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201
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
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Vo
l.
6
,
No
.
6
,
Dec
em
b
er
2
0
1
6
:
2
6
2
9
–
2
6
4
2
2630
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ltag
e,
c
u
r
r
en
t
a
n
d
v
o
lta
g
e
h
ar
m
o
n
ics,
a
s
w
ell
a
s
in
p
u
t
p
o
w
er
f
ac
to
r
.
I
t
ca
u
s
ed
b
y
tr
ac
k
i
n
g
o
f
MP
PT
w
h
ic
h
is
in
f
l
u
e
n
ce
d
b
y
n
o
n
-
l
in
ea
r
ch
ar
a
cter
is
tic
p
an
e
l
d
ep
en
d
s
u
p
o
n
v
ar
y
i
n
g
e
n
v
ir
o
n
m
en
ta
l
co
n
d
itio
n
s
u
ch
a
s
te
m
p
er
atu
r
e
an
d
s
o
lar
ir
r
ad
ian
ce
.
A
n
o
t
h
er
ca
u
s
e
is
p
r
esen
ce
o
f
co
n
v
er
ter
as
a
m
ed
iu
m
to
tr
an
s
f
o
r
m
DC
i
n
to
AC
v
o
lta
g
e
f
o
r
(
o
n
e
s
ta
g
e
co
n
v
er
ter
)
a
s
w
el
l
a
s
D
C
i
n
t
o
D
C
a
n
d
D
C
i
n
to
AC
v
o
lta
g
e
(
t
w
o
s
ta
g
e
co
n
v
er
ter
)
.
T
h
e
u
s
in
g
o
f
m
u
ltil
e
v
el
in
v
er
t
er
b
ased
s
h
u
n
t
ac
ti
v
e
p
o
w
er
f
i
lter
(
SA
P
F)
to
im
p
r
o
v
e
p
o
w
er
q
u
alit
y
d
u
e
to
P
V
g
en
er
ato
r
s
y
s
te
m
co
n
n
ec
ted
to
g
r
id
h
av
e
b
ee
n
i
m
p
le
m
e
n
ted
[
3
]
.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
ca
n
ef
f
icie
n
tl
y
b
e
u
s
ed
f
o
r
r
ea
ctiv
e
p
o
w
er
co
m
p
en
s
at
io
n
an
d
r
ed
u
cin
g
s
o
u
r
ce
cu
r
r
en
t
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
u
p
to
0
.
5
7
%.
T
h
e
s
y
s
te
m
is
also
ca
p
ab
le
o
f
d
eliv
er
i
n
g
ac
ti
v
e
p
o
w
er
w
it
h
u
n
it
y
p
o
w
er
f
ac
to
r
to
g
r
id
.
T
h
e
w
ea
k
n
e
s
s
o
f
it
w
er
e
n
o
t d
is
c
u
s
s
i
n
g
i
m
p
r
o
v
e
m
en
t h
ar
m
o
n
ic
v
o
lta
g
e
an
d
P
V
g
en
er
ato
r
co
n
n
ec
t
ed
to
g
r
id
o
n
l
y
o
n
e.
An
al
y
s
is
o
f
i
m
p
ac
t
o
f
P
V
g
e
n
er
ato
r
co
n
n
ec
ted
to
g
r
id
co
n
s
id
er
in
g
p
o
w
er
q
u
alit
y
(
h
ar
m
o
n
ic
c
u
r
r
en
t)
o
n
th
e
d
is
tr
ib
u
tio
n
alr
ea
d
y
p
er
f
o
r
m
ed
[
4
]
.
T
h
e
r
e
s
u
lt
s
s
h
o
w
ed
t
h
at
i
n
j
ec
tio
n
o
f
cu
r
r
en
t
h
ar
m
o
n
ics
g
e
n
er
ated
b
y
t
h
e
cu
s
to
m
er
s
id
e
o
f
th
e
g
r
id
co
n
n
ec
ted
P
V
g
en
er
atio
n
to
s
till
m
ee
t
s
tan
d
ar
t
r
eq
u
ir
em
e
n
t.
Ho
w
ev
er
th
e
r
esear
ch
d
id
n
o
t
d
is
cu
s
s
ed
i
n
f
l
u
e
n
ce
o
f
P
V
in
t
eg
r
atio
n
o
n
h
ar
m
o
n
ics,
f
l
u
ct
u
ati
o
n
s
,
a
n
d
v
o
ltag
e
f
l
ick
er
,
as
k
e
y
p
ar
a
m
eter
in
p
o
w
er
q
u
alit
y
.
R
esear
ch
o
n
a
p
p
licatio
n
o
f
f
u
zz
y
lo
g
ic
a
s
M
P
PT
f
o
r
co
n
tr
o
llin
g
P
V
o
u
tp
u
t
v
o
lta
g
e
to
ac
h
iev
e
clo
s
ed
cy
c
le
co
n
tr
o
l
as
s
m
o
o
th
an
d
f
a
s
t
i
n
o
r
d
er
to
ac
h
iev
e
m
ax
i
m
u
m
v
al
u
e
p
o
w
er
p
o
in
t
o
f
P
V
ar
r
ay
h
a
v
e
b
ee
n
alr
ea
d
y
d
o
n
e
[
5
]
.
