
cr
ea
s
e
in
ir
r
ad
ian
ce
as s
h
o
w
n
in
F
ig
u
r
e
1
2
.
d
.
Fig
u
r
e
12
: I
NC
alg
o
r
ith
m
s
i
m
u
latio
n
r
es
u
lt a
t
v
ar
iab
le
ir
r
ad
ian
ce
(
a)
o
u
tp
u
t v
o
ltag
e
(
b
)
cu
r
r
en
t r
esp
o
n
s
e
(
c)
o
u
tp
u
t p
o
w
er
(
d
)
ef
f
icien
c
y
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:
2088
-
8
694
Tit
le
o
f m
a
n
u
s
crip
t is sh
o
r
t a
n
d
clea
r
,
imp
lies
r
esea
r
ch
r
esu
l
ts
(
F
i
r
s
t A
u
th
o
r
)
1763
5
.
CO
NCLUS
I
O
N
A
d
is
c
u
s
s
io
n
o
f
th
e
MP
PT
w
a
s
d
o
n
e
in
t
h
is
ar
tic
le,
an
d
its
tr
ac
k
in
g
w
a
s
also
s
i
g
n
i
f
ican
tl
y
i
m
p
r
o
v
ed
.
T
h
e
MP
PT
’
s
ab
i
lit
y
to
tr
ac
k
th
e
MP
P
,
en
h
a
n
ce
d
it
s
ab
ilit
y
to
o
p
ti
m
ize
t
h
e
lo
w
e
f
f
icie
n
c
y
o
f
th
e
o
u
tp
u
t
o
f
s
o
lar
ar
r
a
y
s
.
T
h
e
o
v
er
all
s
y
s
t
e
m
ca
n
g
r
ea
tl
y
b
e
i
m
p
r
o
v
ed
w
h
e
n
t
h
e
MP
P
T
ca
p
ab
le
o
f
tr
ac
k
in
g
t
h
e
MP
P
is
i
m
p
r
o
v
ed
b
ec
au
s
e
t
h
e
s
o
lar
ar
r
a
y
is
t
h
e
s
y
s
te
m
s
’
p
o
w
er
s
o
u
r
c
e.
Fu
r
t
h
er
m
o
r
e,
a
d
is
c
u
s
s
io
n
o
n
th
e
s
o
lar
ar
r
ay
m
o
d
el
w
a
s
d
o
n
e,
an
d
t
h
e
s
i
n
g
le
d
io
d
e
m
o
d
el
w
as
u
s
ed
in
d
esig
n
i
n
g
t
h
e
s
o
lar
ar
r
ay
.
A
m
ea
s
u
r
e
m
e
n
t
o
f
th
e
o
u
tp
u
t
cu
r
r
en
t
an
d
v
o
ltag
e
w
as
m
ad
e
p
o
s
s
ib
le
th
r
o
u
g
h
t
h
e
m
o
d
eli
n
g
o
f
t
h
e
s
o
lar
ar
r
ay
u
s
in
g
t
h
e
m
ea
s
u
r
i
n
g
p
a
r
a
m
eter
s
,
o
u
tp
u
t
c
u
r
r
en
t
an
d
v
o
lta
g
e
w
h
ic
h
w
er
e
u
s
ed
i
n
d
r
iv
in
g
th
e
b
u
ck
co
n
v
er
ter
.
An
ex
is
t
in
g
ass
e
m
b
l
y
o
f
d
ata
r
u
n
s
w
a
s
ca
r
r
ied
o
u
t
in
t
w
o
p
h
ases
.
T
h
e
f
ir
s
t
p
h
ase
in
v
o
l
v
ed
u
s
i
n
g
th
e
P
&
O
al
g
o
r
ith
m
a
t
co
n
s
ta
n
t
1
0
0
0
W
/m
2
ir
r
ad
ian
ce
,
a
v
ar
iab
le
s
tep
i
n
ir
r
ad
ian
ce
f
r
o
m
6
0
0
W
/
m
2
to
1
0
0
0
W
/m
2
at
0
:0
8
s
to
0
.
0
1
s
,
in
ad
d
itio
n
to
r
an
d
o
m
v
ar
y
i
n
g
o
f
ir
r
ad
ian
c
e
in
th
e
s
o
lar
ar
r
ay
.
Af
ter
w
ar
d
s
,
th
e
s
a
m
e
th
r
ee
i
n
p
u
t
s
i
g
n
a
ls
w
er
e
u
s
ed
in
te
s
ti
n
g
co
n
s
tan
t
D.
