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J
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Vo
l.
1
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2
,
J
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n
e
20
2
6
,
p
p
.
646
~
6
6
2
I
SS
N:
2252
-
8
7
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2
,
DOI
:
1
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.
1
1
5
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1
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.
v
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.
i
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.
pp
646
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662
646
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h
ttp
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//
ija
p
e.
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co
m/
Ana
ly
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t
he
a
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lity o
f
ca
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citor
e
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in
a
mo
dul
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suppo
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nfo
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ticle
his
to
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y:
R
ec
eiv
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Oct
6
,
2
0
2
5
R
ev
is
ed
J
an
1
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,
2
0
2
6
Acc
ep
ted
Ma
r
1
2
,
2
0
2
6
F
lex
ib
le
DC
tran
sm
issio
n
sy
ste
m
s
b
a
se
d
o
n
m
o
d
u
lar
m
u
lt
i
lev
e
l
c
o
n
v
e
rters
h
a
v
e
t
h
e
p
o
ten
ti
a
l
to
su
p
p
o
rt
th
e
in
e
rti
a
o
f
AC
p
o
we
r
g
ri
d
s
b
y
u
sin
g
s
u
b
-
m
o
d
u
le
c
a
p
a
c
it
o
r
e
n
e
rg
y
st
o
ra
g
e
.
Ho
we
v
e
r,
e
x
isti
n
g
st
u
d
ies
g
e
n
e
ra
ll
y
b
e
li
e
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e
t
h
a
t
t
h
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i
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a
p
ro
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y
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le
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s
y
ste
m
s
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li
m
it
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y
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e
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e
n
e
rg
y
sto
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g
e
ti
m
e
c
o
n
sta
n
ts,
wh
ich
is
we
a
k
e
r
th
a
n
th
a
t
o
f
sy
n
c
h
ro
n
o
u
s
m
o
to
rs,
a
n
d
lac
k
s
q
u
a
n
ti
tati
v
e
i
n
d
ica
to
rs
t
o
m
e
a
su
re
t
h
e
ir
s
u
p
p
o
rt
stre
n
g
t
h
.
In
tro
d
u
c
i
n
g
t
h
e
flex
i
b
le
-
DC
e
q
u
i
v
a
len
t
in
e
rt
ia
c
o
n
sta
n
t
(
F
DEIC)
a
s
a
p
re
c
ise
m
e
tri
c
fo
r
a
ss
e
s
sin
g
in
e
rti
a
su
p
p
o
rt
u
n
d
e
r
d
iffere
n
t
m
a
n
a
g
e
m
e
n
t
sc
h
e
m
e
s,
th
is
re
se
a
rc
h
p
re
se
n
ts
a
n
e
w
a
n
a
ly
ti
c
a
l
fra
m
e
wo
rk
b
a
se
d
o
n
fre
q
u
e
n
c
y
re
sp
o
n
se
s.
Re
su
lt
s
sh
o
w
t
h
a
t
t
h
e
in
e
rti
a
l
re
sp
o
n
se
is
in
fl
u
e
n
c
e
d
b
y
c
o
n
tr
o
l
b
a
n
d
wi
d
th
,
DC
-
v
o
lt
a
g
e
d
y
n
a
m
ics
,
a
n
d
c
ircu
latin
g
-
c
u
rre
n
t
b
e
h
a
v
i
o
u
r.
A m
o
re
g
e
n
e
ra
li
z
e
d
m
u
lt
i
-
term
in
a
l
F
DEI
C
is
c
re
a
ted
to
a
c
c
o
u
n
t
f
o
r
t
h
e
imp
a
c
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o
f
ra
ise
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to
tal
c
a
p
a
c
it
o
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e
n
e
rg
y
,
a
n
d
th
e
t
h
e
o
ry
is
fu
rt
h
e
r
e
x
p
a
n
d
e
d
t
o
c
o
v
e
r
DC
g
rid
s
wit
h
m
o
re
th
a
n
o
n
e
ter
m
in
a
l.
A
th
re
e
-
term
in
a
l
flex
ib
l
e
DC
g
rid
sim
u
latio
n
m
o
d
e
l
is
b
u
il
t
in
th
e
P
S
CAD
e
n
v
ir
o
n
m
e
n
t
,
a
n
d
th
e
sim
u
latio
n
re
su
lt
s v
e
rify
th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
th
e
p
r
o
p
o
se
d
q
u
a
n
ti
tativ
e
a
n
a
l
y
sis m
e
th
o
d
.
K
ey
w
o
r
d
s
:
C
ap
ac
ito
r
en
er
g
y
Fra
ctio
n
al
r
esp
o
n
s
e
I
n
er
tia
co
n
s
tan
t
Mo
d
u
lar
m
u
ltil
ev
el
co
n
v
e
r
ter
Su
p
p
o
r
t stre
n
g
th
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Du
n
y
a
Sh
.
W
ais
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
C
o
lleg
e
o
f
E
n
g
in
ee
r
i
n
g
,
Mu
s
tan
s
ir
iy
ah
Un
i
v
er
s
ity
B
ag
h
d
ad
,
I
r
aq
E
m
ail:
d
u
n
y
a.
s
h
.
wais@
u
o
m
u
s
tan
s
ir
iy
ah
.
ed
u
.
i
q
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
m
o
d
u
lar
m
u
ltil
ev
el
co
n
v
e
r
ter
b
ased
h
ig
h
v
o
ltag
e
d
ir
ec
t
cu
r
r
en
t
(
MM
C
-
HVDC)
tech
n
o
lo
g
y
h
as
th
e
ad
v
an
ta
g
es
o
f
s
tr
o
n
g
s
ca
lab
ilit
y
,
h
ig
h
c
o
n
tr
o
llab
ilit
y
,
d
ir
ec
t
ac
ce
s
s
an
d
tr
an
s
m
is
s
io
n
o
f
win
d
an
d
s
o
lar
p
o
wer
g
en
e
r
atio
n
,
a
n
d
th
e
a
b
ilit
y
to
s
u
p
p
ly
p
o
wer
to
wea
k
A
C
g
r
id
s
an
d
ev
en
p
ass
iv
e
s
y
s
t
em
s
.
I
t
is
cu
r
r
en
tl
y
a
r
elativ
ely
ad
v
a
n
ce
d
tr
a
n
s
m
is
s
io
n
tech
n
o
lo
g
y
[
1
]
-
[
7
]
.
W
ith
th
e
ac
ce
s
s
o
f
a
h
ig
h
p
r
o
p
o
r
tio
n
o
f
p
o
wer
elec
tr
o
n
ic
d
e
v
ices,
th
e
tr
ad
itio
n
al
p
o
wer
s
y
s
tem
with
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
(
SG)
a
s
th
e
m
ain
p
o
wer
s
o
u
r
ce
is
g
r
a
d
u
ally
tr
a
n
s
f
o
r
m
in
g
i
n
to
a
lo
w
-
in
er
tia
wea
k
g
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id
,
an
d
th
e
s
y
s
tem
f
r
eq
u
en
cy
s
ta
b
ilit
y
is
co
n
s
tan
tly
wea
k
en
in
g
[
8
]
,
[
9
]
.
U
n
d
er
tr
a
d
itio
n
al
f
lex
ib
le
DC
co
n
tr
o
l,
m
o
d
u
lar
m
u
ltil
ev
el
co
n
v
er
ter
(
MM
C
)
ca
n
n
o
t
r
esp
o
n
d
to
t
h
e
f
r
eq
u
en
cy
ch
a
n
g
es
o
f
th
e
AC
s
y
s
tem
,
n
o
r
c
an
it
s
im
u
late
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
to
p
r
o
v
i
d
e
in
er
tia
f
o
r
t
h
e
s
y
s
tem
,
s
o
it
is
d
if
f
icu
lt
to
s
u
p
p
o
r
t
t
h
e
g
r
id
f
r
eq
u
e
n
cy
s
tab
ilit
y
[
1
0
]
,
[
1
1
]
.
Ho
w
to
g
iv
e
f
u
ll
p
lay
to
t
h
e
s
u
p
p
o
r
t
ca
p
ab
ilit
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o
f
MM
C
in
th
e
f
lex
ib
le
DC
s
y
s
tem
to
ac
tiv
ely
s
u
p
p
o
r
t
th
e
f
r
eq
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e
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cy
o
f
th
e
r
ec
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g
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s
y
s
tem
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as
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ec
o
m
e
o
n
e
o
f
th
e
k
ey
tech
n
ical
p
r
o
b
lem
s
th
at
u
r
g
en
tly
n
ee
d
t
o
b
e
s
o
lv
ed
in
th
e
co
n
s
tr
u
ctio
n
o
f
n
ew
p
o
wer
s
y
s
tem
s
[
1
2
]
,
[
1
3
]
.
T
h
er
e
ar
e
m
an
y
s
tu
d
ies
o
n
th
e
f
r
eq
u
en
c
y
s
u
p
p
o
r
t
s
tr
ateg
y
o
f
MM
C
f
o
r
AC
p
o
wer
g
r
id
.
T
h
e
s
tu
d
y
in
[
1
4
]
s
u
m
m
ar
ize
th
e
c
o
m
m
o
n
g
r
id
-
f
o
llo
win
g
an
d
g
r
id
-
b
u
il
d
in
g
c
o
n
tr
o
l
s
tr
ateg
ies
an
d
a
n
aly
ze
th
eir
s
u
p
p
o
r
t
p
er
f
o
r
m
an
ce
an
d
p
er
f
o
r
m
a
n
c
e
f
o
r
AC
p
o
wer
g
r
id
.
Kh
a
n
et
a
l
.
[
1
5
]
p
r
o
p
o
s
es
a
co
n
tr
o
l
s
ch
em
e
th
at
ca
n
p
r
o
v
id
e
in
e
r
tia
an
d
d
am
p
i
n
g
f
o
r
th
e
two
-
en
d
g
r
id
s
f
o
r
th
e
b
ac
k
-
to
-
b
ac
k
MM
C
-
HVDC
s
y
s
tem
,
an
d
em
b
ed
s
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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E
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I
SS
N:
2252
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8
7
9
2
A
n
a
lyzi
n
g
th
e
a
b
ilit
y
o
f c
a
p
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ci
to
r
en
erg
y
in
a
mo
d
u
la
r
mu
ltil
ev
el
co
n
ve
r
ter to
…
(
Du
n
ya
S
h
.
Wa
is
)
647
n
ew
s
u
p
p
o
r
t
m
o
d
e
s
elec
tio
n
alg
o
r
ith
m
.
Me
i
et
a
l
.
[
1
6
]
p
r
o
p
o
s
es
an
ad
a
p
tiv
e
v
ir
tu
al
in
er
tia
f
r
eq
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e
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cy
r
eg
u
latio
n
s
tr
ateg
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,
wh
ich
in
cr
ea
s
es
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e
in
er
tia
co
ef
f
icien
t
o
f
MM
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wh
en
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d
ev
i
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is
s
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all,
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ly
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tag
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r
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u
en
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y
f
lu
ct
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n
.
W
an
g
et
a
l.
[
1
7
]
d
ee
p
ly
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al
y
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s
th
e
d
if
f
e
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en
ce
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etwe
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er
e
ar
e
m
an
y
d
is
cr
ete
s
u
b
-
m
o
d
u
le
ca
p
ac
ito
r
s
in
s
id
e
th
e
MM
C
.
I
f
t
h
e
en
er
g
y
in
s
id
e
ca
n
b
e
f
lex
i
b
ly
an
d
ef
f
ec
tiv
ely
u
tili
ze
d
,
th
e
MM
C
'
s
o
wn
en
er
g
y
s
to
r
ag
e
al
o
n
e
ca
n
p
r
o
v
id
e
a
ce
r
tain
s
u
p
p
o
r
t e
f
f
ec
t
o
n
th
e
g
r
id
.
I
n
o
r
d
er
to
f
u
r
th
er
u
tili
ze
th
e
MM
C
ca
p
ac
ito
r
en
er
g
y
,
Z
h
u
et
a
l.
[
1
8
]
,
[
1
9
]
u
s
e
ca
p
ac
ito
r
en
er
g
y
to
s
im
u
late
th
e
r
o
to
r
k
in
etic
e
n
er
g
y
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
to
s
u
p
p
o
r
t
th
e
g
r
id
i
n
er
tia
,
b
u
t
t
h
ey
u
s
e
th
e
tr
ad
itio
n
al
d
o
u
b
le
clo
s
ed
-
lo
o
p
v
ec
to
r
c
o
n
tr
o
l
s
tr
ateg
y
,
an
d
th
e
ca
p
ac
ito
r
v
o
ltag
e
is
co
u
p
led
with
th
e
DC
v
o
ltag
e,
wh
ic
h
lim
its
th
e
u
tili
za
tio
n
o
f
ca
p
ac
ito
r
en
er
g
y
.
