I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
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(
I
J
AP
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)
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
,
p
p
.
1
0
9
~
1
17
I
SS
N:
2252
-
8
7
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2
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DOI
:
1
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.
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.
v
1
4
.
i
1
.
pp
109
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1
17
109
J
o
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na
l ho
m
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a
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e
:
h
ttp
:
//ij
a
p
e
.
ia
esco
r
e.
co
m
Energ
y
stora
g
e participa
tion for
f
r
equency
regula
tio
n of
micro
g
rid in
PV
-
do
mina
ted
po
wer
sy
stem
Nirdesh
Sin
g
h
, D
i
nes
h
K
um
a
r
J
a
in
D
e
p
a
r
t
me
n
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o
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El
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Art
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nfo
AB
S
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RAC
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A
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ticle
his
to
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y:
R
ec
eiv
ed
Ma
r
1
8
,
2
0
2
4
R
ev
is
ed
Au
g
4
,
2
0
2
4
Acc
ep
ted
Au
g
1
5
,
2
0
2
4
Th
e
fre
q
u
e
n
c
y
sta
b
i
li
ty
o
f
a
p
o
w
e
r
g
rid
is
e
ffe
c
ti
v
e
ly
m
a
n
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d
th
ro
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th
e
in
e
rti
a
a
n
d
p
o
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re
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rv
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p
p
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d
b
y
sy
n
c
h
ro
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s
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e
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e
ra
to
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s.
Du
e
to
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re
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sin
g
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a
b
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t
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se
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ffe
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t
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n
d
g
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l
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rm
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g
,
re
n
e
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b
le
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n
e
rg
y
so
u
rc
e
s
(o
r
m
icro
g
rid
s)
a
r
e
i
n
c
re
a
sin
g
ly
re
p
lac
in
g
trad
it
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a
l
f
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b
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se
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m
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th
o
d
s
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.
As
m
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d
e
p
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tes
,
p
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s
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m
s'
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p
lex
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ty
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d
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ics
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it
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F
a
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to
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h
a
s
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e
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a
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trati
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f
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e
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s,
a
n
d
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g
n
ifi
c
a
n
t
p
o
we
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flu
c
tu
a
ti
o
n
s
with
in
c
o
n
fin
e
d
tr
a
n
sm
issio
n
sy
ste
m
s
h
a
v
e
h
e
ig
h
ten
e
d
th
e
v
u
l
n
e
ra
b
il
it
y
o
f
m
icro
g
ri
d
fre
q
u
e
n
c
ies
to
in
sta
b
il
it
y
.
T
h
is
p
a
p
e
r
e
lu
c
id
a
tes
th
e
c
o
n
c
e
p
t
o
f
m
icro
g
ri
d
s,
e
x
a
m
in
e
s
fre
q
u
e
n
c
y
fl
u
c
tu
a
ti
o
n
s
in
th
e
p
r
e
se
n
c
e
o
f
so
lar
a
n
d
d
ies
e
l
g
e
n
e
ra
to
rs
a
lo
n
g
s
id
e
l
o
a
d
v
a
riatio
n
s,
a
n
d
p
re
se
n
ts
si
m
u
latio
n
-
b
a
se
d
a
n
a
ly
s
e
s.
M
o
re
o
v
e
r,
it
p
r
o
v
i
d
e
s
a
su
c
c
in
c
t
o
v
e
r
v
iew
o
f
fre
q
u
e
n
c
y
c
o
n
tro
l
m
e
th
o
d
o
lo
g
ies
.
Va
li
d
a
ti
o
n
o
u
tc
o
m
e
s
d
e
m
o
n
stra
te
th
e
e
ffica
c
y
o
f
t
h
e
p
ro
p
o
se
d
c
o
n
tr
o
ll
e
r
in
m
a
in
tain
in
g
sy
ste
m
fre
q
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e
n
c
y
a
m
id
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flu
c
t
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a
ti
n
g
lo
a
d
d
e
m
a
n
d
s a
n
d
re
n
e
wa
b
le en
e
rg
y
i
n
p
u
ts.
K
ey
w
o
r
d
s
:
E
n
er
g
y
s
to
r
ag
e
Fre
q
u
en
cy
c
o
n
tr
o
l
Mic
r
o
g
r
id
R
en
ewa
b
le
en
er
g
y
r
eso
u
r
ce
So
lar
PV sy
s
tem
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Nir
d
esh
Sin
g
h
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
Dee
n
b
an
d
h
u
C
h
h
o
tu
R
am
Un
iv
er
s
ity
o
f
Scien
ce
an
d
T
ec
h
n
o
lo
g
y
Mu
r
th
al,
So
n
ip
at,
Har
y
an
a,
I
n
d
ia
E
m
ail:
s
in
g
h
.
n
ir
u
2
8
@
g
m
ail.
c
o
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
ec
en
t
y
ea
r
s
,
th
er
e
h
as
b
ee
n
a
g
r
o
win
g
im
p
er
ativ
e
to
tr
an
s
i
tio
n
to
war
d
s
g
e
n
er
atin
g
elec
tr
i
ca
l
p
o
wer
f
r
o
m
r
e
n
ewa
b
le
en
er
g
y
r
eso
u
r
ce
s
(
R
E
Ss
)
,
p
r
o
p
elled
b
y
t
h
e
d
ep
letio
n
o
f
tr
a
d
itio
n
al
f
o
s
s
il
f
u
el
r
eser
v
es
[
1
]
.
T
h
is
tr
an
s
itio
n
h
as
led
to
an
in
cr
ea
s
i
n
g
in
te
g
r
atio
n
o
f
R
E
Ss
in
to
c
o
n
v
en
tio
n
al
el
ec
tr
icity
g
r
id
s
,
th
er
eb
y
d
ec
en
tr
alizin
g
b
u
lk
p
o
wer
p
r
o
d
u
ctio
n
.
Ho
wev
er
,
th
is
in
teg
r
atio
n
in
tr
o
d
u
ce
s
ch
allen
g
es
ass
o
ciate
d
with
v
ar
iab
ilit
y
an
d
d
is
tu
r
b
an
ce
s
s
tem
m
in
g
f
r
o
m
th
e
in
h
er
en
t
u
n
p
r
ed
ictab
ilit
y
o
f
R
E
Ss
an
d
d
is
tr
ib
u
ted
g
en
er
ato
r
s
(
DGs).
