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ticu
lar
ly
in
p
o
we
r
d
eliv
er
y
n
etwo
r
k
s
f
ac
in
g
in
cr
ea
s
in
g
o
p
er
atio
n
al
v
ar
ia
b
ilit
y
.
T
h
is
r
ev
iew
p
r
esen
ts
a
f
r
am
e
wo
r
k
f
o
r
ad
d
r
ess
in
g
ch
allen
g
es
in
h
er
en
t
in
b
u
s
n
etwo
r
k
s
an
d
v
o
ltag
e
co
n
t
r
o
l,
esp
ec
ially
u
n
d
er
th
e
ev
o
lv
in
g
co
n
d
itio
n
s
in
tr
o
d
u
ce
d
b
y
R
E
S.
Nu
m
er
ical
s
im
u
latio
n
tech
n
iq
u
es
p
r
o
v
id
e
en
g
in
ee
r
s
with
th
e
ab
ilit
y
to
p
r
ed
ict
v
o
ltag
e
an
d
cu
r
r
en
t
b
eh
av
io
r
ac
r
o
s
s
n
o
d
es
an
d
b
r
an
ch
es
with
h
ig
h
p
r
ec
is
io
n
,
in
d
e
p
en
d
e
n
t o
f
p
h
y
s
ical
to
p
o
lo
g
y
o
r
e
n
v
ir
o
n
m
en
ta
l c
o
n
s
tr
ain
ts
.
T
r
ad
itio
n
al
s
tead
y
-
s
tate
s
im
u
latio
n
s
ty
p
ically
r
ely
o
n
r
o
o
t
-
f
in
d
in
g
al
g
o
r
ith
m
s
,
s
u
ch
as
t
h
e
New
to
n
-
R
ap
h
s
o
n
m
eth
o
d
,
wh
ich
ar
e
well
-
s
u
ited
f
o
r
s
o
lv
in
g
n
o
n
lin
ea
r
eq
u
atio
n
s
at
s
y
s
tem
eq
u
ilib
r
iu
m
.
B
y
co
n
tr
ast,
d
y
n
am
ic
s
im
u
latio
n
s
ca
p
tu
r
e
i
n
s
tan
tan
eo
u
s
an
d
f
lu
ct
u
atin
g
b
eh
av
io
r
in
v
a
r
iab
les
s
u
ch
as
v
o
ltag
e,
cu
r
r
e
n
t,
an
d
g
en
er
ato
r
r
o
to
r
s
p
ee
d
.
T
h
ese
s
im
u
latio
n
s
o
f
ten
r
eq
u
ir
e
s
o
lv
in
g
f
ir
s
t
-
o
r
d
e
r
d
if
f
er
en
tial
eq
u
ati
o
n
s
to
r
ef
lect
tim
e
-
d
ep
en
d
e
n
t
ir
r
eg
u
lar
ities
in
s
y
s
tem
p
er
f
o
r
m
an
ce
.
Am
o
n
g
th
e
n
u
m
er
ical
in
teg
r
atio
n
tec
h
n
iq
u
e
s
,
th
e
R
u
n
g
e
-
Ku
tta
m
eth
o
d
is
f
r
e
q
u
en
tly
e
m
p
lo
y
e
d
to
co
m
p
u
te
d
y
n
am
ic
s
tates with
en
h
an
ce
d
tem
p
o
r
al
a
cc
u
r
ac
y
.
T
h
e
in
cr
ea
s
in
g
p
en
etr
atio
n
o
f
R
E
S
in
to
n
atio
n
al
g
r
id
s
h
as
f
u
r
th
er
co
m
p
licated
th
is
lan
d
s
ca
p
e,
ex
p
o
s
in
g
th
e
lim
itatio
n
s
o
f
co
n
v
en
tio
n
al
s
im
u
latio
n
to
o
ls
.
T
h
ese
to
o
ls
o
f
ten
f
all
s
h
o
r
t
in
m
o
d
elin
g
tr
a
n
s
ien
t
ev
en
ts
,
r
ap
id
f
lu
ctu
atio
n
s
,
an
d
f
au
lt
-
d
r
iv
en
i
n
s
tab
i
lity
with
s
u
f
f
icien
t
r
eso
lu
tio
n
[
6
]
.
T
h
e
s
to
ch
asti
c
n
atu
r
e
o
f
R
E
S
g
en
er
atio
n
in
tr
o
d
u
ce
s
v
o
ltag
e
v
ar
iab
ilit
y
,
wea
k
en
s
tr
ad
itio
n
al
p
r
o
tectio
n
s
ch
em
es,
an
d
alter
s
s
y
s
tem
i
n
er
tia,
all
o
f
wh
ich
co
m
p
licate
s
tab
ilit
y
ass
es
s
m
en
ts
[
7
]
.
I
n
th
is
r
eg
a
r
d
,
R
T
S
h
as
em
e
r
g
ed
as
a
t
r
a
n
s
f
o
r
m
at
iv
e
t
o
o
l
f
o
r
an
al
y
zi
n
g
p
o
we
r
s
y
s
te
m
s
u
n
d
e
r
d
y
n
a
m
i
c
o
p
e
r
at
in
g
co
n
d
it
io
n
s
[
8
]
.
R
T
S
en
a
b
les
r
ea
l
-
t
im
e
m
o
d
e
li
n
g
t
h
at
al
ig
n
s
s
im
u
l
ati
o
n
o
u
tp
u
ts
wit
h
p
h
y
s
i
ca
l
ti
m
e
,
th
e
r
eb
y
o
f
f
e
r
i
n
g
cl
ea
r
e
r
in
s
ig
h
t
s
i
n
t
o
tr
a
n
s
ie
n
t
p
h
e
n
o
m
e
n
a,
p
a
r
tic
u
la
r
l
y
t
h
o
s
e
a
r
is
i
n
g
i
n
R
E
S
-
i
n
te
g
r
a
te
d
n
etw
o
r
k
s
[
9
]
.
T
h
is
is
es
p
e
cia
ll
y
c
r
u
cia
l
i
n
m
o
d
e
r
n
g
r
i
d
s
,
w
h
e
r
e
h
i
g
h
le
v
els
o
f
d
is
tr
ib
u
t
e
d
g
e
n
er
ati
o
n
m
a
y
tr
ig
g
er
s
u
d
d
e
n
v
o
lta
g
e
d
e
v
i
ati
o
n
s
,
c
o
n
d
iti
o
n
s
th
a
t
tr
ad
iti
o
n
al
s
i
m
u
lat
o
r
s
o
f
t
e
n
f
a
il
t
o
p
r
e
d
ic
t
o
r
m
it
ig
ate
e
f
f
ec
ti
v
el
y
[
1
0
]
.
−
Pro
b
lem
s
tatem
en
t
R
ec
en
t
ad
v
an
ce
m
en
ts
in
n
u
m
er
ical
m
o
d
elin
g
h
av
e
d
e
m
o
n
s
tr
ated
th
at
o
p
tim
ized
s
tate
-
s
p
ac
e
f
o
r
m
u
latio
n
s
an
d
im
p
r
o
v
ed
d
er
iv
ativ
e
ap
p
r
o
x
im
atio
n
s
ca
n
s
ig
n
if
ican
tly
en
h
an
ce
r
ea
l
-
tim
e
co
m
p
u
tatio
n
al
ef
f
icien
cy
a
n
d
ac
cu
r
ac
y
in
d
y
n
am
ic
s
y
s
tem
s
im
u
latio
n
s
[
1
1
]
.
T
h
ese
d
e
v
elo
p
m
e
n
ts
co
m
p
lem
en
t
tr
a
d
itio
n
al
n
u
m
er
ical
ap
p
r
o
ac
h
es
th
at
r
e
m
ain
ce
n
tr
al
to
elec
tr
ical
p
o
wer
s
y
s
tem
an
aly
s
is
,
wh
eth
er
th
r
o
u
g
h
co
m
m
er
cial
s
o
f
twar
e
o
r
c
u
s
to
m
-
co
d
e
d
p
l
atf
o
r
m
s
,
f
o
r
s
tu
d
y
i
n
g
b
u
s
n
e
two
r
k
s
u
n
d
e
r
d
i
v
er
s
e
o
p
e
r
atin
g
co
n
d
itio
n
s
[
1
2
]
.
Dy
n
am
ic
s
im
u
l
atio
n
s
ar
e
p
ar
ticu
lar
ly
v
alu
ab
le
f
o
r
ca
p
tu
r
i
n
g
in
s
tan
tan
eo
u
s
v
ar
iatio
n
s
in
v
o
ltag
e,
cu
r
r
e
n
t,
an
d
r
o
to
r
s
p
ee
d
[
1
3
]
.
Ho
wev
e
r
,
th
e
ir
ac
cu
r
ac
y
s
till
d
ep
en
d
s
o
n
d
is
cr
etiza
tio
n
m
eth
o
d
s
th
at
a
p
p
r
o
x
im
ate
co
n
tin
u
o
u
s
-
tim
e
d
er
iv
ativ
es
o
v
er
f
in
ite
ti
m
e
s
tep
s
.
Sm
aller
tim
e
s
tep
s
in
cr
ea
s
e
p
r
ec
is
io
n
b
u
t
r
aise
c
o
m
p
u
tatio
n
al
co
s
t,
wh
er
ea
s
lar
g
er
s
tep
s
im
p
r
o
v
e
ef
f
icien
cy
at
th
e
e
x
p
en
s
e
o
f
f
i
d
elity
.
T
h
is
tr
ad
e
-
o
f
f
b
ec
o
m
es
cr
itical
in
r
ea
l
-
tim
e
en
v
ir
o
n
m
en
ts
wh
er
e
ea
ch
s
ec
o
n
d
o
f
s
y
s
tem
ac
tiv
ity
m
u
s
t
b
e
co
m
p
u
ted
with
in
th
e
s
am
e
s
ec
o
n
d
.
Alth
o
u
g
h
ad
v
an
ce
d
s
o
lv
er
s
s
u
ch
as
th
e
R
u
n
g
e
–
Ku
tta
f
am
ily
r
ed
u
ce
th
ese
er
r
o
r
s
,
th
eir
s
eq
u
en
tial
co
m
p
u
tatio
n
lim
its
p
er
f
o
r
m
an
ce
wh
e
n
m
o
d
elin
g
f
ast
tr
an
s
ien
ts
o
r
h
ig
h
-
f
r
eq
u
e
n
c
y
s
witch
in
g
ev
en
ts
.
T
h
ei
r
ac
cu
r
ac
y
o
f
te
n
r
elies
o
n
n
u
m
er
ical
s
o
lv
er
s
s
u
c
h
as
th
e
R
u
n
g
e
-
Ku
tta
f
am
ily
,
wh
ich
e
x
t
en
d
th
e
f
in
ite
-
d
if
f
er
en
ce
d
er
iv
a
tiv
e
ap
p
r
o
x
im
atio
n
:
(
)
=
l
im
→
0
(
+
)
−
(
)
(
1
)
I
n
d
ig
ital
en
v
ir
o
n
m
en
ts
,
th
is
ti
m
e
s
tep
is
f
in
ite
r
ath
er
th
an
in
f
in
ites
im
al,
cr
ea
tin
g
a
tr
ad
e
-
o
f
f
:
s
m
aller
in
ter
v
als
y
ield
ac
cu
r
ac
y
b
u
t
d
e
m
an
d
m
o
r
e
c
o
m
p
u
tatio
n
,
wh
il
e
lar
g
er
o
n
es
im
p
r
o
v
e
s
p
ee
d
at
th
e
co
s
t
o
f
f
id
elity
.
