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1.
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v
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io
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s
r
en
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b
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r
eso
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s
[
1
]
.
An
in
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2
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.
B
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[
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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N:
2088
-
8
6
9
4
A
s
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r
ev
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w
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b
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a
n
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(
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2423
A
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aj
o
r
c
au
s
es
o
f
v
o
lta
g
e
in
s
t
ab
ilit
y
,
h
o
we
v
e
r
,
a
r
e
u
n
a
n
ti
cip
at
ed
in
cr
ea
s
es
i
n
l
o
a
d
,
t
h
e
d
estr
u
cti
o
n
o
f
p
o
we
r
s
y
s
te
m
ele
m
e
n
ts
,
a
n
i
m
b
al
an
ce
am
o
n
g
a
cti
v
e
an
d
r
ea
cti
v
e
p
o
w
er
,
as
wel
l
as
th
e
f
ail
u
r
e
o
f
o
n
-
l
o
a
d
ta
p
c
h
a
n
g
i
n
g
tr
an
s
f
o
r
m
e
r
s
.
Ne
tw
o
r
k
e
n
g
i
n
ee
r
s
m
u
s
t b
e
awa
r
e
o
f
h
o
w
n
e
ar
o
r
h
o
w
f
a
r
t
h
e
y
ar
e
f
r
o
m
t
h
e
v
o
lt
ag
e
s
ta
b
i
lit
y
l
im
it i
n
o
r
d
er
t
o
ta
k
e
c
o
r
r
e
cti
v
e
ac
ti
o
n
to
l
ess
e
n
o
r
c
o
m
p
l
et
el
y
r
em
o
v
e
t
h
e
i
m
p
a
ct
o
f
v
o
lt
a
g
e
i
n
s
t
a
b
i
lit
y
f
o
r
p
o
we
r
s
y
s
te
m
n
et
wo
r
k
s
to
o
p
e
r
a
te
s
a
f
el
y
an
d
r
eli
ab
ly
.
A
s
a
r
esu
lt
,
m
o
n
ito
r
i
n
g
a
n
d
ass
ess
i
n
g
v
o
lt
ag
e
s
tab
ilit
y
b
ec
o
m
e
s
i
g
n
i
f
ic
an
tl
y
m
o
r
e
cr
u
c
ial
w
h
il
e
r
u
n
n
i
n
g
a
n
d
o
r
g
a
n
is
i
n
g
t
h
e
p
o
wer
s
y
s
te
m
.
T
h
u
s
,
r
esea
r
c
h
er
s
h
a
v
e
d
em
o
n
s
t
r
a
te
d
a
k
ee
n
in
te
r
est
i
n
th
e
p
r
e
d
ic
ti
o
n
o
f
p
o
we
r
s
y
s
t
em
b
e
h
a
v
i
o
u
r
ass
o
ci
at
ed
wi
th
t
h
e
ass
e
s
s
m
e
n
t
a
n
d
m
o
n
it
o
r
in
g
o
f
v
o
l
ta
g
e
s
t
ab
ili
ty
.
Sev
er
al
m
ec
h
an
is
m
s
an
d
m
eth
o
d
s
h
av
e
b
ee
n
u
s
ed
d
u
r
i
n
g
th
e
p
ast
th
r
ee
d
ec
ad
es
to
p
r
o
p
o
s
e
to
o
ls
an
d
p
r
o
ce
d
u
r
es f
o
r
v
o
ltag
e
s
tab
ilit
y
an
aly
s
is
.
An
aly
tical
m
eth
o
d
s
an
d
o
p
tim
izatio
n
tech
n
iq
u
es
ar
e
th
e
two
p
r
im
ar
y
s
u
b
ca
teg
o
r
ies
o
f
v
o
ltag
e
s
tab
ilit
y
an
aly
s
is
.
Vo
ltag
e
s
tab
ilit
y
an
aly
s
is
h
as
s
tatic
an
d
d
y
n
am
ic
s
u
b
-
b
r
an
ch
es.
T
h
e
aim
s
o
f
th
e
s
tu
d
y
ar
e
to
p
r
es
en
t
an
o
v
e
r
v
iew
o
f
th
e
V
o
lta
g
e
s
tab
ilit
y
o
f
m
icr
o
-
g
r
id
s
in
tr
an
s
m
is
s
io
n
li
n
es
ch
allen
g
es.
T
o
d
em
o
n
s
tr
ate
th
e
u
n
iq
u
en
ess
o
f
s
tatic
v
o
ltag
e
s
tab
ilit
y
ev
alu
atio
n
s
,
s
i
m
u
lati
o
n
test
s
em
p
lo
y
in
g
th
e
J
ac
o
b
ian
m
et
h
o
d
o
lo
g
y
,
v
o
ltag
e
s
en
s
itiv
ity
m
eth
o
d
,
r
e
ac
tiv
e
an
d
ac
tiv
e
lo
s
s
s
en
s
iti
v
ity
tech
n
iq
u
e,
an
d
en
er
g
y
f
u
n
ctio
n
ap
p
r
o
ac
h
wer
e
co
n
tr
asted
.
Un
lik
e
s
tatic
v
o
lt
ag
e
s
tab
ilit
y
an
aly
s
is
ap
p
r
o
ac
h
es,
d
y
n
am
ic
v
o
ltag
e
s
tab
ilit
y
an
aly
s
is
m
eth
o
d
o
lo
g
i
es
h
av
e
n
o
t
b
ee
n
th
o
r
o
u
g
h
ly
cl
ass
if
ied
.
State
v
ar
iab
les
th
at
af
f
ec
t
s
y
s
tem
s
tab
ilit
y
ar
e
u
s
ed
in
s
tab
ilit
y
an
aly
s
is
.
B
ec
au
s
e
th
e
m
icr
o
g
r
id
en
v
ir
o
n
m
en
t
d
ep
en
d
s
m
o
s
tly
o
n
R
E
S
s
,
au
to
n
o
m
o
u
s
p
o
wer
r
eg
u
latio
n
,
a
n
d
lo
ca
lis
ed
p
o
w
er
g
en
er
atio
n
,
it
i
s
p
r
o
jecte
d
th
at
ad
o
p
tin
g
s
m
ar
t
tech
n
o
lo
g
y
wo
u
ld
r
esu
lt
in
ex
p
o
n
e
n
tial
d
ata
u
s
ag
e.
Sm
a
r
t
g
ad
g
ets
ca
p
tu
r
e
s
tate
v
ar
i
ab
les
as
d
ata.
Usi
n
g
is
o
lated
o
r
g
r
id
-
c
o
n
n
ec
te
d
o
p
er
atin
g
m
o
d
es
to
s
er
v
ice
d
i
s
tan
t
en
d
lo
ad
s
is
ea
s
ier
with
a
m
icr
o
g
r
id
.
Dec
o
u
p
le
d
co
n
t
r
o
ller
s
,
s
u
ch
as
th
e
in
s
tan
tan
eo
u
s
r
ea
l/re
ac
tiv
e
p
o
wer
(
PQ)
an
d
d
ir
ec
t
ax
is
/q
u
ad
r
atu
r
e
(
DQ)
ax
is
co
n
tr
o
ller
s
,
ar
e
u
tili
s
ed
in
th
e
g
r
id
-
co
n
n
ec
ted
o
p
e
r
atin
g
m
o
d
e
to
s
y
n
ch
r
o
n
is
e
r
e
n
ewa
b
le
en
e
r
g
y
t
o
th
e
m
ain
g
r
id
.
Sy
n
ch
r
o
n
is
atio
n
in
cl
u
d
es
th
e
u
s
e
o
f
co
n
tr
o
l m
ec
h
a
n
is
m
s
to
m
ain
tain
co
n
s
tan
t v
o
ltag
e
lev
els
an
d
p
h
ase
an
g
les in
p
ar
allel
in
v
er
ter
s
.
T
h
e
ca
p
ac
it
y
o
f
a
m
icr
o
g
r
i
d
to
o
p
er
ate
as
a
n
is
lan
d
is
en
ab
led
b
y
th
e
in
c
r
ea
s
in
g
p
en
etr
atio
n
o
f
R
E
S
s
in
p
o
wer
n
etwo
r
k
s
.
Mo
r
e
p
r
o
ce
s
s
in
g
p
o
wer
is
r
e
q
u
ir
ed
d
u
e
to
th
e
d
y
n
a
m
ics
o
f
th
e
p
ar
allel
-
co
n
n
ec
te
d
in
v
er
ter
s
as
wel
l
as
th
e
m
u
ltip
le
s
y
s
tem
s
tate
v
ar
iab
les em
p
lo
y
ed
in
th
e
s
tab
ilit
y
ass
ess
m
en
t o
f
th
e
is
lan
d
ed
m
icr
o
g
r
id
[
4
]
,
[
5
]
.
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
atic
liter
atu
r
e
r
ev
iews
h
av
e
th
r
ee
m
ai
n
g
o
als
,
th
ey
ar
e
to
in
v
esti
g
ate
th
e
n
ee
d
f
o
r
v
o
ltag
e
s
tab
ilit
y
an
aly
s
is
in
s
m
ar
t
an
d
is
lan
d
m
icr
o
g
r
id
s
,
t
o
in
v
esti
g
ate
v
o
ltag
e
s
tab
ilit
y
u
s
in
g
r
ea
l
-
tim
e
an
d
s
im
u
latio
n
m
eth
o
d
s
,
an
d
u
s
e
of
s
o
f
t
co
m
p
u
tin
g
tech
n
iq
u
es
f
o
r
f
ea
tu
r
e
-
r
ed
u
ce
d
s
tab
ilit
y
an
aly
s
is
o
f
p
ar
allel
in
v
er
ter
s
.
T
h
e
r
est
o
f
th
e
tex
t
i
s
s
tr
u
ctu
r
ed
as:
i)
T
h
e
tech
n
ica
l
asp
ec
ts
o
f
th
e
is
lan
d
ed
m
icr
o
g
r
id
is
ex
p
lain
ed
i
n
s
ec
tio
n
2
;
ii)
P
o
wer
-
s
h
ar
in
g
c
o
n
tr
o
l
in
is
lan
d
e
d
m
icr
o
g
r
id
s
is
co
v
er
ed
i
n
s
ec
tio
n
3
;
iii)
Se
ctio
n
4
p
r
o
v
id
es
an
ex
p
lan
atio
n
o
f
p
ar
allel
in
v
er
t
er
s
an
d
c
o
n
tr
o
ller
s
u
s
ed
f
o
r
v
o
ltag
e
s
tab
ilit
y
an
d
an
aly
s
is
is
ca
r
r
ied
o
u
t
u
s
in
g
s
im
u
latio
n
an
d
e
x
p
er
im
e
n
tal
m
eth
o
d
s
;
iv
)
Sectio
n
5
d
escr
ib
es
v
ar
io
u
s
v
o
lta
g
e
s
tab
ilit
y
an
a
ly
s
is
m
eth
o
d
o
lo
g
ies
an
d
im
p
lem
en
tatio
n
to
o
ls
;
v
)
T
h
e
m
o
s
t
m
o
d
er
n
s
o
f
t
co
m
p
u
tin
g
m
eth
o
d
s
ar
e
co
v
er
e
d
in
s
ec
tio
n
6
;
an
d
v
i)
Sectio
n
7
d
is
cu
s
s
es th
e
o
v
er
all
co
n
clu
s
io
n
o
f
th
e
r
ev
iew
p
ap
er
.
2.
T
E
CH
N
I
CA
L
ASP
E
CT
S O
F
I
SL
AN
DE
D
M
I
CRO
G
RI
D
I
n
th
e
d
er
e
g
u
lated
en
v
ir
o
n
m
en
t
m
ad
e
p
o
s
s
ib
le
b
y
th
e
e
n
t
r
y
o
f
n
u
m
er
o
u
s
d
is
tr
ib
u
tio
n
co
m
p
an
ies
(
DI
SC
OM
S),
d
is
tr
ib
u
ted
g
en
e
r
atio
n
(
DG)
s
y
s
tem
s
ar
e
f
ea
s
i
b
le.
R
u
r
al
elec
tr
if
icatio
n
will
b
e
m
ad
e
p
o
s
s
ib
le
b
y
th
is
lib
er
aliza
tio
n
.
Acc
o
r
d
in
g
to
p
r
ev
io
u
s
r
esear
ch
[
6
]
,
DG
in
s
tallatio
n
s
at
th
e
m
o
m
en
t
ar
e
ac
tu
ally
in
s
o
m
e
way
s
a
r
etu
r
n
to
th
e
ea
r
l
y
d
a
y
s
o
f
elec
tr
if
icatio
n
.
DG
is
n
o
t
a
n
o
v
el
c
o
n
ce
p
t
f
o
r
th
e
p
o
wer
in
d
u
s
tr
ies.
Af
te
r
s
o
m
e
tim
e,
a
n
ew
tech
n
o
lo
g
y
h
as
ev
o
lv
ed
.
T
h
e
em
er
g
en
ce
o
f
DG
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
r
e
ce
n
t
c
h
an
g
es
in
th
e
en
er
g
y
s
ec
to
r
.
T
h
e
co
s
t
o
f
win
d
an
d
s
o
lar
g
en
er
atin
g
is
co
n
tin
u
in
g
to
d
ec
lin
e,
ac
co
r
d
in
g
to
th
e
Fra
n
k
f
u
r
t
Sch
o
o
l
-
UNE
P
C
o
llab
o
r
atin
g
C
en
tr
e's
s
tu
d
y
,
"
Glo
b
al
tr
e
n
d
s
in
r
en
ewa
b
le
en
er
g
y
i
n
v
estme
n
t
2
0
1
5
"
[
7
]
.
C
o
s
t
r
ed
u
ctio
n
s
,
g
o
v
er
n
m
en
t
in
ce
n
tiv
es,
an
d
g
r
o
win
g
p
o
p
u
lar
ity
in
r
ep
lacin
g
f
o
s
s
il
f
u
el
s
o
u
r
ce
s
o
f
en
er
g
y
ar
e
d
r
iv
in
g
th
e
r
ap
id
g
r
o
wth
o
f
th
e
g
l
o
b
al
m
ar
k
et
f
o
r
DG.
Acc
o
r
d
in
g
to
a
r
ec
en
t
Nav
ig
a
n
t
R
esear
ch
an
a
ly
s
is
titl
ed
"Glo
b
al
DG
I
n
s
tallatio
n
Fo
r
ec
asti
n
g
2
0
1
4
-
2
0
2
3
,
"
th
e
g
lo
b
al
in
s
talled
ca
p
ac
ity
o
f
DG
is
p
r
ed
icted
to
in
cr
ea
s
e
f
r
o
m
8
7
.
3
GW
i
n
2
0
1
4
to
1
6
5
.
5
G
W
in
2023
[
8
]
.
