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DS
Rev
iew
of DC
O
f
f
set Co
m
pensa
tion
Techniqu
es for
G
rid
Co
nnected
Inv
ert
ers
Ah
m
ed
O
m
a
r
1
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E
l
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a
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2
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o
na
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a
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a
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De
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l
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A
r
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c
a
d
em
y
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T
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c
h
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y
an
d
M
a
r
it
im
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T
r
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p
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E
g
y
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t
Art
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I
nfo
AB
ST
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A
r
ticle
his
to
r
y:
R
ec
eiv
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Dec
1
6
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2
0
1
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R
ev
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an
1
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8
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cc
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Feb
2
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2
0
1
8
L
i
m
it
a
ti
o
n
s
o
f
DC
in
jec
ti
o
n
in
t
o
th
e
A
C
n
e
tw
o
rk
is
a
n
im
p
o
rtan
t
o
p
e
ra
ti
o
n
a
l
re
q
u
irem
e
n
t
f
o
r
g
rid
c
o
n
n
e
c
ted
p
h
o
to
v
o
lt
a
ic
sy
ste
m
s.
T
h
e
re
is
o
n
e
w
a
y
to
e
n
su
re
th
a
t
th
is
issu
e
n
e
e
d
s
a
p
o
w
e
r
tran
s
f
o
r
m
e
r
a
s
a
c
o
n
n
e
c
ti
o
n
to
t
h
e
A
C
n
e
tw
o
rk
.
Ho
we
v
e
r,
th
is
so
lu
ti
o
n
a
d
d
s
c
o
st,
v
o
l
u
m
e
,
m
a
ss
,
a
n
d
p
o
w
e
r
lo
ss
e
s.
Id
e
a
ll
y
th
e
re
sh
o
u
ld
n
'
t
b
e
a
n
y
DC a
t
th
e
o
u
t
p
u
t
o
f
th
e
i
n
v
e
rter,
b
u
t
p
ra
c
ti
c
a
ll
y
,
a
sm
a
ll
a
m
o
u
n
t
o
f
DC
c
u
rre
n
t
is
p
re
se
n
t.
T
h
e
re
f
o
re
,
in
t
h
is
p
a
p
e
r
th
e
re
a
re
tec
h
n
iq
u
e
s
f
o
r
th
e
DC o
f
f
s
e
t
e
li
m
in
a
ti
o
n
a
re
p
r
o
p
o
se
d
.
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o
m
e
h
a
v
e
d
ra
w
b
a
c
k
s
w
h
ich
w
a
s
trea
ted
b
y
a
n
o
th
e
r
t
e
c
h
n
iq
u
e
.
A
lso
th
e
re
a
re
b
e
st
so
lu
ti
o
n
s
f
o
r
e
li
m
in
a
ti
n
g
DC
o
ff
s
e
t
a
s
in
se
c
ti
o
n
1
7
,
a
n
d
1
8
a
s
it
e
x
p
lain
s
h
o
w
to
re
d
u
c
e
th
e
DC
o
ff
se
t
in
a
tran
s
f
o
r
m
e
rles
s
o
p
e
ra
ti
o
n
w
it
h
re
d
u
c
i
n
g
th
e
p
o
w
e
r
lo
ss
e
s,
m
a
ss
a
n
d
th
e
c
o
st ef
f
e
c
t.
.
K
ey
w
o
r
d
:
DC
o
f
f
s
et
c
o
m
p
e
n
s
a
tio
n
t
ec
h
n
iq
u
es
Gr
id
c
o
n
n
ec
ted
i
n
v
er
ter
s
Co
p
y
rig
h
t
©
201
8
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ah
m
ed
O
m
ar
,
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ar
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m
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t o
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lectr
ical
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n
g
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A
r
ab
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a
h
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t
m
a
il.c
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m
1.
I
NT
RO
D
UCT
I
O
N
P
o
w
er
q
u
ality
is
an
ess
en
tial
is
s
u
e
f
o
r
th
e
co
m
b
in
atio
n
o
f
g
r
id
co
n
n
ec
ted
in
v
er
ter
s
.
T
h
e
is
s
u
es
id
en
tif
ied
to
DC
cu
r
r
en
t
in
j
ec
tio
n
in
in
v
er
ter
b
ased
d
is
tr
ib
u
ted
g
en
er
atio
n
h
av
e
b
ee
n
g
en
er
ally
o
v
er
lo
o
k
ed
,
in
s
p
ite
o
f
d
ev
elo
p
in
g
co
n
ce
r
n
s
r
eg
ar
d
in
g
its
im
p
ac
t
o
n
d
is
tr
ib
u
tio
n
s
y
s
tem
co
m
p
o
n
en
ts
.
On
e
o
f
th
e
m
o
s
t
ex
tr
em
e
is
s
u
es
b
r
o
u
g
h
t
o
n
b
y
DC
cu
r
r
en
t
in
j
ec
tio
n
is
s
atu
r
atio
n
o
f
th
e
d
is
tr
ib
u
tio
n
tr
an
s
f
o
r
m
er
s
b
r
in
g
in
g
ab
o
u
t
w
av
ef
o
r
m
d
is
to
r
tio
n
,
ex
ce
s
s
iv
e
lo
s
s
es,
o
v
er
h
ea
tin
g
an
d
d
im
en
s
io
n
ed
lif
e
ex
p
ec
tan
cy
.
I
n
ad
d
itio
n
,
it
also
m
ay
ca
u
s
e
m
is
tak
es
in
s
o
m
e
o
f
th
e
m
ea
s
u
r
em
e
n
t
an
d
p
r
o
tectiv
e
r
elay
s
s
y
s
te
m
s
[
1
]
.
A
n
ac
ce
p
tab
le
s
o
u
r
ce
o
f
DC
cu
r
r
en
t
in
j
e
ctio
n
in
to
th
e
g
r
id
em
er
g
es
f
r
o
m
th
e
s
em
ico
n
d
u
cto
r
cir
cu
its
in
in
v
er
ter
f
r
am
ew
o
r
k
s
.
T
h
e
p
r
esen
ce
o
f
u
n
d
esira
b
le
DC
cu
r
r
en
t
co
m
p
o
n
en
ts
in
th
e
o
u
tp
u
t
cu
r
r
en
ts
o
f
s
u
ch
f
r
am
ew
o
r
k
s
ca
n
b
e
ascr
ib
ed
to
s
ev
er
al
f
ac
to
r
s
s
u
ch
as
p
u
ls
e
w
id
th
m
o
d
u
latio
n
s
ig
n
als,
n
o
n
-
l
in
ea
r
ity
o
f
th
e
s
w
itch
in
g
d
ev
ices,
an
d
th
e
d
r
if
t
in
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
m
ea
s
u
r
em
en
t
s
en
s
o
r
s
u
s
ed
to
g
iv
e
f
ee
d
b
ac
k
s
ig
n
als
f
o
r
th
e
co
n
tr
o
l
f
r
am
ew
o
r
k
s
.
A
n
u
m
b
er
o
f
r
u
les
an
d
s
tan
d
ar
d
s
ar
e
f
o
r
ce
d
to
lim
it
th
e
ef
f
ec
t
o
f
DC
cu
r
r
en
t
in
j
ec
tio
n
in
to
th
e
g
r
id
[
2]
,
[3
]
.
A
m
o
n
g
th
ese
p
r
in
cip
les
an
d
p
r
o
p
o
s
als
ar
e
r
u
les
to
r
estra
in
th
e
allo
w
ab
le
am
o
u
n
t
o
f
DC
cu
r
r
en
t
in
j
ec
tio
n
in
to
th
e
d
is
tr
ib
u
tio
n
n
etw
o
r
k
.
T
h
ey
v
ar
y
f
r
o
m
co
u
n
tr
y
to
co
u
n
tr
y
.
Fo
r
in
s
tan
ce
,
B
r
itis
h
s
tan
d
ar
d
lim
its
DC
in
j
ec
tio
n
to
2
0
m
A
f
o
r
d
is
tr
ib
u
ted
g
e
n
er
atio
n
w
ith
s
tag
e
s
tr
ea
m
s
b
en
ea
th
16A
rm
s
[
4
]
.
I
n
I
E
E
E
s
tan
d
ar
d
'
I
E
E
E
9
2
9
-
2
0
0
0
'
th
e
DC
lim
its
is
0
.
5
%
o
f
th
e
in
v
er
ter
r
ated
cu
r
r
en
t [
5
].
T
h
e
DC
cu
r
r
en
t
in
j
ec
tio
n
in
th
e
A
u
s
tr
alian
s
tan
d
ar
d
A
S4
7
7
7
.
2
s
h
o
u
ld
n
o
t
ex
ce
ed
0
.
5
%
o
f
th
e
in
v
er
ter
r
ated
o
u
tp
u
t
cu
r
r
e
nt
o
r
5
m
A
,
w
h
ich
is
th
e
g
r
ea
ter
[
6
]
.
Var
io
u
s
m
eth
o
d
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
p
r
ev
en
t
o
r
m
in
im
ize
DC
cu
r
r
en
t
in
j
ec
tio
n
b
y
g
r
id
-
co
n
n
ec
ted
in
v
er
ter
s
in
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
T
h
is
p
ap
er
p
r
esen
ts
a
r
ev
iew
o
n
th
e
is
s
u
e
o
f
th
e
DC
o
f
f
s
et
an
d
h
o
w
to
o
v
er
co
m
e
it
w
ith
d
if
f
er
en
t
m
eth
o
d
s
th
r
o
u
g
h
ex
is
tin
g
tech
n
iq
u
es
th
at
h
av
e
b
ee
n
s
u
b
m
itted
to
lim
it
DC
cu
r
r
en
t
in
j
ec
tio
n
in
to
th
e
d
is
tr
ib
u
tio
n
n
etw
o
r
k
as
w
ill
b
e
illu
s
tr
ated
in
ea
ch
s
ec
tio
n
.
s
ec
tio
n
1
is
th
e
I
n
tr
o
d
u
ctio
n
,
s
ec
tio
n
2
p
r
esen
ts
th
e
is
o
latio
n
tr
an
s
f
o
r
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er
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s
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r
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en
t
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an
s
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o
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ec
tio
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th
e
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r
r
en
t
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en
s
o
r
s
,
s
ec
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n
8
p
r
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ts
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e
p
o
w
er
in
ter
f
ac
in
g
tr
an
s
f
o
r
m
er
m
eth
o
d
,
s
ec
tio
n
9
p
r
o
p
o
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th
e
m
ath
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atica
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o
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el
m
eth
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ab
o
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t
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e
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ew
co
m
p
en
s
atio
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cir
cu
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m
eth
o
d
,
s
ec
tio
n
11
g
iv
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a
b
r
ief
ab
o
u
t
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AC
-
co
u
p
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g
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s
ec
tio
n
13
p
r
esen
ts
th
e
d
if
f
er
en
tial
am
p
lif
ier
m
eth
o
d
,
s
ec
tio
n
14
talk
s
ab
o
u
t
th
e
f
ee
d
b
ac
k
s
y
s
tem
tech
n
iq
u
e,
s
ec
tio
n
1
5
p
r
o
p
o
s
es
a
n
ew
ap
p
r
o
ac
h
o
f
f
o
r
DC
lin
k
cu
r
r
en
t
s
en
s
o
r
s
,
s
ec
tio
n
16
talk
s
ab
o
u
t
th
e
DC
cu
r
r
en
t
m
ea
s
u
r
em
en
t
in
in
v
er
ter
o
u
tp
u
t,
in
s
ec
tio
n
1
7
th
e
au
th
o
r
s
p
r
esen
t
a
n
o
v
el
co
n
tr
o
l
s
tr
ateg
y
f
o
r
r
ed
u
ctio
n
o
f
DC
o
f
f
s
et,
s
ec
tio
n
1
8
s
h
o
w
s
th
e
tr
an
s
f
o
r
m
e
r
less
m
eth
o
d
f
o
r
s
u
p
p
r
ess
io
n
o
f
DC
o
f
f
s
et,
an
d
s
ec
tio
n
1
9
is
th
e
co
n
clu
s
io
n
.