R
ea
l
-
tim
e
co
n
tex
ts
m
ak
e
th
is
b
alan
ce
c
r
itical
wh
en
s
im
u
la
tin
g
f
ast
tr
an
s
ien
ts
o
r
h
ig
h
-
f
r
eq
u
en
cy
s
witch
in
g
ev
en
ts
.
R
u
n
g
e
-
Ku
tta
m
eth
o
d
s
m
itig
ate
th
e
tr
a
d
e
-
o
f
f
b
y
in
co
r
p
o
r
atin
g
in
ter
m
ed
iate
d
e
r
iv
ativ
e
ev
alu
atio
n
s
,
en
ab
lin
g
p
r
ec
is
e
tr
ac
k
in
g
o
f
s
y
s
tem
d
y
n
am
ics with
o
u
t im
p
r
a
ctica
lly
s
m
all
s
tep
s
.
B
u
ild
in
g
o
n
th
is
f
o
u
n
d
atio
n
,
s
tate
-
s
p
ac
e
m
o
d
elin
g
p
r
o
v
i
d
e
s
a
m
atr
ix
-
b
ased
f
r
am
ewo
r
k
t
o
s
im
u
late
tr
an
s
ien
t
p
h
en
o
m
en
a
with
g
r
ea
ter
ac
cu
r
ac
y
,
esp
ec
ially
in
g
r
id
s
with
h
ig
h
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
(
R
E
S)
p
en
etr
atio
n
.
Su
ch
en
v
ir
o
n
m
e
n
ts
f
ac
e
ch
allen
g
es
,
in
clu
d
in
g
v
o
ltag
e
in
s
tab
ilit
y
,
b
id
ir
ec
tio
n
a
l
f
lo
ws,
an
d
alter
e
d
p
r
o
tectio
n
c
o
o
r
d
i
n
atio
n
.
So
lar
PV
in
teg
r
atio
n
,
in
p
ar
ticu
lar
,
in
tr
o
d
u
ce
s
v
o
ltag
e
r
is
e,
r
ev
e
r
s
e
p
o
wer
f
lo
w,
an
d
h
eig
h
ten
ed
f
au
lt
lev
els
co
n
d
iti
o
n
s
th
at
tr
ad
itio
n
al
s
tead
y
-
s
tate
m
eth
o
d
s
s
tr
u
g
g
le
to
a
d
d
r
e
s
s
.
I
n
teg
r
atin
g
s
tate
-
s
p
ac
e
ap
p
r
o
ac
h
es with
R
T
S e
n
ab
les im
p
r
o
v
ed
p
r
ed
ictio
n
a
n
d
m
an
ag
e
m
en
t
o
f
th
ese
d
y
n
am
i
c
b
eh
a
v
io
r
s
.
I
n
th
is
r
eg
ar
d
,
p
r
in
ci
p
les
f
r
o
m
ad
v
an
ce
d
d
is
cr
ete
-
tim
e
co
n
tr
o
l
t
h
eo
r
y
em
p
h
asize
th
at
d
ig
ital
-
d
o
m
a
in
im
p
lem
en
tatio
n
s
m
u
s
t a
d
d
r
ess
s
am
p
lin
g
,
d
ela
y
,
an
d
g
ain
-
ad
ju
s
tm
en
t e
f
f
ec
ts
to
p
r
eser
v
e
s
y
s
tem
s
tab
ilit
y
an
d
p
r
ec
is
io
n
[
1
4
]
.
Un
lik
e
o
f
f
lin
e
s
im
u
latio
n
s
,
r
ea
l
-
tim
e
s
im
u
latio
n
r
eq
u
ir
es
ea
ch
s
ec
o
n
d
o
f
s
y
s
tem
ac
tiv
ity
to
b
e
co
m
p
u
ted
with
in
th
e
s
am
e
s
ec
o
n
d
,
a
ch
allen
g
e
m
a
g
n
if
ied
in
lar
g
e
-
s
ca
le
s
y
s
tem
s
wh
er
e
co
m
p
u
tatio
n
al
d
em
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
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lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
I
mp
r
o
vin
g
vo
lta
g
e
s
ta
b
ilit
y
in
is
o
la
ted
r
en
ewa
b
le
en
erg
y
micro
g
r
id
s
u
s
in
g
virt
u
a
l
…
(
A
h
m
a
d
S
u
p
a
w
i O
s
ma
n
)
685
g
r
o
ws
ex
p
o
n
en
tially
.
C
o
n
v
en
tio
n
al
s
im
u
lato
r
s
o
f
ten
f
ail
to
m
ee
t
th
is
r
eq
u
ir
em
e
n
t,
lim
itin
g
th
eir
a
b
ilit
y
to
ca
p
tu
r
e
tr
an
s
ien
t
d
y
n
am
ics
in
R
E
S
-
h
ea
v
y
m
icr
o
g
r
id
s
[
1
5
]
.
B
u
ild
in
g
o
n
th
ese
f
o
u
n
d
atio
n
s
,
s
tate
-
s
p
ac
e
m
o
d
elin
g
p
r
o
v
id
es
a
m
atr
ix
-
b
ased
f
r
a
m
ewo
r
k
ca
p
ab
le
o
f
r
e
p
r
esen
t
in
g
tr
an
s
ien
t
p
h
en
o
m
en
a
with
g
r
ea
ter
p
r
ec
is
io
n
,
p
ar
ticu
lar
ly
in
g
r
id
s
with
h
ig
h
-
R
E
S
p
en
etr
atio
n
.
Su
ch
s
y
s
tem
s
f
ac
e
p
er
s
is
ten
t
ch
allen
g
es
o
f
v
o
ltag
e
in
s
tab
ilit
y
,
b
id
ir
ec
tio
n
al
p
o
wer
f
lo
w,
a
n
d
p
r
o
tectio
n
co
o
r
d
in
atio
n
,
wh
ich
tr
ad
itio
n
al
s
tead
y
-
s
tat
e
m
eth
o
d
s
ca
n
n
o
t
ad
eq
u
ately
ca
p
tu
r
e.
T
h
is
u
n
d
er
s
co
r
es
th
e
n
ee
d
f
o
r
ad
v
an
ce
d
,
s
tate
-
s
p
ac
e
-
b
ased
r
e
al
-
tim
e
s
im
u
latio
n
f
r
am
ewo
r
k
s
th
at
co
m
b
i
n
e
th
e
ac
cu
r
ac
y
o
f
m
o
d
er
n
n
u
m
er
ic
al
alg
o
r
ith
m
s
with
th
e
co
m
p
u
tatio
n
al
ef
f
icien
cy
r
eq
u
ir
ed
f
o
r
en
s
u
r
in
g
v
o
ltag
e
s
tab
ilit
y
in
d
is
tr
ib
u
ted
r
e
n
ewa
b
le
g
r
id
s
.
−
Ob
jectiv
es
R
ea
l
-
tim
e
s
im
u
latio
n
im
p
o
s
es
a
u
n
iq
u
e
co
m
p
u
tatio
n
al
d
em
an
d
:
s
y
s
tem
ev
en
ts
m
u
s
t
b
e
m
o
d
eled
with
in
th
e
s
am
e
tim
e
win
d
o
w
in
wh
ic
h
th
ey
o
cc
u
r
.
A
o
n
e
-
s
ec
o
n
d
tr
a
n
s
ien
t,
f
o
r
in
s
tan
ce
,
m
u
s
t
b
e
p
r
o
ce
s
s
ed
in
p
r
ec
is
ely
o
n
e
s
ec
o
n
d
.
T
h
is
r
eq
u
ir
e
m
en
t
b
ec
o
m
es
p
ar
ticu
lar
l
y
ch
allen
g
in
g
in
m
o
d
e
r
n
g
r
id
s
with
h
ig
h
-
R
E
S
p
en
etr
atio
n
,
wh
er
e
s
in
g
le
-
p
r
o
ce
s
s
o
r
s
y
s
tem
s
o
f
ten
b
u
ck
le
u
n
d
er
th
e
h
e
av
y
co
m
p
u
tatio
n
al
lo
ad
[
1
6
]
.
Par
allel
p
r
o
ce
s
s
in
g
o
f
f
er
s
a
p
ar
tial
r
em
e
d
y
b
y
d
is
tr
ib
u
tin
g
task
s
ac
r
o
s
s
m
u
ltip
le
p
r
o
ce
s
s
o
r
s
to
r
e
d
u
ce
laten
cy
an
d
b
o
o
s
t
th
r
o
u
g
h
p
u
t
[
1
7
]
.
Yet,
tr
u
e
r
ea
l
-
tim
e
f
id
elity
r
eq
u
ir
es
m
o
r
e
th
an
s
p
ee
d
;
it
d
em
a
n
d
s
s
ea
m
le
s
s
in
ter
ac
tio
n
with
ex
ter
n
al
d
e
v
ices
s
u
ch
as
r
elay
s
,
elec
tr
ical
m
ac
h
in
es,
an
d
p
r
o
te
ctio
n
u
n
its
,
wh
er
e
h
u
m
a
n
an
d
h
ar
d
war
e
r
esp
o
n
s
es
ar
e
also
p
ar
t o
f
th
e
lo
o
p
[
1
8
]
,
[
1
9
]
.
W
ith
in
th
is
co
n
tex
t,
h
ar
d
war
e
-
in
-
th
e
-
lo
o
p
(
HI
L
)
an
d
p
o
wer
h
ar
d
war
e
-
in
-
t
h
e
-
lo
o
p
(
PHI
L
)
m
eth
o
d
s
h
av
e
b
ec
o
m
e
ess
en
tial.
B
y
e
m
b
ed
d
in
g
p
h
y
s
ical
co
m
p
o
n
en
ts
in
to
th
e
s
im
u
latio
n
lo
o
p
th
r
o
u
g
h
s
tan
d
ar
d
ized
p
r
o
to
co
ls
,
t
h
ey
c
r
ea
te
clo
s
ed
-
l
o
o
p
e
n
v
ir
o
n
m
en
ts
th
at
ac
cu
r
at
ely
r
ef
lect
o
p
er
atio
n
al
d
y
n
am
i
cs
[
2
0
]
.
T
h
is
s
tu
d
y
em
p
lo
y
s
an
OPAL
-
R
T
p
latf
o
r
m
i
n
teg
r
ate
d
with
MA
T
L
A
B
/Si
m
u
lin
k
an
d
R
T
-
L
AB
to
m
o
d
el
a
m
icr
o
g
r
id
in
co
r
p
o
r
atin
g
p
h
o
to
v
o
ltaic
g
en
er
atio
n
,
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
b
eh
av
io
r
,
an
d
b
u
s
in
ter
co
n
n
ec
tio
n
s
,
en
ab
lin
g
r
ea
l
-
tim
e
p
r
o
to
ty
p
in
g
a
n
d
v
alid
atio
n
[
2
1
]
.
T
h
e
o
b
jectiv
es
o
f
th
is
r
e
v
iew
a
r
e
f
o
u
r
f
o
l
d
.
First,
to
in
v
esti
g
ate
th
e
tr
an
s
ien
t
b
eh
av
io
r
o
f
R
E
S
-
in
teg
r
ated
s
y
s
tem
s
d
u
r
in
g
f
au
lts
,
with
e
m
p
h
asis
o
n
v
o
ltag
e
s
tab
ilit
y
,
f
au
lt
d
u
r
atio
n
,
an
d
m
itig
atio
n
.