Fro
m
$
9
7
b
illi
o
n
in
2
0
1
4
to
ev
en
m
o
r
e
th
an
$
1
8
2
b
illi
o
n
i
n
2
0
2
3
,
it
is
ex
p
ec
ted
th
at
g
lo
b
al
DG
i
n
co
m
e
will
r
is
e.
T
o
d
eliv
er
el
ec
tr
icity
to
k
ey
lo
ca
tio
n
s
,
a
m
i
cr
o
g
r
id
is
m
ad
e
u
p
o
f
DGs,
en
er
g
y
s
to
r
ag
e
d
ev
ice
s
(
E
SDs
)
,
an
d
lo
ca
l
lo
ad
s
.
T
h
e
p
r
im
ar
y
g
o
al
o
f
m
icr
o
g
r
id
(
MG
)
is
to
m
ain
tain
th
e
s
y
s
tem
r
eliab
le
in
th
e
f
ac
e
o
f
m
u
ltip
le
n
etwo
r
k
o
u
ta
g
es.
I
n
th
e
liter
atu
r
e,
th
er
e
ar
e
s
ev
er
al
d
ef
in
itio
n
s
[
9
]
an
d
f
u
n
ctio
n
al
class
if
icatio
n
m
eth
o
d
s
[
1
0
]
f
o
r
MG
s
.
A
m
icr
o
g
r
id
,
ac
co
r
d
in
g
to
th
e
MG
E
x
c
h
an
g
e
Gr
o
u
p
o
f
th
e
US
Dep
ar
tm
en
t
o
f
E
n
er
g
y
,
is
a
s
y
s
tem
co
n
ce
p
t
co
m
p
r
is
ed
o
f
s
ev
er
al
y
et
co
o
r
d
in
ated
l
o
ad
s
a
n
d
g
e
n
er
atin
g
u
n
its
,
as
well
a
s
g
r
id
is
lan
d
in
g
.
I
t
als
o
s
er
v
es
as
a
co
n
tr
o
lled
s
tr
u
ctu
r
e
to
th
e
m
ain
g
r
id
d
esp
ite
r
em
ain
in
g
co
n
s
tr
ain
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2422
-
2
4
3
4
2424
b
y
well
d
ef
in
e
d
elec
tr
ical
b
o
u
n
d
ar
ies.
A
MG
ca
n
c
o
n
n
ec
t
to
an
d
d
is
en
g
ag
e
f
r
o
m
t
h
e
elec
tr
ic
g
r
id
,
allo
win
g
it
to
f
u
n
ctio
n
in
b
o
th
g
r
id
-
tied
a
n
d
in
d
e
p
en
d
e
n
t
m
o
d
es [
1
1
]
.
W
h
en
o
p
er
atin
g
in
g
r
id
-
co
n
n
e
cted
m
o
d
e,
a
p
h
y
s
ical
s
witch
is
af
f
ec
ted
,
co
n
n
ec
tin
g
th
e
m
icr
o
g
r
id
to
th
e
u
tili
ty
g
r
id
.
Sin
ce
th
e
r
e
is
n
o
g
r
id
s
u
p
p
o
r
t
in
is
lan
d
m
o
d
e,
m
icr
o
g
r
id
m
an
ag
e
m
en
t
is
s
u
b
s
tan
tially
m
o
r
e
ch
allen
g
in
g
.
T
h
e
h
o
s
t
u
tili
ty
g
r
id
im
p
o
s
es
th
e
m
icr
o
g
r
id
v
o
ltag
e.
Ho
wev
er
,
a
m
icr
o
g
r
id
'
s
p
o
wer
f
lo
w
is
b
id
ir
ec
tio
n
al,
an
d
wh
en
it is
lin
k
ed
to
t
h
e
ex
ter
n
al
g
r
id
,
th
is
m
ay
s
witch
elec
tr
icity
to
m
ain
tain
a
s
tead
y
s
u
p
p
ly
in
th
e
s
u
r
r
o
u
n
d
in
g
m
icr
o
g
r
id
.
W
h
en
in
is
lan
d
ed
m
o
d
e,
t
h
e
m
icr
o
g
r
id
'
s
p
o
wer
s
o
u
r
ce
m
u
s
t
b
e
ab
le
to
s
u
p
p
ly
th
e
r
eq
u
ir
ed
l
o
ad
.
An
ess
en
tial
an
d
p
o
ten
t
m
icr
o
g
r
id
r
u
n
n
in
g
in
is
lan
d
m
o
d
e
wo
u
l
d
r
ep
r
esen
t
th
e
in
ter
co
n
n
ec
ted
p
h
ase.
Dep
en
d
in
g
o
n
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
,
th
e
m
icr
o
g
r
id
c
o
u
ld
b
e
an
AC
an
d
a
DC
p
o
wer
s
y
s
tem
,
o
r
a
h
y
b
r
i
d
s
y
s
tem
,
with
ea
ch
h
av
in
g
ad
v
an
tag
es
an
d
d
is
ad
v
an
ta
g
es
d
ep
en
d
in
g
o
n
h
o
w
it
is
u
tili
ze
d
.
T
h
er
e
h
av
e
b
ee
n
n
u
m
er
o
u
s
s
tu
d
ies
o
n
th
e
b
en
e
f
its
an
d
d
r
awb
ac
k
s
o
f
b
o
th
D
C
an
d
AC
m
icr
o
g
r
id
s
.
T
h
e
ef
f
icien
cy
o
f
R
E
S
s
is
af
f
ec
ted
b
y
a
v
ar
iety
o
f
v
a
r
iab
les
th
at
s
h
if
t
th
r
o
u
g
h
o
u
t
tim
e.
As
a
r
esu
lt,
th
e
p
er
f
o
r
m
an
c
e
o
f
th
e
m
ic
r
o
g
r
i
d
,
wh
ich
is
d
ep
en
d
e
n
t
o
n
h
o
w
th
ese
r
eso
u
r
ce
s
ar
e
u
s
ed
,
is
also
af
f
ec
ted
.
A
m
icr
o
g
r
id
o
f
f
er
s
a
m
o
r
e
p
r
ac
tical
an
d
d
ep
en
d
a
b
le
ap
p
r
o
ac
h
to
g
e
n
er
ate
p
o
wer
an
d
c
o
n
s
u
m
e
l
ess
n
o
n
r
en
ewa
b
le
en
er
g
y
wh
ile
s
im
u
ltan
eo
u
s
ly
en
h
an
cin
g
th
e
s
tab
ilit
y
,
r
eliab
i
lity
,
h
ig
h
q
u
ality
,
an
d
s
ec
u
r
ity
o
f
co
n
v
en
tio
n
al
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
.
Ho
wev
er
,
co
n
n
ec
tin
g
m
icr
o
g
r
id
s
to
th
e
m
ain
n
etwo
r
k
m
ig
h
t
p
o
s
e
a
v
a
r
iety
o
f
tech
n
ical
an
d
f
in
an
cial
d
if
f
icu
lties
.
Gr
id
-
co
n
n
e
cted
m
icr
o
g
r
id
s
h
av
e
s
ev
er
al
d
is
ad
v
a
n
tag
es,
in
clu
d
in
g
v
o
ltag
e
co
llap
s
e,
s
ig
n
if
ican
t
in
v
estme
n
t,
p
o
o
r
p
o
wer
q
u
alit
y
,
an
d
s
u
b
s
tan
tial
tr
an
s
m
is
s
io
n
lo
s
s
.
MG
s
em
p
lo
y
a
v
ar
iety
o
f
p
r
im
ar
y
m
o
v
er
tech
n
o
lo
g
ies,
i
n
clu
d
in
g
p
h
o
to
v
o
ltaic
o
r
PV
,
f
u
el
ce
lls
,
win
d
m
ills
,
an
d
in
ter
n
al
co
m
b
u
s
tio
n
en
g
in
es
(
I
C
E
)
[
1
2
]
.
Vo
ltag
e
s
o
u
r
ce
in
v
er
ter
s
an
d
s
u
itab
le
co
n
tr
o
ller
s
ar
e
r
eq
u
ir
ed
f
o
r
s
o
lar
p
o
wer
s
y
s
tem
s
,
f
u
el
ce
ll
tech
n
o
lo
g
y
,
en
er
g
y
s
to
r
ag
e
s
y
s
tem
s
,
an
d
win
d
tech
n
o
lo
g
ies
to
e
n
ab
l
e
f
lex
ib
le
o
p
er
atio
n
.
Fro
m
t
h
e
v
iewp
o
in
t
o
f
t
h
e
cu
s
to
m
er
,
a
m
icr
o
g
r
i
d
is
a
g
r
id
s
y
s
tem
th
at
o
f
f
er
s
d
ep
en
d
ab
le,
in
d
ep
en
d
e
n
t,
an
d
h
ig
h
-
q
u
a
lity
elec
tr
icity
.
T
h
e
co
n
s
tr
u
ctio
n
o
f
a
r
eliab
le
f
r
e
q
u
en
cy
an
d
v
o
ltag
e
co
n
tr
o
llin
g
m
ic
r
o
g
r
i
d
s
y
s
tem
r
eq
u
ir
es
th
e
c
o
o
r
d
in
atio
n
o
f
s
ev
er
al
m
icr
op
o
wer
k
in
d
s
.
I
t
is
f
ea
s
ib
le
to
cla
s
s
if
y
th
e
r
esea
r
ch
b
ased
o
n
th
e
tr
ee
d
iag
r
a
m
in
Fig
u
r
e
1
,
wh
ich
an
aly
s
e
s
m
icr
o
g
r
id
co
n
tr
o
l.
T
h
e
co
n
tr
o
l
s
tr
ateg
ies
m
u
s
t
co
n
s
id
er
all
s
y
s
tem
tim
e
s
ca
les.
P
r
im
ar
y
,
s
ec
o
n
d
ar
y
,
an
d
ter
tiar
y
m
icr
o
g
r
i
d
co
n
tr
o
l
lev
els
ar
e
of
th
r
ee
tier
s
,
w
h
er
e
th
e
co
n
tr
o
l
m
eth
o
d
with
o
u
t
co
m
m
u
n
icatio
n
in
d
icate
s
an
in
d
ep
e
n
d
en
t
o
p
e
r
atio
n
o
f
a
m
icr
o
g
r
id
an
d
with
co
m
m
u
n
icatio
n
s
in
d
icate
s
co
o
r
d
i
n
atio
n
o
f
a
m
icr
o
g
r
id
a
n
d
h
o
s
t
n
etwo
r
k
.
I
n
th
e
m
o
d
er
n
p
o
wer
g
r
id
s
,
h
i
er
ar
ch
ical
m
an
a
g
em
en
t
is
wid
ely
u
s
ed
to
c
o
n
tr
o
l
v
o
ltag
e,
f
r
eq
u
e
n
cy
,
a
n
d
m
ain
t
ain
p
o
wer
b
alan
ce
.
Fig
u
r
e
1
.
C
o
n
tr
o
l o
f
m
icr
o
g
r
id
[
1
2
]
B
y
co
m
p
r
eh
en
d
in
g
th
e
im
p
o
r
t
an
t
p
o
in
ts
in
th
is
s
ec
tio
n
T
ab
le
1
d
is
cu
s
s
es
th
e
im
p
o
r
tan
t
to
p
i
cs
an
d
k
ey
p
o
in
ts
f
r
o
m
t
h
e
liter
atu
r
e.
T
h
i
s
s
ec
tio
n
d
is
cu
s
s
es
ab
o
u
t
th
e
d
er
eg
u
lated
en
v
ir
o
n
m
en
t
b
ac
k
g
r
o
u
n
d
,
an
d
th
e
id
ea
ab
o
u
t
t
h
e
g
l
o
b
al
DG
m
ar
k
et
an
d
th
e
ca
p
ac
ity
a
n
d
r
ev
en
u
e
g
r
o
wth
.
Def
i
n
itio
n
o
f
m
icr
o
g
r
id
a
n
d
v
ar
io
u
s
class
if
icatio
n
o
f
m
icr
o
g
r
id
is
d
is
cu
s
s
ed
.
Dif
f
er
en
t
ty
p
es
o
f
m
icr
o
g
r
id
s
an
d
o
p
er
atio
n
m
o
d
es
ar
e
d
etailed
.
Var
iab
les
af
f
ec
tin
g
m
icr
o
g
r
id
ef
f
icien
cy
,
ch
allen
g
es,
co
n
tr
o
l
s
tr
ateg
ies
an
d
cu
s
to
m
er
p
er
s
p
ec
tiv
e
o
f
m
icr
o
g
r
id
is
d
etailed
in
th
is
s
ec
tio
n
.
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
A
s
ystema
tic
r
ev
ie
w
o
n
vo
lta
g
e
s
ta
b
ilit
y
a
n
a
lysi
s
in
s
ma
r
t a
n
d
is
la
n
d
ed
…
(
S
o
w
mya
R
en
u
k
a
B
a
n
g
a
r
i
)
2425
T
ab
le
1
.
T
ec
h
n
ical
asp
ec
ts
o
f
m
icr
o
g
r
id
–
a
s
u
m
m
a
r
y
To
p
i
c
K
e
y
p
o
i
n
t
s
B
a
c
k
g
r
o
u
n
d
I
n
a
d
e
r
e
g
u
l
a
t
e
d
e
n
v
i
r
o
n
m
e
n
t
f
a
c
i
l
i
t
a
t
e
d
b
y
v
a
r
i
o
u
s
D
I
S
C
O
M
S
,
t
h
e
f
e
a
s
i
b
i
l
i
t
y
o
f
D
G
s
y
s
t
e
ms
e
m
e
r
g
e
s,
a
l
l
o
w
i
n
g
f
o
r
r
u
r
a
l
e
l
e
c
t
r
i
f
i
c
a
t
i
o
n
.
D
G
i
n
s
t
a
l
l
a
t
i
o
n
s
h
a
r
k
e
n
b
a
c
k
t
o
e
a
r
l
y
e
l
e
c
t
r
i
f
i
c
a
t
i
o
n
d
a
y
s
a
n
d
r
e
p
r
e
se
n
t
a
si
g
n
i
f
i
c
a
n
t
e
v
o
l
u
t
i
o
n
i
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e
m
o
d
el
o
f
th
e
m
ic
r
o
g
r
i
d
,
th
ese
eq
u
atio
n
s
ar
e
lin
ea
r
ized
ar
o
u
n
d
s
tead
y
-
s
tate
o
p
e
r
atin
g
p
o
in
ts
.
T
h
e
m
ath
em
atica
l
m
o
d
el
is
d
e
r
iv
ed
f
r
o
m
a
n
av
e
r
ag
ed
m
o
d
el,
w
h
ich
y
ield
s
a
s
im
p
ler
s
et
o
f
eq
u
ati
o
n
s
.
