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Fu
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I
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Du
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p
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tan
tial
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[
1
]
.
T
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Ad
d
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n
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m
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f
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[
2
]
,
th
is
tr
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s
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,
wh
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cr
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f
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m
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p
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s
tan
tial
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allen
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es
f
o
r
m
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tain
in
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g
r
id
s
tab
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[
2
]
.
T
h
e
in
ter
n
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(
I
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A)
p
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clim
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s
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g
as
em
is
s
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s
in
th
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p
o
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s
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to
r
[
3
]
.
T
h
is
tr
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s
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h
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,
p
r
esen
ts
s
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allen
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f
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m
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tain
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g
g
r
id
s
tab
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,
p
ar
ticu
lar
l
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f
r
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q
u
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s
tab
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,
as
in
cr
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s
in
g
R
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S
p
en
etr
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n
with
v
ar
iab
le
p
o
wer
o
u
tp
u
t
ca
n
lead
to
p
o
wer
im
b
alan
c
es
an
d
f
r
eq
u
e
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cy
d
ev
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s
.
A
m
ajo
r
co
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ce
r
n
in
th
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co
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tex
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is
th
e
r
ed
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s
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due
to
th
e
d
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p
lace
m
en
t
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
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4
I
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t J Po
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E
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&
Dr
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s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
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20
25
:
200
5
-
2
0
1
6
2006
co
n
v
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tio
n
al
g
e
n
er
ato
r
s
with
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es
[
4
]
(
s
ee
Fig
u
r
e
1
)
.
Fu
r
t
h
er
m
o
r
e,
th
e
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p
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e
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ch
ar
ac
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R
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p
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lem
o
f
m
ain
tai
n
in
g
f
r
eq
u
e
n
cy
s
tab
ilit
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[
5
]
.
Fig
u
r
e
1
.
Glo
b
al
en
er
g
y
tr
an
s
i
tio
n
[
6
]
T
h
e
in
c
r
ea
s
in
g
in
te
g
r
atio
n
o
f
r
en
ewa
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o
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r
ce
s
,
p
ar
ticu
lar
ly
th
o
s
e
r
e
p
lacin
g
co
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v
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tio
n
al
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
s
with
th
eir
r
o
tatin
g
m
ass
es,
r
aises
m
ajo
r
co
n
ce
r
n
s
r
eg
ar
d
in
g
s
y
s
tem
in
er
tia
[
6
]
,
[
7
]
.
Un
lik
e
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es
,
p
o
wer
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tr
o
n
ic
in
ter
f
ac
es
co
n
tr
ib
u
te
m
in
im
al
in
e
r
tia
to
th
e
g
r
id
,
in
cr
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s
in
g
s
u
s
ce
p
tib
ilit
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to
f
r
eq
u
en
c
y
d
ev
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n
s
an
d
h
ig
h
r
ates
o
f
ch
an
g
e
o
f
f
r
e
q
u
en
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(
R
OC
OF)
d
u
r
in
g
p
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im
b
alan
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s
[
8
]
.
L
o
w
-
in
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tia
s
y
s
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ar
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p
ar
ticu
lar
ly
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ex
p
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h
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f
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eq
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c
y
d
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n
a
m
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d
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r
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d
is
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r
b
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s
an
d
in
c
r
e
ased
r
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o
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s
ca
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p
a
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to
h
ig
h
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[
9
]
,
[
1
0
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.
Ad
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r
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v
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(
VI
)
h
as
em
er
g
ed
as a
p
r
o
m
is
in
g
s
o
lu
ti
o
n
.
R
esear
ch
er
s
h
av
e
p
r
o
p
o
s
ed
v
ar
io
u
s
VI
co
n
tr
o
l
s
tr
ateg
ies
th
at
em
u
late
th
e
in
er
tial
r
esp
o
n
s
e
o
f
s
y
n
ch
r
o
n
o
u
s
m
ac
h
i
n
es
th
r
o
u
g
h
ad
v
an
ce
d
in
v
er
ter
-
b
ased
tech
n
iq
u
es.
T
h
ese
a
p
p
r
o
ac
h
es,
co
llectiv
ely
k
n
o
wn
as
v
ir
tu
al
in
er
tia,
p
r
o
v
id
e
a
c
o
n
tr
o
llab
le
s
o
u
r
ce
o
f
in
e
r
tia
-
lik
e
r
esp
o
n
s
e
to
f
r
eq
u
e
n
cy
d
ev
iatio
n
s
,
en
h
a
n
cin
g
s
y
s
tem
s
tab
ilit
y
an
d
f
r
eq
u
en
c
y
r
eg
u
latio
n
in
l
o
w
-
in
er
tia
g
r
i
d
s
with
h
ig
h
r
en
ewa
b
le
e
n
er
g
y
p
en
etr
atio
n
[
1
1
]
.
VI
ap
p
r
o
ac
h
es
aim
to
em
u
late
th
e
b
eh
av
io
r
o
f
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es
u
s
in
g
in
v
e
r
ter
-
b
ased
co
n
tr
o
l
s
tr
ateg
ies.
A
v
ar
iety
o
f
VI
co
n
tr
o
l
tech
n
iq
u
es
h
av
e
b
ee
n
ex
p
lo
r
ed
,
r
an
g
in
g
f
r
o
m
class
ic
m
eth
o
d
s
lik
e
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI)
an
d
p
r
o
p
o
r
tio
n
al
-
r
eso
n
an
t
(
PR
)
c
o
n
tr
o
l
to
ad
v
a
n
ce
d
a
p
p
r
o
ac
h
es
lev
er
a
g
in
g
m
o
d
el
p
r
ed
ictio
n
an
d
m
ac
h
in
e
lear
n
in
g
[
1
2
]
.
Sp
ec
i
f
ic
VI
tech
n
iq
u
es
in
clu
d
e
v
ir
tu
al
s
y
n
ch
r
o
n
o
u
s
m
ac
h
i
n
es
(
VSMs)
[
1
3
]
,
[
1
4
]
,
v
ir
tu
al
in
d
u
ctio
n
m
ac
h
i
n
es
(
V
I
Ms)
,
an
d
in
er
tia
em
u
latio
n
in
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
lik
e
win
d
tu
r
b
i
n
es
an
d
s
o
lar
PV
p
an
els
[
1
5
]
.
Ad
d
it
io
n
ally
,
s
p
ec
if
ic
co
n
tr
o
l
s
tr
ateg
ies
lik
e,
s
y
n
ch
r
o
n
v
er
ter
,
I
s
eL
ab
,
an
d
v
ir
tu
al
o
s
cillato
r
co
n
tr
o
l
h
a
v
e
b
ee
n
in
v
esti
g
ated
[
1
3
]
.