Seco
n
d
,
to
ass
ess
ad
v
an
ce
d
c
o
n
tr
o
l
an
d
p
r
o
tect
io
n
s
tr
ateg
i
es
u
s
in
g
r
ea
l
-
tim
e
s
im
u
latio
n
f
o
r
v
alid
atio
n
.
T
h
ir
d
,
to
p
r
o
p
o
s
e
an
im
p
r
o
v
e
d
f
r
am
ewo
r
k
th
at
m
e
r
g
es
s
tate
-
s
p
ac
e
m
o
d
elin
g
with
p
ar
allel
p
r
o
ce
s
s
in
g
f
o
r
h
i
g
h
er
ef
f
icien
cy
an
d
f
id
elity
.
Fin
ally
,
to
ev
alu
ate
HI
L
test
in
g
as
a
b
r
id
g
e
b
etwe
en
s
im
u
latio
n
an
d
r
ea
l
-
wo
r
ld
ap
p
licatio
n
.
C
o
llectiv
ely
,
th
ese
aim
s
p
o
s
iti
o
n
r
ea
l
-
tim
e,
m
o
d
el
-
d
r
iv
en
s
i
m
u
latio
n
as
a
to
o
l
n
o
t
o
n
l
y
f
o
r
s
af
eg
u
ar
d
in
g
v
o
ltag
e
s
tab
ilit
y
an
d
r
ed
u
cin
g
o
u
tag
es
b
u
t
also
f
o
r
o
p
tim
izin
g
p
er
f
o
r
m
an
ce
u
n
d
e
r
f
lu
ctu
ati
n
g
g
e
n
er
atio
n
an
d
d
em
an
d
[
2
2
]
,
[
2
3
]
.
As
r
en
ewa
b
le
in
teg
r
atio
n
ac
ce
le
r
ates,
s
u
ch
ap
p
r
o
ac
h
es
will
b
e
v
ital
f
o
r
in
f
o
r
m
in
g
p
r
esen
t
p
r
ac
tice
an
d
s
h
a
p
in
g
f
u
tu
r
e
-
r
e
ad
y
g
r
i
d
in
f
r
astru
ct
u
r
es [
2
4
]
.
2.
M
E
T
H
O
D
T
h
is
s
tu
d
y
ad
o
p
ts
a
s
tr
u
ctu
r
ed
m
eth
o
d
o
lo
g
ical
f
r
a
m
ewo
r
k
to
i
n
v
esti
g
ate
d
y
n
am
ic
s
im
u
latio
n
ap
p
r
o
ac
h
es
f
o
r
m
o
d
elin
g
p
o
w
er
s
y
s
tem
s
with
h
i
g
h
p
en
etr
at
io
n
o
f
R
E
S.
T
h
e
o
b
jectiv
e
is
to
o
p
tim
ize
s
y
s
tem
o
p
er
atio
n
,
im
p
r
o
v
e
en
e
r
g
y
in
t
er
ac
tio
n
b
etwe
en
c
o
m
p
o
n
en
ts
,
an
d
d
ev
elo
p
p
r
ac
tical
s
tr
ateg
ies
f
o
r
en
h
an
cin
g
v
o
ltag
e
s
tab
ilit
y
.
As
illu
s
tr
ated
in
Fig
u
r
e
1
,
th
e
m
eth
o
d
o
lo
g
y
p
r
o
g
r
ess
es
th
r
o
u
g
h
th
r
ee
s
tag
es:
p
r
elim
in
ar
y
,
im
p
lem
en
tatio
n
,
a
n
d
r
esu
lt
.
I
n
th
e
p
r
elim
i
n
ar
y
s
tag
e
,
s
y
s
te
m
co
n
f
ig
u
r
atio
n
a
n
d
d
ata
c
o
llectio
n
estab
lis
h
f
o
u
n
d
atio
n
al
p
ar
am
eter
s
u
s
in
g
s
p
ec
if
icatio
n
d
ata.
T
h
e
im
p
lem
en
tatio
n
s
tag
e
f
o
llo
ws
with
co
m
p
o
n
en
t
m
o
d
el
d
ev
elo
p
m
en
t,
s
y
s
tem
in
teg
r
atio
n
,
a
n
d
v
alid
atio
n
,
s
u
p
p
o
r
ted
b
y
r
ea
l
o
p
er
atin
g
d
ata
to
en
s
u
r
e
f
id
elity
.
Fin
all
y
,
th
e
r
esu
lt
s
tag
e
en
co
m
p
ass
es
s
ce
n
ar
io
s
im
u
lat
io
n
an
d
th
e
d
ev
elo
p
m
en
t
o
f
ef
f
ec
tiv
e
o
p
er
atio
n
al
s
tr
ateg
ies,
v
er
if
ied
th
r
o
u
g
h
v
alid
ated
d
atasets
.
T
h
is
s
tag
e
d
p
r
o
g
r
ess
io
n
e
n
s
u
r
es
s
im
u
latio
n
s
ev
o
lv
e
f
r
o
m
ab
s
tr
ac
t
m
o
d
els
to
r
e
al
-
wo
r
ld
r
elev
an
ce
,
en
a
b
lin
g
iter
ativ
e
r
ef
in
em
en
t o
f
s
y
s
tem
p
er
f
o
r
m
a
n
ce
.
T
o
co
n
te
x
tu
alize
th
is
ap
p
r
o
ac
h
,
it
is
im
p
o
r
ta
n
t
to
n
o
te
th
e
d
if
f
er
en
ce
b
etwe
en
d
y
n
am
ic
an
d
s
tatic
s
im
u
latio
n
s
.
Dy
n
am
ic
s
im
u
latio
n
s
p
r
o
v
id
e
c
o
m
p
lex
,
ac
cu
r
ate
in
s
ig
h
ts
b
u
t
ar
e
tim
e
-
co
n
s
u
m
in
g
an
d
less
ef
f
ec
tiv
e
at
id
en
tify
in
g
f
ailu
r
e
b
o
u
n
d
ar
ies,
wh
er
ea
s
s
tati
c
s
im
u
latio
n
s
ar
e
q
u
ick
er
,
s
i
m
p
ler
,
an
d
b
etter
at
in
d
icatin
g
a
p
p
r
o
x
im
ate
lim
its
[
2
5
]
.
T
h
is
co
m
p
a
r
is
o
n
r
ei
n
f
o
r
ce
s
wh
y
d
y
n
am
ic
ap
p
r
o
ac
h
e
s
,
th
o
u
g
h
r
eso
u
r
ce
-
in
ten
s
iv
e,
ar
e
b
etter
s
u
ited
f
o
r
ca
p
tu
r
in
g
t
h
e
tr
an
s
ien
t b
e
h
av
i
o
r
s
ce
n
tr
al
to
R
E
S
-
in
teg
r
ated
s
y
s
tem
s
[
2
5]
.
2
.
1
.
St
a
t
e
-
s
pa
ce
mo
del
T
h
e
s
tate
-
s
p
ac
e
m
o
d
el
p
r
o
v
id
es
a
r
o
b
u
s
t
m
ath
e
m
atica
l
f
r
a
m
ewo
r
k
f
o
r
d
escr
ib
in
g
d
y
n
a
m
ic
s
y
s
tem
b
eh
av
io
r
,
p
a
r
ticu
lar
ly
v
alu
ab
l
e
in
m
o
d
er
n
co
n
tr
o
l
ap
p
licatio
n
s
with
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
(
R
E
S)
[
2
5
]
.
B
y
ex
p
r
ess
in
g
s
y
s
tem
d
y
n
am
ics
t
h
r
o
u
g
h
f
ir
s
t
-
o
r
d
er
d
if
f
er
en
tial
eq
u
atio
n
s
,
it
ca
p
tu
r
es
th
e
co
n
ti
n
u
o
u
s
e
v
o
lu
tio
n
o
f
in
ter
n
al
s
tates
u
n
d
e
r
v
a
r
y
in
g
in
p
u
ts
an
d
f
ee
d
b
ac
k
,
m
ak
in
g
it
well
-
s
u
ited
f
o
r
r
ea
l
-
tim
e
s
im
u
l
atio
n
s
.
Hig
h
er
-
o
r
d
e
r
d
if
f
er
en
tial
s
y
s
tem
s
ca
n
also
b
e
s
im
p
lifie
d
in
to
f
ir
s
t
-
o
r
d
e
r
f
o
r
m
s
,
im
p
r
o
v
in
g
co
m
p
u
tati
o
n
al
ef
f
icien
c
y
a
n
d
en
ab
lin
g
co
n
tr
o
ller
d
esig
n
[
2
6
]
.
T
h
e
g
en
er
al
co
n
tin
u
o
u
s
-
tim
e
lin
ea
r
tim
e
-
in
v
ar
ian
t
(
L
T
I
)
s
tate
-
s
p
ac
e
r
ep
r
esen
tatio
n
is
:
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.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
683
-
695
686
(
)
=
(
)
+
(
)
(
)
=
(
)
+
(
)
(
2
)
W
h
er
e:
(
)
is
th
e
s
tate
v
ec
to
r
,
r
ep
r
esen
tin
g
in
ter
n
al
s
y
s
tem
s
tates,
(
)
is
th
e
in
p
u
t
v
ec
to
r
,
r
e
p
r
esen
tin
g
ex
ter
n
al
d
r
iv
in
g
s
ig
n
als,
(
)
is
th
e
o
u
tp
u
t
v
ec
to
r
s
,
co
n
tain
in
g
th
e
m
ea
s
u
r
ab
le
o
u
tp
u
ts
,
,
,
an
d
m
atr
ices
d
escr
ib
e
s
y
s
tem
d
y
n
am
ics,
in
p
u
t e
f
f
ec
t
s
,
o
u
tp
u
t m
a
p
p
in
g
s
,
a
n
d
d
i
r
ec
t tr
an
s
m
is
s
io
n
p
ath
s
,
r
esp
ec
tiv
e
ly
.
T
h
ese
r
elatio
n
s
h
ip
s
a
r
e
clea
r
l
y
illu
s
tr
ated
in
Fig
u
r
e
2
,
wh
ic
h
p
r
o
v
id
es
a
s
tr
u
ctu
r
al
v
iew
o
f
h
o
w
th
e
s
tate
-
s
p
ac
e
co
m
p
o
n
e
n
ts
in
ter
c
o
n
n
ec
t.
T
h
e
in
p
u
t
u
(
t)
in
f
l
u
en
ce
s
th
e
s
y
s
tem
b
o
th
d
ir
ec
tly
th
r
o
u
g
h
m
atr
ix
D
an
d
in
d
ir
ec
tly
v
ia
th
e
s
tate
ev
o
lu
tio
n
p
ath
,
wh
er
e
it c
o
m
b
in
es with
cu
r
r
en
t state
v
alu
es
x(
t)
th
r
o
u
g
h
m
atr
ices
A
an
d
B
.
T
h
e
r
esu
ltin
g
s
tate
u
p
d
ates
ar
e
th
en
p
r
o
ce
s
s
ed
b
y
m
atr
ix
C
to
y
ield
th
e
o
u
tp
u
t
y(
t)
.
T
h
e
in
teg
r
ato
r
b
lo
c
k
1
ca
p
tu
r
es th
e
co
n
tin
u
o
u
s
ac
cu
m
u
latio
n
o
f
s
y
s
tem
d
y
n
am
ics
o
v
er
tim
e.
Fig
u
r
e
1
.
Mo
d
el
d
ev
el
o
p
m
e
n
t
an
d
ev
alu
atio
n
m
eth
o
d
o
l
o
g
y
f
r
am
e
wo
r
k
Fig
u
r
e
2
.
