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I
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f
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ctu
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co
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s
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id
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[
1
]
.
As
co
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p
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ed
to
w
h
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r
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w
a
b
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ev
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p
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cities
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d
ter
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n
g
s
b
ased
o
n
o
u
r
r
eq
u
ir
e
m
e
n
t
s
[
2
]
.
T
h
e
w
i
n
d
p
o
w
er
g
en
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atio
n
an
d
s
o
lar
p
h
o
to
v
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s
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m
s
ar
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n
o
n
-
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ea
r
ch
ar
ac
ter
is
tic
s
d
u
e
to
th
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v
ar
iab
le
n
atu
r
e
r
eso
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ce
s
o
f
w
in
d
v
elo
cities
a
n
d
s
o
lar
ir
r
a
d
iatio
n
[
3
]
.
Ma
n
y
r
esear
ch
er
s
h
a
v
e
tr
ied
to
e
x
tr
ac
t
th
e
m
a
x
i
m
u
m
p
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f
r
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p
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to
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ltaic
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s
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esig
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in
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co
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ter
s
w
it
h
s
u
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tab
le
co
n
tr
o
l
alg
o
r
it
h
m
s
[
4
]
.
T
h
e
s
ev
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m
a
x
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m
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m
p
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t
tr
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(
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(
I
&
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[
5
]
.
B
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m
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ased
DC
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DC
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d
w
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th
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m
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x
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m
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m
p
o
w
er
at
f
l
u
ct
u
ated
p
o
w
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g
en
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n
[
6
]
.
Var
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s
to
p
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lo
g
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o
f
d
c
-
d
c
co
n
v
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s
ar
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p
r
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p
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s
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to
in
teg
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w
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it
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
9
,
No
.
3
,
Dec
em
b
er
2
0
2
0
:
223
–
244
224
bu
ck
,
b
o
o
s
t
o
r
b
u
ck
-
b
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o
s
t
o
p
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n
s
[
3
]
.
T
h
e
o
v
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all
ef
f
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c
y
o
f
m
o
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t
t
w
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tech
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P
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Ob
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v
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I
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cr
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m
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C
o
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d
u
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ce
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An
an
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o
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ith
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ased
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M
A
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B
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v
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ch
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g
es
i
n
s
o
lar
ir
r
ad
ian
ce
i
s
p
r
esen
t
[
7
]
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
o
lar
P
V
s
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s
te
m
is
v
ar
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r
o
u
g
h
ex
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er
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m
e
n
tal
r
esu
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d
er
p
ar
ticle
s
h
ad
o
w
ed
co
n
d
it
io
n
s
w
it
h
s
er
ies
an
d
p
ar
allel
[
8
]
.
A
co
m
m
o
n
DC
b
u
s
h
a
s
a
m
aj
o
r
ad
v
an
tag
e
f
o
r
co
n
tr
o
llin
g
an
d
p
o
w
er
m
a
n
a
g
e
m
en
t
o
f
th
e
s
o
u
r
ce
s
id
e
as
w
ell
as
lo
ad
s
id
e
co
n
v
er
ter
s
[
9
]
.
C
o
m
m
o
n
l
y
P
I
an
d
P
I
D
co
n
tr
o
ller
ar
e
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s
in
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t
o
co
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DC
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D
C
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an
d
d
c
-
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in
v
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ter
in
th
e
w
i
n
d
-
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lar
-
b
atter
y
s
to
r
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g
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s
y
s
te
m
a
s
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r
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p
o
s
ed
i
n
[
1
0
].
T
h
e
PI
co
n
tr
o
ller
u
s
ed
p
u
ls
e
w
id
th
m
o
d
u
latio
n
(
P
W
M)
b
ased
g
r
id
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co
n
n
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ted
h
y
b
r
id
w
i
n
d
-
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lar
s
y
s
te
m
w
i
t
h
a
s
to
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e
s
y
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te
m
an
d
w
it
h
o
u
t
s
to
r
ag
e
is
p
r
esen
t
in
[
1
1
]
.
A
2
.
5
k
W
s
o
lar
ar
r
ay
s
y
s
te
m
is
d
ev
elo
p
ed
an
d
r
es
u
l
ts
ar
e
o
b
tain
ed
u
n
d
er
p
ar
tial
s
h
ad
ed
co
n
d
itio
n
b
y
u
s
i
n
g
o
n
li
n
e
r
ea
ctin
g
m
ax
i
m
u
m
p
o
w
er
p
o
in
t o
p
ti
m
izatio
n
[
1
2
].
I
n
lar
g
e
-
s
ize
d
is
tr
ib
u
ted
p
o
wer
g
en
er
atio
n
s
y
s
te
m
ca
n
d
ir
ec
tl
y
p
o
w
er
f
ee
d
i
n
to
t
h
e
g
r
id
o
r
lo
ad
w
it
h
o
u
t
a
n
y
s
to
r
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s
y
s
te
m
e
v
en
n
o
n
-
li
n
ea
r
r
eso
u
r
ce
s
b
u
t
t
h
e
s
m
a
ll
s
y
s
te
m
,
th
e
s
to
r
ag
e
s
y
s
te
m
is
r
eq
u
ir
ed
to
f
ee
d
co
n
s
ta
n
t
an
d
u
n
in
ter
r
u
p
ted
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o
w
er
to
th
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g
r
id
o
r
lo
ad
es
p
ec
ially
f
o
r
s
tan
d
alo
n
e
m
o
d
e
[
1
3
]
.
Ma
n
y
to
p
o
lo
g
ies
h
a
v
e
p
r
o
p
o
s
ed
f
o
r
s
tan
d
alo
n
e
w
it
h
a
s
to
r
ag
e
s
y
s
te
m
,
e
s
p
ec
iall
y
f
o
r
r
esid
en
tia
l
ap
p
licatio
n
s
[
1
4
]
.
T
h
e
C
o
-
o
r
d
in
ate
co
n
tr
o
l
tech
n
iq
u
e
s
f
o
r
a
s
y
s
te
m
h
av
i
n
g
w
i
n
d
,
s
o
lar
P
V,
b
atter
y
en
er
g
y
s
to
r
ag
e
s
y
s
te
m
s
ar
e
p
r
o
p
o
s
es
f
o
r
s
i
n
g
le
-
p
h
as
e
g
r
id
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co
n
n
ec
ted
a
n
d
Sta
n
d
alo
n
e
m
o
d
e
o
p
er
atio
n
[
1
5
]
.
