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6
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g
er
in
g
o
f
p
o
w
er
s
w
itc
h
es
i
n
9
lev
el
M
L
I
.
Sin
ce
s
in
u
s
o
id
al
–
PW
M
is
u
s
ed
i
n
th
is
w
o
r
k
,
th
e
r
eso
n
an
ce
o
f
in
v
er
ter
f
o
u
n
d
to
b
e
r
ed
u
ce
d
w
h
e
n
co
m
p
ar
ed
w
it
h
th
e
co
n
v
en
t
io
n
al
P
W
M.
T
h
e
w
id
th
o
f
t
h
e
p
u
ls
e
is
t
w
ea
k
ed
to
a
s
p
ec
if
ic
v
alu
e
i
n
o
r
d
er
to
g
et
th
e
c
o
n
tr
o
lled
o
u
tp
u
t v
o
lta
g
e
w
it
h
less
r
ev
er
b
er
atio
n
.
Fig
u
r
e
1.
Sin
u
s
o
id
al
–
P
W
M
o
u
tp
u
t
Sin
u
s
o
id
al
–
P
W
M
s
ee
m
s
to
b
e
th
e
m
o
s
t
co
m
m
o
n
l
y
u
t
iliz
ed
tech
n
iq
u
e
f
o
r
th
e
i
n
v
er
ter
f
ed
s
p
ee
d
co
n
tr
o
l
o
f
a
m
o
to
r
.
T
h
e
o
p
e
r
atin
g
f
r
eq
u
e
n
c
y
o
f
t
h
e
ca
r
r
ier
s
ig
n
al
as
w
el
l
as
r
ef
er
e
n
c
e
s
ig
n
al
i
s
u
s
ed
as
d
is
cu
s
s
ed
in
[
1
1
]
.
A
ls
o
t
h
i
s
k
i
n
d
o
f
P
W
M
p
u
ls
e
s
ar
e
p
r
o
g
r
e
s
s
i
v
el
y
u
s
ed
in
A
C
d
r
iv
es
w
it
h
m
o
r
e
p
er
s
p
ec
ti
v
e
to
w
ar
d
s
t
h
e
d
i
m
in
i
s
h
in
g
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y
m
p
h
o
n
io
u
s
cu
r
r
e
n
t
an
d
to
o
b
tai
n
t
h
e
b
est
o
u
tp
u
t
v
o
ltag
e
to
d
r
iv
e
th
e
m
o
to
r
[
1
2
]
.
An
al
y
ze
d
all
th
e
P
W
M
tech
n
i
q
u
es a
cti
n
g
i
n
t
h
e
h
i
s
to
r
y
an
d
i
ts
f
u
n
d
a
m
e
n
tals
p
r
in
c
ip
les.
3.
P
V
SYST
E
M
A
D
C
s
u
p
p
l
y
o
b
tain
ed
a
P
V
p
an
el
is
u
s
ed
as
t
h
e
in
p
u
t
f
o
r
th
e
p
r
o
p
o
s
ed
ML
I
.
Fo
r
ex
a
m
p
le,
a
1
0
W
P
V
p
an
el
th
at
h
as
1
7
.
6
V
an
d
0
.
5
6
A
is
u
s
ed
as
a
n
in
p
u
t
f
o
r
ML
I
.
P
V
ce
ll
is
th
e
b
asic
u
n
it
o
f
a
P
V
p
an
el.
C
o
m
b
i
n
atio
n
o
f
n
u
m
b
er
o
f
P
V
ce
lls
f
o
r
m
s
a
P
V
m
o
d
u
le.
C
o
m
b
i
n
a
tio
n
o
f
n
u
m
b
er
o
f
P
V
m
o
d
u
les
f
o
r
m
s
a
P
V
p
an
el.
Fig
u
r
e
2
r
ep
r
esen
ts
t
h
e
eq
u
iv
ale
n
t c
ir
c
u
it o
f
a
P
V
m
o
d
u
le.
T
h
e
en
er
g
y
ar
is
e
s
f
r
o
m
t
h
e
ea
r
th
’
s
s
u
n
i
s
ter
m
ed
as
ea
r
th
’
s
r
ad
iatio
n
.
I
t
is
o
f
f
lo
at
t
y
p
e
o
r
d
if
f
u
s
ed
t
y
p
e.
T
h
e
d
if
f
u
s
ed
t
y
p
e
r
ad
iati
o
n
ca
n
d
ef
lect
p
ar
t o
f
r
ad
iatio
n
b
ac
k
to
th
e
s
u
r
f
ac
e
w
h
ic
h
co
n
s
u
m
es
m
is
t
s
.
P
V
o
r
ien
ted
ce
ll
ar
r
an
g
e
m
e
n
t
to
w
ar
d
s
s
u
n
ca
n
g
a
th
er
t
h
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e
n
er
g
y
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elea
s
ed
f
r
o
m
t
h
e
s
u
n
d
u
r
in
g
d
a
y
.