2.
I
SO
L
A
T
I
O
N
T
RAN
SFO
R
M
E
R
T
h
e
au
th
o
r
s
p
r
esen
t
A
lin
e
f
r
eq
u
en
cy
is
o
latio
n
tr
an
s
f
o
r
m
er
w
h
ich
is
f
r
eq
u
en
tly
em
p
lo
y
ed
at
th
e
in
v
er
ter
to
p
r
ev
en
t
p
en
etr
atio
n
o
f
u
n
w
an
ted
DC
cu
r
r
en
ts
in
t
o
th
e
g
r
id
.
A
ls
o
,
it
p
r
o
v
id
es
g
alv
an
ic
is
o
latio
n
b
etw
ee
n
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
an
d
th
e
g
r
id
.
Ho
w
ev
er
,
a
5
0
/6
0
Hz
tr
an
s
f
o
r
m
er
is
lar
g
e,
h
ea
v
y
an
d
is
a
s
u
b
s
tan
tial
co
s
t
in
g
r
id
co
n
n
ec
ted
in
v
er
ter
s
y
s
tem
s
.
A
d
d
itio
n
ally
,
it
co
n
tr
ib
u
tes
to
s
y
s
tem
lo
s
s
es
an
d
f
o
o
tp
r
in
t.
T
h
u
s
,
tr
an
s
f
o
r
m
er
less
s
y
s
tem
h
as
b
ec
o
m
e
attr
ac
tiv
e
in
th
e
r
ec
en
t
y
ea
r
s
.
I
t
h
as
b
ee
n
claim
ed
th
at
ad
o
p
tio
n
o
f
a
tr
an
s
f
o
r
m
er
less
P
V
in
v
er
ter
s
y
s
tem
r
ed
u
ce
s
th
e
o
v
er
all
s
y
s
tem
co
s
ts
b
y
2
5
%
co
m
p
ar
ed
to
th
e
co
s
t
o
f
a
s
y
s
te
m
th
at
in
clu
d
es
a
tr
an
s
f
o
r
m
er
[
7
]
an
d
im
p
r
o
v
es
s
y
s
t
em
ef
f
icien
cy
ab
o
u
t
1
.
5
to
2
%
[
8
]
.
So
th
is
tech
n
iq
u
e
h
as
s
ev
er
al
d
r
aw
b
ac
k
s
as
th
e
co
s
t,
s
y
s
tem
lo
s
s
es
d
u
e
to
th
e
tr
an
s
f
o
r
m
er
th
at
lead
u
s
to
u
s
e
o
th
er
tech
n
iq
u
e
w
ith
o
u
t
tr
an
s
f
o
r
m
er
s
u
ch
as th
e
u
s
e
o
f
ca
p
ac
ito
r
s
in
s
ec
tio
n
3
.
3.
C
AP
ACI
T
O
RS
T
h
e
au
th
o
r
p
r
esen
ts
h
er
e
t
h
at
T
h
e
u
s
e
o
f
ca
p
ac
ito
r
s
eith
er
it
i
s
AC
o
r
DC
f
o
r
p
r
ev
en
ti
n
g
D
C
cu
r
r
en
t
in
j
ec
tio
n
i
n
to
t
h
e
g
r
id
.
T
h
er
e
ar
e
s
o
m
e
ap
p
r
o
ac
h
es
u
s
i
n
g
AC
o
r
D
C
ca
p
ac
ito
r
s
,
w
e
w
il
l
ill
u
s
tr
ate
s
o
m
e
o
f
th
e
m
.
First
o
n
e
g
i
v
es
a
s
i
n
g
l
e
-
p
h
a
s
e
h
al
f
-
b
r
id
g
e
in
v
er
ter
w
it
h
D
C
ca
p
ac
ito
r
s
.
DC
n
o
d
e
f
o
r
m
ed
f
r
o
m
t
h
e
co
n
n
ec
tio
n
o
f
t
w
o
D
C
ca
p
ac
i
to
r
s
in
s
er
ie
s
[
9]
,
[
1
0
]
.
I
t
is
n
o
ted
th
at
th
i
s
ap
p
r
o
ac
h
is
n
o
t
ex
te
n
d
ed
to
th
r
ee
-
p
h
ase
i
n
v
er
ter
s
as
s
h
o
w
n
in
Fig
u
r
e
.
1
.
Seco
n
d
o
n
e
th
at
d
o
esn
’
t
al
lo
w
DC
cu
r
r
e
n
t
i
n
j
ec
tio
n
i
n
to
th
e
g
r
id
b
y
p
u
ttin
g
a
n
A
C
ca
p
ac
ito
r
in
s
er
ies
w
it
h
th
e
g
r
id
[
1
1
]
.
Fig
u
r
e
2
illu
s
tr
ates
t
h
at
th
er
e
ar
e
s
er
ie
s
d
io
d
es
co
n
n
ec
ted
ac
r
o
s
s
th
e
ca
p
ac
ito
r
to
p
r
ev
en
t
o
v
er
v
o
lta
g
e
p
r
o
tectio
n
.
T
h
is
m
eth
o
d
b
etter
t
h
a
n
t
h
at
o
f
t
h
e
is
o
latio
n
tr
an
s
f
o
r
m
er
b
u
t
also
h
as
s
o
m
e
li
m
itat
io
n
s
a
s
it
ca
n
'
t
b
e
u
s
ed
f
o
r
th
r
ee
p
h
ase
i
n
v
er
ter
.
So
w
e
g
o
t
h
r
o
u
g
h
an
o
th
er
p
o
in
t o
f
v
ie
w
as t
h
e
v
o
ltag
e
tr
an
s
f
o
r
m
er
.
Fig
u
r
e
1
.
Sin
g
le
p
h
ase
h
al
f
b
r
id
g
e
in
v
er
ter
w
i
th
D
C
ca
p
ac
ito
r
s
Fig
u
r
e
2
.
Sin
g
le
p
h
ase
H
-
b
r
id
g
e
in
v
er
ter
w
it
h
A
C
ca
p
ac
ito
r
4.
VO
L
T
A
G
E
T
R
ANSF
O
RM
E
R
T
h
e
au
th
o
r
s
ex
p
lain
A
ctiv
e
m
eth
o
d
s
th
at
ar
e
u
s
ed
f
o
r
p
r
ev
en
tin
g
DC
cu
r
r
en
t
in
j
ec
tio
n
in
to
th
e
g
r
id
b
ased
o
n
cu
r
r
en
t
s
en
s
o
r
s
in
co
n
tact
w
ith
v
o
ltag
e
tr
an
s
f
o
r
m
er
(
VT
)
to
lim
it
DC
in
j
ec
tio
n
,
alth
o
u
g
h
th
e
cu
r
r
en
t
s
en
s
o
r
is
ex
p
en
s
iv
e
in
d
etec
tin
g
s
m
all
DC
co
m
p
o
n
en
t.
I
t
talk
s
ab
o
u
t
a
v
o
ltag
e
tr
an
s
f
o
r
m
er
w
ith
1
:1
tu
r
n
’
s
r
atio
,
an
d
R
C
cir
cu
it.
T
h
e
p
r
im
ar
y
s
id
e
o
f
th
e
v
o
ltag
e
tr
an
s
f
o
r
m
er
is
co
n
n
ec
ted
ac
r
o
s
s
th
e
g
r
id
w
h
ile
th
e
s
ec
o
n
d
ar
y
o
n
e
is
co
n
n
ec
ted
in
s
er
ies
w
ith
th
e
R
C
cir
cu
it
as
illu
s
tr
ated
in
Fig
u
r
e
3
T
h
e
DC
cu
r
r
en
t
is
lim
ited
b
y
th
e
f
ee
d
b
ac
k
o
f
t
h
e
p
r
o
p
o
r
tio
n
al
in
teg
r
al
co
n
tr
o
ller
w
h
ich
ad
j
u
s
ts
th
e
in
v
er
ter
cu
r
r
en
t
b
y
th
is
co
n
v
en
tio
n
al
co
n
tr
o
ller
.
T
h
is
m
eth
o
d
is
ex
p
en
s
iv
e
as
it
r
eq
u
ir
es
co
m
p
lex
tr
an
s
f
o
r
m
er
s
an
d
cu
r
r
en
t
s
en
s
o
r
s
s
o
it
ad
d
s
co
s
t
an
d
p
o
w
er
lo
s
s
[
1
2
]
.
T
h
is
tech
n
iq
u
e
lim
its
th
e
s
m
all
DC
co
m
p
o
n
en
t
as
p
o
s
s
ib
le
at
it
ca
n
b
u
t
it
is
to
o
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
.
2
,
J
u
n
e
2
0
1
8
:
478
–
494
480
ex
p
en
s
iv
e
as
it
is
n
o
t
o
n
ly
u
s
e
th
e
v
o
ltag
e
tr
an
s
f
o
r
m
er
w
h
ich
co
s
ts
to
o
m
u
ch
b
u
t
also
cu
r
r
en
t
s
en
s
o
r
s
.
Hen
ce
,
w
e
w
ill
u
s
e
a
p
o
w
er
tr
an
s
f
o
r
m
er
as a
DC
o
f
f
s
et
s
en
s
o
r
in
th
e
f
o
llo
w
in
g
s
ec
tio
n
.
Fig
u
r
e
3
.
DC
o
f
f
s
et
c
u
r
r
en
t c
o
n
tr
o
l
lo
o
p
w
ith
a
v
o
ltag
e
tr
a
n
s
f
o
r
m
er
5.
L
O
W
P
O
WE
R
T
RANSF
O
R
M
E
R
T
h
e
au
th
o
r
s
ill
u
s
tr
ate
tec
h
n
iq
u
e
ab
o
u
t
DC
co
m
p
e
n
s
atio
n
u
s
in
g
lo
w
p
o
w
er
tr
an
s
f
o
r
m
er
as a
DC
o
f
f
s
e
t
s
en
s
o
r
.
A
DC
s
e
n
s
o
r
i
s
co
n
n
ec
ted
ac
r
o
s
s
t
h
e
i
n
v
er
ter
ter
m
in
als
an
d
co
n
s
i
s
ts
o
f
a
m
a
g
n
e
tic
cir
cu
it
w
h
ich
is
ap
p
licab
le
b
y
u
s
i
n
g
lo
w
p
o
w
e
r
tr
an
s
f
o
r
m
er
as ill
u
s
tr
ated
in
Fig
.
