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[
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a
n
i
n
j
ec
ti
n
g
r
ef
er
en
ce
r
ea
l
o
r
r
ea
ctiv
e
p
o
w
er
in
to
th
e
lin
e.
I
t’
s
w
o
r
t
h
n
o
tin
g
th
at
th
e
m
ag
n
it
u
d
e
o
f
t
h
e
r
e
f
er
en
ce
cu
r
r
en
t
p
r
o
v
id
ed
b
y
th
e
g
r
id
o
p
er
ato
r
w
o
u
ld
o
n
l
y
co
n
tr
o
l
th
e
H
-
b
r
id
g
e
in
v
e
r
ter
o
p
er
atio
n
eith
er
ca
p
ac
iti
v
e
o
r
in
d
u
ct
iv
e.
I
n
o
th
er
w
o
r
d
s
,
th
e
v
alu
e
o
f
th
e
li
n
e
cu
r
r
e
n
t
m
ag
n
it
u
d
e
w
ill
n
o
t
f
o
llo
w
o
r
b
e
th
e
s
a
m
e
as
t
h
e
r
ef
er
en
ce
c
u
r
r
en
t
v
alu
e.
T
h
e
r
ef
er
en
ce
c
u
r
r
en
t
is
r
esp
o
n
s
ib
l
e
o
n
l
y
o
f
i
n
j
ec
tin
g
eit
h
er
ca
p
ac
itiv
e
o
r
in
d
u
cti
v
e
s
er
i
e
s
v
o
lta
g
e
in
to
th
e
li
n
e
b
y
v
ar
y
i
n
g
t
h
e
m
o
d
u
latio
n
in
d
e
x
.
T
h
e
H
-
b
r
id
g
e
co
n
tr
o
l is
s
y
n
c
h
r
o
n
ized
w
it
h
t
h
e
li
n
e
c
u
r
r
en
t b
y
u
s
i
n
g
a
p
h
ase
lo
c
k
ed
lo
o
p
.
B
esid
es,
th
e
i
n
j
ec
ted
v
o
ltag
e
th
r
o
u
g
h
th
e
lin
e
is
)
p
h
ase
s
h
i
f
ted
d
ep
en
d
in
g
o
n
t
h
e
P
I
co
n
tr
o
ller
o
u
tp
u
t
eith
er
p
o
s
itiv
e
o
r
n
eg
at
iv
e
.
T
h
e
lin
e
c
u
r
r
en
t
m
a
g
n
it
u
d
e
is
co
m
p
ar
ed
w
it
h
th
e
r
ef
er
en
ce
c
u
r
r
en
t
a
s
s
i
g
n
ed
b
y
th
e
g
r
id
o
p
er
ato
r
an
d
u
s
i
n
g
P
I
co
n
tr
o
ller
,
th
e
r
ef
er
e
n
ce
q
u
ad
r
atu
r
e
v
o
lta
g
e
is
g
e
n
er
ated
.
Mo
r
e
o
v
er
,
b
y
d
iv
id
i
n
g
th
e
m
ea
s
u
r
ed
DC
lin
k
v
o
lta
g
e
o
v
er
t
h
e
r
ef
er
e
n
ce
q
u
ad
r
atu
r
e
v
o
lta
g
e,
th
e
n
t
h
e
m
o
d
u
latio
n
i
n
d
ex
o
f
t
h
e
i
n
j
ec
ted
q
u
ad
r
atu
r
e
v
o
ltag
e
is
ass
ig
n
ed
.
T
h
e
r
ef
er
en
ce
v
alu
e
o
f
th
e
DC
li
n
k
v
o
ltag
e
is
co
m
p
ar
ed
w
ith
t
h
e
m
ea
s
u
r
ed
v
alu
e
o
f
t
h
e
ca
p
ac
ito
r
v
o
ltag
e
,
an
d
th
e
n
th
e
er
r
o
r
is
p
ass
ed
th
r
o
u
g
h
P
I
co
n
tr
o
ller
s
o
th
at
t
h
e
in
-
p
h
ase
p
ar
t
o
f
th
e
in
j
ec
ted
v
o
ltag
e
is
g
en
er
at
ed
.
T
o
m
ai
n
tai
n
t
h
e
v
o
ltag
e
a
m
p
lit
u
d
e
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th
e
in
-
p
h
a
s
e
in
j
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t
ed
v
o
ltag
e
w
it
h
i
n
its
ap
p
r
o
p
r
iate
r
an
g
e,
a
li
m
iter
w
ith
b
o
u
n
d
ar
ies
is
ap
p
lied
.
T
h
e
o
v
er
all
co
n
tr
o
l
s
tr
ateg
y
is
s
h
o
w
n
in
F
ig
u
r
e
1
.
Fig
u
r
e
1
.
L
in
e
c
u
r
r
en
t c
o
n
tr
o
l stra
teg
y
3.
DG
CO
N
T
RO
L
S
T
RA
T
E
G
Y
I
n
s
i
n
g
le
p
h
ase
p
o
w
er
s
y
s
te
m
s
,
g
e
n
er
atin
g
t
h
e
s
ec
o
n
d
ar
y
o
r
th
o
g
o
n
al
p
h
ase
i
s
q
u
ite
c
h
all
en
g
i
n
g
.