P
V
s
y
s
te
m
s
b
o
th
s
ta
n
d
-
alo
n
e
an
d
co
n
n
ec
ted
to
g
r
id
h
as
b
ee
n
m
o
d
eled
a
n
d
s
i
m
u
late
d
.
T
h
e
r
esu
lts
s
h
o
w
ed
th
at
P
-
Q
co
n
tr
o
l
s
ch
e
m
e
w
as
ab
le
to
p
r
o
v
id
e
clo
s
ed
co
n
tr
o
l
r
ap
id
ly
an
d
P
V
s
y
s
te
m
w
as
ab
le
to
g
en
er
ate
a
s
i
n
u
s
o
id
al
v
o
ltag
e
w
i
th
v
er
y
s
m
a
ll
T
HD
as
2
.
0
8
%.
T
h
e
w
ea
k
n
e
s
s
o
f
r
esear
ch
is
n
o
t
d
is
s
cu
s
s
i
n
g
cu
r
r
en
t T
HD
im
p
r
o
v
e
m
e
n
t d
u
e
to
in
teg
r
atio
n
o
f
P
V
to
g
r
id
an
d
n
u
m
b
er
o
f
u
s
e
d
P
V
o
n
ly
a
s
i
n
g
le.
An
al
y
s
i
s
o
f
p
o
w
er
q
u
al
it
y
d
u
e
to
in
te
g
r
atio
n
o
f
m
u
lti
-
u
n
it
o
f
P
V
g
en
er
ato
r
co
n
n
ec
ted
to
th
r
ee
p
h
ase
g
r
id
u
n
d
er
v
ar
iab
le
s
o
lar
ir
r
ad
iatio
n
le
v
el
h
av
e
b
ee
n
i
m
p
l
e
m
en
ted
[
6
]
.
R
esear
ch
s
h
o
w
s
t
h
at
g
r
id
v
o
l
ta
g
e
an
d
cu
r
r
en
t
o
n
p
o
in
t
co
m
m
o
n
co
u
p
lin
g
(
P
C
C
)
b
u
s
b
ef
o
r
e
u
s
e
d
o
u
b
le
tu
n
ed
p
ass
iv
e
f
ilter
o
n
co
n
d
itio
n
o
n
l
y
co
n
n
ec
t
o
n
e
p
lan
t
is
s
t
ill
u
n
s
tab
le.
Ho
w
e
v
er
,
if
P
V
g
en
er
a
to
r
co
n
n
ec
ted
to
th
r
ee
-
p
h
ase
g
r
id
,
am
o
u
n
ted
to
m
o
r
e
t
h
a
n
o
n
e
g
e
n
er
ato
r
,
th
en
g
r
id
v
o
lta
g
e
an
d
c
u
r
r
en
t
b
ec
o
m
e
s
u
n
s
tab
le.
A
t
le
v
el
o
f
s
o
lar
ir
r
ad
iatio
n
r
e
m
ain
s
,
th
e
g
r
ea
ter
n
u
m
b
er
o
f
P
V
g
en
er
ato
r
co
n
n
ec
ted
to
th
r
ee
-
p
h
ase
g
r
id
,
th
e
n
av
er
a
g
e
T
HD
o
f
g
r
id
v
o
lta
g
e
an
d
cu
r
r
en
t
i
n
cr
ea
s
es.
A
t
le
v
e
l
o
f
s
o
lar
ir
r
ad
iatio
n
in
cr
ea
s
es
,
av
er
ag
e
T
HD
o
f
g
r
id
v
o
ltag
e
an
d
cu
r
r
en
t
also
h
av
e
i
n
cr
ea
s
ed
.
A
v
ar
a
g
e
T
HD
o
f
g
r
id
v
o
ltag
e
a
n
d
cu
r
r
en
t
r
e
d
u
ce
d
af
ter
d
o
u
b
le
tu
n
ed
p
ass
iv
e
f
i
lter
in
s
talled
.
Nev
er
th
e
less
,
MP
P
T
c
o
n
tr
o
l
o
f
P
V
g
en
er
ato
r
s
till
u
s
e
P
an
d
O
alg
o
r
ith
m
an
d
d
id
n
o
t
u
s
e
in
telli
g
e
n
t
co
n
tr
o
l.
P
o
w
er
q
u
ali
t
y
i
m
p
r
o
v
e
m
e
n
t
o
f
P
V
g
en
er
ato
r
co
n
n
ec
ted
t
o
th
r
ee
p
h
ase
g
r
id
u
s
in
g
F
u
z
z
y
L
o
g
ic
co
n
tr
o
ller
u
n
d
er
ch
a
n
g
es
i
n
at
m
o
s
p
h
er
ic
co
n
d
itio
n
s
a
n
d
s
o
lar
r
ad
iatio
n
h
a
s
b
ee
n
d
o
n
e
[
7
]
.