T
h
e
test
in
g
o
f
D
w
a
s
d
o
n
e
as
th
e
b
asis
f
o
r
co
m
p
ar
in
g
it
w
it
h
o
th
er
alg
o
r
ith
m
s
.
L
ast
l
y
,
th
e
test
i
n
g
o
f
th
e
I
NC
w
a
s
p
er
f
o
r
m
ed
,
ev
e
n
th
o
u
g
h
tu
n
in
g
t
h
e
p
ar
a
m
eter
s
f
o
r
th
is
alg
o
r
it
h
m
w
a
s
n
o
t
e
as
y
.
I
t
w
a
s
o
b
s
er
v
ed
th
at
v
er
y
r
ap
id
r
esp
o
n
s
e
to
tr
an
s
ie
n
ts
o
r
u
n
d
er
s
h
o
o
ti
n
g
o
f
th
e
MP
P
w
a
s
ca
u
s
ed
b
y
th
e
a
lg
o
r
ith
m
.
T
h
e
o
p
ti
m
izat
io
n
o
f
th
e
I
NC
al
g
o
r
ith
m
to
co
r
r
esp
o
n
d
w
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p
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m
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icu
lt
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o
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o
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tio
n
.
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n
g
e
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er
al,
th
e
test
r
es
u
lt
s
o
f
th
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P
&
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al
g
o
r
it
h
m
w
er
e
r
elativ
el
y
g
o
o
d
.
T
h
e
r
esp
o
n
s
e
o
f
t
h
e
P
&
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alg
o
r
ith
m
w
as
f
aster
an
d
its
p
er
f
o
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m
an
ce
w
a
s
b
etter
th
an
th
at
o
f
I
NC
,
b
ec
au
s
e
o
f
th
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alg
o
r
ith
m
’
s
ab
ilit
y
to
b
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o
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tim
ized
to
m
ee
t
s
p
ec
i
f
ic
t
i
m
i
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g
r
eq
u
ir
e
m
e
n
ts
.
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h
is
ca
n
b
e
attr
ib
u
ted
to
th
e
co
m
p
lex
n
a
tu
r
e
o
f
t
h
e
co
m
p
u
tatio
n
s
f
o
r
I
NC
al
g
o
r
it
h
m
as
w
el
l
as
o
p
er
atio
n
s
p
ee
d
.
T
h
e
o
p
tim
al
f
u
n
ctio
n
i
n
g
o
f
th
e
al
g
o
r
ith
m
co
u
ld
n
o
t
b
e
ac
cu
r
atel
y
p
r
o
v
id
ed
b
y
t
h
e
r
es
u
lts
o
f
th
e
r
u
n
s
as
a
r
esu
lt
o
f
h
o
w
d
if
f
ic
u
lt
it
is
t
o
o
p
tim
ize
th
e
I
N
C
alg
o
r
ith
m
.
RE
F
E
R
E
NC
E
S
[1
]
A
h
m
e
d
J,
S
a
lam
Z.
A
n
im
p
r
o
v
e
d
p
e
rtu
r
b
a
n
d
o
b
se
rv
e
(P
&
O) m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
(M
P
P
T
)
a
lg
o
rit
h
m
f
o
r
h
ig
h
e
r
e
ff
icie
n
c
y
.
A
p
p
l
En
e
rg
y
2
0
1
5
;1
5
0
:
9
7
–
1
0
8
.
[2
]
Zh
a
o
,
J.
;
Z
h
o
u
,
X
.
;
M
a
,
Y
.
;
L
iu
,
W
.
A
n
o
v
e
l
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
stra
teg
y
b
a
se
d
o
n
o
p
t
im
a
l
v
o
lt
a
g
e
c
o
n
tro
l
f
o
r
p
h
o
t
o
v
o
lt
a
ic sy
ste
m
s
u
n
d
e
r
v
a
riab
le en
v
ir
o
n
m
e
n
tal
c
o
n
d
it
io
n
s.
S
o
l.
En
e
rg
y
2015
,
1
2
2
,
6
4
0
–
6
4
9
.
[3
]
Ku
p
e
rm
a
n
,
A
.
;
A
v
e
rb
u
k
h
,
M
.
;
L
in
e
y
k
in
,
S
.
M
a
x
im
u
m
p
o
we
r
p
o
i
n
t
m
a
tch
in
g
v
e
rsu
s
m
a
x
i
m
u
m
p
o
we
r
p
o
in
t
trac
k
in
g
f
o
r
so
lar g
e
n
e
ra
to
rs.
Re
n
e
w
.
S
u
sta
in
.