A
g
r
id
-
co
n
n
ec
ted
bi
-
d
ir
ec
tio
n
al
co
n
v
er
ter
is
p
r
esen
t
f
o
r
s
tan
d
alo
n
e
o
p
er
at
in
g
m
o
d
e
w
it
h
a
b
atter
y
s
to
r
a
g
e
s
y
s
te
m
to
s
u
p
p
l
y
t
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
to
th
e
lo
ad
[
1
6
]
.
T
h
e
s
in
g
le
-
p
h
ase
tr
an
s
f
o
r
m
er
is
co
n
n
ec
ti
n
g
b
et
w
ee
n
th
e
s
in
g
le
-
p
h
a
s
e
i
n
v
er
ter
a
n
d
lo
ad
o
r
g
r
id
f
o
r
in
ter
li
n
k
s
t
h
e
a
u
to
n
o
m
o
u
s
p
o
w
er
g
en
er
atio
n
s
y
s
te
m
an
d
d
is
tr
ib
u
ted
p
o
w
er
li
n
e
s
.
T
h
e
tr
an
s
f
o
r
m
er
in
ter
li
n
k
ed
g
r
i
d
-
co
n
n
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ted
r
en
e
w
ab
le
en
er
g
y
co
n
v
er
s
io
n
s
y
s
te
m
is
p
r
o
p
o
s
ed
in
[
1
7
]
.
A
s
lid
i
n
g
m
o
d
e
co
n
tr
o
ller
f
o
r
a
n
o
n
-
is
o
l
ated
DC
/D
C
,
b
id
ir
ec
tio
n
al
co
n
v
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ter
i
s
p
r
esen
ted
an
d
co
m
p
ar
ativ
e
s
tu
d
y
w
it
h
P
I
co
n
tr
o
ller
is
d
o
n
e
to
an
al
y
s
i
s
i
n
o
r
d
er
to
d
o
p
er
f
o
r
m
an
ce
an
al
y
s
is
[
1
8
]
.
I
n
g
r
id
-
co
n
n
ec
ted
m
o
d
e,
t
h
e
p
h
ase
s
eq
u
e
n
ce
,
v
o
lta
g
e
an
d
f
r
eq
u
e
n
c
y
s
y
n
ch
r
o
n
izati
o
n
b
et
w
ee
n
p
o
w
er
g
en
er
atio
n
s
y
s
te
m
an
d
d
is
tr
ib
u
ted
g
r
id
lin
e
s
ar
e
n
ee
d
ed
f
o
r
tr
an
s
f
er
p
o
w
er
to
th
e
g
r
id
[
1
9
]
.
T
h
e
p
h
ase
lo
ck
lo
o
p
ed
(
P
L
L
)
alg
o
r
ith
m
b
a
s
ed
g
r
id
s
y
n
ch
r
o
n
izatio
n
h
as b
ee
n
p
r
esen
t in
[
2
0
].
T
h
e
o
b
j
ec
tiv
e
o
f
th
i
s
s
y
s
te
m
is
to
ex
tr
ac
t
th
e
m
a
x
i
m
u
m
p
o
w
e
r
f
r
o
m
t
h
e
w
i
n
d
-
s
o
lar
p
o
w
er
g
en
er
atio
n
s
y
s
te
m
u
s
in
g
t
h
e
MP
PT
tech
n
iq
u
e,
w
h
ic
h
is
p
o
w
er
f
ee
d
in
to
th
e
lo
ca
l
lo
ad
o
r
d
is
tr
ib
u
tio
n
g
r
id
th
r
o
u
g
h
a
s
i
n
g
le
-
p
h
a
s
e
in
v
er
ter
.
I
n
t
h
is
in
v
er
ter
is
o
p
er
atin
g
eit
h
er
s
t
an
d
alo
n
e
m
o
d
e
o
r
g
r
id
-
co
n
n
e
cted
m
o
d
e
d
ep
en
d
s
o
n
th
e
av
ai
lab
ilit
ie
s
o
f
p
o
w
e
r
g
en
er
atio
n
a
n
d
lo
ad
d
em
an
d
s
.
W
h
en
th
e
s
y
s
te
m
i
s
o
p
er
atin
g
at
s
ta
n
d
alo
n
e
m
o
d
e,
t
h
e
g
e
n
er
ated
elec
tr
ica
l
p
o
w
er
i
s
f
lo
w
to
t
h
e
lo
ca
l
l
o
ad
an
d
ex
ce
s
s
p
o
w
er
is
c
h
ar
g
in
g
to
th
e
b
atter
y
s
to
r
ag
e.
I
f
th
e
p
o
w
er
g
e
n
er
ati
o
n
d
ec
r
ea
s
es
in
th
e
s
o
u
r
ce
s
id
e,
th
e
lo
ad
p
o
w
er
is
to
co
m
p
e
n
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ate
b
y
d
is
c
h
ar
g
i
n
g
th
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s
to
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h
e
n
th
e
s
y
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m
is
o
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in
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m
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g
e
n
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tr
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g
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1
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1
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1
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P
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as r
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[
2
2
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T
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e
2
.
Fig
u
r
e
2
.
T
i
p
-
s
p
ee
d
r
atio
v
er
s
u
s
r
o
to
r
co
-
ef
f
icie
n
t p
o
w
er
2
.
1
.
1
.
M
o
delin
g
o
f
per
m
a
ne
n
t
m
a
g
net
s
y
nchro
no
u
s
g
ener
a
t
o
r
T
h
e
P
MSG
w
i
n
d
g
e
n
er
ato
r
is
b
est
s
u
itab
le
f
o
r
th
e
v
ar
iab
le
s
p
ee
d
w
in
d
e
n
er
g
y
co
n
v
er
s
io
n
s
y
s
te
m
s
.
