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llo
w
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n
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e
s
y
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te
m
to
ac
h
iev
e
tr
u
e
r
ed
u
n
d
an
c
y
[
1
4
]
-
[
1
6
]
.
I
n
th
is
p
ap
er
,
P
-
V/Q
-
F
d
r
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o
p
co
n
tr
o
l
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im
p
le
m
en
ted
f
o
r
p
ar
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v
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ter
s
i
n
m
icr
o
g
r
id
u
s
in
g
Ma
tlab
/Si
m
u
l
in
k
s
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m
u
latio
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t,to
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y
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h
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e
f
f
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tiv
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ess
o
f
t
h
e
m
o
d
el
d
esig
n
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d
co
n
tr
o
l.
2.
M
I
CRO
G
RID
DRO
O
P
CO
NT
RO
L
P
R
I
NC
I
P
L
E
C
o
n
s
id
er
an
ac
b
u
s
co
n
n
ec
ted
to
an
in
v
er
ter
eq
u
i
v
ale
n
t
cir
c
u
it
is
s
h
o
w
n
i
n
F
i
g
u
r
e
1
.
I
n
v
e
r
ter
o
u
tp
u
t
v
o
ltag
e
is
E
,
th
e
co
m
m
o
n
lo
ad
ter
m
in
a
l
v
o
ltag
e
is
0
V
,
th
e
o
u
tp
u
t
o
f
t
h
e
in
v
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ter
an
d
a
co
m
m
o
n
lo
ad
en
d
th
r
o
u
g
h
t
h
e
i
n
v
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ter
co
n
n
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ted
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e
o
u
tp
u
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i
m
p
ed
a
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ce
.
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h
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ter
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m
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as
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el
f
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Z
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S
P
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Fig
u
r
e
1
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AC
b
u
s
i
n
v
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ter
eq
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t c
ir
cu
it
s
ch
e
m
atic
T
h
e
DG
u
n
it o
u
tp
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t p
o
w
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s
:
*
*
j
j
E
e
V
P
j
Q
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V
I
V
Ze
(1
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Ou
tp
u
t c
u
r
r
en
t i
s
:
()
s
i
n
s
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n
c
o
s
(
)
c
o
s
jj
EV
E
e
V
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E
V
Ij
Z
Z
Z
(
2)
(2
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in
to
E
q
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atio
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(
1
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to
g
iv
e
th
e
d
g
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it o
u
tp
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f
ac
t
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r
ea
ctiv
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p
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w
er
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e
as
f
o
llo
w
s
:
[
c
o
s
(
)
c
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]
V
P
E
V
Z
(
3)
[
s
i
n
(
)
s
i
n
]
V
Q
E
V
Z
(
4)
(
3
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an
d
(
4
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th
r
o
u
g
h
s
i
m
p
licati
o
n
ca
n
b
e
w
r
it
ten
as
:
[
(
c
o
s
)
c
o
s
s
i
n
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n
]
V
P
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V
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Z
(
5
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[
(
c
o
s
)
s
i
n
s
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]
V
Q
E
V
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Z
(
6)
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I
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N
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2
0
8
8
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IJ
PEDS
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6
6
656
I
n
v
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ter
o
u
tp
u
t i
m
p
ed
an
ce
i
s
j
Z
e
R
j
X
is
s
u
b
s
tit
u
ted
in
to
t
h
e
eq
u
atio
n
(
5
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an
d
(
6
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to
g
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e:
22
22
[
R
(
E
c
o
s
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s
i
n
]
[
(
c
o
s
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s
i
n
]
V
P
V
X
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RX
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Q
X
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RX
(
7)
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cc
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d
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(
7
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,
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tr
an
s
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ce
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o
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eq
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(
8
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Q
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(
9)
T
y
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n
n
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tio
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m
all,
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h
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s
s
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n
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c
o
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1
s
u
b
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i
n
to
th
e
eq
u
at
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n
(
8
)
an
d
(
9)
to
g
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e:
EV
P
X
(
1
0
)
2
E
V
V
Q
X
(
1
1
)
As
it
ca
n
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e
s
ee
n
f
r
o
m
th
e
E
q
u
atio
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(
1
0
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an
d
(
1
1
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ac
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d
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elate
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ch
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elate
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f
r
eq
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en
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y
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f
t
h
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o
u
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r
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p
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d
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a
m
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r
elate
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it
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s
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ti
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en
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y
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eg
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late
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m
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w
h
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is
t
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tr
ad
itio
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al
d
r
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o
p
c
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tr
o
l
[
1
0
]
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[
11]
.