State
-
s
p
ac
e
b
lo
c
k
d
i
ag
r
am
s
tr
u
ctu
r
e
I
n
r
ea
l
-
tim
e
ap
p
licatio
n
s
s
u
ch
as
HI
L
test
in
g
,
s
tate
-
s
p
ac
e
m
o
d
els
m
u
s
t
r
em
ain
s
y
n
ch
r
o
n
ize
d
with
r
e
al
-
tim
e
clo
ck
s
to
en
s
u
r
e
ac
cu
r
ate
co
n
tr
o
ller
in
ter
ac
tio
n
[
2
7
]
,
[
2
8
]
.
T
o
ac
h
ie
v
e
th
is
p
r
ec
is
io
n
,
f
ield
p
r
o
g
r
a
m
m
ab
le
g
ate
ar
r
a
y
s
(
FP
GAs)
ar
e
in
c
r
ea
s
in
g
ly
em
p
l
o
y
ed
f
o
r
th
eir
p
ar
allel
p
r
o
ce
s
s
in
g
s
p
ee
d
an
d
u
ltra
-
lo
w
laten
cy
.
E
m
b
ed
d
in
g
m
o
d
els
d
ir
ec
tly
i
n
FP
GA
lo
g
ic
en
a
b
les
s
u
b
-
m
icr
o
s
ec
o
n
d
r
eso
lu
tio
n
,
allo
win
g
d
etailed
s
im
u
latio
n
o
f
elec
tr
o
m
ec
h
an
ical
d
y
n
am
ic
s
cr
itical
f
o
r
m
icr
o
g
r
id
s
a
n
d
p
o
wer
elec
tr
o
n
ics
[
2
9
]
.
Hy
b
r
id
HI
L
s
etu
p
s
,
w
h
er
e
p
ar
t o
f
th
e
s
y
s
tem
is
p
h
y
s
ically
r
ea
lized
a
n
d
th
e
r
est s
im
u
lat
ed
,
f
u
r
th
er
allo
w
s
af
e
test
in
g
o
f
co
n
tr
o
l a
lg
o
r
ith
m
s
u
n
d
er
c
o
n
d
itio
n
s
s
u
ch
as f
r
eq
u
en
cy
d
e
v
iatio
n
s
o
r
g
r
id
f
a
u
lts
.
T
h
e
ad
v
an
ta
g
es
o
f
FP
GA
-
en
h
an
ce
d
s
tate
-
s
p
ac
e
s
im
u
latio
n
s
in
clu
d
e
n
an
o
s
ec
o
n
d
-
le
v
el
ac
cu
r
ac
y
,
p
ar
allel
co
m
p
u
tatio
n
f
o
r
s
p
ee
d
,
r
ep
r
o
g
r
am
m
ab
ilit
y
f
o
r
d
iv
er
s
e
s
ce
n
ar
io
s
,
an
d
s
ca
lab
ilit
y
f
o
r
c
o
m
p
lex
ar
ch
itectu
r
es
[
3
0
]
.
T
h
ese
f
ea
tu
r
es
m
ak
e
th
em
in
d
is
p
en
s
ab
le
f
o
r
r
e
n
ewa
b
le
-
in
teg
r
ate
d
g
r
id
s
wh
er
e
ad
ap
ta
b
ilit
y
an
d
p
r
ec
is
io
n
a
r
e
p
ar
am
o
u
n
t
[
3
1
]
–
[
3
3
]
.
T
o
alig
n
co
n
tin
u
o
u
s
m
o
d
els
with
d
i
g
ital
p
r
o
c
ess
o
r
s
,
s
tat
e
-
s
p
ac
e
eq
u
atio
n
s
ar
e
ty
p
ically
d
is
cr
eti
ze
d
u
s
in
g
m
eth
o
d
s
lik
e
E
u
ler
o
r
R
u
n
g
e
–
Ku
tta,
e
n
s
u
r
in
g
u
p
d
at
es
m
atch
r
ea
l
-
tim
e
s
am
p
lin
g
f
r
e
q
u
en
cies.
O
n
ce
d
ep
lo
y
ed
o
n
FP
GA
p
latf
o
r
m
s
o
r
d
i
g
ital
s
ig
n
al
p
r
o
ce
s
s
o
r
s
,
t
h
ese
m
o
d
els
en
a
b
le
h
ig
h
-
f
i
d
elity
em
u
latio
n
o
f
v
o
lt
ag
e
an
d
c
u
r
r
e
n
t f
lu
ctu
atio
n
s
,
as we
ll a
s
liv
e
in
ter
ac
tio
n
with
an
alo
g
/d
ig
ital I
/O.
R
ec
en
t
ap
p
licatio
n
s
h
ig
h
lig
h
t
t
h
eir
r
elev
an
ce
:
s
tate
-
s
p
ac
e
esti
m
ato
r
s
em
b
ed
d
ed
in
r
ea
l
-
tim
e
s
im
u
lato
r
s
h
av
e
im
p
r
o
v
e
d
p
h
ase
tr
ac
k
in
g
an
d
v
o
ltag
e
p
r
o
f
ile
r
eg
u
latio
n
,
wh
ile
FP
GA
-
b
ased
f
r
ac
tio
n
al
-
o
r
d
er
em
u
latio
n
s
with
an
alo
g
in
ter
f
ac
es
h
av
e
d
e
m
o
n
s
tr
ated
ef
f
ec
t
iv
e
o
p
e
r
atio
n
in
v
o
ltag
e
-
s
en
s
itiv
e
en
v
ir
o
n
m
en
ts
.
C
o
llectiv
ely
,
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
o
f
s
tate
-
s
p
ac
e
m
o
d
els
s
tr
en
g
th
en
s
b
o
th
th
e
ac
cu
r
ac
y
o
f
tr
an
s
ie
n
t
an
aly
s
is
an
d
th
e
d
ep
lo
y
a
b
ilit
y
o
f
ad
v
an
ce
d
v
o
lt
ag
e
co
n
tr
o
l stra
teg
ies in
is
o
lated
o
r
wea
k
l
y
co
u
p
led
m
ic
r
o
g
r
i
d
s
.
2
.
1
.
M
a
t
hema
t
ica
l
m
o
del in dig
it
a
l sim
ula
t
o
r
T
h
i
s
s
e
c
ti
o
n
d
e
l
v
e
s
i
n
t
o
t
h
e
i
m
p
l
e
m
e
n
t
a
ti
o
n
o
f
m
a
t
h
e
m
a
ti
c
a
l
m
o
d
e
l
l
i
n
g
m
e
t
h
o
d
s
,
p
a
r
t
i
c
u
l
a
r
l
y
th
e
R
u
n
g
e
-
K
u
t
t
a
a
n
d
s
t
a
t
e
-
s
p
a
c
e
t
e
c
h
n
i
q
u
e
s
,
f
o
r
s
i
m
u
la
t
i
n
g
d
y
n
a
m
i
c
s
y
s
t
e
m
s
i
n
d
i
g
it
a
l
e
n
v
i
r
o
n
m
e
n
t
s
.
T
h
e
s
e
m
et
h
o
d
s
a
r
e
e
s
s
e
n
t
i
a
l
f
o
r
t
r
a
n
s
l
at
i
n
g
c
o
n
t
i
n
u
o
u
s
-
t
i
m
e
b
e
h
a
v
i
o
r
s
i
n
t
o
d
i
s
c
r
e
te
-
t
i
m
e
f
o
r
m
a
ts
s
u
it
a
b
l
e
f
o
r
d
i
g
i
ta
l
c
o
m
p
u
t
a
t
i
o
n
.
T
h
e
R
u
n
g
e
-
K
u
t
t
a
m
e
t
h
o
d
,
f
o
r
i
n
s
t
an
c
e
,
i
s
w
i
d
e
l
y
r
e
c
o
g
n
i
z
e
d
f
o
r
i
t
s
a
b
i
li
t
y
t
o
g
e
n
e
r
a
t
e
a
c
c
u
r
a
t
e
a
p
p
r
o
x
i
m
a
t
i
o
n
s
o
f
i
n
s
t
a
n
ta
n
e
o
u
s
s
ta
t
e
v
a
l
u
es
d
e
r
i
v
e
d
f
r
o
m
f
i
r
s
t
-
o
r
d
e
r
d
i
f
f
e
r
e
n
t
i
a
l
e
q
u
a
t
i
o
n
s
.
W
h
e
n
h
i
g
h
e
r
-
o
r
d
e
r
e
q
u
a
t
i
o
n
s
a
r
e
i
n
v
o
l
v
e
d
,
t
h
e
y
a
r
e
t
y
p
i
c
a
ll
y
d
e
co
m
p
o
s
e
d
i
n
t
o
a
n
e
q
u
i
v
a
l
e
n
t
s
e
t
o
f
f
i
r
s
t
-
o
r
d
e
r
e
q
u
a
t
i
o
n
s
p
r
i
o
r
to
d
i
s
c
r
e
t
iz
a
t
i
o
n
.
T
o
s
i
m
u
l
a
t
e
t
h
e
s
e
s
y
s
te
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it
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i
t
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o
l
v
e
r
s
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w
h
i
c
h
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p
er
a
t
e
o
n
a
f
i
n
i
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e
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i
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t
e
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e
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o
te
d
a
s
δt
.
A
r
e
p
r
e
s
e
n
ta
t
i
v
e
e
x
a
m
p
l
e
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a
n
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e
f
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n
d
i
n
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h
e
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l
as
s
ic
R
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ci
r
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i
t
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w
h
i
c
h
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o
n
s
i
s
t
s
o
f
a
r
es
is
t
o
r
(
R
)
,
i
n
d
u
c
t
o
r
(
L
)
,
a
n
d
c
a
p
a
c
i
t
o
r
(
C
)
a
r
r
a
n
g
e
d
i
n
s
e
r
i
es
[
3
4
]
.
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
I
mp
r
o
vin
g
vo
lta
g
e
s
ta
b
ilit
y
in
is
o
la
ted
r
en
ewa
b
le
en
erg
y
micro
g
r
id
s
u
s
in
g
virt
u
a
l
…
(
A
h
m
a
d
S
u
p
a
w
i O
s
ma
n
)
687
T
h
e
R
L
C
cir
cu
it
s
er
v
es
as
an
id
ea
l
ca
n
d
id
ate
to
illu
s
tr
at
e
th
e
s
tate
-
s
p
ac
e
f
r
am
ewo
r
k
d
u
e
to
its
s
im
p
licity
an
d
well
-
d
e
f
in
ed
d
y
n
am
ic
b
eh
av
io
r
.
I
n
t
h
is
s
etu
p
,
th
e
ca
p
ac
ito
r
v
o
lta
g
e
an
d
i
n
d
u
cto
r
cu
r
r
en
t
a
r
e
ty
p
ically
ch
o
s
en
as
th
e
s
tate
v
a
r
iab
les.
T
h
e
s
y
s
tem
’
s
g
o
v
er
n
in
g
eq
u
atio
n
s
ar
e
d
e
r
iv
ed
f
r
o
m
Kir
ch
h
o
f
f
’
s
Vo
ltag
e
an
d
C
u
r
r
e
n
t
L
aws,
an
d
th
e
n
r
e
f
o
r
m
u
lated
in
to
a
s
tate
-
s
p
ac
e
s
tr
u
ctu
r
e
to
s
im
p
lify
c
o
m
p
u
tat
io
n
al
an
aly
s
is
.