A
s
ec
o
n
d
o
r
d
er
g
en
er
alize
d
in
te
g
r
ato
r
(
SOGI
)
is
ap
p
lied
to
o
b
tain
th
e
f
ic
titi
o
u
s
p
h
a
s
e
s
o
a
s
to
f
o
r
m
a
v
ir
t
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al
t
w
o
-
p
h
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s
e
s
y
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te
m
i
n
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ic
h
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th
e
f
u
n
d
a
m
e
n
tal
a
n
g
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lar
f
r
eq
u
en
c
y
,
a
n
d
k
i
s
th
e
d
a
m
p
i
n
g
f
ac
to
r
.
A
cc
o
r
d
in
g
to
th
e
s
elec
ted
d
a
m
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g
f
ac
to
r
,
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er
f
o
r
m
a
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ca
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b
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m
p
r
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u
n
d
er
d
is
to
r
ted
g
r
id
v
o
lt
ag
es
i
n
ad
d
itio
n
to
th
e
f
ilter
i
n
g
f
ea
t
u
r
e
th
at
ca
n
b
e
o
b
tain
ed
[
1
5
]
.
Fro
m
Fi
g
u
r
e
2
(
a)
,
th
e
ch
ar
ac
ter
is
tic
tr
an
s
f
er
f
u
n
ctio
n
o
f
t
h
e
SOGI
is
s
tated
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
:
602
–
609
604
T
h
en
th
e
f
o
llo
w
i
n
g
o
r
th
o
g
o
n
al
t
w
o
-
p
h
ase
s
y
s
te
m
is
o
b
tai
n
ed
w
i
th
o
u
t
co
n
s
id
er
in
g
t
h
e
h
ar
m
o
n
ic
co
n
ten
t o
f
th
e
c
u
r
r
en
t a
n
d
v
o
lt
ag
e:
I
n
lo
w
v
o
lta
g
e
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
,
t
h
e
v
o
ltag
e
d
ep
en
d
s
m
ai
n
l
y
o
n
t
h
e
r
ea
l
p
o
w
er
.
S
o
th
at,
th
e
f
o
llo
w
in
g
eq
u
at
io
n
is
ap
p
lied
f
o
r
ev
er
y
D
G
co
n
tr
o
l stra
teg
y
:
W
h
er
e,
is
r
ef
er
en
ce
r
ea
l
p
o
w
e
r
,
is
th
e
in
itia
l
r
ea
l
p
o
w
er
,
is
th
e
d
r
o
o
p
g
ain
,
is
th
e
m
ea
s
u
r
ed
r
m
s
v
o
ltag
e
o
f
e
v
er
y
D
G,
is
t
h
e
in
i
tial r
m
s
v
o
lta
g
e.
Fig
u
r
e
2
(
b
)
d
e
p
ict
th
e
p
o
w
er
co
n
tr
o
l
an
d
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
s
o
f
ev
er
y
DG
u
n
it.
I
n
t
h
e
p
o
w
er
co
n
t
r
o
l
lo
o
p
,
th
e
P
/V
d
r
o
o
p
co
n
tr
o
l
is
ap
p
li
ed
to
g
en
er
ate
th
e
r
e
f
er
en
ce
r
e
al
p
o
w
er
o
f
ev
er
y
DG
w
h
ile
t
h
e
r
ea
ctiv
e
p
o
w
er
is
ass
i
g
n
ed
as
f
i
x
ed
v
al
u
e.
I
n
th
e
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
,
th
e
r
ef
er
en
ce
d
q
cu
r
r
en
t
co
m
p
o
n
en
ts
ar
e
c
o
m
p
ar
ed
w
it
h
th
e
m
ea
s
u
r
ed
d
q
cu
r
r
en
t
co
m
p
o
n
en
t
s
an
d
b
y
u
s
in
g
P
I
co
n
tr
o
ller
s
,
th
e
r
e
f
er
en
ce
d
q
v
o
lta
g
e
co
m
p
o
n
e
n
t
s
o
f
t
h
e
DG
v
o
lta
g
e
is
g
e
n
er
ated
.
Fi
n
all
y
,
t
h
e
s
in
w
av
e
s
i
g
n
al
o
f
th
e
DG
v
o
lta
g
e
i
s
e
s
tab
lis
h
ed
b
y
in
v
er
s
e
d
q
tr
an
s
f
o
r
m
atio
n
.
Fig
u
r
e
2
.
Dis
tr
ib
u
ted
g
e
n
er
ato
r
co
n
tr
o
l stra
teg
y
4.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
T
h
e
s
i
m
u
latio
n
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
n
et
w
o
r
k
is
d
ep
icted
in
Fi
g
u
r
e
3
.
T
h
e
m
icr
o
g
r
id
co
n
s
is
t
s
o
f
1
0
d
is
tr
ib
u
ted
g
en
er
ato
r
s
an
d
th
e
tr
an
s
f
o
r
m
er
less
H
-
b
r
id
g
e
in
v
er
ter
is
lo
ca
ted
at
P
C
C
to
co
n
tr
o
l
th
e
r
ea
l
p
o
w
er
f
lo
w
.
E
v
er
y
DG
i
s
m
o
d
elled
as
a
co
n
tr
o
lled
v
o
ltag
e
s
o
u
r
ce
w
h
ich
i
s
co
n
tr
o
lled
b
y
d
r
o
o
p
ch
ar
ac
ter
is
tic
an
d
th
e
u
tili
t
y
lo
ad
is
ass
u
m
e
d
to
b
e
r
esis
tiv
e.
T
h
e
s
i
m
u
lati
o
n
p
ar
am
e
ter
s
ar
e
all
g
i
v
e
n
in
T
a
b
le
1
.