Mo
r
eo
v
er
,
th
e
ex
p
a
n
s
io
n
o
f
elec
tr
ical
n
et
wo
r
k
s
an
d
tr
an
s
m
is
s
io
n
lin
es
to
s
er
v
e
r
e
m
o
te
elec
tr
ical
lo
a
d
s
escalate
s
th
e
co
s
ts
o
f
elec
tr
icity
p
r
o
d
u
ctio
n
an
d
tr
an
s
m
is
s
io
n
,
ex
ac
er
b
ated
b
y
in
cr
ea
s
in
g
d
em
an
d
.
T
o
ad
d
r
ess
th
e
co
n
s
tr
ain
t
s
ass
o
ciate
d
with
in
teg
r
atin
g
R
E
Ss
/DG
s
in
to
th
e
g
r
id
,
th
e
c
o
n
c
ep
t
o
f
a
m
icr
o
g
r
id
(
MG
)
h
as
e
m
er
g
ed
as
a
v
iab
le
s
o
lu
tio
n
[
2
]
.
A
m
icr
o
g
r
id
is
ch
ar
ac
ter
ize
d
as
a
lo
w
-
v
o
lt
ag
e
n
etwo
r
k
i
n
teg
r
atin
g
n
u
m
er
o
u
s
s
m
all
-
s
ca
le
d
is
tr
ib
u
ted
en
er
g
y
g
e
n
er
atio
n
an
d
s
to
r
ag
e
u
n
its
[
3
]
,
[
4
]
.
I
t
f
u
n
ctio
n
s
in
d
u
al
m
o
d
es:
in
ter
co
n
n
ec
te
d
with
t
h
e
p
r
im
ar
y
g
r
id
an
d
in
d
ep
en
d
en
t
ly
is
o
lated
f
r
o
m
it.
T
y
p
ically
,
th
e
m
icr
o
g
r
id
is
lin
k
e
d
to
th
e
n
atio
n
al
g
r
id
,
y
et
d
u
r
in
g
em
er
g
e
n
cies
m
ar
k
ed
b
y
s
ig
n
if
ican
t
d
is
r
u
p
tio
n
s
,
it
au
to
n
o
m
o
u
s
ly
d
is
co
n
n
ec
ts
f
r
o
m
th
e
m
ain
g
r
i
d
.
T
h
is
en
ab
les
it
to
ex
clu
s
iv
ely
s
u
p
p
ly
p
o
wer
t
o
cr
itical
lo
ca
l
lo
ad
s
,
en
s
u
r
in
g
th
eir
co
n
tin
u
ed
o
p
er
atio
n
[
5
]
,
[
6
]
.
I
n
tr
o
d
u
cin
g
t
h
is
co
n
ce
p
t
in
to
p
o
wer
s
y
s
tem
s
aim
s
to
en
h
an
ce
r
eliab
ilit
y
,
f
lex
ib
ilit
y
,
an
d
ad
ap
tab
ilit
y
wh
ile
ad
d
r
ess
in
g
ec
o
n
o
m
ic
an
d
en
v
i
r
o
n
m
en
tal
c
h
allen
g
es in
h
e
r
en
t
in
co
n
v
en
tio
n
al
p
o
wer
s
y
s
tem
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
109
-
1
17
110
Acc
o
r
d
in
g
to
t
h
e
I
n
ter
n
atio
n
a
l
E
n
er
g
y
Ag
e
n
cy
(
I
E
A)
,
g
lo
b
al
en
er
g
y
d
e
m
an
d
c
o
n
tin
u
es
t
o
r
is
e
with
ec
o
n
o
m
ic
a
n
d
tech
n
o
lo
g
ical
ad
v
an
ce
m
e
n
ts
[
7
]
.
C
u
r
r
en
t
ly
,
co
n
v
e
n
tio
n
al
en
er
g
y
g
en
er
a
to
r
s
co
n
s
titu
te
th
e
p
r
im
ar
y
s
o
u
r
ce
o
f
m
ee
tin
g
th
is
g
lo
b
al
en
e
r
g
y
d
em
an
d
.
Ho
we
v
er
,
th
e
f
i
n
ite
n
atu
r
e
o
f
n
o
n
-
r
e
n
ewa
b
le
f
o
s
s
il
f
u
els
lead
s
to
th
eir
g
r
a
d
u
al
d
e
p
letio
n
,
with
well
-
d
o
cu
m
en
ted
a
d
v
e
r
s
e
en
v
ir
o
n
m
en
tal
co
n
s
eq
u
en
c
es
[
8
]
.
Fig
u
r
e
1
(
a)
d
e
m
o
n
s
tr
ates
th
e
wo
r
ld
wid
e
n
ew
in
s
tallatio
n
o
f
R
E
S
f
o
r
th
e
y
ea
r
s
2
0
1
3
–
2
0
1
9
[
9
]
.
Sy
s
tem
o
p
er
ato
r
s
wo
r
ld
wid
e
ar
e
e
x
p
l
o
r
in
g
v
a
r
io
u
s
r
en
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
(
R
E
S),
in
clu
d
in
g
s
o
lar
,
win
d
,
b
io
m
ass
,
h
y
d
r
o
,
g
e
o
th
er
m
al,
an
d
o
ce
a
n
p
o
wer
,
t
o
m
ee
t
t
h
e
en
e
r
g
y
d
e
m
an
d
s
s
tip
u
lated
b
y
r
esp
ec
tiv
e
r
eg
u
lato
r
y
b
o
d
ies.
W
in
d
p
o
wer
p
lan
ts
an
d
g
r
id
-
co
n
n
ec
ted
s
o
lar
p
h
o
to
v
o
ltaic
(
PV)
h
av
e
em
er
g
e
d
as
u
p
-
a
n
d
-
co
m
in
g
o
p
tio
n
s
.
Mo
r
eo
v
er
,
r
en
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
(
R
E
S)
h
av
e
th
e
p
o
ten
tia
l
to
m
ee
t
th
e
g
r
o
win
g
g
lo
b
al
p
o
wer
d
em
a
n
d
.
I
t
is
p
r
o
jecte
d
th
at
with
in
th
e
n
ex
t
3
0
y
ea
r
s
,
Den
m
a
r
k
'
s
p
o
wer
s
y
s
tem
will
ac
h
iev
e
1
0
0
%
R
E
S
p
en
etr
atio
n
.
T
h
e
E
u
r
o
p
ea
n
Un
io
n
,
T
h
e
Un
ited
States
,
an
d
C
h
in
a
h
av
e
also
esta
b
lis
h
ed
am
b
itio
u
s
tar
g
ets
f
o
r
i
n
teg
r
atin
g
R
E
S
in
to
th
eir
p
o
wer
s
y
s
tem
s
.
C
u
r
r
en
t
r
en
ewa
b
le
p
en
etr
atio
n
lev
els
an
d
f
u
tu
r
e
tar
g
ets
f
o
r
s
ev
er
al
c
o
u
n
tr
ies
ar
e
illu
s
tr
ated
in
Fig
u
r
e
1
(
b
)
[
9
]
.