I
n
o
r
d
er
to
k
ee
p
th
e
s
y
s
te
m
s
tab
le
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
i
s
u
s
ed
to
ac
h
iev
e
it
s
till
h
as
a
u
n
it
y
p
o
w
er
f
ac
to
r
u
n
d
er
al
l
co
n
d
itio
n
s
.
F
u
zz
y
lo
g
ic
co
n
tr
o
ller
ca
n
i
m
p
r
o
v
e
o
v
er
all
s
y
s
te
m
s
tab
ilit
y
o
n
a
th
r
ee
-
p
h
ase
g
r
id
co
n
n
ec
ted
PV
s
y
s
te
m
s
i
n
s
o
m
e
v
ar
iatio
n
o
f
p
ar
a
m
eter
s
.
F
u
z
z
y
lo
g
ic
co
n
tr
o
l
m
et
h
o
d
is
ca
p
ab
le
to
r
e
d
u
ce
cu
r
r
en
t
T
HD
co
m
p
ar
ed
to
p
r
o
p
o
r
tio
n
al
in
te
g
r
al
(
P
I
)
an
d
r
o
b
u
s
t c
o
n
tr
o
l.
T
h
e
v
a
lu
e
o
f
c
u
r
r
en
t
h
ar
m
o
n
ics
u
s
i
n
g
P
I
,
r
o
b
u
s
t,
a
n
d
f
u
zz
y
lo
g
ic
co
n
tr
o
l
s
u
cc
ess
iv
el
y
r
ed
u
ce
d
f
r
o
m
4
.
0
5
%,
2
.
0
8
%,
u
p
to
1
.
0
5
%
in
o
r
d
er
to
ac
h
ie
v
e
m
a
x
i
m
u
m
p
o
w
er
.
Ho
w
e
v
er
,
n
u
m
b
er
o
f
P
V
g
en
e
r
ato
r
co
n
n
ec
ted
to
th
e
g
r
id
i
s
o
n
l
y
s
i
n
g
le.
T
h
e
r
esear
ch
o
f
i
m
p
r
o
v
e
m
en
t
p
o
w
er
q
u
a
lit
y
o
n
g
r
id
s
u
p
p
lied
b
y
P
V
ar
r
ay
u
s
i
n
g
u
n
i
f
i
ed
p
o
w
er
q
u
alit
y
co
n
d
itio
n
er
(
UP
QC
)
h
as
b
ee
n
d
o
n
e
[
8
]
.
P
V
ar
r
ay
is
co
n
n
ec
ted
to
th
e
DC
li
n
k
o
f
UP
QC
u
s
i
n
g
P
I
co
m
p
ar
ed
w
it
h
Fu
zz
y
L
o
g
ic
co
n
tr
o
l
ler
.
P
o
w
er
q
u
ali
t
y
e
n
h
an
ce
m
e
n
t
in
c
lu
d
es
v
o
lta
g
e
s
a
g
a
n
d
h
ar
m
o
n
ic
o
f
v
o
ltag
e
s
o
u
r
ce
.
T
h
e
s
i
m
u
latio
n
s
h
o
w
ed
t
h
at
f
u
zz
y
co
n
tr
o
l
le
r
o
n
UP
QC
an
d
P
V
ar
r
a
y
is
a
b
le
to
i
m
p
r
o
v
e
th
e
q
u
alit
y
o
f
s
o
u
r
ce
v
o
lta
g
e
b
ett
er
th
a
n
P
I
co
n
tr
o
l
ler
.
T
h
e
g
r
i
d
v
o
ltag
e
u
s
in
g
P
I
a
n
d
F
u
zz
y
co
n
tr
o
ller
r
es
u
lt
s
T
HD
v
o
ltag
e
as
7
.
0
6
an
d
1
.
3
6
%
r
esp
ec
tiv
el
y
.
T
h
e
r
esear
ch
d
o
es
n
o
t
ad
d
r
ess
i
m
p
r
o
v
e
m
en
t
o
f
lo
ad
cu
r
r
en
t
q
u
alit
y
d
u
e
to
a
co
m
b
in
at
io
n
UP
QC
an
d
th
e
P
V
ar
r
a
y
.
T
h
e
m
et
h
o
d
o
f
P
ar
allel
A
cti
v
e
P
o
w
er
Fil
ter
(
P
A
P
F)
u
s
i
n
g
P
V
ce
lls
e
n
er
g
y
to
f
ee
d
lin
ea
r
o
r
n
o
n
lin
ea
r
lo
ad
s
w
it
h
c
u
r
r
en
t
p
er
tu
r
b
atio
n
s
co
m
p
e
n
s
atio
n
a
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f
th
e
e
n
er
g
y
h
av
e
b
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p
r
o
p
o
s
ed
[
9
]
.
A
s
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lls
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tif
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ce
p
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el
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ce
lev
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t
te
m
p
er
at
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r
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lo
ad
u
s
in
g
f
u
zz
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lo
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Mo
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C
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n
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ter
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ased
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ls
e
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t
h
m
o
d
u
latio
n
(
P
W
M)
alg
o
r
ith
m
i
n
to
a
th
r
ee
-
p
h
a
s
e
A
C
v
o
lta
g
e
to
th
r
ee
-
p
h
ase
g
r
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.
