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s
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terfa
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n
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g
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ti
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th
e
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v
e
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m
p
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ter
Du
al
A
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Har
m
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p
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©
201
7
I
n
s
t
it
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Ad
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C
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p
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uth
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r
:
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ab
u
,
Dep
ar
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en
t o
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lectr
ical
an
d
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lectr
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ics E
n
g
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m
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co
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1.
I
NT
RO
D
UCT
I
O
N
Dis
tr
ib
u
ted
g
en
er
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n
(
DG)
p
la
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s
a
v
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r
o
le
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u
e
to
ad
v
a
n
c
e
m
en
ts
i
n
p
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y
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te
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li
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m
ar
t
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s
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d
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f
ti
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tr
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atio
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co
n
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tio
n
al
en
er
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ies
to
s
u
s
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n
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le
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ies.
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h
e
n
a
m
e
d
is
tr
ib
u
ted
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e
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ib
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ted
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ca
n
b
e
d
ef
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as
s
m
a
ll
s
ca
le
elec
tr
ical
p
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w
er
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e
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at
io
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n
ter
s
in
co
n
j
u
n
ctio
n
w
ith
p
o
w
er
g
r
id
[
1
-
2
]
.
W
h
ile
DG
is
f
ee
d
i
n
g
g
r
id
,
th
e
p
o
w
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en
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atio
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t
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ai
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s
o
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r
ce
is
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ce
d
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d
th
e
d
e
m
a
n
d
p
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w
e
r
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et
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o
m
b
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th
m
ai
n
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d
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n
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o
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ated
in
t
w
o
m
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d
e
s
o
f
o
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m
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d
e
o
f
o
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atio
n
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d
g
r
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n
n
ec
ted
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o
d
e
o
f
o
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er
atio
n
.
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n
g
r
id
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n
n
ec
ted
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e
o
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o
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atio
n
,
t
h
e
p
o
w
er
f
r
o
m
DG
is
f
ed
to
g
r
id
r
ed
u
ci
n
g
th
e
a
m
o
u
n
t
o
f
p
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w
er
f
r
o
m
m
ai
n
p
o
w
er
s
o
u
r
ce
.
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n
s
tan
d
alo
n
e
m
o
d
e
o
f
D
G
o
p
er
atio
n
,
p
o
w
er
f
r
o
m
DG
i
s
f
ed
d
ir
ec
tl
y
to
lo
ad
s
.
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ca
n
b
e
m
o
r
e
o
f
a
b
ac
k
-
u
p
t
y
p
e
o
f
p
o
w
er
to
i
m
p
r
o
v
e
th
e
r
eliab
ilit
y
o
f
t
h
e
p
o
w
er
s
y
s
te
m
.
DG
r
ed
u
ce
s
t
h
e
in
v
es
t
m
e
n
t
to
g
en
er
ate
elec
t
r
ical
p
o
w
er
t
h
a
n
co
m
p
ar
ed
to
th
at
o
f
co
n
v
e
n
tio
n
al
p
o
w
er
s
tatio
n
s
.
S
in
ce
DG
i
s
i
n
s
tal
led
at
lo
ad
p
o
in
ts
,
tr
a
n
s
m
is
s
io
n
lo
s
s
e
s
ar
e
g
r
ad
u
all
y
r
ed
u
ce
s
a
n
d
p
r
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v
is
io
n
s
f
o
r
p
o
w
er
tr
an
s
m
i
s
s
io
n
an
d
d
is
tr
ib
u
tio
n
is
eli
m
i
n
ated
[
3
]
.
A
l
s
o
DG
o
p
er
ates
w
it
h
r
en
e
w
ab
l
e
s
o
u
r
ce
s
o
f
e
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w
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ar
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f
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l
y
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n
d
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ile
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in
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tr
ical
p
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p
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tio
n
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s
ac
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v
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w
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s
la
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b
y
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lo
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al
b
o
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ies.
T
h
e
m
aj
o
r
r
ea
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n
f
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r
p
en
etr
atio
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o
f
d
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s
tr
ib
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ted
g
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atio
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n
p
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w
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y
s
te
m
is
d
u
e
to
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n
o
m
ic,
e
n
v
ir
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m
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n
tal
an
d
tech
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o
n
s
.