4
W
h
e
n
a
DC
v
o
lta
g
e
ap
p
ea
r
s
at
th
e
i
n
v
er
ter
o
u
tp
u
t
in
a
clo
s
ed
lo
o
p
co
n
d
itio
n
,
th
er
e
is
a
b
ig
d
is
to
r
tio
n
r
esu
lt
s
in
t
h
e
r
ea
cto
r
cu
r
r
en
t.
T
h
e
r
esu
lts
ap
p
r
o
v
e
th
at
t
h
is
tec
h
n
iq
u
e
i
s
ab
le
to
m
i
n
i
m
ize
th
e
DC
c
u
r
r
en
t
co
m
p
o
n
en
t
[
1
3
]
.
Ho
w
e
v
er
,
it
also
co
n
tain
s
th
e
p
o
w
er
tr
an
s
f
o
r
m
er
w
h
ic
h
w
il
l
to
i
n
c
r
ea
s
e
th
e
co
s
t.
W
e
m
o
v
e
t
h
r
o
u
g
h
t
h
e
n
e
x
t
s
ec
tio
n
w
h
ic
h
d
i
s
cu
s
s
es
th
e
cu
r
r
e
n
t
tr
an
s
d
u
ce
r
i
n
d
etec
tin
g
a
n
d
r
em
o
v
i
n
g
th
e
D
C
co
m
p
o
n
e
n
t
f
r
o
m
th
e
s
y
s
te
m
.
6.
CURR
E
NT
T
RANSD
UCE
R
T
h
is
m
eth
o
d
w
as
d
is
cu
s
s
e
d
b
y
th
e
au
th
o
r
s
as
th
e
cu
r
r
en
t
tr
an
s
d
u
ce
r
w
h
ich
is
em
p
lace
d
b
etw
ee
n
DC
ca
p
ac
ito
r
an
d
in
v
er
ter
s
w
itch
es
as
illu
s
tr
ated
in
Fig
.
5
to
m
ea
s
u
r
e
th
e
cu
r
r
en
t
w
h
ich
is
d
r
aw
n
f
r
o
m
th
e
o
u
tp
u
t.
T
h
er
e
ar
e
tw
o
s
tates
f
o
r
co
n
n
ec
tio
n
f
o
r
th
e
o
p
er
atio
n
o
f
th
e
in
v
er
ter
,
in
itial
o
n
e
is
th
e
co
n
n
ec
tin
g
s
tate
w
h
ich
h
ap
p
en
ed
w
h
en
th
e
o
u
tp
u
t
cu
r
r
en
t
s
tr
ea
m
s
to
th
e
lo
ad
th
r
o
u
g
h
th
e
DC
co
n
n
ec
t
s
en
s
o
r
,
an
d
th
e
s
ec
o
n
d
o
n
e
is
th
e
f
r
ee
w
h
ee
lin
g
s
tate
w
h
er
e
th
e
cu
r
r
en
t
s
en
s
o
r
o
u
tp
u
t
ca
n
b
e
u
tili
ze
d
to
ex
p
el
th
e
o
f
f
s
et
cu
r
r
en
t
ac
ce
s
s
ib
le
in
th
e
in
v
er
ter
cu
r
r
en
t.
No
tw
ith
s
tan
d
in
g
th
is
f
av
o
r
ab
le
p
o
s
itio
n
th
is
p
r
o
ce
d
u
r
e
h
as
th
e
ab
ilit
y
to
o
p
er
ate
w
ith
o
u
t
tr
an
s
f
o
r
m
er
s
o
it
r
ed
u
ce
s
th
e
co
s
t
[
1
0
]
.
T
h
is
m
eth
o
d
is
b
etter
th
an
b
ef
o
r
e,
as
th
e
cu
r
r
en
t
s
en
s
o
r
o
u
tp
u
t
ca
n
b
e
u
s
ed
to
r
em
o
v
e
an
y
DC
o
f
f
s
et
f
o
u
n
d
in
th
e
in
v
er
ter
o
u
tp
u
t
cu
r
r
en
t
in
a
tr
an
s
f
o
r
m
er
less
o
p
er
atio
n
s
o
it
r
ed
u
ce
s
th
e
co
s
t.
Ho
w
ev
er
,
th
e
au
th
o
r
s
s
h
o
w
ed
ex
p
er
im
en
tal
r
esu
lts
p
r
o
v
e
th
at
th
e
elim
in
atio
n
o
f
th
e
DC
co
m
p
o
n
en
t
in
th
is
m
eth
o
d
is
lim
ited
w
ith
in
ce
r
tain
r
an
g
e.
Hen
ce
w
e
g
o
th
r
o
u
g
h
an
o
th
er
tech
n
iq
u
e
as
th
e
tw
o
DC
j
o
in
cu
r
r
en
t sen
s
o
r
s
in
s
ec
tio
n
7
.
Fig
u
r
e
4.
DC
co
m
p
en
s
atio
n
te
ch
n
iq
u
e
u
s
i
n
g
lo
w
p
o
w
er
tr
an
s
f
o
r
m
er
as a
D
C
o
f
f
s
et
s
e
n
s
o
r
Fig
u
r
e
5.
H
-
b
r
id
g
e
in
v
er
ter
u
s
i
n
g
D
C
-
li
n
k
c
u
r
r
en
t
s
en
s
o
r
to
co
m
p
en
s
ate
DC
c
u
r
r
en
t in
j
ec
tio
n
i
n
to
th
e
g
r
id
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
R
ev
iew
o
f D
C
Off
s
et
C
o
mp
en
s
a
tio
n
Tech
n
iq
u
es fo
r
Gri
d
C
o
n
n
ec
ted
I
n
ve
r
ters
(
A
h
med
Om
a
r
)
481
7.
DC
CURR
E
NT
S
E
NSO
R
S
T
h
e
au
th
o
r
s
E
x
am
in
e
tw
o
DC
j
o
in
cu
r
r
en
t
s
en
s
o
r
s
ar
e
u
tili
ze
d
to
r
em
u
n
er
ate
th
e
DC
o
f
f
s
et
cu
r
r
en
t
in
th
e
th
r
ee
-
lev
el
h
alf
-
b
r
id
g
e
in
v
er
te
r
as
d
elin
ea
ted
in
Fig
.
6
th
e
u
p
p
er
s
en
s
o
r
is
ass
o
ciate
d
b
etw
ee
n
th
e
u
p
p
er
ter
m
in
al
o
f
ca
p
ac
ito
r
C
1
an
d
th
e
u
p
p
er
s
w
itch
S
1
to
q
u
an
tif
y
th
e
p
o
s
itiv
e
DC
lin
k
cu
r
r
en
t
d
u
r
in
g
th
e
p
o
s
itiv
e
p
o
r
tio
n
o
f
th
e
m
ain
cy
cle.
T
h
e
DC
o
f
f
s
et
is
alig
n
ed
d
u
r
in
g
th
e
n
eg
ativ
e
h
alf
cy
cle,
w
h
en
th
e
p
o
s
itiv
e
DC
lin
k
cu
r
r
en
t
d
r
o
p
s
to
ze
r
o
.
T
h
e
lo
w
er
s
en
s
o
r
is
co
u
p
led
b
etw
ee
n
th
e
b
ase
ter
m
in
al
o
f
DC
c
ap
ac
ito
r
C
2
an
d
s
w
itch
S
4
to
g
au
g
e
th
e
n
eg
ativ
e
DC
lin
k
cu
r
r
en
t
d
u
r
in
g
th
e
n
eg
ativ
e
h
alf
cy
cle.
Fo
r
th
is
s
itu
atio
n
,
th
e
DC
o
f
f
s
et
is
ex
p
elled
d
u
r
in
g
th
e
p
o
s
itiv
e
h
alf
cy
cle
w
h
en
th
e
n
eg
ativ
e
DC
in
ter
f
ac
e
d
r
o
p
s
to
ze
r
o
d
u
r
in
g
th
e
p
o
s
itiv
e
h
alf
m
ain
s
cy
cle.
Ho
w
ev
er
,
th
e
g
u
ar
an
teed
ac
h
iev
em
en
t
o
f
th
is
tech
n
iq
u
e
is
lim
ited
b
ec
au
s
e
th
e
p
r
esen
t
s
en
s
o
r
s
ar
e
s
et
w
h
er
e
th
ey
m
ea
s
u
r
e
d
is
co
n
tin
u
o
u
s
cu
r
r
en
ts
,
w
h
ich
is
illo
g
ical
[
1
0
]
.
T
h
is
tech
n
iq
u
e
u
s
es
tw
o
DC
j
o
in
cu
r
r
en
t
s
en
s
o
r
s
n
o
t
o
n
ly
w
h
ich
p
lay
ed
th
e
r
o
le
o
f
th
e
p
o
w
er
tr
an
s
f
o
r
m
er
as
in
s
ec
tio
n
5
s
o
it
allo
w
s
th
e
tr
an
s
f
o
r
m
er
less
o
p
er
atio
n
,
b
u
t
it
h
as
a
b
ig
d
is
ad
v
an
tag
e
th
at
it
m
ea
s
u
r
es
th
e
d
is
co
n
tin
u
o
u
s
cu
r
r
en
t
w
h
ich
is
im
p
r
ac
tical.
Fig
u
r
e
6.
T
h
r
ee
-
lev
el
h
al
f
b
r
id
g
e
in
v
er
ter
u
s
in
g
p
o
s
iti
v
e
an
d
n
eg
at
iv
e
D
C
cu
r
r
e
n
t se
n
s
o
r
s
t
o
co
m
p
en
s
ate
D
C
cu
r
r
en
t i
n
j
ec
tio
n
to
th
e
lo
ad
8.
P
O
WE
R
I
N
T
E
RF
ACI
NG
T
RANSF
O
RM
E
R
T
h
e
au
th
o
r
s
P
r
esen
t
th
e
lim
itatio
n
o
f
th
e
DC
in
j
ec
tio
n
in
to
A
C
n
etw
o
r
k
b
y
g
r
id
co
n
n
ec
ted
in
v
e
r
ter
s
.
T
h
is
p
r
o
ce
d
u
r
e
is
m
ad
e
b
y
u
s
in
g
a
p
o
w
er
tr
an
s
f
o
r
m
er
as
an
in
ter
f
ac
e
b
etw
ee
n
th
e
o
u
tp
u
t
o
f
th
e
in
v
er
ter
an
d
th
e
A
C
n
etw
o
r
k
.
T
h
is
tech
n
iq
u
e
h
as
s
o
m
e
s
er
io
u
s
d
is
ad
v
an
tag
es,
id
ea
lly
n
o
DC
cu
r
r
en
t
ca
n
b
e
av
ailab
le
at
th
e
o
u
tp
u
t
o
f
th
e
in
v
er
ter
,
b
u
t
p
r
ac
t
ically
in
th
e
ab
s
en
ce
o
f
s
o
m
e
s
p
ec
ial
m
ea
s
u
r
es,
a
litt
le
am
o
u
n
t
o
f
DC
is
av
ailab
le
as
a
r
esu
lt
o
f
cir
cu
it
co
m
p
o
n
en
t
im
p
er
f
ec
tio
n
s
.
T
h
e
f
o
cu
s
o
f
th
is
tech
n
iq
u
e
is
o
n
th
e
m
ath
em
atica
l
m
o
d
elin
g
o
f
a
p
r
o
p
o
s
ed
DC
o
f
f
s
et
s
en
s
o
r
an
d
DC
o
f
f
s
et
co
n
tr
o
l
s
y
s
tem
.