T
h
en
s
i
n
g
le
P
V
g
en
er
ato
r
is
m
o
d
eled
an
d
u
s
ed
to
cr
ea
te
m
u
lti
P
V
g
en
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ato
r
co
n
n
ec
ted
to
g
r
id
th
r
o
u
g
h
a
th
r
ee
-
p
h
a
s
e
d
is
tr
ib
u
tio
n
tr
a
n
s
f
o
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.
An
a
l
y
s
i
s
o
f
r
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ch
i
n
cl
u
d
es
ef
f
e
ct
o
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s
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lar
ir
r
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ian
ce
an
d
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r
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n
o
f
a
n
u
m
b
er
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f
P
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g
e
n
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ato
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to
p
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o
n
co
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ta
n
t
te
m
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d
lo
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h
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ar
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t
w
o
s
ce
n
ar
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en
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ato
r
co
n
n
ec
ted
to
t
h
r
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e
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ase
g
r
i
d
.
T
h
ey
ar
e
u
s
in
g
MP
PT
alg
o
r
ith
m
P
a
n
d
O
a
n
d
MP
P
T
w
it
h
F
u
zz
y
L
o
g
ic
co
n
tr
o
ller
(
MP
PT
Fu
zz
y
)
.
E
ac
h
MP
P
T
co
n
tr
o
l
ler
h
as f
o
u
r
s
c
en
ar
io
s
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t
h
en
f
o
r
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to
tal
h
a
s
ei
g
h
t
s
ce
n
ar
io
s
o
f
P
V
g
en
er
ato
r
in
te
g
r
atio
n
le
v
el.
F
u
th
er
m
o
r
e
is
to
d
eter
m
in
e
u
n
b
alan
ce
v
o
l
tag
e
a
n
d
cu
r
r
en
t,
v
o
ltag
e
a
n
d
cu
r
r
en
t
T
HD,
an
d
p
o
w
er
f
ac
to
r
in
p
u
t
o
n
P
C
C
b
u
s
o
f
lo
w
-
v
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lta
g
e
th
r
ee
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p
h
ase
g
r
id
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T
h
e
f
in
al
p
r
o
ce
s
s
is
to
v
alid
ate
th
e
r
esu
lt
s
o
f
r
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c
h
r
ef
er
s
AN
SI/I
E
E
E
2
4
1
-
1
9
9
0
Stan
d
ar
d
(
v
o
ltag
e
a
n
d
cu
r
r
e
n
t
u
n
b
ala
n
c
ed
)
,
I
E
E
E
5
1
9
-
1
9
9
2
Stan
d
a
r
d
(
v
o
ltag
e
a
n
d
cu
r
r
en
t
h
ar
m
o
n
ics
g
r
id
)
,
an
d
P
L
N
Sta
n
d
ar
d
(
in
p
u
t p
o
w
er
f
ac
to
r
)
.
T
h
e
r
est
o
f
th
i
s
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
.
Sectio
n
2
s
h
o
w
s
p
r
o
p
o
s
ed
m
o
d
el
o
f
s
i
n
g
l
e
an
d
th
r
ee
P
V
g
en
er
ato
r
s
y
s
te
m
co
n
n
ec
te
d
to
th
r
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p
h
a
s
e
g
r
id
,
MP
PT
P a
n
d
O
m
et
h
o
d
,
MP
PT
Fu
zz
y
m
et
h
o
d
,
u
n
b
alan
ce
v
o
ltag
e
an
d
c
u
r
r
ec
t
,
p
o
w
er
q
u
alit
y
a
n
d
h
ar
m
o
n
ics,
a
s
w
el
l
as
p
o
w
er
f
ac
to
r
co
r
r
ec
tio
n
.
Sectio
n
3
d
e
s
cr
ib
es
in
f
lu
e
n
ce
o
f
s
o
lar
ir
r
ad
ian
ce
an
d
in
teg
r
atio
n
o
f
P
V
g
e
n
er
at
o
r
to
v
o
ltag
e
a
n
d
c
u
r
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en
t
u
n
b
alan
ce
,
v
o
ltag
e
an
d
cu
r
r
en
t
T
HD
o
f
t
h
r
ee
p
h
ase
g
r
id
,
as
w
el
l
as
i
n
p
u
t
p
o
w
er
f
ac
t
o
r
o
n
co
n
s
tan
t
te
m
p
er
at
u
r
e
an
d
lo
ad
u
s
in
g
MP
PT
P
an
d
O
an
d
M
PP
T
Fu
zz
y
m
eth
o
d
.
I
n
th
is
s
ec
tio
n
,
ex
a
m
p
l
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ca
s
es
s
tu
d
ied
ar
e
p
r
esen
ted
an
d
th
e
r
esu
lt
s
ar
e
v
er
if
ied
w
it
h
t
h
o
s
e
o
f
Ma
tlab
/
Si
m
u
li
n
k
.