T
h
e
P
MSG
o
u
tp
u
t
p
o
w
er
d
ep
en
d
s
o
n
r
atin
g
o
f
t
h
e
g
en
er
at
o
r
an
d
s
w
ep
t
ar
ea
o
f
th
e
w
i
n
d
b
lad
es,
its
o
u
tp
u
t
v
o
ltag
e
d
ep
en
d
s
o
n
s
tato
r
r
esi
s
tan
ce
,
s
tato
r
cu
r
r
en
t a
n
d
r
ate
o
f
ch
a
n
g
e
o
f
f
l
u
x
li
n
k
a
g
e
b
et
wee
n
s
ta
to
r
an
d
r
o
to
r
as r
ep
r
esen
ted
in
(
3
)
[
2
3
].
R
Y
B
R
Y
B
R
Y
B
s
s
s
s
d
V
R
i
dt
(
3
)
w
h
er
e
V
s
RYB
is
t
h
e
o
u
tp
u
t
v
o
lt
ag
e
o
f
th
e
P
MSG
s
tato
r
w
in
d
in
g
,
R
s
is
th
e
r
esi
s
tan
ce
o
f
t
h
e
s
tato
r
w
i
n
d
i
n
g
s
,
i
s
RYB
is
t
h
e
o
u
tp
u
t
cu
r
r
en
t
v
al
u
es
o
f
th
e
P
MSG
s
tato
r
w
in
d
i
n
g
s
,
ψ
s
RYB
i
s
th
e
f
l
u
x
l
in
k
a
g
e
b
et
w
ee
n
th
e
s
tato
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
9
,
No
.
3
,
Dec
em
b
er
2
0
2
0
:
223
–
244
226
an
d
r
o
to
r
.
T
h
e
th
r
ee
-
p
h
ase
(
R
YB
)
is
tr
an
s
f
o
r
m
ed
in
to
a
d
ir
ec
t
ax
is
(
d
)
an
d
q
u
ad
r
atu
r
e
ax
is
(
q
)
an
d
s
y
n
ch
r
o
n
o
u
s
r
e
f
er
en
ce
f
r
a
m
e
w
it
h
9
0
0
p
h
ase
d
if
f
e
r
e
n
ce
s
as
d
ef
in
ed
as
f
o
llo
w
s
[
2
4
].
s
d
s
s
d
s
d
m
s
q
d
V
R
i
p
dt
(
4
)
s
q
s
s
q
s
q
m
s
d
d
V
R
i
p
dt
(
5
)
w
h
er
e
V
sd
,
i
sd
a
n
d
ψ
sd
ar
e
th
e
d
ir
ec
t
ax
i
s
s
ta
to
r
v
o
ltag
e,
cu
r
r
en
t
a
n
d
f
l
u
x
lin
k
a
g
e
r
esp
ec
tiv
el
y
,
V
sq
,
i
sq
an
d
ψ
sq
ar
e
th
e
q
u
ad
r
atu
r
e
ax
is
s
tato
r
v
o
ltag
e,
c
u
r
r
en
t
an
d
f
l
u
x
l
in
k
a
g
e
r
esp
ec
tiv
el
y
,
P
is
a
n
u
m
b
er
o
f
th
e
p
o
le
in
m
ac
h
in
e,
R
s
i
s
a
r
esis
ta
n
ce
o
f
t
h
e
s
tato
r
w
in
d
i
n
g
,
ω
m
i
s
a
r
o
tatin
g
s
p
ee
d
o
f
t
h
e
r
o
to
r
.
T
h
e
v
alu
e
o
f
th
e
d
-
q
ax
i
s
f
l
u
x
lin
k
a
g
e
d
ep
en
d
s
o
n
th
e
s
ta
to
r
in
d
u
cta
n
ce
(
L
d
=L
q
=L
s
)
a
n
d
f
l
u
x
li
n
k
ag
e
(
ψ
m
)
b
et
w
ee
n
th
e
s
tato
r
an
d
r
o
to
r
as r
ep
r
ese
n
ted
in
(
6
)
an
d
(
7
):
s
d
d
s
d
m
LI
(
6
)
q
q
s
q
LI
(
7
)
E
q
u
atio
n
s
(
6
)
an
d
(
7
)
ar
e
s
u
b
s
u
ited
to
(
4
)
an
d
(
5
)
.
T
h
e
d
-
q
a
x
is
s
t
ato
r
v
o
ltag
e
i
s
r
e
w
r
i
tten
as [
2
5
]
:
s
d
s
s
d
d
s
d
m
q
s
q
d
V
R
i
L
i
p
L
i
dt
(
8
)
s
d
s
s
d
s
s
d
m
s
s
q
d
V
R
i
L
i
p
L
i
dt
(
9
)
s
q
s
s
q
q
s
q
m
s
s
d
m
d
V
R
i
L
i
p
L
i
dt
(
1
0
)
s
q
s
s
q
s
s
q
m
s
s
d
m
d
V
R
i
L
i
p
L
i
dt
(
1
1
)
T
h
e
g
en
er
ated
p
o
w
er
o
f
th
e
P
MSG
as
d
ef
i
n
ed
b
y
t
h
e
co
m
b
i
n
atio
n
o
f
d
ir
ec
t
a
n
d
q
u
ad
r
atu
r
e
p
ar
am
eter
s
o
f
th
e
s
tato
r
.
T
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
o
f
P
MS
G
ca
n
b
e
d
er
iv
ed
f
r
o
m
(
1
2
)
:
3
2
s
e
s
d
s
d
s
q
s
q
P
v
i
v
i
(
1
2
)
Af
ter
s
u
b
-
s
u
i
tin
g
(
9
)
an
d
(
1
1
)
in
to
(
1
2
)
th
e
p
o
w
er
i
s
:
22
22
3
2
sd
sd
sq
sq
se
s
sd
sq
m
sd
sq
sq
sd
R
i
R
i
P
dd
L
i
i
p
i
i
dt
dt
(
1
3
)
T
h
e
f
ir
s
t,
s
ec
o
n
d
an
d
th
ir
d
t
er
m
s
r
ep
r
esen
t
th
e
p
o
w
er
lo
s
s
,
s
to
r
ed
en
er
g
y
in
t
h
e
m
ag
n
etic
f
iel
d
an
d
en
er
g
y
co
n
v
er
s
io
n
f
r
o
m
elec
tr
ical
to
m
ec
h
a
n
ical
en
er
g
y
r
esp
ec
tiv
e
l
y
.