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h
e
d
r
o
o
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co
n
t
r
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l e
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g
i
v
e
n
b
y
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(
P
P
)
m
(
1
2
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(
Q
Q
)
E
E
n
(
13)
T
h
e
in
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ter
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o
-
lo
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u
tp
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t
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m
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d
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V
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a
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d
r
ea
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d
r
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co
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f
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ts
ar
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m
,
n
.
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h
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i
n
v
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ter
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ated
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t
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ti
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an
d
r
ea
ctiv
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p
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W
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en
th
e
tr
an
s
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er
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m
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ce
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s
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el
y
r
esis
tiv
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th
at
=0
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e
s
a
m
e
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o
v
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d
e
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ti
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d
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v
e
p
o
w
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ca
n
b
e
o
b
tain
ed
:
2
E
V
V
P
R
(
1
4
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EV
Q
R
(
1
5
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B
y
E
q
u
atio
n
(
1
4
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d
(
1
5
)
c
an
b
e
s
ee
n
,
t
h
e
d
i
f
f
er
e
n
ce
b
et
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n
ac
t
iv
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a
n
d
v
o
ltag
e
a
m
p
lit
u
d
e
r
elate
d
to
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p
o
w
er
an
d
p
o
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er
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ela
ted
an
g
le,
w
h
ich
i
s
P
-
V/Q
-
F
d
r
o
o
p
c
o
n
tr
o
l m
et
h
o
d
.
m
,
n
d
r
o
o
p
co
-
ef
f
icien
ts
.
**
()
n
Q
Q
(
1
6
)
**
(
P
P
)
E
E
m
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Mu
ltip
le
I
n
ve
r
ters
Op
era
ted
i
n
P
a
r
a
llel fo
r
P
r
o
p
o
r
tio
n
a
l Lo
a
d
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h
a
r
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g
in
Micr
o
g
r
id
(
C
h
eth
a
n
R
a
j D
)
657
1
P
2
P
1
Q
2
Q
P
*
E
E
*
Q
1
m
2
m
1
n
2
n
0
0
Fig
u
r
e
2.
Dr
o
o
p
C
o
n
tr
o
l Cu
r
v
e
1
P
2
P
1
Q
2
Q
P
E
*
E
*
Q
1
m
2
m
1
n
2
n
0
0
Fig
u
r
e
3.
R
ev
er
s
e
Dr
o
o
p
C
o
n
t
r
o
l Cu
r
v
e
3.
M
O
DE
L
I
N
G
O
F
M
I
CRO
G
RID
3
.
1
.