T
h
e
d
is
ad
v
an
tag
es
o
f
th
is
tech
n
iq
u
e
ar
e
p
o
w
er
lo
s
s
es
an
d
it
ad
d
s
co
s
ts
,
m
ass
an
d
v
o
lu
m
e.
DC
p
o
w
er
f
r
o
m
th
e
s
o
lar
p
an
el
is
ch
an
g
ed
to
A
C
b
y
an
in
v
er
ter
.
T
h
eo
r
etica
lly
th
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
in
v
er
ter
s
h
o
u
ld
b
e
p
u
r
ely
A
C
,
b
u
t
p
r
ac
tically
it
w
ill
co
n
tain
s
m
all
am
o
u
n
t
o
f
DC
.
A
s
th
e
DC
in
j
ec
tio
n
in
cr
ea
s
e
in
th
e
A
C
n
etw
o
r
k
,
th
is
ca
n
r
esu
lt
in
tr
o
u
b
les
as
tr
an
s
f
o
r
m
er
s
atu
r
atio
n
,
tr
an
s
f
o
r
m
er
m
ag
n
etizin
g
cu
r
r
en
t
d
is
to
r
tio
n
,
m
eter
in
g
er
r
o
r
s
,
an
d
m
alf
u
n
ctio
n
o
f
p
r
o
tectiv
e
eq
u
ip
m
en
t.
Fo
r
th
is
ca
u
s
es
th
er
e
ar
e
s
o
m
e
s
tan
d
a
r
d
s
th
at
p
u
t
lim
its
f
o
r
DC
in
j
ec
tio
n
[
1
4
]
.
A
s
illu
s
tr
ated
in
th
is
tech
n
iq
u
e
h
as
s
ev
er
al
d
r
aw
b
ac
k
s
,
th
is
lead
u
s
to
u
s
e
an
o
th
er
m
eth
o
d
in
th
e
n
ex
t
s
ec
tio
n
s
.
9.
M
AT
H
E
M
AT
I
CAL
M
O
DE
L
T
h
e
au
th
o
r
s
d
em
o
n
s
tr
ate
alter
n
ativ
e
s
o
lu
tio
n
s
f
o
r
th
e
DC
in
j
ec
tio
n
tr
o
u
b
le
t
h
at
h
as
b
ee
n
in
tr
o
d
u
ce
d
:
I
t
p
r
o
v
id
es
th
e
u
s
ag
e
o
f
a
f
ee
d
b
ac
k
lo
o
p
to
elim
in
ate
th
e
DC
o
f
f
s
et.
A
s
im
p
le
m
ath
em
atica
l
m
o
d
el
is
en
h
an
ce
d
f
o
r
th
e
f
ee
d
b
ac
k
s
y
s
tem
.
I
t
is
p
r
o
p
o
s
ed
th
at
th
e
in
v
er
ter
is
v
o
ltag
e
co
n
tr
o
lled
.
B
u
t
th
er
e
is
n
o
ex
p
er
im
en
tatio
n
v
alid
ated
f
o
r
th
is
tech
n
iq
u
e.
Of
f
s
et
cu
r
r
en
t
is
d
u
e
to
cir
cu
it
co
m
p
o
n
en
t
im
p
er
f
ec
tio
n
s
.
W
ith
th
e
DC
o
f
f
s
et
co
n
tr
o
ller
o
p
er
atin
g
,
a
co
m
p
en
s
atin
g
cu
r
r
en
t
is
p
r
o
d
u
ce
d
at
s
tead
y
s
tate,
w
h
ich
th
eo
r
etica
lly
ca
n
ce
l
s
o
f
f
s
et
cu
r
r
en
t[
1
4
].
T
h
e
co
n
tr
o
l
s
y
s
tem
r
ec
eiv
ed
f
o
r
th
e
DC
b
u
s
v
o
ltag
e
is
s
h
o
w
n
in
Fig
.
8
E
f
f
ec
tiv
e
co
n
tr
o
l
o
f
th
e
DC
b
u
s
v
o
ltag
e
g
u
ar
an
tees
b
alan
ce
b
etw
ee
n
p
o
w
er
o
u
tp
u
t
o
f
th
e
DC
to
DC
co
n
v
er
ter
an
d
p
o
w
er
in
j
ec
ted
in
to
th
e
A
C
n
etw
o
r
k
.
A
b
asic
co
r
r
esp
o
n
d
in
g
co
n
tr
o
ller
w
ith
g
ain
is
u
tili
ze
d
.
T
h
e
DC
b
u
s
v
o
ltag
e
s
ig
n
al
is
w
ea
k
en
ed
b
y
a
f
ac
to
r
an
d
f
ilter
ed
.
A
t
s
tead
y
s
tate
th
e
o
u
tp
u
t
o
f
th
e
co
r
r
esp
o
n
d
in
g
co
n
tr
o
l
w
ill
b
e
a
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
.
2
,
J
u
n
e
2
0
1
8
:
478
–
494
482
co
n
s
tan
t
v
alu
e.
T
h
is
is
m
u
ltip
lied
b
y
a
s
in
u
s
o
id
al
s
ig
n
al
w
h
ich
is
in
p
h
ase
w
ith
A
C
s
u
p
p
ly
v
o
ltag
e
.
T
h
er
e
is
an
o
u
tp
u
t
o
f
th
e
m
u
ltip
lier
,
is
th
e
cu
r
r
en
t
r
ef
er
en
ce
f
o
r
th
e
in
v
er
ter
.
A
n
in
cr
ea
s
e
in
th
e
o
u
tp
u
t
p
o
w
er
f
r
o
m
th
e
s
o
lar
p
an
els
w
ill
af
f
ec
t
th
e
DC
b
u
s
v
o
ltag
e
to
in
cr
ea
s
e
co
n
s
eq
u
en
tly
.
T
h
is
m
ak
es
th
e
er
r
o
r
v
o
ltag
e
at
th
e
in
p
u
t
o
f
th
e
co
r
r
esp
o
n
d
in
g
co
n
tr
o
ller
t
o
in
cr
ea
s
e
w
h
ich
lead
to
an
in
cr
ea
s
e
in
th
e
in
v
er
ter
cu
r
r
en
t
r
ef
er
en
ce
s
ig
n
al.
So
th
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
in
v
er
ter
g
o
es
u
p
an
d
m
o
r
e
p
o
w
er
is
s
u
s
tain
ed
in
to
th
e
A
C
n
etw
o
r
k
.
E
v
en
tu
ally
,
a
r
is
e
in
p
o
w
er
o
u
tp
u
t
f
r
o
m
th
e
s
o
lar
p
an
els
lead
s
to
ex
p
an
s
io
n
f
o
r
th
e
DC
b
u
s
v
o
ltag
e
s
tead
y
s
tate
er
r
o
r
[
1
4
]
.
T
h
is
tech
n
iq
u
e
is
p
er
f
ec
t
m
ath
em
atica
lly
at
it
p
r
o
v
id
es
th
e
is
s
u
e
w
ith
a
f
ee
d
b
ac
k
s
y
s
tem
th
r
o
u
g
h
a
m
ath
em
atica
l
m
o
d
el,
b
u
t
th
er
e
ar
e
n
o
ex
p
er
im
en
tal
r
esu
lts
v
alid
ate
th
is
tech
n
iq
u
e.
Hen
ce
,
a
n
ew
m
eth
o
d
is
p
r
esen
ted
in
s
ec
tio
n
X.
Fig
u
r
e
7.
Gr
id
-
C
o
n
n
ec
ted
P
V
S
y
s
te
m
Fig
u
r
e
8
.
I
n
v
er
ter
C
o
n
tr
o
l S
y
s
te
m
W
h
ich
co
m
p
en
s
atin
g
cu
r
r
en
t,
r
ef
er
en
ce
cu
r
r
en
t,
o
f
f
s
et
cu
r
r
en
t,
P
I
co
n
tr
o
ller
g
ain
,
h
all
ef
f
ec
t c
o
n
s
tan
t=1
V/A
,
DC
b
u
s
v
o
ltag
e.
10.
NE
W
CO
M
P
E
NSAT
I
O
N
CI
RCUI
T
T
h
e
au
th
o
r
s
clar
if
y
a
n
ew
cu
r
r
en
t
d
etec
tin
g
m
eth
o
d
f
o
r
th
e
cu
r
r
en
t
-
m
o
d
e
DC
-
DC
b
u
ck
co
n
v
er
ter
,
h
o
w
ev
er
th
e
cu
r
r
en
t
m
ir
r
o
r
in
g
s
ch
em
e
h
elp
s
to
p
r
ev
en
t
co
n
v
er
s
io
n
ef
f
icien
cy
f
r
o
m
d
ec
r
ea
s
in
g
,
an
d
it
en
d
u
r
es
f
r
o
m
th
e
v
o
ltag
e
o
f
f
s
et
o
f
t
h
e
am
p
lif
ier
f
ee
d
b
ac
k
.
So
th
is
ap
p
r
o
ac
h
p
r
o
p
o
s
es
a
n
ew
co
m
p
en
s
atio
n
cir
cu
it
in
v
o
lv
ed
in
to
th
e
cu
r
r
en
t
s
en
s
in
g
b
lo
ck
to
o
v
er
co
m
e
th
e
o
f
f
s
et
v
o
ltag
e
[
1
5
].
T
h
e
in
teg
r
atio
n
o
f
a
s
y
s
tem
in
to
s
in
g
le
ch
ip
is
s
u
cc
ess
iv
ely
f
ig
u
r
ed
o
u
t
n
o
w
ad
ay
s
,
d
if
f
er
en
t
s
tr
u
ctu
r
e
to
p
ics
s
h
o
u
ld
k
n
o
w
f
o
r
SOC
(
Sy
s
tem
-
On
-
C
h
ip
)
im
p
lem
en
tatio
n
s
[
1
6
]
,
[
1
7
]
.
Fo
r
attain
in
g
th
e
ch
allen
g
in
g
h
ar
d
w
ar
e,
th
e
in
teg
r
ated
cir
cu
its
as
DC
-
DC
co
n
v
er
ter
s
ar
e
in
v
o
lv
ed
in
to
a
ch
ip
as
m
ix
ed
-
s
ig
n
al
cir
cu
its
in
ad
d
itio
n
to
d
ig
ital
p
r
o
ce
s
s
in
g
s
y
s
tem
[
1
8
]
,
[
1
9
].
T
h
e
g
en
er
al
b
lo
ck
d
iag
r
am
o
f
th
e
cu
r
r
en
t
m
o
d
e
DC
-
DC
b
u
ck
co
n
v
er
ter
is
ap
p
ea
r
ed
in
Fig
.
9
.
T
h
e
in
d
u
cto
r
an
d
ca
p
ac
ito
r
h
av
e
a
u
s
ag
e
in
th
e
o
u
tp
u
t
f
ilter
.
T
h
e
P
MO
S
an
d
NM
OS
s
w
itch
es
ar
e
co
n
tr
o
lled
b
y
th
e
ON
an
d
OFF
tim
e
s
ig
n
als.
T
h
at
is
ch
ar
ac
ter
ized
b
y
th
e
d
u
ty
cy
cle
o
f
th
e
P
W
M
(
P
u
ls
e
-
W
id
th
Mo
d
u
latio
n
)
s
ig
n
al
g
en
er
ato
r
.