E
n
e
rg
y
Re
v
.
2013
,
1
9
,
1
1
–
17.
[4
]
S
e
y
e
d
m
a
h
m
o
u
d
ian
,
M
.
;
M
e
k
h
il
e
f
,
S
.
;
Ra
h
m
a
n
i,
R.
;
Yu
so
f
,
R
.
;
A
s
g
h
a
r
S
h
o
jae
i,
A
.
M
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
o
f
p
a
rti
a
l
sh
a
d
e
d
p
h
o
to
v
o
lt
a
ic
a
rra
y
u
sin
g
a
n
e
v
o
lu
ti
o
n
a
ry
a
lg
o
rit
h
m
:
A
p
a
rti
c
le
s
w
a
r
m
o
p
ti
m
iza
ti
o
n
tec
h
n
i
q
u
e
.
J.
Re
n
e
w
.
S
u
sta
in
.
E
n
e
rg
y
2014
,
6
.
[5
]
S
h
e
ik
,
S
.
;
De
v
a
ra
j,
D.;
Im
th
ias
,
T
.
A
n
o
v
e
l
h
y
b
rid
M
a
x
i
m
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
in
g
T
e
c
h
n
iq
u
e
u
sin
g
P
e
rtu
r
b
&
Ob
se
rv
e
a
lg
o
rit
h
m
a
n
d
L
e
a
rn
in
g
A
u
to
m
a
ta
f
o
r
so
lar
P
V
sy
ste
m
.
E
n
e
rg
y
2
0
1
6
,
1
1
2
,
1
0
9
6
–
1
1
0
6
.
[6
]
M
.
A
b
d
u
r
Ra
z
z
a
k
,
e
t
a
l.
,
,
De
sig
n
o
f
a
G
rid
-
c
o
n
n
e
c
ted
P
h
o
t
o
v
o
lt
a
ic
In
v
e
rter
w
it
h
M
a
x
im
u
m
P
o
w
e
r
P
o
i
n
t
T
ra
c
k
in
g
u
sin
g
P
e
rtu
r
b
a
n
d
Ob
se
rv
e
T
e
c
h
n
iq
u
e
,
I
n
tern
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
S
y
ste
m
(IJP
EDS
)
Vo
l.
7
,
No
.
4
,
De
c
e
m
b
e
r
2
0
1
6
,
p
p
.
1
2
1
2
~
1
2
2
0
.
[7
]
J.
A
h
m
e
d
a
n
d
Z.
S
a
la
m
,
"
A
M
o
d
if
ied
P
&
O
M
a
x
i
m
u
m
P
o
w
e
r
P
o
i
n
t
T
ra
c
k
in
g
M
e
th
o
d
W
it
h
Re
d
u
c
e
d
S
tea
d
y
-
S
tate
Os
c
il
latio
n
a
n
d
Im
p
ro
v
e
d
T
ra
c
k
i
n
g
Eff
icie
n
c
y
,
"
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
S
u
sta
i
n
a
b
le
En
e
rg
y
,
v
o
l.
7
,
n
o
.
4
,
p
p
.
1
5
0
6
-
1
5
1
5
,
2
0
1
6
.
[8
]
Hu
y
n
h
,
D.C.
;
Du
n
n
ig
a
n
,
M
.
W
.
De
v
e
lo
p
m
e
n
t
a
n
d
Co
m
p
a
riso
n
o
f
a
n
Im
p
ro
v
e
d
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
T
ra
c
k
in
g
th
e
M
P
P
o
f
a
S
o
lar
P
V
P
a
n
e
l.
IE
EE
T
ra
n
s.
S
u
sta
in
.
E
n
e
rg
y
2
0
1
6
,
7
,
1
4
2
1
–
1
4
2
9
.
[9
]
Ka
ra
m
i,
N.;
M
o
u
b
a
y
e
d
,
N.;
Ou
tb
ib
,
R.
G
e
n
e
ra
l
re
v
ie
w
a
n
d
c
las
si
f
ica
ti
o
n
o
f
d
iffere
n
t
M
P
P
T
Tec
h
n
iq
u
e
s.
Re
n
e
w
.
S
u
sta
in
.
E
n
e
rg
y
Re
v
.
2
0
1
7
,
6
8
,
1
–
1
8
.
[1
0
]
S
e
y
e
d
m
a
h
m
o
u
d
ian
,
M
.
;
Ho
ra
n
,
B.
;
S
o
o
n
,
T
.
K.;
Ra
h
m
a
n
i,
R.
;
Oo
,
A
.
M
.
T
.
;
M
e
k
h
il
e
f
,
S
.