T
h
is
f
ig
u
r
e
in
d
icate
s
th
at
I
r
elan
d
,
C
h
in
a,
Sp
a
in
,
I
n
d
ia,
an
d
E
u
r
o
p
e
p
lan
to
in
co
r
p
o
r
ate
m
o
r
e
th
an
9
0
% r
e
n
ewa
b
le
r
eso
u
r
ce
s
in
to
th
eir
p
o
wer
s
y
s
tem
s
b
y
2
0
5
0
.
T
h
e
p
r
o
life
r
atio
n
o
f
m
icr
o
g
r
id
s
with
in
p
o
we
r
s
y
s
tem
s
h
as
f
u
n
d
am
en
tally
alter
e
d
o
p
er
atio
n
al
d
y
n
am
ics
.
C
o
n
s
eq
u
en
tly
,
th
is
h
as
in
d
u
ce
d
h
ei
g
h
ten
ed
c
o
m
p
lex
ity
an
d
n
o
n
-
lin
ea
r
ity
with
in
p
o
wer
n
etwo
r
k
s
.
M
an
ag
in
g
m
ic
r
o
g
r
id
(
MG
)
o
p
er
atio
n
s
in
is
lan
d
ed
m
o
d
e
p
r
esen
ts
g
r
ea
ter
co
m
p
le
x
ity
co
m
p
ar
ed
t
o
n
etwo
r
k
-
co
n
n
ec
ted
m
o
d
e.
Mo
r
e
o
v
er
,
with
in
is
lan
d
ed
m
icr
o
g
r
id
s
in
co
r
p
o
r
atin
g
r
en
ewa
b
le
s
o
u
r
ce
s
lik
e
win
d
an
d
s
o
lar
en
er
g
y
,
f
lu
ctu
atio
n
s
in
win
d
s
p
ee
d
an
d
v
ar
iatio
n
s
in
s
o
lar
r
ad
iatio
n
in
ten
s
ity
p
r
esen
t
s
u
b
s
tan
tial
en
er
g
y
p
er
tu
r
b
atio
n
s
to
th
e
m
icr
o
g
r
i
d
.
Hen
ce
,
ad
d
r
ess
in
g
f
r
eq
u
en
cy
d
ev
iatio
n
s
with
in
is
lan
d
ed
m
i
cr
o
g
r
id
s
s
tan
d
s
o
u
t
as a
p
ar
am
o
u
n
t c
o
n
tr
o
l c
h
allen
g
e
in
m
icr
o
g
r
id
r
esear
ch
.
(
a)
(
b
)
Fig
u
r
e
1
.
T
h
e
g
lo
b
al
in
s
tallatio
n
an
d
f
u
tu
r
e
tar
g
et
in
s
tallatio
n
o
f
R
E
S
:
(
a)
w
o
r
l
d
wid
e
y
ea
r
-
wis
e
in
s
tallat
io
n
o
f
R
E
S a
n
d
(
b
)
c
u
r
r
en
t a
n
d
f
u
t
u
r
e
tar
g
ets o
f
r
en
ewa
b
le
p
en
et
r
atio
n
lev
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
E
n
erg
y
s
to
r
a
g
e
p
a
r
ticip
a
tio
n
fo
r
fr
eq
u
en
cy
r
eg
u
la
tio
n
o
f m
ic
r
o
g
r
id
in
P
V
-
d
o
min
a
ted
…
(
N
ir
d
esh
S
in
g
h
)
111
Nu
m
er
o
u
s
r
ef
er
e
n
ce
s
h
av
e
in
v
esti
g
ated
an
d
p
r
esen
ted
d
iv
er
s
e
m
eth
o
d
o
lo
g
ies
f
o
r
m
icr
o
g
r
id
f
r
eq
u
en
c
y
co
n
tr
o
l,
f
o
cu
s
in
g
o
n
o
p
tim
izin
g
co
n
tr
o
ller
p
ar
am
ete
r
s
th
r
o
u
g
h
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
.
Pre
v
io
u
s
s
tu
d
ies
[
1
0
]
,
[
1
1
]
e
m
p
lo
y
PI
c
o
n
tr
o
l
a
n
d
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
-
d
e
r
iv
ativ
e
(
PID
)
c
o
n
tr
o
ller
s
,
r
esp
ec
tiv
ely
.
I
n
[
1
2
]
,
th
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
alg
o
r
ith
m
is
em
p
lo
y
e
d
,
wh
er
ea
s
in
[
13
]
,
th
e
s
p
id
e
r
s
o
cial
b
eh
av
io
r
(
SS
O)
alg
o
r
ith
m
is
u
tili
ze
d
f
o
r
t
h
e
o
p
tim
izatio
n
o
f
PID
c
o
n
tr
o
l
p
a
r
am
eter
s
.
Ad
d
itio
n
all
y
,
it
e
m
p
lo
y
s
th
e
h
ar
m
o
n
ic
s
ea
r
ch
(
HS)
alg
o
r
ith
m
f
o
r
lo
ad
-
f
r
eq
u
en
cy
co
n
tr
o
l.
Ab
az
ar
i
et
a
l
.
[
1
4
]
in
tr
o
d
u
ce
s
a
f
u
z
zy
co
n
tr
o
ller
with
co
ef
f
icien
ts
o
p
tim
ized
u
s
in
g
t
h
e
PS
O
alg
o
r
ith
m
.
Fu
r
th
er
m
o
r
e,
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l (
M
PC
)
is
ex
p
lo
r
ed
f
o
r
lo
ad
-
f
r
e
q
u
en
c
y
c
o
n
tr
o
l
in
[
1
5
]
,
[
1
6
]
,
wh
ile
Ab
az
ar
i
et
a
l
.
[
1
7
]
u
tili
ze
s
a
f
u
zz
y
co
n
tr
o
ller
to
r
eg
u
late
th
e
f
r
eq
u
e
n
cy
o
f
a
m
u
lti
-
m
icr
o
g
r
i
d
s
y
s
tem
.
L
en
g
et
a
l
.
[
1
8
]
i
n
tr
o
d
u
ce
s
a
two
-
lev
el
m
o
d
el
p
r
ed
i
ctiv
e
co
n
tr
o
l
(
MPC
)
ap
p
r
o
ac
h
,
as
well
as
m
u
ltip
le
MPC
co
n
tr
o
l
s
tr
ateg
ies
in
[
1
9
]
,
wh
ile
Z
h
an
g
et
a
l
.