Ma
n
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r
esea
r
ch
er
s
h
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v
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w
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r
k
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to
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s
DG’
s
an
d
t
h
e
s
izi
n
g
o
f
a
p
ar
ticu
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DG
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v
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i
m
p
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r
tan
t f
ac
to
r
to
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e
co
n
s
id
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n
s
ta
lli
n
g
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n
p
o
w
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s
y
s
te
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
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8
8
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8
694
Dis
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ted
Gen
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I
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P
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Du
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1442
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r
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1
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Sch
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m
atic
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a
m
o
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A
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n
p
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[
4
-
5]
.
T
h
er
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o
r
e,
it
ca
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b
e
o
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s
er
v
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r
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w
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th
h
ar
m
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o
f
v
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r
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er
s
,
in
cl
u
d
in
g
in
ter
-
h
ar
m
o
n
ics
[
6
]
.
Har
m
o
n
ic
cu
r
r
en
t
s
cir
cu
lati
n
g
th
r
o
u
g
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t
h
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lin
e
i
m
p
ed
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ce
p
r
o
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d
is
to
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tio
n
in
t
h
e
s
y
s
te
m
v
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lta
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es
.
T
o
c
o
m
p
e
n
s
ate
t
h
e
h
ar
m
o
n
ics,
F
AC
T
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co
n
tr
o
ller
s
ar
e
d
ev
elo
p
ed
.
Sh
u
n
t
A
P
F
is
a
d
ev
ice
d
ev
e
lo
p
ed
to
n
u
lli
f
y
t
h
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h
ar
m
o
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ic
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i
s
to
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tio
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i
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s
o
u
r
ce
co
m
p
o
n
en
ts
.
T
h
e
Sh
u
n
t
A
cti
v
e
P
o
w
er
Fil
ter
b
e
h
av
e
s
as
a
co
n
tr
o
lled
cu
r
r
en
t
-
s
o
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r
ce
d
r
ain
i
n
g
t
h
e
u
n
d
es
ir
ed
co
m
p
o
n
e
n
t
s
f
r
o
m
th
e
lo
ad
cu
r
r
en
ts
,
s
u
c
h
t
h
at
t
h
e
cu
r
r
en
ts
i
n
t
h
e
elec
tr
ical
p
o
w
er
g
r
id
b
ec
o
m
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s
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s
o
id
al,
b
alan
ce
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d
in
p
h
a
s
e
w
it
h
f
u
n
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a
m
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tal
p
o
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iti
v
e
s
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q
u
en
ce
co
m
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en
t
o
f
t
h
e
s
y
s
te
m
v
o
ltag
e
s
[7
-
11]
.
T
h
e
s
ch
e
m
atic
d
ia
g
r
a
m
o
f
A
P
F
in
p
o
w
er
s
y
s
te
m
is
s
h
o
wn
in
f
ig
u
r
e
1
.
I
n
th
is
co
n
tex
t,
d
u
al
A
P
F
is
e
m
p
lo
y
ed
f
o
r
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
.
Du
al
A
P
F
is
t
h
e
co
n
ce
p
t
o
f
h
av
i
n
g
t
w
o
p
ar
allel
A
P
F
’
s
f
o
r
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
i
n
p
o
w
er
s
y
s
te
m
s
o
u
r
ce
co
m
p
o
n
e
n
t
s
.
D
i
o
d
e
B
r
i
d
g
e
R
e
c
t
i
f
i
e
r
S
o
u
r
c
e
R
L
P
o
i
n
t
o
f
C
o
m
m
o
n
C
o
u
p
l
i
n
g
S
o
u
r
c
e
I
m
p
e
d
a
n
c
e
D
G
I
n
v
e
r
t
e
r
a
n
d
a
s
A
P
F
A
c
t
i
v
e
P
o
w
e
r
F
i
l
t
e
r
D
i
s
t
r
i
b
u
t
e
d
G
e
n
e
r
a
t
i
o
n
V
d
c
Fig
u
r
e
2
.