T
h
e
lin
es
co
n
n
ec
ti
n
g
th
e
DGs
to
P
C
C
ar
e
ass
u
m
ed
to
b
e
m
o
r
e
r
esis
ti
v
e
an
d
ea
c
h
li
n
e
h
as
len
g
t
h
.
T
h
e
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:
2088
-
8
694
A
N
o
ve
l Lin
e
C
u
r
r
en
t Co
n
tr
o
l
S
tr
a
teg
y
to
C
o
n
tr
o
l th
e
R
ea
l P
o
w
er F
lo
w
a
t P
C
C
U
s
in
g
…
(
Qu
s
a
y
S
a
lem
)
605
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
H
-
b
r
id
g
e
in
v
er
ter
is
v
alid
ated
in
b
o
th
in
d
u
ct
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e
an
d
ca
p
ac
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v
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o
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er
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n
m
o
d
es
u
s
i
n
g
th
e
li
n
e
c
u
r
r
en
t c
o
n
tr
o
l s
tr
ateg
y
.
Fig
u
r
e
3
.
Si
m
u
latio
n
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
n
et
w
o
r
k
T
ab
le
1
S
im
u
lat
io
n
n
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w
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r
k
p
ar
a
m
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s
G
r
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d
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s
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-
b
r
i
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e
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y
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o
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d
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c
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g
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i
d
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1
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Ca
s
e
1
:
I
n
th
i
s
ca
s
e
,
th
e
H
-
b
r
id
g
e
in
v
er
ter
b
eh
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a
s
an
i
n
d
u
cti
v
e
i
m
p
ed
an
ce
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ed
u
ce
th
e
r
ea
l
p
o
w
e
r
ex
p
o
r
t
at
P
C
C
f
r
o
m
t
h
e
m
icr
o
g
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id
to
th
e
m
ai
n
g
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id
d
ep
en
d
in
g
o
n
th
e
co
n
tr
o
lled
lin
e
cu
r
r
e
n
t
v
alu
e.
B
ef
o
r
e
(
t
<
1
s
)
,
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e
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-
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lo
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n
s
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e
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e
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o
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e
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i
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led
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e
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e
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r
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en
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lled
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r
o
m
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5
A
to
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4
0
A
a
s
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ep
icted
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g
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r
e
4
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.
Fig
u
r
e
4
(
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)
d
ep
ict
th
e
r
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l
a
n
d
r
ea
ctiv
e
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o
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er
o
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e
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ter
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e
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l
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er
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e
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ze
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o
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r
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g
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e
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cti
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n
m
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i
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t
h
e
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n
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e
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e
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t.
T
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e
r
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w
er
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er
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t
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f
r
o
m
t
h
e
H
-
b
r
id
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e
in
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ter
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a
r
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lt
o
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g
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er
ies
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cti
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e
v
o
lt
ag
e.
T
h
e
DC
lin
k
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e
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r
eg
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ce
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alu
e
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0
V)
as
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ep
icted
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Fi
g
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r
e
4
(
c)
.
Fig
u
r
e
4
(
d
)
d
e
m
o
n
s
tr
ates
t
h
e
i
n
j
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v
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ich
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e
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er
m
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e.
I
t
is
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r
l
y
s
h
o
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th
at
t
h
e
in
j
ec
ted
v
o
ltag
e
is
ze
r
o
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o
r
e
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ce
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e
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n
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er
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s
a
f
ter
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in
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g
e
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ap
p
e
ar
ed
as
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0
V
p
ea
k
to
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ea
k
.
Fi
g
u
r
e
4
(
e)
-
(
f
)
d
ep
ict
th
e
H
-
b
r
id
g
e
v
o
lta
g
e
m
ag
n
it
u
d
e
an
d
p
h
ase
a
n
g
le
w
i
th
r
esp
ec
t
to
t
h
e
li
n
e
c
u
r
r
en
t.
As
d
e
m
o
n
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tr
ated
,
th
e
in
j
ec
ted
v
o
ltag
e
m
a
g
n
it
u
d
e
o
f
th
e
H
-
b
r
id
g
e
is
o
s
cil
latin
g
n
ea
r
th
e
d
c
lin
k
v
o
lta
g
e
r
ef
er
en
ce
.
A
ls
o
,
th
e
p
h
a
s
e
an
g
le
i
s
w
it
h
r
esp
ec
t to
th
e
li
n
e
cu
r
r
en
t.
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
:
602
–
609
606
Fig
u
r
e
5
(
a)
s
h
o
w
t
h
e
R
MS
v
o
ltag
e
(
o
r
an
g
e
li
n
e)
a
n
d
r
ea
l
p
o
w
er
(
b
lu
e
li
n
e)
at
P
C
C
b
ef
o
r
e
an
d
a
f
ter
th
e
H
-
b
r
id
g
e
o
p
er
atio
n
.
T
h
e
R
MS
v
o
lta
g
e
at
P
C
C
i
s
i
n
cr
e
ased
as
a
r
e
s
u
l
t
o
f
in
j
ec
ti
n
g
in
d
u
ctiv
e
v
o
lta
g
e
i
n
to
th
e
li
n
e
a
n
d
t
h
e
r
ea
l
p
o
w
er
a
t
P
C
C
i
s
co
n
tr
o
lled
f
r
o
m
to
ze
r
o
as
a
co
n
s
eq
u
e
n
ce
o
f
t
h
e
b
alan
ce
b
et
w
ee
n
t
h
e
to
tal
g
e
n
er
ated
p
o
w
er
an
d
t
h
e
u
tili
t
y
lo
ad
d
e
m
an
d
.