C
o
n
tr
o
l
s
tr
ateg
ies
lik
e
th
e
co
ef
f
icien
t
d
i
ag
r
am
m
eth
o
d
,
H
-
in
f
in
ity
co
n
t
r
o
l [
1
6
]
,
a
n
d
a
d
ap
tiv
e
lear
n
in
g
h
av
e
b
e
en
p
r
o
p
o
s
ed
to
im
p
r
o
v
e
tr
a
n
s
ien
t
s
tab
ilit
y
[
1
7
]
.
I
n
t
h
i
s
p
a
p
e
r
,
we
i
n
v
e
s
t
i
g
a
te
t
h
e
r
o
l
e
o
f
v
i
r
t
u
a
l
i
n
er
t
i
a
in
i
m
p
r
o
v
in
g
th
e
s
t
ab
i
l
i
t
y
o
f
lo
w
-
i
n
e
r
t
i
a
p
o
w
er
s
y
s
t
e
m
s
w
i
th
h
i
g
h
r
e
n
e
w
a
b
l
e
en
er
g
y
p
e
n
e
tr
a
t
i
o
n
.
W
e
p
r
o
p
o
s
e
a
n
a
d
v
a
n
c
e
d
c
o
n
t
r
o
l
f
r
a
m
e
wo
r
k
f
o
r
i
n
t
e
g
r
a
t
i
n
g
v
ir
t
u
a
l
i
n
er
t
i
a
i
n
to
v
o
l
t
ag
e
s
o
u
r
c
e
in
v
e
r
t
er
s
(
V
SI
s
)
t
o
en
h
a
n
c
e
tr
a
n
s
i
en
t
s
t
a
b
i
li
t
y
a
n
d
f
r
e
q
u
e
n
c
y
r
e
s
p
o
n
s
e
.
Ou
r
a
p
p
r
o
a
ch
l
ev
e
r
a
g
e
s
ad
a
p
t
iv
e
co
n
tr
o
l
s
t
r
a
t
eg
ie
s
a
n
d
f
u
z
z
y
l
o
g
i
c
-
b
a
s
e
d
r
eg
u
l
a
t
i
o
n
to
i
m
p
r
o
v
e
s
y
s
t
e
m
r
o
b
u
s
tn
e
s
s
a
c
r
o
s
s
v
ar
i
o
u
s
o
p
er
a
t
i
n
g
s
c
en
a
r
io
s
.
T
h
r
o
u
g
h
d
e
t
a
i
l
ed
s
i
m
u
l
a
t
io
n
s
a
n
d
p
e
r
f
o
r
m
an
c
e
a
n
a
l
y
s
e
s
,
w
e
c
o
m
p
ar
e
f
i
x
ed
a
n
d
a
d
a
p
t
iv
e
v
i
r
tu
a
l
in
e
r
t
ia
im
p
l
e
m
e
n
t
a
t
io
n
s
,
a
s
s
e
s
s
i
n
g
t
h
e
i
r
ef
f
e
c
t
iv
en
e
s
s
i
n
m
a
i
n
t
a
in
i
n
g
f
r
eq
u
en
c
y
s
t
a
b
i
l
it
y
.
T
h
e
f
o
llo
win
g
s
ec
tio
n
s
o
f
th
i
s
wo
r
k
ar
e
s
tr
u
ctu
r
ed
as
f
o
llo
ws:
i)
S
ec
tio
n
2
p
r
o
v
id
es
th
e
th
eo
r
etica
l
b
ac
k
g
r
o
u
n
d
,
co
v
e
r
in
g
th
e
r
o
l
e
o
f
in
er
tia
in
p
o
wer
s
y
s
tem
s
tab
ilit
y
an
d
th
e
co
n
ce
p
t
o
f
v
ir
tu
al
in
er
tia
;
ii)
Sectio
n
3
p
r
esen
ts
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
,
in
cl
u
d
in
g
th
e
im
p
lem
en
tatio
n
o
f
ad
a
p
tiv
e
v
ir
tu
al
in
er
tia,
p
ar
am
eter
s
elec
tio
n
,
an
d
th
e
d
esig
n
o
f
m
e
m
b
er
s
h
ip
f
u
n
cti
o
n
s
f
o
r
th
e
f
u
zz
y
l
o
g
ic
co
n
tr
o
ller
;
iii)
Sectio
n
4
d
is
cu
s
s
es
th
e
r
esu
lts
o
b
tain
ed
f
r
o
m
s
im
u
latio
n
s
;
iv
)
S
ec
tio
n
5
p
r
o
v
id
es
a
d
etailed
d
is
cu
s
s
i
o
n
an
d
a
n
aly
s
is
o
f
th
e
f
in
d
in
g
s
;
f
in
ally
,
v
)
Sectio
n
6
s
u
m
m
ar
izes k
e
y
co
n
clu
s
io
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
F
u
z
z
y
lo
g
ic
-
b
a
s
ed
a
d
a
p
tive
vi
r
tu
a
l in
erti
a
co
n
tr
o
l fo
r
en
h
a
n
cin
g
fr
eq
u
en
cy
…
(
Oma
r
B
o
u
t
fa
r
jo
u
te
)
2007
2.
T
H
E
O
R
E
T
I
CA
L
B
ACK
G
R
O
UND
2
.
1
.
T
he
ro
le
o
f
inert
ia
in po
wer
s
y
s
t
em
s
t
a
bil
it
y
I
n
p
o
we
r
s
y
s
tem
s
,
in
er
tia
r
ef
e
r
s
to
th
e
r
esis
tan
ce
ag
ain
s
t
ch
an
g
es
in
f
r
e
q
u
en
c
y
.
I
t'
s
d
ir
ec
tly
lin
k
ed
t
o
th
e
r
o
tatin
g
m
ass
o
f
g
e
n
er
ato
r
s
co
n
n
ec
ted
to
t
h
e
g
r
id
,
s
u
ch
as
tu
r
b
in
es
in
tr
ad
itio
n
al
p
o
w
er
p
lan
ts
[
1
8
]
,
[
1
9
]
.
A
h
ig
h
er
in
e
r
tia
co
n
s
tan
t
s
ig
n
if
ies
a
s
lo
wer
ad
ju
s
tm
en
t
to
f
r
eq
u
e
n
cy
d
e
v
iatio
n
s
b
u
t
als
o
a
lar
g
er
j
u
m
p
in
f
r
eq
u
e
n
cy
f
o
llo
win
g
a
d
is
tu
r
b
an
ce
in
th
e
s
y
s
tem
's
b
alan
ce
b
etwe
en
p
o
wer
g
en
e
r
atio
n
an
d
co
n
s
u
m
p
tio
n
,
as
s
h
o
wn
in
Fig
u
r
e
2
[
2
0
]
.
Fig
u
r
e
2
.
Po
wer
g
en
er
atio
n
an
d
lo
ad
b
alan
ce
T
h
e
g
r
o
u
p
tu
r
b
i
n
e
-
s
y
n
ch
r
o
n
o
u
s
g
en
e
r
ato
r
is
th
e
f
o
u
n
d
a
tio
n
o
f
all
co
n
v
en
tio
n
al
p
o
wer
p
lan
ts
,
in
clu
d
in
g
n
u
clea
r
,
h
y
d
r
o
,
an
d
th
er
m
al
o
n
es.