Sch
e
m
atic
s
y
s
te
m
with
d
u
al
A
P
F a
n
d
DG
in
te
g
r
ati
n
g
s
ch
e
m
e
T
h
is
p
ap
er
p
r
esen
ts
t
h
e
h
ar
m
o
n
ic
co
m
p
en
s
atio
n
u
s
in
g
d
u
al
A
P
F
s
h
ar
in
g
co
m
p
e
n
s
ati
n
g
s
i
g
n
al
s
w
h
il
e
ac
tiv
e
p
o
w
er
is
f
ed
f
r
o
m
d
is
tr
i
b
u
ted
g
en
er
atio
n
to
g
r
id
.
Du
al
A
P
F
is
th
e
co
n
ce
p
t
o
f
h
av
i
n
g
t
w
o
p
ar
allel
A
P
F
’
s
f
o
r
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
i
n
p
o
w
er
s
y
s
te
m
s
o
u
r
ce
co
m
p
o
n
e
n
ts
.
DG
i
n
v
er
ter
ac
ts
a
s
a
n
i
n
t
er
f
ac
e
b
et
w
ee
n
DG
s
y
s
te
m
a
n
d
g
r
id
to
f
ee
d
ac
tiv
e
p
o
w
er
f
r
o
m
DG
to
g
r
id
.
I
n
th
is
co
n
te
x
t,
t
h
e
DG
in
v
er
ter
ac
ts
b
o
th
as
in
v
er
ter
an
d
A
P
F,
u
s
ed
as
in
v
er
ter
to
in
v
er
t
s
u
p
p
l
y
f
r
o
m
DG
an
d
f
ee
d
s
g
r
id
f
o
r
s
p
ec
if
ied
ti
m
e
an
d
also
as
A
P
F
f
o
r
h
ar
m
o
n
ic
co
m
p
e
n
s
at
io
n
t
h
er
e
af
ter
alo
n
g
w
it
h
d
u
al
A
P
F.
T
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
is
d
ev
elo
p
ed
an
d
r
esu
lt
s
ar
e
o
b
tain
ed
u
s
i
n
g
M
A
T
L
A
B
/SI
MU
L
I
NK
s
o
f
t
w
ar
e.
R
e
s
u
lt
s
a
r
e
s
h
o
w
n
f
o
r
DG
i
n
v
er
ter
f
ee
d
in
g
ac
tiv
e
p
o
w
er
to
g
r
id
an
d
also
ac
ti
n
g
a
s
A
P
F.
Du
al
A
P
F
c
h
ar
ac
ter
is
tic
s
ar
e
also
s
h
o
w
n
.
D
u
al
A
P
F
is
co
n
tr
o
lled
u
s
in
g
in
s
ta
n
ta
n
eo
u
s
P
Q
th
eo
r
y
a
n
d
DG
in
v
er
ter
is
co
n
tr
o
lled
u
s
i
n
g
s
i
m
p
le
co
n
tr
o
l
s
tr
ate
g
y
to
f
ee
d
5
KW
p
o
w
er
to
g
r
id
.
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
.
3
,
Sep
tem
b
er
2
0
1
7
:
144
1
–
14
54
1443
2.
P
RO
P
O
SE
D
D
I
S
T
RIB
U
T
I
O
N
SYS
T
E
M
WI
T
H
DU
AL
AP
F
A
ND
D
G
I
N
T
E
G
RAT
I
N
G
SCH
E
M
E
Fig
u
r
e
2
s
h
o
w
s
t
h
e
s
c
h
e
m
a
tic
s
y
s
te
m
o
f
p
o
w
er
d
is
tr
ib
u
tio
n
s
y
s
te
m
w
it
h
d
u
a
l
A
P
F
an
d
DG
in
te
g
r
atio
n
s
ch
e
m
e.
D
u
al
A
P
F
is
m
ea
n
t
f
o
r
h
ar
m
o
n
ic
eli
m
i
n
atio
n
a
n
d
DG
i
n
te
g
r
ati
n
g
in
v
er
ter
ac
ts
as
a
n
in
ter
f
ac
in
g
in
v
er
ter
to
in
v
er
t
t
h
e
t
y
p
e
o
f
DG
s
u
p
p
l
y
.
I
n
th
is
co
n
tex
t,
f
o
r
a
p
r
escr
ib
e
d
tim
e
w
h
e
n
th
e
DG
is
s
w
itc
h
ed
in
to
t
h
e
p
o
w
er
d
is
tr
ib
u
tio
n
s
y
s
te
m
,
D
G
i
n
v
er
ter
a
cts
as
an
i
n
ter
f
ac
i
n
g
i
n
v
er
ter
t
o
in
v
er
t
t
h
e
t
y
p
e
o
f
DG
s
u
p
p
l
y
f
r
o
m
D
C
to
AC
.
