I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
,
p
p
.
55
1
~
5
5
9
I
SS
N:
2252
-
8
7
9
2
,
DOI
:
1
0
.
1
1
5
9
1
/ijap
e
.
v
1
4
.
i
3
.
pp
55
1
-
559
551
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//
ija
p
e.
ia
esco
r
e.
co
m/
M
o
del predic
tive
co
ntrol ba
sed f
re
quency
regula
tio
n of
micro
g
rid wit
h
in
tegra
tion o
f
dis
tri
buted
energy
reso
urces
Sa
rbj
ee
t
K
a
ur,
Su
rbhi G
up
t
a
El
e
c
t
r
i
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a
l
E
n
g
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e
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p
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t
,
C
h
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n
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i
g
a
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n
i
v
e
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si
t
y
,
P
u
n
j
a
b
,
I
n
d
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
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y:
R
ec
eiv
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Ap
r
2
4
,
2
0
2
4
R
ev
is
ed
No
v
3
0
,
2
0
2
4
Acc
ep
ted
J
an
1
9
,
2
0
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5
P
o
we
r
g
e
n
e
ra
ti
o
n
se
c
to
r
h
a
s
b
e
c
o
m
e
m
o
re
p
re
v
a
len
t
in
th
e
u
se
o
f
r
e
n
e
wa
b
le
e
n
e
rg
y
so
u
rc
e
s
re
su
lt
in
g
i
n
m
o
re
c
o
m
p
lex
a
n
d
n
o
n
-
l
in
e
a
r
n
e
two
rk
.
M
icro
g
ri
d
s
a
re
b
e
c
o
m
in
g
t
h
e
b
e
st
a
lt
e
rn
a
ti
v
e
so
lu
ti
o
n
i
n
re
m
o
te
a
re
a
s
wh
e
re
th
e
d
istri
b
u
ti
o
n
n
e
two
r
k
is
in
fe
a
sib
le.
Ho
we
v
e
r,
t
h
e
in
term
it
ten
t
n
a
tu
re
o
f
d
istri
b
u
ted
re
n
e
wa
b
le
e
n
e
r
g
y
r
e
so
u
rc
e
s
c
a
n
re
su
lt
in
a
g
e
n
e
r
a
ti
o
n
a
n
d
d
e
m
a
n
d
m
ism
a
tch
in
sti
g
a
ti
n
g
fre
q
u
e
n
c
y
v
a
riati
o
n
w
h
ich
is
a
c
r
u
c
ial
c
o
n
c
e
rn
.
Th
u
s,
m
o
d
e
r
n
p
o
we
r
s
y
ste
m
re
q
u
ires
in
c
re
a
sin
g
i
n
telli
g
e
n
c
e
a
n
d
flex
ib
il
it
y
to
c
o
p
e
u
p
wit
h
t
h
e
g
e
n
e
ra
ti
o
n
-
l
o
a
d
m
ism
a
tch
.
Eff
icie
n
t
c
o
n
tro
l
t
e
c
h
n
iq
u
e
s
a
re
o
f
v
it
a
l
im
p
o
rtan
c
e
i
n
m
a
in
tai
n
in
g
t
h
e
fre
q
u
e
n
c
y
n
e
a
r
t
h
e
n
o
m
i
n
a
l
v
a
l
u
e
,
a
n
d
th
e
se
lec
ti
o
n
o
f
t
h
e
c
o
n
tr
o
l
ler
is
c
ru
c
ial
in
m
a
in
tain
in
g
t
h
e
re
li
a
b
le,
e
ffe
c
ti
v
e
,
a
n
d
ste
a
d
y
f
u
n
c
ti
o
n
in
g
o
f
t
h
e
p
o
we
r
sy
ste
m
.
T
h
e
p
re
se
n
t
stu
d
y
d
e
m
o
n
stra
tes
fre
q
u
e
n
c
y
c
o
n
tro
l
in
islan
d
e
d
m
icro
g
ri
d
with
d
isr
u
p
ti
o
n
s
in
lo
a
d
d
e
m
a
n
d
u
sin
g
t
h
e
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tr
o
l
b
y
e
fficie
n
tl
y
m
a
n
a
g
in
g
th
e
e
n
e
rg
y
st
o
ra
g
e
with
in
te
g
ra
ti
o
n
o
f
larg
e
-
sc
a
le
re
n
e
wa
b
le
e
n
e
rg
y
so
u
rc
e
s.