T
h
e
lin
ea
r
ized
m
o
d
el
is
u
s
ed
to
co
n
d
u
ct
an
e
ig
en
v
alu
e
an
al
y
s
is
to
ass
es
s
t
h
e
s
y
s
tem
's
s
m
all
-
s
ig
n
al
s
tab
i
lity
.
T
h
e
s
u
g
g
ested
m
icr
o
g
r
id
s
y
s
tem
,
wh
ich
co
n
s
i
s
ts
o
f
two
DE
R
s
with
in
v
er
ter
tech
n
o
lo
g
y
,
p
ass
iv
e
lo
ad
s
,
as
w
ell
as
a
d
i
s
tr
ib
u
tio
n
lin
e,
is
s
im
u
lated
.
T
o
ex
am
in
e
th
e
s
y
s
tem
'
s
d
y
n
am
ic
s
u
n
d
er
lo
ad
p
er
tu
r
b
atio
n
,
an
ex
p
e
r
im
en
tal
test
b
ed
i
s
cr
ea
ted
.
T
o
en
s
u
r
e
th
e
m
ath
e
m
atica
l
m
o
d
el'
s
co
r
r
ec
tn
ess
,
s
im
u
latio
n
,
an
d
h
ar
d
war
e
e
x
p
er
im
en
t
r
esu
lts
ar
e
co
m
p
ar
ed
to
th
o
s
e
a
n
ticip
ated
b
y
th
e
m
o
d
el.
P
a
r
a
l
le
l
i
n
v
e
r
t
e
r
s
wi
t
h
s
t
a
n
d
a
l
o
n
e
A
C
s
u
p
p
l
y
s
y
s
t
e
m
s
[
1
5
]
a
r
e
a
n
a
l
y
z
e
d
f
o
r
s
m
a
l
l
s
i
g
n
a
l
s
ta
b
il
i
t
y
.
B
o
t
h
v
o
l
t
a
g
e
a
n
d
f
r
e
q
u
e
n
c
y
d
r
o
o
p
i
s
d
e
v
e
l
o
p
e
d
t
o
a
n
a
l
y
z
e
t
h
e
s
m
a
l
l
s
i
g
n
a
l
s
t
a
b
i
l
it
y
o
f
t
h
e
s
y
s
t
e
m
.
T
h
e
r
o
o
t
l
o
c
u
s
m
e
t
h
o
d
i
s
u
s
e
d
t
o
a
n
a
l
y
z
e
t
h
e
s
m
a
l
l
s
i
g
n
a
l
s
t
a
b
il
i
t
y
o
f
t
h
e
s
y
s
t
e
m
.
A
s
t
u
d
y
b
y
A
l
e
n
i
u
s
e
t
a
l
.
[
1
6
]
d
e
s
c
r
i
b
e
d
h
o
w
a
n
i
m
p
e
d
a
n
c
e
-
b
a
s
e
d
s
t
a
b
i
l
it
y
c
r
i
t
e
r
i
o
n
i
s
u
s
e
d
t
o
v
e
r
i
f
y
t
h
e
s
t
ab
i
l
i
t
y
o
f
m
a
n
y
p
a
r
a
l
l
e
l
i
n
v
e
r
t
e
r
s
l
i
n
k
e
d
t
o
t
h
e
g
r
i
d
.
U
t
i
li
t
y
-
s
ca
l
e
w
i
n
d
a
n
d
s
o
l
a
r
e
l
ec
t
r
i
c
it
y
g
e
n
e
r
a
t
i
o
n
a
r
e
o
f
t
e
n
w
i
r
e
d
i
n
p
a
r
a
l
l
e
l
t
h
r
e
e
-
p
h
a
s
e
i
n
v
e
r
te
r
s
t
o
t
h
e
e
l
e
c
t
r
i
c
al
g
r
i
d
.
T
h
e
h
a
r
m
o
n
i
c
r
e
s
o
n
a
n
c
e
b
r
o
u
g
h
t
o
n
b
y
i
n
t
e
r
a
c
t
i
o
n
s
b
et
w
ee
n
t
h
e
g
r
i
d
a
n
d
i
n
v
e
r
t
e
r
s
is
o
n
e
o
f
t
h
e
k
e
y
p
r
o
b
l
e
m
s
w
i
t
h
s
u
c
h
g
r
i
d
-
c
o
n
n
e
c
t
e
d
s
y
s
t
em
s
.
T
h
e
i
m
p
e
d
a
n
c
e
-
b
a
s
e
d
s
t
a
b
i
l
i
t
y
c
r
it
e
r
i
a
h
a
v
e
b
e
e
n
a
w
i
d
ely
u
s
e
d
t
e
c
h
n
i
q
u
e
f
o
r
t
h
e
s
t
u
d
y
o
f
t
h
es
e
s
y
s
t
e
m
s
.
T
h
e
c
o
m
p
l
e
x
i
t
y
o
f
t
h
e
s
y
s
t
e
m
a
n
d
t
h
e
d
i
f
f
i
c
u
l
ti
es
i
n
g
e
tt
i
n
g
t
h
e
n
ec
e
s
s
a
r
y
i
m
p
e
d
a
n
c
e
m
e
a
s
u
r
e
m
e
n
ts
,
h
o
w
e
v
e
r
,
m
a
y
r
e
d
u
c
e
t
h
e
a
c
c
u
r
a
c
y
o
f
t
h
e
im
p
e
d
a
n
c
e
-
b
a
s
e
d
t
e
c
h
n
i
q
u
e
i
n
s
y
s
te
m
s
w
i
t
h
m
a
n
y
p
a
r
a
l
l
e
l
i
n
v
e
r
te
r
s
.
T
h
e
c
o
m
b
i
n
at
i
o
n
o
f
p
a
r
a
l
l
e
l
i
n
v
e
r
t
e
r
s
a
n
d
t
h
e
s
t
a
b
il
i
t
y
s
t
u
d
y
o
f
s
u
c
h
g
r
i
d
-
c
o
n
n
e
c
t
e
d
s
y
s
t
e
m
s
a
r
e
c
o
v
e
r
e
d
i
n
t
h
i
s
w
o
r
k
.
T
h
e
m
a
x
im
u
m
n
u
m
b
e
r
o
f
p
a
r
a
l
l
e
l
e
d
i
n
v
e
r
t
e
r
s
t
h
a
t
m
a
y
b
e
u
s
e
d
w
i
t
h
o
u
t
th
e
s
y
s
t
e
m
b
e
c
o
m
i
n
g
u
n
s
t
a
b
l
e
i
s
d
e
f
i
n
e
d
u
s
i
n
g
a
s
t
r
a
ig
h
t
f
o
r
w
a
r
d
a
p
p
r
o
a
c
h
t
h
a
t
is
b
ase
d
o
n
i
m
p
e
d
a
n
c
e
m
e
a
s
u
r
e
m
e
n
ts
.
P
o
w
e
r
h
a
r
d
wa
r
e
-
in
-
t
h
e
-
l
o
o
p
s
e
t
u
p
e
x
p
e
r
i
m
e
n
ta
l
f
i
n
d
i
n
g
s
f
r
o
m
n
e
w
l
y
p
r
o
d
u
c
e
d
a
t
D
NV
G
L
Fl
e
x
i
b
l
e
P
o
w
e
r
G
r
i
d
L
a
b
.
I
m
p
ed
an
ce
-
b
ased
s
tab
ilit
y
s
tu
d
y
em
p
lo
y
in
g
o
f
f
s
h
o
r
e
lo
n
g
ca
b
le
p
ar
allel
in
v
er
ter
s
is
in
tr
o
d
u
c
ed
in
[
1
7
]
.
T
h
is
r
esear
ch
p
r
esen
ts
th
e
s
tab
ilit
y
an
aly
s
is
o
f
a
m
u
ltip
le
o
f
f
s
h
o
r
e
p
a
r
allel
lo
n
g
-
ca
b
le
-
co
n
n
ec
ted
in
v
er
ter
s
(
MO
PLI
)
s
y
s
tem
.
I
t
is
d
em
o
n
s
tr
ated
th
at
th
e
MO
PLI
s
y
s
tem
co
n
s
is
ts
o
f
s
o
m
a
n
y
d
if
f
er
en
t
in
v
er
ter
s
a
n
d
ex
ten
s
iv
e
co
n
n
ec
tio
n
s
,
h
en
ce
d
eter
m
in
in
g
its
s
tab
ilit
y
is
r
ea
lly
d
if
f
icu
lt.
Mo
r
eo
v
er
,
ev
e
n
th
o
u
g
h
th
er
e
ar
e
s
ev
er
al
im
p
ed
an
ce
-
b
ased
s
tab
ilit
y
cr
iter
ia
f
o
r
p
ar
allel
in
v
er
t
er
s
,
th
e
m
ajo
r
ity
o
f
th
e
m
ar
e
f
o
u
n
d
o
n
two
f
alse
p
r
em
is
es
,
th
e
f
i
r
s
t
is
th
at
is
all
in
v
er
ter
s
ar
e
i
d
en
tical
,
a
n
d
t
h
e
s
ec
o
n
d
is
th
at
ca
b
le
ef
f
ec
ts
m
ay
b
e
d
is
r
eg
a
r
d
ed
.
Nev
er
th
eless
,
th
e
ac
tu
al
MO
P
L
I
s
y
s
tem
d
o
es
n
o
t
s
u
p
p
o
r
t
th
e
se
two
h
y
p
o
th
eses
.
T
h
is
s
tu
d
y
in
itially
r
ec
r
ea
tes
th
e
m
o
d
els
o
f
th
e
in
v
er
ter
s
an
d
len
g
th
y
ca
b
les
o
n
e
at
a
tim
e
in
o
r
d
er
to
ad
d
r
ess
th
e
ch
allen
g
e.
A
b
r
o
ad
a
n
d
s
u
cc
in
ct
th
r
ee
-
s
tep
im
p
ed
a
n
c
e
-
b
ased
s
tab
ilit
y
cr
iter
ia
h
as
b
ee
n
g
iv
e
n
f
o
r
th
e
MO
PLI
s
y
s
tem
b
ased
o
n
t
h
e
re
v
i
s
ed
m
o
d
els.
T
h
e
s
u
g
g
ested
cr
iter
io
n
is
n
o
t
o
n
ly
s
tr
aig
h
tf
o
r
war
d
an
d
wo
r
k
ab
le
b
u
t
als
o
co
m
p
letely
tak
es
in
to
co
n
s
id
er
atio
n
th
e
v
ar
iatio
n
s
in
in
v
er
ter
s
a
n
d
t
h
e
ef
f
ec
ts
o
f
wir
es.
D
u
e
to
th
e
r
eq
u
ir
em
en
t
f
o
r
s
o
u
r
ce
lo
a
d
s
u
b
-
s
y
s
tem
an
aly
s
is
,
r
esear
c
h
o
n
im
p
ed
an
ce
-
b
ased
an
d
e
ig
en
v
alu
e
-
b
ased
s
m
all
s
ig
n
al
s
tab
ilit
y
an
aly
s
i
s
ap
p
licatio
n
s
is
co
n
f
in
ed
to
th
e
f
ew
s
tates st
ated
in
[
1
8
]
.
T
h
e
ab
o
v
e
-
m
en
tio
n
ed
r
esear
c
h
lo
o
k
s
at
e
n
h
an
ce
d
im
p
e
d
an
c
e
-
b
ased
co
n
t
r
o
ller
s
f
o
r
p
ar
alle
l
in
v
er
ter
s
r
eg
u
lated
b
o
th
b
y
PQ
-
b
ased
i
m
p
ed
an
ce
an
d
d
r
o
o
p
c
o
n
tr
o
ller
-
b
ased
ap
p
r
o
ac
h
es.
T
h
e
im
p
ed
an
ce
ap
p
r
o
ac
h
is
u
s
ed
b
y
d
o
u
b
le
clo
s
ed
-
l
o
o
p
c
o
n
tr
o
lled
p
ar
allel
in
v
e
r
ter
s
to
an
aly
ze
s
tab
ilit
y
.
Dr
o
o
p
c
o
n
tr
o
ll
er
s
ar
e
th
e
m
o
s
t
u
s
ed
s
y
n
ch
r
o
n
izatio
n
a
p
p
r
o
ac
h
wh
en
is
lan
d
e
d
m
icr
o
g
r
id
s
ar
e
also
co
n
s
id
er
ed
.
As a
s
u
m
m
ar
y
o
f
th
is
s
ec
tio
n
,
a
tab
le
th
at
co
m
p
r
eh
en
d
s
k
ey
p
o
in
ts
o
n
th
e
liter
atu
r
e
s
u
r
v
ey
is
g
iv
en
in
T
a
b
le
2
(
s
ee
Ap
p
en
d
i
x
)
.
4.
P
ARAL
L
E
L
I
NV
E
R
T
E
RS
AND
CO
NT
RO
L
L
E
RS
A
m
icr
o
g
r
id
'
s
p
ar
allel
in
v
er
ter
s
ca
n
b
e
m
an
ag
ed
in
a
v
ar
iety
o
f
way
s
,
in
clu
d
i
n
g
m
aster
/s
lav
e,
cu
r
r
en
t
s
h
ar
in
g
,
d
r
o
o
p
c
o
n
tr
o
l,
v
ir
tu
al
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
(
VSM)
-
b
ased
an
d
v
ir
t
u
al
o
s
cillato
r
co
n
tr
o
l.
T
h
e
d
o
wn
s
id
e
o
f
b
o
th
th
e
m
icr
o
g
r
id
a
n
d
e
x
is
tin
g
s
h
ar
in
g
s
y
s
tem
s
is
th
e
r
eq
u
ir
em
en
t
f
o
r
co
m
m
u
n
icatio
n
n
e
two
r
k
s
.
As
a
r
esu
lt,
th
e
s
y
s
tem
n
o
w
co
n
tain
s
a
s
in
g
le
p
o
in
t o
f
f
ailu
r
e.
T
h
e
VSM
co
n
tr
o
l a
p
p
r
o
ac
h
o
u
t
p
er
f
o
r
m
s
a
tr
ad
itio
n
al
d
r
o
o
p
co
n
tr
o
ller
in
a
v
a
r
iety
o
f
way
s
.
Nev
er
th
eless
,
m
o
s
t
o
f
th
e
VSM
-
b
ased
r
esear
ch
p
u
b
lis
h
ed
in
th
e
liter
atu
r
e
f
o
cu
s
es
o
n
th
e
s
y
s
tem
'
s
ac
tiv
e
p
o
wer
an
d
f
r
e
q
u
en
c
y
ch
a
r
a
cter
is
tics
.
T
h
e
is
o
lated
AC
M
G's
r
ea
ctiv
e
p
o
wer
v
ar
ies
d
u
e
to
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
in
d
u
ctiv
e
lo
ad
.