[
2
0
]
p
r
es
en
ts
an
MP
C
-
b
ased
m
eth
o
d
f
o
r
co
o
r
d
in
ate
d
co
n
tr
o
l
o
f
win
d
tu
r
b
in
e
b
lad
es
an
d
elec
tr
ic
h
y
b
r
id
v
eh
icles
aim
ed
a
t
m
itig
atin
g
p
o
wer
f
lu
ctu
atio
n
s
an
d
e
n
h
an
ci
n
g
m
icr
o
g
r
id
f
r
eq
u
en
cy
s
tab
ilit
y
.
C
o
n
v
er
s
ely
,
Kh
o
d
ja
et
a
l
.
[
2
1
]
d
elv
es
in
to
th
e
Z
ieg
ler
-
Nich
o
ls
-
b
ased
PID
m
eth
o
d
(
Z
N
-
PID
)
,
wh
ile
Z
ah
ee
r
u
d
d
in
[
2
2
]
s
cr
u
tin
izes
th
e
f
r
a
ctio
n
al
-
o
r
d
e
r
-
b
ased
PID
m
eth
o
d
(
FOPID)
,
an
d
Os
h
n
o
ei
et
a
l
.
[
2
3
]
s
u
g
g
ests
th
e
i
m
p
lem
en
tatio
n
o
f
f
u
zz
y
co
n
tr
o
l
-
b
ased
f
r
ac
tio
n
al
-
o
r
d
er
PID
(
f
u
z
zy
FOPID)
.
Ad
d
itio
n
ally
,
Kh
o
s
r
av
i
et
a
l
.
[
2
4
]
u
tili
ze
s
a
k
r
ig
in
g
-
b
ased
s
u
r
r
o
g
ate
f
r
ac
tio
n
al
-
o
r
d
e
r
PID
m
eth
o
d
f
o
r
c
o
n
tr
o
l
s
y
s
tem
d
esig
n
.
T
o
en
h
an
ce
t
h
e
s
et
p
o
in
t
o
f
ac
tiv
e
p
o
wer
an
d
b
o
ls
ter
f
r
eq
u
en
cy
s
tab
ilit
y
in
is
lan
d
ed
m
icr
o
g
r
id
s
(
MG
s
)
,
v
ir
tu
al
in
er
tia
co
n
tr
o
l
is
im
p
le
m
en
ted
,
lev
e
r
ag
in
g
th
e
r
ate
o
f
ch
an
g
e
o
f
f
r
eq
u
e
n
c
y
(
R
o
C
o
F)
f
u
n
ctio
n
[
2
5
]
,
[
2
6
]
.
I
n
v
esti
g
atio
n
in
t
o
t
h
e
f
r
eq
u
e
n
cy
s
tab
ilit
y
o
f
a
n
au
to
n
o
m
o
u
s
m
icr
o
g
r
id
(
MG
)
s
y
s
tem
,
as
d
o
cu
m
en
ted
in
[
2
7
]
,
em
p
lo
y
ed
a
co
e
f
f
icien
t
d
iag
r
am
ap
p
r
o
ac
h
alo
n
g
s
id
e
a
PID
ac
ce
le
r
ato
r
co
n
tr
o
ller
.
A
co
m
p
a
r
ativ
e
an
aly
s
is
o
f
p
u
b
lis
h
ed
PID
an
d
2
Do
F
-
PID
co
n
tr
o
ller
s
was
co
n
d
u
cted
to
ev
alu
ate
p
er
f
o
r
m
an
ce
.
Gh
eisar
n
ejad
a
n
d
Kh
o
o
b
a
n
[
2
8
]
d
elib
e
r
ated
o
n
d
esig
n
in
g
a
f
u
zz
y
PID
co
n
tr
o
ller
f
o
r
a
m
u
lti
-
m
icr
o
g
r
id
s
y
s
tem
as
a
s
ec
o
n
d
ar
y
co
n
tr
o
l
m
ec
h
an
is
m
.
Ad
d
it
io
n
ally
,
Patel
et
a
l
.
[
2
9
]
im
p
le
m
en
ted
a
f
u
zz
y
tilt
in
teg
r
al
d
er
iv
ativ
e
co
n
t
r
o
ller
to
en
h
an
ce
f
r
e
q
u
en
c
y
s
tab
ilit
y
with
in
a
h
y
b
r
id
m
icr
o
g
r
id
(
MG
)
,
d
em
o
n
s
tr
atin
g
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
th
r
o
u
g
h
co
m
p
ar
ativ
e
an
al
y
s
is
ag
ain
s
t
class
ical
PID
co
n
tr
o
ller
s
.
Mo
r
eo
v
er
,
Kh
o
k
h
a
r
et
al
.
[
3
0
]
in
t
r
o
d
u
ce
d
th
e
s
lap
s
war
m
o
p
tim
izatio
n
(
SS
O)
tech
n
i
q
u
e
-
ad
ju
s
ted
ca
s
ca
d
e
(
PI
-
PD)
co
n
tr
o
ller
,
tailo
r
e
d
f
o
r
r
eg
u
latin
g
s
y
s
tem
f
r
eq
u
e
n
cy
in
an
MG
in
te
g
r
ated
w
ith
an
elec
tr
ic
v
e
h
icle,
s
h
o
wca
s
in
g
in
n
o
v
ativ
e
ad
v
an
ce
m
e
n
ts
in
co
n
tr
o
l
s
tr
ate
g
y
.
Z
an
d
et
a
l
.
[
3
1
]
a
n
d
B
ald
in
elli
et
a
l
.
[
3
2
]
i
n
tr
o
d
u
ce
a
n
o
v
e
l
ap
p
r
o
ac
h
to
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
f
o
r
s
c
h
ed
u
lin
g
d
is
tr
ib
u
te
d
e
n
er
g
y
r
eso
u
r
ce
s
(
DE
R
s
)
with
in
m
icr
o
g
r
id
s
.
Similar
ly
,
in
[
3
3
]
,
th
e
f
o
cu
s
s
h
if
ts
t
o
en
e
r
g
y
m
a
n
ag
em
e
n
t
with
in
a
n
is
o
lated
m
icr
o
g
r
id
,
em
p
h
asizin
g
m
ax
im
izin
g
DE
R
u
tili
za
tio
n
wh
ile
m
in
im
izin
g
o
p
er
atio
n
al
c
o
s
ts
.
No
n
eth
eless
,
t
h
ese
r
ef
er
en
ce
s
o
v
er
lo
o
k
th
e
s
u
b
s
tan
tial
im
p
ac
ts
o
f
ab
r
u
p
t
lo
ad
f
lu
ctu
atio
n
s
o
r
u
n
p
r
e
d
ictab
le
ch
an
g
es
in
r
en
e
wab
le
en
er
g
y
s
o
u
r
ce
s
(
R
E
S)
p
o
wer
o
u
tp
u
t
d
u
r
in
g
m
icr
o
g
r
id
r
eso
u
r
ce
p
lan
n
in
g
.