Th
e
e
ffe
c
ti
v
e
n
e
ss
a
n
d
s
u
p
e
rio
r
it
y
o
f
th
e
p
ro
p
o
se
d
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tr
o
ll
e
r
(M
P
C)
is
p
re
se
n
ted
b
y
c
o
m
p
a
rin
g
it
s
p
e
rf
o
rm
a
n
c
e
with
p
r
o
p
o
rti
o
n
a
l
in
te
g
ra
l
c
o
n
tro
ll
e
r
a
n
d
p
r
o
p
o
rti
o
n
a
l
in
t
e
g
ra
l
tu
n
e
d
wit
h
a
d
a
p
ti
v
e
n
e
u
ro
fu
z
z
y
in
fe
re
n
c
e
sy
ste
m
(AN
F
IS
)
th
r
o
u
g
h
sim
u
lati
o
n
s i
n
M
AT
LAB
e
n
v
ir
o
n
m
e
n
t.
K
ey
w
o
r
d
s
:
Ad
ap
tiv
e
n
eu
r
o
f
u
zz
y
in
f
er
e
n
ce
s
y
s
tem
Dis
tr
ib
u
ted
en
er
g
y
s
o
u
r
ce
s
L
o
ad
f
r
e
q
u
en
c
y
co
n
tr
o
l
Mic
r
o
g
r
id
Mo
d
el
p
r
ed
ictiv
e
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
:
Sar
b
jeet
Kau
r
E
lectr
ical
E
n
g
in
ee
r
in
g
Dep
ar
t
m
en
t,
C
h
an
d
ig
a
r
h
Un
iv
e
r
s
ity
Gh
ar
au
n
,
Pu
n
jab
-
1
4
0
4
1
3
,
I
n
d
i
a
E
m
ail:
s
ar
b
jeet.
ee
@
cu
m
ail.
in
1.
I
NT
RO
D
UCT
I
O
N
A
m
icr
o
g
r
id
is
a
s
m
all
en
er
g
y
zo
n
e
th
at
ca
n
f
u
n
ctio
n
i
n
b
o
th
is
lan
d
e
d
a
n
d
g
r
id
-
c
o
n
n
e
cted
m
o
d
e
wh
ile
in
teg
r
atin
g
v
ar
io
u
s
d
is
tr
ib
u
ted
en
e
r
g
y
r
eso
u
r
ce
s
[
1
]
.
Dis
tr
ib
u
ted
r
eso
u
r
ce
s
in
clu
d
e
co
n
tr
o
llab
le
s
o
u
r
ce
s
s
u
ch
as
d
iesel
g
en
er
ato
r
s
,
f
u
e
l
ce
lls
,
an
d
b
atter
ies,
as
well
as
r
en
ewa
b
le
s
o
u
r
ce
s
lik
e
s
o
lar
an
d
win
d
e
n
er
g
y
s
y
s
tem
s
.
T
h
e
m
icr
o
g
r
i
d
en
co
u
n
ter
s
f
r
eq
u
e
n
cy
a
n
d
p
o
wer
f
lu
ctu
atio
n
s
as
a
r
esu
lt
o
f
t
h
e
v
ar
iab
le
an
d
u
n
ce
r
tain
n
atu
r
e
o
f
r
e
n
ewa
b
le
s
o
u
r
ce
s
,
as
well
a
s
g
en
er
atio
n
an
d
lo
ad
d
em
an
d
m
is
m
atch
[
2
]
.
I
f
a
m
icr
o
g
r
i
d
is
co
n
n
ec
ted
to
t
h
e
g
r
id
,
th
e
a
s
s
o
ciate
d
elec
tr
ical
p
o
wer
s
y
s
tem
ca
n
p
r
o
v
id
e
lo
ad
s
.
Oth
er
wis
e,
d
is
tr
ib
u
ted
g
en
er
atio
n
m
u
s
t
o
p
er
ate
in
an
is
o
lated
m
o
d
e
wh
ile
d
ea
lin
g
with
f
lu
ctu
atio
n
s
in
lo
ad
a
n
d
v
ar
iab
le
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
n
ec
ess
itatin
g
s
tr
ict
m
icr
o
g
r
id
m
an
ag
em
en
t
to
en
s
u
r
e
f
r
e
q
u
en
c
y
an
d
v
o
ltag
e
s
tab
ilit
y
an
d
m
ain
tain
h
ig
h
-
q
u
ality
p
o
wer
d
eliv
er
y
to
clien
ts
.