L
i
u
et
a
l
.
[
2
0
]
u
s
es
ad
ap
tiv
e
d
a
m
p
in
g
a
n
d
in
er
tia
co
ef
f
icien
ts
to
im
p
r
o
v
e
th
e
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
ca
p
ac
ito
r
en
er
g
y
,
b
u
t
its
ca
p
ac
ito
r
v
o
ltag
e
is
s
till
r
elate
d
to
th
e
DC
v
o
ltag
e.
Yan
g
et
a
l.
[
2
1
]
u
s
es
a
ca
p
ac
it
o
r
en
e
r
g
y
s
y
n
ch
r
o
n
izatio
n
lo
o
p
to
r
ep
lace
th
e
p
o
wer
s
y
n
ch
r
o
n
izatio
n
lo
o
p
in
th
e
tr
ad
itio
n
al
g
r
id
co
n
tr
o
l
to
im
p
r
o
v
e
s
tab
ilit
y
,
b
u
t
th
e
r
ef
er
e
n
c
e
b
eliev
es
th
at
th
e
ca
p
ac
ito
r
en
er
g
y
s
u
p
p
o
r
t
ef
f
e
ct
is
ex
tr
em
ely
s
m
all,
s
o
it
is
o
n
ly
u
s
ed
f
o
r
s
y
n
ch
r
o
n
izat
io
n
with
th
e
g
r
id
.
Sin
g
h
et
a
l.
[
2
2
]
p
r
o
p
o
s
es
an
MM
C
ac
tiv
e
en
er
g
y
co
n
tr
o
l
s
tr
ateg
y
,
wh
ich
m
at
h
em
atica
lly
d
ec
o
u
p
les
th
e
DC
v
o
ltag
e
a
n
d
ca
p
ac
ito
r
v
o
ltag
e,
an
d
im
p
r
o
v
es
t
h
e
e
n
er
g
y
u
tili
za
tio
n
m
ar
g
in
an
d
co
n
tr
o
l
f
lex
ib
ilit
y
co
m
p
a
r
ed
to
tr
ad
itio
n
al
co
n
tr
o
l.
Z
h
an
g
et
a
l.
[
2
3
]
,
[
2
4
]
.
Acc
o
r
d
in
g
to
Sin
g
h
et
a
l.
[
2
2
]
,
it
lo
o
k
s
at
ad
a
p
tiv
e
an
d
in
tellig
en
t
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
p
o
wer
-
elec
tr
o
n
ic
co
n
v
e
r
ter
s
th
at
wo
r
k
in
lo
w
-
in
er
tia
g
r
i
d
s
.
I
t
s
h
o
ws
h
o
w
ad
ap
tiv
e,
p
r
ed
ictiv
e,
an
d
AI
-
b
ased
s
o
lu
tio
n
s
im
p
r
o
v
e
f
r
e
q
u
en
c
y
s
tab
ilit
y
,
v
ir
tu
al
in
er
tia
em
u
latio
n
,
an
d
s
tr
en
g
th
wh
en
th
e
g
r
i
d
is
u
n
p
r
ed
ictab
le.
So
m
e
o
f
th
e
b
ig
g
est
p
r
o
b
lem
s
ar
e
m
ak
in
g
co
n
tr
o
l
m
o
r
e
co
m
p
licated
,
lim
itin
g
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
,
a
n
d
m
a
k
in
g
s
u
r
e
s
tab
ilit
y
th
r
o
u
g
h
o
u
t a
wid
e
r
an
g
e
o
f
o
p
er
atin
g
s
itu
ati
o
n
s
.
Ho
wev
er
,
th
e
ab
o
v
e
MM
C
en
er
g
y
u
tili
za
tio
n
s
tr
ateg
ies h
av
e
n
o
t b
ee
n
a
b
le
to
q
u
a
n
titativ
ely
ca
lcu
late
th
e
ac
tu
al
s
u
p
p
o
r
t
s
tr
en
g
th
o
f
MM
C
f
o
r
th
e
p
o
wer
g
r
id
,
an
d
it
is
d
if
f
icu
lt
to
q
u
a
n
tify
th
e
s
u
p
p
o
r
t
ef
f
ec
t.
Alth
o
u
g
h
m
o
s
t
ex
is
tin
g
s
tu
d
ies
b
eliev
e
th
at
th
e
in
er
tia
co
n
s
tan
t
o
f
MM
C
is
o
n
ly
ab
o
u
t
4
0
m
s
[
2
1
]
,
wh
ich
is
v
er
y
s
m
all
co
m
p
ar
e
d
to
th
e
e
f
f
ec
t
o
f
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
s
,
it
is
m
ain
ly
o
b
tain
ed
b
y
an
alo
g
y
with
th
e
en
er
g
y
s
to
r
ag
e
tim
e
co
n
s
tan
t
o
f
MM
C
,
an
d
d
o
es
n
o
t
co
n
s
id
er
th
e
im
p
ac
t
o
f
ac
tu
al
g
r
id
ch
a
r
ac
ter
is
tics
an
d
MM
C
co
n
tr
o
l stra
teg
ies o
n
s
u
p
p
o
r
t c
ap
ac
ity
.
I
n
o
r
d
er
to
q
u
an
titativ
ely
an
al
y
ze
th
e
g
r
id
in
er
tia
af
ter
a
h
ig
h
p
r
o
p
o
r
tio
n
o
f
n
ew
en
er
g
y
an
d
p
o
wer
elec
tr
o
n
ic
eq
u
i
p
m
en
t
is
co
n
n
e
cted
,
th
e
Su
n
et
a
l.
[
9
]
d
e
f
in
e
s
th
e
g
en
er
alize
d
i
n
er
tia
o
f
t
h
e
g
r
id
b
y
u
s
in
g
th
e
r
atio
o
f
th
e
g
e
n
er
alize
d
k
in
et
ic
en
er
g
y
o
f
th
e
AC
s
y
s
tem
to
th
e
to
tal
ca
p
ac
ity
,
w
h
ich
c
o
v
er
s
all
f
o
r
m
s
o
f
in
er
tia
in
t
h
e
s
y
s
tem
,
b
u
t
is
n
o
t
s
u
itab
le
f
o
r
an
aly
zin
g
th
e
i
n
er
tia
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
th
e
f
lex
ib
le
DC
MM
C
alo
n
e.
Yan
g
et
a
l
.
[
2
5
]
p
r
o
p
o
s
es
an
MM
C
in
er
tia
co
n
s
tan
t
c
o
n
s
id
er
in
g
th
e
p
en
etr
atio
n
r
ate
o
f
n
ew
en
er
g
y
a
n
d
an
aly
ze
s
th
e
f
r
eq
u
en
cy
r
esp
o
n
s
e
o
f
th
e
AC
g
r
id
af
ter
th
e
i
n
tr
o
d
u
ctio
n
o
f
MM
C
in
er
tia.
Ho
wev
er
,
th
e
m
o
to
r
s
p
ee
d
is
eq
u
iv
alen
t
to
th
e
ca
p
ac
ito
r
v
o
ltag
e
d
u
r
in
g
t
h
e
ca
l
cu
latio
n
,
wh
ich
is
in
co
n
s
is
ten
t
with
th
e
p
h
y
s
ical
d
ef
in
itio
n
o
f
th
e
in
er
tia
co
n
s
ta
n
t.
I
n
ad
d
itio
n
,
th
e
to
tal
ca
p
ac
i
ty
o
f
th
e
g
r
id
is
u
s
ed
as
th
e
b
a
s
e
v
alu
e
f
o
r
p
o
wer
ca
lcu
latio
n
,
wh
ich
m
a
k
es
it
d
if
f
icu
lt
to
r
ef
lect
th
e
ac
tu
al
ef
f
ec
t
o
f
ca
p
ac
ito
r
en
er
g
y
o
n
g
r
i
d
in
er
tia.
Kim
et
a
l
.
[
2
6
]
d
er
iv
es
t
h
e
in
e
r
tia
co
n
s
ta
n
t
o
f
th
e
c
o
n
v
e
r
ter
s
tatio
n
b
y
an
alo
g
y
b
etwe
en
ca
p
ac
ito
r
en
er
g
y
a
n
d
th
e
k
in
etic
en
er
g
y
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
r
o
to
r
.
Ho
wev
e
r
,
th
is
l
iter
atu
r
e
o
n
ly
co
n
s
id
er
s
th
e
im
p
ac
t
o
f
th
e
t
h
ir
d
h
ar
m
o
n
ic
in
jectio
n
o
n
th
e
n
u
m
b
er
o
f
s
u
b
m
o
d
u
les
p
u
t
in
to
o
p
er
atio
n
,
an
d
d
o
es
n
o
t
a
n
aly
ze
th
e
im
p
r
o
v
em
en
t
o
f
th
e
en
e
r
g
y
u
tili
za
tio
n
r
an
g
e
b
r
o
u
g
h
t
b
y
th
e
d
ec
o
u
p
lin
g
o
f
DC
v
o
ltag
e
a
n
d
ca
p
ac
ito
r
v
o
ltag
e.
I
t
also
d
o
es
n
o
t
c
o
n
s
id
er
t
h
e
d
if
f
er
e
n
t
ab
ilit
ies
o
f
ca
p
ac
ito
r
s
to
a
b
s
o
r
b
an
d
r
elea
s
e
en
er
g
y
,
an
d
t
h
e
o
b
tain
ed
in
er
tia
co
n
s
tan
t is to
o
s
m
all.
I
n
v
iew
o
f
th
e
ab
o
v
e
p
r
o
b
le
m
s
,
th
is
p
ap
er
f
ir
s
t
s
tar
ts
f
r
o
m
th
e
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
m
o
d
el
o
f
th
e
f
lex
ib
le
DC
tr
an
s
m
is
s
io
n
s
y
s
t
em
,
d
er
iv
es
th
e
q
u
a
n
titativ
e
an
aly
s
is
m
eth
o
d
o
f
th
e
in
e
r
tia
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
a
s
in
g
le
f
lex
ib
le
DC
co
n
v
er
ter
s
tatio
n
,
an
d
p
r
o
p
o
s
es
th
e
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
t
HM
MC
o
f
th
e
f
lex
i
b
le
DC
MM
C
to
th
e
AC
s
y
s
tem
a
s
an
an
aly
s
is
in
d
icato
r
.
T
h
en
,
t
h
e
ex
is
tin
g
v
ar
io
u
s
in
er
tia
s
u
p
p
o
r
t
c
o
n
tr
o
ls
ar
e
co
m
p
ar
ed
,
an
d
th
e
s
u
p
p
o
r
t
p
o
wer
s
o
u
r
ce
,
s
u
p
p
o
r
t
p
er
f
o
r
m
an
ce
,
p
ar
am
eter
d
esig
n
,
an
d
o
th
er
asp
ec
ts
ar
e
an
aly
ze
d
to
o
b
tain
th
e
e
q
u
i
v
alen
t
in
er
tia
co
n
s
tan
t
o
f
th
e
f
lex
ib
le
DC
s
y
s
tem
u
n
d
er
d
if
f
er
en
t
c
o
n
tr
o
ls
.
Fu
r
th
er
m
o
r
e
,
th
is
m
eth
o
d
is
ex
ten
d
ed
to
th
e
m
u
lti
-
ter
m
in
al
f
lex
ib
le
DC
s
y
s
tem
to
o
b
tain
th
e
to
tal
eq
u
iv
alen
t
in
er
tia
th
at
ca
n
b
e
p
r
o
v
id
ed
wh
en
u
s
in
g
th
e
en
er
g
y
o
f
m
u
ltip
le
MM
C
ca
p
ac
ito
r
s
.
Fin
ally
,
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
q
u
an
titativ
e
an
al
y
s
is
m
eth
o
d
an
d
t
h
e
s
u
p
p
o
r
t
ch
ar
ac
ter
is
tics
o
f
d
if
f
er
e
n
t
co
n
tr
o
ls
an
d
d
i
f
f
er
en
t
n
u
m
b
er
s
o
f
ter
m
in
als ar
e
v
er
if
ied
th
r
o
u
g
h
s
im
u
latio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
646
-
662
648
2.
Q
UANTI
T
A
T
I
V
E
ANA
L
YS
I
S M
E
T
H
O
D
O
F
E
Q
U
I
VA
L
E
N
T
I
N
E
R
T
I
A
CO
N
ST
A
NT
O
F
SI
NG
L
E
M
M
C
I
n
th
e
e
x
is
tin
g
r
esear
ch
,
wh
en
u
s
in
g
ca
p
ac
ito
r
en
er
g
y
to
s
u
p
p
o
r
t
th
e
in
er
tia
o
f
AC
p
o
wer
g
r
id
,
it
is
g
en
er
ally
b
eliev
e
d
th
at
its
s
u
p
p
o
r
t
ca
p
ac
ity
ca
n
b
e
co
m
p
a
r
ed
to
th
e
d
ef
in
itio
n
o
f
th
e
i
n
er
tia
co
n
s
tan
t
o
f
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
,
an
d
th
e
MM
C
en
er
g
y
s
to
r
ag
e
tim
e
c
o
n
s
tan
t
T
E
,
wh
ic
h
is
u
s
ed
t
o
m
ea
s
u
r
e
it
[
2
1
]
.