;
S
t
o
jc
e
v
sk
i,
A
.
S
tate
o
f
th
e
a
rt
a
rti
f
icia
l
in
telli
g
e
n
c
e
-
b
a
se
d
M
P
P
T
tec
h
n
iq
u
e
s
f
o
r
m
it
ig
a
ti
n
g
p
a
rti
a
l
sh
a
d
i
n
g
e
ff
e
c
ts
o
n
P
V
sy
ste
m
s
—
A
re
v
ie
w
.
Re
n
e
w
.
S
u
sta
in
.
E
n
e
rg
y
Re
v
.
2
0
1
6
,
6
4
,
4
3
5
–
4
5
5
.
[1
1
]
M
.
A
.
A
b
d
o
u
rra
z
i
q
a
n
d
M
.
M
a
a
ro
u
f
i,
"
Ex
p
e
ri
m
e
n
tal
V
e
rif
ic
a
ti
o
n
o
f
th
e
M
a
in
M
P
P
T
T
e
c
h
n
iq
u
e
s
f
o
r
P
h
o
t
o
v
o
lt
a
ic
S
y
st
e
m
"
,
In
tern
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
S
y
ste
m
s
(IJP
EDS
)
V
o
l
.
8
,
No
.
1
,
M
a
rc
h
2
0
1
7
,
p
p
.
3
8
4
–
3
9
1
[1
2
]
S
o
o
n
,
T
.
K.;
M
e
k
h
il
e
f
,
S
.
A
f
a
st
-
c
o
n
v
e
r
g
in
g
M
P
P
T
tec
h
n
i
q
u
e
f
o
r
p
h
o
to
v
o
lt
a
ic
sy
ste
m
u
n
d
e
r
f
a
st
-
v
a
r
y
in
g
so
lar
irrad
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n
a
n
d
lo
a
d
re
sista
n
c
e
.
IE
EE
T
ra
n
s.
In
d
.
In
f
o
rm
.
2
0
1
5
,
1
1
,
1
7
6
–
1
8
6
.
[1
3
]
Je
d
a
ri,
M
.
;
G
h
a
re
h
p
e
ti
a
n
,
G
.
;
F
a
th
i,
S
.
H
.
;
V
a
h
i
d
s,
S
.
A
n
a
d
a
p
ti
v
e
In
C
o
n
M
P
P
T
a
lg
o
rit
h
m
c
o
n
sid
e
ri
n
g
irrad
ian
c
e
slo
p
e
trac
k
in
g
f
o
r
P
V
a
p
p
l
ica
ti
o
n
.
In
P
ro
c
e
e
d
in
g
s
o
f
th
e
2
0
1
6
4
th
In
ter
n
a
ti
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n
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l
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y
m
p
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En
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F
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ly
En
e
rg
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p
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ti
o
n
s (E
F
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),
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lg
ra
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e
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e
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1
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1
6
S
e
p
tem
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e
r
2
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1
6
;
p
p
.
1
–
6.
[1
4
]
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
t
a
n
c
e
a
lg
o
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h
m
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p
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s
y
ste
m
u
n
d
e
r
p
a
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a
l
sh
a
d
in
g
c
o
n
d
it
i
o
n
s an
d
lo
a
d
v
a
riatio
n
,
"
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
In
d
u
strial
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
,
2
0
1
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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0
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8
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8
694
I
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t J
P
o
w
E
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&
Dr
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S
y
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t
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Vo
l.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
1755
–
1
7
6
4
1764
[
1
5
]
H.
Isla
m
,
S
.
M
e
k
h
il
e
f
,
N.
M
o
h
a
m
e
d
S
h
a
h
,
T
.
K.
S
o
o
n
,
M
.
S
e
y
e
d
m
a
h
m
o
u
sia
n
,
B.
Ho
ra
n
,
a
n
d
A
.
S
to
jce
v
sk
i.
P
e
rf
o
rm
a
n
c
e
Ev
a
lu
a
ti
o
n
o
f
M
a
x
im
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
in
g
A
p
p
ro
a
c
h
e
s
a
n
d
P
h
o
to
v
o
lt
a
ic
S
y
ste
m
s,
En
e
rg
ies
2
0
1
8
,
1
1
,
3
6
5
.
[1
6
]
A
h
m
e
d
J.
A
b
id
,
F
a
w
z
i
M
.
A
l
-
Na
i
m
a
a
n
d
A
d
n
a
n
Hu
ss
e
in
A
li
,
"
Co
m
p
re
h
e
n
siv
e
M
o
d
e
li
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