T
h
is
ar
r
an
g
e
m
e
n
t
co
m
p
r
i
s
es
o
f
a
d
io
d
e
co
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ted
i
n
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allel
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d
a
n
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n
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ter
.
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h
is
ca
n
b
e
t
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ed
as
a
cu
r
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en
t
s
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ce
co
n
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a
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allel
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allel
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h
e
P
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cu
r
r
en
t
o
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f
r
o
m
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n
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i
v
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in
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q
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at
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(
1
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-
1]
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ph
(
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C
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t (
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J
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I
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th
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it
s
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illag
e
s
tr
ea
m
s
as id
en
t
if
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a
n
d
ter
m
ed
to
in
[
1
3
]
.
I
n
r
ec
en
t
tr
en
d
s
P
V’
s
s
o
u
r
ce
a
r
e
g
r
ea
tl
y
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til
ized
in
en
o
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m
o
u
s
ap
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licatio
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s
s
u
c
h
as
ch
ar
g
in
g
a
b
atter
y
,
h
o
u
s
e
p
o
w
er
s
u
p
p
lies
,
p
u
m
p
in
g
o
f
d
e
h
y
d
r
o
g
e
n
ated
m
o
n
o
x
id
e,
s
atellite
p
o
w
er
s
y
s
te
m
s
etc.
Sin
ce
P
V
is
n
o
ted
to
b
e
a
p
r
o
g
r
ess
i
v
el
y
h
i
g
h
s
i
n
ce
it
h
as
in
e
x
h
a
u
s
tib
le
en
er
g
y
.
I
t
h
as
m
an
y
ad
v
a
n
ta
g
es
li
k
e
co
n
ta
m
i
n
atio
n
f
r
ee
,
co
m
m
o
tio
n
f
r
ee
a
n
d
to
ll f
r
ee
.
T
h
e
m
aj
o
r
d
r
a
w
b
ac
k
o
f
P
V
s
y
s
te
m
is
it i
s
m
o
r
e
d
ep
en
d
en
t o
n
cli
m
atic
co
n
d
it
io
n
ch
an
g
es.
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n
ce
o
f
f
er
s
e
n
er
g
y
th
at
d
ep
en
d
s
o
n
t
h
e
li
g
h
t a
s
well
te
m
p
er
atu
r
e.
Fig
u
r
e
2
.
E
q
u
iv
ale
n
t c
ir
cu
it o
f
a
P
V
m
o
d
u
le
4.
VARIO
US M
L
I
SCH
E
M
E
S
4
.
1
.
E
x
is
t
ing
s
y
s
t
e
m
T
h
e
f
u
ll
M
L
I
,
4
-
H
B
r
id
g
es
w
er
e
i
n
ter
co
n
n
ec
ted
b
ac
k
to
b
ac
k
i
n
s
er
ies
w
it
h
an
in
d
i
v
id
u
al
s
o
u
r
ce
as
s
h
o
w
n
i
n
F
ig
u
r
e
3
.
A
ca
s
ca
d
e
d
ML
I
u
tili
ze
1
6
p
o
w
er
s
w
itc
h
es to
o
f
f
er
1
3
-
lev
el
o
u
tp
u
t
v
o
lt
ag
e.
T
h
e
p
u
l
s
es
f
o
r
s
w
itc
h
in
g
t
h
e
p
o
w
er
s
w
itc
h
es
in
i
n
v
er
ter
ar
e
s
i
n
u
s
o
id
al
P
W
M
tr
ig
g
er
i
n
g
tech
n
iq
u
e.
W
h
ile
co
m
p
ar
i
n
g
th
e
n
u
m
b
er
o
f
i
n
p
u
t
s
o
f
an
i
n
v
er
te
r
w
i
th
its
M
L
I
o
u
tp
u
t,
t
h
e
o
u
tp
u
t
s
ee
m
s
to
b
e
m
o
r
e
t
h
a
n
t
h
e
i
n
p
u
t.
T
h
e
lev
el
s
o
f
o
u
tp
u
t
v
o
lta
g
es
ap
p
ea
r
ed
to
b
e
4V
-
3V
-
2V
-
V
-
0
-
(
-
V)
-
(
-
2
V)
-
(
-
3
V)
-
(
4
V)
.
S
y
m
m
etr
ical
ca
s
ca
d
e
is
a
n
in
d
iv
id
u
al
ca
s
ca
d
e
o
f
f
u
ll
b
r
id
g
e
w
it
h
4
p
o
w
er
s
w
itc
h
es.
So
it
r
eq
u
ir
ed
m
o
r
e
n
u
m
b
er
o
f
v
o
lta
g
e
s
o
u
r
ce
s
a
n
d
p
o
w
er
s
w
itc
h
es.
He
n
ce
t
h
e
ca
p
ital
c
o
s
t
o
f
t
h
e
s
y
s
te
m
a
ls
o
i
n
cr
ea
s
es.