E
lectr
o
m
ag
n
etic
to
r
q
u
e
o
f
th
e
m
ac
h
i
n
e
ca
n
b
e
d
er
iv
ed
f
r
o
m
t
h
e
t
h
ir
d
ter
m
.
3
2
e
m
e
e
s
d
s
q
e
s
q
s
d
P
T
i
i
(
1
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
P
erfo
r
ma
n
ce
ev
a
lu
a
tio
n
a
n
d
Lo
a
d
d
em
a
n
d
m
a
n
a
g
eme
n
t
…
(
K
.
M.
V
en
ka
ta
ch
a
la
m)
227
T
h
e
r
elatio
n
b
etw
ee
n
th
e
m
ec
h
an
ica
l
an
d
elec
tr
ical
v
elo
cit
y
o
f
th
e
m
ac
h
in
e
d
ep
en
d
s
o
n
t
h
e
n
u
m
b
er
o
f
p
o
le
p
air
s
o
f
th
e
m
ac
h
i
n
e
as
p
r
esen
ted
in
(
1
5
)
.
em
p
(
1
5
)
3
2
e
m
s
q
d
q
s
d
s
q
T
p
i
L
L
i
i
(
1
6
)
T
h
e
f
in
a
l
e
x
p
r
ess
io
n
o
f
t
h
e
e
l
ec
tr
o
m
a
g
n
etic
to
r
q
u
e
is
r
ep
r
es
en
ted
i
n
(
1
6
)
.
Her
e
ca
n
o
b
s
er
v
e
t
h
e
t
w
o
d
i
f
f
e
r
en
t
t
o
r
q
u
e
e
q
u
at
i
o
n
t
e
r
m
s
;
th
e
f
i
r
s
t
te
r
m
is
a
s
y
n
ch
r
o
n
o
u
s
t
o
r
q
u
e
d
u
e
t
o
t
h
e
f
lu
x
l
in
k
ag
e
o
f
th
e
p
e
r
m
a
n
e
n
t
ma
g
n
et,
th
e
s
ec
o
n
d
ter
m
is
a
r
elu
ctan
ce
to
r
q
u
e
d
u
e
to
th
e
d
if
f
er
e
n
ce
b
et
w
ee
n
d
ir
ec
t
(
d
)
an
d
q
u
ad
r
atu
r
e
(
q
)
ax
is
.
I
n
t
h
is
to
r
q
u
e
eq
u
atio
n
,
t
h
e
r
elu
cta
n
ce
to
r
q
u
e
is
to
b
e
c
o
n
s
id
er
ed
as
ze
r
o
an
d
o
n
ly
s
y
n
ch
r
o
n
o
u
s
to
r
q
u
e
is
p
r
esen
ted
b
ec
au
s
e
o
f
t
h
e
P
MSG
m
ac
h
in
e
h
as a
s
u
r
f
ac
e
m
o
u
n
ted
p
er
m
an
e
n
t
m
ag
n
etic
r
o
to
r
[
2
6
].
3
2
e
m
s
q
T
p
i
(
1
7
)
2
.
2
.
So
la
r
ph
o
t
o
v
o
lt
a
ic
a
rr
a
y
s
y
s
t
e
m
T
h
e
SP
V
ar
r
ay
s
y
s
te
m
i
s
to
co
n
v
er
t
th
e
s
o
lar
ir
r
ad
iatio
n
in
to
DC
elec
tr
ical
en
er
g
y
.
T
h
e
r
atin
g
o
f
th
e
s
o
lar
s
y
s
te
m
d
ep
en
d
s
o
n
th
e
n
u
m
b
er
o
f
p
a
n
els
th
at
a
r
e
co
n
n
ec
ted
i
n
ar
r
a
y
a
n
d
r
at
in
g
o
f
ea
c
h
p
an
e
l.
T
h
e
o
u
tp
u
t
v
o
ltag
e
a
n
d
cu
r
r
en
t
v
al
u
es
ar
e
d
esire
d
b
y
s
er
ies
an
d
p
ar
allel
co
n
n
ec
tio
n
s
o
f
th
e
s
o
lar
p
an
els
a
s
p
r
esen
ted
in
1
8
.
m
a
x
m
a
x
m
a
x
m
a
x
DC
se
rie
s
P
DC
pa
ra
ll
e
l
P
V
N
V
I
N
I
(
1
8
)
w
h
er
e
V
m
a
x
DC,
I
m
ax
DC
m
ax
i
m
u
m
o
u
tp
u
t
v
o
lta
g
e
an
d
cu
r
r
en
t
v
al
u
es
o
f
th
e
SP
V
ar
r
ay
,
V
m
ax
P,
I
m
ax
P
ar
e
m
ax
i
m
u
m
o
u
tp
u
t
v
o
lta
g
e
a
n
d
cu
r
r
en
t
v
alu
e
s
o
f
ea
c
h
p
an
el.
Sp
ec
if
icatio
n
d
etails
o
f
th
e
W
E
C
s
ca
n
b
e
s
ee
n
in
T
ab
le
1
.
T
ab
le
1
.
Sp
ec
if
icatio
n
d
etails
o
f
th
e
W
E
C
s
P
a
r
a
me
t
e
r
V
a
l
u
e
M
o
d
e
l
:
W
h
i
sp
e
r
2
0
0
R
o
t
a
t
i
o
n
a
x
i
s
:
H
o
r
i
z
o
n
t
a
l
O
r
i
e
n
t
a
t
i
o
n
&
r
o
t
a
t
i
o
n
d
i
r
e
c
t
i
o
n
:
L
o
o
k
i
n
g
u
p
w
i
n
d
&
c
l
o
c
k
w
i
se
N
u
mb
e
r
o
f
b
l
a
d
e
s
:
3
R
o
t
o
r
d
i
a
me
t
e
r
:
2
.