Fin
a
ll
y
,
t
h
e
p
ap
er
in
c
o
n
clu
d
ed
in
Sectio
n
4
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Resea
rc
h P
ro
ce
du
re
Fig
u
r
e
1
s
h
o
w
s
m
o
d
el
P
V
g
e
n
er
ato
r
co
n
n
ec
ted
to
t
h
r
ee
p
h
ase
g
r
id
u
s
i
n
g
MP
PT
w
it
h
F
u
zz
y
L
o
g
ic
C
o
n
tr
o
ller
(
MP
PT
Fu
zz
y
)
.
Mo
d
el
o
f
P
V
g
e
n
er
ato
r
s
y
s
t
e
m
i
n
s
in
g
u
lar
to
t
h
r
ee
-
p
h
as
e
o
u
tp
u
t
v
o
lta
g
e
a
n
d
co
n
n
ec
ted
t
h
r
ee
-
p
h
ase
g
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id
.
D
C
/D
C
co
n
v
er
ter
co
n
s
is
t
s
o
f
a
b
o
o
s
t
co
n
v
er
ter
t
h
at
f
u
n
ctio
n
s
to
r
aise
D
C
o
u
tp
u
t
v
o
ltag
e
o
f
P
V
g
en
er
ato
r
.
DC
o
u
tp
u
t
v
o
lta
g
e
o
f
b
o
o
s
t
co
n
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ter
cir
cu
it
is
th
e
n
co
n
v
er
t
ed
b
y
th
e
DC
/
A
C
in
v
er
ter
in
to
a
t
h
r
ee
-
p
h
ase
A
C
v
o
lta
g
e
to
th
r
ee
-
p
h
ase
g
r
id
.
T
h
en
s
i
n
g
le
P
V
g
e
n
er
ato
r
is
m
o
d
eled
an
d
u
s
ed
to
cr
ea
te
m
u
lti
P
V
g
e
n
er
ato
r
co
n
n
ec
ted
to
g
r
id
t
h
r
o
u
g
h
a
t
h
r
ee
-
p
h
ase
d
is
tr
ib
u
tio
n
tr
an
s
f
o
r
m
er
(
Fi
g
u
r
e
2
)
.
T
h
e
s
tu
d
y
u
s
ed
t
h
r
ee
g
r
o
u
p
s
o
f
P
V
g
e
n
er
ato
r
m
o
d
el
w
it
h
a
n
a
ctiv
e
p
o
w
er
o
f
1
0
0
k
W
ea
c
h
.
B
esid
e
th
at,
P
V
g
en
er
ato
r
is
also
co
n
n
ec
ted
o
n
th
r
e
e
g
r
o
u
p
s
o
f
t
h
r
ee
p
h
ase
lo
ad
w
it
h
ac
tiv
e
p
o
w
er
2
0
k
W
r
esp
ec
tiv
el
y
.
Fig
u
r
e
1
.
Sin
g
le
P
V
Gen
er
ato
r
C
o
n
n
ec
ted
T
h
r
ee
P
h
ase
Gr
id
Usi
n
g
MP
P
T
Fu
zz
y
T
h
e
p
ap
er
p
r
esen
ts
p
o
w
er
q
u
alit
y
e
n
h
a
n
ce
m
e
n
t
o
n
lo
w
v
o
ltag
e
o
f
t
h
r
ee
p
h
a
s
e
g
r
id
ca
u
s
ed
b
y
P
V
g
en
er
ato
r
i
n
teg
r
atio
n
u
n
d
er
v
ar
iab
el
s
o
lar
ir
r
ad
ian
ce
lev
el
o
n
co
n
s
tan
t
te
m
p
er
at
u
r
e
an
d
lo
ad
.
Fu
zz
y
lo
g
ic
co
n
tr
o
ller
h
elp
s
to
g
en
er
ate
d
u
t
y
c
y
cle
(
D)
w
ith
a
v
ar
ia
b
le
s
tep
to
co
n
tr
o
l
DC
/DC
b
o
o
s
t
co
n
v
er
ter
an
d
s
u
b
s
eq
u
en
t
l
y
r
es
u
lt
in
r
ap
id
co
n
v
er
g
e
n
ce
ca
lc
u
latio
n
s
an
d
m
o
r
e
s
tab
le
to
d
eter
m
i
n
e
MP
PT
o
f
P
V
g
en
er
ato
r
.
DC
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C
co
n
v
er
ter
g
en
er
ate
a
DC
v
o
lta
g
e
th
a
t
w
ill
b
e
as
in
p
u
t
to
DC
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AC
co
n
v
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ter
u
s
i
n
g
P
W
M.
T
h
is
m
o
d
el
is
ex
p
ec
ted
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r
ed
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ce
lo
s
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es
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u
e
to
u
n
b
alan
ce
v
o
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g
e
an
d
cu
r
r
en
t,
lo
w
v
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lta
g
e
an
d
cu
r
r
en
t
h
ar
m
o
n
i
cs,
an
d
lo
w
in
p
u
t
p
o
w
er
f
ac
to
r
.
T
h
er
e
a
r
e
t
w
o
s
ce
n
ar
io
s
P
V
g
e
n
er
ato
r
co
n
n
ec
ted
to
th
r
ee
-
p
h
ase
g
r
id
.