T
h
e
R
MS
v
o
ltag
e
a
n
d
r
ea
l
p
o
w
er
o
f
e
v
er
y
d
is
tr
ib
u
ted
g
e
n
er
ato
r
ar
e
d
ep
i
cted
in
Fi
g
u
r
e
5
(
b
)
.
A
f
ter
(
t
>
1
s
)
,
i
t
is
clea
r
l
y
s
h
o
w
n
t
h
at
t
h
e
R
M
S
v
o
lta
g
e
o
f
th
e
DG
is
in
cr
ea
s
ed
to
a
v
al
u
e
w
h
ic
h
s
a
tis
f
y
t
h
e
P
C
C
v
o
lta
g
e
i
n
cr
ea
s
e
.
A
l
s
o
,
th
e
r
ea
l
p
o
w
er
o
f
ev
er
y
DG
is
d
ec
r
ea
s
ed
at
(
t
>
1
s
)
f
r
o
m
to
as
th
eir
R
MS
v
o
lta
g
e
s
ar
e
in
cr
ea
s
ed
.
T
h
is
v
ar
iatio
n
o
f
t
h
e
D
Gs
r
ea
l
p
o
w
er
is
d
u
e
to
th
e
d
r
o
o
p
ch
ar
ac
ter
is
t
ic
b
et
w
ee
n
t
h
e
g
e
n
er
ated
r
ea
l
p
o
w
er
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n
d
t
h
e
R
MS
v
o
lta
g
e
o
f
ev
er
y
D
G
u
n
it.
Mo
r
eo
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er
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s
e
o
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r
esis
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e
t
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n
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t
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tili
t
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ad
is
p
r
o
p
o
r
tio
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to
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e
PC
C
v
o
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g
e,
th
e
r
ea
l
p
o
w
er
o
f
th
e
lo
ad
is
in
cr
e
ased
f
r
o
m
to
as
s
h
o
w
n
i
n
F
ig
u
r
e
5
(
c)
.
Fi
g
u
r
e
5
(
d
)
d
ep
ict
th
e
in
j
ec
ted
v
o
lta
g
e
a
n
d
th
e
li
n
e
c
u
r
r
en
t
i
n
t
h
e
i
n
d
u
cti
v
e
o
p
er
atio
n
m
o
d
e.
Fig
u
r
e
4
.
P
er
f
o
r
m
a
n
ce
o
f
th
e
H
-
b
r
id
g
e
i
n
v
er
ter
in
t
h
e
i
n
d
u
ct
iv
e
o
p
er
atio
n
m
o
d
e
Fig
u
r
e
5.
S
y
s
te
m
p
er
f
o
r
m
a
n
ce
b
ef
o
r
e
an
d
af
ter
th
e
H
-
b
r
id
g
e
in
d
u
cti
v
e
o
p
er
atio
n
.
4
.
2
.
Ca
s
e
2
:
I
n
th
i
s
ca
s
e,
th
e
H
-
b
r
id
g
e
in
v
er
ter
b
eh
av
es
a
s
a
ca
p
ac
itiv
e
i
m
p
ed
an
ce
to
r
ed
u
ce
th
e
r
ea
l
p
o
w
er
i
m
p
o
r
t a
t P
C
C
f
r
o
m
t
h
e
m
ai
n
g
r
id
to
t
h
e
m
icr
o
g
r
id
d
ep
en
d
in
g
o
n
th
e
co
n
tr
o
lled
li
n
e
c
u
r
r
en
t v
al
u
e.
B
ef
o
r
e
(
t
<
1
s
)
,
th
e
H
-
b
r
id
g
e
co
n
tr
o
l
u
n
i
t
is
b
lo
ck
ed
an
d
co
n
s
eq
u
e
n
tl
y
,
th
e
in
j
ec
ted
v
o
ltag
e
is
d
i
s
ab
led
.
A
f
ter
(
t
>
1
s
)
,
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:
2088
-
8
694
A
N
o
ve
l Lin
e
C
u
r
r
en
t Co
n
tr
o
l
S
tr
a
teg
y
to
C
o
n
tr
o
l th
e
R
ea
l P
o
w
er F
lo
w
a
t P
C
C
U
s
in
g
…
(
Qu
s
a
y
S
a
lem
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607
th
e
H
-
b
r
id
g
e
co
n
tr
o
l
u
n
it
s
tar
t
s
to
o
p
er
ate
an
d
th
e
in
j
ec
ted
v
o
ltag
e
is
e
n
ab
led
,
r
e
s
p
ec
tiv
el
y
.
T
h
e
lin
e
cu
r
r
en
t
i
s
co
n
tr
o
lled
f
r
o
m
2
0
0
A
to
1
4
5
A
a
s
d
ep
icted
in
Fi
g
u
r
e
6
(
a)
.
Fig
u
r
e
6
(
b
)
d
ep
ict
th
e
r
ea
l
a
n
d
r
ea
ctiv
e
p
o
w
er
o
f
th
e
H
-
b
r
id
g
e
i
n
v
er
ter
.