Ho
wev
er
,
d
ev
elo
p
i
n
g
a
d
y
n
am
ic
p
o
we
r
b
alan
ce
b
etwe
en
g
en
er
atio
n
an
d
d
em
an
d
is
ch
allen
g
in
g
,
as
elec
tr
ical
p
o
wer
h
as
b
ec
o
m
e
a
d
er
eg
u
lated
e
n
tity
.
C
o
n
s
eq
u
en
tly
,
th
e
an
aly
s
is
an
d
d
ev
elo
p
m
en
t
o
f
im
p
r
o
v
e
d
f
r
eq
u
en
cy
c
o
n
tr
o
ller
u
n
its
h
av
e
b
ec
o
m
e
cr
u
cial
in
ad
d
r
ess
in
g
th
e
is
s
u
e
o
f
p
o
wer
g
e
n
er
atio
n
a
n
d
co
n
s
u
m
p
tio
n
m
is
m
atch
es,
wh
ich
ca
n
lead
to
f
r
e
q
u
en
c
y
f
lu
ctu
atio
n
s
a
n
d
n
eg
ativ
ely
im
p
ac
t t
h
e
ef
f
icien
cy
an
d
r
eliab
ilit
y
o
f
m
ic
r
o
g
r
i
d
p
o
wer
f
lo
w
[
3
]
.
Fro
m
th
e
p
er
s
p
ec
tiv
e
o
f
p
r
im
ar
y
r
e
g
u
latio
n
,
f
r
e
q
u
en
c
y
d
r
o
o
p
c
h
ar
ac
ter
is
tics
ar
e
co
m
m
o
n
l
y
em
p
lo
y
ed
to
m
an
a
g
e
s
y
s
tem
f
r
eq
u
e
n
cy
[
4
]
-
[
8
]
.
Ho
wev
er
,
in
co
n
tr
ast
to
a
v
ast
in
ter
co
n
n
ec
ted
s
y
s
tem
,
th
e
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.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
55
1
-
559
552
s
y
s
tem
in
er
tia
o
f
an
is
o
lated
m
icr
o
g
r
id
is
s
ig
n
if
ican
tly
lo
w
er
.
C
o
n
s
eq
u
en
tly
,
b
ec
a
u
s
e
o
f
g
r
o
win
g
p
en
etr
atio
n
o
f
r
en
ewa
b
le
en
e
r
g
y
r
eso
u
r
c
es,
p
o
wer
g
en
er
atio
n
m
ay
e
x
p
er
ien
ce
r
a
p
id
f
lu
ctu
atio
n
s
.
Ho
wev
er
,
en
er
g
y
s
to
r
ag
e
s
y
s
tem
s
ar
e
a
lik
el
y
s
o
lu
tio
n
th
at
ca
n
co
u
n
ter
ac
t
th
e
ad
v
er
s
e
e
f
f
ec
ts
o
f
r
ed
u
ce
d
i
n
er
tia.
T
h
e
r
eser
v
e
p
o
wer
in
th
e
en
e
r
g
y
s
to
r
ag
e
d
ev
ices
h
elp
s
to
in
cr
ea
s
e
t
h
e
m
icr
o
g
r
id
in
er
tia
lead
in
g
to
g
r
e
ater
lo
ad
f
r
eq
u
e
n
cy
s
tab
ilit
y
[
9
]
-
[
1
2
]
.
T
h
u
s
,
to
r
e
aso
n
ab
ly
co
n
tr
o
l
g
r
ea
ter
s
u
r
g
e
cu
r
r
en
ts
,
a
h
ig
h
-
p
o
wer
d
en
s
ity
s
to
r
ag
e
d
ev
ice
s
u
ch
as
f
ly
wh
ee
l
en
er
g
y
s
to
r
ag
e
s
u
p
er
ca
p
ac
ito
r
en
er
g
y
s
to
r
ag
e
ca
n
b
e
u
s
ed
with
b
att
er
y
en
e
r
g
y
s
to
r
ag
e
d
ev
ices.