2.
RE
S
E
ARCH
O
B
J
E
CT
I
V
E
(
I
NT
E
L
L
E
CT
UAL CO
N
T
R
I
B
UT
I
O
N)
T
h
e
ex
ten
s
iv
e
in
te
g
r
atio
n
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
(
R
E
S)
wo
r
ld
wid
e
h
as
s
ig
n
if
ica
n
tly
alter
ed
p
o
wer
s
y
s
tem
d
y
n
a
m
ics.
T
r
ad
i
tio
n
ally
,
th
e
k
in
etic
e
n
er
g
y
s
to
r
ed
in
th
e
r
o
tatin
g
m
ass
o
f
s
y
n
c
h
r
o
n
o
u
s
g
en
er
at
o
r
s
(
SGs
)
h
as
b
ee
n
r
elied
u
p
o
n
to
co
m
p
e
n
s
ate
f
o
r
g
e
n
e
r
atio
n
d
e
f
icits
.
Ho
wev
er
,
with
th
e
wid
e
s
p
r
ea
d
ad
o
p
tio
n
o
f
R
E
S,
co
n
v
en
tio
n
al
SGs
ar
e
b
ein
g
d
is
p
lace
d
.
R
E
S
in
s
tallatio
n
s
ty
p
ically
lack
in
h
er
en
t
s
y
s
tem
in
er
tia,
n
ec
ess
itatin
g
ad
d
itio
n
al
c
o
n
tr
o
l
m
ec
h
a
n
is
m
s
to
en
s
u
r
e
s
tab
ilit
y
.
C
o
n
s
eq
u
en
tly
,
th
e
o
v
er
a
ll
s
y
s
tem
in
er
tia
is
d
im
in
is
h
in
g
,
r
en
d
er
i
n
g
lo
w
-
in
er
tia
p
o
wer
s
y
s
tem
s
m
o
r
e
s
u
s
ce
p
tib
le
to
v
a
r
io
u
s
d
is
tu
r
b
an
c
es
an
d
u
n
ce
r
tain
ties
in
h
er
en
t
i
n
m
o
d
er
n
p
o
wer
g
r
id
s
.
C
h
allen
g
es
ass
o
ciate
d
with
lo
w
in
er
tia
g
r
id
s
in
cl
u
d
e
h
eig
h
ten
ed
r
ates
o
f
f
r
eq
u
e
n
cy
ch
a
n
g
e,
in
cr
ea
s
ed
f
r
e
q
u
en
cy
d
ev
iatio
n
,
an
d
d
is
tr
ib
u
ted
p
h
o
to
v
o
ltaic
(
PV)
tr
ip
ev
en
ts
,
am
o
n
g
o
th
er
s
.
T
h
e
o
b
jectiv
e
o
f
th
is
p
ap
er
i
s
to
co
u
n
ter
t
h
ese
ch
allen
g
es
an
d
to
r
eg
u
late
th
e
f
r
eq
u
en
c
y
o
f
th
e
s
y
s
tem
b
y
co
n
tr
o
llin
g
t
h
e
ac
tiv
e
p
o
wer
o
f
th
e
b
atter
y
.
T
h
e
r
est
o
f
th
e
m
an
u
s
cr
ip
t
is
o
r
g
an
ized
as
f
o
llo
ws:
th
e
s
ec
o
n
d
s
ec
tio
n
o
u
tlin
es
th
e
m
icr
o
g
r
id
'
s
ar
ch
itectu
r
e
an
d
its
co
r
r
esp
o
n
d
in
g
m
o
d
el,
alo
n
g
with
th
e
m
o
d
ellin
g
o
f
t
h
e
b
atter
y
.
Fo
llo
win
g
th
is
,
s
ec
tio
n
3
o
f
f
er
s
in
s
ig
h
t
in
to
th
e
s
im
u
latio
n
im
p
lem
e
n
tatio
n
a
n
d
p
r
es
en
ts
th
e
r
esu
lts
o
f
f
r
eq
u
e
n
cy
co
n
tr
o
l
with
in
th
e
m
icr
o
g
r
id
u
n
d
er
i
n
v
esti
g
atio
n
.
L
astl
y
,
th
e
c
o
n
clu
s
io
n
a
n
d
f
u
tu
r
e
r
ec
o
m
m
en
d
atio
n
s
ar
e
p
r
o
v
id
ed
in
th
e
f
o
u
r
t
h
s
ec
tio
n
o
f
th
e
ar
ticle.
3.
M
O
DE
L
L
I
NG
O
F
T
H
E
S
T
O
RAG
E
SYS
T
E
M
W
I
T
H
M
E
T
H
O
DO
L
O
G
Y
T
O
CO
NT
RO
L
F
RE
Q
UE
N
CY
T
h
e
m
o
d
eli
n
g
p
r
o
ce
s
s
en
h
an
ce
s
u
n
d
er
s
tan
d
in
g
o
f
b
atter
y
b
eh
av
io
r
an
d
p
lay
s
a
cr
u
ci
al
r
o
le
in
im
p
r
o
v
in
g
o
v
er
all
s
y
s
tem
p
e
r
f
o
r
m
a
n
ce
an
d
ef
f
icien
c
y
.
B
atter
ies
ar
e
cr
u
cial
as
v
er
s
at
ile
en
er
g
y
s
to
r
a
g
e
s
o
lu
tio
n
s
,
ca
ter
in
g
to
v
ar
io
u
s
ap
p
licatio
n
s
with
v
ar
y
i
n
g
p
o
we
r
d
em
an
d
s
.
T
h
ese
d
ev
ices
ar
e
in
d
is
p
en
s
ab
le
ac
r
o
s
s
n
u
m
er
o
u
s
in
d
u
s
tr
ies,
u
tili
ze
d
in
b
o
th
s
er
ies
an
d
p
ar
allel
s
et
u
p
s
to
ac
c
o
m
m
o
d
ate
s
p
ec
if
ic
lo
ad
r
e
q
u
ir
em
e
n
ts
.
B
atter
y
m
o
d
elin
g
is
a
p
o
ten
t
tech
n
iq
u
e
f
o
r
p
r
e
d
ictin
g
an
d
e
n
h
an
cin
g
k
ey
p
a
r
am
eter
s
,
s
u
ch
as
s
tate
o
f
ch
ar
g
e,
b
atter
y
lo
n
g
ev
ity
,
an
d
c
h
ar
g
e
/d
is
ch
ar
g
e
b
e
h
av
io
r
.