A
m
id
th
e
ON
tim
e
th
e
P
MO
S
d
r
aw
s
th
e
cu
r
r
en
t
f
r
o
m
th
e
b
atter
y
an
d
s
u
p
p
ly
th
e
in
d
u
cto
r
w
ith
th
e
cu
r
r
en
t
w
h
ich
r
en
ew
s
th
e
o
u
tp
u
t
ca
p
ac
ito
r
.
T
h
is
ca
p
ac
ito
r
h
as
a
g
r
ea
t
u
s
ag
e
in
k
ee
p
in
g
u
p
th
e
o
u
tp
u
t
v
o
ltag
e
d
u
r
in
g
p
r
o
v
id
in
g
th
e
o
u
tp
u
t lo
ad
cu
r
r
en
t
.
B
esid
e
th
at
th
e
f
ee
d
b
ac
k
s
en
s
in
g
o
f
th
e
cu
r
r
en
t.
I
n
th
e
cu
r
r
en
t
-
m
o
d
e
DC
-
DC
co
n
v
er
ter
,
th
e
cu
r
r
en
t
f
lo
w
in
g
th
r
o
u
g
h
th
e
in
d
u
cto
r
ca
n
b
e
u
s
ed
f
o
r
co
n
tr
o
llin
g
th
e
co
n
v
er
ter
o
p
er
atio
n
s
an
d
ac
co
r
d
in
g
ly
p
r
o
d
u
cin
g
th
e
co
r
r
esp
o
n
d
in
g
P
W
M
s
ig
n
als
f
o
r
th
e
o
u
tp
u
t
s
w
itch
es.
T
h
e
o
r
d
in
ar
y
ap
p
r
o
ac
h
to
d
etec
t
th
e
cu
r
r
en
t
f
lo
w
in
g
th
r
o
u
g
h
th
e
in
d
u
cto
r
is
to
p
u
t
th
e
r
esis
to
r
alo
n
g
th
e
cu
r
r
en
t
p
ath
an
d
s
cr
ee
n
th
e
v
o
ltag
e
d
r
o
p
o
v
er
th
e
r
esis
to
r
[
2
0
]
,
[
2
1
]
.
I
t
s
v
alu
e
o
u
g
h
t
to
b
e
v
er
y
s
m
all
in
o
r
d
er
n
o
t
to
co
r
r
u
p
t
th
e
co
n
v
er
s
io
n
ef
f
icien
cy
in
lig
h
t
o
f
th
e
f
ac
t
th
at
th
e
co
n
d
u
ctio
n
lo
s
s
o
f
th
e
co
n
v
er
ter
f
u
n
d
am
en
tally
co
m
es
f
r
o
m
en
er
g
y
s
ca
tter
in
g
d
u
e
to
th
e
r
esis
tiv
e
co
m
p
o
n
en
t
alo
n
g
th
e
cu
r
r
en
t
p
ath
.
B
esid
e
th
at
th
e
cu
r
r
en
t
o
f
th
e
in
d
u
cto
r
w
ill
b
e
s
u
f
f
icien
tly
in
cr
ea
s
ed
f
o
r
th
e
in
s
tan
ce
o
f
lar
g
e
d
u
ty
cy
cle
o
p
er
atio
n
.
C
u
r
r
en
t
m
ir
r
o
r
in
g
b
etw
ee
n
th
e
o
u
tp
u
t
s
w
itch
an
d
s
en
s
in
g
tr
an
s
is
to
r
s
ca
n
b
e
u
s
ed
to
s
cr
ee
n
th
e
cu
r
r
en
t
w
h
ich
f
lo
w
s
ac
r
o
s
s
th
e
in
d
u
cto
r
.
T
h
e
o
p
er
atin
g
p
o
in
ts
s
h
o
u
ld
b
e
id
en
tical
b
etw
ee
n
th
e
tw
o
tr
an
s
is
to
r
s
b
y
u
s
in
g
th
e
f
ee
d
b
ac
k
lo
o
p
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
R
ev
iew
o
f D
C
Off
s
et
C
o
mp
en
s
a
tio
n
Tech
n
iq
u
es fo
r
Gri
d
C
o
n
n
ec
ted
I
n
ve
r
ters
(
A
h
med
Om
a
r
)
483
Fig
u
r
e
9.
B
lo
ck
d
iag
r
am
o
f
th
e
cu
r
r
en
t
-
m
o
d
e DC
-
DC
b
u
ck
co
n
v
er
ter
Fig
u
r
e
10.
C
ir
cu
it sc
h
e
m
atic
o
f
th
e
c
u
r
r
en
t
-
s
e
n
s
in
g
o
p
er
atio
n
T
h
e
cu
r
r
en
t
s
e
n
s
i
n
g
cir
cu
it
w
h
ich
w
il
l
b
e
p
r
o
p
o
s
ed
,
th
e
s
en
s
ed
cu
r
r
en
t
in
it
is
d
i
v
id
ed
in
to
s
m
al
l
b
ias
cu
r
r
en
t
an
d
s
e
n
s
ed
c
u
r
r
en
t
th
a
t
w
il
l
b
e
ch
an
g
ed
in
to
v
o
lta
g
e
s
ig
n
al.
I
n
Fi
g
u
r
e
1
0
th
er
e
ar
e
t
w
el
v
e
tr
an
s
is
to
r
s
(M
1,
M
2,
M
3
,
M
4
,
M
5
,
M
6
,
M
7
,
M
8
,
M
9,
M
10,
M
swp,
M
swn
)
,
f
o
u
r
s
w
itc
h
es
(
SW
1
,
SW
2
,
SW
3
,
SW
4
)
,
o
n
e
r
esis
to
r
an
d
A
1
w
h
ic
h
is
a
n
a
m
p
li
f
ier
.
I
n
th
i
s
cir
cu
it
tr
a
n
s
i
s
to
r
M
4
d
er
iv
ed
b
y
t
h
e
o
u
tp
u
t
o
f
th
e
f
ee
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b
ac
k
a
m
p
lif
ier
A
1
in
o
r
d
er
to
m
a
k
e
t
h
e
s
en
s
ed
c
u
r
r
en
t
o
f
tr
a
n
s
i
s
to
r
M
1
f
lo
w
s
in
M
4
th
a
t
w
ill
en
h
a
n
ce
t
h
e
a
cc
u
r
ac
y
o
f
s
e
n
s
in
g
.
T
h
e
t
w
o
tr
an
s
i
s
to
r
s
M
swp
a
n
d
M
swn
ar
e
th
e
o
u
tp
u
t
s
w
i
tch
e
s
t
h
at
ar
e
d
er
iv
ed
b
y
th
e
ON
-
ti
m
e
w
h
ic
h
i
s
g
iv
e
n
t
h
e
s
y
m
b
o
l
Φ
1
an
d
th
e
O
FF
-
ti
m
e
w
h
ic
h
is
g
iv
e
n
t
h
e
s
y
m
b
o
l
Φ
2
,
s
ep
ar
ately
.
I
f
th
e
f
ee
d
b
ac
k
is
n
eg
at
iv
e
b
y
t
h
e
a
m
p
li
f
ier
,
it
w
ill
lead
t
h
e
n
o
d
es
o
f
(
A
)
an
d
(
B
)
t
y
p
ical
i
n
o
r
d
er
to
m
ak
e
th
e
c
u
r
r
en
t
co
n
n
ec
tin
g
b
et
w
ee
n
M
1
an
d
M
2
ca
n
b
e
ac
co
m
p
lis
h
ed
b
ec
au
s
e
o
f
t
h
e
s
i
m
i
lar
it
y
o
f
th
e
s
o
u
r
ce
-
d
r
ain
v
o
lta
g
es.
Fig
u
r
e
11.
C
ir
cu
it sc
h
e
m
at
ic
o
f
th
e
o
p
er
atio
n
al
a
m
p
li
f
ier
Fig
u
r
e
1
2
.
Op
er
atio
n
al
am
p
li
f
ier
in
clu
d
i
n
g
th
e
o
f
f
s
et
v
o
ltag
e
d
u
r
i
n
g
Φ
1
T
h
e
v
o
ltag
e
o
f
f
s
et
o
f
t
h
e
C
M
OS
o
p
er
atio
n
al
a
m
p
li
f
ier
m
a
y
b
e
s
u
f
f
icien
t
l
y
lar
g
e
i
n
o
r
d
er
to
b
r
ea
k
d
o
w
n
t
h
e
er
r
o
r
in
t
h
e
co
n
f
i
g
u
r
atio
n
o
f
t
h
e
clo
s
ed
lo
o
p
.
Fig
u
r
e
1
2
illu
s
tr
ates
t
h
e
o
p
er
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Fi
g
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u
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R
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1
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
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P
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w
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&
Dr
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y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
478
–
494
484
T
h
e
cu
r
r
en
t
o
f
t
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in
d
u
cto
r
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w
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e
ON
-
ti
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e
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tp
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t
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g
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EN2
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m
e,
th
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te
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ap
p
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w
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t
h
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g
h
t
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an
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to
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h
is
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u
tp
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t
c
u
r
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t
ca
n
b
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ilized
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o
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co
m
p
en
s
a
tin
g
t
h
e
o
f
f
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et
v
o
ltag
e.
Si
n
ce
t
h
e
lo
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p
o
f
co
m
p
en
s
atio
n
in
Fi
g
u
r
e
1
3
co
n
tain
s
th
e
i
n
te
g
r
at
o
r
,
a
h
u
g
e
D
C
g
ai
n
co
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ld
b
e
s
u
f
f
ici
en
t
to
d
ec
r
ea
s
e
th
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er
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o
r
w
h
ic
h
w
as
f
o
u
n
d
i
n
th
e
o
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n
o
f
t
h
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clo
s
ed
lo
o
p
.
T
h
e
ca
p
ac
itan
ce
p
r
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p
o
r
tio
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o
f
th
e
in
teg
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ato
r
a
n
d
th
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clo
ck
f
r
eq
u
en
c
y
d
ec
id
e
th
e
s
ettli
n
g
ti
m
e
o
f
o
f
f
s
et
co
m
p
e
n
s
atio
n
o
p
er
atio
n
.
T
h
is
o
p
er
atio
n
a
m
p
li
f
ier
h
as
lo
w
p
o
w
er
-
c
o
n
s
u
m
p
tio
n
ca
u
s
ed
li
m
ita
tio
n
f
o
r
th
e
a
m
p
li
f
ier
b
an
d
w
id
th
a
n
d
a
h
u
g
e
er
r
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co
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ld
o
cc
u
r
w
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ile
i
n
teg
r
at
io
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w
h
e
n
t
h
e
D
C
-
DC
co
n
v
er
ter
w
o
r
k
s
w
it
h
lo
w
d
u
t
y
c
y
cle.
I
n
s
p
ite
o
f
all
o
f
t
h
e
s
e
d
r
a
w
b
ac
k
s
th
e
co
m
p
e
n
s
a
tio
n
o
f
th
e
o
f
f
s
et
v
o
ltag
e
co
n
tin
u
es
w
o
r
k
i
n
g
[
2
2
]
.
T
h
is
ap
p
r
o
ac
h
h
as a
co
m
p
en
s
atio
n
cir
cu
it to
o
v
er
co
m
e
t
h
e
o
f
f
s
et
v
o
ltag
e
f
o
u
n
d
i
n
th
e
a
m
p
li
f
ier
f
ee
d
b
ac
k
.