7
2
m
W
e
i
g
h
t
:
3
0
k
g
R
a
t
e
d
p
o
w
e
r
:
1
0
0
0
W
R
a
t
e
d
o
u
t
p
u
t
v
o
l
t
a
g
e
:
4
8
V
(
A
C
)
En
e
r
g
y
p
r
o
d
u
c
e
d
:
2
0
0
k
w
h
/
mo
n
t
h
a
t
5
.
4
m
/
s
R
a
t
e
d
w
i
n
d
s
p
e
e
d
:
1
1
.
6
m/
s
t
o
1
3
m/
s
S
t
a
r
t
u
p
/
c
u
t
i
n
w
i
n
d
s
p
e
e
d
:
2
.
7
m
/
s
–
3
.
1
m
/
s
C
u
t
o
u
t
w
i
n
d
s
p
e
e
d
:
1
6
t
o
1
8
m/
s
S
u
r
v
i
v
a
l
w
i
n
d
s
p
e
e
d
:
5
5
m/
s
S
w
e
p
t
a
r
e
a
:
5
.
8
me
t
e
r
sq
u
a
r
e
B
l
a
d
e
p
i
t
c
h
:
F
i
x
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d
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l
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i
l
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m
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r
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:
F
r
e
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.
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.
1
.
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o
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SP
V
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le
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as
ic
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it
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t
in
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th
e
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d
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ar
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esis
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s
,
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ti
-
p
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e,
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r
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en
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ce
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s
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p
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i
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alen
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
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8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
9
,
No
.
3
,
Dec
em
b
er
2
0
2
0
:
223
–
244
228
cir
cu
it
o
f
t
h
e
s
o
lar
p
h
o
to
v
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c
ce
ll
is
s
h
o
w
n
in
Fig
u
r
e
3
.
I
-
V
ch
ar
ac
ter
is
tic
eq
u
at
io
n
o
f
a
n
SP
V
ce
ll
is
g
i
v
e
n
b
y
[
2
7
]:
()
0
1
pv
s
pv
q
V
R
I
pv
s
pv
A
K
T
pv
ph
sh
V
R
I
I
I
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e
R
(
1
9
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w
h
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ph
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a
p
h
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r
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en
t
b
y
t
h
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n
cid
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o
lar
ir
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ad
iatio
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I
0
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io
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r
ev
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s
e
s
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r
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r
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ch
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sh
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se
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t
a
n
d
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esis
ta
n
ce
r
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tiv
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I
pv
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s
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o
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pv
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t
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o
lar
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ll,
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tr
o
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d
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e
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o
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a
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ta
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t (
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J
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r
esp
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tiv
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1
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s
pv
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R
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N
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T
pv
sc
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e
(
2
0
)
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v
s
p
v
sh
V
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is
o
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itted
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o
m
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0
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e
s
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s
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ed
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b
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te
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d
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th
e
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-
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cu
r
v
e
i
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h
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io
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cti
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ph
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lace
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s
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N
sc
i
s
a
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tal
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m
b
er
o
f
th
e
s
o
lar
ce
l
ls
co
n
n
ec
ted
in
SP
V
p
an
el.
T
h
e
p
h
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r
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en
t
(
I
ph
=0
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is
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r
o
u
n
d
er
o
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en
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it
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n
d
itio
n
s
.
He
n
ce
,
in
(
2
0
)
w
ill
b
e
w
r
itten
a
s
[
2
8
]
:
0
()
l
n
1
0
11
p
h
s
p
h
sc
oc
V
R
I
I
I
V
p
v
s
c
sc
I
I
I
e
I
(
2
1
)
w
h
er
e
V
OC
i
s
o
p
en
cir
cu
it
v
o
ltag
e
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
.
Sp
ec
if
icatio
n
d
etails
o
f
t
h
e
s
o
lar
p
h
o
to
v
o
ltaic
p
an
el
ca
n
b
e
s
ee
n
i
n
T
ab
le
2
.
Fig
u
r
e
3
.
E
q
u
iv
ale
n
t c
ir
cu
it o
f
a
s
o
lar
p
h
o
to
v
o
ltaic
ce
ll
T
ab
le
2
.
Sp
ec
if
icatio
n
d
etails
o
f
th
e
s
o
lar
p
h
o
to
v
o
ltaic
p
a
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e
l
P
a
r
a
me
t
e
r
V
a
l
u
e
M
o
d
e
l
:
EF
S
1
2
2
5
0
M
C
7
2
C
e
l
l
t
y
p
e
:
M
u
l
t
i
c
r
y
st
a
l
l
i
n
e
S
o
l
a
r
c
e
l
l
p
e
r
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d
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l
e
:
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2
C
e
l
l
M
a
x
i
m
u
m
p
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r
(
P
max
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:
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5
0
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p
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p
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n
c
i
r
c
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i
t
v
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e
(
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:
4
4
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6
4
V
S
h
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r
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c
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r
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n
t
(
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sc
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:
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.
2
7
A
M
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x
i
m
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v
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(
V
mp
)
:
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r
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t
(
I
mp
)
:
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.
9
5
A
M
a
x
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a
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5
3
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
P
erfo
r
ma
n
ce
ev
a
lu
a
tio
n
a
n
d
Lo
a
d
d
em
a
n
d
m
a
n
a
g
eme
n
t
…
(
K
.
M.
V
en
ka
ta
ch
a
la
m)
229
2
.
3
.
B
a
t
t
er
y
ener
g
y
s
t
o
ra
g
e
s
y
s
t
e
m
T
h
e
b
atter
y
s
to
r
ag
e
s
y
s
te
m
i
s
a
m
aj
o
r
r
o
le
f
o
r
s
m
all
s
ca
le
r
en
e
w
ab
le
p
o
w
er
g
e
n
er
atio
n
s
y
s
te
m
to
f
ee
d
u
n
i
n
ter
r
u
p
ted
p
o
w
er
s
u
p
p
ly
to
s
tan
d
alo
n
e
lo
ad
s
w
i
t
h
o
u
t
an
y
f
l
u
ct
u
atio
n
s
.
T
h
e
f
lu
ct
u
ated
p
o
w
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is
g
en
er
ati
n
g
f
r
o
m
th
e
w
i
n
d
an
d
s
o
lar
s
y
s
te
m
is
ch
ar
g
i
n
g
to
t
h
e
b
atter
y
.