I
t
r
o
tates
as
a
r
esu
lt
o
f
two
o
p
p
o
s
in
g
to
r
q
u
es
,
th
e
m
ec
h
a
n
ical
to
r
q
u
e
T
m
o
f
th
e
t
u
r
b
in
e
a
n
d
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
T
e
o
f
th
e
s
y
n
c
h
r
o
n
o
u
s
g
en
e
r
at
o
r
.
T
h
e
m
ec
h
an
ical
p
o
wer
Pm
g
en
er
ated
b
y
f
o
s
s
il
f
u
el
f
o
r
co
n
v
en
tio
n
al
p
o
wer
p
lan
ts
,
wh
ich
p
o
wer
s
th
e
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
,
r
ep
r
esen
ts
th
e
f
ir
s
t to
r
q
u
e,
an
d
th
e
p
o
wer
d
em
an
d
o
f
th
e
elec
tr
ical
g
r
id
lo
ad
r
ep
r
esen
ts
th
e
s
ec
o
n
d
to
r
q
u
e
[
2
1
]
,
ac
co
r
d
in
g
to
(
1
)
.
−
=
−
(
1
)
Sin
ce
th
e
tu
r
b
in
e
-
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
s
y
s
tem
r
ep
r
esen
ts
a
co
n
tin
u
o
u
s
ly
r
o
tatin
g
m
ass
,
it
s
to
r
e
s
k
in
etic
en
er
g
y
,
d
e
n
o
ted
as
K
in
etic
.
=
1
2
2
(
2
)
W
h
er
e
J
d
en
o
tes
th
e
m
o
m
en
t
o
f
i
n
er
tia
o
f
th
e
s
y
s
tem
an
d
r
ep
r
esen
ts
th
e
r
o
to
r
s
p
ee
d
,
wh
ich
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
th
e
p
o
we
r
g
r
i
d
f
r
eq
u
e
n
cy
.
Acc
o
r
d
in
g
to
(
3
)
,
th
e
k
in
etic
en
er
g
y
s
to
r
ed
in
th
e
r
o
tatin
g
m
ass
is
r
elea
s
ed
wh
en
th
er
e
is
an
im
b
alan
ce
b
etwe
en
p
o
wer
g
en
e
r
at
io
n
an
d
co
n
s
u
m
p
tio
n
[
2
1
]
.
=
−
(
3
)
I
n
th
e
p
e
r
-
u
n
it
s
y
s
tem
,
th
e
co
r
r
esp
o
n
d
in
g
eq
u
ati
o
n
ca
n
b
e
r
e
f
o
r
m
u
lated
as
(
4
)
.
=
−
2
.
.
(
4
)
W
h
er
e
H
d
en
o
tes
th
e
in
er
tia
co
n
s
tan
t,
ch
ar
ac
ter
izin
g
th
e
e
n
er
g
y
s
to
r
ed
in
t
h
e
r
o
tatin
g
m
ass
es
o
f
th
e
p
o
wer
s
y
s
tem
,
as in
(
5
)
.
=
=
1
2
.
.
²
(
5
)
T
h
e
d
er
i
v
ativ
e
d
/
dt
d
en
o
tes
t
h
e
r
ate
o
f
ch
an
g
e
o
f
f
r
eq
u
e
n
cy
R
o
C
o
F
in
th
e
p
o
wer
s
y
s
tem
.
I
t
r
e
f
lects
th
e
d
y
n
am
ic
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
to
im
b
alan
ce
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etwe
en
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ical
p
o
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p
u
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an
d
elec
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ical
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o
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u
tp
u
t
,
ess
en
tially
,
s
u
p
p
ly
an
d
d
em
a
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d
.
T
h
is
r
ate
is
in
tr
in
s
ically
l
in
k
ed
to
th
e
s
y
s
tem
’
s
in
er
tia
co
n
s
tan
t
H
,
wh
ich
g
o
v
er
n
s
h
o
w
s
ev
er
ely
f
r
eq
u
e
n
cy
is
af
f
ec
ted
d
u
r
in
g
d
is
tu
r
b
an
ce
s
.
A
p
o
wer
s
y
s
tem
with
h
ig
h
er
in
er
tia
will
ex
h
ib
it a
s
lo
wer
f
r
e
q
u
en
c
y
d
ec
lin
e,
th
er
eb
y
en
h
a
n
cin
g
its
s
tab
ilit
y
d
u
r
in
g
s
u
ch
e
v
en
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
200
5
-
2
0
1
6
2008
2
.
2
.
T
he
co
ncept
o
f
v
irt
ua
l i
nert
ia
Vir
tu
al
in
er
tia
is
a
co
n
tr
o
l
t
ec
h
n
iq
u
e
d
esig
n
ed
to
em
u
lat
e
th
e
in
er
tia
o
f
t
r
ad
itio
n
al
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
s
in
in
v
er
te
r
-
b
ased
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
[
2
2
]
.
As
th
e
p
en
etr
atio
n
o
f
R
E
Ss
in
cr
ea
s
es,
th
e
o
v
er
all
in
er
tia
o
f
th
e
p
o
wer
s
y
s
tem
d
ec
r
ea
s
es,
co
m
p
r
o
m
is
in
g
g
r
i
d
s
tab
ilit
y
an
d
r
eliab
ilit
y
[
2
3
]
.
VI
-
b
ased
in
v
er
ter
s
,
in
clu
d
in
g
VSM
[
2
4
]
,
v
ir
tu
a
l
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
s
(
VSGs
)
[
2
5
]
,
an
d
s
y
n
ch
r
o
n
v
er
ter
s
,
ad
d
r
ess
th
is
ch
allen
g
e
b
y
m
ath
em
atica
lly
em
u
latin
g
th
e
b
eh
av
i
o
r
o
f
s
y
n
ch
r
o
n
o
u
s
g
e
n
er
ato
r
s
th
r
o
u
g
h
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
PW
M)
co
n
tr
o
ller
s
[
2
3
]
.
T
h
e
im
p
lem
en
tatio
n
o
f
VI
co
n
tr
o
l
h
as
b
ee
n
s
h
o
wn
to
en
h
an
ce
f
r
e
q
u
en
c
y
s
tab
ilit
y
in
in
ter
co
n
n
ec
ted
p
o
wer
s
y
s
tem
s
with
h
ig
h
R
E
S
p
en
etr
atio
n
[
2
6
]
.
Var
io
u
s
VI
co
n
tr
o
l
to
p
o
lo
g
ies
ex
is
t,
an
d
th
eir
s
u
itab
ilit
y
d
ep
en
d
s
o
n
th
e
s
p
ec
if
ic
s
y
s
te
m
co
n
tr
o
l
ar
ch
itectu
r
e
an
d
th
e
d
esire
d
lev
el
o
f
r
ep
licatio
n
o
f
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
d
y
n
am
ics
[
2
7
]
.