L
ith
iu
m
-
io
n
b
atter
ies
h
o
ld
p
ar
ticu
lar
p
r
o
m
in
e
n
ce
am
o
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
109
-
1
17
112
b
atter
y
ty
p
es
d
u
e
to
t
h
eir
lig
h
t
weig
h
t
d
esig
n
,
h
i
g
h
-
e
n
er
g
y
d
e
n
s
ity
,
an
d
m
i
n
im
al
s
elf
-
d
is
ch
a
r
g
e
r
ates,
o
f
f
er
in
g
s
ig
n
if
ican
t
ad
v
an
tag
es
in
v
ar
io
u
s
co
n
tex
ts
.
A
p
r
ec
is
e
elec
tr
ic
al
eq
u
iv
alen
t
m
o
d
el,
s
u
ch
as
th
e
r
esis
to
r
-
ca
p
ac
ito
r
(
R
C
)
cir
cu
it
b
atter
y
b
lo
ck
ill
u
s
tr
ated
in
Fig
u
r
e
2
,
b
ec
o
m
e
s
es
s
en
tial
f
o
r
co
n
d
u
ctin
g
th
o
r
o
u
g
h
an
aly
s
es
an
d
m
ak
in
g
in
f
o
r
m
e
d
d
ec
is
io
n
s
r
e
g
ar
d
in
g
s
y
s
tem
d
esig
n
a
n
d
o
p
er
atio
n
.
To
ca
lcu
late
th
e
c
o
m
b
in
ed
v
o
lta
g
e
o
f
th
e
b
atter
y
n
etwo
r
k
:
=
−
0
−
∑
1
(
1
)
=
∫
[
−
]
0
(
2
)
=
−
1
∫
0
(
3
)
=
(
4
)
=
(
5
)
=
2
0
+
∑
2
1
(
6
)
=
−
(
2
0
+
∑
2
1
)
(
7
)
=
+
(
8
)
=
∫
0
(
9
)
w
h
er
e
SOC
is
a
s
tate
o
f
ch
ar
g
e
;
is
b
atter
y
o
p
en
-
cir
c
u
it
v
o
lt
ag
e
;
is
p
er
m
o
d
u
le
b
atter
y
cu
r
r
en
t
;
is
th
e
t
o
tal
c
u
r
r
en
t
f
lo
win
g
f
r
o
m
th
e
b
atter
y
n
etwo
r
k
;
0
is
s
er
ies r
esis
tan
ce
;
is
n
o
.
o
f
p
ar
allel
b
r
an
ch
es
;
,
is
a
c
o
m
b
in
ed
v
o
ltag
e
o
f
th
e
b
atter
y
n
etwo
r
k
;
is
a
v
o
ltag
e
o
f
n
th
R
C
p
air
;
is
th
e
r
esis
tan
ce
o
f
th
e
n
th
R
C
p
air
;
is
th
e
c
ap
ac
itan
ce
o
f
n
th
R
C
p
air
;
is
b
atter
y
ca
p
ac
ity
;
is
b
atter
y
p
o
wer
;
is
b
atter
y
n
etwo
r
k
p
o
wer
lo
s
s
;
i
s
n
eg
ativ
e
o
f
b
atter
y
n
etwo
r
k
p
o
wer
lo
s
s
;
is
b
atter
y
n
etwo
r
k
p
o
wer
s
to
r
ed
;
an
d
T
is
b
atter
y
tem
p
er
atu
r
e
.
Po
s
itiv
e
cu
r
r
e
n
t
in
d
icate
s
b
atter
y
d
is
ch
ar
g
e
a
n
d
n
e
g
ativ
e
cu
r
r
en
t
in
d
icate
s
b
atter
y
ch
ar
g
e
.
T
h
e
(
1
)
to
(
9
)
h
as b
ee
n
u
s
ed
f
o
r
t
h
e
m
o
d
elin
g
o
f
th
e
b
atter
y
.
W
av
ef
o
r
m
s
f
o
r
b
atter
y
s
tate
o
f
ch
ar
g
e
(
SOC
)
,
cu
r
r
en
t
,
an
d
v
o
ltag
e
ar
e
s
h
o
wn
in
F
i
g
u
r
e
3
.
I
n
Fig
u
r
e
3
(
a
)
,
th
e
s
tate
o
f
ch
ar
g
e
(
SOC
)
o
f
th
e
b
atter
y
is
d
ep
icted
at
5
0
%
in
itially
,
with
a
ch
ar
g
in
g
p
r
o
ce
s
s
in
itiated
at
3
s
ec
o
n
d
s
in
to
th
e
s
im
u
latio
n
.
T
h
r
o
u
g
h
o
u
t
th
e
d
u
r
a
tio
n
o
f
th
e
s
im
u
latio
n
,
th
e
b
atter
y
'
s
SO
C
in
cr
ea
s
es
m
ar
g
in
ally
f
r
o
m
4
7
.
9
%
to
4
8
.
0
2
%.
Fig
u
r
e
3
(
b
)
illu
s
tr
ates
th
e
b
atter
y
'
s
cu
r
r
en
t
p
r
o
f
ile,
in
d
i
ca
tin
g
a
s
tate
o
f
ze
r
o
cu
r
r
en
t
p
r
io
r
to
3
s
ec
o
n
d
s
.
S
u
b
s
eq
u
en
tly
,
p
o
s
t
th
e
3
-
s
ec
o
n
d
m
ar
k
,
th
e
b
atter
y
b
e
g
in
s
ch
ar
g
in
g
at
a
r
ate
o
f
3
0
k
W
,
co
r
r
esp
o
n
d
in
g
to
a
cu
r
r
en
t
o
f
-
2
0
0
A.
Fig
u
r
e
3
(
c)
d
e
m
o
n
s
tr
ates
a
v
o
ltag
e
in
cr
ea
s
e
o
cc
u
r
r
in
g
p
r
ec
is
ely
at
3
s
ec
o
n
d
s
,
s
tab
ilizin
g
at
2
6
2
V
f
o
r
th
e
d
u
r
atio
n
o
f
th
e
s
im
u
latio
n
.
R
1
R
2
R
n
C
1
C
2
C
n
R
0
E
0
I
b
a
t
t
Fig
u
r
e
2
.