Mo
r
eo
v
e
r
,
th
e
elec
tr
i
ca
l
v
eh
icle
wh
en
in
teg
r
ates
as
v
eh
icle
-
to
-
g
r
id
(
V2
G
)
,
b
alan
c
es
th
e
en
er
g
y
f
lo
ws
[
1
3
]
an
d
p
r
o
v
id
es
f
r
eq
u
en
cy
s
u
p
p
o
r
t
to
th
e
g
r
id
[
1
4
]
.
I
n
th
e
s
e
ci
r
cu
m
s
tan
ce
s
,
th
e
s
tan
d
ar
d
co
n
tr
o
l
tech
n
iq
u
es
m
ay
n
o
t
b
e
s
u
f
f
icien
tly
co
p
e
as
with
th
e
q
u
ick
s
win
g
s
in
o
u
tp
u
t
p
o
wer
f
r
o
m
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
r
esu
ltin
g
in
s
ig
n
if
ican
t
an
d
f
r
eq
u
e
n
t
d
ev
iatio
n
s
f
r
o
m
th
e
n
o
m
in
al
o
p
er
atin
g
f
r
eq
u
e
n
c
y
p
o
in
t.
Stan
d
a
r
d
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
(
PI
)
c
o
n
tr
o
ller
s
ar
e
s
im
p
le,
u
s
er
-
f
r
ien
d
ly
,
a
n
d
co
s
t
-
ef
f
ec
tiv
e.
No
n
e
th
eless
,
th
eir
m
ai
n
d
r
awb
ac
k
s
a
r
e
p
o
o
r
d
y
n
am
ic
r
esp
o
n
s
e,
lim
ited
ac
cu
r
ac
y
,
a
n
d
ex
ten
d
e
d
s
ettlin
g
tim
e.
T
h
er
ef
o
r
e,
it
is
cr
u
cial
to
in
v
esti
g
ate
an
d
d
e
v
elo
p
th
e
im
p
r
o
v
e
d
f
r
e
q
u
en
c
y
co
n
t
r
o
ller
u
n
its
in
s
u
ch
s
itu
atio
n
s
.
T
h
e
ch
o
ice
o
f
a
n
ef
f
ec
tiv
e
co
n
tr
o
ller
is
a
cr
itical
f
ac
to
r
in
an
aly
zin
g
th
e
lo
ad
f
r
eq
u
en
cy
co
n
tr
o
l
o
f
lar
g
e
p
o
wer
s
y
s
tem
n
etwo
r
k
s
,
esp
ec
ially
with
th
e
in
te
g
r
atio
n
o
f
r
en
ewa
b
le
an
d
en
er
g
y
s
to
r
ag
e
d
ev
ices.
I
n
tellig
en
t
co
n
tr
o
ller
s
u
tili
zin
g
o
p
tim
izatio
n
tech
n
i
q
u
es
s
u
ch
as
m
etah
eu
r
is
tic
ap
p
r
o
ac
h
es
lik
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PSO
)
[
1
5
]
,
[
1
6
]
,
teac
h
in
g
lear
n
in
g
[
1
7
]
,
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
[
1
8
]
-
[
2
0
]
m
etah
eu
r
is
tic
ap
p
r
o
ac
h
es
lik
e
g
r
ass
h
o
p
p
er
o
p
tim
izatio
n
wer
e
p
r
o
p
o
s
ed
f
o
r
f
r
eq
u
en
cy
co
n
tr
o
l
[
2
1
]
.
T
h
e
f
r
eq
u
en
c
y
d
e
v
iatio
n
o
f
a
s
tan
d
alo
n
e
m
icr
o
g
r
id
was
m
itig
ated
with
a
d
ee
p
lea
r
n
in
g
-
b
ased
m
eth
o
d
em
p
lo
y
i
n
g
th
e
r
m
o
s
tatically
co
n
tr
o
lled
lo
a
d
m
an
a
g
em
en
t
[
2
2
]
.
I
t h
as b
ee
n
s
u
g
g
ested
th
at
lin
ea
r
q
u
ad
r
atic
r
e
g
u
lato
r
s
ar
e
th
e
o
p
tim
al
co
n
tr
o
ller
s
[
2
3
]
,
[
2
4
]
.