W
h
ile
VI
tech
n
iq
u
es
o
f
f
er
s
ig
n
if
ican
t
p
r
o
m
is
e
f
o
r
m
ain
tain
in
g
g
r
id
s
tab
ilit
y
in
h
ig
h
-
R
E
S
g
r
id
s
,
ch
allen
g
es
r
e
m
ain
r
eg
ar
d
in
g
s
y
s
tem
-
lev
el
i
n
teg
r
atio
n
.
Fu
r
th
er
r
esear
ch
is
n
ee
d
e
d
to
a
d
d
r
ess
t
h
ese
in
teg
r
atio
n
ch
allen
g
es
an
d
o
p
tim
ize
VI
co
n
t
r
o
l
s
tr
ateg
i
es
f
o
r
d
if
f
er
en
t g
r
id
s
ce
n
ar
io
s
[
2
7
]
.
T
o
ad
d
r
ess
th
e
ch
allen
g
e
o
f
d
ec
r
ea
s
in
g
in
er
tia
with
in
cr
ea
s
i
n
g
r
en
ewa
b
le
en
er
g
y
p
en
etr
ati
o
n
,
v
ir
tu
al
in
er
tia
o
f
f
e
r
s
s
ig
n
if
ican
t
b
e
n
ef
its
f
o
r
p
o
wer
s
y
s
tem
s
.
VI
-
b
as
ed
in
v
e
r
ter
s
,
in
clu
d
in
g
VSM,
VSG
,
an
d
s
y
n
ch
r
o
n
v
er
ter
s
,
c
an
e
m
u
late
th
e
b
eh
av
i
o
r
o
f
tr
ad
itio
n
al
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
s
.
T
h
i
s
em
u
latio
n
h
elp
s
m
itig
ate
f
r
eq
u
en
cy
in
s
tab
ilit
y
ca
u
s
ed
b
y
th
e
lack
o
f
i
n
h
er
en
t
in
er
tia
in
s
o
lar
a
n
d
win
d
p
o
w
er
s
y
s
tem
s
[
2
3
]
.
VI
d
ev
ices
ac
h
iev
e
th
is
b
y
p
r
o
v
id
in
g
a
f
aster
f
r
eq
u
en
cy
r
esp
o
n
s
e
an
d
m
o
r
e
e
f
f
ec
tiv
e
d
is
tu
r
b
an
ce
m
itig
atio
n
co
m
p
ar
ed
to
tr
a
d
itio
n
al
d
r
o
o
p
co
n
tr
o
l.
Ad
d
itio
n
ally
,
VI
h
elp
s
s
lo
w
d
o
wn
th
e
R
o
C
o
F,
p
r
ev
en
tin
g
r
a
p
id
f
lu
ctu
atio
n
s
th
at
c
o
u
ld
lead
t
o
g
r
id
in
s
tab
ilit
y
[
2
8
]
.
VI
ca
n
b
e
im
p
lem
en
ted
th
r
o
u
g
h
g
r
id
-
co
n
n
ec
te
d
p
o
wer
co
n
v
er
ter
s
,
u
tili
zin
g
e
n
er
g
y
s
to
r
ed
in
DC
-
lin
k
ca
p
ac
ito
r
s
to
em
u
late
in
er
tia
with
o
u
t
r
eq
u
ir
in
g
h
a
r
d
war
e
m
o
d
if
icatio
n
s
[
2
9
]
.
Var
io
u
s
VI
-
b
ased
in
v
er
ter
s
y
s
tem
s
h
av
e
b
ee
n
d
e
v
elo
p
e
d
,
a
n
d
s
tu
d
ies
s
h
o
w
th
ey
ca
n
s
ig
n
if
ican
tly
im
p
r
o
v
e
f
r
eq
u
e
n
cy
s
tab
ilit
y
,
with
u
p
to
a
5
0
%
im
p
r
o
v
em
e
n
t
in
R
o
C
o
F
[
2
9
]
.
As
r
e
n
ewa
b
le
en
er
g
y
p
e
n
etr
atio
n
in
cr
ea
s
es
g
lo
b
ally
,
VI
s
tr
ateg
ies
ar
e
b
ec
o
m
in
g
in
cr
ea
s
in
g
ly
cr
u
cial
f
o
r
m
ain
tain
in
g
p
o
wer
s
y
s
tem
s
tab
ilit
y
an
d
r
eliab
ilit
y
[
3
0
]
.
T
h
e
in
er
tial
r
esp
o
n
s
e
is
ess
en
tial
f
o
r
m
ain
tain
in
g
f
r
e
q
u
en
c
y
s
tab
ilit
y
in
s
y
s
tem
s
with
lo
w
r
o
tatio
n
al
in
er
tia,
s
u
ch
as
th
o
s
e
d
o
m
in
ated
b
y
p
o
wer
elec
tr
o
n
ic
in
ter
f
a
ce
s
.
B
y
co
u
n
ter
in
g
r
ap
id
f
r
e
q
u
en
cy
f
lu
ctu
atio
n
s
,
v
ir
tu
al
in
er
tia
h
elp
s
p
r
ev
e
n
t
ab
r
u
p
t
ch
a
n
g
es
th
at
co
u
ld
d
estab
ilize
th
e
g
r
id
[
3
1
]
.
I
n
co
n
tr
ast,
d
am
p
in
g
m
ec
h
an
is
m
s
ar
e
d
esig
n
ed
to
atten
u
ate
o
s
cillatio
n
s
in
th
e
s
y
s
tem
f
r
e
q
u
en
c
y
f
o
llo
win
g
d
is
tu
r
b
an
ce
s
.
T
h
e
d
am
p
in
g
ef
f
ec
t
en
s
u
r
es
th
at
th
e
s
y
s
tem
r
etu
r
n
s
s
m
o
o
th
ly
to
its
s
tead
y
-
s
tate
o
p
er
atin
g
p
o
in
t.
W
h
ile
v
ir
tu
al
in
er
tia
ad
d
r
ess
es
th
e
in
itial
r
esp
o
n
s
e
to
f
r
eq
u
e
n
cy
tr
a
n
s
ien
ts
,
d
am
p
in
g
p
r
o
v
i
d
es
lo
n
g
-
t
er
m
s
tab
ilit
y
[
3
2
]
.
T
o
g
eth
er
,
th
ese
m
ec
h
an
is
m
s
ar
e
cr
u
cial
f
o
r
en
h
a
n
cin
g
t
h
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
f
m
o
d
er
n
p
o
wer
s
y
s
tem
s
,
p
ar
ticu
lar
ly
th
o
s
e
with
h
ig
h
p
e
n
etr
atio
n
o
f
r
en
ewa
b
le
e
n
er
g
y
r
eso
u
r
ce
s
,
as illu
s
tr
ated
in
(
3
)
.