Ho
wev
er
,
in
f
ac
t,
th
e
r
esp
o
n
s
e
m
o
d
e
an
d
s
p
ee
d
o
f
MM
C
t
o
s
y
s
tem
f
r
eq
u
en
cy
ar
e
d
if
f
er
en
t
f
r
o
m
th
o
s
e
o
f
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
.
Un
d
e
r
th
i
s
d
ef
in
itio
n
,
th
e
i
n
er
tia
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
MM
C
is
o
v
er
ly
lim
ited
.
T
h
is
s
ec
tio
n
will
d
er
iv
e
th
e
q
u
a
n
titativ
e
ex
p
r
ess
io
n
o
f
MM
C
in
er
tia
co
n
s
tan
t
f
r
o
m
th
e
f
r
eq
u
en
cy
r
esp
o
n
s
e
m
o
d
el
o
f
MM
C
to
AC
s
y
s
tem
.
Fig
u
r
e
1
s
h
o
ws
th
e
s
in
g
le
MM
C
g
r
id
-
co
n
n
ec
t
ed
s
y
s
tem
s
tu
d
ied
in
th
is
p
ap
e
r
.
I
n
Fig
u
r
e
1
:
∆
is
th
e
p
er
-
u
n
it
v
al
u
e
o
f
AC
s
y
s
tem
lo
ad
d
is
tu
r
b
a
n
ce
;
∆
is
th
e
p
er
-
u
n
it
v
alu
e
o
f
ac
tiv
e
o
u
tp
u
t
ch
an
g
e
o
f
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
in
p
r
im
ar
y
f
r
eq
u
en
cy
m
o
d
u
latio
n
p
r
o
c
ess
;
Δ
P
MM
C
is
th
e
p
er
-
u
n
i
t
v
alu
e
o
f
s
u
p
p
o
r
t
p
o
wer
p
r
o
v
id
e
d
b
y
MM
C
wh
e
n
s
y
s
tem
lo
ad
is
d
is
tu
r
b
ed
;
th
e
b
ase
v
alu
es
o
f
th
e
ab
o
v
e
p
o
w
er
item
s
ar
e
all
th
e
r
ated
ca
p
ac
ity
o
f
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
in
t
h
e
p
o
we
r
g
r
id
.
Fig
u
r
e
1
.
Sch
em
atic
d
iag
r
am
o
f
r
ec
eiv
in
g
-
en
d
AC
p
o
wer
g
r
id
Fo
r
a
r
ec
eiv
in
g
-
e
n
d
p
o
wer
g
r
id
,
its
f
r
eq
u
en
cy
r
esp
o
n
s
e
m
o
d
el
ca
n
b
e
r
e
p
r
esen
ted
b
y
Fig
u
r
e
2
.
I
n
Fig
u
r
e
2
:
∆
is
th
e
p
er
-
u
n
it
v
alu
e
o
f
f
r
e
q
u
en
c
y
ch
an
g
e,
an
d
its
b
ase
v
alu
e
is
th
e
p
o
wer
f
r
e
q
u
en
cy
5
0
Hz
;
HSG
is
th
e
eq
u
iv
alen
t
i
n
er
tia
co
n
s
tan
t
o
f
th
e
s
y
n
c
h
r
o
n
o
u
s
m
o
to
r
;
D
is
th
e
lo
ad
d
am
p
in
g
r
esp
o
n
s
e
co
ef
f
icien
t;
R
SG
is
th
e
d
r
o
o
p
co
ef
f
icien
t
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
g
o
v
er
n
o
r
;
T
G
is
th
e
g
o
v
er
n
o
r
tim
e
co
n
s
tan
t;
FHP,
T
C
H,
T
R
H
ar
e
th
e
m
ain
p
ar
am
eter
s
in
th
e
r
eh
ea
t
tu
r
b
in
e
,
r
ep
r
esen
tin
g
th
e
h
ig
h
-
p
r
ess
u
r
e
cy
lin
d
er
wo
r
k
p
r
o
p
o
r
tio
n
al
c
o
ef
f
icien
t,
th
e
p
r
im
e
m
o
v
er
tim
e
co
n
s
tan
t a
n
d
t
h
e
r
eh
ea
ter
tim
e
c
o
n
s
tan
t r
esp
ec
tiv
ely
.
Fig
u
r
e
2
.
Fre
q
u
en
cy
r
esp
o
n
s
e
m
o
d
el
o
f
AC
s
y
s
tem
Un
d
er
n
o
r
m
al
co
n
tr
o
l,
th
e
M
MC
s
en
d
s
co
n
s
tan
t
p
o
wer
to
th
e
AC
s
y
s
tem
,
an
d
∆
=
0
in
th
e
f
ig
u
r
e.
Acc
o
r
d
in
g
to
th
e
r
elatio
n
s
h
ip
in
th
e
f
ig
u
r
e,
th
e
f
r
eq
u
en
cy
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
is
:
2
SG
d
Δ
pu
d
+
Δ
pu
=
Δ
SG
−
Δ
L
(
1
)
w
h
en
th
e
lo
ad
d
is
tu
r
b
an
ce
Δ
L
ju
s
t
o
cc
u
r
s
,
s
in
ce
th
e
f
r
eq
u
en
cy
d
ev
iatio
n
is
v
er
y
s
m
all
an
d
th
er
e
is
a
d
ea
d
zo
n
e
in
th
e
p
r
im
a
r
y
f
r
e
q
u
en
c
y
m
o
d
u
latio
n
o
f
th
e
s
y
n
c
h
r
o
n
o
u
s
m
o
to
r
,
Δ
SG
in
(
1
)
is
ap
p
r
o
x
im
ately
ze
r
o
.
At
th
is
tim
e,
th
e
s
y
s
tem
f
r
eq
u
en
cy
ch
an
g
e
in
Fig
u
r
e
1
is
o
n
ly
af
f
ec
ted
b
y
Δ
L
let
th
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
r
eh
ea
t tu
r
b
i
n
e
b
e
G(
s
)
,
a
n
d
th
e
s
y
s
tem
f
r
eq
u
en
c
y
ch
a
n
g
e
r
ate
at
tim
e
ze
r
o
ca
n
b
e
ca
lcu
lated
as
(
2
)
.
d
Δ
pu
d
|
0
+
=
→
∞
SG
(
1
+
G
)
2
SG
SG
(
1
+
G
)
+
(
)
Δ
L
=
Δ
L
2
SG
(
2
)
T
h
at
is
,
in
co
n
v
en
tio
n
al
c
o
n
tr
o
l,
th
e
ca
lcu
latio
n
f
o
r
th
e
s
y
s
te
m
eq
u
iv
alen
t i
n
er
tia
co
n
s
tan
t i
s
g
iv
en
b
y
(
3
)
.
SG
=
Δ
L
2
d
Δ
d
|
0
∘
=
Δ
L
2
0
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lyzi
n
g
th
e
a
b
ilit
y
o
f c
a
p
a
ci
to
r
en
erg
y
in
a
mo
d
u
la
r
mu
ltil
ev
el
co
n
ve
r
ter to
…
(
Du
n
ya
S
h
.
Wa
is
)
649
W
h
er
e
0
is
th
e
m
ax
im
u
m
v
alu
e
o
f
th
e
f
r
eq
u
en
cy
p
er
u
n
it v
al
u
e
ch
an
g
e
r
ate,
wh
ich
ca
n
also
b
e
co
n
s
id
er
ed
as
th
e
f
r
eq
u
en
cy
c
h
an
g
e
r
ate
wh
e
n
th
e
lo
ad
d
is
tu
r
b
an
ce
ju
s
t o
cc
u
r
s
.
I
f
MM
C
ca
n
s
u
p
p
o
r
t
th
e
in
e
r
t
ia
o
f
th
e
AC
s
y
s
tem
d
u
r
in
g
lo
ad
d
is
tu
r
b
an
ce
,
th
e
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
m
o
d
el
af
ter
co
n
s
id
er
i
n
g
MM
C
s
u
p
p
o
r
t
ca
n
b
e
r
ep
r
esen
ted
b
y
Fig
u
r
e
3
[
2
5
]
.
I
n
Fig
u
r
e
3
:
HM
MC
i
s
th
e
eq
u
iv
alen
t
i
n
er
tia
co
n
s
tan
t
o
f
MM
C
to
th
e
AC
s
y
s
tem
.
R
ef
er
r
in
g
to
t
h
e
in
e
r
tia
co
n
s
tan
t
ex
p
r
ess
io
n
o
f
th
e
g
en
er
ato
r
(
3
)
,
HM
MC
is
d
ef
in
ed
as
h
alf
o
f
th
e
s
u
p
p
o
r
tin
g
p
o
wer
p
r
o
v
id
ed
b
y
MM
C
to
th
e
AC
s
y
s
tem
u
n
d
er
th
e
u
n
it f
r
e
q
u
en
c
y
ch
a
n
g
e
r
ate
.
Fig
u
r
e
3
.
Fre
q
u
en
cy
r
esp
o
n
s
e
m
o
d
el
o
f
AC
s
y
s
tem
with
MM
C
in
er
tia
r
esp
o
n
s
e
I
n
th
is
m
o
d
el,
Δ
MM
C
is
n
o
t
z
er
o
,
an
d
its
s
ize
is
d
eter
m
in
ed
b
y
H
MMC
.
Acc
o
r
d
in
g
to
Fig
u
r
e
3
,
th
e
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
m
o
d
el
o
f
t
h
e
f
lex
ib
le
DC
tr
an
s
m
is
s
io
n
s
y
s
tem
ca
n
b
e
ex
p
r
ess
ed
as
(
4
)
.
2
SG
d
Δ
pu
d
+
Δ
pu
=
Δ
SG
+
Δ
MM
C
−
Δ
L
(
4
)
Δ
MMC
is
th
e
in
er
tia
s
u
p
p
o
r
t p
o
wer
p
r
o
v
id
ed
b
y
th
e
c
o
n
v
er
te
r
s
tatio
n
.
I
ts
r
esp
o
n
s
e
s
h
o
u
ld
b
e
s
im
ilar
to
th
at
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
a
n
d
ca
n
b
e
ex
p
r
ess
ed
as
(
5
)
.
Δ
MM
C
=
−
2
MMC
d
Δ
pu
d
(
5
)
Un
d
er
th
e
s
am
e
lo
a
d
d
is
tu
r
b
a
n
ce
,
th
e
s
y
s
tem
f
r
eq
u
en
cy
c
h
an
g
e
r
ate
at
tim
e
ze
r
o
ca
n
b
e
ca
lcu
lated
as
(
6
)
.
d
Δ
pu
d
|
O
∗
=
→
→
∞
SG
(
1
+
G
)
2
(
SG
+
MMC
)
SG
(
1
+
G
)
+
(
)
Δ
L
=
Δ
L
2
(
SG
+
MMC
)
(
6
)
An
alo
g
o
u
s
ly
to
(
3
)
,
th
e
to
tal
i
n
er
tia
co
n
s
tan
t o
f
th
e
s
y
s
tem
c
an
b
e
ca
lcu
lated
as
(
7
)
.
to
t
a
l
=
Δ
L
2
0
=
SG
+
MMC
(
7
)
W
h
er
e
to
t
a
l
is
th
e
to
tal
in
er
tia
co
n
s
tan
t
o
f
th
e
AC
s
y
s
tem
.
Fro
m
(
7
)
,
we
ca
n
s
ee
th
at
af
ter
th
e
lo
ad
d
is
tu
r
b
an
ce
o
cc
u
r
s
,
th
e
in
er
tia
co
n
s
tan
t:
tot
a
l
th
at
th
e
s
y
s
tem
c
an
p
r
o
v
i
d
e
co
n
s
is
ts
o
f
two
p
ar
ts
:
o
n
e
is
th
e
in
er
tia
co
n
s
tan
t
o
f
t
h
e
s
y
n
c
h
r
o
n
o
u
s
m
o
to
r
its
elf
;
th
e
o
t
h
er
i
s
th
e
eq
u
i
v
alen
t
in
e
r
tia
co
n
s
ta
n
t
p
r
o
v
id
ed
b
y
th
e
MM
C
.