Af
ter
p
r
escr
ib
ed
ti
m
e,
DG
i
n
v
er
ter
ac
ts
a
s
an
A
P
F
f
o
r
h
ar
m
o
n
ic
e
li
m
in
a
tio
n
alo
n
g
w
i
th
A
P
F.
D
G
in
v
er
ter
is
co
n
tr
o
lled
w
it
h
s
i
m
p
le
co
n
tr
o
l
s
tr
ate
g
y
to
f
ee
d
p
o
w
er
o
f
5
KW
to
g
r
id
.
DG
in
v
er
ter
co
n
s
is
ts
o
f
s
o
lid
-
s
tat
e
s
w
itc
h
es
i
n
t
h
r
ee
leg
s
f
o
r
t
h
r
ee
-
p
h
a
s
e
o
u
tp
u
t.
T
h
e
o
u
tp
u
t
o
f
DG
i
n
v
er
ter
i
s
f
ilter
ed
o
u
t
to
g
iv
e
s
m
o
o
th
s
i
n
u
s
o
id
al
o
u
tp
u
t
u
s
i
n
g
f
ilter
ci
r
cu
it.
I
n
i
tiall
y
t
h
e
D
G
i
s
s
w
itc
h
ed
i
n
to
t
h
e
p
o
w
er
s
y
s
te
m
at
t
h
e
i
n
s
ta
n
t o
f
0
.
1
s
ec
o
n
d
s
.
Fro
m
0
.
1
s
ec
,
th
e
DG
i
n
v
er
ter
j
u
s
t a
cts
as a
n
i
n
v
er
ter
c
o
n
v
er
ti
n
g
DC
t
y
p
e
f
r
o
m
DG
to
AC
t
y
p
e
to
f
ee
d
p
o
w
er
o
f
5
KW
to
g
r
id
.
A
t 0
.
2
s
ec
o
n
d
s
,
th
e
DG
i
n
v
er
ter
i
s
s
w
i
tch
ed
to
ac
t a
s
A
P
F
to
f
ee
d
co
m
p
e
n
s
ati
n
g
s
i
g
n
als t
o
p
o
in
t o
f
co
m
m
o
n
co
u
p
lin
g
.
Du
al
A
P
F
is
th
e
co
n
ce
p
t
o
f
h
av
i
n
g
t
w
o
p
ar
allel
A
P
F’s
f
o
r
h
ar
m
o
n
ic
eli
m
i
n
atio
n
.
E
ac
h
in
d
iv
id
u
a
l
A
P
F s
h
ar
es t
h
e
co
m
p
e
n
s
at
in
g
cu
r
r
en
t lo
ad
s
u
ch
t
h
at
t
h
e
s
tr
es
s
an
d
ca
p
ac
it
y
o
f
t
h
e
in
d
i
v
id
u
a
l A
P
F r
ed
u
ce
s
an
d
as
a
r
esu
lt
lo
s
s
es
g
e
t
r
ed
u
ce
d
.
E
ac
h
in
d
i
v
id
u
al
A
P
F
o
f
d
u
al
A
P
F
co
n
s
is
t
s
o
f
p
o
w
er
s
w
i
tch
es
w
ith
a
s
m
all
D
C
s
o
u
r
ce
.
T
h
e
t
w
o
p
ar
allel
A
P
F
’
s
in
d
i
v
id
u
al
l
y
s
e
n
d
s
co
m
p
e
n
s
atin
g
s
i
g
n
al
s
to
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
s
u
ch
th
at
h
ar
m
o
n
ics
i
n
s
o
u
r
ce
co
m
p
o
n
en
ts
ar
e
r
ed
u
ce
d
.
A
p
ar
t
f
r
o
m
DG
i
n
v
er
ter
ac
tin
g
as
A
P
F,
A
P
F
w
o
r
k
s
in
d
iv
id
u
all
y
to
r
ed
u
ce
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
s
o
u
r
ce
cu
r
r
en
ts
.
3.