2H
d
ω
dt
=
P
r
ef
−
P
ω
−
K
d
(
ω
−
ω
r
ef
)
(
6
)
W
h
er
e:
-
P a
n
d
P
ref
ar
e
th
e
m
ea
s
u
r
e
d
ac
t
iv
e
p
o
wer
a
n
d
r
e
f
er
en
ce
ac
tiv
e
p
o
wer
.
-
an
d
ref
d
e
n
o
te
th
e
m
ea
s
u
r
e
d
an
d
r
ef
er
en
ce
f
r
eq
u
en
cies,
r
esp
ec
tiv
ely
.
-
H
an
d
K
d
d
en
o
tin
g
th
e
in
er
tia
an
d
d
am
p
in
g
c
o
n
s
tan
ts
,
r
esp
ec
tiv
ely
.
3.
M
E
T
H
O
D
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
f
o
r
im
p
lem
en
tin
g
v
ir
tu
al
in
er
t
ia
in
v
o
lv
es
a
VSI
co
n
tr
o
l
s
ch
em
e
with
in
n
er
an
d
o
u
ter
co
n
tr
o
l lo
o
p
s
.
T
h
e
o
u
ter
lo
o
p
m
an
a
g
es a
ctiv
e
an
d
r
ea
ctiv
e
p
o
we
r
r
ef
er
e
n
ce
s
,
ad
ju
s
tin
g
v
o
ltag
e
an
d
cu
r
r
en
t
s
etp
o
in
ts
b
ased
o
n
p
o
wer
m
ea
s
u
r
em
e
n
ts
.
T
h
es
e
s
etp
o
in
ts
ar
e
tr
ac
k
ed
b
y
t
h
e
in
n
er
lo
o
p
,
wh
ich
in
clu
d
es
v
o
ltag
e
an
d
c
u
r
r
en
t
c
o
n
tr
o
ller
s
,
e
n
s
u
r
in
g
ac
cu
r
ate
o
u
tp
u
t.
A
n
ad
a
p
tiv
e
v
ir
tu
al
in
e
r
tia
s
tr
ateg
y
,
b
ased
o
n
f
u
zz
y
lo
g
ic,
d
y
n
am
ically
a
d
ju
s
ts
th
e
in
er
tia
co
n
s
tan
t
u
s
i
n
g
r
ea
l
-
tim
e
m
ea
s
u
r
em
e
n
ts
o
f
s
y
s
tem
f
r
eq
u
en
cy
an
d
th
e
R
o
C
o
F.
T
h
is
ap
p
r
o
ac
h
,
im
p
lem
en
ted
in
MA
T
L
AB
/
Simu
lin
k
,
en
h
an
ce
s
s
y
s
tem
s
t
ab
ilit
y
co
m
p
ar
ed
to
f
ix
ed
v
ir
t
u
al
in
er
tia
m
eth
o
d
s
.
T
h
e
h
ier
ar
ch
ical
co
n
tr
o
l
ar
ch
i
tectu
r
e
s
h
o
wn
in
Fig
u
r
e
3
,
wh
er
e
th
e
o
u
ter
co
n
tr
o
l
lo
o
p
is
r
esp
o
n
s
ib
le
f
o
r
r
eg
u
latin
g
ac
tiv
e
a
n
d
r
ea
c
tiv
e
p
o
wer
.
T
h
e
ac
tiv
e
p
o
wer
co
n
tr
o
ller
(
APC
)
m
an
a
g
es
th
e
s
y
s
tem
'
s
p
o
wer
o
u
tp
u
t
b
y
r
ec
ei
v
in
g
a
r
ef
er
e
n
ce
f
r
eq
u
e
n
cy
ref
,
p
o
wer
P
ref
,
an
d
th
en
ad
ju
s
tin
g
th
e
p
h
ase
an
g
le
θ,
an
d
f
r
eq
u
e
n
cy
,
ac
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atch
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tr
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u
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u
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,
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Fig
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.
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5
.
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tia
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ased
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ller
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I
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No
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3
,
Sep
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20
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u
r
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ased
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wer
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3
.
2
.
P
a
ra
m
et
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elec
t
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E
x
p
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tal
s
tu
d
ies h
av
e
s
h
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wn
th
at
ch
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s
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v
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3
s
ec
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es a
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etwe
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tem
s
tab
ilit
y
an
d
d
y
n
a
m
ic
p
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f
o
r
m
an
ce
[
3
3
]
,
p
r
o
v
id
ed
it
r
em
ain
s
ab
o
v
e
th
e
m
in
im
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esh
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eq
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ir
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o
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ad
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ate
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r
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u
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tem
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eq
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ir
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ile
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a
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ilit
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ase
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f
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7
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th
e
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b
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ated
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tem
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0
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th
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s
tem
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eq
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en
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y
T
h
e
o
b
jectiv
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o
f
t
h
e
f
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n
g
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tio
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t
a
co
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o
ller
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ased
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n
ad
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f
u
zz
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ic,
with
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r
eq
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e
n
cy
an
d
R
OC
OF
a
s
in
p
u
ts
,
an
d
th
e
v
ir
tu
al
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n
s
tan
t
H
a
s
th
e
o
u
tp
u
t.
T
h
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
an
d
r
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les g
o
v
er
n
in
g
th
e
s
y
s
tem
will b
e
d
escr
ib
ed
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th
e
f
o
ll
o
win
g
s
ec
tio
n
s
.
3
.
3
.
Desig
n o
f
f
un
ct
io
n o
f
f
u
zz
y
lo
g
ic
co
ntr
o
ller
T
h
e
ef
f
ec
tiv
e
n
ess
o
f
t
h
e
p
r
o
p
o
s
ed
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
h
ea
v
ily
r
elies
o
n
th
e
p
r
o
p
er
s
elec
tio
n
o
f
f
u
zz
y
r
u
les
[3
4
]
.
I
n
th
e
d
esig
n
ed
co
n
tr
o
ller
,
th
e
s
y
s
tem
'
s
f
r
eq
u
en
c
y
r
esp
o
n
s
e
f
o
llo
w
s
an
u
n
d
er
d
am
p
ed
b
eh
av
io
r
.
As
d
ep
icted
in
th
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
Fig
u
r
e
7
(
a
)
,
f
r
eq
u
e
n
cy
d
e
v
iatio
n
s
ar
e
ca
teg
o
r
ized
in
t
o
th
r
ee
r
eg
io
n
s
:
L
o
w,
r
ep
r
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tin
g
f
r
eq
u
e
n
cies
b
elo
w
th
e
n
o
m
in
al
r
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g
e;
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m
in
al,
c
o
v
er
in
g
th
e
s
tan
d
ar
d
o
p
er
atin
g
f
r
eq
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en
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;
a
n
d
Hig
h
,
in
d
icatin
g
f
r
eq
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en
c
ies
ex
ce
ed
in
g
th
e
n
o
m
in
al
v
alu
e,
t
h
is
class
if
icatio
n
allo
ws
th
e
co
n
tr
o
ller
to
ad
a
p
tiv
ely
ad
ju
s
t
v
ir
tu
al
in
er
tia
to
m
itig
ate
f
r
eq
u
en
cy
d
ev
iatio
n
s
an
d
en
h
a
n
ce
s
y
s
tem
s
tab
ilit
y
.