T
h
e
y
ar
e
u
s
in
g
MP
PT
alg
o
r
ith
m
P
a
n
d
O
a
n
d
MP
PT
w
i
th
F
u
zz
y
L
o
g
ic
C
o
n
tr
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I
J
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iab
le
s
tep
to
co
n
tr
o
l
DC
/D
C
b
o
o
s
t
co
n
v
er
ter
cir
cu
it
w
i
th
MP
PT
P
an
d
O
alg
o
r
ith
m
.
F
o
r
P
V
co
n
v
er
ter
,
m
a
x
i
m
u
m
p
o
w
er
av
ailab
le
i
s
d
eter
m
in
ed
b
y
P
V
ce
ll
ch
ar
ac
t
er
is
tics
,
b
u
t t
h
is
v
al
u
e
o
f
ten
m
is
m
a
tch
e
s
w
it
h
t
h
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t (
MP
P
)
o
f
t
h
e
lo
ad
.
B
y
i
m
p
le
m
en
tin
g
MP
PT
in
P
V
s
y
s
te
m
s
,
MP
P
in
P
V
ce
ll
s
ca
n
b
e
m
ai
n
tai
n
ed
s
o
th
at
t
h
e
n
u
m
b
er
an
d
s
ize
o
f
P
V
p
an
els ca
n
b
e
r
ed
u
ce
d
o
r
en
er
g
y
y
ie
ld
ca
n
b
e
o
p
tim
ized
[
1
1
]
.
Du
e
to
m
o
v
i
n
g
o
f
s
u
n
,
w
h
ic
h
lead
s
to
ch
an
g
e
i
n
ir
r
ad
ian
ce
,
P
V
p
an
els
an
g
le
an
d
v
ar
iatio
n
o
f
ir
r
ad
ian
ce
r
ea
ch
in
g
t
h
e
p
an
els
,
en
er
g
y
g
e
n
er
ated
f
r
o
m
P
V
p
an
els
ar
e
ab
s
o
r
b
ed
d
o
es
n
o
t
c
o
n
s
ta
n
t
o
v
er
ti
m
e.
W
h
en
th
is
co
n
d
itio
n
o
cc
u
r
s
,
th
e
VI
ch
ar
ac
ter
is
tics
c
h
an
g
es
an
d
MP
P
w
ill
m
o
v
e.
I
f
th
e
s
y
s
te
m
w
as
p
r
ev
io
u
s
l
y
o
p
er
atin
g
at
MP
P
,
th
er
e
w
ill
m
o
s
t p
r
o
b
ab
ly
a
p
o
w
er
lo
s
s
w
i
th
t
h
e
s
a
m
e
o
p
er
atin
g
p
o
in
t a
n
d
n
e
w
co
n
d
itio
n
.
T
o
o
v
er
co
m
e
t
h
ese
p
r
o
b
lem
s
,
M
P
PT
h
as
b
ee
n
d
e
v
elo
p
ed
.
T
h
e
s
y
s
te
m
i
n
cl
u
d
es
n
o
m
o
v
in
g
p
ar
ts
(
w
h
er
e
t
h
e
mo
d
u
les
ar
e
m
o
v
ed
to
tr
ac
k
t
h
e
s
u
n
)
.
MP
P
T
s
ea
r
ch
f
o
r
th
e
m
a
x
i
m
u
m
p
o
w
er
in
d
ep
en
d
en
t
b
ased
o
n
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
(
f
o
llo
w
i
n
g
ch
a
n
g
e
s
in
s
o
lar
r
ad
iatio
n
an
d
te
m
p
er
atu
r
e)
an
d
m
ai
n
tai
n
th
e
P
V
ter
m
i
n
al
v
o
lta
g
e
r
e
m
ai
n
s
co
n
s
ta
n
t
at
m
a
x
i
m
u
m
v
al
u
e.
T
h
e
m
o
s
t
u
s
ed
m
e
th
o
d
o
f
MP
PT
is
P
er
tu
r
b
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
6
,
No
.
6
,
Dec
em
b
er
2
0
1
6
:
2
6
2
9
–
2
6
4
2
2634
Ob
s
er
v
e
(
P
an
d
O)
th
at
alg
o
r
ith
m
is
s
h
o
w
n
in
F
ig
u
r
e
4
[
1
2
]
.
Fig
u
r
e
5
s
h
o
w
s
Ma
t
lab
/Si
m
u
lin
k
m
o
d
el
f
o
r
co
n
tr
o
l M
P
PT
u
s
in
g
P
an
d
O
alg
o
r
ith
m
.
S
t
a
r
t
S
e
n
s
e
V
(
k
)
,
I
(
k
)
C
a
l
c
u
l
a
t
e
P
o
w
e
r
d
P
=
P
(
k
)
-
P
(
k
-
1
)
d
P
>
0
V
(
k
)
-
V
(
k
-
1
)
>
0
V
(
k
)
-
V
(
k
-
1
)
>
0
D
=
D
+
d
D
D
=
D
-
d
D
D
=
D
-
d
D
D
=
D
+
d
D
Y
e
s
N
o
N
o
Y
e
s
N
o
Y
e
s
R
e
t
u
r
n
Fig
u
r
e
4
.