T
h
e
d
y
n
am
ic
b
eh
av
io
r
is
f
ir
s
t e
x
p
r
ess
ed
th
r
o
u
g
h
th
e
f
o
ll
o
win
g
d
i
f
f
er
en
tial e
q
u
ati
o
n
s
:
(
)
=
(
)
−
∗
(
)
−
(
)
(
)
=
(
)
(
3
)
W
h
er
e:
L
r
ep
r
esen
ts
th
e
i
n
d
u
cto
r
,
C
r
ep
r
esen
ts
th
e
ca
p
ac
ito
r
,
(
)
r
ep
r
esen
ts
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
ca
p
ac
ito
r
(
s
tate
v
ar
iab
le)
,
(
)
r
ep
r
esen
ts
t
h
e
cu
r
r
en
t
s
tate
o
f
th
e
in
d
u
ct
o
r
(
s
tate
v
ar
iab
le)
,
an
d
(
)
)
r
ep
r
esen
ts
th
e
s
o
u
r
ce
in
p
u
t
v
o
ltag
e.
T
o
f
ac
ili
tate
d
ig
ital simu
latio
n
,
th
ese
eq
u
atio
n
s
ar
e
r
e
p
r
esen
ted
in
m
a
tr
ix
f
o
r
m
as
(
4
)
.
[
(
)
(
)
]
=
[
0
−
1
1
−
R
L
]
[
(
)
(
)
]
+
[
0
1
L
]
(
)
(
4)
T
h
is
co
n
tin
u
o
u
s
-
tim
e
m
o
d
el
c
an
th
en
b
e
d
is
cr
etize
d
b
y
ap
p
l
y
in
g
th
e
d
e
f
in
itio
n
o
f
th
e
d
er
i
v
ativ
e
u
s
in
g
a
f
in
ite
tim
e
s
tep
,
T
S
.
Af
ter
wa
r
d
s
,
u
s
in
g
th
e
d
ef
in
itio
n
g
iv
e
n
in
(
1
)
a
n
d
r
ep
lacin
g
it
in
(
4
)
f
o
r
ev
e
r
y
d
er
iv
ativ
e,
th
e
r
elatio
n
s
in
(
5
)
.
[
(
+
)
−
(
)
(
+
)
−
(
)
]
=
[
0
−
1
1
−
R
L
]
[
(
)
(
)
]
+
[
0
1
L
]
(
)
(
5
)
Usi
n
g
th
e
d
is
cr
ete
tim
e
v
ar
iab
l
e
=
,
we
ca
n
r
e
f
o
r
m
u
late
th
e
eq
u
atio
n
s
as
(
6
)
.
[
(
+
1
)
(
+
1
)
]
=
[
1
−
−
R
∗
L
+
1
]
[
(
)
(
)
]
+
[
0
L
]
(
)
(6
)
I
n
co
m
p
ac
t f
o
r
m
(
6
)
ca
n
b
e
ex
p
r
ess
ed
in
(
7
)
.
⃗
(
+
1
)
=
⃗
(
)
+
⃗
⃗
(
)
(
7
)
Giv
en
th
at
th
e
s
y
s
tem
is
g
iv
en
a
s
et
o
f
in
itial
s
tate
v
alu
es
d
esig
n
ated
as
⃗
(
0
)
th
e
v
alu
es
o
f
t
h
e
s
tates
ca
n
b
e
s
tated
as in
(
8
)
.
T
h
is
d
e
r
iv
atio
n
was p
r
ev
io
u
s
ly
d
o
n
e
in
[
1
3
]
,
[
1
4
]
.
⃗
(
)
=
⃗
(
0
)
+
∑
−
1
=
0
(
−
1
−
)
(
8
)
T
h
e
m
a
t
r
i
x
i
s
d
e
f
i
n
e
d
as
t
h
e
s
t
a
t
e
t
r
a
n
s
i
t
i
o
n
m
a
t
r
i
x
w
h
i
c
h
m
a
p
s
t
h
e
i
n
it
i
a
l
v
a
l
u
es
o
f
t
h
e
s
t
at
e
s
a
n
d
i
n
p
u
t
s
o
f
t
h
e
s
y
s
t
e
m
t
o
t
h
e
s
y
s
te
m
s
ta
t
e
p
r
es
e
n
t
v
a
l
u
e
s
.
I
n
a
d
ig
i
t
a
l
s
i
m
u
la
t
i
o
n
,
t
h
e
s
t
a
t
e
t
r
a
n
s
i
t
i
o
n
m
a
t
r
i
x
is
u
s
e
d
t
o
p
r
e
d
i
c
t
f
u
t
u
r
e
s
t
a
te
s
f
r
o
m
t
h
e
i
n
i
t
i
al
s
t
at
e
s
.
I
n
t
h
e
c
a
s
e
p
r
e
s
e
n
te
d
i
n
F
i
g
u
r
e
3
,
t
h
e
s
y
s
t
e
m
is
a
l
in
e
a
r
t
i
m
e
-
i
n
v
a
r
i
a
n
t
(
L
T
I
)
s
y
s
t
e
m
.
F
o
r
s
y
s
t
e
m
s
t
h
a
t
a
r
e
l
i
n
e
a
r
b
u
t
ti
m
e
-
v
a
r
y
i
n
g
,
t
h
e
r
e
l
a
t
i
o
n
i
n
(
8
)
n
e
e
d
s
t
o
b
e
c
h
an
g
e
d
t
o
(
9
)
.
⃗
(
)
=
∏
=
0
(
)
⃗
(
0
)
+
∑
−
1
=
0
∑
=
0
(
)
(
−
1
−
)
(
9
)
T
o
v
alid
ate
th
is
d
is
cr
etize
d
m
o
d
el
in
s
im
u
latio
n
,
a
test
c
ase
was
co
n
s
tr
u
cted
b
y
ass
ig
n
in
g
in
itial
co
n
d
itio
n
s
:
th
e
ca
p
ac
ito
r
v
o
lta
g
e
was
s
et
to
1
0
0
V,
th
e
in
d
u
c
to
r
cu
r
r
en
t
to
1
A,
an
d
th
e
s
o
u
r
ce
v
o
ltag
e
to
0
V
(
is
o
latin
g
th
e
in
itial r
esp
o
n
s
e
o
n
ly
)
.
T
h
e
r
esu
ltin
g
s
tate
ev
o
lu
tio
n
s
im
p
l
if
ies to
(
1
0
)
.
⃗
(
)
=
∏
=
0
(
)
⃗
(
0
)
(
1
0
)
Sin
ce
th
e
s
am
p
lin
g
tim
e
was
s
et
to
0
.
1
,
it
wo
u
l
d
,
th
e
r
ef
o
r
e,
ta
k
e
2
0
0
,
0
0
0
s
am
p
les
f
o
r
th
e
r
e
s
p
o
n
s
e
o
f
2
0
s
ec
o
n
d
s
to
b
e
o
b
tain
e
d
.
I
n
ea
c
h
iter
atio
n
,
th
e
in
s
tan
tan
e
o
u
s
s
tate
will
b
e
ca
lcu
lated
u
s
in
g
(
1
1
)
.
T
h
e
s
im
u
late
d
r
esp
o
n
s
e
is
o
f
ten
th
e
ac
c
u
r
ac
y
o
f
th
e
d
is
cr
etize
d
m
o
d
el,
clea
r
ly
ca
p
tu
r
i
n
g
th
e
tr
an
s
ien
t
o
s
cillatio
n
s
an
d
s
ettlin
g
b
eh
av
io
r
in
h
er
e
n
t to
th
e
R
L
C
cir
cu
it u
n
d
e
r
th
e
s
p
ec
if
ied
i
n
itial
co
n
d
itio
n
s
.
=
∑
=
1
(
1
1
)
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.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
683
-
695
688
2.
2
.
St
a
t
e
-
s
pa
ce
mo
dels
a
nd
a
dv
a
nced
co
ntr
o
l t
ec
hn
iqu
es
State
-
s
p
ac
e
m
o
d
els
u
n
d
er
p
in
m
an
y
ad
v
a
n
ce
d
co
n
tr
o
l
s
tr
a
teg
ies
f
o
r
m
icr
o
g
r
id
v
o
ltag
e
r
eg
u
latio
n
,
esp
ec
ially
u
n
d
e
r
in
ter
m
itten
t
r
en
ewa
b
le
in
p
u
ts
.
B
y
esti
m
at
in
g
k
e
y
s
y
s
tem
s
tates,
s
u
ch
a
s
in
v
er
ter
te
r
m
in
al
v
o
ltag
es
an
d
cu
r
r
en
ts
,
th
ey
e
n
ab
le
r
ea
l
-
tim
e
f
ee
d
b
ac
k
an
d
p
r
ed
ictiv
e
ad
ju
s
tm
en
ts
,
f
o
r
m
i
n
g
th
e
b
ac
k
b
o
n
e
o
f
r
o
b
u
s
t a
n
d
ad
ap
tiv
e
co
n
tr
o
ller
s
[
3
5
]
.
As
s
h
o
wn
in
Fig
u
r
e
3
,
m
ix
ed
H∞
an
d
p
ass
iv
ity
-
b
ased
d
esi
g
n
in
teg
r
ates
GPS
s
y
n
ch
r
o
n
iz
atio
n
an
d
v
ir
tu
al
im
p
e
d
an
ce
s
h
a
p
in
g
to
ac
h
iev
e
d
ec
en
tr
alize
d
v
o
ltag
e
an
d
f
r
e
q
u
en
c
y
r
eg
u
l
atio
n
,
ev
e
n
wh
e
n
co
m
m
u
n
icatio
n
lin
k
s
a
r
e
wea
k
[
3
6
]
.
A
s
im
p
ler
o
p
tio
n
is
th
e
s
in
g
le
-
lo
o
p
s
tate
f
ee
d
b
ac
k
d
esig
n
in
Fig
u
r
e
4
,
wh
ich
r
ed
u
ce
s
s
en
s
o
r
r
eq
u
ir
e
m
en
ts
wh
ile
m
ain
tain
in
g
ac
c
u
r
ate
v
o
ltag
e
tr
ac
k
in
g
,
well
-
s
u
ited
f
o
r
em
b
ed
d
e
d
m
icr
o
g
r
id
ap
p
licatio
n
s
[
3
6
]
.
Fig
u
r
e
3
.
Mix
e
d
H
in
f
in
ity
an
d
p
ass
iv
ity
co
n
tr
o
l
d
esig
n
[
3
6
]
Fig
u
r
e
4
.
Sin
g
le
l
o
o
p
s
tate
f
ee
d
b
ac
k
d
esig
n
[
3
6
]
B
ac
k
-
s
tep
p
in
g
tech
n
iq
u
es
e
x
ten
d
th
is
to
o
lb
o
x
b
y
a
p
p
ly
in
g
r
ec
u
r
s
iv
e
L
y
a
p
u
n
o
v
t
u
n
in
g
to
s
tab
ilize
DC
-
lin
k
v
o
ltag
e
an
d
p
o
wer
f
lo
w
at
th
e
PC
C
(
Fig
u
r
e
5
)
.
Ad
a
p
tiv
e
o
b
s
er
v
er
s
an
d
r
ef
er
en
ce
-
s
ig
n
al
g
en
e
r
atio
n
,
illu
s
tr
ated
in
Fig
u
r
e
6
,
f
u
r
th
er
en
h
an
ce
r
esil
ien
ce
b
y
esti
m
atin
g
s
y
s
tem
s
tate
s
in
r
ea
l
tim
e
an
d
co
r
r
ec
tin
g
v
o
ltag
e
d
ev
iatio
n
s
d
u
r
in
g
lo
ad
s
h
o
c
k
s
o
r
v
ar
iab
le
r
e
n
ewa
b
le
in
p
u
t
[
3
7
]
,
[
3
8
]
.