B
u
t
it
h
as
a
p
r
o
b
lem
th
at
t
h
e
v
o
ltag
e
d
r
o
p
ac
r
o
s
s
th
e
r
esis
to
r
m
i
g
h
t
b
e
n
o
t
s
m
all
an
d
ca
n
ca
u
s
e
a
co
r
r
u
p
tio
n
f
o
r
th
e
co
n
v
er
s
io
n
e
f
f
icien
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y
in
ca
s
e
o
f
t
h
e
f
ac
t
th
a
t
th
e
co
n
d
u
ct
io
n
lo
s
s
o
f
th
e
co
n
v
er
ter
co
m
e
s
f
r
o
m
en
er
g
y
s
ca
tter
in
g
d
u
e
to
th
e
r
esis
t
iv
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co
m
p
o
n
en
t
alo
n
g
t
h
e
cu
r
r
en
t p
at
h
.
11.
AC
-
CO
UP
L
I
N
G
M
E
T
H
O
D
A
n
ew
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
b
y
th
e
au
th
o
r
f
o
r
DC
-
o
f
f
s
et
r
em
o
v
al,
in
in
teg
r
ated
w
ir
eless
r
ec
eiv
er
s
as
DC
R
s
(
d
ir
ec
t
-
co
n
v
er
s
io
n
r
ec
eiv
er
s
)
w
h
ich
u
s
e
b
an
d
w
id
th
ef
f
icien
t
m
o
d
u
latio
n
s
ch
em
es
as
QA
M
(
q
u
ad
r
atu
r
e
am
p
litu
d
e
m
o
d
u
latio
n
)
,
DC
-
o
f
f
s
et
is
a
b
ig
is
s
u
e
w
h
ich
f
ac
es
th
ese
r
ec
eiv
er
s
,
s
o
if
it
r
em
ain
s
as
it
is
w
ith
o
u
t
an
y
co
m
p
en
s
atio
n
,
it
ca
n
ca
u
s
e
d
am
ag
e
to
th
e
o
v
er
all
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
er
e
is
a
s
o
lu
tio
n
h
er
e
w
h
ich
ca
n
elim
in
ate
th
is
DC
-
o
f
f
s
et
b
y
u
s
in
g
A
C
-
co
u
p
lin
g
to
elim
in
ate
th
e
lo
w
-
f
r
eq
u
en
cy
d
is
tu
r
b
an
ce
s
[
2
3
].
DC
R
h
as
th
e
R
F
(
r
ad
io
f
r
eq
u
en
cy
)
s
ig
n
al
w
h
ich
is
ch
an
g
ed
to
ze
r
o
f
r
eq
u
en
cy
an
d
in
s
eq
u
en
ce
o
f
th
at
th
e
DC
-
o
f
f
s
et
w
il
l
ca
u
s
e
er
r
o
r
s
to
th
e
s
ig
n
al
[
2
4
]
,
[
2
5
]
,
[
2
6
].
T
h
e
DC
-
o
f
f
s
et
ca
n
eli
m
i
n
ate
th
e
r
ec
eiv
er
p
er
f
o
r
m
an
ce
a
s
s
aid
b
ef
o
r
e.
B
y
p
u
tti
n
g
f
ir
s
t
-
o
r
d
er
A
C
-
co
u
p
lin
g
h
ig
h
p
as
s
f
ilter
,
i
n
th
e
i
n
-
p
h
a
s
e
a
n
d
q
u
ad
r
atu
r
e
s
i
g
n
al
p
ath
s
,
as
i
llu
s
tr
ated
in
Fi
g
u
r
e
1
4
,
th
a
t
eli
m
i
n
ate
t
h
e
r
es
u
lt
s
o
f
DC
-
o
f
f
s
et.
B
u
t
also
it
ca
n
m
a
k
e
a
b
ig
r
ed
u
ctio
n
in
p
er
f
o
r
m
a
n
ce
if
t
h
e
u
s
a
g
e
o
f
t
h
e
b
aseb
an
d
o
f
th
e
s
i
g
n
a
l
s
p
ec
tr
u
m
o
f
th
e
m
o
d
u
lati
o
n
s
ch
e
m
e
h
as
en
er
g
y
n
ea
r
D
C
[
2
6
]
.
T
h
is
is
ap
p
lied
if
th
e
QA
M
s
ch
e
m
e
is
u
s
ed
.
B
P
F
(
b
an
d
p
ath
f
ilter
)
,
L
N
A
(
lo
w
-
n
o
is
e
a
m
p
lifie
r
)
.
A
s
ill
u
s
tr
ated
in
th
i
s
s
ec
tio
n
t
h
at
T
h
e
A
C
-
co
u
p
li
n
g
h
i
g
h
p
ass
f
il
ter
ca
n
eli
m
in
ate
t
h
e
D
C
co
m
p
o
n
en
t.
A
lt
h
o
u
g
h
,
it h
a
s
a
d
r
a
w
b
ac
k
w
h
ic
h
r
es
u
lts
in
a
b
ig
r
e
d
u
ctio
n
in
p
er
f
o
r
m
an
ce
if
t
h
e
u
s
a
g
e
o
f
t
h
e
b
ase
b
an
d
o
f
th
e
s
p
ec
tr
u
m
h
as
e
n
e
r
g
y
n
ea
r
DC
.
T
h
is
tech
n
iq
u
e
w
as
s
k
ip
p
ed
f
o
r
its
d
r
a
w
b
ac
k
s
a
n
d
m
o
v
e
th
r
o
u
g
h
th
e
f
o
llo
w
i
n
g
tech
n
iq
u
e.
F
i
g
u
r
e 1
3
.
Pro
p
o
s
ed
s
c
h
em
e to
co
m
p
en
s
ate th
e o
f
f
s
et
v
o
ltag
e o
f
th
e
am
p
lif
ier
Fig
u
r
e
1
4
.
A
d
ir
ec
t
-
co
n
v
e
r
s
io
n
r
ec
eiv
er
w
it
h
A
C
-
co
u
p
lin
g
12.
DC
O
F
F
SE
T
CO
M
P
E
NSA
T
E
D
VO
L
T
A
G
E
B
UF
F
E
R
T
h
e
au
th
o
r
s
h
o
w
s
a
n
ew
DC
o
f
f
s
et
co
m
p
en
s
atio
n
tech
n
iq
u
e
f
o
r
v
o
ltag
e
b
u
f
f
er
s
.
I
t
ca
n
b
e
u
tili
ze
d
to
en
h
an
ce
th
e
ac
cu
r
ac
y
o
f
d
ata
co
n
v
er
ter
s
.
T
h
at
tech
n
iq
u
e
d
ec
r
ea
s
es
th
e
er
r
o
r
o
f
th
e
g
ain
o
f
th
e
o
p
er
atio
n
am
p
lif
ier
[
2
7
].
T
h
e
r
eq
u
est
f
o
r
m
o
r
e
r
eso
lu
tio
n
an
d
m
u
ch
m
o
r
e
s
p
ee
d
DA
C
'
s
(
d
ig
ital
an
alo
g
u
e
co
n
v
er
ter
s
)
is
ex
ten
d
ed
ev
er
y
y
ea
r
w
ith
th
e
d
em
an
d
elec
tr
o
n
ics
ap
p
licatio
n
s
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
DA
C
s
co
u
ld
b
e
en
h
an
ce
d
b
y
u
s
in
g
o
f
f
s
et
co
m
p
en
s
atio
n
tech
n
iq
u
e
s
.
P
r
o
b
ab
ly
a
lar
g
e
p
ar
t
o
f
th
e
co
n
v
en
tio
n
al
tech
n
iq
u
es
co
m
p
en
s
ates
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
R
ev
iew
o
f D
C
Off
s
et
C
o
mp
en
s
a
tio
n
Tech
n
iq
u
es fo
r
Gri
d
C
o
n
n
ec
ted
I
n
ve
r
ters
(
A
h
med
Om
a
r
)
485
o
n
ly
f
o
r
th
e
DC
o
f
f
s
et
v
o
ltag
e
o
f
th
e
o
p
er
atio
n
am
p
lif
ier
b
u
t
n
o
t
th
e
er
r
o
r
o
f
th
e
g
ain
[
2
8
]
.
T
h
er
e
is
a
n
ee
d
f
o
r
r
eset
o
p
er
atio
n
am
p
lif
ier
o
u
tp
u
t
to
ze
r
o
at
ev
er
y
cy
cle,
s
o
th
is
ap
p
r
o
ac
h
p
r
o
p
o
s
es
a
DC
o
f
f
s
et
co
m
p
en
s
atio
n
tech
n
iq
u
e
w
h
ich
co
m
p
en
s
ates
f
o
r
o
f
f
s
et
v
o
ltag
e
an
d
er
r
o
r
o
f
th
e
g
ain
o
f
th
e
o
p
er
atio
n
am
p
lif
ier
.
T
h
is
cir
cu
it
as
o
th
er
ex
ch
an
g
ed
ca
p
ac
ito
r
cir
cu
its
en
d
u
r
es
f
r
o
m
ch
an
n
el
ch
ar
g
e
in
j
ec
tio
n
w
h
ich
ca
n
b
e
lim
ited
b
y
tu
r
n
in
g
S
1
o
f
f
s
o
m
ew
h
at
b
ef
o
r
e
S
3
,
w
h
en
S
1
is
tu
r
n
ed
o
f
f
,
ch
ar
g
e
(
w
h
ich
is
th
e
elem
en
t
o
f
th
e
v
o
ltag
e
at
n
o
d
e
X)
is
in
f
u
s
ed
o
n
to
th
e
ca
p
ac
ito
r
an
d
th
is
ch
ar
g
e
s
h
o
w
s
u
p
a
co
n
s
tan
t
o
f
f
s
et
at
th
e
o
u
tp
u
t.
A
f
ter
S
1
is
o
f
f
,
th
e
to
tal
ch
ar
g
e
at
n
o
d
e
X
s
tay
co
n
s
tan
t
m
ak
in
g
th
e
cir
cu
it
aw
ay
f
r
o
m
th
e
ch
ar
g
e
in
f
u
s
io
n
o
f
S
3
o
r
ch
ar
g
e
ab
s
o
r
p
tio
n
o
f
S
2
.
T
h
e
cir
cu
it
is
q
u
ick
as
th
e
tr
an
s
itio
n
o
f
th
e
v
o
ltag
e
at
th
e
o
u
tp
u
t
n
o
d
e
is
s
m
all
en
o
u
g
h
,
h
o
w
ev
er
th
e
co
n
v
en
tio
n
al
cir
cu
its
o
f
th
e
o
f
f
s
et
co
m
p
en
s
atio
n
ar
e
d
ec
eler
atin
g
b
ec
au
s
e
o
f
th
e
lar
g
e
tr
an
s
ien
ts
o
f
th
e
v
o
ltag
e
at
th
e
o
u
tp
u
t
[
2
8
].