E
q
u
iv
alen
t
m
o
d
el
o
f
b
atter
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
E
n
erg
y
s
to
r
a
g
e
p
a
r
ticip
a
tio
n
fo
r
fr
eq
u
en
cy
r
eg
u
la
tio
n
o
f m
ic
r
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g
r
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in
P
V
-
d
o
min
a
ted
…
(
N
ir
d
esh
S
in
g
h
)
113
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
B
atter
y
wav
e
f
o
r
m
s
:
(
a)
b
atter
y
SOC
,
(
b
)
b
atter
y
c
u
r
r
en
t,
an
d
(
c)
b
atter
y
v
o
ltag
e
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
's
n
u
m
er
o
u
s
co
m
p
o
n
en
ts
ar
e
r
ep
r
ese
n
ted
to
cr
ea
te
a
f
u
ll
m
o
d
el.
T
h
e
co
n
tr
o
l
s
ch
em
e
d
ep
icted
in
Fig
u
r
e
4
is
p
r
im
ar
ily
u
tili
ze
d
to
d
er
iv
e
r
e
f
er
en
ce
s
o
u
r
ce
cu
r
r
en
ts
,
wh
ich
ar
e
th
en
em
p
lo
y
e
d
in
th
e
b
atter
y
en
er
g
y
s
to
r
a
g
e
s
y
s
tem
(
B
E
S
S
)
VSI
'
s
p
u
ls
e
w
id
th
m
o
d
u
latio
n
(
PW
M
)
cu
r
r
e
n
t
co
n
tr
o
ller
.
T
h
e
r
e
ar
e
two
co
m
p
o
n
e
n
ts
to
th
e
r
e
f
e
r
en
ce
s
o
u
r
ce
cu
r
r
e
n
ts
:
an
in
-
p
h
ase
co
m
p
o
n
e
n
t
an
d
a
q
u
ad
r
atu
r
e
co
m
p
o
n
en
t.
T
h
e
in
-
p
h
ase
c
o
m
p
o
n
en
t
o
f
t
h
e
r
e
f
er
en
ce
s
o
u
r
ce
cu
r
r
en
ts
is
r
e
q
u
ir
ed
to
ch
ar
g
e
th
e
b
atter
y
o
f
B
E
SS
an
d
/o
r
to
f
ee
d
ac
tiv
e
p
o
wer
to
th
e
lo
a
d
.
T
h
is
ac
tiv
e
p
o
wer
co
m
p
o
n
e
n
t
m
ay
b
e
k
ep
t
co
n
s
tan
t
to
g
en
er
ate
c
o
n
s
tan
t
p
o
wer
at
th
e
p
o
in
t
o
f
c
o
m
m
o
n
co
u
p
lin
g
(
P
C
C
)
.
T
h
e
s
u
r
p
lu
s
p
o
wer
is
ab
s
o
r
b
ed
b
y
th
e
B
E
SS
an
d
d
u
r
i
n
g
p
ea
k
in
g
lo
a
d
B
E
SS
r
ep
len
is
h
es
th
e
in
cr
ea
s
ed
r
eq
u
i
r
em
en
t
o
f
lo
ad
r
esu
ltin
g
in
f
r
e
q
u
en
cy
r
e
g
u
latio
n
.
Her
e,
th
e
a
ctiv
e
co
m
p
o
n
e
n
t
o
f
th
e
s
o
u
r
ce
cu
r
r
en
t
r
em
ain
s
f
ix
ed
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er
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s
th
e
r
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ctiv
e
p
o
wer
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m
p
o
n
e
n
t
d
ep
en
d
s
u
p
o
n
th
e
r
eq
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ir
em
en
t
o
f
AC
ter
m
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al
v
o
ltag
e
c
o
n
tr
o
l.
Su
c
h
co
n
tr
o
ller
s
b
ased
o
n
B
E
SS
,
in
ad
d
itio
n
,
p
er
f
o
r
m
th
e
task
s
o
f
f
r
eq
u
en
cy
an
d
v
o
ltag
e
co
n
tr
o
l in
ca
s
e
o
f
u
n
b
alan
ce
d
an
d
n
o
n
-
lin
ea
r
lo
a
d
s
.
T
h
is
h
as b
ee
n
s
h
o
wn
i
n
(
1
0
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t
o
(
2
4
)
.
T
h
ey
ar
e
esti
m
ated
in
th
e
f
o
ll
o
win
g
o
r
d
er
:
t
h
e
u
n
it
v
ec
to
r
s
i
n
p
h
ase
with
Va,
Vb
,
an
d
Vc
ar
e
d
er
iv
ed
as
in
(
1
0
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=
;
=
;
=
(1
0
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W
h
er
e
is
th
e
am
p
litu
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e
o
f
th
e
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ter
m
in
al
v
o
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e
at
th
e
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C
C
an
d
ca
n
b
e
ca
lcu
lated
as
(
1
1
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.
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3
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2
+
2
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2
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(
11
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W
h
er
e
V
a
, V
b
,
an
d
V
c
ar
e
t
h
e
i
n
s
tan
tan
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u
s
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o
ltag
es a
t PC
C
an
d
ca
n
b
e
d
er
i
v
ed
as:
=
-
-
,
=
-
-
,
=
-
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
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n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
109
-
1
17
114
w
h
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e
P
r
ep
r
esen
ts
th
e
tim
e
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if
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er
en
tial
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d
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ase
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r
ce
in
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u
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esis
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ce
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r
esp
ec
tiv
ely
.
,
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an
d
ar
e
th
e
th
r
ee
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p
h
ase
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s
tan
tan
eo
u
s
in
p
u
t
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p
p
ly
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at
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d
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e
e
x
p
r
ess
ed
as
(
1
2
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.
=
(
)
;
=
(
−
2
/
3
)
;
=
(
+
2
/
3
)
(
12
)
T
h
e
p
ea
k
v
alu
e,
d
en
o
ted
as
,
an
d
th
e
an
g
u
lar
f
r
eq
u
e
n
cy
(
ω
=2
πf
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o
f
th
e
p
o
wer
s
u
p
p
ly
ar
e
estab
lis
h
ed
p
ar
am
eter
s
in
th
is
co
n
tex
t.
T
h
e
d
er
iv
atio
n
o
f
u
n
it
v
ec
to
r
s
o
r
t
h
o
g
o
n
al
to
,
,
an
d
in
v
o
lv
es
im
p
lem
en
tin
g
a
q
u
ad
r
at
u
r
e
tr
an
s
f
o
r
m
atio
n
o
n
th
e
i
n
-
p
h
ase
u
n
it
v
ec
to
r
s
,
,
an
d
as
(
1
3
)
-
(
1
5
)
.