As
s
h
o
wn
,
th
e
r
en
ewa
b
le
s
o
u
r
ce
ex
tr
ac
to
r
an
d
ass
o
ciate
d
p
o
wer
-
elec
tr
o
n
ic
co
n
v
er
ter
e
n
s
u
r
e
m
a
x
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
in
g
o
f
t
h
e
s
o
lar
-
o
r
win
d
-
b
ased
s
o
u
r
ce
,
wh
ile
a
DC
-
lin
k
ca
p
ac
ito
r
an
d
s
in
g
le
-
p
h
ase
f
u
ll
-
b
r
id
g
e
in
v
er
ter
f
ee
d
th
e
AC
b
u
s
th
r
o
u
g
h
an
L
C
f
ilter
.
T
h
e
m
ea
s
u
r
ed
v
o
ltag
e
an
d
cu
r
r
en
t
s
ig
n
als
ar
e
p
r
o
ce
s
s
ed
b
y
a
s
tate
o
b
s
er
v
er
th
at
r
ec
o
n
s
tr
u
cts
u
n
m
ea
s
u
r
ed
s
tates
an
d
an
ad
a
p
t
iv
e
r
ef
e
r
en
ce
m
o
d
u
le
th
at
u
p
d
ates
th
e
co
n
tr
o
l
tar
g
ets.
T
h
ese
o
u
tp
u
ts
d
r
iv
e
th
e
b
ac
k
-
s
tep
p
in
g
co
n
tr
o
ller
,
wh
ich
g
e
n
er
ates
th
e
p
u
ls
e
wid
t
h
m
o
d
u
latio
n
(
PW
M
)
co
n
tr
o
l
s
ig
n
als
f
o
r
i
n
v
e
r
ter
s
witch
es
S₁
–
S₄,
th
er
eb
y
m
ain
tai
n
in
g
v
o
ltag
e
s
tab
ilit
y
u
n
d
er
f
lu
ctu
atin
g
l
o
a
d
a
n
d
g
en
e
r
atio
n
co
n
d
itio
n
s
.
Acr
o
s
s
th
ese
s
tr
ateg
ies,
s
tate
-
s
p
ac
e
m
o
d
els
r
em
ain
th
e
s
tr
u
ctu
r
al
c
o
r
e
t
h
at
lin
k
s
s
y
s
tem
d
y
n
am
ics
to
ad
v
an
ce
d
c
o
n
tr
o
ller
s
.
W
h
eth
er
th
r
o
u
g
h
r
o
b
u
s
t
H∞
d
esig
n
,
s
im
p
lifie
d
s
tate
f
ee
d
b
ac
k
,
o
r
a
d
ap
tiv
e
b
ac
k
-
s
tep
p
in
g
,
th
ei
r
in
teg
r
atio
n
en
s
u
r
es
r
esp
o
n
s
iv
e
an
d
s
u
s
tain
ab
le
v
o
l
tag
e
s
tab
ilit
y
in
m
o
d
er
n
r
e
n
ewa
b
le
-
in
teg
r
ated
m
icr
o
g
r
id
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
I
mp
r
o
vin
g
vo
lta
g
e
s
ta
b
ilit
y
in
is
o
la
ted
r
en
ewa
b
le
en
erg
y
micro
g
r
id
s
u
s
in
g
virt
u
a
l
…
(
A
h
m
a
d
S
u
p
a
w
i O
s
ma
n
)
689
Fig
u
r
e
5
.
B
ac
k
-
s
tep
p
i
n
g
co
n
tr
o
l te
ch
n
iq
u
e
[
3
7
]
Fig
u
r
e
6
.
Ad
a
p
tiv
e
r
ef
e
r
en
ce
s
ig
n
al
an
d
s
tate
o
b
s
er
v
er
with
wo
r
k
in
g
o
f
b
ac
k
-
s
tep
p
in
g
in
m
icr
o
g
r
id
[
3
8
]
3.
RE
A
L
-
T
I
M
E
DIGI
T
A
L
SI
M
UL
AT
O
R
R
ea
l
-
tim
e
d
ig
ital
s
im
u
latio
n
r
ep
r
esen
ts
a
k
ey
a
d
v
an
ce
m
e
n
t
in
s
y
s
tem
an
aly
s
is
,
en
ab
lin
g
m
o
d
els
to
r
u
n
in
s
tr
ict
s
y
n
ch
r
o
n
y
with
ac
tu
al
clo
ck
tim
e.
E
ac
h
co
m
p
u
tatio
n
al
s
tep
m
u
s
t
b
e
co
m
p
leted
w
ith
in
th
e
p
r
e
d
ef
in
ed
in
ter
v
al;
o
th
e
r
wis
e,
an
o
v
er
r
u
n
o
cc
u
r
s
,
d
e
g
r
ad
i
n
g
ac
c
u
r
ac
y
o
r
h
altin
g
th
e
s
im
u
latio
n
[
3
9
]
.
T
o
m
an
a
g
e
th
is
,
p
latf
o
r
m
s
r
a
n
g
e
f
r
o
m
ac
ce
s
s
ib
le
to
o
ls
lik
e
Simu
lin
k
d
esk
to
p
r
ea
l
-
tim
e
(
SDR
T
)
to
ad
v
an
ce
d
u
tili
ty
-
s
ca
le
s
y
s
tem
s
s
u
ch
as
R
T
DS
an
d
OPAL
-
R
T
,
th
e
latter
n
o
ted
f
o
r
its
p
ar
allel
-
p
r
o
ce
s
s
in
g
ar
ch
itectu
r
e
a
n
d
h
ig
h
-
f
id
elit
y
p
er
f
o
r
m
an
ce
[
4
0
]
,
[
4
1
]
.
A
ce
n
tr
al
f
ea
tu
r
e
o
f
th
is
p
ar
ad
ig
m
is
HI
L
test
in
g
,
wh
ich
lin
k
s
d
ig
ital
s
im
u
latio
n
s
with
r
ea
l
h
ar
d
war
e
v
ia
co
m
m
u
n
icatio
n
p
r
o
to
co
ls
(
E
th
er
n
et,
s
er
ial,
p
ar
allel)
.
T
h
i
s
s
etu
p
allo
ws
co
n
tr
o
ller
s
,
r
elay
s
,
an
d
in
v
e
r
ter
s
to
in
ter
ac
t
with
s
im
u
lated
g
r
i
d
c
o
n
d
itio
n
s
in
r
ea
l
tim
e,
o
f
f
er
i
n
g
a
s
af
e,
c
o
s
t
-
ef
f
ec
tiv
e
m
ea
n
s
o
f
v
alid
atin
g
d
e
v
ices
u
n
d
er
ex
t
r
em
e
o
r
f
a
u
lted
s
ce
n
a
r
io
s
[
4
2
]
,
[
4
3
]
.
Fo
r
in
s
tan
ce
,
p
r
o
tectiv
e
r
elay
r
esp
o
n
s
es
ca
n
b
e
test
ed
u
s
in
g
SDR
T
lin
k
ed
v
ia
E
th
er
n
et
with
o
u
t
n
ee
d
in
g
p
h
y
s
ical
f
ield
h
ar
d
war
e,
ac
ce
ler
a
tin
g
p
r
o
t
o
ty
p
in
g
an
d
r
ed
u
ci
n
g
d
ev
elo
p
m
e
n
t r
is
k
s
.
Am
o
n
g
av
ailab
le
p
latf
o
r
m
s
,
OPAL
-
R
T
s
tan
d
s
o
u
t
f
o
r
its
ab
ilit
y
to
d
is
tr
ib
u
te
task
s
ac
r
o
s
s
m
u
lti
-
co
r
e
p
r
o
ce
s
s
o
r
s
an
d
in
te
g
r
ate
s
ea
m
less
ly
with
R
T
-
L
AB
an
d
MA
T
L
AB
Simu
lin
k
.
T
h
is
en
v
ir
o
n
m
en
t
s
u
p
p
o
r
ts
in
tu
itiv
e
m
o
d
el
d
ev
elo
p
m
en
t
,
r
ap
i
d
v
alid
atio
n
,
an
d
d
y
n
a
m
ic
p
a
r
am
ete
r
tu
n
in
g
.
Mo
r
e
o
v
er
,
OPAL
-
R
T
’
s
co
m
p
atib
ilit
y
with
FP
GAs
en
h
an
ce
s
s
p
ee
d
,
ac
cu
r
ac
y
,
an
d
f
lex
ib
ilit
y
b
y
em
b
e
d
d
in
g
s
tate
-
s
p
ac
e
m
o
d
els
d
ir
ec
tly
in
to
cu
s
to
m
izab
le
h
a
r
d
war
e
lo
g
ic
[
4
4
]
,
[
4
5
]
.
As
s
h
o
wn
in
Fig
u
r
e
7
,
OPAL
-
R
T
s
etu
p
s
in
teg
r
ate
co
n
tr
o
ller
s
at
m
u
ltip
le
lev
els
(
p
r
im
a
r
y
,
s
ec
o
n
d
ar
y
,
ter
tiar
y
)
with
e
n
er
g
y
s
o
u
r
ce
s
,
r
elay
s
,
an
d
s
to
r
a
g
e
d
ev
ices
co
n
n
ec
ted
th
r
o
u
g
h
AC
/DC
b
u
s
es
an
d
co
m
m
u
n
icatio
n
ch
an
n
els
[
4
6
]
.
T
h
is
co
n
f
i
g
u
r
atio
n
p
r
o
v
id
es
a
co
m
p
r
e
h
en
s
iv
e
r
ea
l
-
tim
e
en
v
ir
o
n
m
en
t
w
h
er
e
h
ar
d
wa
r
e
an
d
s
o
f
twar
e
co
-
ex
is
t,
en
ab
lin
g
en
g
in
ee
r
s
to
ev
alu
ate
m
icr
o
g
r
id
b
eh
av
io
r
u
n
d
er
a
v
ar
iety
o
f
o
p
er
atin
g
co
n
d
itio
n
s
.
3
.
1
.
M
a
t
rix
m
ultiplica
t
io
n a
l
g
o
rit
hm
o
r
it
er
a
t
i
v
e
a
lg
o
rit
hm
W
h
e
n
a
p
p
l
y
i
n
g
t
h
e
c
l
a
s
s
i
c
al
d
e
f
i
n
i
t
i
o
n
o
f
m
a
t
r
i
x
m
u
l
t
i
p
l
i
ca
t
i
o
n
d
i
r
e
c
t
l
y
,
t
h
e
r
e
s
u
l
t
i
n
g
a
l
g
o
r
i
t
h
m
i
n
v
o
l
v
e
s
a
c
o
m
p
u
t
a
t
i
o
n
a
l
ti
m
e
c
o
m
p
l
e
x
i
t
y
o
f
O
(n
3
)
,
r
e
q
u
i
r
i
n
g
a
p
p
r
o
x
i
m
a
t
e
l
y
n
3
f
i
e
l
d
o
p
e
r
a
ti
o
n
s
t
o
m
u
l
t
i
p
l
y
t
w
o
n
×
n
×
n
m
a
t
r
i
c
es
[
4
7
]
.