Ho
wev
er
,
th
eir
im
p
lem
en
tatio
n
r
eq
u
ir
es
k
n
o
wled
g
e
o
f
all
s
y
s
tem
s
tates
th
r
o
u
g
h
o
u
t
o
p
er
atio
n
,
wh
ic
h
ca
n
b
e
ch
allen
g
i
n
g
in
co
m
p
lex
p
o
wer
n
etwo
r
k
s
d
u
e
to
th
e
lar
g
e
n
u
m
b
e
r
o
f
v
ar
i
ab
les
th
at
in
f
lu
en
ce
p
er
f
o
r
m
an
ce
.
Ob
s
er
v
er
-
b
ased
co
n
tr
o
l
is
b
ec
o
m
in
g
m
o
r
e
wi
d
ely
ac
k
n
o
wled
g
e
d
as
a
r
em
ed
y
f
o
r
th
is
p
r
o
b
lem
.
An
o
b
s
er
v
er
esti
m
ates
th
e
s
y
s
tem
'
s
v
ar
iab
les,
an
d
a
well
-
lik
ed
s
tate
esti
m
atio
n
alg
o
r
ith
m
,
lik
e
th
e
Kalm
a
n
f
ilter
,
ca
n
b
e
u
s
ed
to
esti
m
ate
th
ese
v
ar
iab
les
ef
f
icien
tly
[
2
5
]
.
Mo
d
el
p
r
ed
ictiv
e
c
o
n
tr
o
l
(
MPC
)
is
a
tech
n
iq
u
e
o
f
o
p
tim
al
co
n
tr
o
l
th
at
s
ee
k
s
to
m
in
im
ize
a
n
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
a
co
n
s
tr
ain
ed
d
y
n
a
m
ical
s
y
s
tem
o
v
er
a
f
in
ite,
r
e
ce
d
in
g
h
o
r
izo
n
.
I
t
is
r
ap
id
ly
b
ec
o
m
i
n
g
a
v
iab
le
alt
er
n
ativ
e
f
o
r
m
an
ag
i
n
g
v
o
ltag
e
r
eg
u
latio
n
,
f
r
eq
u
en
cy
co
n
t
r
o
l,
p
o
wer
f
l
o
w,
an
d
o
p
tim
izin
g
ec
o
n
o
m
ic
o
p
er
ati
o
n
s
.
T
h
e
im
p
ac
t
o
f
p
r
ed
ictiv
e
co
n
tr
o
l
f
o
r
two
ar
ea
s
y
s
te
m
f
o
r
a
s
tan
d
al
o
n
e
m
icr
o
g
r
id
is
p
r
esen
ted
[
2
6
]
.
MPC
is
th
e
in
tellig
en
t
co
n
tr
o
ller
s
u
itab
le
f
o
r
th
e
r
ap
id
r
esp
o
n
s
e,
r
o
b
u
s
tn
ess
ag
ain
s
t lo
ad
v
ar
iatio
n
s
,
an
d
u
n
ce
r
tain
ty
in
p
a
r
am
eter
s
[
2
7
]
-
[
3
0
]
.
T
h
e
p
r
im
ar
y
aim
o
f
th
is
s
tu
d
y
is
to
ex
am
in
e
th
e
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
o
f
a
m
icr
o
g
r
i
d
wh
en
s
u
b
jecte
d
to
s
u
d
d
en
l
o
ad
p
e
r
tu
r
b
atio
n
s
.
T
h
e
k
ey
c
o
n
tr
ib
u
tio
n
o
f
th
is
s
tu
d
y
lies
in
:
-
An
aly
s
in
g
th
e
im
p
ac
t
o
f
en
er
g
y
s
to
r
ag
e
d
ev
ices
o
n
f
r
eq
u
e
n
cy
r
eg
u
latio
n
s
u
p
p
o
r
t
in
a
m
icr
o
g
r
id
,
tak
in
g
in
to
ac
co
u
n
t th
e
s
to
ch
asti
c
b
eh
av
io
u
r
o
f
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
.
-
Dev
elo
p
in
g
a
f
r
eq
u
e
n
cy
c
o
n
t
r
o
l
s
y
s
tem
f
o
r
d
am
p
in
g
f
r
eq
u
en
cy
o
s
cillatio
n
s
in
lo
w
v
o
l
tag
e
m
icr
o
g
r
i
d
s
u
s
in
g
a
MPC
tech
n
iq
u
e,
wh
ile
s
im
u
ltan
eo
u
s
ly
esti
m
atin
g
th
e
s
tates
o
f
p
ar
am
eter
s
with
a
Kalm
an
f
ilter
ap
p
r
o
ac
h
.