W
h
en
th
e
in
er
tial
s
u
p
p
o
r
t
p
o
wer
Δ
MMC
b
o
r
n
e
b
y
t
h
e
MM
C
is
co
m
p
letely
p
r
o
v
i
d
ed
b
y
t
h
e
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
e
n
er
g
y
s
to
r
ag
e,
th
e
en
er
g
y
r
elatio
n
s
h
i
p
ca
n
b
e
ex
p
r
ess
ed
as
(
8
)
.
Δ
MM
C
=
−
0
SG
d
Δ
MMc
.
pu
d
(
8
)
W
h
er
e
SG
is
th
e
r
ated
ca
p
ac
ity
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
in
th
e
p
o
wer
g
r
i
d
;
Δ
MMc
.
pu
is
th
e
p
er
u
n
it
v
alu
e
o
f
th
e
MM
C
ca
p
ac
ito
r
en
er
g
y
ch
an
g
e;
0
is
th
e
ca
p
ac
ito
r
en
er
g
y
u
n
d
er
r
ated
co
n
d
itio
n
s
,
wh
ich
is
also
th
e
ca
lcu
latio
n
b
ase
v
alu
e
o
f
Δ
MMc
.
pu
.
C
o
m
b
in
e
(
5
)
an
d
(
8
)
,
in
teg
r
ate
b
o
th
s
id
es
o
f
th
e
eq
u
atio
n
,
an
d
ass
u
m
e
th
at
th
e
in
itial
v
al
u
e
o
f
ea
ch
p
h
y
s
ical
q
u
an
tity
at
tim
e
ze
r
o
is
eq
u
al
to
its
r
ated
v
alu
e,
an
d
we
ca
n
g
et
(
9
)
.
0
SG
Δ
MMC
.
pu
=
2
MMc
Δ
pu
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
646
-
662
650
T
h
er
ef
o
r
e
,
th
e
e
q
u
iv
alen
t in
e
r
t
ia
co
n
s
tan
t o
f
MM
C
is
ex
p
r
ess
ed
as
(
1
0
)
.
M
MC
=
0
2
sG
Δ
MMC
.
pu
Δ
pu
(
1
0
)
T
h
e
ca
p
ac
ito
r
en
e
r
g
y
0
at
th
e
r
ated
s
tate
o
f
MM
C
is
ex
p
r
ess
ed
b
y
th
e
e
n
er
g
y
s
to
r
ag
e
tim
e
co
n
s
tan
t
T
E
,
MMC
[
1
7
]
a
n
d
s
u
b
s
titu
ted
in
t
o
(
1
0
)
t
o
o
b
tain
:
M
MC
=
E
,
MMC
2
MMC
SG
Δ
MMC
,
pu
Δ
pu
(
1
1
)
W
h
er
e
MMC
is
th
e
r
ated
ca
p
ac
ity
o
f
th
e
f
lex
ib
le
DC
co
n
v
er
ter
s
tatio
n
.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
(
1
1
)
th
at
th
e
eq
u
iv
alen
t
in
e
r
tia
co
n
s
tan
t
o
f
MM
C
f
o
r
AC
s
y
s
tem
is
n
o
t
o
n
ly
r
elate
d
to
T
E,
MMC
,
b
u
t
also
a
f
f
ec
ted
b
y
th
e
ca
p
ac
ity
p
r
o
p
o
r
tio
n
o
f
MM
C
in
AC
s
y
s
te
m
an
d
th
e
r
atio
o
f
ca
p
ac
ito
r
en
er
g
y
to
f
r
eq
u
en
c
y
ch
an
g
e
(
e
n
er
g
y
-
f
r
e
q
u
en
c
y
r
atio
)
.
T
h
e
ca
p
ac
ity
p
r
o
p
o
r
tio
n
r
ef
lects
th
e
ac
tu
al
ef
f
ec
t
o
f
th
e
ch
a
r
g
in
g
an
d
d
is
ch
ar
g
in
g
p
r
o
ce
s
s
o
f
th
e
ca
p
ac
ito
r
o
n
th
e
AC
s
y
s
tem
,
an
d
th
e
en
er
g
y
-
f
r
e
q
u
en
c
y
r
atio
is
r
elate
d
t
o
th
e
co
n
tr
o
l
s
tr
ateg
y
o
f
th
e
MM
C
co
n
v
er
t
er
s
tatio
n
,
wh
ich
will
b
e
d
is
cu
s
s
ed
in
d
etail
later
.
T
h
e
MM
C
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
t
MM
C
o
b
tain
ed
b
y
co
n
s
id
er
in
g
v
a
r
io
u
s
f
ac
to
r
s
s
u
ch
as
ca
p
ac
ity
p
r
o
p
o
r
tio
n
an
d
co
n
tr
o
l
s
tr
ateg
y
ca
n
b
etter
r
ef
lect
th
e
ac
tu
al
in
er
tia
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
th
e
co
n
v
er
ter
s
tatio
n
f
o
r
th
e
AC
s
y
s
tem
th
an
T
E
,
MMC
.
2
.
1
.
Ana
ly
s
is
o
f
inert
ia
s
up
po
rt
ca
pa
cit
y
o
f
M
M
C
s
y
s
t
e
m
un
der
diff
er
ent
co
ntr
o
l
2
.
1
.
1
.
Su
dd
en
increa
s
e
in AC
s
y
s
t
em
lo
a
d
As
m
en
tio
n
ed
in
s
ec
tio
n
2
,
th
e
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
t
HM
MC
o
f
MM
C
i
s
af
f
ec
ted
b
y
th
e
en
er
g
y
-
f
r
eq
u
e
n
cy
r
atio
,
wh
ich
is
d
et
er
m
in
ed
b
y
t
h
e
co
n
tr
o
l
s
tr
ate
g
y
o
f
MM
C
.
T
h
is
p
ap
er
will
d
is
cu
s
s
th
e
en
er
g
y
-
f
r
eq
u
e
n
cy
r
atio
u
n
d
e
r
d
if
f
e
r
en
t
co
n
tr
o
l
s
tr
ateg
ies
in
d
etail
an
d
an
aly
ze
th
e
e
q
u
iv
alen
t
i
n
er
ti
a
co
n
s
tan
t
HM
MC
o
f
d
if
f
er
en
t
co
n
tr
o
ls
.
Fig
u
r
e
4
s
h
o
ws
th
e
s
ch
em
atic
d
iag
r
a
m
o
f
VSG
co
n
tr
o
l
[
1
4
]
,
wh
ic
h
is
o
n
e
o
f
th
e
m
o
s
t
co
m
m
o
n
in
er
tia
s
u
p
p
o
r
t c
o
n
tr
o
ls
.
I
ts
co
n
tr
o
l p
r
in
cip
le
ca
n
b
e
ex
p
r
ess
ed
as
(
1
2
)
.
0
−
r
ef
=
2
ct
r
l
d
pu
d
+
Δ
pu
(
1
2
)
W
h
er
e:
0
is
th
e
r
ated
p
o
wer
o
f
th
e
AC
s
id
e;
r
ef
is
th
e
ac
tu
al
o
u
tp
u
t
p
er
u
n
it
v
alu
e
o
f
th
e
AC
s
id
e,
an
d
its
b
ase
v
alu
e
is
th
e
r
ated
ca
p
ac
ity
o
f
th
e
MM
C
;
ct
r
l
is
th
e
in
er
tia
co
n
s
tan
t in
th
e
co
n
tr
o
l.
Fro
m
(
1
2
)
,
it
ca
n
b
e
s
ee
n
th
a
t
th
e
co
n
tr
o
l
p
r
in
cip
le
is
v
er
y
s
im
ilar
to
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
r
o
to
r
m
o
tio
n
eq
u
atio
n
.
Du
e
t
o
th
e
ad
d
itio
n
o
f
th
e
d
am
p
in
g
lin
k
D,
th
e
co
n
tr
o
l
ca
n
n
o
t
o
n
ly
s
u
p
p
o
r
t
th
e
s
y
s
tem
in
er
tia,
b
u
t
also
r
aise
t
h
e
lo
we
s
t
f
r
eq
u
en
c
y
p
o
in
t
an
d
th
e
s
te
ad
y
-
s
tate
v
alu
e
af
ter
f
lu
ctu
ati
o
n
,
a
n
d
h
as
a
s
tr
o
n
g
s
u
p
p
o
r
tin
g
ca
p
ac
ity
.
Ho
wev
er
,
VSG
co
n
tr
o
l
f
ails
to
in
d
icate
th
e
s
o
u
r
ce
o
f
th
e
s
u
p
p
o
r
tin
g
p
o
wer
.
T
ak
in
g
th
e
r
ec
eiv
in
g
-
e
n
d
s
u
p
p
o
r
t
as
an
e
x
am
p
le,
th
e
liter
atu
r
es
C
ar
d
o
zo
et
a
l.
an
d
Ma
et
a
l
.
[
2
7
]
,
[
2
8
]
.
p
o
in
t
o
u
t
th
at
u
n
d
er
th
is
co
n
tr
o
l,
th
e
s
u
p
p
o
r
tin
g
p
o
wer
p
r
o
v
id
ed
b
y
th
e
MM
C
m
o
s
tly
co
m
es
f
r
o
m
th
e
s
en
d
in
g
-
en
d
AC
s
y
s
tem
,
r
ath
er
th
a
n
th
e
MM
C
's
o
wn
ca
p
ac
ito
r
en
e
r
g
y
s
to
r
ag
e,
s
o
th
e
in
er
tial
s
u
p
p
o
r
tin
g
ca
p
ac
ity
o
f
th
e
MM
C
ca
n
n
o
t b
e
q
u
an
titativ
ely
d
eter
m
in
ed
.
At
th
e
s
am
e
tim
e,
VS
G
co
n
tr
o
l
will
ca
u
s
e
th
e
s
en
d
i
n
g
-
en
d
AC
s
y
s
tem
to
f
lu
ctu
ate
in
f
r
eq
u
e
n
cy
d
u
e
t
o
ch
an
g
es
in
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
o
u
tp
u
t,
th
er
e
b
y
af
f
e
ctin
g
th
e
o
p
er
atin
g
s
tab
ilit
y
o
f
th
e
s
en
d
in
g
-
en
d
p
o
wer
g
r
id
.
T
o
o
v
er
c
o
m
e
th
e
ab
o
v
e
p
r
o
b
l
em
s
,
Fig
u
r
e
s
5
an
d
6
s
h
o
w
t
wo
co
n
tr
o
l
s
tr
ateg
ies
th
at
ca
n
u
s
e
MM
C
ca
p
ac
ito
r
en
er
g
y
to
s
u
p
p
o
r
t
th
e
p
o
wer
g
r
id
.
Un
d
er
th
ese
s
tr
ateg
ies,
th
e
lo
ad
d
is
tu
r
b
an
ce
o
f
th
e
r
ec
eiv
in
g
-
en
d
p
o
wer
g
r
id
will
n
o
t
af
f
ec
t
th
e
f
r
eq
u
e
n
cy
s
tab
ilit
y
o
f
th
e
s
en
d
in
g
-
en
d
p
o
wer
g
r
id
,
an
d
th
e
s
u
p
p
o
r
t
p
o
ten
tial
o
f
MM
C
its
e
lf
ca
n
b
e
b
r
o
u
g
h
t in
t
o
p
lay
.
Fig
u
r
e
4
.
Sch
em
atic
d
iag
r
am
o
f
VSG
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lyzi
n
g
th
e
a
b
ilit
y
o
f c
a
p
a
ci
to
r
en
erg
y
in
a
mo
d
u
la
r
mu
ltil
ev
el
co
n
ve
r
ter to
…
(
Du
n
ya
S
h
.
Wa
is
)
651
Fig
u
r
e
5
.
Sch
em
atic
d
iag
r
am
o
f
I
NE
C
s
tr
ateg
y
Fig
u
r
e
6
.
Fo
u
r
-
d
im
e
n
s
io
n
al
co
n
tr
o
l o
f
MM
C
Fig
u
r
e
5
s
h
o
ws
an
MM
C
in
er
tia
em
u
latio
n
co
n
tr
o
l
(
I
NE
C
)
p
r
o
p
o
s
ed
in
th
e
Z
h
u
et
a
l.
[
1
8
]
.
I
ts
p
r
in
cip
le
is
to
ad
d
ad
d
itio
n
al
c
o
n
tr
o
l
o
f
DC
v
o
ltag
e
o
n
th
e
b
asis
o
f
d
o
u
b
le
cl
o
s
ed
-
lo
o
p
v
ec
to
r
co
n
tr
o
l,
an
d
u
s
e
th
e
co
u
p
lin
g
c
h
ar
ac
ter
is
tics
o
f
DC
v
o
ltag
e
an
d
ca
p
ac
ito
r
v
o
ltag
e
to
r
elea
s
e/ab
s
o
r
b
c
ap
ac
ito
r
en
er
g
y
b
y
ch
an
g
in
g
DC
v
o
ltag
e,
th
er
e
b
y
s
im
u
latin
g
th
e
in
er
tia
lin
k
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
.