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h
e
r
e
al
p
o
w
er
v
a
lu
e
i
s
ze
r
o
d
u
r
in
g
th
e
ca
p
ac
itiv
e
o
p
er
atio
n
m
o
d
e
s
in
ce
th
e
a
n
g
le
is
)
w
it
h
r
esp
ec
t
to
th
e
lin
e
cu
r
r
e
n
t.
T
h
e
r
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ctiv
e
p
o
w
er
g
en
er
at
ed
f
r
o
m
t
h
e
H
-
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id
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e
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ter
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r
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lt
o
f
in
j
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tin
g
s
er
ies
ca
p
ac
iti
v
e
v
o
lt
ag
e.
T
h
e
DC
lin
k
v
o
ltag
e
i
s
r
eg
u
la
ted
to
its
r
ef
er
en
ce
v
al
u
e
(
2
0
V)
as
d
e
p
icted
in
Fi
g
u
r
e
6
(
c)
.
Fig
u
r
e
6
(
d
)
d
e
m
o
n
s
t
r
ates
t
h
e
i
n
j
ec
ted
p
ea
k
to
p
ea
k
v
o
lta
g
e
w
h
ich
ap
p
ea
r
s
at
th
e
ter
m
i
n
als
o
f
th
e
H
-
b
r
id
g
e.
Fig
u
r
e
6
(
e)
-
(
f
)
d
ep
ict
th
e
H
-
b
r
id
g
e
v
o
ltag
e
m
ag
n
i
tu
d
e
a
n
d
p
h
ase
an
g
le
w
i
th
r
esp
ec
t
to
th
e
lin
e
cu
r
r
en
t.
As
d
e
m
o
n
s
tr
ated
,
th
e
in
j
ec
ted
v
o
lta
g
e
m
a
g
n
it
u
d
e
o
f
t
h
e
H
-
b
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id
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e
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ap
p
r
o
x
i
m
ate
l
y
1
7
V.
Als
o
,
t
h
e
p
h
ase
an
g
le
i
s
w
it
h
r
esp
ec
t to
th
e
li
n
e
cu
r
r
e
n
t.
Fi
g
u
r
e
7
(
a)
s
h
o
w
th
e
R
MS
v
o
lta
g
e
(
o
r
an
g
e
lin
e)
an
d
r
ea
l
p
o
w
er
(
b
lu
e
lin
e)
at
P
C
C
b
ef
o
r
e
an
d
af
ter
th
e
H
-
b
r
id
g
e
o
p
er
atio
n
.
T
h
e
R
MS
v
o
ltag
e
at
P
C
C
is
d
ec
r
ea
s
ed
as
a
r
esu
lt
o
f
in
j
ec
tin
g
ca
p
ac
iti
v
e
v
o
ltag
e
in
to
th
e
li
n
e
an
d
t
h
e
r
ea
l
p
o
w
er
at
P
C
C
is
co
n
tr
o
lled
f
r
o
m
to
ze
r
o
as
a
co
n
s
eq
u
en
ce
o
f
th
e
b
alan
ce
b
et
w
ee
n
th
e
to
tal
g
e
n
er
ated
p
o
w
er
a
n
d
th
e
u
ti
lit
y
lo
ad
d
em
an
d
.
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h
e
R
MS
v
o
lta
g
e
an
d
r
ea
l
p
o
w
er
o
f
ev
er
y
d
is
tr
ib
u
ted
g
e
n
er
ato
r
ar
e
d
e
p
icted
in
Fig
u
r
e
7
(
b
)
.
Af
ter
(
t
>
1
s
)
,
i
t
is
clea
r
l
y
s
h
o
w
n
th
at
th
e
R
M
S
v
o
ltag
e
o
f
t
h
e
DG
is
d
ec
r
ea
s
ed
to
a
v
al
u
e
w
h
ich
s
ati
s
f
y
t
h
e
P
C
C
v
o
lta
g
e
d
ec
r
ea
s
e
.
A
ls
o
,
th
e
r
ea
l
p
o
w
er
o
f
ev
er
y
DG
is
i
n
cr
ea
s
ed
at
(
t
>
1
s
)
ap
p
r
o
x
im
ate
l
y
f
r
o
m
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ir
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h
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ated
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u
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(
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.
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u
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ep
ict
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u
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er
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u
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e
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4
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3
.
T
H
D
o
f
t
he
P
CC
v
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lt
a
g
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
694
I
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t J
P
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w
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lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
602
–
609
608
I
n
lo
w
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v
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g
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d
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ib
u
tio
n
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et
w
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k
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h
e
to
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ar
m
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n
ic
d
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o
r
tio
n
(
T
HD)
lim
it
at
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C
C
s
h
o
u
ld
n
o
t
e
x
ce
ed
5
%
as
s
tate
d
in
[
1
6
]
.
T
h
er
ef
o
r
e,
th
e
P
C
C
v
o
ltag
e
h
as
b
ee
n
te
s
ti
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ied
r
eg
a
r
d
in
g
t
h
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
d
u
r
in
g
b
o
th
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s
e
s
ei
th
er
if
t
h
e
H
-
b
r
id
g
e
i
n
v
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ter
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s
o
p
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atin
g
i
n
its
in
d
u
ctiv
e
o
p
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atio
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m
o
d
e
o
r
its
ca
p
ac
itiv
e
o
p
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atio
n
m
o
d
e.