T
h
e
p
r
o
p
o
s
ed
DC
o
f
f
s
et
co
m
p
en
s
a
ted
v
o
ltag
e
b
u
f
f
er
s
h
o
w
n
in
Fig
u
r
e
1
5
is
im
p
lem
en
ted
u
s
in
g
th
r
ee
s
w
itch
es
S
1
,
S
2
an
d
S
3
an
d
a
ca
p
ac
ito
r
C
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
cir
cu
it
lik
e
o
th
er
s
w
itch
ed
ca
p
ac
ito
r
cir
cu
its
b
r
o
o
k
s
f
r
o
m
th
e
ch
ar
g
e
in
j
ec
tio
n
o
f
th
e
ch
an
n
el
w
h
ich
ca
n
b
e
r
ed
u
ce
d
b
y
o
p
en
in
g
S
1
s
lo
w
ly
b
ef
o
r
e
S
3
.
W
h
en
S
1
o
p
en
ed
,
th
e
ch
ar
g
e
is
g
o
in
g
to
th
e
ca
p
ac
ito
r
C
an
d
th
is
ch
ar
g
e
is
f
o
u
n
d
as a
n
o
f
f
s
et
at
th
e
o
u
tp
u
t.
W
h
en
S
1
is
o
f
f
,
th
e
to
tal
ch
ar
g
e
s
tay
s
co
n
s
tan
t
as
it
is
w
h
ich
w
ill
lead
th
e
cir
cu
it
in
s
en
s
itiv
e
f
o
r
ch
ar
g
in
g
in
j
ec
tio
n
to
S
3
o
r
th
e
ch
ar
g
in
g
ab
s
o
r
p
tio
n
f
o
r
S
2
[
2
8
].
Fig
u
r
e
1
5
.
(
a)
New
D
C
o
f
f
s
et
co
m
p
e
n
s
ated
v
o
ltag
e
b
u
f
f
er
,
,
(
b
)
cir
cu
it d
u
r
in
g
p
h
a
s
e
-
1
,
(
c)
cir
cu
it d
u
r
i
n
g
p
h
ase
-
2
,
(
d
)
clo
ck
s
□
1a
, □
1
, □
2
.
ap
p
lied
to
th
e
s
w
itc
h
es S
1
, S
2
,
an
d
S
3
r
esp
ec
tiv
el
y
T
h
e
co
n
v
en
tio
n
al
o
f
f
s
et
co
m
p
en
s
atio
n
cir
cu
its
h
av
e
a
lo
w
s
p
ee
d
d
u
e
to
b
ig
tr
an
s
ien
ts
in
th
e
o
u
tp
u
t.
Fro
m
th
e
ab
o
v
e
s
ec
tio
n
w
e
g
et
th
at
th
is
m
eth
o
d
n
o
t
o
n
ly
o
v
er
co
m
e
th
e
DC
o
f
f
s
et
b
u
t
also
it
im
p
r
o
v
es
th
e
ac
cu
r
ac
y
o
f
th
e
d
ata
co
n
v
er
ter
s
an
d
d
ec
r
ea
s
es
th
e
er
r
o
r
o
f
th
e
g
ain
in
th
e
o
p
er
atio
n
al
am
p
lif
ier
.
A
lth
o
u
g
h
it
h
as
a
b
ig
d
is
ad
v
an
tag
e
th
at
th
e
co
n
v
en
tio
n
al
cir
cu
its
o
f
th
e
o
f
f
s
et
co
m
p
en
s
atio
n
ar
e
d
ec
eler
ate
b
ec
au
s
e
o
f
th
e
lar
g
e
tr
an
s
ien
ts
o
f
th
e
v
o
ltag
e
at
th
e
o
u
tp
u
t
o
f
th
e
o
p
er
atio
n
al
am
p
lif
ier
.
T
h
is
d
r
aw
b
ac
k
let
u
s
tr
y
to
f
in
d
a
n
ew
s
o
lu
tio
n
b
etter
th
an
th
at
in
th
e
f
o
llo
w
in
g
s
ec
tio
n
s
.
13.
DIFF
E
R
E
N
T
I
A
L
AM
P
L
I
F
I
E
R
T
h
is
tech
n
iq
u
e
w
as
in
tr
o
d
u
ce
d
b
y
th
e
au
th
o
r
w
h
ich
g
iv
e
a
b
r
ief
ab
o
u
t
th
e
DC
o
f
f
s
et
w
h
ich
is
alr
ea
d
y
k
n
o
w
n
as
b
ef
o
r
e,
as
th
e
ex
ce
s
s
iv
e
in
j
ec
tio
n
o
f
DC
in
to
A
C
ca
n
p
r
o
m
p
t
is
s
u
es
s
u
ch
as
co
r
r
o
s
io
n
in
u
n
d
er
g
r
o
u
n
d
eq
u
ip
m
en
t
[
2
9
]
,
tr
an
s
f
o
r
m
er
m
ag
n
etizin
g
cu
r
r
en
t
d
is
to
r
tio
n
an
d
tr
an
s
f
o
r
m
er
s
atu
r
atio
n
[
3
0
]
an
d
f
ailu
r
e
in
th
e
f
u
n
ctio
n
o
f
th
e
p
r
o
tectiv
e
eq
u
ip
m
en
t
[
3
1
]
.
I
n
th
is
m
an
n
er
r
u
les
an
d
m
ea
s
u
r
es
h
av
e
b
ee
n
s
et
u
p
to
co
n
tr
o
l
th
e
DC
in
j
ec
tio
n
[
3
2
]
.
A
u
s
tr
alian
Stan
d
ar
d
A
S4
7
7
7
.
2
lim
its
th
e
DC
in
j
ec
tio
n
to
5
m
A
o
r
0
.
5
%
o
f
th
e
r
ated
o
u
tp
u
t
as
illu
s
tr
ated
b
ef
o
r
e
in
th
e
in
tr
o
d
u
ctio
n
,
w
h
ile
in
th
e
Un
ited
Kin
g
d
o
m
,
E
R
G8
3
/1
p
u
t
a
lim
it
o
f
2
0
m
A
[
3
3
].
T
h
er
e
w
as
a
s
u
g
g
esti
o
n
ca
n
b
e
ap
p
lied
u
s
in
g
a
v
o
ltag
e
s
en
s
o
r
at
th
e
in
v
er
ter
o
u
tp
u
t
co
n
tain
s
th
e
d
if
f
er
en
tial
am
p
lif
ier
an
d
a
lo
w
p
ass
f
ilter
.
Hen
ce
,
an
y
DC
co
m
p
o
n
en
t
is
d
etec
ted
at
th
e
o
u
tp
u
t
o
f
th
e
lo
w
p
ass
f
ilter
w
h
ich
r
etu
r
n
s
b
ac
k
to
th
e
co
n
tr
o
ller
th
at
m
ak
es
th
e
in
v
er
ter
elim
in
ates
th
e
DC
o
f
f
s
et
an
d
th
er
e
w
as
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
.
2
,
J
u
n
e
2
0
1
8
:
478
–
494
486
a
m
ath
em
atica
l
m
o
d
el
f
o
r
th
at
co
n
tr
o
l
s
y
s
tem
[
3
3
]
.
I
t
s
ee
m
s
th
at
th
is
m
eth
o
d
h
as
a
b
ig
s
im
ilar
ity
to
th
e
tech
n
iq
u
e
w
h
ich
w
as
ex
p
lain
ed
in
s
ec
tio
n
9
,
s
o
th
er
e
ar
e
n
o
ex
p
er
im
en
tal
r
esu
lts
v
alid
ate
th
is
tech
n
iq
u
e.
14.
F
E
E
DB
ACK
SY
ST
E
M
T
h
e
s
i
m
p
les
t
w
a
y
to
eli
m
i
n
at
e
DC
i
n
j
ec
tio
n
i
s
to
k
ee
p
a
g
r
id
f
r
eq
u
e
n
c
y
tr
an
s
f
o
r
m
er
.
T
h
at
is
t
h
e
s
o
lu
tio
n
ad
j
u
s
ted
i
n
a
n
u
m
b
er
o
f
co
m
m
er
cial
s
y
s
te
m
s
[
3
4
]
,
[
3
5
]
.
T
h
e
m
ea
s
u
r
e
m
e
n
t
s
o
f
D
C
c
u
r
r
en
ts
f
r
o
m
t
h
e
AC
o
u
tp
u
t
o
f
co
m
m
er
cial
s
y
s
t
e
m
s
ar
e
also
p
r
o
p
o
s
ed
in
[
3
5
]
.
T
h
er
e
ar
e
n
u
m
b
er
o
f
s
y
s
te
m
co
n
f
i
g
u
r
atio
n
s
t
h
at
h
av
e
b
ee
n
p
r
ese
n
ted
f
o
r
s
i
n
g
l
e
-
p
h
a
s
e
g
r
id
co
n
n
ec
ted
P
V
s
y
s
te
m
s
[
3
6
]
.
T
h
e
co
n
f
ig
u
r
atio
n
th
at
h
a
s
b
ee
n
u
s
ed
an
d
w
a
s
in
tr
o
d
u
ce
d
b
y
t
h
e
au
t
h
o
r
to
g
et
th
e
D
C
o
f
f
s
et
eli
m
i
n
ati
o
n
m
et
h
o
d
w
h
ic
h
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1
6.
Fig
u
r
e
1
6
.
Gr
id
co
n
n
ec
ted
P
V
s
y
s
te
m
Fig
u
r
e
1
7
.
I
n
v
er
ter
m
ai
n
co
m
p
o
n
en
t
s
an
d
DC
-
o
f
f
s
et
s
e
n
s
o
r
T
h
e
m
ai
n
co
m
p
o
n
e
n
t
s
o
f
t
h
e
in
v
er
ter
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
1
7
.
T
h
e
u
n
it
y
p
o
w
er
f
ac
to
r
u
s
ed
f
o
r
r
ef
er
en
ce
c
u
r
r
en
t
f
o
r
th
e
h
y
s
t
er
esis
cu
r
r
e
n
t
co
n
tr
o
ller
[
3
6
]
,
[
3
7
]
.
is
co
o
r
d
in
ated
to
b
e
in
p
h
ase
w
it
h
th
e
AC
s
u
p
p
l
y
v
o
lta
g
e
.
Du
r
i
n
g
t
h
e
p
o
s
iti
v
e
h
alf
c
y
c
le
o
f
th
e
s
o
u
r
ce
v
o
ltag
e,
in
s
u
lated
g
ate
b
ip
o
lar
tr
an
s
i
s
to
r
T
B+
i
s
k
ep
t
o
f
f
an
d
T
B
-
is
k
ep
t
o
n
.
T
r
an
s
i
s
to
r
T
A+
is
t
u
r
n
ed
o
n
w
h
e
n
th
e
c
u
r
r
en
t
o
f
t
h
e
i
n
v
er
ter
o
u
tp
u
t
(
)
g
o
es
b
elo
w
th
e
b
o
tto
m
s
ta
n
d
ar
d
o
f
th
e
h
y
s
ter
etic
b
an
d
.
T
h
is
lead
s
to
r
is
e
w
h
ile
it
f
lo
w
s
th
r
o
u
g
h
T
A+
an
d
T
B
-
.
W
h
en
cu
r
r
en
t
ex
ce
ed
s
th
e
u
p
p
er
lim
it
o
f
t
h
e
b
an
d
T
A+
i
s
s
w
i
tch
ed
o
f
f
.
T
h
is
lead
s
to
f
all
w
h
e
n
f
lo
w
i
n
g
th
r
o
u
g
h
D
A
-
an
d
T
B
-
.