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
h
a
v
e
b
ee
n
v
alid
ated
ag
ain
s
t tr
ad
itio
n
al
co
n
tr
o
ller
s
.
T
h
e
r
em
ai
n
in
g
o
f
th
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
s
ec
tio
n
1
r
e
p
r
esen
t
i
n
tr
o
d
u
ctio
n
,
s
ec
tio
n
2
p
r
esen
ts
m
o
d
ellin
g
o
f
m
icr
o
g
r
id
,
s
ec
tio
n
3
r
e
p
r
esen
ts
th
e
c
o
n
tr
o
ller
d
esig
n
,
s
ec
tio
n
4
s
h
o
ws
th
e
r
esu
lts
an
d
f
u
r
th
er
lead
s
to
d
is
cu
s
s
io
n
,
an
d
f
i
n
ally
th
e
co
n
clu
s
io
n
.
2.
M
O
DE
L
DE
SCR
I
P
T
I
O
N
T
h
e
test
s
y
s
tem
o
f
th
e
m
icr
o
g
r
id
in
th
e
is
lan
d
ed
m
o
d
e
co
n
s
id
er
ed
in
th
is
s
tu
d
y
is
p
r
esen
ted
in
Fig
u
r
e
1.
Nu
m
er
o
u
s
co
m
p
o
n
e
n
ts
o
f
m
icr
o
g
r
id
m
o
d
el
s
u
ch
a
s
d
iesel
en
g
in
e
,
b
atter
y
e
n
er
g
y
s
to
r
ag
e,
f
l
y
wh
ee
l
en
er
g
y
s
to
r
ag
e
s
y
s
tem
,
s
o
lar
,
an
d
win
d
tu
r
b
i
n
es
ar
e
co
n
s
id
er
ed
f
o
r
th
is
s
tu
d
y
[
3
1
].
T
h
e
in
cr
em
en
tal
p
o
wer
f
r
eq
u
e
n
cy
d
y
n
am
ics
o
f
th
e
m
i
cr
o
g
r
id
wh
ic
h
s
er
v
es
an
ar
ea
with
ch
an
g
e
in
lo
ad
d
em
an
d
r
ep
r
esen
ted
as
∆PL
.
T
h
e
s
u
r
p
l
u
s
p
o
wer
∆Pm
-
∆PL
is
ac
co
u
n
ted
f
o
r
,
b
y
in
c
r
ea
s
in
g
th
e
r
ate
o
f
r
is
e
o
f
k
in
etic
en
er
g
y
a
n
d
in
cr
ea
s
e
d
lo
ad
co
n
s
u
m
p
tio
n
wh
ic
h
is
ex
p
r
ess
ed
b
y
(
1
)
r
esp
ec
tiv
ely
.
∆
−
∆
=
2
∆
+
∆
(
1
)
W
h
er
e
∆Pm
is
th
e
ch
an
g
e
in
m
icr
o
g
r
id
p
o
wer
wh
ich
co
n
s
is
t
o
f
s
u
m
o
f
th
e
p
o
wer
s
o
f
all
th
e
d
is
tr
ib
u
ted
en
er
g
y
s
o
u
r
ce
s
an
d
s
to
r
a
g
e
d
e
v
ice
co
n
n
ec
ted
to
s
y
s
tem
;
D
is
th
e
d
am
p
in
g
c
o
n
s
tan
t
wh
ich
r
ep
r
esen
ts
th
e
r
atio
o
f
p
er
ce
n
ta
g
e
ch
an
g
e
in
th
e
l
o
ad
to
th
at
o
f
p
er
ce
n
tag
e
c
h
a
n
g
e
in
th
e
f
r
e
q
u
en
c
y
in
p
er
u
n
it
MW/Hz
;
an
d
H
r
ep
r
esen
t
th
e
i
n
er
tia
co
n
s
tan
t
o
f
th
e
r
o
tatin
g
m
ass
es.
T
h
e
v
ar
io
u
s
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
co
n
n
ec
ted
to
th
e
m
icr
o
g
r
id
ar
e
r
ep
r
esen
ted
b
y
th
eir
r
esp
ec
tiv
e
tr
an
s
f
er
f
u
n
ctio
n
[
3
2
]
,
[
3
3
]
as in
d
icate
d
in
Fig
u
r
e
2
.