Fig
u
r
e
s
7
(
b
)
an
d
7
(
c
)
illu
s
tr
ates
th
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
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f
o
r
b
o
th
th
e
R
o
C
o
F
an
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v
ir
tu
al
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h
ig
h
lig
h
tin
g
th
e
d
is
tr
ib
u
tio
n
o
f
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
u
s
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n
th
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f
u
zz
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ic
-
b
ased
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n
tr
o
l a
p
p
r
o
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h
.
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h
e
f
u
zz
y
r
u
les
ar
e
c
o
n
s
tr
u
ct
ed
to
in
ject
h
ig
h
er
v
i
r
tu
al
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er
tia
d
u
r
in
g
e
x
tr
em
e
f
r
eq
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e
n
cy
d
ev
iatio
n
s
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PH
an
d
NH
r
eg
io
n
s
)
,
wh
ich
h
elp
s
s
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w
th
e
r
ate
o
f
ch
an
g
e
an
d
s
tab
ilize
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r
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n
cy
.
C
o
n
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er
s
ely
,
lo
wer
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ap
p
lied
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en
th
e
f
r
e
q
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en
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k
t
o
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s
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m
in
al
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alu
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win
g
f
o
r
q
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r
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o
v
er
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h
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p
r
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h
en
s
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r
e
s
th
at
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ir
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r
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I
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2
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8
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4
I
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t J Po
w
E
lec
&
Dr
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s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
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20
25
:
200
5
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2012
4.
RE
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p
r
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ip
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e
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er
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ig
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ize
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r
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o
r
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er
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u
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er
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b
r
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p
t
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e
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.
Fig
u
r
e
9
illu
s
tr
ates
th
e
r
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o
t
m
ea
n
s
q
u
ar
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(
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MS)
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er
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lied
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ilit
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n
am
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ile
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ased
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ilit
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o
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e
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Fig
u
r
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.
Fre
q
u
en
cy
m
ea
s
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r
e
m
en
t o
f
f
ix
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r
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VSI
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r
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d
ad
a
p
tiv
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in
er
tia
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o
n
tr
o
ller
VSI
(
b
lu
e)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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lec
&
Dr
i Sy
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I
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N:
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2013
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u
r
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.
Vo
ltag
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m
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s
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r
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e
n
t o
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f
i
x
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VSI
(
r
ed
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n
d
ad
ap
tiv
e
i
n
er
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co
n
tr
o
ller
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SI
(
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lu
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Fig
u
r
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1
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5.
DIS
CU
SS
I
O
N
T
h
e
r
ap
id
g
r
o
wth
an
d
in
te
g
r
atio
n
o
f
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en
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y
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in
m
o
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e
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n
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g
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atica
lly
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esh
ap
i
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h
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n
d
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e
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en
e
r
g
y
g
e
n
er
atio
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d
d
is
tr
ib
u
tio
n
.
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h
is
tr
a
n
s
itio
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,
d
r
iv
en
b
y
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e
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cr
ea
s
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g
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s
e
o
f
in
v
e
r
ter
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b
a
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ed
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eso
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r
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s
u
c
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h
o
t
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y
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d
win
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tu
r
b
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es,
p
r
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b
o
th
o
p
p
o
r
tu
n
ities
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d
ch
allen
g
es
f
o
r
g
r
id
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tab
ilit
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.
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h
e
m
ass
iv
e
in
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r
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o
f
th
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r
en
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le
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o
f
ten
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ter
f
ac
e
d
th
r
o
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g
h
p
o
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elec
tr
o
n
ics
r
at
h
er
th
an
co
n
v
en
tio
n
al
s
y
n
ch
r
o
n
o
u
s
m
ac
h
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es,
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tr
o
d
u
ce
s
a
s
ig
n
if
ican
t
ch
allen
g
e
in
ter
m
s
o
f
s
y
s
tem
in
er
tia.
Un
lik
e
tr
ad
itio
n
al
g
en
e
r
ato
r
s
,
wh
ich
in
h
er
e
n
tly
p
r
o
v
id
e
in
er
tia
th
r
o
u
g
h
th
eir
r
o
tatin
g
m
ass
es,
in
v
er
ter
-
b
as
ed
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en
ewa
b
les
o
f
f
e
r
m
in
im
a
l
o
r
n
o
in
er
tia,
lead
i
n
g
to
a
f
aster
an
d
m
o
r
e
p
r
o
n
o
u
n
ce
d
r
esp
o
n
s
e
to
p
o
wer
im
b
alan
ce
s
in
th
e
g
r
id
.
As
a
r
esu
lt,
f
r
eq
u
en
c
y
s
tab
ilit
y
is
b
ec
o
m
in
g
a
cr
itical
co
n
ce
r
n
,
esp
ec
ially
wh
en
f
ac
e
d
with
s
u
d
d
en
lo
ad
c
h
an
g
es o
r
g
en
er
atio
n
f
lu
ctu
atio
n
s
.
I
n
s
u
ch
lo
w
-
in
e
r
tia
p
o
wer
s
y
s
tem
s
,
th
e
R
o
C
o
F
b
ec
o
m
es
a
k
ey
m
etr
ic
f
o
r
g
r
i
d
s
tab
ilit
y
.
W
h
en
a
p
o
wer
im
b
alan
ce
o
cc
u
r
s
—
wh
eth
er
d
u
e
to
an
in
cr
ea
s
e
in
lo
ad
o
r
a
d
ec
r
ea
s
e
in
g
en
er
atio
n
—
R
o
C
o
F
in
d
icate
s
h
o
w
q
u
ick
ly
th
e
f
r
eq
u
e
n
cy
d
e
v
iates
f
r
o
m
its
n
o
m
in
al
v
alu
e.
A
h
ig
h
R
o
C
o
F
s
u
g
g
ests
th
at
th
e
s
y
s
tem
is
m
o
r
e
v
u
ln
er
ab
le
to
r
ap
id
f
r
e
q
u
en
cy
d
r
o
p
s
,
in
cr
ea
s
in
g
th
e
r
is
k
o
f
in
s
tab
ilit
y
o
r
ev
en
g
r
id
f
ailu
r
es.