Acc
o
r
d
in
g
t
o
Fig
u
r
e
5
,
we
ca
n
g
et
(
1
3
)
.
dc
,
pu
=
√
dc
,
p
uv
2
+
fv
Δ
pu
(
1
3
)
W
h
er
e
dc
,
pu
is
th
e
p
er
u
n
it
v
alu
e
o
f
th
e
DC
v
o
ltag
e
o
f
th
e
c
o
n
v
e
r
ter
s
tatio
n
;
u
n
d
er
r
ated
co
n
d
i
tio
n
s
,
an
d
its
v
alu
e
is
1
;
fv
is
th
e
d
r
o
o
p
c
o
n
tr
o
l g
ain
.
C
o
n
s
id
er
in
g
th
at
in
t
h
e
p
e
r
-
u
n
it
s
y
s
tem
,
th
e
MM
C
en
er
g
y
Δ
MMC
.
pu
is
th
e
s
q
u
a
r
e
o
f
t
h
e
DC
v
o
lta
g
e
dc
,
pu
,
th
e
r
elatio
n
s
h
ip
b
etwe
en
en
er
g
y
an
d
f
r
eq
u
en
c
y
ch
an
g
e
wh
e
n
th
e
I
NE
C
s
tr
ateg
y
is
ad
o
p
ted
is
:
Δ
MMC
,
pu
=
dc
,
pu
2
−
dc
,
pu
0
2
=
fv
Δ
pu
(
1
4
)
f
r
o
m
(
1
4
)
,
we
ca
n
s
ee
th
at
th
e
en
er
g
y
f
r
e
q
u
en
c
y
r
atio
u
n
d
e
r
th
e
I
NE
C
s
tr
ateg
y
is
th
e
d
r
o
o
p
co
e
f
f
icien
t
fv
.
Su
b
s
titu
tin
g
(
1
4
)
in
to
(
1
1
)
,
we
ca
n
g
et
th
e
i
n
er
tia
co
n
s
tan
t u
n
d
er
th
e
I
NE
C
s
tr
ateg
y
as g
iv
e
n
b
y
(
1
5
)
.
M
MC
=
E
,
MMC
2
MMC
SG
fv
(
1
5
)
T
h
e
s
elec
tio
n
o
f
d
r
o
o
p
co
n
tr
o
l
g
ain
fv
is
d
eter
m
in
ed
b
y
th
e
s
y
s
tem
DC
v
o
ltag
e
lim
it
p
er
u
n
it
v
alu
e
dc
,
pu
l
i
m
an
d
t
h
e
AC
s
y
s
tem
f
r
eq
u
en
cy
d
ev
iatio
n
lim
it
p
e
r
u
n
it
v
alu
e
Δ
pu
,
wh
ich
ca
n
b
e
e
x
p
r
ess
ed
as
(
1
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
646
-
662
652
fv
=
dc
,
pu
,
l
im
2
−
dc
,
pu
0
2
Δ
pu
,
l
im
(
1
6
)
Acc
o
r
d
in
g
to
Z
h
an
g
et
a
l.
[
2
4
]
,
th
e
f
r
eq
u
e
n
cy
d
e
v
iatio
n
lim
it
is
g
en
er
ally
co
n
s
id
er
ed
to
b
e
±
0
.
5
Hz,
th
at
is
,
0
.
0
1
p
.
u
.
Acc
o
r
d
in
g
t
o
J
o
v
cic
[
2
9
]
,
th
e
DC
v
o
ltag
e
o
f
th
e
co
n
v
er
te
r
s
tatio
n
ca
n
b
e
o
p
er
ated
to
Ma
c
dc
at
th
e
lo
west,
wh
er
e
Ma
c
is
t
h
e
AC
m
o
d
u
latio
n
r
atio
,
an
d
its
v
alu
e
is
g
en
er
ally
0
.
8
5
~0
.
9
5
,
a
n
d
dc
is
th
e
r
ated
DC
v
o
ltag
e
,
th
at
is
,
th
e
DC
v
o
ltag
e
ca
n
b
e
as
lo
w
as
0
.
8
5
p
.
u
.
T
h
e
u
p
p
er
lim
it
o
f
th
e
DC
v
o
ltag
e
o
p
er
atio
n
g
en
er
ally
d
o
es
n
o
t
ex
ce
ed
1
.
1
0
p
.
u
.
[
3
0
]
.
T
h
er
ef
o
r
e,
th
e
DC
v
o
ltag
e
d
e
v
iatio
n
lim
it
dc
,
pu
l
i
m
=
[
0
.
8
5
,
1
.
1
0
]
p
.
u
.
Fro
m
(
1
5
)
an
d
(
1
6
)
,
it
ca
n
b
e
s
ee
n
th
at
t
h
e
DC
/cap
ac
ito
r
v
o
ltag
e
d
ev
iatio
n
lim
it
o
f
t
h
e
d
u
al
clo
s
ed
-
lo
o
p
v
ec
to
r
co
n
t
r
o
l
d
e
ter
m
in
es
th
e
g
ai
n
co
e
f
f
icien
t
fv
o
f
t
h
e
I
NE
C
s
tr
ateg
y
,
an
d
it
s
v
alu
e
d
ir
ec
tly
af
f
ec
ts
th
e
eq
u
iv
ale
n
t
in
er
tia
co
n
s
tan
t
o
f
t
h
e
f
lex
ib
le
DC
MM
C
.
Ass
u
m
in
g
th
e
en
er
g
y
s
to
r
ag
e
tim
e
co
n
s
tan
t
T
E,
MMC
is
4
0
m
s
,
tak
in
g
an
AC
s
y
s
tem
co
n
s
is
t
in
g
o
f
a
1
0
0
0
MW/±5
0
0
k
V
MM
C
an
d
a
2
0
0
0
MW
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
as
an
ex
a
m
p
le,
s
u
b
s
titu
tin
g
th
e
p
ar
am
et
er
s
in
to
(
1
5
)
a
n
d
(
1
6
)
,
it
ca
n
b
e
ca
lcu
lated
th
at
th
e
in
er
tia
co
n
s
tan
t
HM
MC
th
at
t
h
e
I
NE
C
s
tr
ateg
y
ca
n
p
r
o
v
id
e
is
0
.
2
8
s
an
d
0
.
2
1
s
r
esp
ec
ti
v
ely
wh
en
th
e
lo
ad
s
u
d
d
en
ly
in
c
r
ea
s
es/d
ec
r
ea
s
es.
Fig
u
r
e
6
s
h
o
ws
th
e
MM
C
f
o
u
r
-
d
im
en
s
io
n
al
co
n
t
r
o
l
s
ch
em
e
p
r
o
p
o
s
ed
in
Z
h
an
g
et
a
l.
[
2
4
]
.
T
h
e
DC
m
o
d
u
latio
n
r
atio
M
dc
en
ab
les
th
e
co
n
tr
o
l
to
co
n
tr
o
l
th
e
DC
v
o
ltag
e
an
d
AC
v
o
ltag
e
s
ep
ar
ately
,
wh
ile
th
e
im
p
r
o
v
e
d
n
ea
r
est
lev
el
m
o
d
u
l
atio
n
s
tr
ateg
y
u
s
es
th
e
v
ar
iab
le
ca
p
ac
ito
r
v
o
ltag
e
_
to
r
ep
lace
th
e
ca
p
ac
ito
r
v
o
ltag
e
r
atin
g
u
n
d
e
r
th
e
tr
ad
it
io
n
al
s
ch
em
e,
s
o
th
at
th
e
DC
lin
e
v
o
ltag
e
an
d
th
e
s
u
b
m
o
d
u
l
e
ca
p
ac
ito
r
v
o
ltag
e
ar
e
m
ath
em
atica
lly
d
ec
o
u
p
led
.
At
th
e
s
am
e
tim
e,
b
y
u
s
in
g
th
e
f
r
eq
u
en
cy
-
ca
p
ac
itan
ce
e
n
er
g
y
(
f
-
W
)
d
r
o
o
p
c
o
n
tr
o
l
in
th
e
r
ed
d
ash
ed
b
o
x
o
f
Fig
u
r
e
6
,
th
e
s
u
b
m
o
d
u
le
ca
p
ac
itan
ce
en
e
r
g
y
c
an
b
e
ch
an
g
ed
p
r
o
p
o
r
tio
n
ally
with
th
e
f
r
eq
u
e
n
cy
f
lu
ctu
atio
n
,
s
o
th
at
it
h
as
an
i
n
er
tia
s
u
p
p
o
r
t
ca
p
ac
ity
s
im
ilar
to
th
at
o
f
a
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
.
T
h
e
r
ef
o
r
e
,
wh
en
th
e
f
-
W
d
r
o
o
p
co
n
tr
o
l
s
tr
ateg
y
is
ad
o
p
ted
,
th
e
in
er
tia
co
n
s
tan
t
th
at
th
e
MM
C
en
er
g
y
ca
n
p
r
o
v
id
e
ca
n
b
e
ex
p
r
ess
ed
as
(
1
7
)
.
M
MC
=
E
,
MMC
2
MMC
SG
fw
(
1
7
)
W
h
er
e
fw
is
th
e
d
r
o
o
p
c
o
ef
f
ici
en
t
in
c
o
n
tr
o
l,
th
at
is
,
t
h
e
en
er
g
y
-
f
r
eq
u
e
n
cy
r
atio
.
T
h
e
s
el
ec
tio
n
o
f
fw
is
d
eter
m
in
ed
b
y
th
e
MM
C
ca
p
ac
ito
r
e
n
er
g
y
u
tili
za
tio
n
lim
it
p
er
u
n
it
v
alu
e
pu
l
i
m
an
d
th
e
AC
s
y
s
tem
f
r
eq
u
e
n
cy
d
e
v
iatio
n
lim
it p
er
u
n
it v
alu
e
Δ
pu
,
l
i
m
wh
ich
ca
n
b
e
ex
p
r
e
s
s
ed
as
(
1
8
)
.
fw
=
pu
,
l
im
−
pu
0
Δ
pu
,
l
im
(
1
8
)
W
h
er
e:
pu
0
is
th
e
p
er
u
n
it v
alu
e
o
f
th
e
ca
p
ac
itan
ce
en
er
g
y
o
f
th
e
MM
C
u
n
d
er
r
ated
co
n
d
itio
n
s
,
an
d
its
v
alu
e
is
1
.
Acc
o
r
d
in
g
to
t
h
e
Z
h
an
g
e
t
a
l.
[
2
4
]
,
th
e
v
ar
iatio
n
r
a
n
g
e
o
f
th
e
ca
p
ac
ito
r
v
o
ltag
e
p
e
r
u
n
i
t
v
alu
e
u
n
d
e
r
f
o
u
r
-
d
im
en
s
io
n
al
co
n
tr
o
l
is
,
,
=
[
0
.
7
6
8
,
1
.
5
0
0
]
p
.
u
.
,
th
at
is
,
th
e
v
ar
iatio
n
r
an
g
e
o
f
th
e
ca
p
ac
ito
r
e
n
er
g
y
is
pu
l
i
m
=
[
0
.
5
9
,
2
.
2
5
]
p
.
u
.
Fro
m
(
1
7
)
an
d
(
1
8
)
,
it
ca
n
b
e
s
ee
n
th
at
th
e
ca
p
ac
ito
r
v
o
ltag
e/en
er
g
y
d
ev
iatio
n
lim
it
o
f
th
e
MM
C
f
o
u
r
-
d
im
en
s
io
n
al
co
n
tr
o
l
d
eter
m
in
es
th
e
d
r
o
o
p
co
ef
f
icien
t
fw
o
f
th
e
f
-
W
d
r
o
o
p
co
n
tr
o
l,
a
n
d
its
v
alu
e
d
ir
ec
tly
af
f
ec
ts
th
e
eq
u
i
v
alen
t
in
er
tia
co
n
s
tan
t
o
f
th
e
f
lex
ib
le
DC
MM
C
.
Usi
n
g
th
e
s
am
e
test
s
y
s
tem
as
th
e
I
NE
C
s
tr
ateg
y
,
it
ca
n
b
e
ca
lcu
lated
th
at
th
e
in
er
tia
co
n
s
tan
t
H
MMC
p
r
o
v
id
ed
b
y
th
e
MM
C
en
er
g
y
wh
en
th
e
f
-
W
d
r
o
o
p
co
n
tr
o
l is ad
o
p
te
d
i
s
0
.
4
1
s
an
d
1
.
2
5
s
r
esp
ec
tiv
el
y
wh
en
th
e
l
o
ad
in
c
r
ea
s
es/d
ec
r
ea
s
es su
d
d
en
ly
.