On
ce
t
h
e
s
er
ies
co
n
v
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ter
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t
ar
ts
to
in
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ec
t
in
d
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ct
i
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e
o
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ca
p
ac
itiv
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v
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g
e
a
t
,
th
e
f
ir
s
t
t
h
r
ee
c
y
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o
f
t
h
e
P
C
C
v
o
lta
g
e
is
tak
e
n
to
m
ea
s
u
r
e
th
e
T
HD
as
d
ep
icted
in
Fig
u
r
e
8
(
a)
an
d
(
b
)
.
I
t
is
clea
r
l
y
s
h
o
w
n
t
h
at
t
h
e
T
HD
f
ac
to
r
o
f
t
h
e
P
C
C
v
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is
s
m
all
a
n
d
b
el
o
w
5
%
d
u
r
i
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g
b
o
th
o
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m
o
d
e
s
.
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n
t
h
e
i
n
d
u
ctiv
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o
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atio
n
m
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e,
t
h
e
T
HD
is
ab
o
u
t
1
.
7
9
%.
Ho
w
ev
e
r
,
in
th
e
ca
p
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it
iv
e
m
o
d
e,
t
h
e
T
HD
is
f
air
l
y
1
.
9
7
%.
Fig
u
r
e
8
: T
HD
o
f
P
C
C
v
o
ltag
e
d
u
r
in
g
(
a)
in
d
u
cti
v
e
m
o
d
e
(
b
)
ca
p
ac
itiv
e
m
o
d
e
5.
CO
NCLU
SI
O
N
I
n
th
i
s
p
ap
er
,
an
H
-
b
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id
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ter
is
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at
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n
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o
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r
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en
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r
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n
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o
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s
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ateg
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h
a
s
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n
d
esi
g
n
ed
in
o
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er
to
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h
iev
e
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et.
T
h
e
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m
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lat
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w
t
h
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o
p
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ed
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tr
o
l
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ateg
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ed
u
ci
n
g
t
h
e
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ea
l
p
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at
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C
to
ze
r
o
d
u
r
in
g
b
o
th
in
d
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cti
v
e
an
d
ca
p
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iti
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e
o
p
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atio
n
m
o
d
es.
B
esid
es,
it
w
a
s
o
b
s
er
v
ed
th
at
t
h
e
T
HD
v
alu
es
o
f
t
h
e
P
C
C
v
o
l
tag
e
in
b
o
th
o
p
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atio
n
m
o
d
es
ar
e
b
elo
w
t
h
e
s
p
ec
if
ied
lim
i
t
i
n
lo
w
v
o
ltag
e
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
.
.
RE
F
E
R
E
NC
E
S
[1
]
B.
K.
P
e
re
ra
,
P
.
Ci
u
f
o
a
n
d
S
.
P
e
re
ra
,
"
P
o
in
t
o
f
c
o
m
m
o
n
c
o
u
p
li
n
g
(P
CC)
v
o
lt
a
g
e
c
o
n
tro
l
o
f
a
g
rid
-
c
o
n
n
e
c
ted
so
lar
p
h
o
to
v
o
lt
a
ic
(
P
V
)
sy
ste
m
,
"
in
In
d
u
strial
El
e
c
tro
n
ics
S
o
c
iety
,
IECON
2
0
1
3
-
3
9
t
h
A
n
n
u
a
l
Co
n
f
e
re
n
c
e
o
f
th
e
IEE
E,
V
ien
n
a
,
2
0
1
3
.
[2
]
S
.
M
.
Am
in
,
"
S
m
a
rt
g
rid
se
c
u
rit
y
,
p
riv
a
c
y
,
a
n
d
r
e
sili
e
n
t
a
rc
h
it
e
c
tu
re
s:
Op
p
o
rt
u
n
it
ie
s
a
n
d
c
h
a
ll
e
n
g
e
s,"
in
P
o
w
e
r
a
n
d
En
e
rg
y
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
IEE
E,
S
a
n
Die
g
o
,
2
0
1
2
.
[3
]
J.
M
.
G
u
e
rre
ro
,
J.
C.
V
a
sq
u
e
z
,
J.
M
a
tas
,
L
.
G
.
V
icu
n
a
a
n
d
M
.
Ca
stil
la,
"
Hie
ra
rc
h
ica
l
c
o
n
tro
l
o
f
d
ro
o
p
-
c
o
n
tr
o
ll
e
d
A
C
a
n
d
DC
m
ic
ro
g
rid
s
–
A
g
e
n
e
ra
l
a
p
p
r
o
a
c
h
to
w
a
rd
sta
n
d
a
rd
iza
ti
o
n
,
"
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
str
ial
El
e
c
tro
n
ics
,
v
o
l.
5
8
,
n
o
.
1
,
p
.
1
5
8
–
1
7
2
,
2
0
1
1
.
[4
]
A
.
Bid
ra
m
a
n
d
A
.
Da
v
o
u
d
i,
"
Hie
ra
rc
h
ica
l
stru
c
tu
re
o
f
m
icro
g
rid
s c
o
n
tr
o
l
sy
ste
m
,
"
IEE
E
T
r
a
n
sa
c
ti
o
n
s o
n
S
m
a
rt
G
rid
,
vo
l.
3
,
n
o
.
4
,
p
.
1
9
6
3
–
1
9
7
6
,
2
0
1
2
.
[5
]
B.
Ha
n
,
S
.
Ba
e
k
a
n
d
H.
Ki
m
,
"
S
t
a
ti
c
s
y
n
c
h
ro
n
o
u
s
se
ries
c
o
m
p
e
n
sa
to
r
b
a
se
d
o
n
c
a
sc
a
d
e
d
H
-
b
rid
g
e
in
v
e
rter,"
El
e
c
tri
c
P
o
w
e
r
S
y
ste
m
s R
e
se
a
r
c
h
,
v
o
l.