P
an
d
O
A
lg
o
r
it
h
m
Fig
u
r
e
5
.
Ma
tlab
/Si
m
u
li
n
k
M
o
d
el
f
o
r
MPPT
U
s
in
g
P
an
d
O
A
l
g
o
r
ith
m
T
h
e
n
ex
t
p
r
o
ce
s
s
i
s
to
p
er
f
o
r
m
s
a
m
e
p
r
o
ce
d
u
r
e
f
o
r
d
eter
m
i
n
in
g
i
t
u
s
i
n
g
MP
P
T
Fu
zz
y
m
eth
o
d
s
h
o
w
ed
i
n
Fi
g
u
r
e
1
.
F
u
zz
y
lo
g
ic
co
n
tr
o
ller
h
a
v
e
b
ee
n
w
id
el
y
u
s
ed
i
n
in
d
u
s
tr
ial
p
r
o
ce
s
s
in
t
h
e
r
ese
n
t
y
ea
r
s
d
u
e
to
th
eir
h
eu
r
i
s
tic
n
a
tu
r
e
as
s
o
ciate
d
w
it
h
s
i
m
p
licit
y
,
ef
f
ec
ti
v
en
e
s
s
a
n
d
its
m
u
lti
-
r
u
le
-
b
ased
v
ar
iab
le
‟
s
co
n
s
id
er
atio
n
f
o
r
b
o
th
li
n
ea
r
a
n
d
n
o
n
-
lin
ea
r
p
ar
a
m
eter
v
ar
iat
io
n
o
f
th
e
s
y
s
te
m
.
Fu
zz
y
s
y
s
te
m
i
s
co
m
p
o
s
ed
o
f
k
n
o
w
led
g
e
b
ased
r
u
les
s
y
s
te
m
;
th
e
m
a
in
p
ar
t
o
f
Fu
zz
y
L
o
g
i
c
co
n
tr
o
ller
is
k
n
o
w
led
g
e
o
f
b
ase
co
n
s
is
ti
n
g
o
f
th
e
I
f
-
T
h
e
n
r
u
les.
Fu
zz
y
L
o
g
ic
is
i
m
p
le
m
e
n
ted
to
o
b
tai
n
t
h
e
MP
P
o
p
er
atio
n
v
o
lta
g
e
p
o
in
t
f
a
s
ter
w
it
h
less
o
v
er
s
h
o
o
t
an
d
al
s
o
it
ca
n
m
i
n
i
m
ize
t
h
e
v
o
lta
g
e
f
l
u
ctu
a
tio
n
a
f
ter
MP
P
h
as
b
ee
n
r
ec
o
g
n
ized
.
I
t
also
is
ca
p
ab
le
to
en
h
a
n
ce
p
o
w
er
q
u
ali
t
y
p
r
o
b
le
m
f
o
r
ex
a
m
p
le
u
n
b
ala
n
ce
c
u
r
r
en
t a
n
d
v
o
ltag
e,
cu
r
r
en
t
an
d
v
o
ltag
e
h
ar
m
o
n
ic
s
,
as
w
e
ll
as
i
n
p
u
t
p
o
w
er
f
ac
to
r
.
T
h
e
co
n
tr
o
l
o
b
j
ec
tiv
e
is
to
tr
ac
k
m
a
x
i
m
u
m
p
o
w
er
w
ill
le
ad
co
n
s
eq
u
en
t
l
y
to
ef
f
ec
tiv
e
o
p
er
atio
n
o
f
t
h
e
P
V
p
an
el.
T
o
d
esig
n
t
h
e
F
L
C
,
v
ar
iab
les
w
h
ic
h
r
ep
r
esen
t
t
h
e
d
y
n
a
m
ic
p
er
f
o
r
m
an
ce
o
f
th
e
s
y
s
te
m
s
h
o
u
ld
b
e
ch
o
s
en
as
t
h
e
in
p
u
t
to
th
e
co
n
tr
o
ller
.
T
h
e
b
asic
b
lo
ck
d
iag
r
am
i
m
p
le
m
e
n
ted
in
F
u
zz
y
L
o
g
ic
C
o
n
tr
o
ller
is
s
h
o
w
n
in
Fig
u
r
e
6
[
1
2
]
.
Du
e
ac
co
u
n
t
MP
PT
Fu
zz
y
m
eth
o
d
is
in
ter
m
s
o
f
i
n
tell
ig
e
n
ce
a
n
d
s
p
ee
d
.