B
ased
o
n
th
e
ab
o
v
e
d
is
cu
s
s
i
o
n
,
th
e
eq
u
iv
ale
n
t
in
er
tia
co
n
s
tan
t
o
f
th
e
f
lex
ib
le
DC
tr
a
n
s
m
is
s
io
n
s
y
s
tem
is
co
m
p
ar
ed
b
etwe
en
th
e
f
-
W
d
r
o
o
p
c
o
n
tr
o
l
u
s
in
g
f
o
u
r
-
d
im
en
s
io
n
al
c
o
n
tr
o
l
a
n
d
th
e
I
NE
C
s
tr
ateg
y
u
s
in
g
d
o
u
b
le
clo
s
ed
-
l
o
o
p
v
ec
t
o
r
co
n
tr
o
l
wh
e
n
th
e
lo
a
d
in
cr
e
ases
/d
ec
r
ea
s
es
s
u
d
d
en
ly
,
as
s
h
o
wn
in
T
a
b
le
1
.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
T
a
b
le
1
th
at
f
o
r
th
e
s
am
e
s
y
s
tem
wo
r
k
in
g
co
n
d
itio
n
,
co
m
p
ar
ed
with
th
e
I
NE
C
s
tr
ateg
y
,
u
n
d
er
th
e
f
-
W
d
r
o
o
p
co
n
tr
o
l
b
ased
o
n
f
o
u
r
-
d
im
en
s
io
n
al
co
n
t
r
o
l,
th
e
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
t
H
o
f
MM
C
is
lar
g
er
an
d
th
e
in
er
tia
s
u
p
p
o
r
t c
ap
ac
ity
is
s
tr
o
n
g
er
.
T
ab
le
1.
C
o
m
p
a
r
is
o
n
o
f
MM
C
eq
u
iv
alen
t in
e
r
tia
co
n
s
tan
ts
u
n
d
er
d
i
f
f
er
en
t c
o
n
tr
o
l stra
teg
ie
s
C
o
n
t
r
o
l
st
r
a
t
e
g
y
H
mm
/
s
Lo
a
d
i
n
c
r
e
a
si
n
g
Lo
a
d
r
e
d
u
c
t
i
o
n
I
N
EC
0
.
2
8
0
.
2
1
f
-
W
d
r
o
o
p
c
o
n
t
r
o
l
0
.
4
1
1
.
2
5
C
o
n
t
r
o
l
st
r
a
t
e
g
y
H
mm
/
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lyzi
n
g
th
e
a
b
ilit
y
o
f c
a
p
a
ci
to
r
en
erg
y
in
a
mo
d
u
la
r
mu
ltil
ev
el
co
n
ve
r
ter to
…
(
Du
n
ya
S
h
.
Wa
is
)
653
2
.
2
.
Co
m
pa
ra
t
iv
e
a
na
ly
s
is
o
f
equiv
a
lent
inert
ia
co
ns
t
a
nt
a
nd
ex
is
t
ing
ind
ica
t
o
rs
I
n
o
r
d
er
to
q
u
an
titativ
ely
a
n
a
ly
ze
th
e
MM
C
'
s
ab
ilit
y
to
s
u
p
p
o
r
t
g
r
id
in
er
tia,
e
x
is
tin
g
s
tu
d
ies
h
av
e
p
r
o
p
o
s
ed
a
v
ar
iety
o
f
in
er
tia
q
u
an
tific
atio
n
in
d
icato
r
s
.
T
h
is
s
ec
tio
n
co
m
p
ar
es
th
e
p
r
o
p
o
s
e
d
MM
C
eq
u
iv
ale
n
t
in
er
tia
co
n
s
tan
t
with
ex
is
tin
g
s
tu
d
ies
to
v
er
if
y
th
e
ad
v
an
tag
es
an
d
c
o
m
p
leten
ess
o
f
th
e
in
d
icato
r
s
p
r
o
p
o
s
ed
in
th
is
p
ap
er
.
Yan
g
et
a
l
.
[
2
5
]
d
ef
in
es
an
MM
C
in
er
tia
co
n
s
ta
n
t
th
at
tak
es
in
to
ac
co
u
n
t
th
e
p
r
o
p
o
r
tio
n
o
f
n
e
w
en
er
g
y
p
en
etr
atio
n
.
Ass
u
m
e
th
at
th
e
r
o
t
o
r
k
in
etic
en
er
g
y
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
i
s
0
.
5
2
,
an
d
t
h
e
ca
p
ac
ito
r
en
er
g
y
s
to
r
ag
e
in
t
h
e
MM
C
is
0
.
5
2
,
wh
er
e
is
th
e
m
o
m
en
t
o
f
in
er
tia,
is
th
e
s
p
ee
d
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
,
an
d
C
is
t
h
e
s
ize
o
f
th
e
MM
C
ca
p
ac
ito
r
.
Yan
g
et
a
l
.
[
2
5
]
eq
u
ates
th
e
two
an
d
m
ak
es
th
e
ca
p
ac
ito
r
v
o
ltag
e
ch
a
n
g
e
p
r
o
p
o
r
tio
n
ally
with
t
h
e
s
p
ee
d
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
(
g
r
id
f
r
e
q
u
en
c
y
)
to
s
im
u
late
th
e
in
er
tia
r
esp
o
n
s
e
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
.
Ass
u
m
e
th
at
th
e
s
y
s
tem
allo
ws
a
m
ax
im
u
m
f
r
eq
u
e
n
cy
d
e
v
iatio
n
lim
it
Δ
l
i
m
=
,
an
d
th
e
m
ax
im
u
m
ca
p
ac
ito
r
v
o
ltag
e
d
e
v
iatio
n
Δ
C
l
i
m
s
atis
f
ie
s
Δ
C
l
i
m
with
th
e
r
ated
ca
p
ac
ito
r
v
o
lt
ag
e
Δ
C
l
i
m
=
C0
,
wh
er
e
an
d
ar
e
co
r
r
esp
o
n
d
in
g
p
r
o
p
o
r
tio
n
al
co
ef
f
icien
ts
.
T
h
en
th
e
MM
C
ca
p
ac
ito
r
v
o
ltag
e
c
h
an
g
e
c
o
m
m
an
d
v
alu
e
Δ
C
∗
an
d
th
e
f
r
eq
u
e
n
c
y
d
ev
iatio
n
Δ
s
h
o
u
ld
s
atis
f
y
.
Δ
C
∗
=
C
0
Δ
(
1
9
)
Def
in
e
th
e
to
tal
g
r
id
ca
p
ac
ity
G
r
i
d
=
MMC
+
SG
,
th
en
th
e
MM
C
in
er
tia
c
o
n
s
tan
t
H
MMC1
d
ef
in
e
d
i
n
th
e
Z
h
u
et
a
l.
[
1
8
]
is
g
iv
en
b
y
(
2
0
)
.
1
=
(
2
0
)
Fro
m
Sectio
n
2
.
1
.
1
,
we
k
n
o
w
th
at
th
e
f
r
eq
u
e
n
cy
d
e
v
iatio
n
lim
it
is
0
.
0
1
p
.
u
.
,
t
h
at
is
,
=
0
.
0
1
.
W
h
en
MM
C
ad
o
p
ts
f
o
u
r
-
d
im
e
n
s
io
n
al
co
n
tr
o
l,
th
e
p
er
-
u
n
it
v
alu
e
v
ar
iatio
n
r
an
g
e
o
f
ca
p
ac
ito
r
v
o
ltag
e
.
,
=
[
0
.
7
6
8
,
1
.
5
0
0
]
p
.
u
.
,
th
at
is
,
is
0
.
2
3
2
an
d
0
.
5
0
0
,
r
esp
ec
tiv
el
y
,
wh
en
th
e
lo
a
d
in
cr
ea
s
es/d
e
cr
ea
s
es
s
u
d
d
en
ly
.
T
ak
in
g
th
e
f
lex
ib
le
DC
tr
an
s
m
is
s
io
n
s
y
s
tem
p
ar
am
eter
s
d
e
s
cr
ib
ed
in
Sectio
n
2
.
1
.
1
as
an
ex
am
p
le,
th
e
MM
C
in
er
tia
co
n
s
tan
t
H
MMC1
u
n
d
er
t
h
is
d
ef
in
itio
n
ca
n
b
e
ca
lcu
late
d
to
b
e
0
.
3
1
s
an
d
0
.
6
7
s
,
r
esp
ec
tiv
ely
,
wh
e
n
th
e
lo
ad
in
cr
ea
s
es/d
ec
r
ea
s
es su
d
d
en
ly
.
Fro
m
th
e
ab
o
v
e
an
aly
s
is
,
it
ca
n
b
e
s
ee
n
th
at
th
e
H
MMC1
d
e
f
in
ed
in
th
e
Z
h
an
g
a
t
a
l
.
[
2
3
]
u
n
d
er
t
h
e
s
am
e
co
n
tr
o
l
is
s
m
aller
th
an
th
e
f
lex
ib
le
DC
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
t
d
ef
in
ed
in
th
i
s
p
ap
er
.
T
h
e
m
ain
r
ea
s
o
n
s
ar
e
as f
o
llo
ws:
i)
T
h
e
p
o
wer
b
ase
v
alu
e
s
elec
ted
in
th
e
ca
lc
u
latio
n
o
f
Ya
n
g
et
a
l
.
[
2
5
]
is
G
r
i
d
.
Sin
g
h
et
a
l.
[
8
]
p
o
in
ts
o
u
t
th
at
wh
en
th
e
ac
ce
s
s
o
f
n
ew
en
er
g
y
s
o
u
r
ce
s
in
cr
ea
s
es,
if
t
h
e
n
u
m
b
er
o
f
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
s
in
th
e
g
r
id
r
em
ain
s
u
n
ch
a
n
g
ed
an
d
t
h
e
k
in
etic
en
er
g
y
r
em
ain
s
u
n
ch
an
g
ed
,
th
e
r
ate
o
f
c
h
an
g
e
o
f
s
y
s
tem
f
r
eq
u
en
c
y
u
n
d
er
th
e
s
am
e
d
is
tu
r
b
an
ce
p
o
wer
r
em
ain
s
u
n
c
h
an
g
e
d
.
T
h
er
e
is
n
o
eq
u
iv
ale
n
t
r
elatio
n
s
h
ip
b
etwe
en
th
e
in
er
tia
co
n
s
tan
t
ca
lcu
lated
b
y
t
h
e
ab
o
v
e
m
eth
o
d
an
d
th
e
s
y
s
tem
f
r
eq
u
en
cy
.
T
h
is
p
ap
e
r
u
s
es
th
e
ca
p
ac
ity
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
o
f
th
e
g
r
id
SG
as
th
e
b
ase
v
alu
e
f
o
r
p
o
wer
ca
lcu
latio
n
,
wh
ich
ca
n
b
et
ter
r
ef
lect
th
e
ac
tu
al
im
p
ac
t o
f
ca
p
ac
ito
r
en
e
r
g
y
o
n
th
e
AC
s
y
s
tem
.
ii)
I
n
Z
h
u
et
a
l.
[
1
8
]
,
th
e
ca
p
ac
it
o
r
v
o
ltag
e
C
is
p
r
o
p
o
r
tio
n
al
to
t
h
e
s
y
s
tem
f
r
eq
u
en
cy
,
wh
ich
is
in
co
n
s
is
ten
t
with
th
e
p
h
y
s
ical
m
ea
n
in
g
o
f
th
e
in
er
tia
co
n
s
tan
t.
T
h
e
MM
C
in
er
tia
co
n
s
tan
t
is
d
ef
in
e
d
as
h
alf
o
f
th
e
p
o
wer
s
u
p
p
o
r
ted
b
y
th
e
MM
C
f
o
r
th
e
AC
s
y
s
tem
u
n
d
er
th
e
u
n
it
f
r
eq
u
e
n
cy
ch
an
g
e
r
ate,
th
at
is
,
th
e
s
y
s
tem
f
r
eq
u
e
n
cy
s
h
o
u
ld
b
e
p
r
o
p
o
r
tio
n
al
to
th
e
ca
p
ac
ito
r
en
er
g
y
.
Kim
et
a
l.
[
2
6
]
co
m
p
ar
e
d
th
e
MM
C
ca
p
ac
ito
r
en
er
g
y
s
to
r
ag
e
to
th
e
k
in
etic
en
er
g
y
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
r
o
to
r
an
d
p
r
o
p
o
s
ed
th
e
f
lex
ib
le
DC
in
er
tia
co
n
s
tan
t
HM
M
C
2
.
Ass
u
m
i
n
g
th
e
r
ated
s
p
ee
d
o
f
th
e
s
y
n
c
h
r
o
n
o
u
s
m
o
t
o
r
is
,
its
r
o
to
r
k
in
etic
en
e
r
g
y
ca
n
b
e
ex
p
r
ess
ed
as
(
2
1
)
.