S
p
e
c
i
f
i
ca
l
l
y
,
i
f
C
=
A
B
,
w
h
e
r
e
A
is
a
n
n
×
m
m
a
t
r
i
x
a
n
d
B
i
s
a
n
m×
p
m
a
t
r
i
x
,
f
r
o
m
t
h
i
s
,
a
s
i
m
p
l
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.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
683
-
695
690
a
l
g
o
r
i
t
h
m
c
a
n
b
e
c
o
n
s
t
r
u
ct
e
d
wh
i
c
h
l
o
o
p
s
o
v
e
r
t
h
e
i
n
d
i
c
es
f
r
o
m
1
t
h
r
o
u
g
h
a
n
d
f
r
o
m
1
t
h
r
o
u
g
h
,
c
o
m
p
u
t
i
n
g
t
h
e
a
b
o
v
e
u
s
i
n
g
a
n
e
s
t
e
d
l
o
o
p
,
th
e
n
t
h
e
r
e
s
u
l
ti
n
g
m
a
t
r
i
x
C
o
f
s
iz
e
n
×
p
i
s
d
e
f
i
n
e
d
e
l
e
m
e
n
t
-
w
i
s
e
a
s
(
1
1
)
.
Ma
tr
ix
o
p
er
atio
n
s
f
o
r
m
th
e
co
m
p
u
tatio
n
al
b
ac
k
b
o
n
e
o
f
r
ea
l
-
tim
e
s
im
u
lato
r
s
.
I
n
R
T
S
en
v
i
r
o
n
m
en
ts
,
th
ese
o
p
er
atio
n
s
m
u
s
t
b
e
co
m
p
leted
with
in
s
tr
ict
tim
e
co
n
s
tr
ain
ts
,
as
o
v
er
r
u
n
s
co
m
p
r
o
m
is
e
b
o
th
ac
cu
r
ac
y
an
d
s
im
u
latio
n
s
tab
ilit
y
[
4
7
]
.
Alg
o
r
ith
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er
ter
s
u
s
in
g
s
u
b
h
ar
m
o
n
ic
o
r
s
p
ac
e
-
v
ec
to
r
m
o
d
u
latio
n
.
T
h
ese
in
v
er
ter
s
a
im
to
lo
ca
lly
s
tab
ilize
th
e
g
r
id
b
y
s
u
p
p
ly
in
g
th
e
n
ec
ess
ar
y
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
b
ased
o
n
r
ea
l
-
tim
e
g
r
i
d
co
n
d
itio
n
s
.
Ho
wev
er
,
a
k
ey
li
m
itatio
n
lies
in
th
eir
d
is
s
im
ila
r
ity
to
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es,
th
e
v
e
r
y
s
y
s
tem
s
o
n
wh
ich
h
is
to
r
ical
g
r
id
s
tab
ilit
y
h
as b
ee
n
b
u
ilt [
4
8
]
.
T
o
p
r
eser
v
e
th
e
g
r
i
d
’
s
ess
en
tial
p
r
o
p
er
ties
,
s
u
ch
as
au
to
m
ati
c
b
alan
cin
g
ac
r
o
s
s
ar
ea
s
an
d
p
r
ed
ictab
le
d
y
n
am
ic
b
e
h
av
io
r
,
it
is
th
er
ef
o
r
e
cr
itical
to
d
ev
elo
p
in
v
e
r
ter
-
b
ased
s
y
s
tem
s
th
at
r
ep
licate
th
e
f
u
n
ctio
n
al
id
en
tit
y
o
f
s
y
n
ch
r
o
n
o
u
s
g
en
e
r
ato
r
s
.
T
h
is
in
v
o
lv
es
m
o
r
e
th
a
n
ju
s
t
c
o
n
tr
o
l
s
tr
ateg
y
r
ef
in
em
e
n
t;
it
r
eq
u
ir
es
a
s
y
s
tem
ic
r
eth
in
k
in
g
o
f
h
o
w
in
v
e
r
ter
s
in
ter
f
ac
e
with
b
o
th
e
n
er
g
y
s
o
u
r
ce
s
an
d
th
e
g
r
i
d
.
T
h
e
g
o
al
is
to
cr
ea
te
a
s
ea
m
less
in
teg
r
atio
n
wh
er
e
in
v
er
ter
s
ac
t
n
o
t
as
is
o
lated
co
n
tr
o
ller
s
,
b
u
t
as
g
r
id
-
p
ar
ticip
atin
g
en
titi
es
with
in
er
tia,
d
r
o
o
p
ch
ar
ac
ter
is
tics
,
an
d
f
au
lt r
id
e
-
t
h
r
o
u
g
h
b
e
h
av
io
r
co
m
p
ar
ab
le
t
o
elec
tr
o
m
ec
h
a
n
ical
s
y
s
tem
s
.
Fig
u
r
e
8
.
C
h
an
g
e
in
th
e
s
tr
u
ctu
r
e
o
f
g
en
er
atio
n
an
d
d
is
tr
ib
u
t
io
n
o
f
elec
tr
ical
e
n
er
g
y
[
4
8
]
4.
RE
A
L
-
T
I
M
E
SI
M
U
L
AT
I
O
N
Simu
latio
n
cr
ea
tes
m
ath
em
ati
ca
l
m
o
d
els
to
r
e
p
licate
r
ea
l
-
w
o
r
ld
s
y
s
tem
b
e
h
av
io
r
.
T
h
is
p
a
p
er
f
o
c
u
s
es
o
n
f
ix
ed
-
s
tep
d
is
cr
ete
-
tim
e
s
im
u
latio
n
s
,
wid
ely
u
s
ed
in
r
e
al
-
tim
e
ap
p
licatio
n
s
f
o
r
th
ei
r
p
r
ed
ictab
ilit
y
an
d
co
n
s
is
ten
t
u
p
d
ate
in
ter
v
als,
u
n
lik
e
v
ar
iab
le
-
s
tep
m
eth
o
d
s
th
at
ar
e
u
n
s
u
itab
le
f
o
r
r
ea
l
-
tim
e
o
p
er
atio
n
[
5
0
]
.
I
n
s
u
ch
en
v
ir
o
n
m
en
ts
,
ea
ch
s
tate
is
u
p
d
ated
u
s
in
g
eq
u
atio
n
s
s
o
lv
ed
at
ev
er
y
tim
e
s
tep
.
T
h
e
ch
allen
g
e
lies
in
co
m
p
u
tin
g
all
u
p
d
ates
with
in
th
e
allo
tted
in
ter
v
al:
if
f
aster
,
it
is
an
ac
ce
ler
ated
s
im
u
latio
n
;
if
s
lo
wer
,
it
b
ec
o
m
es
an
o
f
f
lin
e
s
im
u
latio
n
.
R
ea
l
-
tim
e
s
im
u
latio
n
,
h
o
wev
e
r
,
d
em
an
d
s
s
tr
ict
s
y
n
ch
r
o
n
izat
io
n
with
wall
-
clo
ck
tim
e.
Fo
r
in
s
tan
ce
,
a
1
m
s
s
y
s
tem
s
tep
r
eq
u
ir
es
al
l
ca
lcu
latio
n
s
an
d
an
y
h
a
r
d
war
e
in
ter
ac
tio
n
s
to
co
m
p
lete
with
in
th
at
s
am
e
1
m
s
.
Fin
is
h
in
g
ea
r
ly
r
esu
lts
in
id
le
waitin
g
,
wh
ile
o
v
er
r
u
n
s
ca
u
s
e
th
e
s
im
u
latio
n
to
lo
s
e
f
id
elity
[
4
8
]
.
A
v
alid
r
ea
l
-
tim
e
s
im
u
lato
r
,
th
er
e
f
o
r
e
,
r
eq
u
ir
es
b
o
th
co
m
p
u
tatio
n
al
ac
c
u
r
ac
y
an
d
tim
in
g
co
m
p
lian
ce
,
p
r
o
v
id
i
n
g
a
cr
ed
ib
l
e
d
ig
ital twin
f
o
r
h
ar
d
war
e
-
in
-
th
e
-
lo
o
p
test
in
g
,
c
o
n
tr
o
l
v
alid
ati
o
n
,
an
d
f
au
lt e
m
u
lat
io
n
[
4
9
]
.
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.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
683
-
695
692
4
.
1
.
P
o
wer
g
ener
a
t
i
o
n a
pp
lica
t
io
n
R
ea
l
-
tim
e
s
im
u
latio
n
p
lay
s
a
ce
n
tr
al
r
o
le
i
n
v
alid
atin
g
p
o
wer
g
en
e
r
atio
n
an
d
co
n
tr
o
l
s
y
s
tem
s
,
in
clu
d
in
g
h
ig
h
v
o
ltag
e
d
ir
ec
t
c
u
r
r
en
t
(
HVDC)
lin
k
s
,
f
lex
ib
le
alter
n
atin
g
cu
r
r
e
n
t
tr
an
s
m
is
s
io
n
s
y
s
tem
s
(
FA
C
T
S
)
d
ev
ices,
STAT
C
OM
s
,
an
d
p
r
o
tectio
n
s
y
s
tem
s
.
B
ef
o
r
e
d
ep
lo
y
m
e
n
t,
c
o
n
tr
o
ller
s
u
n
d
er
g
o
th
o
u
s
an
d
s
o
f
d
eter
m
in
is
tic
an
d
r
an
d
o
m
ized
test
ca
s
es
in
HI
L
e
n
v
ir
o
n
m
e
n
ts
to
en
s
u
r
e
r
esil
ien
ce
u
n
d
er
d
iv
er
s
e
f
au
lts
an
d
in
ter
ac
tio
n
s
with
o
th
er
d
e
v
ices
[
5
0
]
.
Pr
o
tectio
n
v
alid
atio
n
f
u
r
th
er
b
en
ef
its
f
r
o
m
r
ea
l
-
tim
e
te
s
tin
g
.
W
h
ile
o
f
f
lin
e
to
o
ls
s
u
ch
as
th
e
al
ter
n
ativ
e
tr
an
s
ien
t
p
r
o
g
r
a
m
(
AT
P
)
an
d
elec
tr
o
m
ag
n
etic
tr
an
s
ien
ts
’
p
r
o
g
r
am
(
EMTP
)
aid
ea
r
ly
d
e
v
elo
p
m
e
n
t,
o
n
ly
r
ea
l
-
t
im
e
s
etu
p
s
ca
n
r
ep
licate
b
id
ir
e
ctio
n
al
in
ter
ac
tio
n
s
b
etwe
en
p
r
o
tectiv
e
r
ela
y
s
an
d
th
e
g
r
id
.
T
h
is
allo
ws
clo
s
ed
-
lo
o
p
ev
al
u
atio
n
o
f
r
ela
y
r
esp
o
n
s
es
ac
r
o
s
s
v
ar
y
in
g
co
n
d
itio
n
s
,
r
ed
u
cin
g
th
e
r
is
k
o
f
m
is
-
co
o
r
d
in
atio
n
o
r
ca
s
ca
d
i
n
g
f
ailu
r
es.
As
d
is
tr
ib
u
ted
g
en
er
atio
n
(
D
G)
an
d
R
E
S
p
en
etr
atio
n
g
r
o
ws,
co
n
v
er
ter
s
in
tr
o
d
u
ce
f
ast
-
s
witch
in
g
d
y
n
am
ics
th
at
co
ex
is
t
with
s
lo
wer
elec
tr
o
m
ec
h
an
ical
r
esp
o
n
s
es
f
r
o
m
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es.
Simu
latin
g
s
u
ch
h
y
b
r
id
s
y
s
tem
s
is
co
m
p
u
tatio
n
ally
d
em
an
d
in
g
,
esp
ec
ially
a
t la
r
g
e
s
ca
les.