T
h
r
o
u
g
h
o
u
t
th
e
n
eg
ati
v
e
h
al
f
-
c
y
cle
o
f
t
h
e
AC
s
u
p
p
l
y
v
o
lta
g
e,
tr
an
s
is
to
r
T
B
-
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B+
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
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lec
&
Dr
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I
SS
N:
2
0
8
8
-
8
694
R
ev
iew
o
f D
C
Off
s
et
C
o
mp
en
s
a
tio
n
Tech
n
iq
u
es fo
r
Gri
d
C
o
n
n
ec
ted
I
n
ve
r
ters
(
A
h
med
Om
a
r
)
487
is
k
ep
t
o
n
.
T
r
an
s
i
s
to
r
T
A
-
is
s
w
itc
h
ed
o
n
w
h
e
n
t
h
e
cu
r
r
en
t
o
f
th
e
i
n
v
er
ter
o
u
tp
u
t
g
o
es
a
b
o
v
e
th
e
to
p
li
m
it
o
f
th
e
h
y
s
ter
et
ic
b
an
d
[
3
8
]
.
T
h
er
e
i
s
n
o
s
u
b
s
ta
n
tial
s
to
r
ag
e
b
et
w
ee
n
t
h
e
s
o
lar
p
an
e
l
o
u
t
p
u
t
an
d
t
h
e
i
n
v
er
ter
o
u
tp
u
t.
I
f
th
e
is
o
lat
io
n
lev
el
f
alls
o
r
r
is
es,
th
e
r
o
o
t
m
ea
n
s
q
u
ar
e
(
r
m
s
)
v
al
u
e
s
h
o
u
ld
r
is
e
o
r
f
all
d
ep
en
d
o
n
th
e
is
o
latio
n
le
v
el.
I
n
s
eq
u
en
ce
o
f
th
a
t
th
e
p
o
w
er
b
alan
ce
w
ill
b
e
p
r
o
tec
ted
.
I
t
is
th
e
r
o
le
o
f
th
e
v
o
lta
g
e
co
n
tr
o
l
lo
o
p
to
k
ee
p
b
alan
ce
b
et
w
ee
n
t
h
e
D
C
o
u
tp
u
t
o
f
th
e
P
V
p
an
el
an
d
t
h
e
o
u
tp
u
t
o
f
t
h
e
in
v
er
ter
i
n
t
h
e
AC
n
et
w
o
r
k
.
A
r
is
e
in
t
h
e
o
u
tp
u
t p
o
w
er
f
r
o
m
th
e
s
o
lar
p
an
els
m
a
k
es a
n
i
n
cr
ea
s
e
in
th
e
D
C
b
u
s
v
o
ltag
e
w
h
ic
h
w
il
l
m
ak
e
a
r
is
e
in
t
h
e
.
T
h
is
w
ill
l
ea
d
th
e
r
m
s
v
al
u
e
o
f
th
e
to
in
cr
ea
s
e
r
esu
lti
n
g
i
n
th
e
r
m
s
o
f
th
e
in
v
er
ter
o
u
tp
u
t
cu
r
r
en
t
as
it
f
o
llo
w
s
.
T
h
e
r
is
e
in
th
e
i
n
v
er
ter
o
u
t
p
u
t
cu
r
r
en
t
s
to
r
es
b
ac
k
t
h
e
b
alan
ce
o
f
th
e
p
o
w
er
b
et
w
ee
n
t
h
e
DC
o
u
tp
u
t
p
o
w
er
o
f
t
h
e
P
V
p
an
els
a
n
d
t
h
e
A
C
o
u
tp
u
t
p
o
w
er
o
f
th
e
i
n
v
er
ter
.
So
th
e
tar
g
et
o
f
th
e
v
o
ltag
e
co
n
tr
o
l lo
o
p
is
to
k
ee
p
p
o
w
er
b
alan
ce
b
et
w
ee
n
th
e
t
w
o
o
u
tp
u
t
s
.
I
n
th
is
tech
n
iq
u
e
u
s
es
m
ax
im
u
m
p
o
w
er
tr
ac
k
er
.
T
h
e
m
ax
im
u
m
p
o
w
er
tr
ac
k
er
is
a
co
n
tr
o
l
lo
o
p
in
w
h
ich
th
e
v
o
ltag
e
co
n
tr
o
l
lo
o
p
tar
g
ets
f
o
r
b
alan
ce
b
etw
ee
n
th
e
DC
an
d
th
e
A
C
o
u
tp
u
t.
T
h
e
m
ax
im
u
m
p
o
w
er
tr
ac
k
er
g
o
al
is
to
o
p
er
ate
th
e
s
o
lar
p
an
els
at
a
v
o
ltag
e
lev
el
th
at
p
er
m
its
m
ax
im
u
m
ex
tr
ac
tio
n
o
f
p
o
w
er
[
3
8
]
,
[
3
9
].
T
h
is
m
eth
o
d
ex
p
lain
s
th
e
DC
o
f
f
s
et
co
n
tr
o
ller
:
A
s
th
e
DC
o
f
f
s
et
s
en
s
o
r
is
b
u
ilt
f
r
o
m
a
d
o
u
b
le
s
tag
e
R
C
f
ilter
.
T
h
e
v
o
ltag
e
ac
r
o
s
s
th
e
r
ip
p
le
f
ilter
in
d
u
cto
r
s
(
)
is
s
en
s
ed
an
d
f
ilter
ed
.
I
f
th
e
DC
co
m
p
o
n
en
t
in
th
e
in
v
er
ter
cu
r
r
en
t
w
as
co
n
s
tan
t,
th
e
DC
o
u
tp
u
t
v
o
ltag
e
s
h
o
u
ld
b
e
eq
u
al
to
I
R
,
w
h
er
e
R
is
th
e
r
esis
tan
ce
o
f
th
e
tw
o
s
er
ies
co
n
n
ec
ted
in
d
u
cto
r
s
an
d
I
is
th
e
DC
co
m
p
o
n
en
t
o
f
th
e
cu
r
r
en
t.
T
h
is
v
o
ltag
e
k
n
o
w
n
as
in
Fig
u
r
e
1
8
.
T
h
e
f
ilter
o
u
tp
u
t
is
f
ed
to
a
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
P
I
)
co
n
tr
o
ller
w
h
ich
h
as
i
n
p
u
t
r
ef
er
en
ce
eq
u
al
to
ze
r
o
[
3
8
]
.
T
h
e
co
n
tr
o
ller
o
u
tp
u
t
w
as
p
u
tin
s
u
ch
a
w
ay
s
o
as
to
ca
u
s
e
V
0
w
h
ich
is
th
e
m
ea
n
v
alu
e
o
f
to
m
o
v
e
d
o
w
n
to
ze
r
o
.
T
h
e
in
teg
r
al
ac
tio
n
o
f
th
e
DC
o
f
f
s
et
co
n
tr
o
ller
is
to
m
ak
e
s
u
r
e
th
at
V
0
is
eq
u
al
to
ze
r
o
at
s
tead
y
s
tate.
T
h
e
DC
o
f
f
s
et
co
n
tr
o
ller
n
ee
d
s
s
o
m
e
r
eq
u
ir
em
en
ts
to
b
e
ca
r
ef
u
lly
d
esig
n
ed
:
1.
I
t sh
o
u
ld
n
o
t g
et
in
v
o
lv
ed
w
ith
th
e
o
p
er
atio
n
o
f
th
e
o
th
er
co
n
tr
o
l lo
o
p
s
an
d
v
ice
v
er
s
a.
2.
I
ts
d
y
n
am
ic
r
esp
o
n
s
e
m
u
s
t
b
e
r
ea
s
o
n
ab
le.
Fig
u
r
e
1
8
.
DC
o
f
f
s
e
t se
n
s
o
r
b
lo
ck
d
iag
r
a
m
T
h
e
d
esig
n
er
o
f
t
h
e
D
C
o
f
f
s
et
s
e
n
s
o
r
h
as
to
c
h
o
o
s
e
v
alu
es
f
o
r
th
e
p
ar
a
m
eter
s
o
f
t
h
at
s
e
n
s
o
r
to
m
ai
n
tai
n
t
h
e
d
esi
g
n
r
eq
u
ir
em
en
ts
a
n
d
s
p
ec
i
f
icatio
n
s
.
R
esis
ta
n
ce
(
R
)
co
u
ld
b
e
j
u
s
t
th
e
i
n
h
er
en
t
s
er
ies
r
esis
ta
n
ce
o
f
t
h
e
i
n
d
u
cto
r
s
.
Al
th
o
u
g
h
,
it
is
f
o
u
n
d
t
h
at
th
is
f
o
r
r
esis
ta
n
ce
i
s
to
o
s
m
al
l
t
h
e
o
p
er
atio
n
o
f
t
h
e
DC
o
f
f
s
et
co
n
tr
o
l
lo
o
p
,
s
o
a
d
d
itio
n
al
r
esis
ta
n
ce
co
u
ld
b
e
ad
d
ed
b
u
t
w
ill
lead
to
an
in
cr
ea
s
e
i
n
th
e
p
o
w
er
lo
s
s
[
3
8
]
.
T
h
er
e
ar
e
tw
o
m
a
in
co
n
ce
p
t
s
f
o
r
th
e
DC
o
f
f
s
et
co
n
tr
o
ller
:
1.
Su
f
f
icien
tl
y
d
a
m
p
ed
o
u
tp
u
t r
e
s
p
o
n
s
e.
2.
T
h
e
f
r
eq
u
en
cy
co
m
p
o
n
en
t
s
h
o
u
ld
r
ea
ch
th
e
m
ax
i
m
u
m
v
alu
e
in
its
o
u
tp
u
t sig
n
al.
T
h
e
co
n
clu
s
io
n
f
o
r
th
is
tech
n
iq
u
e
is
th
at
th
er
e
is
a
s
im
p
le
f
ee
d
b
ac
k
s
y
s
tem
h
as
b
ee
n
p
r
esen
ted
to
r
ed
u
ce
th
e
DC
o
f
f
s
et
f
r
o
m
th
e
o
u
tp
u
t
o
f
a
s
in
g
le
p
h
ase
g
r
id
-
co
n
n
ec
ted
in
v
er
ter
.
DC
o
f
f
s
et
g
et
m
o
n
ito
r
ed
b
y
s
en
s
in
g
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
r
ip
p
le
f
ilter
in
d
u
cto
r
.
T
h
e
DC
s
ig
n
al
is
k
n
o
w
n
b
y
u
s
in
g
th
e
tw
o
s
tag
e
R
C
f
ilter
in
g
.
T
h
e
co
n
tr
o
ller
u
s
ed
is
th
e
P
I
co
n
tr
o
ller
w
h
ich
p
er
f
o
r
m
s
v
er
y
s
atis
f
ac
to
r
ily
an
d
its
co
m
p
o
n
en
ts
co
s
t
ar
e
v
er
y
lo
w
.
A
lth
o
u
g
h
,
w
h
en
th
is
tec
h
n
iq
u
e
is
u
s
ed
p
r
ac
tically
th
er
e
is
s
m
all
DC
o
f
f
s
et
r
em
ain
s
w
h
ich
lead
u
s
to
f
o
u
n
d
a
b
etter
s
o
lu
tio
n
co
u
ld
h
av
e
b
etter
r
esu
lts
th
an
th
at
o
n
e.
Evaluation Warning : The document was created with Spire.PDF for Python.