As
r
en
ewa
b
le
p
en
etr
atio
n
i
n
cr
ea
s
es,
R
o
C
o
F
is
ev
o
lv
in
g
t
o
b
ec
o
m
e
a
p
r
im
ar
y
p
a
r
am
eter
f
o
r
g
r
id
r
e
q
u
ir
em
en
ts
,
with
g
r
i
d
o
p
er
ato
r
s
ar
o
u
n
d
th
e
wo
r
ld
s
ettin
g
s
tr
icter
lim
its
o
n
R
o
C
o
F
to
en
s
u
r
e
s
ec
u
r
e
o
p
er
atio
n
.
Fo
r
ex
am
p
le,
m
a
n
y
g
r
id
co
d
es
m
an
d
ate
th
at
R
o
C
o
F
s
h
o
u
ld
r
e
m
ain
b
el
o
w
1
to
2
Hz/s
d
u
r
in
g
d
is
tu
r
b
an
ce
s
to
al
lo
w
s
u
f
f
icien
t
tim
e
f
o
r
co
r
r
ec
tiv
e
m
ea
s
u
r
es.
T
h
e
ch
allen
g
e
is
f
u
r
th
er
am
p
lifie
d
in
m
icr
o
g
r
id
s
,
wh
er
e
t
h
e
s
y
s
tem
'
s
r
e
s
ilien
ce
to
f
r
eq
u
e
n
cy
d
is
tu
r
b
a
n
ce
s
is
cr
u
cial.
I
n
th
ese
s
y
s
tem
s
,
th
e
f
r
eq
u
en
cy
d
r
o
p
r
eq
u
ir
e
m
en
t
is
o
f
ten
s
et
to
b
e
with
in
±
0
.
2
Hz
to
±
0
.
5
Hz
u
n
d
er
n
o
r
m
al
o
p
er
atin
g
co
n
d
itio
n
s
a
n
d
m
a
y
allo
w
d
ev
iatio
n
s
o
f
u
p
to
±
1
Hz
d
u
r
in
g
d
is
tu
r
b
an
ce
s
.
W
h
en
th
e
f
r
eq
u
e
n
cy
d
ev
iatio
n
e
x
ce
ed
s
th
ese
lim
its
,
th
e
m
icr
o
g
r
id
em
p
lo
y
s
m
ec
h
an
is
m
s
s
u
ch
as
u
n
d
er
-
f
r
eq
u
en
cy
l
o
ad
s
h
ed
d
in
g
(
UFLS)
to
m
ain
tain
s
y
s
tem
s
tab
ilit
y
.
Fu
r
th
er
m
o
r
e,
R
o
C
o
F
in
m
icr
o
g
r
id
s
is
ty
p
ically
co
n
s
tr
ain
e
d
to
a
r
a
n
g
e
o
f
0
.
5
Hz/s
to
2
Hz/s
f
o
r
s
af
ety
a
n
d
o
p
er
atio
n
al
r
el
iab
ilit
y
,
with
m
o
r
e
co
n
s
er
v
ativ
e
g
r
id
s
o
p
er
atin
g
a
t e
v
en
lo
wer
lim
its
,
ar
o
u
n
d
0
.
1
Hz/s to
0
.
2
Hz/s.
Ad
d
r
ess
in
g
th
ese
ev
o
l
v
in
g
g
r
i
d
r
eq
u
ir
em
en
ts
,
th
is
wo
r
k
f
o
c
u
s
es
o
n
th
e
im
p
lem
en
tatio
n
o
f
ad
ap
tiv
e
v
ir
tu
al
in
er
tia
in
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
s
(
VSI
s
)
to
im
p
r
o
v
e
th
eir
r
esp
o
n
s
e
to
f
r
eq
u
en
cy
n
ad
ir
an
d
R
o
C
o
F.
T
h
e
ad
ap
tiv
e
v
ir
t
u
al
in
er
tia
co
n
tr
o
ller
d
y
n
am
ically
ad
ju
s
ts
th
e
in
er
tia
co
n
s
tan
t
H
in
r
esp
o
n
s
e
to
r
ea
l
-
tim
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
200
5
-
2
0
1
6
2014
m
ea
s
u
r
em
en
ts
o
f
f
r
eq
u
e
n
cy
a
n
d
R
o
C
o
F,
en
ab
lin
g
th
e
s
y
s
te
m
to
p
r
o
v
id
e
ad
d
itio
n
al
in
er
tia
d
u
r
in
g
p
er
i
o
d
s
o
f
s
ig
n
if
ican
t
p
o
wer
im
b
ala
n
ce
.
T
h
r
o
u
g
h
s
im
u
latio
n
s
,
it
was
o
b
s
er
v
ed
th
at
a
d
ap
tiv
e
v
ir
tu
al
in
er
tia
r
ed
u
ce
s
th
e
v
u
ln
er
ab
ilit
y
o
f
VSI
s
to
p
o
wer
im
b
alan
ce
s
,
p
ar
ticu
lar
ly
b
y
m
itig
atin
g
R
o
C
o
F
an
d
m
in
im
izin
g
th
e
f
r
eq
u
e
n
cy
n
ad
ir
.
B
o
th
f
ix
ed
an
d
ad
a
p
tiv
e
v
ir
tu
al
in
er
tia
s
y
s
tem
s
we
r
e
test
ed
u
n
d
er
a
s
ce
n
ar
io
wh
er
e
a
1
0
k
W
VSI
ex
p
er
ien
ce
d
a
s
u
d
d
en
lo
ad
in
cr
ea
s
e
o
f
5
k
W
at
0
.
5
s
ec
o
n
d
s
.
I
n
th
e
ca
s
e
o
f
th
e
VSI
with
ad
ap
tiv
e
in
er
tia
(
r
an
g
in
g
f
r
o
m
0
.
5
to
3
s
ec
o
n
d
s
)
,
th
e
s
y
s
tem
ex
h
ib
ited
a
m
o
r
e
co
n
tr
o
lled
f
r
e
q
u
en
c
y
r
esp
o
n
s
e
with
a
s
h
allo
wer
f
r
eq
u
e
n
cy
n
a
d
ir
an
d
l
o
wer
R
o
C
o
F
co
m
p
ar
ed
to
t
h
e
f
ix
ed
in
er
tia
s
y
s
tem
(
H
=
1
.
5
s
ec
o
n
d
s
)
.
T
h
ese
r
esu
lts
d
em
o
n
s
tr
ate
th
at
in
co
r
p
o
r
atin
g
ad
ap
tiv
e
v
ir
tu
al
in
e
r
tia
ca
n
s
ig
n
if
ican
tly
en
h
an
ce
th
e
r
es
ilien
ce
o
f
in
v
er
ter
-
b
ased
s
y
s
tem
s
b
y
p
r
o
v
i
d
in
g
a
d
y
n
a
m
ic
r
esp
o
n
s
e
to
g
r
id
d
is
tu
r
b
an
ce
s
,
co
n
tr
i
b
u
tin
g
to
i
m
p
r
o
v
e
d
f
r
eq
u
e
n
cy
s
tab
ilit
y
in
lo
w
-
in
er
tia
g
r
id
s
.