F
u
zz
y
MP
P
T
m
et
h
o
d
is
d
o
n
e
b
y
d
eter
m
i
n
i
n
g
i
n
p
u
t
v
a
r
iab
les,
n
a
m
el
y
f
u
zz
y
co
n
tr
o
l
o
u
tp
u
t
p
o
w
er
(
Δ
P
)
an
d
o
u
tp
u
t
v
o
lta
g
e
(
Δ
V)
P
V
g
en
er
ato
r
,
s
ev
e
n
lin
g
u
is
t
ic
v
ar
iab
les
f
u
zz
y
s
et
s
,
f
u
zz
y
o
p
er
atin
g
s
y
s
te
m
b
lo
ck
(
f
u
zz
y
f
icatio
n
,
f
u
zz
y
r
u
le
b
ase,
an
d
d
ef
u
zz
y
f
icat
io
n
)
,
F
u
n
c
tio
n
Δ
P
an
d
Δ
V
d
u
r
i
n
g
f
u
zz
y
f
i
ca
tio
n
,
a
tab
le
f
u
zz
y
r
u
le
b
a
s
e,
cr
is
p
v
a
lu
e
s
to
d
eter
m
in
e
d
u
t
y
c
y
cle
(
D)
in
d
ef
u
zz
y
f
icatio
n
p
h
a
s
e
w
it
h
v
ar
iab
le
s
tep
to
co
n
tr
o
l
DC
/DC
b
o
o
s
t
co
n
v
er
ter
cir
cu
it.
Fi
g
u
r
e
7
s
h
o
w
s
Ma
tlab
/
Si
m
u
li
n
k
m
o
d
el
f
o
r
co
n
tr
o
l M
P
PT
u
s
in
g
F
u
zz
y
L
o
g
ic
C
o
n
tr
o
ller
.
D
a
t
a
b
a
s
e
R
e
a
s
o
n
M
e
c
h
a
n
i
s
m
R
u
l
e
b
a
s
e
D
e
f
u
z
z
i
f
i
c
a
t
i
o
n
F
u
z
z
i
f
i
c
a
t
i
o
n
P
r
e
-
P
r
o
c
e
s
s
i
n
g
P
o
s
t
-
P
r
o
c
e
s
s
i
n
g
F
u
z
z
y
L
o
g
i
c
C
o
n
t
r
o
l
l
e
r
Fig
u
r
e
6
.
B
lo
k
Di
ag
r
a
m
o
f
Fu
zz
y
L
o
g
ic
Co
n
tr
o
ller
Fig
u
r
e
7
.
Ma
tlab
/Si
m
u
li
n
k
M
o
d
el
f
o
r
MPPT
u
s
in
g
Fu
zz
y
L
o
g
ic
C
o
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
P
o
w
er Qu
a
lity E
n
h
a
n
ce
men
t
o
f I
n
teg
r
a
tio
n
P
h
o
to
v
o
lta
ic
G
en
era
to
r
to
Gri
d
u
n
d
er V
a
r
ia
b
le
…
(
A
mir
u
lla
h
)
2635
A
t
f
u
zz
y
f
icatio
n
p
h
a
s
e
s
h
o
w
n
in
Fi
g
u
r
e
6
,
a
n
u
m
b
er
o
f
i
n
p
u
t
v
ar
iab
les
is
ca
lcu
la
ted
an
d
co
n
v
er
ted
in
to
a
lin
g
u
i
s
tic
v
ar
iab
le
b
ase
d
o
n
th
e
s
u
b
s
et
ca
lled
m
e
m
b
e
r
s
h
ip
f
u
n
c
tio
n
(
MF)
.
T
o
tr
an
s
late
v
alu
e
o
f
v
o
ltag
e
ch
an
g
e
a
n
d
p
o
w
er
c
h
an
g
e
i
n
,
i
n
p
u
t
f
u
zz
y
"
ch
an
g
e
o
f
v
o
lta
g
e
"
an
d
"
ch
an
g
e
o
f
p
o
w
er
"
is
d
esig
n
ed
to
u
s
e
s
e
v
e
n
f
u
zz
y
v
ar
iab
le
ca
lled
P
B
(
P
o
s
itiv
e
B
ig
)
,
P
M
(
P
o
s
itiv
e
Me
d
iu
m
)
,
N
S
(
Neg
at
iv
e
S
m
al
l)
,
PS
(
P
o
s
itiv
e
S
m
all
)
Z
E
(
Z
er
o
)
,
NM
(
Neg
ati
v
e
Me
d
iu
m
)
,
a
n
d
Neg
a
tiv
e
B
ig
(
NB
)
.
Vo
ltag
e
ch
a
n
g
e
(
Δ
V)
a
n
d
p
o
w
er
ch
a
n
g
es
(
Δ
P
)
is
a
p
r
o
p
o
s
ed
s
y
s
te
m
i
n
p
u
t
v
ar
iab
les
an
d
o
u
tp
u
t
v
ar
iab
le
f
u
z
z
y
lo
g
ic
co
n
tr
o
l
is
d
u
t
y
c
y
cle
ch
an
g
e
v
al
u
e
(
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[
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].
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].
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Sta
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t d
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m
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t [
1
5
].
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.
5
.
Vo
lt
a
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a
nd
Curre
nt
Unba
la
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T
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ased
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d
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[
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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I
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Vo
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–
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2638
T
ab
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4
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Fig
u
r
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1
1
s
h
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ase
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et
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)
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Fig
u
r
e
1
1
.
Si
m
u
latio
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Re
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id
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ase
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B
us
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