I
t
m
a
y
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s
o
lead
to
h
i
g
h
T
HD
an
d
s
w
itch
in
g
m
is
f
o
r
tu
n
e
s
as e
x
p
lai
n
ed
in
[
1
4
]
.
Nu
m
b
er
o
f
le
v
el
(
2
)
Fig
u
r
e
3
.
Sin
g
le
p
h
ase
ca
s
ca
d
ed
f
u
ll b
r
id
g
e
I
n
v
er
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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8
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8708
I
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T
h
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th
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s
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u
n
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ased
9
–
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ev
el
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v
er
ter
is
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i
s
cu
s
s
ed
in
t
h
i
s
ar
ticle.
I
t
is
g
en
er
ated
f
r
o
m
a
9
–
L
ev
el
in
v
er
ter
.
I
t
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n
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s
ts
o
f
a
b
a
s
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b
r
id
g
e
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n
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ted
M
L
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alo
n
g
a
3
b
id
ir
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tio
n
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o
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er
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w
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h
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d
4
n
u
m
b
er
ed
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p
ac
ito
r
as
v
o
lt
ag
e
c
u
tter
as
s
h
o
w
n
in
F
i
g
u
r
e
4
.
T
h
is
t
y
p
ical
n
e
w
to
p
o
lo
g
y
i
s
u
tili
ze
d
i
n
t
h
i
s
w
o
r
k
.
I
t
u
s
es
ea
r
th
’
s
s
u
n
r
ath
er
th
an
li
k
e
a
co
n
v
e
n
tio
n
al
D
C
v
o
lta
g
e.
T
h
er
e
ar
e
d
if
f
er
en
t
t
y
p
es
o
f
lo
ad
s
s
u
c
h
as
R
,
R
L
etc
ca
n
b
e
co
n
n
ec
t
ed
to
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
.
T
h
er
e
ex
is
ts
n
in
e
d
i
f
f
er
e
n
t
o
p
er
atio
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w
h
ich
ar
e
s
eq
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en
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er
f
o
r
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ed
b
y
th
e
s
in
u
s
o
id
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p
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ls
e
w
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t
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m
o
d
u
lated
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ig
n
al
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o
f
f
er
ed
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e
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o
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er
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w
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.
A
ll
t
h
ese
o
p
er
atio
n
s
w
er
e
p
er
f
o
r
m
ed
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n
M
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ased
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.
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NC
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S
[1
]
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ra
k
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ter
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ive
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le
x
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a
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in
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it
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lt
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tres
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[3
]
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r
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b
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t
a
l.
,
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sc
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lt
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sic
Un
it
s,”
IEE
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T
ra
n
sa
c
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o
n
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o
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In
d
u
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l
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p
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[4
]
Am
a
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p
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g
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,
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EE
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ra
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l.
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.
1
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[5
]
Bil
l
Dio
n
g
,
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t
a
l.
,
“
Ha
r
m
o
n
ic
Dis
to
rti
o
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m
iza
ti
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f
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p
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teg
e
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o
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tag
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ti
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s,
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stria
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tro
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l.
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p
.
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[6
]
P
.
D.H.Da
rm
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rd
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p
p
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[7
]
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ra
k
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sh
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G
,
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a
l.
,
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rid
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w
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ter
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Ch
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rles
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o
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sc
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[9
]
G
.
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a
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v
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it
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0
]
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a
sa
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sh
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sh
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o
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re
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sig
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in
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p
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P
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p
led
In
d
u
c
to
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a
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d
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w
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DC
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s,
”
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p
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1
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k
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sh
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b
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ra
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.
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Ku
lk
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rn
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M
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Ad
v
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n
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En
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(
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2
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2
]
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h
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Ya
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l.
,“
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p
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f
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trate
g
y
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In
v
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2
4
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,
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p
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2
2
5
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2
.
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3
]
Us
h
a
S
a
n
d
S
u
b
ra
m
a
n
i
C,
“
P
e
rf
o
rm
a
n
c
e
A
n
a
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sis
o
f
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b
rid
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n
d
T
-
Brid
g
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M
u
lt
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l
In
v
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f
o
r
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r
m
o
n
ics
Re
d
u
c
ti
o
n
,
”
In
ter
n
a
ti
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n
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J
o
u
rn
a
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f
P
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we
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lec
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d
Dr
ive
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ste
ms
,
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l.
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o
.
1
,
p
p
.
2
3
1
-
2
3
9
,
2
0
1
8
.
[1
4
]
K.
Dh
in
e
sh
k
u
m
a
r
a
n
d
C.
S
u
b
ra
m
a
n
i,
“
Ka
lm
a
n
F
il
ter
A
lg
o
rit
h
m
f
o
r
M
it
ig
a
ti
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n
o
f
P
o
w
e
r
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
t
e
r E
n
g
i
n
e
e
rin
g
,
v
o
l.
8
,
n
o
.
2
,
p
p
.
771
-
7
7
9
,
2
0
1
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.