6
5
,
n
o
.
2
,
p
p
.
1
5
9
-
1
6
8
,
2
0
0
3
.
[6
]
B.
P
a
n
,
H.
Y
u
,
K.
L
i,
Z.
Zh
a
o
,
Y.
Jia
n
g
a
n
d
L
.
Yu
a
n
,
"
A
h
iera
rc
h
ica
l
c
o
n
tro
l
stra
teg
y
f
o
r
c
a
s
c
a
d
e
d
H
-
b
ri
d
g
e
m
u
lt
il
e
v
e
l
sta
ti
c
s
y
n
c
h
ro
n
o
u
s
se
ries
c
o
m
p
e
n
sa
to
r,
"
in
2
0
1
6
1
9
th
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
El
e
c
tri
c
a
l
M
a
c
h
in
e
s
a
n
d
S
y
ste
m
s (ICE
M
S
),
Ch
i
b
a
,
2
0
1
6
.
[7
]
A
.
P
a
sh
a
e
i,
B.
Zah
a
w
i
a
n
d
D.
G
iao
u
ris,
"
N
e
w
c
o
n
tro
l
m
e
th
o
d
f
o
r
d
istri
b
u
ti
o
n
n
e
tw
o
rk
d
istri
b
u
ted
sta
ti
c
se
rie
s
c
o
m
p
e
n
sa
to
r,
"
in
5
t
h
IET
In
ter
n
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
P
o
w
e
r
El
e
c
tro
n
ics
,
M
a
c
h
i
n
e
s
a
n
d
Dr
iv
e
s
(
P
EM
D
2
0
1
0
),
Brig
h
to
n
,
2
0
1
0
.
[8
]
M
.
S
a
ra
d
a
rz
a
d
e
h
,
S
.
F
a
rh
a
n
g
i,
J.
L
.
S
c
h
a
n
e
n
,
P
.
O.
Je
a
n
n
i
n
a
n
d
D
.
F
re
y
,
"
A
p
p
li
c
a
ti
o
n
o
f
c
a
sc
a
d
e
d
H
-
b
rid
g
e
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:
2088
-
8
694
A
N
o
ve
l Lin
e
C
u
r
r
en
t Co
n
tr
o
l
S
tr
a
teg
y
to
C
o
n
tr
o
l th
e
R
ea
l P
o
w
er F
lo
w
a
t P
C
C
U
s
in
g
…
(
Qu
s
a
y
S
a
lem
)
609
d
istri
b
u
ti
o
n
-
sta
ti
c
sy
n
c
h
ro
n
o
u
s
se
ries
c
o
m
p
e
n
sa
to
r
in
e
lec
tri
c
a
l
d
istri
b
u
t
io
n
sy
ste
m
p
o
w
e
r
f
lo
w
c
o
n
tro
l,
"
IET
P
o
w
e
r
El
e
c
tro
n
ics
,
v
o
l
.
5
,
n
o
.
9
,
p
p
.
1
6
6
0
-
1
6
7
5
,
2
0
1
2
.
[9
]
M
.
S
a
ra
d
a
rz
a
d
e
h
,
S
.
F
a
rh
a
n
g
i,
J.
L
.
S
c
h
a
n
e
n
a
n
d
P
.
O.
Je
a
n
n
i
n
,
"
A
n
o
v
e
l
f
u
z
z
y
lo
g
ic
DC
b
u
s
v
o
lt
a
g
e
b
a
lan
c
in
g
c
o
n
tro
ll
e
r
f
o
r
a
D
-
S
S
S
C
c
a
sc
a
d
e
d
H
-
b
ri
d
g
e
c
o
n
v
e
rter,"
in
2
0
1
0
1
st
P
o
w
e
r
El
e
c
tro
n
ic
&
Driv
e
S
y
ste
m
s
&
T
e
c
h
n
o
lo
g
ies
Co
n
f
e
re
n
c
e
(P
EDS
T
C),
T
e
h
ra
n
,
2
0
1
0
.
[1
0
]
E.
L
.
p
e
ll
e
ter,
s.b
a
c
h
a
,
r.
c
a
ire
a
n
d
J.g
u
irau
d
,
"
Ac
ti
v
e
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
f
lo
w
c
o
n
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se
d
o
n
D
-
S
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f
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a
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m
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sh
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d
d
istri
b
u
ti
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n
G
rid
s,"
i
n
1
9
th
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
El
e
c
tri
c
it
y
Distr
ib
u
ti
o
n
,
Vie
n
n
a
,
2
0
0
7
.
[1
1
]
K.
D.
Bra
b
a
n
d
e
re
,
B.
Bo
lse
n
s,
J.
V
.
d
.
Ke
y
b
u
s,
A
.
W
o
y
te,
J.
Drie
se
n
a
n
d
R.
Be
lm
a
n
s,
"
A
v
o
lt
a
g
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a
n
d
f
re
q
u
e
n
c
y
d
ro
o
p
c
o
n
tro
l
m
e
th
o
d
f
o
r
p
a
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ll
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l
in
v
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rters
,
"
IEE
E
T
ra
n
sa
c
ti
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1
0
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.
[1
2
]
Y.
X
ia,
Y.
P
e
n
g
,
P
.
Ya
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g
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.
Yu
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.