T
h
is
s
tu
d
y
alig
n
s
with
o
n
g
o
in
g
ef
f
o
r
ts
to
r
ed
ef
in
e
g
r
id
s
tab
ilit
y
in
th
e
er
a
o
f
h
ig
h
r
en
ewa
b
le
p
en
etr
atio
n
,
p
ar
ticu
lar
ly
as
th
e
f
r
eq
u
en
c
y
n
ad
ir
a
n
d
R
o
C
o
F
b
ec
o
m
e
cr
itical
p
ar
am
eter
s
in
m
ee
tin
g
ev
o
lv
in
g
g
r
id
r
eq
u
ir
em
en
ts
.
B
y
ad
ap
tin
g
th
e
i
n
er
tia
in
r
ea
l
tim
e,
p
o
wer
s
y
s
tem
s
ca
n
b
etter
h
an
d
le
f
lu
ctu
atio
n
s
,
u
ltima
tely
r
e
d
u
ci
n
g
th
e
r
is
k
o
f
in
s
tab
ilit
y
a
n
d
h
elp
in
g
e
n
s
u
r
e
t
h
e
s
ec
u
r
e
o
p
er
a
tio
n
o
f
m
ic
r
o
g
r
i
d
s
an
d
lar
g
e
r
g
r
id
s
alik
e.
6.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
in
v
esti
g
ates
th
e
d
y
n
am
ic
p
er
f
o
r
m
a
n
ce
o
f
two
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
s
(
VSI
s
)
eq
u
ip
p
ed
with
d
if
f
er
en
t
v
ir
tu
al
in
er
tia
c
o
n
tr
o
l
s
tr
ateg
ies
u
n
d
er
a
s
tep
ch
an
g
e
in
lo
ad
.
B
o
th
s
y
s
tem
s
wer
e
d
esig
n
ed
with
id
en
tical
p
ar
am
eter
s
a
n
d
f
ed
id
en
tical
1
0
k
W
lo
ad
s
at
4
0
0
V.
T
h
e
p
r
im
ar
y
d
is
tin
ctio
n
b
etwe
en
th
e
two
s
y
s
tem
s
lie
s
in
th
eir
v
ir
tu
al
in
er
tia
co
n
tr
o
l
ap
p
r
o
ac
h
es.
T
h
e
f
ir
s
t
VSI
em
p
lo
y
ed
a
co
n
v
en
t
io
n
al
f
ix
ed
v
ir
tu
al
in
er
tia
co
n
tr
o
l
s
tr
ateg
y
,
wh
il
e
th
e
s
ec
o
n
d
im
p
lem
en
ted
a
n
ad
ap
tiv
e
v
ir
tu
al
in
e
r
tia
co
n
tr
o
l
s
ch
em
e.
T
h
e
ad
ap
tiv
e
s
tr
ateg
y
d
y
n
am
icall
y
ad
ju
s
ted
th
e
v
ir
tu
al
i
n
er
ti
a
v
alu
e
b
ased
o
n
r
ea
l
-
tim
e
m
ea
s
u
r
em
en
ts
o
f
f
r
eq
u
e
n
cy
an
d
its
d
er
iv
ativ
e.
B
o
th
s
y
s
tem
s
wer
e
s
u
b
jecte
d
to
a
5
0
%
s
tep
in
cr
ea
s
e
in
l
o
ad
to
ass
ess
th
eir
tr
an
s
ien
t r
esp
o
n
s
e
an
d
s
tab
ilit
y
.
T
h
e
f
r
eq
u
en
cy
r
esp
o
n
s
e
o
f
b
o
th
VSI
s
to
th
e
lo
ad
p
e
r
tu
r
b
ati
o
n
s
h
o
ws
a
tr
an
s
ien
t
d
r
o
p
,
as
ex
p
ec
ted
,
d
u
e
to
th
e
in
cr
ea
s
ed
p
o
wer
d
em
an
d
.
Ho
wev
e
r
,
a
n
o
ta
b
le
d
is
p
ar
ity
in
th
eir
d
y
n
am
ic
b
eh
av
io
r
was
o
b
s
er
v
ed
.
T
h
e
VSI
with
t
h
e
a
d
ap
tiv
e
v
ir
tu
al
in
er
tia
e
x
h
ib
ited
a
s
u
p
e
r
io
r
tr
a
n
s
ien
t
r
esp
o
n
s
e.
T
h
e
f
r
e
q
u
en
cy
d
ip
was
less
p
r
o
n
o
u
n
ce
d
,
an
d
th
e
s
y
s
tem
r
etu
r
n
ed
to
th
e
n
o
m
in
al
f
r
e
q
u
en
cy
m
o
r
e
r
ap
id
l
y
with
m
in
im
al
o
s
cillatio
n
s
.
C
o
n
v
er
s
ely
,
th
e
VSI
with
th
e
f
ix
ed
v
ir
tu
al
in
er
tia
d
is
p
lay
ed
a
lar
g
er
f
r
eq
u
e
n
cy
o
v
er
s
h
o
o
t
an
d
a
s
lo
wer
r
ec
o
v
er
y
tim
e.
T
h
e
en
h
a
n
ce
d
p
er
f
o
r
m
an
ce
o
f
th
e
a
d
ap
tiv
e
in
e
r
tia
s
y
s
tem
ca
n
b
e
attr
ib
u
ted
to
its
ab
ilit
y
to
d
y
n
am
ically
ad
ju
s
t th
e
v
ir
tu
al
in
er
tia
v
alu
e
in
r
esp
o
n
s
e
to
ch
an
g
in
g
s
y
s
tem
co
n
d
itio
n
s
.
T
h
i
s
allo
ws
f
o
r
a
m
o
r
e
p
r
ec
is
e
an
d
tailo
r
e
d
d
am
p
in
g
o
f
f
r
eq
u
e
n
cy
o
s
cillatio
n
s
,
th
er
eb
y
im
p
r
o
v
in
g
s
y
s
tem
s
tab
ilit
y
an
d
d
y
n
am
ic
p
er
f
o
r
m
an
ce
.
T
h
e
f
ix
ed
in
er
ti
a
s
y
s
tem
,
o
n
th
e
o
th
er
h
an
d
,
i
s
lim
ited
b
y
a
p
r
e
-
d
eter
m
in
ed
in
er
tia
v
alu
e,
wh
ich
m
ay
n
o
t
b
e
o
p
tim
al
f
o
r
v
ar
y
in
g
lo
ad
c
o
n
d
itio
n
s
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
Om
ar
B
o
u
tf
ar
jo
u
te
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Ham
id
C
h
ek
en
b
ah
✓
✓
✓
✓
✓
✓
Yass
ir
Ma
atao
u
i
✓
✓
✓
✓
✓
✓
R
af
ik
L
asri
✓
✓
✓
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
i
z
a
t
i
o
n
Su
:
Su
p
e
r
v
i
s
i
o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
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