=
-
/
√
3
+
/
√
3
,
(
13
)
=
√
3
/2
+
(
−
)
/(
2
√
3
),
(
14
)
=
-
√
3
/2
+
(
−
)
/(
2
√
3
)
(
15
)
T
h
e
q
u
ad
r
atu
r
e
co
m
p
o
n
en
t
o
f
th
e
r
ef
er
en
ce
s
o
u
r
ce
cu
r
r
e
n
ts
is
co
m
p
u
ted
as
f
o
llo
ws.
T
h
e
v
o
ltag
e
er
r
o
r
at
PC
C
at
th
e
n
th
s
am
p
lin
g
in
s
ta
n
t is as
(
1
6
)
.
(
)
=
(
)
-
(
)
(
16
)
3
.
1
.
M
o
dellin
g
o
f
B
E
SS
T
h
e
B
E
SS
is
o
p
er
ated
in
cu
r
r
en
t
-
co
n
tr
o
lled
m
o
d
e,
an
d
th
e
v
o
lt
-
cu
r
r
e
n
t
eq
u
ati
o
n
s
ar
e
ca
l
cu
lated
as
illu
s
tr
ated
in
Fig
u
r
e
4.
=
+
+
−
−
(
17
)
=
+
+
−
−
(
18
)
Fu
r
th
er
:
+
+
=
0
(
1
9
)
t
o
ca
lcu
late
an
d
,
u
s
e
(
1
7
)
to
(
19
)
.
=
{
(
−
)
+
2
(
−
)
−
3
}
/
3
=
0
(
20
)
=
{
(
−
)
−
(
−
)
−
3
}
/
3
=
0
(2
1
)
Fro
m
(
1
9
)
,
ca
n
b
e
e
x
p
r
ess
ed
as (
2
2
)
.
=
−
(
+
)
(
22
)
T
h
e
DC
b
u
s
v
o
ltag
e
d
er
iv
atio
n
ca
n
b
e
ex
p
r
ess
ed
as:
=
+
+
−
)
/
(
23
)
wh
er
e
is
th
e
b
atter
y
'
s
ch
ar
g
i
n
g
/d
is
ch
ar
g
in
g
cu
r
r
en
t.
SA,
SB
,
an
d
SC
ar
e
s
witch
in
g
f
u
n
cti
o
n
s
th
at
s
p
ec
if
y
th
e
ON/OFF
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tates
o
f
th
e
B
E
S
S
VSI
b
r
id
g
e
s
witch
es
S
1
-
S
6
.
T
h
e
in
v
er
ter
'
s
AC
o
u
tp
u
t
v
o
lta
g
es
ar
e
r
ep
r
esen
ted
in
th
e
th
r
ee
-
p
h
ase
PW
M
AC
v
o
ltag
es
,
,
an
d
o
f
th
e
B
E
SS
.
AC
lin
e
v
o
ltag
es o
f
B
E
SS
ar
e
:
=
(
−
)
,
=
(
−
)
,
=
(
−
)
(
24
)
f
o
r
th
e
ON
an
d
OFF
co
n
d
itio
n
s
o
f
th
e
u
p
p
er
an
d
lo
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s
witch
es
o
f
th
e
p
h
ase
'
a
'
leg
o
f
t
h
e
VSI
b
r
id
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e,
th
e
s
witch
in
g
f
u
n
ctio
n
SA
h
as
v
al
u
es
o
f
0
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d
1
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r
esp
ec
tiv
el
y
.
T
h
e
o
th
er
p
h
ase
lag
s
f
o
llo
w
a
s
im
ilar
r
atio
n
ale.
T
h
e
b
atter
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m
o
d
elled
b
y
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s
in
g
T
h
ev
en
in
’
s
e
q
u
iv
a
len
t c
ir
c
u
it m
o
d
el.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
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E
n
g
I
SS
N:
2252
-
8
7
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2
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to
r
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p
a
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g
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115
3
-
P
h
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a
d
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Fig
u
r
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4
.
Prin
cip
le
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f
c
o
n
tr
o
l
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
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O
N
I
n
Fig
u
r
e
5
,
f
o
llo
win
g
a
1
2
-
s
ec
o
n
d
s
im
u
latio
n
,
th
e
f
r
eq
u
en
cy
ex
h
ib
its
d
r
o
p
to
5
9
.
6
8
Hz,
5
9
.
8
0
Hz,
an
d
5
9
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7
7
Hz
at
0
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5
s
ec
o
n
d
s
,
3
s
ec
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n
d
s
,
an
d
4
.
5
s
ec
o
n
d
s
,
r
esp
ec
tiv
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.
T
h
ese
r
ed
u
ctio
n
s
ar
e
attr
i
b
u
ted
to
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itio
n
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s
o
f
5
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3
0
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W
,
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d
5
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k
W
,
r
esp
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in
ad
d
itio
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e
x
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g
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0
k
W
.
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4
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5
s
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n
d
s
,
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e
b
at
ter
y
b
e
g
in
s
d
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g
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g
at
a
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f
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ee
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e
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e
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em
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d
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a
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to
5
9
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7
5
Hz.
I
n
Fig
u
r
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6
,
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o
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g
a
1
2
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n
d
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im
u
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,
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e
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r
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e
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to
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9
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6
8
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s
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ted
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o
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d
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A
s
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b
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en
t
d
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p
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u
r
s
at
3
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n
d
s
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a
f
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r
th
er
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ad
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n
cr
ea
s
e
o
f
3
0
k
W
.
At
th
e
3
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s
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o
n
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m
ar
k
,
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e
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atter
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e
g
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g
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g
at
a
r
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te
o
f
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k
W
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ca
u
s
in
g
th
e
f
r
eq
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en
cy
t
o
d
ec
lin
e
to
5
9
.
9
2
Hz.
Su
b
s
eq
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en
tly
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e
f
r
eq
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en
cy
s
t
ab
ilizes at
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9
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9
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Fig
u
r
e
5
.
Fre
q
u
en
cy
at
lo
ad
b
u
s
with
o
u
t a
n
y
co
n
tr
o
ller
Fig
u
r
e
6
.
Fre
q
u
en
cy
at
lo
ad
b
u
s
with
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
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17
116
5.
CO
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tain
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a
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n
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u
m
p
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tan
d
s
as
a
p
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ac
to
r
in
g
u
a
r
an
teein
g
f
r
eq
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e
n
cy
s
tab
ilit
y
with
in
m
icr
o
g
r
id
s
y
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tem
s
.
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h
is
p
a
p
er
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t
o
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e
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t
o
f
m
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d
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e
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r
e
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u
en
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lu
ctu
atio
n
d
y
n
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ics
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n
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er
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e
in
f
lu
en
ce
o
f
s
o
lar
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iesel
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en
er
ato
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s
,
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d
lo
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n
s
,
s
u
b
s
eq
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e
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d
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in
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ry
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In
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in
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