Dr
o
o
p
co
n
t
r
o
l,
a
cr
u
cial
tech
n
i
q
u
e
f
o
r
th
e
p
a
r
allel
f
u
n
ctio
n
in
g
o
f
in
v
er
te
r
s
,
is
als
o
well
-
ex
p
lain
ed
i
n
[
1
9
]
-
[
2
2
]
.
A
s
tu
d
y
b
y
Ma
ju
m
d
er
et
a
l
.
[
1
9
]
ex
am
in
es
t
h
e
is
s
u
e
o
f
a
d
eq
u
ate
l
o
ad
s
h
a
r
in
g
in
a
s
elf
-
s
u
f
f
icien
t
m
icr
o
g
r
id
.
Un
d
er
wea
k
s
y
s
tem
s
ettin
g
s
,
h
ig
h
g
ain
a
n
g
le
d
r
o
o
p
co
n
t
r
o
l
g
u
ar
a
n
tees
co
r
r
e
ct
lo
ad
d
is
tr
ib
u
tio
n
.
No
n
eth
eless
,
it
h
as
a
d
etr
im
en
tal
ef
f
ec
t
o
n
s
tab
ilit
y
.
T
h
is
d
is
ag
r
ee
m
en
t
is
d
em
o
n
s
tr
ated
u
s
in
g
tim
e
-
d
o
m
ain
s
im
u
latio
n
s
,
eig
en
v
al
u
e
an
aly
s
is
,
an
d
f
r
eq
u
en
cy
-
d
o
m
ai
n
m
o
d
ellin
g
.
I
t
is
s
u
g
g
ested
to
ad
d
a
n
ad
d
itio
n
al
lo
o
p
to
ea
ch
DG
co
n
v
er
ter
'
s
tr
ad
itio
n
al
d
r
o
o
p
c
o
n
tr
o
l
in
o
r
d
e
r
to
s
tab
ilize
th
e
s
y
s
tem
wh
ile
em
p
lo
y
in
g
h
ig
h
an
g
le
d
r
o
o
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
6
9
4
A
s
ystema
tic
r
ev
ie
w
o
n
vo
lta
g
e
s
ta
b
ilit
y
a
n
a
lysi
s
in
s
ma
r
t a
n
d
is
la
n
d
ed
…
(
S
o
w
mya
R
en
u
k
a
B
a
n
g
a
r
i
)
2427
g
ain
s
.
L
o
ca
l
p
o
wer
m
ea
s
u
r
e
m
en
t
an
d
m
o
d
u
latio
n
o
f
ea
c
h
co
n
v
er
ter
'
s
d
-
ax
is
v
o
ltag
e
r
e
f
er
en
ce
s
er
v
e
as
th
e
f
o
u
n
d
atio
n
f
o
r
co
n
tr
o
l
l
o
o
p
s
.
T
h
e
ch
allen
g
e
o
f
c
o
o
r
d
in
ated
d
esig
n
o
f
s
u
p
p
lem
en
tal
c
o
n
tr
o
l
lo
o
p
s
f
o
r
ea
ch
DG
is
s
tated
a
s
an
ev
o
lu
tio
n
ar
y
p
r
o
b
lem
th
at
h
a
s
to
b
e
s
o
lv
ed
.
I
t
is
d
em
o
n
s
tr
ated
th
at
th
e
s
u
p
p
le
m
en
tal
d
r
o
o
p
co
n
tr
o
l
lo
o
p
s
tab
ilizes th
e
s
y
s
tem
u
n
d
er
v
ar
io
u
s
o
p
er
atin
g
s
itu
atio
n
s
wh
ile
g
u
ar
an
teein
g
ad
e
q
u
ate
l
o
ad
s
h
ar
in
g
.
A
s
tu
d
y
b
y
B
ar
k
lu
n
d
et
a
l
.
[
2
0
]
o
f
f
e
r
s
an
e
n
er
g
y
m
an
a
g
em
en
t
s
y
s
tem
(
E
MS)
f
o
r
a
s
tan
d
alo
n
e
d
r
o
o
p
-
co
n
tr
o
lled
m
ic
r
o
g
r
id
th
at
r
e
g
u
l
ates
th
e
o
u
tp
u
t
p
o
wer
o
f
th
e
g
e
n
er
ato
r
s
to
r
e
d
u
ce
f
u
el
co
n
s
u
m
p
tio
n
an
d
g
u
a
r
an
tee
s
tab
le
o
p
er
atio
n
.
Fre
q
u
e
n
cy
-
d
r
o
o
p
in
c
r
ea
s
es
h
av
e
b
ee
n
d
e
m
o
n
s
tr
ated
to
h
a
v
e
a
c
o
n
s
id
er
ab
le
im
p
ac
t
o
n
s
tab
ilit
y
in
th
ese
m
icr
o
g
r
id
s
in
th
e
p
a
s
t.
I
n
o
r
d
er
to
d
eter
m
in
e
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
ese
f
ac
to
r
s
an
d
s
tab
ilit
y
m
ar
g
in
s
,
s
m
all
-
s
ig
n
al
m
et
h
o
d
s
ar
e
c
o
m
b
in
e
d
with
q
u
alitativ
e
an
aly
s
is
.
T
h
is
en
ab
les
th
e
ir
s
elec
tio
n
to
g
u
ar
a
n
tee
s
tab
ilit
y
.
T
h
e
E
MS
th
e
n
im
p
lem
en
ts
o
p
tim
ized
g
en
e
r
ato
r
o
u
t
p
u
ts
in
r
ea
l
tim
e
b
y
m
o
d
if
y
in
g
th
e
d
r
o
o
p
ch
ar
ac
ter
is
tics
with
in
th
is
r
estr
ictio
n
.
A
m
icr
o
g
r
id
th
e
s
ize
o
f
a
lab
o
r
ato
r
y
co
n
f
ir
m
s
th
e
E
M
S f
u
n
ctio
n
th
r
o
u
g
h
ex
p
er
im
en
tal
r
esu
lts
.
A
s
tu
d
y
b
y
Mo
h
am
ed
a
n
d
E
l
-
Saad
an
y
[
2
1
]
ad
d
r
ess
es
th
e
DG
u
n
its
in
m
icr
o
g
r
id
s
th
at
u
s
e
p
ar
alleled
in
v
er
ter
tech
n
o
lo
g
y
a
n
d
h
a
v
e
lo
w
-
f
r
eq
u
e
n
cy
r
elativ
e
s
tab
ilit
y
is
s
u
es.
I
t
ca
n
b
e
d
em
o
n
s
tr
ated
u
s
in
g
t
h
e
s
m
all
-
s
ig
n
al
d
y
n
am
ics
o
f
a
m
icr
o
g
r
id
th
at
wh
en
th
e
r
eq
u
ir
ed
p
o
wer
o
f
ea
ch
in
v
er
ter
in
cr
ea
s
e
s
,
th
e
lo
w
-
f
r
eq
u
e
n
cy
m
o
d
es
o
f
th
e
p
o
wer
-
s
h
ar
in
g
d
y
n
am
ics
d
r
if
t
t
o
n
ew
p
lace
s
,
s
ig
n
if
ican
tly
af
f
ec
tin
g
t
h
eir
r
el
ativ
e
s
tab
ilit
y
u
n
til
th
ey
f
in
ally
g
iv
e
in
s
tab
ilit
y
.
T
h
is
wo
r
k
p
r
esen
ts
an
a
d
ap
t
iv
e
d
ec
en
tr
alize
d
d
r
o
o
p
co
n
t
r
o
l
ler
o
f
p
ar
alleled
in
v
er
ter
-
b
ased
DG
u
n
its
to
m
ain
tain
p
o
wer
-
s
h
ar
in
g
s
tab
ilit
y
.
T
h
e
s
tatic
d
r
o
o
p
ch
ar
ac
te
r
is
tics
an
d
an
ad
a
p
tiv
e
tr
an
s
ien
t
d
r
o
o
p
f
u
n
ctio
n
s
er
v
e
as
th
e
f
o
u
n
d
atio
n
f
o
r
t
h
e
s
u
g
g
ested
p
o
wer
-
s
h
ar
in
g
tech
n
i
q
u
e.
T
h
e
s
u
g
g
ested
d
r
o
o
p
co
n
tr
o
ller
p
r
o
d
u
ce
s
a
2
-
two
-
d
eg
r
ee
-
of
-
f
r
ee
d
o
m
o
r
D
OF
tu
n
ab
le
co
n
tr
o
ller
as
o
p
p
o
s
ed
to
th
e
1
-
DOF
tu
n
ab
le
co
n
tr
o
ller
p
r
o
d
u
ce
d
b
y
cu
r
r
en
t
d
r
o
o
p
co
n
tr
o
ller
s
.
T
h
e
p
o
wer
-
s
h
ar
i
n
g
c
o
n
tr
o
ller
'
s
o
s
cillato
r
y
m
o
d
es
ca
n
th
en
b
e
d
am
p
e
n
ed
b
y
alter
in
g
t
h
e
d
y
n
am
ic
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
o
wer
-
s
h
ar
in
g
m
ec
h
an
is
m
with
o
u
t
ch
an
g
in
g
th
e
s
tatic
d
r
o
o
p
g
ain
.
T
h
e
tr
an
s
ie
n
t
d
r
o
o
p
g
ain
s
ar
e
ad
ap
tiv
ely
p
lan
n
ed
u
s
in
g
s
m
all
-
s
ig
n
al
an
aly
s
is
o
f
th
e
p
o
wer
-
s
h
ar
in
g
m
ec
h
an
is
m
alo
n
g
th
e
lo
ad
in
g
tr
ajec
to
r
y
o
f
ea
c
h
D
G
u
n
it
to
p
r
o
d
u
ce
th
e
ap
p
r
o
p
r
iate
tr
an
s
ien
t
an
d
s
tead
y
-
s
tate
r
esp
o
n
s
e
wh
ile
ac
co
u
n
tin
g
f
o
r
t
h
e
p
o
wer
m
o
d
es
im
m
ig
r
atio
n
u
n
d
er
v
ar
io
u
s
lo
ad
in
g
s
itu
atio
n
s
.
As
th
e
f
ilter
ed
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
ar
e
u
s
ed
as
in
d
ices
i
n
th
e
g
ain
ad
ap
tio
n
s
ch
em
e,
a
s
tead
y
an
d
s
m
o
o
th
p
o
wer
in
jectio
n
p
er
f
o
r
m
a
n
ce
m
ay
b
e
p
r
o
d
u
ce
d
u
n
d
e
r
v
a
r
io
u
s
lo
ad
in
g
cir
cu
m
s
tan
ce
s
.
T
h
e
s
u
g
g
ested
co
n
tr
o
ller
'
s
ad
ap
tiv
e
n
atu
r
e
p
r
o
v
id
es
ac
tiv
e
d
am
p
en
in
g
o
f
p
o
wer
o
s
cillatio
n
s
u
n
d
er
v
ar
io
u
s
o
p
er
atin
g
s
itu
atio
n
s
,
r
esu
ltin
g
in
a
s
tab
le
an
d
r
eliab
le
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
ar
alleled
i
n
v
er
t
er
s
y
s
tem
.
An
u
n
in
ter
r
u
p
tib
le
p
o
wer
s
u
p
p
ly
(
UPS)
th
at
ca
n
b
e
r
ap
id
ly
ex
ten
d
ed
to
m
ee
t
th
e
d
em
an
d
s
o
f
a
g
r
o
win
g
d
em
an
d
is
n
ec
ess
ar
y
to
d
eliv
e
r
d
e
p
en
d
a
b
le
p
o
wer
u
n
d
e
r
s
ch
ed
u
led
an
d
u
n
s
ch
e
d
u
led
o
u
tag
es
[
2
2
]
.
A
s
y
s
tem
lik
e
th
is
s
h
o
u
ld
b
e
ca
p
a
b
le
o
f
r
ed
u
n
d
an
c
y
an
d
f
a
u
lt
t
o
ler
an
ce
as
well.
I
f
a
co
n
tr
o
l
s
tr
ateg
y
ca
n
b
e
d
e
v
elo
p
e
d
th
at
en
ab
les
s
m
aller
in
v
er
ter
s
to
f
u
n
ctio
n
in
d
e
p
en
d
e
n
tly
wh
ile
y
et
s
h
ar
in
g
th
e
l
o
ad
,
th
es
e
o
b
jectiv
es
ca
n
b
e
ac
h
iev
ed
b
y
co
n
n
ec
tin
g
th
em
in
p
ar
allel.
T
h
e
au
t
h
o
r
h
as
c
r
ea
ted
a
co
n
tr
o
l
m
eth
o
d
th
at
en
ab
les
th
e
p
ar
allel
o
p
er
atio
n
o
f
two
o
r
m
o
r
e
s
in
g
le
-
p
h
ase
in
v
er
ter
m
o
d
u
les
with
o
u
t
th
e
n
ee
d
o
f
an
y
a
u
x
iliar
y
co
n
n
ec
to
r
s
.
T
h
is
m
eth
o
d
d
iv
id
es
th
e
lo
ad
ac
r
o
s
s
s
ep
ar
ate
in
v
er
ter
s
i
n
p
r
o
p
o
r
tio
n
to
th
eir
ca
p
ac
ity
b
y
u
s
in
g
f
r
e
q
u
en
c
y
,
f
u
n
d
am
e
n
tal
v
o
ltag
e,
an
d
h
ar
m
o
n
ic
v
o
ltag
e
d
r
o
o
p
.
R
esu
lts
f
r
o
m
s
im
u
latio
n
s
ar
e
g
i
v
en
t
o
s
u
p
p
o
r
t th
e
t
h
eo
r
y
.
A
s
tu
d
y
b
y
Diaz
et
a
l
.
[
2
3
]
d
escr
ib
es
a
m
eth
o
d
b
ased
o
n
b
if
u
r
ca
tio
n
th
e
o
r
y
to
ass
ess
th
e
ef
f
ec
ts
o
f
p
r
im
ar
y
r
eser
v
e
s
ch
e
d
u
lin
g
a
n
d
d
r
o
o
p
s
o
n
m
icr
o
g
r
id
s
tab
i
lity
.
T
h
e
a
p
p
r
o
ac
h
is
b
ased
o
n
r
esch
ed
u
lin
g
th
e
d
r
o
o
p
s
o
f
ch
o
s
en
g
e
n
er
atin
g
u
n
its
th
at
en
a
b
le
f
r
eq
u
e
n
cy
(
an
d
v
o
ltag
e)
co
n
tr
o
l
to
d
is
co
v
er
th
e
wo
r
s
t
m
ai
n
r
eser
v
e
s
h
ar
e
o
r
th
e
s
h
ar
e
th
at
is
th
e
clo
s
e
s
t
to
in
s
tab
ilit
y
.