CO
NT
RO
L
O
F
D
G
I
NV
E
R
T
E
R
A
ND
DUA
L
AP
F
3
.
1
.
Co
ntr
o
l o
f
DG
I
nv
er
t
er
I
n
itiall
y
t
h
e
DG
is
s
w
itc
h
ed
i
n
to
t
h
e
p
o
w
er
s
y
s
te
m
at
t
h
e
i
n
s
ta
n
t
o
f
0
.
1
s
ec
o
n
d
s
.
Fro
m
0
.
1
s
ec
,
th
e
DG
in
v
er
ter
j
u
s
t
ac
ts
as
a
n
in
v
er
ter
co
n
v
er
ti
n
g
D
C
t
y
p
e
f
r
o
m
DG
to
AC
t
y
p
e
to
f
ee
d
p
o
w
er
o
f
5
KW
to
g
r
id
.
A
t
0
.
2
s
ec
o
n
d
s
,
t
h
e
DG
i
n
v
er
t
er
is
s
w
itc
h
ed
to
ac
t
as
A
P
F
t
o
f
ee
d
co
m
p
e
n
s
ati
n
g
s
i
g
n
a
ls
t
o
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
.
I
q
(
r
e
f
)
I
d
(
r
e
f
)
I
0
(
r
e
f
)
V
s
(
a
b
c
)
P
L
L
0
1
0
0
θ
P
W
M
G
e
n
e
r
a
t
o
r
I
a
b
c
(
r
e
f
)
I
a
b
c
(
a
c
t
)
G
a
t
e
P
u
l
s
e
s
t
o
D
G
I
n
v
e
r
t
e
r
t
o
a
c
t
a
s
I
n
v
e
r
t
e
r
d
q
-
a
b
c
T
r
a
n
s
f
o
r
m
a
t
i
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n
ω
t
H
C
C
I
*
r
e
f
(
a
b
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)
I
g
(
a
b
c
)
S
t
e
p
C
o
n
t
r
o
l
@
0
.
2
S
e
c
C
o
n
d
i
t
i
o
n
a
l
S
w
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t
c
h
C
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n
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t
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o
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a
s
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g
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g
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a
l
-
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2
>
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e
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h
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a
t
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o
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n
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e
r
t
o
a
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t
a
s
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P
F
Fig
u
r
e
3
.
C
o
n
tr
o
l stra
teg
y
f
o
r
DG
in
v
er
ter
C
o
n
tr
o
l
s
tr
ateg
y
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o
r
co
n
tr
o
llin
g
DG
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ter
p
lace
d
af
ter
D
G
to
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v
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t
p
o
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er
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m
DC
t
y
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e
to
A
C
t
y
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e
is
s
h
o
w
n
i
n
F
i
g
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r
e
3
.
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h
ile
DG
in
v
er
ter
ac
tin
g
as
in
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ter
to
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v
er
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th
e
DG
s
u
p
p
l
y
,
s
o
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r
ce
v
o
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s
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en
t
to
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L
L
to
o
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e
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f
o
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at
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eg
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ase
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g
le.
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n
th
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i
m
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le
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n
tr
o
l
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ateg
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to
co
n
tr
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l
DG
in
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er
ter
,
th
e
r
ef
er
e
n
ce
v
al
u
es
o
f
I
q(ref)
,
I
0(ref)
ar
e
s
et
to
ze
r
o
as
n
o
r
ea
ctiv
e
p
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er
is
f
ed
to
g
r
id
.
On
ly
ac
ti
v
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p
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ed
f
r
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m
DG
to
g
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an
d
t
h
u
s
I
d(ref)
i
s
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e
t
to
a
f
ix
e
d
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al
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e
r
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e
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ce
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al
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es
ar
e
f
ed
to
d
q
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ab
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tr
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o
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i
n
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er
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lar
k
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tr
an
s
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o
r
m
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)
.
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e
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tp
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t
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n
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s
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tr
an
s
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h
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r
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tain
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n
ce
c
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t
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i
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ls
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r
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t
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ig
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im
p
le
P
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er
ato
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to
p
r
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u
ce
p
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ls
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to
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in
v
er
ter
to
in
v
er
t
th
e
D
g
s
u
p
p
l
y
t
y
p
e
to
AC
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Dis
tr
ib
u
ted
Gen
era
tio
n
I
n
ve
r
ter a
s
A
P
F
in
Du
a
l A
P
F
DG
I
n
terf
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cin
g
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ch
eme
(
Ya
d
iki
R
a
je
n
d
r
a
B
a
b
u
)
1444
3
.