M
icro
g
rid B
l
o
ck
Dia
g
ra
m
Mic
r
o
g
r
id
is
m
o
s
tl
y
a
m
in
ia
t
u
r
e
p
o
w
er
,
n
a
m
el
y
s
m
all
u
n
i
ts
co
n
tai
n
p
o
w
er
elec
tr
o
n
ics
in
ter
f
ac
e,
in
cl
u
d
in
g
m
icr
o
tu
r
b
in
e
s
,
f
u
el
c
ells
,
p
h
o
to
v
o
ltaic
ce
lls
,
b
atter
i
es
an
d
o
t
h
er
s
to
r
ag
e
u
n
it.M
icr
o
g
r
id
as
a
w
h
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le
i
s
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m
p
o
s
ed
o
f
a
v
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lta
g
e
s
o
u
r
c
e
in
v
er
ter
s
u
s
i
n
g
SP
W
M
m
o
d
u
lat
io
n
as
s
h
o
w
n
i
n
t
h
e
F
i
g
u
r
e
4
,
th
en
a
s
s
u
m
in
g
th
at
th
e
i
n
v
er
ter
d
c
b
u
s
v
o
ltag
e
V
dc
ess
en
tial
l
y
u
n
c
h
an
g
ed
L
f1
,L
f2
,L
f3
is
a
th
r
ee
p
h
ase
f
ilt
er
in
d
u
cto
r
,
r
1
,r
2
,r
3
f
ilter
in
d
u
cto
r
eq
u
iv
ale
n
t
r
esi
s
tan
ce
,
C
f1
,C
f2
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f3
i
s
a
th
r
ee
p
h
ase
f
il
ter
ca
p
ac
ito
r
.
C
o
m
p
r
eh
en
s
i
v
e
eq
u
iv
ale
n
t
lin
e
i
m
p
ed
a
n
ce
o
f
t
h
e
tr
an
s
m
i
s
s
io
n
l
in
e
o
f
t
h
r
ee
i
n
v
er
ter
s
i
s
ex
p
r
ess
ed
as
Z
1
=R
1
+j
X
1
,
Z
2
=R
2
+j
X
2
,
Z
3
=R
3
+j
X
3
,
.
P
C
C
r
ep
r
esen
ts
a
co
m
m
o
n
co
n
n
ec
t
io
n
p
o
in
t
f
o
r
in
v
er
ter
s
.
3
.
2
.
T
hree
P
ha
s
e
I
nv
er
t
er
dq
m
o
del
T
h
r
ee
p
h
ase
v
o
ltag
e
s
o
u
r
ce
i
n
v
er
ter
w
ith
th
r
ee
p
h
a
s
e
f
u
ll
b
r
i
d
g
e
to
p
o
lo
g
y
th
e
d
etail
s
o
f
t
h
e
s
t
r
u
ct
u
r
e
as
s
h
o
w
n
i
n
t
h
e
F
ig
u
r
e
5
.
I
n
v
er
ter
leg
m
id
p
o
in
t
v
o
lta
g
e
V
A
,
V
B
,
V
C
.
I
n
v
er
ter
o
u
tp
u
t
ter
m
i
n
al
v
o
lta
g
e
v
ao
,
v
bo
,
v
co
.
T
h
r
ee
p
h
ase
in
d
u
cto
r
cu
r
r
en
t
r
esp
ec
tiv
el
y
i
La
,
i
Lb
,
i
Lc
.
L
o
ad
s
id
e
th
r
ee
p
h
ase
i
n
v
e
r
ter
o
u
tp
u
t
cu
r
r
en
t
[
1
7
]
-
[
18
].
A
cc
o
r
d
in
g
to
Kir
ch
h
o
f
f
'
s
v
o
ltag
e
la
w
a
n
d
cu
r
r
en
t la
w
ca
n
b
e
o
b
tain
ed
as:
,,
L
a
L
b
L
c
A
a
o
f
L
a
B
b
o
f
L
b
C
c
o
f
L
c
d
i
d
i
d
i
V
v
L
r
i
V
v
L
r
i
V
v
L
r
i
d
t
d
t
d
t
(
1
8
)
Kir
ch
h
o
f
f
'
s
c
u
r
r
en
t la
w
ca
n
b
e
o
b
tain
ed
as:
,,
a
o
b
o
c
o
L
a
a
o
f
L
b
b
o
f
L
c
c
o
f
d
v
d
v
d
v
i
i
C
i
i
C
i
i
C
d
t
d
t
d
t
(
1
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
2
,
J
u
n
e
2
0
1
7
:
6
5
4
–
6
6
6
658
A
cc
o
r
d
in
g
to
th
e
p
r
in
cip
le
o
f
eq
u
al
a
m
p
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