I
n
a
m
u
lti
-
p
a
r
am
eter
s
p
ac
e
with
co
o
r
d
in
ates
co
r
r
esp
o
n
d
in
g
to
th
e
d
r
o
o
p
c
o
ef
f
icien
ts
,
th
e
s
o
lu
tio
n
wh
ic
h
co
n
s
is
ts
o
f
a
m
ea
s
u
r
em
en
t
o
f
th
e
d
is
tan
ce
to
in
s
tab
ilit
y
in
a
ce
r
tain
d
ir
e
ctio
n
is
d
is
co
v
er
ed
.
An
is
o
lated
m
icr
o
g
r
id
with
6
9
b
u
s
es
an
d
1
1
g
en
er
atin
g
u
n
its
is
u
s
ed
to
ex
am
in
e
th
e
s
u
g
g
ested
s
tr
ateg
y
.
T
h
e
ex
am
in
atio
n
o
f
a
f
ew
s
itu
atio
n
s
d
em
o
n
s
tr
ates
h
o
w
t
h
e
d
is
tan
ce
s
an
d
n
o
r
m
al
v
ec
to
r
s
o
f
f
er
im
p
o
r
tan
t
in
s
ig
h
t
in
to
th
e
p
r
o
p
er
s
ch
ed
u
lin
g
f
r
o
m
th
e
p
er
s
p
ec
tiv
e
o
f
s
tab
ilit
y
,
o
f
f
er
in
g
g
u
id
an
ce
o
n
h
o
w
t
h
e
p
r
im
ar
y
r
eser
v
e
o
u
g
h
t
to
b
e
m
o
r
e
r
eliab
ly
s
ch
ed
u
led
.
T
h
er
e
ar
e
s
till
s
o
m
e
ca
s
es
wh
en
ex
ter
n
al
co
m
m
u
n
icatio
n
tech
n
iq
u
es
ar
e
r
e
q
u
ir
ed
f
o
r
lo
a
d
s
h
ar
in
g
an
d
r
esto
r
in
g
th
e
m
icr
o
g
r
id
'
s
v
o
ltag
e
an
d
f
r
e
q
u
en
c
y
[
2
4
]
.
T
h
e
co
n
t
r
o
l
ap
p
r
o
ac
h
f
o
r
a
f
lex
ib
le
m
icr
o
g
r
id
is
d
is
cu
s
s
ed
in
th
is
r
esea
r
ch
.
T
h
e
m
icr
o
g
r
id
d
escr
ib
ed
h
er
e
is
m
ad
e
u
p
o
f
n
u
m
er
o
u
s
p
ar
alleled
lin
e
-
in
te
r
ac
tiv
e
UPS
s
y
s
tem
s
.
T
h
e
d
r
o
o
p
m
eth
o
d
is
th
e
f
o
u
n
d
atio
n
o
f
t
h
e
co
n
tr
o
l
s
tr
ateg
y
,
wh
ich
p
r
ev
e
n
ts
cr
u
cial
co
n
n
ec
tio
n
s
b
etwe
en
UPS
u
n
its
.
As
a
r
esu
lt,
a
f
lex
ib
le
m
icr
o
g
r
id
t
h
at
ca
n
f
u
n
ctio
n
in
is
lan
d
ed
o
r
g
r
i
d
-
co
n
n
ec
ted
m
o
d
e
is
d
ev
el
o
p
ed
.
T
h
e
s
y
s
tem
s
tab
ilit
y
is
ex
am
in
ed
u
s
in
g
a
s
m
all
-
s
ig
n
al
an
aly
s
is
,
wh
ich
p
r
o
v
id
es
g
u
i
d
elin
es
f
o
r
d
esig
n
in
g
th
e
p
r
im
a
r
y
co
n
tr
o
l
p
ar
am
eter
s
.
R
esu
lts
f
r
o
m
s
im
u
latio
n
s
an
d
ex
p
er
im
en
ts
ar
e
s
h
o
wn
,
d
e
m
o
n
s
tr
atin
g
th
e
v
iab
ilit
y
o
f
th
e
s
u
g
g
este
d
co
n
tr
o
ller
.
I
t
is
f
ea
s
ib
le
to
p
r
o
d
u
ce
a
n
in
c
r
ed
ib
ly
p
r
ec
is
e
e
q
u
al
d
is
tr
ib
u
tio
n
o
f
lin
ea
r
a
n
d
n
o
n
lin
ea
r
l
o
a
d
s
,
as
h
as
b
ee
n
th
o
r
o
u
g
h
l
y
s
tu
d
ied
[
2
5
]
.
T
h
e
to
p
ic
o
f
th
is
s
tu
d
y
is
th
e
d
esig
n
o
f
th
e
o
u
tp
u
t
im
p
e
d
an
c
e
o
f
UPS
in
v
er
ter
s
with
th
e
ca
p
ac
ity
to
lin
k
in
p
a
r
allel.
T
h
e
P/Q
d
r
o
o
p
ap
p
r
o
ac
h
is
th
e
f
o
u
n
d
atio
n
f
o
r
th
e
p
o
wer
-
s
h
ar
in
g
co
n
tr
o
l
lo
o
p
s
,
wh
ich
elim
in
ate
th
e
n
e
ed
f
o
r
a
n
y
co
m
m
u
n
icatio
n
b
e
twee
n
m
o
d
u
les.
As
th
e
p
r
ec
is
io
n
o
f
th
e
p
o
wer
-
s
h
ar
in
g
in
th
ese
s
y
s
tem
s
is
h
ea
v
ily
d
e
p
en
d
e
n
t
o
n
th
e
o
u
tp
u
t
i
m
p
ed
an
ce
o
f
th
e
in
v
e
r
ter
,
i
n
n
o
v
ativ
e
co
n
tr
o
l
l
o
o
p
s
ar
e
d
e
v
elo
p
ed
to
en
s
u
r
e
b
o
t
h
s
t
ab
le
o
u
t
p
u
t
im
p
ed
an
ce
an
d
a
d
e
q
u
ate
p
o
wer
b
alan
cin
g
.
R
esu
lts
f
r
o
m
s
im
u
latio
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2422
-
2
4
3
4
2428
an
d
ex
p
er
im
en
ts
u
s
in
g
a
p
a
r
al
lel
-
co
n
n
ec
ted
UPS
s
y
s
tem
th
a
t
s
h
ar
es
lin
ea
r
an
d
n
o
n
lin
ea
r
l
o
ad
s
ar
e
g
i
v
en
.
A
co
n
tr
o
l
tech
n
iq
u
e
f
o
r
t
h
e
eq
u
al
p
o
wer
s
h
ar
i
n
g
o
f
two
p
a
r
alleled
th
r
ee
-
p
h
ase
p
o
wer
c
o
n
v
er
ter
s
in
clu
d
in
g
h
ar
m
o
n
ic
c
o
r
r
ec
tio
n
is
p
r
o
p
o
s
ed
in
[
2
6
]
.
T
h
e
eq
u
itab
le
s
h
ar
in
g
o
f
lin
ea
r
an
d
n
o
n
lin
ea
r
lo
a
d
s
in
th
r
ee
-
p
h
ase
p
o
wer
co
n
v
er
ter
s
lin
k
ed
i
n
p
ar
allel
with
o
u
t
co
m
m
u
n
icatio
n
b
etwe
en
th
e
co
n
v
er
ter
s
is
m
ad
e
p
o
s
s
ib
le
b
y
a
n
ew
c
o
n
tr
o
l
m
ec
h
a
n
is
m
in
tr
o
d
u
ce
d
in
th
is
r
esear
ch
.
T
h
e
ch
allen
g
e
t
h
at
r
esu
lts
f
r
o
m
co
n
n
ec
tin
g
t
wo
co
n
v
er
ter
s
with
h
ar
m
o
n
ic
co
r
r
ec
tio
n
in
p
ar
allel
is
th
e
m
ain
to
p
ic
o
f
th
is
s
tu
d
y
.
T
h
e
o
u
tco
m
es
d
em
o
n
s
tr
ate
th
at
th
e
s
u
g
g
ested
id
ea
is
ca
p
ab
le
o
f
eq
u
itab
ly
d
is
tr
ib
u
tin
g
b
o
t
h
lin
ea
r
an
d
n
o
n
lin
ea
r
lo
ad
s
.
Fo
r
is
lan
d
in
g
p
a
r
allel
in
v
er
ter
s
in
an
ac
-
di
s
tr
ib
u
ted
s
y
s
tem
,
a
n
o
v
e
l
wir
eless
lo
ad
-
s
h
ar
in
g
co
n
tr
o
ll
er
is
p
r
esen
ted
in
[
2
7
]
.
T
h
is
s
tu
d
y
in
v
esti
g
ates
th
e
p
ar
allel
-
co
n
n
ec
ted
in
v
e
r
ter
s
'
r
esis
tiv
e
o
u
tp
u
t
im
p
ed
an
ce
in
an
is
lan
d
m
icr
o
g
r
id
.
T
h
e
co
n
t
r
o
l
lo
o
p
s
ar
e
d
esig
n
ed
an
d
ass
ess
ed
wh
ile
tak
in
g
in
to
co
n
s
id
er
atio
n
th
e
u
n
iq
u
e
ch
ar
ac
ter
is
tics
o
f
a
lo
w
-
v
o
ltag
e
m
icr
o
g
r
id
,
wh
er
e
th
e
lin
e
im
p
e
d
an
ce
is
p
r
im
ar
ily
r
esis
tiv
e
an
d
th
e
d
is
tan
ce
b
etwe
en
th
e
in
v
er
ter
s
m
ak
es
it
ch
allen
g
in
g
f
o
r
th
em
to
co
m
m
u
n
ica
te
with
o
n
e
an
o
th
er
d
u
r
in
g
co
n
tr
o
l
o
p
er
atio
n
s
.
T
wo
6
-
k
VA
in
v
er
te
r
s
lin
k
ed
in
p
ar
allel
h
a
v
e
p
r
o
d
u
ce
d
ex
p
e
r
im
en
tal
r
esu
lts
th
at
d
em
o
n
s
tr
ate
th
e
b
en
ef
its
o
f
th
e
s
u
g
g
ested
wir
eless
co
n
tr
o
l
[
28]
,
p
r
esen
ted
an
alter
n
ativ
e
co
n
tr
o
l
m
ec
h
an
is
m
th
at
r
ed
u
ce
d
th
e
v
ir
t
u
al
f
lu
x
r
a
th
er
th
an
th
e
lo
ad
v
o
ltag
e
,
a
n
d
d
is
tr
ib
u
ted
p
o
wer
u
n
i
f
o
r
m
ly
.
T
h
er
e
wer
e
n
u
m
er
o
u
s
co
n
t
r
o
l
s
ch
em
es
f
o
r
p
r
o
p
o
r
tio
n
al
p
o
wer
d
is
tr
ib
u
tio
n
[
2
9
]
-
[
3
2
]
s
u
g
g
est
an
u
p
g
r
a
d
ed
c
o
n
tr
o
l
m
eth
o
d
th
a
t
m
ea
s
u
r
es
th
e
r
ea
ctiv
e
p
o
we
r
co
n
t
r
o
l
e
r
r
o
r
b
y
in
jectin
g
s
m
all
ac
tu
al
p
o
wer
d
is
tu
r
b
an
ce
s
,
wh
ic
h
ar
e
ac
tiv
a
ted
b
y
th
e
lo
w
-
b
an
d
wid
th
s
y
n
ch
r
o
n
izatio
n
s
ig
n
als f
r
o
m
th
e
ce
n
tr
al
co
n
tr
o
ller
,
in
o
r
d
er
to
in
cr
ea
s
e
th
e
ac
cu
r
ac
y
o
f
r
ea
ctiv
e
p
o
wer
s
h
ar
i
n
g
.
T
h
e
tr
ad
itio
n
al
r
ea
ctiv
e
p
o
we
r
d
r
o
o
p
co
n
tr
o
l
is
s
im
u
ltan
eo
u
s
ly
s
u
p
p
lem
en
ted
with
a
d
elay
ed
in
teg
r
atio
n
ter
m
f
o
r
th
e
r
ed
u
ctio
n
o
f
r
ea
c
tiv
e
p
o
wer
-
s
h
a
r
in
g
er
r
o
r
s
.
Usi
n
g
f
r
eq
u
e
n
cy
d
r
o
o
p
m
an
ag
em
e
n
t,
th
e
p
r
o
p
o
s
e
d
co
m
p
en
s
atio
n
ap
p
r
o
ac
h
ac
co
m
p
lis
h
es
p
r
ec
is
e
r
ea
ctiv
e
p
o
wer
s
h
ar
in
g
at
a
s
tead
y
s
tate,
m
u
ch
as
g
en
u
in
e
p
o
wer
s
h
ar
in
g
.
R
esu
lts
f
r
o
m
s
im
u
latio
n
s
an
d
ex
p
er
im
en
ts
s
u
p
p
o
r
t th
e
v
iab
il
ity
o
f
th
e
s
u
g
g
ested
ap
p
r
o
ac
h
.
A
s
tu
d
y
b
y
Far
h
a
d
i
an
d
Mo
h
a
m
m
ed
[
3
3
]
e
x
am
in
es
t
h
e
h
a
r
m
o
n
ic
an
al
y
s
is
an
d
r
ea
l
-
tim
e
o
p
er
atio
n
o
f
is
o
lated
an
d
n
o
n
-
is
o
lated
DC
m
icr
o
g
r
id
s
.
A
cu
r
r
en
t
-
v
o
ltag
e
m
an
ag
e
m
en
t
s
tr
ateg
y
b
ased
o
n
th
e
m
aster
-
s
lav
e
co
n
tr
o
l
id
ea
is
s
u
g
g
ested
in
o
r
d
er
to
ef
f
ec
tiv
ely
m
a
n
ag
e
th
e
en
er
g
y
a
n
d
p
r
ev
e
n
t
th
e
ac
g
r
i
d
p
o
wer
p
u
ls
atio
n
.
B
ased
o
n
v
ar
io
u
s
p
o
wer
-
s
h
ar
i
n
g
p
atter
n
s
,
s
ev
e
r
al
o
p
e
r
atin
g
m
o
d
es
wer
e
estab
lis
h
ed
.
B
o
th
g
alv
an
ically
is
o
lated
an
d
n
o
n
-
is
o
lated
DC
g
r
id
s
y
s
tem
s
u
n
d
er
wen
t
th
e
ex
p
er
i
m
en
tal
test
.
T
h
e
o
u
tco
m
es
d
em
o
n
s
tr
ate
th
at
th
e
s
u
g
g
ested
en
er
g
y
m
an
a
g
em
en
t
alg
o
r
ith
m
ef
f
ec
tiv
ely
d
is
tr
ib
u
t
es
p
o
wer
an
d
r
eg
u
lates
v
o
ltag
e
.