1
.
Co
ntr
o
l o
f
Dua
l
AP
F
A
t
0
.
2
s
ec
o
n
d
s
,
th
e
D
G
in
v
er
t
er
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s
w
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n
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ta
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p
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n
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g
en
er
al
th
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y
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co
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tr
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a
v
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s
o
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ce
co
n
v
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ter
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ce
g
ate
p
u
ls
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o
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h
ar
m
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ic
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u
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io
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at
p
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li
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is
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s
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elo
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ed
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ag
i
in
1
9
8
0
’
s
.
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h
is
th
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y
i
s
also
ca
lled
a
s
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tan
eo
u
s
p
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w
er
th
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r
y
o
r
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-
Q
th
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.
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h
e
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ch
e
m
atic
co
n
tr
o
l
f
lo
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o
f
P
-
Q
th
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is
s
h
o
w
n
in
F
ig
u
r
e
4
.
C
l
a
r
k
e
’
s
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r
a
n
s
f
o
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m
a
t
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l
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t
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c
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a
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l
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t
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o
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o
f
r
e
f
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n
c
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C
u
r
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t
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α
-
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e
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s
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l
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r
k
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s
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r
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o
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a
b
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r
a
n
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t
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o
n
H
C
C
G
a
t
e
P
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l
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o
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u
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l
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w
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t
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s
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n
s
t
a
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s
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V
d
c
(
a
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d
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r
e
f
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(
V
s
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L
o
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d
C
u
r
r
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n
t
(
I
L
)
Fig
u
r
e
4
.
C
o
n
tr
o
l a
lg
o
r
ith
m
o
f
P
-
Q
th
eo
r
y
I
n
s
ta
n
tan
eo
u
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
th
eo
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y
i
n
v
o
l
v
es
th
e
tr
a
n
s
f
o
r
m
atio
n
o
f
s
tatio
n
ar
y
a
-
b
-
c
f
r
a
m
e
to
o
r
th
o
g
o
n
al
s
ta
tio
n
ar
y
α
-
β
f
r
a
m
e
b
y
u
s
i
n
g
C
lar
k
e’
s
tr
an
s
f
o
r
m
atio
n
.
[
√
√
]
[
]
(
1
)
[
√
√
]
[
]
(
2
)
[
]
(
3
)
[
√
√
]
(
4
)
[
]
(
5
)
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
.
3
,
Sep
tem
b
er
2
0
1
7
:
144
1
–
14
54
1445
[
√
√
]
(
6
)
T
h
r
ee
-
p
h
ase
v
o
lta
g
e
s
i
g
n
als
i
n
a
-
b
-
c
f
r
a
m
e
is
co
n
v
er
te
d
to
α
-
β
f
r
a
m
e
as
in
d
icate
d
i
n
E
q
u
atio
n
1
an
d
th
r
ee
-
p
h
ase
c
u
r
r
en
t
s
ig
n
als
in
a
-
b
-
c
f
r
a
m
e
is
co
n
v
er
te
d
to
α
-
β
f
r
a
m
e
as
in
d
icate
d
i
n
E
q
u
atio
n
(
2
)
.
Vo
ltag
es
a
n
d
cu
r
r
en
ts
i
n
α
-
β
f
r
a
m
e
ar
e
s
e
n
t
f
o
r
in
s
ta
n
tan
eo
u
s
p
o
w
er
ca
lc
u
l
atio
n
s
.
A
c
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
s
ar
e
ca
lc
u
lated
f
r
o
m
α
-
β f
r
a
m
es o
f
v
o
lta
g
e
an
d
cu
r
r
en
ts
as i
n
(
7
)
an
d
(
8
)
r
e
p
r
esen
ted
as (
9
)
.
(
7
)
(
8
)
[
]
[
]
[
]
(
9
)
P
an
d
Q
ar
e
th
e
in
s
ta
n
ta
n
eo
u
s
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
s
.