W
h
en
th
e
lo
ad
d
em
an
d
in
cr
ea
s
es
m
o
r
e
th
an
th
e
s
o
u
r
ce
p
o
w
er
,
t
h
e
b
at
ter
y
is
d
i
s
ch
ar
g
in
g
to
co
m
p
e
n
s
ate
lo
ad
d
e
m
an
d
.
T
h
e
ch
ar
g
i
n
g
a
n
d
d
is
c
h
ar
g
i
n
g
p
r
o
ce
s
s
o
f
th
e
B
E
SS
is
d
i
v
id
ed
b
y
f
o
u
r
ca
s
es d
u
e
to
a
v
ailab
i
lit
y
o
f
w
i
n
d
an
d
s
o
lar
p
o
w
er
g
en
er
atio
n
as
:
‒
C
ase
1
:
(
)
(
)
(
)
s
o
l
a
r
w
i
n
d
L
o
a
d
P
t
P
t
P
t
(
2
2
)
I
n
th
is
co
n
d
it
io
n
,
th
e
co
m
b
in
ed
w
i
n
d
-
s
o
lar
s
y
s
te
m
g
e
n
er
ated
elec
tr
ical
p
o
w
er
is
eq
u
al
to
r
eq
u
ir
e
m
en
ts
o
f
lo
ad
s
.
T
h
e
b
atter
y
s
to
r
ag
e
s
y
s
te
m
ca
n
n
o
t
b
e
en
ter
ed
to
p
ictu
r
e
f
o
r
th
e
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
p
r
o
ce
s
s
,
h
er
e
th
e
s
to
r
ag
e
s
y
s
te
m
w
ill ac
t a
s
a
h
y
b
r
id
DC
b
u
s
.
‒
C
ase
2
:
(
)
(
)
(
)
s
o
l
a
r
w
i
n
d
L
o
a
d
P
t
P
t
P
t
(
2
3
)
I
n
th
is
co
n
d
itio
n
t
h
e
s
o
u
r
ce
p
o
w
er
is
m
o
r
e
t
h
an
th
e
lo
ad
d
em
an
d
s
,
its
m
ee
t
to
t
h
e
lo
ad
r
eq
u
ir
e
m
e
n
ts
an
d
ex
ce
s
s
p
o
w
er
is
a
c
h
ar
g
e
t
o
a
b
atter
y
.
‒
C
ase
3
:
(
)
(
)
(
)
s
o
l
a
r
w
i
n
d
L
o
a
d
P
t
P
t
P
t
(
2
4
)
I
n
th
i
s
co
n
d
itio
n
t
h
e
s
o
u
r
ce
p
o
w
er
i
s
u
n
ab
le
to
m
ee
t t
h
e
lo
ad
d
em
a
n
d
s
a
n
d
t
h
e
b
atter
y
s
to
r
ag
e
s
y
s
te
m
w
il
l d
eliv
er
p
o
w
er
to
th
e
lo
ad
to
s
atis
f
y
i
n
g
th
e
lo
ad
r
eq
u
ir
e
m
en
ts
.
‒
C
ase
4
:
(
)
(
)
(
)
(
)
s
o
l
a
r
w
i
n
d
B
a
t
t
e
r
y
L
o
a
d
P
t
P
t
P
t
P
t
(
2
5
)
T
h
e
lo
ad
d
em
a
n
d
k
ee
p
s
o
n
in
cr
ea
s
in
g
an
d
t
h
e
av
ail
ab
ilit
y
o
f
s
o
u
r
ce
p
o
w
er
is
to
o
lo
w
.
Her
e
th
e
s
to
r
ag
e
s
y
s
te
m
w
ill
n
o
t
ab
le
to
m
ee
t
th
e
lo
n
g
d
u
r
atio
n
o
f
lo
ad
r
eq
u
ir
em
e
n
t
s
.
I
n
th
is
s
ce
n
ar
io
,
th
e
p
o
w
er
f
lo
w
s
f
r
o
m
t
h
e
g
r
id
to
lo
ad
an
d
b
atter
y
.
Sp
ec
i
f
ica
tio
n
d
etails
o
f
t
h
e
b
atter
y
e
n
er
g
y
s
to
r
ag
e
s
y
s
te
m
ca
n
b
e
s
ee
n
i
n
T
ab
le
3
.
T
ab
le
3
.
Sp
ec
if
icatio
n
d
etails
o
f
b
atter
y
en
er
g
y
s
to
r
ag
e
s
y
s
te
m
P
a
r
a
me
t
e
r
V
a
l
u
e
C
a
p
a
c
i
t
y
:
8
0
0
A
h
(
e
a
c
h
o
n
e
r
a
t
i
n
g
1
2
V
,
1
0
0
A
h
)
B
a
t
t
e
r
y
n
o
mi
n
a
l
v
o
l
t
a
g
e
:
4
8
V
G
r
i
d
c
h
a
r
g
i
n
g
c
u
r
r
e
n
t
:
3
t
o
1
6
A
D
C
G
r
i
d
c
h
a
r
g
e
r
c
a
p
a
c
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t
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k
W
r
a
t
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n
g
)
:
0
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0
%
G
r
i
d
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h
a
r
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c
o
n
t
r
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l
:
C
o
n
st
a
n
t
v
o
l
t
a
g
e
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c
o
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s
t
a
n
t
c
u
r
r
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n
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B
a
t
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y
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y
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:
C
o
mp
a
t
i
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l
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t
u
b
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l
a
r
/
S
M
F
l
e
a
d
a
c
i
d
3.
CO
NT
RO
L
T
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CH
NI
Q
U
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S
F
O
R
WI
ND
-
SO
L
AR
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B
AT
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E
NE
R
G
Y
ST
O
RA
G
E
SYST
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M
T
h
e
co
n
tr
o
llin
g
tech
n
iq
u
es o
f
p
o
w
er
elec
tr
o
n
ics
co
n
v
er
ter
s
f
o
r
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-
s
id
e
w
in
d
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s
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lar
e
n
er
g
y
s
y
s
te
m
an
d
lo
ad
s
id
e
o
f
VSI
a
s
d
escr
i
b
ed
in
t
h
is
s
es
s
io
n
.