Als
o
,
th
e
is
o
latio
n
o
f
th
e
DC
m
icr
o
g
r
i
d
h
as
a
s
u
b
s
tan
tial
im
p
ac
t
o
n
th
e
h
ar
m
o
n
i
c
co
n
ten
t
o
f
th
e
cu
r
r
en
t
d
e
p
en
d
in
g
o
n
th
e
p
o
wer
-
s
h
ar
in
g
p
atter
n
.
A
s
tu
d
y
b
y
G
u
zm
án
et
a
l
.
[
3
4
]
d
escr
ib
es
a
u
n
i
q
u
e
co
n
tr
o
l
te
ch
n
iq
u
e
t
h
at
en
ab
les
lo
ad
s
h
ar
in
g
ac
r
o
s
s
an
ac
m
icr
o
g
r
id
'
s
p
o
wer
s
o
u
r
c
es
with
o
u
t
th
e
n
ee
d
f
o
r
a
ce
n
tr
al
co
n
tr
o
ller
o
r
in
ter
-
v
o
ltag
e
-
s
o
u
r
ce
in
v
e
r
ter
(
VSI
)
co
m
m
u
n
icatio
n
;
in
s
tead
,
ju
s
t
lo
ca
l
o
u
tp
u
t
cu
r
r
en
t
an
d
v
o
lta
g
e
ar
e
m
ea
s
u
r
ed
f
o
r
th
e
co
n
t
r
o
l
tech
n
iq
u
e
.
T
h
e
s
u
g
g
ested
VSI
co
n
tr
o
ller
s
ar
e
b
ased
o
n
th
e
v
o
ltag
e/p
o
we
r
esti
m
atio
n
,
f
r
eq
u
e
n
cy
-
l
o
ck
ed
lo
o
p
,
a
n
d
v
ar
iab
le
f
r
eq
u
e
n
cy
ad
ap
tiv
e
lin
ea
r
n
eu
r
o
n
f
o
r
th
e
VSI
s
y
s
tem
s
y
n
ch
r
o
n
izatio
n
.
T
h
e
v
alid
ity
o
f
th
e
claim
was
v
er
if
ied
b
y
ex
p
er
im
en
tal
f
in
d
in
g
s
em
p
lo
y
in
g
f
ield
-
p
r
o
g
r
a
m
m
ab
le
g
a
te
ar
r
ay
d
ev
ices
f
o
r
th
e
im
p
le
m
en
tatio
n
o
f
ea
ch
VSI
co
n
tr
o
l in
th
e
m
icr
o
g
r
id
t
est b
en
ch
.
T
h
e
u
s
e
o
f
s
ec
o
n
d
ar
y
c
o
n
tr
o
l
i
n
a
m
icr
o
g
r
id
with
d
r
o
o
p
in
g
p
r
im
ar
y
v
o
ltag
e
is
ex
am
in
ed
in
[
3
5
]
.
T
h
e
s
ec
o
n
d
ar
y
co
n
tr
o
l,
in
c
o
n
tr
ast
to
th
e
p
r
im
ar
y
co
n
tr
o
ller
,
is
co
m
m
u
n
icatio
n
-
b
ased
an
d
r
u
n
s
a
t
a
s
lo
wer
r
ate
th
an
th
e
v
o
ltag
e
-
b
ased
p
r
im
ar
y
c
o
n
tr
o
l.
T
h
e
s
ec
o
n
d
ar
y
co
n
tr
o
ller
co
n
tr
o
ls
th
e
p
o
we
r
ex
c
h
an
g
e
b
etwe
en
th
e
m
icr
o
g
r
id
an
d
u
tili
ty
n
etwo
r
k
,
th
e
v
o
l
tag
e
at
p
ilo
t
s
ites
in
th
e
m
icr
o
g
r
id
,
o
r
th
e
v
o
ltag
e
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
n
n
ec
tio
n
.
On
th
e
b
asis
o
f
an
o
p
tim
izatio
n
m
eth
o
d
,
s
u
ch
as
f
o
r
lo
s
s
es,
p
o
wer
q
u
ality
,
an
d
ec
o
n
o
m
ic
in
co
m
e
,
th
e
s
et
p
o
in
ts
f
o
r
s
ec
o
n
d
ar
y
c
o
n
tr
o
l
m
ay
b
e
estab
lis
h
ed
.
T
h
e
m
icr
o
g
r
id
s
ec
o
n
d
ar
y
c
o
n
tr
o
ller
m
o
d
if
ies
th
e
DG
u
n
its
'
p
o
wer
s
et
p
o
in
ts
in
ac
co
r
d
an
ce
with
th
ese
s
et
p
o
in
ts
.
T
o
r
u
n
a
s
in
g
le
-
p
h
ase
DC
/AC
co
n
v
e
r
ter
in
b
o
th
g
r
i
d
-
co
n
n
e
cted
(
GC
)
an
d
s
tan
d
-
alo
n
e
(
S
A)
m
o
d
es,
th
e
u
n
iv
e
r
s
al
in
teg
r
ated
s
y
n
c
h
r
o
n
izatio
n
an
d
co
n
tr
o
l
(
UI
SC
)
is
d
ev
elo
p
ed
[
3
6
]
.
T
h
is
s
y
s
tem
o
f
f
er
s
s
m
o
o
th
tr
an
s
itio
n
s
b
etwe
en
b
o
th
m
o
d
es
with
o
u
t
r
eq
u
ir
in
g
an
y
c
h
an
g
es
to
th
e
co
n
tr
o
l
s
tr
u
ctu
r
e.
T
o
d
em
o
n
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
s
u
g
g
ested
co
n
tr
o
ller
in
a
s
in
g
le
-
p
h
ase
s
ce
n
ar
io
,
t
h
is
s
tu
d
y
o
f
f
er
s
t
h
e
d
er
iv
atio
n
s
,
s
tab
ilit
y
an
aly
s
is
,
an
d
n
u
m
e
r
ical
r
esu
l
ts
.
Als
o
in
clu
d
ed
is
a
m
ath
e
m
atica
l
s
tu
d
y
o
f
t
h
e
s
im
ilar
ities
a
n
d
d
if
f
er
en
c
es
b
etwe
en
th
e
UI
SC
an
d
s
ev
er
al
r
elate
d
ap
p
r
o
ac
h
es.
T
h
e
cu
r
r
en
t
f
ee
d
b
ac
k
s
ig
n
al
a
n
d
p
o
wer
an
g
le
o
f
VSI
s
ar
e
u
s
ed
in
th
e
s
u
g
g
ested
[
3
7
]
c
o
n
tr
o
l
s
tr
ateg
y
,
wh
ich
is
b
ased
o
n
th
e
d
r
o
o
p
co
n
tr
o
l
m
eth
o
d
.
T
h
is
tech
n
iq
u
e
is
ty
p
ically
u
s
ed
to
r
ed
u
ce
t
r
an
s
ien
t
cir
cu
latio
n
cu
r
r
en
t
an
d
p
r
o
v
id
e
g
o
o
d
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
h
ar
i
n
g
.
T
h
is
n
o
v
el
d
r
o
o
p
f
o
r
v
o
ltag
e
a
n
d
f
r
eq
u
e
n
cy
is
u
s
ed
in
th
is
s
tu
d
y
to
s
ig
n
if
ican
tly
i
n
cr
ea
s
e
tr
an
s
ien
t
r
esp
o
n
s
iv
en
ess
.
T
h
e
s
u
g
g
ested
co
n
tr
o
ller
is
v
alid
ated
b
y
th
e
s
im
u
latio
n
r
esu
lts
th
at
ar
e
p
r
e
s
en
ted
.
T
h
e
v
o
ltag
e
d
if
f
e
r
en
c
e
b
etwe
en
th
e
g
r
id
v
o
lta
g
e
a
n
d
th
e
r
e
f
er
en
ce
ac
v
o
ltag
e
s
o
u
r
ce
s
was u
s
ed
to
d
eter
m
in
e
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
cu
r
r
en
ts
.
A
s
tu
d
y
b
y
L
iu
et
a
l
.
[
3
8
]
p
r
o
p
o
s
ed
a
tec
h
n
iq
u
e
f
o
r
id
e
n
tify
in
g
ac
tiv
e
a
n
d
r
ea
ctiv
e
c
u
r
r
en
t
s
b
ased
o
n
th
e
co
m
p
u
tatio
n
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
.
Nev
er
th
eless
,
f
o
r
th
ese
two
m
eth
o
d
s
,
t
h
e
ac
t
u
al
in
v
er
ter
o
u
tp
u
t
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
A
s
ystema
tic
r
ev
ie
w
o
n
vo
lta
g
e
s
ta
b
ilit
y
a
n
a
lysi
s
in
s
ma
r
t a
n
d
is
la
n
d
ed
…
(
S
o
w
mya
R
en
u
k
a
B
a
n
g
a
r
i
)
2429
r
esis
tan
ce
o
v
er
r
ea
ctan
ce
r
at
io
is
n
ec
ess
ar
y
.
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
en
ts
wer
e
i
d
en
tifie
d
u
s
in
g
t
h
e
am
p
litu
d
e,
p
h
ase
an
g
le,
an
d
p
o
wer
an
g
le
o
f
t
h
e
lo
a
d
cu
r
r
en
t,
as
d
escr
ib
ed
b
y
[
3
9
]
.
A
q
u
ick
s
u
m
m
ar
y
o
f
v
ar
io
u
s
liter
atu
r
e
in
th
is
s
ec
tio
n
is
g
iv
en
in
T
ab
le
3
.
T
ab
le
3
.
Par
allel
in
v
e
r
ter
s
an
d
co
n
tr
o
ller
s
–
a
s
u
m
m
ar
y
To
p
i
c
K
e
y
p
o
i
n
t
s
D
r
o
o
p
c
o
n
t
r
o
l
i
n
mi
c
r
o
g
r
i
d
s
Th
e
s
e
p
a
p
e
r
s
e
x
p
l
o
r
e
a
s
p
e
c
t
s
o
f
d
r
o
o
p
c
o
n
t
r
o
l
i
n
m
i
c
r
o
g
r
i
d
s
,
f
o
c
u
s
i
n
g
o
n
i
ss
u
e
s
su
c
h
a
s
l
o
a
d
sh
a
r
i
n
g
,
st
a
b
i
l
i
t
y
,
a
n
d
p
o
w
e
r
ma
n
a
g
e
m
e
n
t
[
1
9
]
-
[
2
1
]
.
T
h
e
p
a
p
e
r
[
1
9
]
d
i
s
c
u
sses
h
i
g
h
g
a
i
n
a
n
g
l
e
d
r
o
o
p
c
o
n
t
r
o
l
f
o
r
l
o
a
d
sh
a
r
i
n
g
u
n
d
e
r
w
e
a
k
s
y
s
t
e
m
se
t
t
i
n
g
s.
S
t
u
d
y
o
f
[
2
0
]
i
n
t
r
o
d
u
c
e
s
a
n
EM
S
f
o
r
a
st
a
n
d
a
l
o
n
e
d
r
o
o
p
-
c
o
n
t
r
o
l
l
e
d
mi
c
r
o
g
r
i
d
.
S
t
u
d
y
o
f
[
2
1
]
a
d
d
r
e
ss
e
s
l
o
w
-
f
r
e
q
u
e
n
c
y
r
e
l
a
t
i
v
e
st
a
b
i
l
i
t
y
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ss
u
e
s
i
n
D
G
u
n
i
t
s
u
s
i
n
g
a
d
a
p
t
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v
e
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e
c
e
n
t
r
a
l
i
z
e
d
d
r
o
o
p
c
o
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t
r
o
l
.
W
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r
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l
o
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d
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a
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t
t
h
e
n
e
e
d
f
o
r
w
i
r
e
d
c
o
mm
u
n
i
c
a
t
i
o
n
[
2
7
]
,
[
2
8
]
.
T
h
e
p
a
p
e
r
[
2
7
]
p
r
e
se
n
t
s
a
w
i
r
e
l
e
ss
l
o
a
d
-
s
h
a
r
i
n
g
c
o
n
t
r
o
l
l
e
r
f
o
r
p
a
r
a
l
l
e
l
i
n
v
e
r
t
e
r
s
i
n
a
n
A
C
-
d
i
st
r
i
b
u
t
e
d
sy
st
e
m.
Th
e
st
u
d
y
o
f
[
2
8
]
p
r
o
p
o
ses
a
n
a
l
t
e
r
n
a
t
i
v
e
c
o
n
t
r
o
l
m
e
c
h
a
n
i
sm
f
o
c
u
si
n
g
o
n
r
e
d
u
c
i
n
g
v
i
r
t
u
a
l
f
l
u
x
f
o
r
u
n
i
f
o
r
m
p
o
w
e
r
d
i
s
t
r
i
b
u
t
i
o
n
.
R
e
a
c
t
i
v
e
p
o
w
e
r
c
o
m
p
e
n
sa
t
i
o
n
Th
i
s
s
e
t
o
f
p
a
p
e
r
s
i
n
t
r
o
d
u
c
e
s
c
o
n
t
r
o
l
st
r
a
t
e
g
i
e
s
f
o
r
p
r
e
c
i
s
e
r
e
a
c
t
i
v
e
p
o
w
e
r
sh
a
r
i
n
g
[
2
9
]
-
[
3
2
]
.
T
h
e
st
u
d
y
o
f
[
2
9
]
su
g
g
e
st
s
a
n
u
p
g
r
a
d
e
d
c
o
n
t
r
o
l
me
t
h
o
d
w
i
t
h
r
e
a
c
t
i
v
e
p
o
w
e
r
c
o
m
p
e
n
sa
t
i
o
n
,
w
h
i
l
e
[
3
0
]
e
x
p
l
o
r
e
s
i
mp
r
o
v
e
d
c
o
n
t
r
o
l
f
o
r
p
r
o
p
o
r
t
i
o
n
a
l
p
o
w
e
r
d
i
s
t
r
i
b
u
t
i
o
n
.
Th
e
p
a
p
e
r
[
3
1
]
d
i
s
c
u
sses
r
e
a
c
t
i
v
e
p
o
w
e
r
d
r
o
o
p
c
o
n
t
r
o
l
su
p
p
l
e
me
n
t
e
d
w
i
t
h
a
d
e
l
a
y
e
d
i
n
t
e
g
r
a
t
i
o
n
t
e
r
m
.
T
h
e
r
e
se
a
r
c
h
o
f
[
3
2
]
f
o
c
u
ses
o
n
c
o
m
p
e
n
sa
t
i
n
g
r
e
a
c
t
i
v
e
p
o
w
e
r
-
sh
a
r
i
n
g
e
r
r
o
r
s
u
si
n
g
f
r
e
q
u
e
n
c
y
d
r
o
o
p
man
a
g
e
me
n
t
.