T
h
e
ca
lcu
lated
in
s
ta
n
tan
eo
u
s
ac
ti
v
e
p
o
w
er
is
p
ass
ed
th
r
o
u
g
h
a
h
i
g
h
p
as
s
f
i
lter
to
o
b
tain
AC
co
m
p
o
n
e
n
t
o
f
ac
tiv
e
p
o
w
er
(
̃
)
.
A
ctu
al
D
C
lin
k
v
o
ltag
e
i
s
m
ea
s
u
r
ed
an
d
co
m
p
ar
ed
w
it
h
r
ef
er
en
ce
DC
li
n
k
v
o
lta
g
e
an
d
th
e
er
r
o
r
is
d
am
p
ed
u
s
i
n
g
a
s
i
m
p
le
P
I
co
n
tr
o
ller
to
o
b
tain
p
o
w
er
lo
s
s
P
loss
co
m
p
o
n
en
t
(
̅
)
.
T
h
e
o
b
tain
ed
p
o
w
er
lo
s
s
co
m
p
o
n
en
t
is
co
m
p
ar
ed
w
i
th
AC
co
m
p
o
n
e
n
t o
f
p
o
w
er
to
o
b
tain
r
ef
er
en
ce
co
m
p
en
s
ati
n
g
ac
t
iv
e
p
o
w
er
co
m
p
o
n
e
n
t a
s
(
1
0
)
.
̃
̅
(
1
0
)
T
h
e
r
ef
er
en
ce
ac
ti
v
e
p
o
w
er
a
n
d
r
ea
ctiv
e
p
o
w
er
co
m
p
o
n
e
n
t
s
ar
e
s
en
t
f
o
r
ca
lcu
la
tio
n
o
f
r
ef
e
r
en
ce
cu
r
r
en
t
s
i
n
α
-
β f
r
a
m
e
w
it
h
(
1
1
)
an
d
ar
e
c
o
n
v
er
ted
to
a
-
b
-
c
co
o
r
d
in
ates u
s
i
n
g
i
n
v
er
s
e
C
lar
k
e
’
s
tr
an
s
f
o
r
m
atio
n
as i
n
(
1
2
)
.
[
]
[
]
[
]
(
1
1
)
[
]
[
√
√
]
[
]
(
1
2
)
w
h
er
e
,
an
d
ar
e
th
e
r
ef
er
en
c
e
cu
r
r
en
ts
o
b
tai
n
ed
f
r
o
m
i
n
v
e
r
s
e
C
lar
k
e
’
s
tr
an
s
f
o
r
m
a
tio
n
.
T
h
e
r
ef
er
en
ce
cu
r
r
en
t
s
i
g
n
a
ls
in
t
h
r
ee
co
-
o
r
d
in
ate
s
y
s
te
m
ar
e
co
m
p
ar
ed
w
it
h
ac
t
u
al
cu
r
r
en
t
s
an
d
th
e
er
r
o
r
s
ig
n
a
l
is
s
en
t
to
h
y
s
ter
esi
s
cu
r
r
en
t c
o
n
tr
o
ller
w
h
ich
p
r
o
d
u
ce
s
g
ate
p
u
l
s
es
to
t
w
o
p
ar
allel
A
P
F’s.
T
h
e
cu
r
r
en
ts
f
r
o
m
t
w
o
p
ar
allel
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
s
(
AP
F’
s
)
s
en
d
s
co
m
p
e
n
s
ati
n
g
s
ig
n
als
to
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
to
r
ed
u
ce
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
p
o
w
er
d
is
tr
ib
u
tio
n
s
o
u
r
ce
co
m
p
o
n
e
n
ts
.
T
h
e
co
m
p
lete
s
c
h
e
m
atic
ar
r
an
g
e
m
en
t
o
f
DG
in
te
g
r
atio
n
to
g
r
id
w
it
h
t
w
o
p
ar
allel
in
v
er
ter
s
f
o
r
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
w
it
h
t
h
eir
r
esp
ec
ti
v
e
co
n
tr
o
l s
tr
ate
g
ies
w
er
e
s
h
o
w
n
i
n
F
i
g
u
r
e
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Dis
tr
ib
u
ted
Gen
era
tio
n
I
n
ve
r
ter a
s
A
P
F
in
Du
a
l A
P
F
DG
I
n
terf
a
cin
g
S
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