Of
f
lin
e
s
tu
d
ies o
f
ten
p
r
o
v
e
to
o
s
lo
w,
wh
er
ea
s
r
ea
l
-
tim
e
s
im
u
latio
n
en
ab
les
ag
ile
s
ce
n
ar
io
-
b
ased
ass
es
s
m
en
ts
,
id
en
tify
in
g
wo
r
s
t
-
ca
s
e
ev
en
ts
an
d
in
f
o
r
m
in
g
p
r
o
ac
tiv
e
g
r
id
p
lan
n
in
g
[
5
1
]
.
4
.
2
.
Renew
a
ble
ener
g
y
i
m
plem
ent
ed
s
t
a
t
e
-
s
pa
ce
mo
dels
State
-
s
p
ac
e
m
o
d
ellin
g
p
r
o
v
id
es
a
r
o
b
u
s
t
f
r
am
ewo
r
k
f
o
r
m
an
ag
in
g
R
E
S
d
y
n
am
ics
b
y
tr
an
s
latin
g
m
u
lti
-
v
ar
iab
le
s
y
s
tem
s
in
to
s
tr
u
ctu
r
ed
eq
u
atio
n
s
.
Un
lik
e
cl
ass
ical
m
o
d
els,
m
o
d
er
n
s
tate
-
s
p
ac
e
f
r
am
ewo
r
k
s
ca
p
tu
r
e
n
o
n
lin
ea
r
ities
in
h
er
en
t
in
p
h
o
to
v
o
ltaics,
b
atter
ies,
an
d
win
d
tu
r
b
in
es,
en
ab
lin
g
a
cc
u
r
ate
p
r
ed
ictio
n
s
u
n
d
er
v
ar
iab
le
c
o
n
d
itio
n
s
.
T
h
ey
also
in
te
g
r
ate
tech
n
ical
an
d
ec
o
n
o
m
ic
p
ar
a
m
eter
s
,
o
f
f
e
r
i
n
g
d
ec
is
io
n
-
m
ak
in
g
to
o
ls
f
o
r
d
is
tr
ib
u
te
d
en
er
g
y
m
an
ag
em
en
t [
5
1
]
.
A
k
ey
ad
v
an
ce
m
e
n
t
is
th
e
in
teg
r
atio
n
o
f
m
o
d
el
p
r
e
d
ictiv
e
co
n
tr
o
l
(
MPC
)
.
Op
er
atin
g
o
n
a
p
r
ed
ictiv
e
b
asis
,
MP
C
an
ticip
ates
d
is
tu
r
b
an
ce
s
an
d
ad
ju
s
ts
r
esp
o
n
s
es
in
r
ea
l
tim
e,
wh
ile
ad
h
er
in
g
to
o
p
er
atio
n
al
co
n
s
tr
ain
ts
[
5
4
]
,
[
5
5
]
.
E
v
e
n
t
-
b
ased
MPC
f
u
r
th
er
r
ef
in
es th
is
b
y
in
ter
v
en
i
n
g
o
n
ly
d
u
r
in
g
s
ig
n
if
ican
t d
ev
iatio
n
s
,
r
ed
u
cin
g
co
n
t
r
o
l
ac
tio
n
s
b
y
u
p
to
6
5
%,
wh
ich
m
in
im
izes
c
o
m
p
o
n
en
t
s
tr
ess
,
lo
wer
s
m
ain
ten
an
ce
co
s
ts
,
an
d
ex
ten
d
s
b
atter
y
life
[
5
6
]
,
[
5
7
]
.
B
ey
o
n
d
r
eliab
ilit
y
,
th
is
ap
p
r
o
ac
h
im
p
r
o
v
es
en
er
g
y
s
ch
e
d
u
lin
g
,
r
e
d
u
ce
s
g
r
id
d
ep
en
d
e
n
cy
d
u
r
in
g
p
ea
k
d
e
m
an
d
,
an
d
s
u
p
p
o
r
ts
d
ec
ar
b
o
n
izatio
n
b
y
lim
itin
g
r
elian
ce
o
n
f
o
s
s
il
p
ea
k
er
s
.
T
o
g
eth
er
,
s
tate
-
s
p
ac
e
m
o
d
ellin
g
an
d
p
r
ed
ictiv
e
c
o
n
tr
o
l
p
r
o
v
id
e
a
s
ca
lab
le
p
ath
way
to
war
d
s
m
ar
t,
f
lex
ib
le,
an
d
s
u
s
tain
ab
le
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
[
5
8
]
.
4
.
3
.
E
v
ent
-
ba
s
ed
co
ntr
o
l
a
rc
hite
ct
ure
E
v
en
t
-
b
ased
co
n
tr
o
l
h
as
g
ai
n
ed
tr
ac
tio
n
as
a
s
o
lu
tio
n
to
t
h
e
co
m
p
u
tatio
n
al
b
u
r
d
en
o
f
co
n
tin
u
o
u
s
co
n
tr
o
l
in
r
en
ewa
b
le
-
in
teg
r
at
ed
m
icr
o
g
r
id
s
.
Un
lik
e
co
n
v
e
n
tio
n
al
m
eth
o
d
s
th
at
o
p
er
ate
o
n
f
ix
e
d
s
am
p
lin
g
in
ter
v
als,
ev
en
t
-
b
ased
s
ch
em
e
s
ac
tiv
ate
co
r
r
ec
tiv
e
ac
tio
n
s
o
n
ly
wh
en
p
r
ed
ef
in
e
d
th
r
esh
o
ld
s
ar
e
ex
ce
ed
ed
.
T
h
is
s
elec
tiv
e
tr
ig
g
er
in
g
r
e
d
u
ce
s
r
ed
u
n
d
an
t
co
m
p
u
tatio
n
s
an
d
co
n
tr
o
l
s
ig
n
als,
allo
win
g
ef
f
icien
t
u
s
e
o
f
c
o
m
m
u
n
i
c
a
t
i
o
n
a
n
d
h
a
r
d
w
a
r
e
r
e
s
o
u
r
c
e
s
[
5
9
]
.
A
g
e
n
e
r
a
l
f
o
r
m
u
l
a
t
i
o
n
o
f
t
h
e
t
r
i
g
g
e
r
c
o
n
d
i
ti
o
n
i
s
e
x
p
r
e
s
s
e
d
a
s
(
1
6
)
.
|
|
(
)
−
(
)
|
|
≥
(
1
6
)
W
h
er
e
x(
t)
is
th
e
s
y
s
tem
s
tate,
x(
t
k
)
is
th
e
last
s
am
p
led
s
tate,
a
n
d
e
p
s
ilo
n
(
ϵ
)
d
ef
in
es
th
e
p
er
m
is
s
ib
le
er
r
o
r
b
o
u
n
d
.
On
ce
th
is
th
r
esh
o
ld
is
cr
o
s
s
ed
,
a
n
ew
c
o
n
tr
o
l
ac
tio
n
is
is
s
u
ed
;
o
th
e
r
wis
e,
th
e
co
n
tr
o
ller
r
em
ain
s
id
le
[
6
0
]
.
Ad
d
itio
n
al
v
ar
iatio
n
s
o
f
th
is
f
o
r
m
u
latio
n
,
in
clu
d
in
g
ad
ap
tiv
e
th
r
esh
o
ld
s
an
d
m
u
lti
-
v
a
r
iab
le
tr
ig
g
er
s
,
ar
e
p
r
o
v
id
e
d
in
th
e
s
u
p
p
lem
en
t
ar
y
m
ater
ial.
T
h
e
r
ev
iewe
d
s
tu
d
ies
co
n
s
is
ten
tly
h
ig
h
lig
h
t
th
at
ev
en
t
-
b
ased
m
ec
h
an
is
m
s
en
h
an
ce
b
o
th
s
ta
b
ilit
y
an
d
ef
f
icien
cy
wh
e
n
in
t
eg
r
ated
with
s
tate
-
s
p
ac
e
m
o
d
e
ls
an
d
MPC
.
T
h
ese
ap
p
r
o
ac
h
es
n
o
t
o
n
ly
r
e
d
u
ce
co
m
p
u
tatio
n
al
d
em
a
n
d
b
u
t
al
s
o
e
x
ten
d
d
ev
ice
life
tim
es
b
y
m
in
i
m
izin
g
u
n
n
ec
ess
ar
y
ac
tu
atio
n
,
p
ar
ticu
lar
ly
f
o
r
co
n
v
er
ter
s
an
d
s
to
r
ag
e
s
y
s
tem
s
[
6
1
]
.
B
ey
o
n
d
tech
n
ical
ef
f
icien
cy
,
ev
en
t
-
tr
i
g
g
er
e
d
f
r
am
ewo
r
k
s
also
im
p
r
o
v
e
r
esi
lien
ce
b
y
f
o
cu
s
in
g
co
n
tr
o
l
r
es
o
u
r
ce
s
o
n
p
er
i
o
d
s
o
f
ac
tu
al
s
y
s
tem
s
tr
ess
,
s
u
ch
as
s
h
ar
p
lo
ad
c
h
an
g
es
o
r
s
u
d
d
e
n
r
en
ewa
b
le
f
lu
ctu
atio
n
s
.
I
n
s
u
m
m
ar
y
,
ev
e
n
t
-
b
ased
c
o
n
tr
o
l
c
o
m
p
lem
en
ts
ad
v
an
ce
d
s
tate
-
s
p
ac
e
an
d
p
r
ed
ictiv
e
f
r
am
ewo
r
k
s
b
y
o
f
f
er
i
n
g
a
lean
y
et
ef
f
ec
tiv
e
m
ec
h
an
is
m
f
o
r
d
y
n
am
ic
s
tab
ilit
y
m
an
ag
em
en
t.
I
ts
s
elec
tiv
e
n
a
tu
r
e
m
in
im
izes
o
v
er
h
ea
d
wh
i
le
p
r
eser
v
in
g
r
o
b
u
s
tn
ess
,
alig
n
in
g
well
with
th
e
d
em
an
d
s
o
f
d
is
tr
ib
u
ted
,
r
en
ew
ab
le
-
d
r
iv
e
n
g
r
id
s
.
5.
CO
NCLU
SI
O
N
T
h
is
r
ev
iew
e
x
am
in
ed
h
o
w
s
tate
-
s
p
ac
e
m
o
d
elin
g
,
r
ea
l
-
t
im
e
s
im
u
latio
n
,
a
n
d
ad
v
a
n
c
ed
co
n
tr
o
l
s
tr
ateg
ies
co
n
tr
ib
u
te
to
v
o
ltag
e
s
tab
ilit
y
in
r
en
ewa
b
le
-
in
teg
r
at
ed
m
icr
o
g
r
id
s
.
A
ce
n
tr
al
f
in
d
in
g
is
th
at
co
m
b
in
in
g
p
r
e
-
s
y
n
ch
r
o
n
izatio
n
tech
n
iq
u
e
s
with
M
PC
o
f
f
er
s
a
d
u
al
-
lay
er
ed
d
ef
en
s
e:
Pre
-
s
y
n
ch
r
o
n
izatio
n
en
s
u
r
es
s
m
o
o
t
h
p
h
ase
an
d
f
r
eq
u
en
cy
alig
n
m
en
t
d
u
r
in
g
g
r
id
tr
an
s
itio
n
s
,
wh
ile
MPC
d
eliv
er
s
p
r
ed
ictiv
e
ad
ap
tab
ilit
y
t
o
co
u
n
ter
ac
t
r
en
ewa
b
le
v
ar
iab
i
lity
.
T
o
g
eth
e
r
,
th
ese
m
ec
h
a
n
is
m
s
ad
d
r
ess
b
o
th
tr
an
s
ien
t
an
d
s
tead
y
-
s
tate
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