T
h
e
co
n
tr
o
ller
is
d
esi
g
n
ed
to
ex
tr
ac
t
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
s
o
u
r
ce
s
an
d
it
s
f
ee
d
to
th
e
l
o
ad
o
r
g
r
id
as
p
er
g
r
id
c
o
d
e
s
tan
d
ar
d
f
r
eq
u
en
c
y
,
v
o
lta
g
e
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d
p
o
w
er
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u
alit
y
.
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h
e
s
y
s
te
m
ca
n
o
p
er
ate
s
tan
d
alo
n
e
o
r
g
r
id
-
co
n
n
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ted
m
o
d
e,
w
h
ic
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s
d
ep
en
d
in
g
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n
t
h
e
g
e
n
er
ated
s
o
u
r
ce
p
o
w
er
an
d
p
o
w
er
d
e
m
a
n
d
o
f
th
e
lo
ad
s
id
e.
3
.
1
.
Co
ntr
o
l t
ec
hn
iqu
e
f
o
r
DC
-
DC
co
nv
er
t
er
1
T
h
e
M
P
PT
tr
ac
k
s
th
e
m
ax
i
m
u
m
p
o
w
er
s
f
r
o
m
th
e
P
MSG
w
i
n
d
en
er
g
y
co
n
v
er
s
io
n
s
y
s
te
m
u
s
in
g
a
s
i
m
p
le
p
er
tu
r
b
an
d
o
b
s
er
v
e
th
e
m
et
h
o
d
b
y
s
e
n
s
i
n
g
th
e
DC
b
u
s
cu
r
r
en
t.
T
o
m
ea
s
u
r
ed
an
d
co
m
p
ar
in
g
th
e
p
r
ev
io
u
s
DC
b
u
s
c
u
r
r
en
t
I
dc
(k
-
1
)
an
d
p
r
esen
t
d
c
-
b
u
s
c
u
r
r
en
t I
dc
(
k
)
.
I
f
t
h
e
p
r
ese
n
t
DC
b
u
s
c
u
r
r
en
t
I
dc
(
k
)
i
s
m
o
r
e
t
h
a
n
t
h
e
p
r
ev
io
u
s
DC
b
u
s
c
u
r
r
en
t
I
dc
(k
-
1
)
,
th
e
p
er
tu
r
b
atio
n
is
i
n
cr
ea
s
ed
u
p
to
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t.
I
f
t
h
e
p
r
esen
t
DC
b
u
s
c
u
r
r
en
t
I
dc
(
k
)
is
less
t
h
an
th
e
p
r
ev
io
u
s
DC
b
u
s
cu
r
r
e
n
t
I
dc
(k
-
1
)
,
t
h
e
p
er
tu
r
b
atio
n
h
as
to
d
ec
r
ea
s
e
as
m
en
tio
n
ed
in
t
h
e
f
lo
w
c
h
ar
t
i
n
Fi
g
u
r
e
4
.
T
h
e
D
C
b
u
s
cu
r
r
e
n
t
is
p
o
s
iti
v
e
w
h
e
n
th
e
P
MSG
p
o
w
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
9
,
No
.
3
,
Dec
em
b
er
2
0
2
0
:
223
–
244
230
av
ailab
le
in
ex
ce
s
s
to
a
b
atter
y
a
n
d
f
ed
to
th
e
g
r
id
.
W
h
en
th
e
w
i
n
d
p
o
w
er
is
n
o
t
s
u
f
f
icie
n
t
f
ee
t
to
g
r
id
,
th
e
d
ef
icit
p
o
w
er
is
f
ed
f
r
o
m
th
e
b
atter
y
b
y
DC
b
u
s
cu
r
r
en
t
is
n
eg
ati
v
e.
T
h
e
DC
b
u
s
v
o
ltag
e
(
Vd
c
-
b
u
s
)
is
co
m
p
ar
ed
w
ith
r
e
f
er
en
ce
d
c
v
o
ltag
e
a
n
d
f
ed
to
th
e
P
I
c
o
n
tr
o
ller
.
T
h
e
er
r
o
r
s
ig
n
al
o
f
t
h
e
P
I
co
n
tr
o
ller
is
co
m
p
ar
ed
w
i
th
ca
r
r
ier
w
av
e
f
o
r
m
an
d
to
p
r
o
d
u
ce
th
e
d
u
ty
c
y
cl
e
o
f
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
(
P
W
M)
g
ate
s
ig
n
al
is
co
n
tr
o
l
T
HE
DC
-
DC
co
n
v
er
ter
s
w
itch
e
s
as
s
h
o
w
n
i
n
Fi
g
u
r
e
5
.
Fig
u
r
e
4
.
MP
PT
alg
o
r
ith
m
f
lo
w
c
h
ar
t f
o
r
W
E
C
s
Fig
u
r
e
5
.
C
o
n
tr
o
l c
ir
cu
it
f
o
r
DC
-
DC
co
n
v
er
ter
1
3
.
2
.
Co
ntr
o
l t
ec
hn
iqu
e
f
o
r
DC
-
DC
co
nv
er
t
er
2
I
n
th
i
s
p
r
esen
t
p
ap
er
,
th
e
d
c
-
d
c
co
n
v
er
ter
i
s
co
n
tr
o
lled
u
s
in
g
t
h
e
P
&
O
al
g
o
r
ith
m
b
as
ed
MPPT
th
r
o
u
g
h
a
P
I
c
o
n
tr
o
ller
.
I
ts
o
b
jectiv
e
is
to
m
a
in
ta
in
th
e
d
esire
d
o
u
tp
u
t
v
o
ltag
e
o
f
s
o
lar
th
e
p
h
o
to
v
o
ltaic
s
y
s
te
m
b
y
co
n
tr
o
llin
g
t
h
e
d
c
-
d
c
co
n
v
er
ter
at
v
ar
iab
le
i
r
r
ad
iatio
n
an
d
te
m
p
er
atu
r
e
o
f
t
h
e
SP
V.