=
0
.
5
2
(
2
1
)
Ass
u
m
in
g
th
e
m
ax
im
u
m
allo
wab
le
s
p
ee
d
(
f
r
e
q
u
en
c
y
)
d
ev
iatio
n
is
,
wh
en
lo
a
d
d
is
tu
r
b
an
ce
o
cc
u
r
s
,
th
e
en
er
g
y
lim
it
∆
,
in
jecte
d
b
y
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
to
s
u
p
p
o
r
t
th
e
AC
p
o
wer
g
r
id
ca
n
b
e
ex
p
r
ess
ed
as
(
2
2
)
.
∆
,
=
(
2
−
2
)
2
=
(
1
−
∆
.
2
)
2
2
=
(
2
2
)
W
h
er
e
is
th
e
r
atio
b
etwe
en
th
e
k
in
etic
e
n
er
g
y
ch
a
n
g
e
lim
it
an
d
th
e
r
ated
k
in
etic
en
er
g
y
.
Kim
et
a
l.
[
2
6
]
co
m
b
in
ed
th
e
DC
v
o
lta
g
e
d
e
v
iatio
n
lim
it
an
d
t
h
e
th
ir
d
h
a
r
m
o
n
ic
in
jectio
n
ef
f
ec
t
t
o
o
b
tain
th
at
th
e
b
r
id
g
e
a
r
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
646
-
662
654
ca
n
b
e
p
u
t
in
to
u
s
e
u
p
to
1
.
2
6
5
N
s
u
b
m
o
d
u
les,
wh
er
e
N
is
th
e
n
u
m
b
er
o
f
s
u
b
m
o
d
u
les
p
u
t
in
to
u
s
e
u
n
d
e
r
th
e
r
ated
s
tate
o
f
th
e
MM
C
.
T
h
en
th
e
ca
p
ac
itan
ce
en
e
r
g
y
c
h
an
g
e
lim
it
Δ
ca
n
b
e
ca
lcu
lated
as
(
2
3
)
.
Δ
=
(
1
−
1
1
.
265
2
)
≈
0
.
375
(
2
3
)
C
o
m
b
in
in
g
(
2
2
)
a
n
d
(
2
3
)
,
let
th
e
MM
C
ca
p
ac
ito
r
en
er
g
y
ch
an
g
e
lim
it
Δ
b
e
eq
u
al
to
th
e
a
n
a
lo
g
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
r
o
to
r
k
in
e
tic
en
er
g
y
ch
an
g
e
lim
it
Δ
,
,
an
d
th
e
f
lex
i
b
le
DC
in
er
tia
co
n
s
tan
t
H
MMC2
d
ef
in
ed
in
Z
h
u
et
a
l.
[
1
9
]
is
o
b
tain
ed
as
(
2
4
)
.
2
=
0
.
375
(
2
4
)
T
ak
in
g
th
e
ab
o
v
e
-
m
en
tio
n
ed
f
lex
ib
le
DC
tr
an
s
m
is
s
io
n
s
y
s
tem
p
ar
am
eter
s
as
an
ex
a
m
p
le,
th
e
HM
MC2
d
ef
in
ed
in
th
e
liter
atu
r
e
ca
n
b
e
ca
lcu
lated
to
b
e
0
.
3
7
5
s
wh
en
th
e
lo
ad
s
u
d
d
e
n
ly
in
cr
ea
s
es.
Similar
ly
,
HM
MC2
u
n
d
er
th
e
l
o
ad
s
u
d
d
en
ly
d
ec
r
ea
s
e
co
n
d
itio
n
is
also
0
.
3
7
5
s
,
b
o
th
o
f
w
h
ich
a
r
e
s
m
aller
th
an
th
e
eq
u
iv
alen
t
in
e
r
tia
co
n
s
tan
t
o
f
th
e
f
lex
ib
le
DC
u
n
d
er
t
h
e
f
o
u
r
-
d
im
en
s
io
n
al
c
o
n
tr
o
l
p
r
o
p
o
s
e
d
in
th
is
p
a
p
er
.
T
h
e
m
ain
r
ea
s
o
n
is
th
at
Kim
et
a
l.
[
2
6
]
d
i
d
n
o
t
f
u
lly
an
aly
ze
t
h
e
en
er
g
y
u
tili
za
tio
n
lim
it
o
f
th
e
MM
C
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
af
ter
th
e
DC
v
o
ltag
e
an
d
ca
p
ac
ito
r
v
o
ltag
e
wer
e
d
ec
o
u
p
led
,
a
n
d
d
id
n
o
t
co
n
s
id
e
r
th
e
ch
an
g
es
in
th
e
in
er
tia
s
u
p
p
o
r
t c
a
p
ac
ity
ca
u
s
e
d
b
y
th
e
d
if
f
e
r
en
t e
n
e
r
g
y
a
b
s
o
r
p
tio
n
an
d
r
elea
s
e
r
an
g
es o
f
th
e
ca
p
ac
ito
r
.
T
h
e
in
er
tia
c
o
n
s
tan
ts
d
ef
in
e
d
in
Z
h
u
et
a
l.
[
1
8
]
,
[
1
9
]
an
d
th
e
MM
C
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
ts
p
r
o
p
o
s
ed
in
th
is
p
ap
er
ar
e
co
m
p
ar
ed
,
as
s
h
o
wn
in
T
ab
le
2
.
Fro
m
th
e
ab
o
v
e
d
is
cu
s
s
io
n
,
it
ca
n
b
e
s
ee
n
th
at
th
e
f
lex
ib
le
DC
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
t
HM
MC
p
r
o
p
o
s
ed
in
th
is
p
ap
er
n
o
t
o
n
l
y
co
n
s
id
er
s
th
e
ac
tu
al
ef
f
ec
t
o
f
ca
p
ac
ito
r
en
er
g
y
s
to
r
ag
e
o
n
th
e
AC
s
y
s
tem
,
b
u
t
also
co
v
er
s
th
e
d
if
f
er
en
ce
s
in
en
e
r
g
y
u
tili
za
tio
n
r
an
g
e
u
n
d
er
d
if
f
er
en
t
c
o
n
tr
o
l
an
d
d
if
f
er
en
t
lo
ad
d
is
tu
r
b
an
ce
c
o
n
d
itio
n
s
,
an
d
ca
n
ac
c
u
r
ately
q
u
an
tify
th
e
in
er
tia
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
MM
C
.
T
ab
le
2
.
C
o
m
p
a
r
is
o
n
o
f
HM
MC
,
HM
MC1
[
1
8
]
,
an
d
HM
MC2
[
1
9
]
W
o
r
k
i
n
g
c
o
n
d
i
t
i
o
n
s
H
M
M
C
/
s
p
r
o
p
o
s
e
d
H
M
M
C
1
/
s
H
M
M
C
2
/
s
Lo
a
d
s
u
r
g
e
0
.
4
1
0
.
3
1
0
.
3
7
5
Lo
a
d
r
e
d
u
c
t
i
o
n
1
.
2
5
0
.
6
7
0
.
3
7
5
3.
ANALY
SI
S O
F
T
H
E
I
N
E
R
T
I
A
S
UP
P
O
RT
CAP
A
B
I
L
I
T
Y
O
F
M
U
L
T
I
-
T
E
RM
I
NA
L
M
M
C
F
O
R
RE
C
E
I
V
I
NG
E
ND
As
ca
n
b
e
s
ee
n
f
r
o
m
s
ec
tio
n
2
,
MM
C
f
o
u
r
-
d
im
en
s
io
n
al
co
n
tr
o
l
ca
n
m
ax
im
ize
th
e
u
s
e
o
f
s
u
b
-
m
o
d
u
l
e
ca
p
ac
ito
r
en
er
g
y
to
p
r
o
v
i
d
e
i
n
er
tia
s
u
p
p
o
r
t
f
o
r
th
e
AC
s
y
s
tem
with
o
u
t
af
f
ec
tin
g
th
e
p
o
w
er
s
tab
ilit
y
o
f
o
th
er
AC
s
y
s
tem
s
.
T
h
is
ch
ap
ter
will
tak
e
f
o
u
r
-
d
im
en
s
io
n
al
co
n
tr
o
l
as
an
ex
am
p
le
to
d
is
cu
s
s
th
e
in
er
tia
s
u
p
p
o
r
t
law
o
f
th
e
m
u
lti
-
ter
m
in
al
m
o
d
u
lar
m
u
lti
-
lev
el
d
ir
ec
t c
u
r
r
en
t (
M
MC
-
MT
DC
)
s
y
s
tem
.
I
n
s
ec
tio
n
1
an
d
2
,
th
e
in
er
tia
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
a
s
in
g
le
MM
C
co
n
v
er
ter
s
tatio
n
f
o
r
th
e
AC
s
y
s
tem
was
ca
lcu
lated
.
Fo
r
a
two
-
ter
m
in
al
s
y
s
tem
,
if
th
e
ca
p
ac
it
o
r
en
er
g
y
in
two
MM
C
s
ca
n
b
e
u
s
ed
to
s
u
p
p
o
r
t
t
h
e
r
ec
eiv
in
g
-
e
n
d
g
r
i
d
at
th
e
s
am
e
tim
e,
it
ca
n
b
e
s
ee
n
f
r
o
m
(
1
1
)
th
at
its
s
u
p
p
o
r
t
ca
p
ac
ity
is
o
b
v
io
u
s
ly
twice
th
at
o
f
a
s
in
g
le
co
n
v
er
ter
s
tatio
n
.
T
h
e
r
esear
ch
o
b
ject
is
ex
ten
d
ed
to
th
e
th
r
ee
-
ter
m
in
al
MM
C
-
MT
DC
s
y
s
tem
.
T
ak
e
th
e
s
y
s
tem
with
o
n
e
tr
an
s
m
is
s
io
n
an
d
two
r
ec
ep
tio
n
s
s
h
o
wn
in
Fig
u
r
e
7
as
an
ex
am
p
le
f
o
r
d
is
cu
s
s
io
n
.
I
n
th
e
f
ig
u
r
e:
th
e
tr
an
s
m
is
s
io
n
en
d
MM
C
1
is
2
0
0
0
MW,
th
e
r
ec
ep
tio
n
en
d
M
MC2
an
d
MM
C
3
ar
e
1
0
0
0
M
W
r
esp
ec
tiv
ely
,
an
d
all
MM
C
s
h
av
e
th
e
s
am
e
en
er
g
y
s
to
r
ag
e
tim
e
c
o
n
s
tan
t,
wh
ich
is
T
E
,
MM
C
=4
0
m
s
.
I
n
th
e
AC
s
y
s
tem
co
n
n
ec
ted
to
MM
C
2
,
th
e
s
y
n
c
h
r
o
n
o
u
s
m
o
to
r
ca
p
ac
it
y
S
G
2
is
2
0
0
0
MW.
T
h
e
in
er
tia
s
u
p
p
o
r
t la
w
o
f
th
e
m
u
lti
-
ter
m
in
al
s
y
s
tem
f
o
r
th
e
AC
s
y
s
tem
co
n
n
ec
ted
to
t
h
e
r
ec
ep
tio
n
en
d
MM
C
2
is
d
is
cu
s
s
ed
.
W
h
en
o
n
ly
th
e
d
ir
ec
tly
co
n
n
e
cted
MM
C
2
s
u
p
p
o
r
ts
th
e
s
y
s
tem
f
r
eq
u
e
n
cy
,
its
s
u
p
p
o
r
tin
g
ca
p
ac
ity
is
th
e
s
am
e
as
th
at
o
f
th
e
s
in
g
l
e
1
0
0
0
MW
MM
C
in
s
ec
tio
n
2
.
As
s
h
o
wn
in
T
a
b
le
1
,
th
e
eq
u
iv
ale
n
t
in
er
tia
co
n
s
tan
t
H
o
f
th
e
s
in
g
le
MM
C
co
n
v
er
ter
s
tatio
n
is
0
.
4
1
s
an
d
1
.
2
5
s
r
esp
ec
tiv
ely
wh
en
th
e
lo
a
d
in
cr
ea
s
es/d
ec
r
ea
s
es.
C
o
n
s
id
er
in
g
th
at
MM
C
3
also
p
ar
ticip
at
es
in
th
e
s
u
p
p
o
r
t,
a
n
d
ass
u
m
i
n
g
th
at
MM
C
3
a
n
d
MM
C
2
h
av
e
t
h
e
s
am
e
en
er
g
y
-
f
r
eq
u
en
cy
r
atio
fw
,
th
e
to
tal
en
er
g
y
o
f
th
e
ca
p
ac
ito
r
s
p
ar
t
icip
atin
g
in
th
e
f
r
eq
u
e
n
cy
s
u
p
p
o
r
t
in
t
h
e
s
y
s
tem
b
ec
o
m
es
twice
th
at
o
f
th
e
s
in
g
le
MM
C
s
u
p
p
o
r
t,
an
d
th
e
eq
u
iv
ale
n
t
in
er
ti
a
co
n
s
tan
t
o
f
th
e
s
y
s
tem
also
b
ec
o
m
es
twice
th
at
o
f
th
e
s
in
g
le
MM
C
s
u
p
p
o
r
t.