W
e
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ted
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C/DC
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rid
,
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T
ra
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3
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p
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4
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4
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.
[1
3
]
Q.
C
.
Zh
o
n
g
,
"
Ro
b
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c
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p
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ra
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p
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[1
4
]
J.
He
a
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d
Y.
W
.
L
i,
"
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n
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n
h
a
n
c
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d
m
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a
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,
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3
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2
.
[1
5
]
M
.
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re
d
,
M
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a
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tk
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r
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.
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o
les
tan
,
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r
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4
–
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2
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2
.
[1
6
]
T
.
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Co
lo
sin
o
a
n
d
M
.
L
e
Do
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x
,
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In
terp
re
ti
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g
IEE
E
S
T
D
5
1
9
a
n
d
m
e
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ti
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g
it
s
h
a
r
m
o
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ic
li
m
it
s
in
V
F
D
a
p
p
li
c
a
ti
o
n
s,"
in
I
EE
E
I
n
d
u
stry
A
p
p
li
c
a
ti
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s
S
o
c
iety
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0
th
A
n
n
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a
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tr
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m
a
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l
In
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f
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,
2
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3
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RAP
H
I
E
S
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F
AUTH
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RS
Qu
sa
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a
le
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wa
s
b
o
rn
in
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rd
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n
.
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re
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th
e
B.
S
c
.
d
e
g
re
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in
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c
a
l
p
o
w
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n
g
in
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ro
m
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f
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tah
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h
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.
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d
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re
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m
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r
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k
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rsit
y
,
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id
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in
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0
1
2
.
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is
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u
rre
n
tl
y
w
o
rk
in
g
to
w
a
rd
th
e
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h
.
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d
e
g
re
e
in
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tri
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l
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rg
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g
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t
th
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stit
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te
o
f
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e
r
g
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n
v
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n
a
n
d
S
t
o
ra
g
e
,
Un
iv
e
rsit
y
o
f
Ul
m
,
U
l
m
,
Ge
r
m
a
n
y
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
p
o
w
e
r
c
o
n
tro
l
a
n
d
p
o
w
e
r
m
a
n
a
g
e
m
e
n
t
in
l
o
w
-
v
o
lt
a
g
e
s
m
a
rt
m
icro
g
rid
s,
Isla
n
d
in
g
d
e
tec
ti
o
n
sc
h
e
m
e
s,
a
n
d
se
ries
p
o
w
e
r
f
lo
w
c
o
n
tro
ll
e
rs.
Jia
n
X
ie
w
a
s
b
o
rn
in
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m
e
n
,
Ch
in
a
.
He
re
c
e
i
v
e
s
th
e
B.
S
c
.
d
e
g
re
e
in
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tri
c
a
l
e
n
g
in
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e
rin
g
f
ro
m
Jia
o
‐
T
o
n
g
Un
iv
e
rsit
y
,
S
h
a
n
g
h
a
i,
in
1
9
8
5
,
a
n
d
t
h
e
Dip
lo
m
a
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
f
ro
m
T
e
c
h
n
ica
l
Un
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e
rsit
y
o
f
Da
r
m
st
a
d
t,
Da
rm
sta
d
t,
in
1
9
8
7
,
a
n
d
th
e
P
h
.
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i
n
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lec
tri
c
a
l
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n
g
in
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rin
g
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ro
m
T
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c
h
n
ica
l
Un
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e
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y
o
f
D
a
r
m
sta
d
t,
Da
r
m
s
tad
t,
in
1
9
9
3
.
F
ro
m
1
9
8
8
to
1
9
9
3
,
h
e
w
a
s
a
Re
se
a
rc
h
A
s
sista
n
t
w
it
h
th
e
Tec
h
n
ica
l
Un
iv
e
rsity
o
f
Da
r
m
sta
d
t.
F
ro
m
1
9
9
3
t
o
1
9
9
8
,
h
e
w
a
s
a
De
v
e
lo
p
m
e
n
t
En
g
in
e
e
r
w
it
h
A
E
G
.
S
in
c
e
1
9
9
8
,
h
e
h
a
s
b
e
e
n
F
u
ll
P
r
o
f
e
ss
o
r
w
it
h
th
e
In
stit
u
te
o
f
En
e
rg
y
Co
n
v
e
rsio
n
a
n
d
S
to
ra
g
e
,
Un
iv
e
rsity
o
f
Ul
m
,
Ul
m
,
G
e
r
m
a
n
y
.
F
ro
m
2
0
0
3
to
2
0
1
0
,
h
e
lea
d
s
tw
o
p
ro
jec
ts
a
t
th
e
Un
iv
e
rsity
o
f
Ul
m
.
He
h
a
s
tw
o
re
g
ister
e
d
p
a
ten
ts.
His
re
se
a
rc
h
i
n
tere
sts
in
c
lu
d
e
a
d
v
a
n
c
e
d
p
o
w
e
r
c
o
n
v
e
rters
,
b
a
tt
e
ry
m
a
n
a
g
e
m
e
n
t
sy
ste
m
s
,
h
ig
h
f
re
q
u
e
n
c
y
h
a
r
m
o
n
ics
in
ra
il
w
a
y
s,
c
a
sc
a
d
e
d
H
-
b
rid
g
e
in
v
e
rters
,
s
m
a
rt
g
rid
a
n
d
s
m
a
rt
m
e
ters
,
d
e
c
e
n
tralize
d
c
o
n
tr
o
l
in
m
icro
g
rid
s.
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