T
h
e
MP
PT
is
s
en
s
ed
g
en
er
ated
o
u
tp
u
t
v
o
ltag
e
a
n
d
cu
r
r
en
t
an
d
co
m
p
ar
e
w
it
h
r
ef
er
en
ce
d
esire
d
v
o
ltag
e
v
al
u
e
o
f
th
e
b
atter
y
as
s
h
o
w
n
i
n
Fig
u
r
e
6
.
T
h
e
b
u
ck
o
r
b
o
o
s
t o
p
er
atin
g
m
o
d
e
o
f
th
e
d
c
-
d
c
c
o
n
v
er
ter
d
ep
en
d
s
o
n
t
h
e
P
W
M
d
u
t
y
c
y
cle
o
f
th
e
DC
-
DC
co
n
v
er
ter
,
w
h
ich
is
g
en
er
ated
f
r
o
m
MP
PT
.
W
h
en
th
e
SP
V
p
o
w
er
g
en
er
atio
n
is
in
cr
ea
s
i
n
g
an
d
d
ec
r
ea
s
in
g
d
u
e
to
th
e
v
ar
iatio
n
o
f
ir
r
ad
iatio
n
,
t
h
e
d
u
t
y
c
y
cle
o
f
t
h
e
DC
-
D
C
co
n
v
er
t
er
w
ill
d
ec
r
ea
s
e
o
r
in
cr
ea
s
e
b
ec
au
s
e
o
f
t
h
e
v
ar
ia
tio
n
o
f
th
e
o
u
tp
u
t
v
o
lta
g
e
o
f
th
e
SP
V.
MPPT
alg
o
r
ith
m
f
lo
w
ch
ar
t
f
o
r
SP
V
s
y
s
te
m
i
s
s
h
o
w
n
i
n
Fi
g
u
r
e
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
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8792
P
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n
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ev
a
lu
a
tio
n
a
n
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a
d
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em
a
n
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m
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n
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g
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n
t
…
(
K
.
M.
V
en
ka
ta
ch
a
la
m)
231
Fig
u
r
e
6
.
C
o
n
tr
o
l c
ir
cu
it
f
o
r
DC
-
DC
co
n
v
er
ter
2
Fig
u
r
e
7
.
MP
PT
alg
o
r
ith
m
f
lo
w
c
h
ar
t f
o
r
SP
V
s
y
s
te
m
T
h
e
to
tal
g
en
er
ated
p
o
w
er
f
r
o
m
th
e
SP
V
s
y
s
te
m
is
ex
p
r
es
s
e
d
as
:
p
v
p
v
p
v
P
V
I
(2
6
)
w
h
er
e,
V
pv
,
I
pv
ar
e
th
e
to
tal
g
en
er
ated
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t
o
f
th
e
SP
V
s
y
s
te
m
.
T
h
e
P
&
O
alg
o
r
ith
m
f
o
r
m
ax
i
m
u
m
p
o
w
er
p
o
in
t tr
ac
k
er
f
o
llo
w
s
t
h
e
p
o
w
er
v
ar
iatio
n
o
f
th
e
SP
V;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
9
,
No
.
3
,
Dec
em
b
er
2
0
2
0
:
223
–
244
232
p
v
p
v
p
v
p
v
p
v
d
P
d
V
I
V
d
I
(2
7
)
T
h
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
o
f
th
e
MP
PT
w
it
h
r
esp
ec
t
to
th
e
v
ar
iatio
n
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
at
v
ar
iab
le
ir
r
ad
iatio
n
is
:
0
p
v
p
v
p
v
p
v
p
v
p
v
d
P
d
I
IV
d
V
d
V
(2
8
)
T
h
e
P
&
O
alg
o
r
ith
m
o
p
er
ati
n
g
d
etails ar
e
r
ep
r
esen
ted
in
(
4
)
an
d
th
e
f
lo
w
ch
ar
t o
f
Fig
u
r
e
7
;
(
)
(
1
)
p
v
p
v
V
k
V
k
V
(
2
9
)
W
h
en
(
)
(
1
)
&
(
)
(
1
)
(
)
(
1
)
&
(
)
(
1
)
pv
pv
pv
pv
pv
pv
pv
pv
P
k
P
k
V
k
V
k
P
k
P
k
V
k
V
k
,
(
)
(
1
)
p
v
p
v
V
k
V
k
V
(
3
0
)
W
h
en
(
)
(
1
)
&
(
)
(
1
)
(
)
(
1
)
&
(
)
(
1
)
pv
pv
pv
pv
pv
pv
pv
pv
P
k
P
k
V
k
V
k
P
k
P
k
V
k
V
k
,
w
h
er
e
V
pv
(
k
)
is
th
e
p
r
esen
t
o
u
tp
u
t
v
o
ltag
e
o
f
t
h
e
SP
V,
V
pv
(k
-
1
)
is
th
e
p
r
ev
io
u
s
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
SP
V,
P
pv
(
k
)
is
th
e
p
r
esen
t
g
en
er
ated
p
o
w
er
o
f
th
e
SP
V,
P
pv
(k
-
1
)
is
th
e
p
r
ev
io
u
s
l
y
g
en
er
ated
p
o
w
er
o
f
th
e
SP
V.
3
.
3
.
Co
ntr
o
l t
ec
hn
iqu
e
f
o
r
bi
-
direct
io
na
l c
o
nv
er
t
er
T
h
e
B
E
SS
s
y
s
te
m
co
n
s
is
t
in
g
o
f
b
atter
y
w
it
h
a
b
i
-
d
ir
ec
tio
n
a
l
co
n
v
er
ter
is
co
n
n
ec
ted
to
th
e
co
m
m
o
n
DC
b
u
s
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
b
i
-
d
ir
ec
tio
n
al
co
n
v
er
ter
is
to
m
ai
n
tai
n
th
e
co
n
s
ta
n
t
DC
v
o
lt
ag
e
in
co
m
m
o
n
DC
b
u
s
w
it
h
h
elp
o
f
b
atter
y
at
f
l
u
ctu
a
ted
g
e
n
er
ated
p
o
w
er
f
r
o
m
w
i
n
d
a
n
d
s
o
lar
s
o
u
r
ce
s
an
d
lo
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