D
C
mi
c
r
o
g
r
i
d
o
p
e
r
a
t
i
o
n
a
n
d
man
a
g
e
me
n
t
Th
e
s
e
p
a
p
e
r
s
c
o
n
c
e
n
t
r
a
t
e
o
n
t
h
e
o
p
e
r
a
t
i
o
n
a
n
d
m
a
n
a
g
e
me
n
t
o
f
D
C
m
i
c
r
o
g
r
i
d
s
[
3
3
]
,
[
3
4
]
.
Th
e
a
r
t
i
c
l
e
[
3
3
]
d
i
s
c
u
ss
e
s
a
c
u
r
r
e
n
t
v
o
l
t
a
g
e
m
a
n
a
g
e
m
e
n
t
s
t
r
a
t
e
g
y
f
o
r
i
s
o
l
a
t
e
d
a
n
d
n
o
n
-
i
s
o
l
a
t
e
d
D
C
mi
c
r
o
g
r
i
d
s.
T
h
e
s
t
u
d
y
[
3
4
]
p
r
o
p
o
ses
a
c
o
n
t
r
o
l
t
e
c
h
n
i
q
u
e
f
o
r
l
o
a
d
s
h
a
r
i
n
g
i
n
A
C
mi
c
r
o
g
r
i
d
s,
e
mp
h
a
si
z
i
n
g
V
S
I
c
o
n
t
r
o
l
l
e
r
s
a
n
d
sy
n
c
h
r
o
n
i
z
a
t
i
o
n
me
t
h
o
d
s
S
e
c
o
n
d
a
r
y
c
o
n
t
r
o
l
i
n
mi
c
r
o
g
r
i
d
s
Th
e
st
u
d
y
o
f
[
3
5
]
e
x
p
l
o
r
e
s
se
c
o
n
d
a
r
y
c
o
n
t
r
o
l
i
n
m
i
c
r
o
g
r
i
d
s
,
f
o
c
u
si
n
g
o
n
c
o
mm
u
n
i
c
a
t
i
o
n
-
b
a
se
d
c
o
n
t
r
o
l
met
h
o
d
s
t
h
a
t
o
p
e
r
a
t
e
a
t
a
sl
o
w
e
r
r
a
t
e
t
h
a
n
p
r
i
m
a
r
y
v
o
l
t
a
g
e
-
b
a
s
e
d
c
o
n
t
r
o
l
.
T
h
e
s
e
c
o
n
d
a
r
y
c
o
n
t
r
o
l
l
e
r
a
d
j
u
s
t
s
p
o
w
e
r
se
t
-
p
o
i
n
t
s
f
o
r
D
G
u
n
i
t
s
b
a
s
e
d
o
n
o
p
t
i
m
i
z
a
t
i
o
n
m
e
t
h
o
d
s
.
S
y
n
c
h
r
o
n
i
z
a
t
i
o
n
a
n
d
c
o
n
t
r
o
l
f
o
r
c
o
n
v
e
r
t
e
r
s
Th
e
s
e
p
a
p
e
r
s
[
3
6
]
,
[
3
7
]
a
d
d
r
e
ss
sy
n
c
h
r
o
n
i
z
a
t
i
o
n
a
n
d
c
o
n
t
r
o
l
f
o
r
c
o
n
v
e
r
t
e
r
s
i
n
mi
c
r
o
g
r
i
d
s.
[
3
6
]
i
n
t
r
o
d
u
c
e
s
t
h
e
U
I
S
C
f
o
r
si
n
g
l
e
-
p
h
a
se
D
C
/
A
C
c
o
n
v
e
r
t
e
r
s.
[
3
7
]
p
r
e
se
n
t
s
a
d
r
o
o
p
c
o
n
t
r
o
l
met
h
o
d
w
i
t
h
i
mp
r
o
v
e
d
t
r
a
n
si
e
n
t
r
e
sp
o
n
s
e
,
u
s
i
n
g
t
h
e
c
u
r
r
e
n
t
f
e
e
d
b
a
c
k
s
i
g
n
a
l
a
n
d
p
o
w
e
r
a
n
g
l
e
o
f
V
S
I
s
.
I
d
e
n
t
i
f
i
c
a
t
i
o
n
o
f
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
c
u
r
r
e
n
t
s
Th
i
s
p
a
p
e
r
p
r
o
p
o
se
s
a
t
e
c
h
n
i
q
u
e
f
o
r
i
d
e
n
t
i
f
y
i
n
g
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
c
u
r
r
e
n
t
s
b
a
s
e
d
o
n
t
h
e
c
o
mp
u
t
a
t
i
o
n
o
f
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
p
o
w
e
r
,
c
o
n
t
r
i
b
u
t
i
n
g
t
o
e
n
h
a
n
c
e
d
c
o
n
t
r
o
l
st
r
a
t
e
g
i
e
s [
3
8
]
.
5.
ST
A
B
I
L
I
T
Y
ANA
L
YS
I
S I
N
M
I
CRO
G
R
I
DS
I
n
th
e
co
n
tex
t
o
f
s
tab
ilit
y
an
aly
s
is
f
o
r
au
to
n
o
m
o
u
s
m
i
cr
o
g
r
id
s
co
m
b
in
in
g
R
E
Ss
with
d
iesel
g
en
er
ato
r
s
,
[
4
0
]
ex
p
lo
r
es
th
e
u
s
e
o
f
d
r
o
o
p
co
n
tr
o
l.
Sp
ec
i
f
ically
,
th
e
s
tu
d
y
ad
d
r
ess
es
s
ce
n
ar
io
s
wh
er
e
a
R
E
S
in
ten
tio
n
ally
r
ed
u
ce
s
its
o
u
tp
u
t
d
u
e
to
is
s
u
es,
ca
u
s
in
g
th
e
d
ies
el
g
en
er
at
o
r
t
o
b
ec
o
m
e
d
esy
n
c
h
r
o
n
ized
.
Ho
wev
e
r
,
th
e
r
ec
o
v
er
y
p
o
s
t
-
f
au
lt
r
eq
u
ir
es
all
r
ea
ctiv
e
p
o
wer
to
b
e
p
r
o
d
u
ce
d
u
s
in
g
r
en
ewa
b
le
en
er
g
y
.
T
h
e
s
tu
d
y
estab
lis
h
es
d
-
q
f
r
am
e
im
p
e
d
an
ce
m
o
d
els
f
o
r
b
o
t
h
PQ
-
co
n
tr
o
lled
an
d
d
r
o
o
p
-
co
n
tr
o
l
led
in
v
e
r
ter
s
.
T
h
e
m
icr
o
g
r
id
'
s
is
lan
d
m
o
d
e
is
an
aly
ze
d
ak
in
to
a
d
o
u
b
le
clo
s
ed
-
lo
o
p
s
y
s
tem
d
u
e
to
t
h
e
d
if
f
er
i
n
g
o
u
tp
u
t
ch
ar
ac
ter
is
tics
o
f
th
ese
c
o
n
tr
o
l m
eth
o
d
s
.
T
h
e
o
p
en
-
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
p
ar
allel
s
y
s
tem
is
d
er
i
v
ed
,
an
d
th
e
s
y
s
tem
's
im
p
ed
an
ce
m
o
d
el
is
f
o
r
m
u
lated
.
T
h
is
p
r
o
p
o
s
ed
i
m
p
ed
an
ce
m
o
d
el
is
th
en
u
s
ed
t
o
ass
ess
th
e
s
tab
ilit
y
o
f
p
ar
allel
s
y
s
tem
s
o
p
er
a
tin
g
in
is
lan
d
m
icr
o
g
r
id
m
o
d
e
th
r
o
u
g
h
th
e
g
en
e
r
alize
d
Ny
q
u
is
t
cr
iter
io
n
(
GNC).
Simu
latio
n
an
d
e
x
p
er
im
en
tal
r
esu
lts
v
alid
ate
th
e
an
aly
s
is
.
As
d
is
cu
s
s
ed
in
[
1
3
]
,
a
n
o
v
el
m
o
d
elin
g
ap
p
r
o
ac
h
a
n
d
s
tab
ili
ty
an
aly
s
is
m
eth
o
d
ar
e
p
r
o
p
o
s
ed
f
o
r
wea
k
p
o
wer
n
etwo
r
k
s
with
s
ig
n
if
ican
t
p
en
etr
atio
n
o
f
p
o
wer
elec
tr
o
n
ics
co
n
v
er
ter
s
.
T
h
is
ap
p
r
o
ac
h
in
clu
d
es
s
m
all
-
s
ig
n
al
s
tate
-
s
p
ac
e
m
o
d
els
f
o
r
v
ar
io
u
s
n
etwo
r
k
elem
en
ts
s
u
ch
as
p
o
wer
lin
es,
lo
a
d
s
,
p
o
wer
c
o
n
v
er
ter
s
,
an
d
th
eir
co
n
tr
o
l
alg
o
r
ith
m
s
,
allo
win
g
f
o
r
co
m
p
r
eh
en
s
iv
e
n
etwo
r
k
m
o
d
elin
g
.
T
h
e
s
u
g
g
ested
lin
ea
r
ized
m
o
d
el
is
co
m
p
ar
ed
to
th
e
n
o
n
lin
ea
r
m
o
d
el'
s
r
esp
o
n
s
e
f
o
r
v
alid
atio
n
.
T
h
e
cr
ea
ted
s
m
all
-
s
ig
n
al
m
o
d
el
is
em
p
lo
y
ed
in
s
tab
ilit
y
an
aly
s
is
b
ased
o
n
th
e
f
r
eq
u
en
cy
r
esp
o
n
s
e
o
f
s
in
g
u
lar
v
al
u
es
to
d
eter
m
in
e
k
ey
n
etwo
r
k
a
n
d
co
n
tr
o
l
p
ar
am
eter
s
in
th
e
p
r
esen
ce
o
f
d
is
tu
r
b
an
ce
s
.
Fin
ally
,
th
e
o
r
ig
in
al
n
o
n
lin
ea
r
m
o
d
el
is
u
s
ed
to
v
er
if
y
th
e
p
r
esen
c
e
o
f
d
etec
ted
r
eso
n
an
t m
o
d
es.
I
n
co
n
tr
ast
to
co
n
v
en
tio
n
al
s
tab
ilit
y
an
aly
s
es,
a
s
tu
d
y
b
y
Z
h
an
g
et
a
l
.
[
1
7
]
co
n
s
id
er
s
t
h
e
u
n
i
q
u
e
ch
ar
ac
ter
is
tics
o
f
ca
b
les
a
n
d
i
n
v
er
ter
s
.
I
m
p
ed
a
n
ce
-
b
ased
an
d
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d
e
r
a
n
g
e
o
f
t
e
c
h
n
i
q
u
e
s
i
n
s
t
a
b
i
l
i
t
y
a
n
a
l
y
s
i
s,
c
o
n
s
i
d
e
r
i
n
g
c
o
m
p
l
e
x
i
t
i
e
s
o
f
c
o
n
t
r
o
l
m
e
t
h
o
d
s
,
mo
d
e
l
i
n
g
s
t
r
a
t
e
g
i
e
s
,
d
i
me
n
si
o
n
a
l
i
t
y
r
e
d
u
c
t
i
o
n
,
a
n
d
f
e
a
t
u
r
e
s
e
l
e
c
t
i
o
n
f
o
r
e
n
su
r
i
n
g
r
e
l
i
a
b
i
l
i
t
y
a
n
d
st
a
b
i
l
i
t
y
o
f
p
o
w
e
r
s
y
st
e
ms
.
6.
SO
F
T
CO
M
P
U
T
I
NG
T
E
CH
NIQU
E
S
T
h
e
tr
an
s
ien
t
s
tab
ilit
y
as
s
es
s
m
en
t
(
T
SA)
is
a
m
eth
o
d
em
p
lo
y
ed
to
ass
ess
th
e
s
tab
ilit
y
o
f
a
p
o
wer
s
y
s
tem
u
n
d
er
v
ar
i
o
u
s
d
is
tu
r
b
an
ce
s
,
en
co
m
p
ass
in
g
p
la
n
n
ed
s
h
o
r
t
-
cir
c
u
it
f
ailu
r
es
a
n
d
elem
en
t
o
u
tag
es.
T
h
is
ev
alu
atio
n
is
cr
u
cial
to
ascer
ta
in
th
e
s
y
s
tem
'
s
b
eh
av
io
r
d
u
r
in
g
tr
an
s
ien
t
ev
e
n
ts
.
W
h
en
th
e
s
y
s
tem
's
r
esp
o
n
s
e
to
a
d
is
tu
r
b
an
ce
is
d
ee
m
ed
u
n
s
tab
le,
em
er
g
en
c
y
m
an
ag
em
e
n
t
p
r
o
ce
d
u
r
es
ar
e
in
itiated
.
T
r
ad
itio
n
ally
,
T
SA
h
as
r
elied
o
n
tim
e
d
o
m
ain
s
im
u
lati
o
n
,
a
p
r
o
ce
s
s
th
at
in
v
o
lv
es n
u
m
er
ically
s
o
lv
in
g
th
e
s
y
s
tem
'
s
d
y
n
am
ic
eq
u
atio
n
s
o
v
er
a
r
an
g
e
o
f
tim
e
s
tep
s
.
H
o
wev
er
,
th
is
m
et
h
o
d
ca
n
b
e
c
o
m
p
u
tatio
n
ally
d
em
a
n
d
in
g
an
d
tim
e
-
co
n
s
u
m
in
g
,
esp
ec
ially
f
o
r
co
m
p
lex
p
o
wer
s
y
s
tem
s
.
T
o
ad
d
r
ess
th
ese
ch
all
en
g
es,
r
esear
ch
er
s
h
a
v
e
b
ee
n
e
x
p
lo
r
in
g
alter
n
ativ
e
ap
p
r
o
ac
h
es
to
s
p
ee
d
u
p
th
e
T
SA
p
r
o
ce
s
s
wh
ile
m
ain
tain
in
g
a
cc
u
r
ac
y
[
4
5
]
.
On
e
s
u
ch
ap
p
r
o
a
ch
in
v
o
lv
es
th
e
u
s
e
o
f
ad
v
an
ce
d
a
n
aly
tical
m
eth
o
d
s
,
s
u
ch
as
eig
en
v
alu
e
an
aly
s
is
an
d
im
p
e
d
an
ce
-
b
ased
tech
n
iq
u
e
s
,
to
q
u
ick
ly
ass
ess
th
e
s
y
s
tem
'
s
tr
an
s
ien
t
s
tab
ilit
y
.