T
h
er
e
f
o
r
e,
wh
e
n
th
e
lo
ad
in
cr
ea
s
es/d
ec
r
ea
s
es
s
u
d
d
en
ly
,
th
e
eq
u
iv
ale
n
t
in
er
tia
co
n
s
tan
t
HM
MC
o
f
th
e
f
lex
ib
le
DC
tr
an
s
m
is
s
io
n
s
y
s
tem
is
0
.
8
2
s
an
d
2
.
5
0
s
,
r
esp
ec
tiv
e
ly
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lyzi
n
g
th
e
a
b
ilit
y
o
f c
a
p
a
ci
to
r
en
erg
y
in
a
mo
d
u
la
r
mu
ltil
ev
el
co
n
ve
r
ter to
…
(
Du
n
ya
S
h
.
Wa
is
)
655
Fig
u
r
e
7
.
Sch
em
atic
d
iag
r
am
o
f
a
th
r
ee
-
ter
m
in
al
MM
C
s
y
s
tem
I
f
th
e
ca
p
ac
itiv
e
en
er
g
y
o
f
th
e
2
0
0
0
MW M
MC1
at
th
e
s
en
d
in
g
en
d
ca
n
also
r
esp
o
n
d
t
o
th
e
in
er
tia
o
f
th
e
AC
s
y
s
tem
co
n
n
ec
ted
to
th
e
r
ec
eiv
in
g
en
d
MM
C
2
,
th
e
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
th
e
s
y
s
tem
will
b
e
f
u
r
th
er
im
p
r
o
v
e
d
.
Ass
u
m
in
g
th
at
MM
C
1
h
as
th
e
s
am
e
en
er
g
y
f
r
eq
u
en
cy
r
atio
fw
as
o
th
er
MM
C
s
,
s
i
n
ce
th
e
ca
p
ac
it
y
o
f
MM
C
1
is
twice
th
at
o
f
MM
C
2
,
th
e
eq
u
iv
alen
t
in
e
r
tia
co
n
s
tan
t
p
r
o
v
id
ed
b
y
MM
C
1
is
twice
th
at
o
f
MM
C
2
,
th
at
is
,
th
e
in
e
r
tia
co
n
s
tan
t
p
r
o
v
id
e
d
wh
e
n
th
e
lo
ad
in
cr
ea
s
es/d
ec
r
ea
s
es
s
u
d
d
en
ly
is
0
.
8
2
s
an
d
2
.
5
0
s
r
esp
ec
tiv
ely
.
C
o
n
s
id
er
in
g
th
e
ca
p
ac
itiv
e
en
er
g
y
o
f
all
MM
C
s
in
th
e
f
lex
ib
le
DC
s
y
s
tem
,
th
e
o
v
er
all
HM
MC
o
f
th
e
s
y
s
tem
is
1
.
6
4
s
an
d
5
.
0
0
s
r
esp
ec
tiv
ely
.
I
n
s
u
m
m
ar
y
,
f
o
r
an
MM
C
-
MT
DC
s
y
s
te
m
,
if
th
e
ca
p
ac
ito
r
en
er
g
y
o
f
all
c
o
n
v
e
r
ter
s
tatio
n
s
ca
n
b
e
u
s
ed
f
o
r
th
e
in
er
tia
s
u
p
p
o
r
t
o
f
t
h
e
r
ec
eiv
i
n
g
s
y
s
tem
at
th
e
s
am
e
tim
e,
u
n
d
er
th
e
s
am
e
en
er
g
y
s
to
r
ag
e
tim
e
co
n
s
tan
t
T
E,
MMC
an
d
en
er
g
y
f
r
e
q
u
en
c
y
r
atio
fw
,
th
e
in
er
tia
s
u
p
p
o
r
t
ca
p
ac
ity
o
f
th
e
MM
C
-
MT
DC
s
y
s
tem
is
d
eter
m
in
ed
b
y
th
e
to
tal
ca
p
ac
ity
o
f
th
e
s
y
s
tem
.
T
h
e
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
t H
MM
C
,
to
t o
f
th
e
M
MC
-
MT
DC
s
y
s
tem
ca
n
b
e
ex
p
r
ess
ed
as
(
2
5
)
.
M
MC
,
tot
=
E
.
MMC
,
tot
MMC
,
t
o
t
GD
,
d
∆
,
∆
(
2
5
)
W
h
er
e
MMC
,
tot
is
th
e
r
ated
ca
p
ac
ity
o
f
th
e
MM
C
-
MT
DC
s
y
s
tem
an
d
SG
,
d
is
th
e
r
ated
ca
p
ac
ity
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
o
f
th
e
AC
s
y
s
tem
with
lo
ad
d
is
tu
r
b
an
ce
.
W
h
en
th
e
t
h
r
ee
-
ter
m
i
n
al
M
MC
-
MT
DC
s
y
s
tem
ad
o
p
ts
th
e
I
NE
C
s
tr
ateg
y
,
d
u
e
to
t
h
e
co
u
p
lin
g
r
elatio
n
s
h
ip
b
etwe
en
th
e
DC
v
o
ltag
e
an
d
th
e
ca
p
ac
ito
r
v
o
ltag
e,
th
e
ch
an
g
e
o
f
th
e
DC
v
o
ltag
e
will
af
f
ec
t
th
e
th
r
ee
co
n
v
er
ter
s
tatio
n
ca
p
ac
ito
r
s
to
r
elea
s
e/ab
s
o
r
b
e
n
er
g
y
to
s
u
p
p
o
r
t
th
e
AC
g
r
id
o
n
t
h
e
d
is
tu
r
b
an
ce
s
id
e.
Acc
o
r
d
in
g
to
t
h
e
d
is
cu
s
s
io
n
in
s
ec
tio
n
2
,
co
m
p
ar
e
d
with
th
e
f
o
u
r
-
d
im
en
s
io
n
al
co
n
tr
o
l,
th
e
I
NE
C
s
tr
ateg
y
o
n
ly
ch
an
g
es
th
e
en
er
g
y
-
f
r
eq
u
e
n
cy
r
atio
.
Su
b
s
titu
tin
g
th
e
e
n
er
g
y
-
f
r
eq
u
e
n
cy
r
atio
u
n
d
er
th
is
s
tr
ateg
y
in
to
(
2
5
)
,
th
e
th
eo
r
etica
l
eq
u
i
v
alen
t
in
e
r
tia
c
o
n
s
tan
t
o
f
th
e
th
r
ee
-
ter
m
in
al
s
y
s
tem
u
n
d
e
r
th
e
I
NE
C
s
tr
ateg
y
ca
n
b
e
ca
lc
u
lated
to
b
e
1
.
1
s
an
d
0
.
8
4
s
wh
en
th
e
lo
ad
in
cr
ea
s
es/d
ec
r
ea
s
es.
T
h
e
co
m
p
a
r
is
o
n
with
th
e
H
MMC
o
f
f
-
W
d
r
o
o
p
co
n
tr
o
l is sh
o
wn
in
T
ab
le
3
.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
T
a
b
le
3
th
at
wh
en
ad
o
p
tin
g
f
-
W
d
r
o
o
p
co
n
tr
o
l,
th
e
eq
u
iv
alen
t
in
er
tia
co
n
s
tan
t
o
f
th
e
th
r
ee
-
t
er
m
in
al
MM
C
-
MT
DC
s
y
s
tem
u
n
d
e
r
d
if
f
er
en
t
w
o
r
k
in
g
co
n
d
itio
n
s
is
lar
g
e,
a
n
d
th
e
f
r
eq
u
en
cy
s
u
p
p
o
r
t
ca
p
ab
ili
ty
o
f
th
e
p
o
wer
g
r
id
is
s
tr
o
n
g
.
T
ab
le
3
.
C
o
m
p
a
r
is
o
n
o
f
HM
MC o
f
th
r
ee
-
ter
m
in
al
MM
C
-
MT
DC
s
y
s
tem
u
n
d
er
d
if
f
er
e
n
t c
o
n
tr
o
l stra
teg
ies
C
o
n
t
r
o
l
st
r
a
t
e
g
y
H
mm
/
s
Lo
a
d
i
n
c
r
e
a
si
n
g
Lo
a
d
r
e
d
u
c
t
i
o
n
I
N
EC
1
.
1
0
0
.
8
4
f
-
W
d
r
o
o
p
c
o
n
t
r
o
l
1
.
6
4
5
.
0
0
W
h
en
th
e
AC
g
r
id
co
n
n
ec
ted
to
MM
C
2
is
d
is
tu
r
b
ed
,
in
o
r
d
er
to
en
s
u
r
e
t
h
at
th
e
ca
p
ac
ito
r
en
er
g
y
o
f
MMC
1
an
d
MM
C
3
ca
n
f
lo
w
to
MM
C
2
,
MM
C
1
,
an
d
MM
C
3
ca
n
b
e
co
n
tr
o
lled
b
y
c
o
n
s
tan
t
AC
p
o
wer
.
Acc
o
r
d
in
g
t
o
th
e
p
o
wer
b
ala
n
ce
,
th
e
p
o
wer
g
e
n
er
ated
b
y
ab
s
o
r
b
in
g
/r
elea
s
in
g
en
er
g
y
th
r
o
u
g
h
th
e
co
n
v
er
ter
s
tatio
n
ca
p
ac
ito
r
ca
n
o
n
ly
f
l
o
w
to
th
e
AC
s
y
s
tem
co
n
n
ec
ted
to
MM
C
2
th
r
o
u
g
h
t
h
e
DC
lin
e.
Fo
r
two
ty
p
ical
th
r
ee
-
ter
m
in
al
MM
C
-
MT
DC
s
y
s
tem
to
p
o
lo
g
ies,
th
e
f
lo
w
o
f
th
e
s
u
p
p
o
r
tin
g
p
o
wer
p
r
o
v
id
ed
b
y
th
e
ca
p
ac
ito
r
en
er
g
y
i
n
th
e
f
le
x
ib
le
DC
tr
an
s
m
is
s
io
n
s
y
s
tem
i
s
s
h
o
wn
in
Fig
u
r
e
8
.
Sin
ce
MM
C
1
an
d
MM
C
3
,
e
x
ce
p
t
MM
C
2
,
ca
n
n
o
t
d
ir
ec
tly
o
b
tain
th
e
f
r
eq
u
en
cy
ch
an
g
e
wh
en
t
h
e
lo
ad
d
is
tu
r
b
an
ce
o
cc
u
r
s
,
in
o
r
d
er
to
en
ab
le
ea
ch
c
o
n
v
er
te
r
s
tatio
n
to
ac
cu
r
ately
r
elea
s
e
en
er
g
y
to
s
u
p
p
o
r
t
th
e
r
ec
eiv
in
g
e
n
d
s
y
s
tem
,
th
e
s
ch
em
e
p
r
o
p
o
s
ed
in
Sin
g
h
et
a
l.
[
8
]
ca
n
b
e
u
s
ed
to
m
ak
e
th
e
DC
v
o
ltag
e
r
e
f
lect
th
e
f
r
eq
u
e
n
cy
ch
an
g
e
th
r
o
u
g
h
f
r
eq
u
en
cy
-
DC
v
o
ltag
e
d
r
o
o
p
co
n
tr
o
l.
T
h
e
DC
v
o
ltag
e
ca
n
also
b
e
ch
an
g
ed
b
y
s
im
u
latin
g
in
er
tia
,
as
p
r
o
p
o
s
ed
in
[
3
0
]
,
an
d
t
h
en
th
e
r
ec
eiv
in
g
en
d
eq
u
i
v
alen
t
f
r
e
q
u
e
n
cy
f
eq
is
o
b
tain
ed
th
r
o
u
g
h
f
r
eq
u
e
n
cy
r
ed
u
ctio
n
co
n
tr
o
l,
an
d
f
eq
is
ad
d
e
d
to
t
h
e
o
u
te
r
lo
o
p
o
f
f
-
W
d
r
o
o
p
c
o
n
tr
o
l
t
o
m
a
k
e
th
e
ca
p
ac
ito
r
r
elea
s
e
en
er
g
y
.
T
h
e
s
p
ec
if
ic
co
n
tr
o
l
d
etails
ar
e
n
o
t
th
e
m
ain
o
b
ject
o
f
th
is
p
ap
er
an
d
will
n
o
t
b
e
in
tr
o
d
u
ce
d
in
d
etail
h
er
e.
Evaluation Warning : The document was created with Spire.PDF for Python.