T
h
ese
m
eth
o
d
s
p
r
o
v
id
e
v
alu
a
b
le
in
s
ig
h
ts
in
to
s
tab
ilit
y
m
a
r
g
in
s
an
d
t
h
e
b
eh
a
v
io
r
o
f
th
e
s
y
s
tem
f
o
llo
win
g
d
is
tu
r
b
an
ce
s
with
o
u
t
th
e
n
ee
d
f
o
r
e
x
ten
s
iv
e
tim
e
d
o
m
ain
s
im
u
lati
o
n
s
.
B
y
co
m
b
in
in
g
an
aly
tical
tech
n
iq
u
es
with
in
tellig
en
t
alg
o
r
ith
m
s
an
d
m
ac
h
in
e
lear
n
in
g
,
r
esear
ch
er
s
ai
m
to
en
h
an
c
e
th
e
ef
f
icien
cy
o
f
T
SA
wh
ile
en
s
u
r
in
g
ac
cu
r
ate
r
esu
lts
.
T
h
ese
ad
v
an
ce
m
en
ts
ar
e
ess
en
tial
f
o
r
m
ain
tain
in
g
th
e
r
eliab
ilit
y
an
d
s
tab
ilit
y
o
f
p
o
w
er
s
y
s
tem
s
,
p
ar
ticu
lar
l
y
as
t
h
e
y
b
ec
o
m
e
m
o
r
e
co
m
p
lex
a
n
d
i
n
ter
co
n
n
ec
te
d
with
th
e
in
teg
r
atio
n
o
f
R
E
Ss
an
d
ad
v
an
ce
d
c
o
n
tr
o
l stra
teg
ies.
T
h
e
f
ield
o
f
T
SA
in
p
o
wer
s
y
s
tem
s
h
as
u
n
d
e
r
g
o
n
e
s
ig
n
if
ican
t
ad
v
an
ce
m
e
n
ts
to
im
p
r
o
v
e
its
ef
f
icien
cy
an
d
ac
c
u
r
ac
y
.
R
esear
ch
er
s
h
av
e
in
tr
o
d
u
ce
d
th
r
ee
m
ain
s
tr
ate
g
ies
aim
ed
at
ac
c
eler
atin
g
T
SA
wh
ile
m
ain
tain
in
g
its
p
r
ec
is
io
n
:
th
e
en
er
g
y
f
u
n
cti
o
n
m
eth
o
d
o
lo
g
y
p
r
o
p
o
s
ed
b
y
[
4
6
]
,
th
e
ex
ten
d
ed
eq
u
al
ar
ea
cr
iter
ia
(
E
E
AC
)
,
an
d
th
e
in
teg
r
atio
n
o
f
ar
tific
ial
in
te
llig
en
ce
(
AI
)
tec
h
n
iq
u
es.
T
h
e
en
er
g
y
f
u
n
ctio
n
m
eth
o
d
o
l
o
g
y
,
as
o
u
tlin
ed
in
[
4
6
]
,
o
f
f
er
s
a
s
y
s
tem
atic
ap
p
r
o
ac
h
t
o
ev
al
u
atin
g
tr
an
s
ien
t
s
tab
ilit
y
.
T
h
is
m
et
h
o
d
f
o
cu
s
es
o
n
q
u
a
n
tify
in
g
th
e
en
er
g
y
f
u
n
ctio
n
o
f
th
e
s
y
s
tem
an
d
an
aly
zin
g
its
tr
ajec
to
r
y
d
u
r
i
n
g
d
is
tu
r
b
an
ce
s
to
p
r
ed
ict
s
ta
b
ilit
y
.
Desp
ite
it
s
co
n
ce
p
tu
al
s
o
u
n
d
n
ess
,
im
p
le
m
en
tin
g
t
h
is
tech
n
iq
u
e
in
co
m
p
lex
s
y
s
tem
s
h
as
p
r
o
v
e
n
c
h
allen
g
in
g
d
u
e
to
th
e
in
tr
icate
m
o
d
elin
g
r
eq
u
ir
em
e
n
ts
it
d
em
an
d
s
.
Similar
ly
,
wh
ile
th
e
E
E
AC
p
r
esen
ts
a
v
iab
le
f
r
am
ewo
r
k
f
o
r
ass
es
s
in
g
s
tab
ilit
y
b
y
an
aly
zin
g
th
e
ar
ea
u
n
d
er
th
e
tr
an
s
ien
t
s
tab
ilit
y
cu
r
v
e,
ap
p
ly
in
g
it
to
lar
g
e
an
d
in
tr
icate
s
y
s
tem
s
p
o
s
es it
s
o
wn
s
et
o
f
d
i
f
f
icu
lties
.
I
n
r
esp
o
n
s
e
to
th
ese
ch
allen
g
e
s
,
r
esear
ch
er
s
ar
e
in
cr
ea
s
in
g
ly
tu
r
n
in
g
t
o
AI
m
eth
o
d
s
to
ex
p
ed
ite
T
SA,
lev
er
ag
in
g
th
e
g
r
o
win
g
a
v
aila
b
ilit
y
o
f
p
h
aso
r
m
ea
s
u
r
em
en
t
u
n
it
(
PMU)
d
ata
a
n
d
a
d
v
an
ce
m
en
ts
in
c
o
m
p
u
te
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
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E
lec
&
Dr
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I
SS
N:
2088
-
8
6
9
4
A
s
ystema
tic
r
ev
ie
w
o
n
vo
lta
g
e
s
ta
b
ilit
y
a
n
a
lysi
s
in
s
ma
r
t a
n
d
is
la
n
d
ed
…
(
S
o
w
mya
R
en
u
k
a
B
a
n
g
a
r
i
)
2431
s
cien
ce
.
I
n
r
ec
e
n
t
s
tu
d
ies,
th
e
f
u
s
io
n
o
f
AI
with
PMU
d
ata
f
o
r
o
n
lin
e
T
SA
h
as
g
ain
ed
tr
ac
tio
n
.
T
h
is
ap
p
r
o
ac
h
tr
ea
ts
T
SA
a
s
a
cla
s
s
if
icat
io
n
p
r
o
b
lem
,
a
n
d
r
esear
ch
er
s
h
av
e
f
o
cu
s
ed
o
n
r
ef
in
i
n
g
d
ata
s
elec
tio
n
f
o
r
tr
ain
in
g
,
o
p
tim
izin
g
alg
o
r
ith
m
s
,
f
in
e
-
tu
n
in
g
p
a
r
am
eter
s
,
an
d
co
n
s
tr
u
ct
in
g
en
s
em
b
les o
f
al
g
o
r
ith
m
s
.
B
y
u
t
i
l
iz
i
n
g
d
a
t
a
m
i
n
i
n
g
t
e
c
h
n
iq
u
e
s
,
i
t
b
e
c
o
m
e
s
p
o
s
s
i
b
l
e
t
o
a
n
a
l
y
z
e
t
i
m
e
s
e
r
i
e
s
d
a
ta
a
n
d
p
r
e
d
i
c
t
t
r
a
n
s
i
e
n
t
v
o
l
t
a
g
e
s
t
a
b
il
i
t
y
wi
t
h
g
r
e
a
t
e
r
ac
c
u
r
a
c
y
.
O
n
e
i
l
l
u
s
t
r
a
t
i
v
e
s
t
u
d
y
,
a
s
p
r
e
s
e
n
t
e
d
b
y
[
4
7
]
,
l
e
v
e
r
a
g
e
s
P
MU
d
a
t
a
a
n
d
a
h
y
b
r
i
d
s
u
p
p
o
r
t
v
e
c
t
o
r
m
a
c
h
i
n
e
(
S
V
M
)
f
o
r
t
r
a
n
s
i
e
n
t
s
t
a
b
i
li
t
y
as
s
ess
m
e
n
t
.
T
h
e
i
n
t
e
g
r
at
i
o
n
o
f
P
M
U
d
a
t
a
e
n
a
b
l
e
s
a
m
o
r
e
c
o
m
p
r
e
h
e
n
s
i
v
e
u
n
d
e
r
s
t
a
n
d
i
n
g
o
f
t
h
e
s
y
s
t
e
m
'
s
d
y
n
a
m
i
cs
,
w
h
i
l
e
t
h
e
h
y
b
r
i
d
SV
M
m
o
d
e
l
en
h
a
n
c
e
s
a
c
c
u
r
a
c
y
.
A
s
tu
d
y
[
4
8
]
in
tr
o
d
u
ce
s
a
n
in
n
o
v
ativ
e
ap
p
r
o
ac
h
th
at
f
r
am
es
o
n
lin
e
p
o
we
r
s
y
s
tem
tr
a
n
s
ien
t
s
tab
ilit
y
ass
es
s
m
en
t
as
a
two
-
class
class
if
icatio
n
p
r
o
b
lem
.
T
h
is
n
o
v
el
m
eth
o
d
o
l
o
g
y
u
tili
ze
s
th
e
co
r
e
v
ec
t
o
r
m
ac
h
in
e
(
C
VM
)
,
a
d
ata
m
in
i
n
g
alg
o
r
ith
m
,
to
a
n
aly
ze
lar
g
e
v
o
lu
m
es
o
f
PMU
d
ata.
T
h
e
C
VM
m
o
d
el
is
tr
ain
ed
an
d
test
ed
o
f
f
lin
e,
a
n
d
t
h
en
a
p
p
lied
in
r
ea
l
-
tim
e
f
o
r
o
n
lin
e
T
SA,
r
esu
ltin
g
in
r
ed
u
ce
d
tim
e
co
n
s
u
m
p
tio
n
an
d
h
eig
h
ten
ed
ac
cu
r
ac
y
co
m
p
ar
e
d
to
co
n
v
en
tio
n
al
SVMs.
I
n
p
ar
allel,
an
i
n
tellig
en
t
s
y
s
tem
(
I
S)
[
4
9
]
h
as
em
er
g
ed
to
a
d
d
r
ess
th
e
d
u
al
d
em
a
n
d
s
o
f
r
a
p
i
d
r
esp
o
n
s
e
an
d
ac
cu
r
ate
ass
ess
m
en
t.
B
y
em
p
lo
y
in
g
en
s
em
b
le
class
if
ier
s
b
ased
o
n
ex
tr
e
m
e
lear
n
i
n
g
m
a
ch
in
es
(
E
L
Ms)
,
th
e
I
S
is
ca
p
ab
le
o
f
class
if
y
in
g
s
y
s
tem
s
tab
ilit
y
p
o
s
t
-
d
is
tu
r
b
an
ce
.
T
h
e
s
y
s
tem
also
f
ea
tu
r
es
a
s
elf
-
ad
ap
tiv
e
d
ec
is
io
n
-
m
ak
in
g
p
r
o
ce
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ically
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o
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ilit
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atin
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w
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k
[
5
0
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ex
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tech
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ata
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en
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T
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ateg
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h
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ilit
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ly
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p
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ield
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tr
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s
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t
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n
s
em
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class
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d
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at
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tech
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T
ab
le
5
.
Su
m
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tab
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ass
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m
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t in
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tem
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g
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f
t c
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m
p
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tin
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tech
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iq
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To
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K
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y
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n
t
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st
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Th
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p
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p
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[
4
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l
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C
V
M
is
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d
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n
[
4
8
]
.
En
se
mb
l
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l
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f
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Th
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p
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[
4
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v
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sem
b
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a
r
n
i
n
g
.
|
7.
CO
NCLU
SI
O
N
T
h
e
R
E
S
h
as
r
ec
en
tly
b
ee
n
p
r
o
v
e
n
to
b
e
a
co
m
p
etitiv
e
a
lter
n
ativ
e
to
ex
is
tin
g
p
o
wer
p
r
o
d
u
ctio
n
m
eth
o
d
s
.
Po
wer
el
ec
tr
o
n
ic
-
b
a
s
ed
co
n
v
er
ter
s
ar
e
th
e
p
r
in
ci
p
a
l
in
ter
f
ac
e
f
o
r
co
n
n
ec
tin
g
R
E
S
to
t
h
e
elec
tr
ic
g
r
id
s
y
s
tem
.
Dr
o
o
p
,
VSM,
o
p
en
cir
cu
it
v
o
ltag
e
(
VOC
)
,
an
d
o
p
en
cir
cu
it
v
o
ltag
e
-
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
VOC
-
PSO
)
co
n
tr
o
l
alg
o
r
ith
m
s
ar
e
u
s
ed
in
an
is
lan
d
ed
MG
to
m
an
ag
e
p
ar
allel
in
v
er
ter
s
an
d
en
s
u
r
e
s
y
n
ch
r
o
n
izatio
n
a
n
d
p
o
wer
s
h
ar
in
g
.
No
co
n
tr
o
l
s
ch
em
e
n
ec
ess
itates
co
m
m
u
n
icatio
n
b
etwe
en
in
v
er
ter
s
.
Sy
n
ch
r
o
n
izatio
n
n
ec
ess
itates
t
h
e
u
s
e
o
f
co
n
tr
o
l
alg
o
r
ith
m
s
to
m
ain
tain
co
n
s
tan
t
v
o
ltag
e
lev
els
an
d
p
h
ase
an
g
les
in
p
ar
allel
in
v
er
ter
s
,
e
n
ab
lin
g
a
m
icr
o
g
r
id
'
s
is
lan
d
ed
m
o
d
e
o
f
o
p
er
atio
n
b
y
in
cr
ea
s
in
g
th
e
a
m
o
u
n
t
o
f
r
en
ewa
b
le
en
er
g
y
p
en
etr
atio
n
in
a
p
o
we
r
s
y
s
tem
.
B
ec
au
s
e
o
f
th
e
la
r
g
e
n
u
m
b
er
o
f
s
y
s
tem
s
tate
v
a
r
iab
les,
th
e
is
lan
d
ed
m
icr
o
g
r
id
'
s
s
tab
ilit
y
r
esear
ch
em
p
lo
y
s
p
ar
allel
lin
k
ed
in
v
er
ter
d
y
n
am
ics,
n
ec
ess
itatin
g
m
o
r
e
co
m
p
u
tatio
n
al
p
o
wer
.
Sev
e
r
al
p
iece
s
o
f
liter
atu
r
e
o
n
t
h
e
s
elf
-
s
y
n
c
h
r
o
n
izatio
n
o
f
p
ar
allel
i
n
v
er
ter
s
a
r
e
c
o
v
er
e
d
in
th
is
o
v
e
r
v
iew.
A
f
ea
tu
r
e
-
r
ed
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ce
d
s
tab
ilit
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aly
s
is
i
s
r
ec
o
m
m
en
d
ed
to
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a
k
e
th
e
s
tab
ilit
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aly
s
is
o
f
p
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allel
in
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ter
s
less
co
m
p
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n
ally
d
em
a
n
d
in
g
.
So
f
t
co
m
p
u
tin
g
tech
n
iq
u
es
lik
e
T
SA
a
m
eth
o
d
s
em
p
lo
y
e
d
t
o
ass
ess
th
e
s
tab
ilit
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