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
Mo
d
el
p
r
ed
ictive
co
n
tr
o
l b
a
s
e
d
fr
eq
u
en
cy
r
eg
u
l
a
tio
n
o
f m
icr
o
g
r
id
w
ith
in
teg
r
a
tio
n
o
f
…
(
S
a
r
b
jeet
K
a
u
r
)
553
Fig
u
r
e
1
.
Mic
r
o
g
r
id
s
tr
u
ct
u
r
e
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
o
f
m
i
cr
o
g
r
id
3.
M
E
T
H
O
DS F
O
R
F
RE
Q
U
E
NCY
CO
NT
RO
L
T
h
e
p
u
r
p
o
s
e
o
f
l
o
ad
f
r
eq
u
en
c
y
co
n
t
r
o
l
is
to
m
ain
tain
t
h
e
f
r
eq
u
en
cy
with
in
ac
ce
p
tab
le
li
m
its
wh
ile
s
u
b
jectin
g
d
is
tu
r
b
an
ce
in
l
o
ad
.
T
h
e
co
n
v
en
tio
n
al
tech
n
iq
u
es
lik
e
d
r
o
o
p
co
n
tr
o
l,
tie
lin
e
co
n
tr
o
l
is
in
ef
f
ec
tiv
e.
An
ef
f
icien
t
co
n
tr
o
ller
is
cr
u
c
ial
f
o
r
s
u
cc
ess
f
u
l
f
r
eq
u
e
n
cy
r
eg
u
latio
n
as
its
p
r
im
ar
y
f
u
n
ct
io
n
is
to
r
ed
u
ce
th
e
er
r
o
r
s
ig
n
al
s
o
th
at
th
e
f
r
eq
u
e
n
cy
d
ev
iatio
n
b
e
co
m
es
clo
s
e
to
ze
r
o
an
d
th
e
f
r
e
q
u
en
c
y
o
f
th
e
s
y
s
tem
r
etu
r
n
s
clo
s
e
to
th
e
n
o
m
in
al
v
alu
e
in
t
h
e
s
p
ec
if
ied
tim
e
wh
ich
is
p
o
s
s
ib
le
with
th
e
in
tellig
en
t c
o
n
tr
o
ller
s
s
u
ch
as M
P
C
an
d
p
r
o
p
o
r
tio
n
al
in
teg
r
al
tu
n
e
d
with
ad
ap
tiv
e
n
eu
r
o
f
u
zz
y
in
f
er
en
ce
s
y
s
tem
(
ANFI
S
)
.
3
.
1
.
P
I
co
ntr
o
ller
T
h
e
PI
co
n
tr
o
ller
is
a
p
r
o
p
o
r
t
io
n
al
in
teg
r
als
co
n
tr
o
l
in
wh
ich
th
e
co
n
tr
o
l
s
ig
n
al
is
p
r
o
p
o
r
tio
n
al
to
b
o
th
th
e
er
r
o
r
s
ig
n
al
an
d
th
e
i
n
teg
r
al
.
T
h
e
m
at
h
em
atica
l
r
ep
r
esen
tatio
n
f
o
r
th
e
p
r
o
p
o
r
tio
n
a
l
-
in
teg
r
al
co
n
tr
o
ller
is
as
(
2
)
.
(
)
=
+
∫
(
)
(
2
)
T
h
e
r
esp
o
n
s
e
o
f
th
e
PI
is
b
etter
as
co
m
p
ar
e
d
to
t
h
e
p
r
o
p
o
r
tio
n
al
an
d
in
teg
r
al
c
o
n
tr
o
l
u
s
ed
s
ep
ar
ately
.
Alth
o
u
g
h
its
r
esp
o
n
s
e
is
s
lu
g
g
is
h
b
u
t
it
ca
n
b
e
en
h
a
n
ce
d
if
i
t
is
tu
n
ed
with
n
eu
r
al
n
etwo
r
k
s
,
f
u
zz
y
n
etwo
r
k
s
,
an
d
ev
en
lin
ea
r
izin
g
th
e
m
o
d
el
b
ased
o
n
th
e
tr
ial
an
d
er
r
o
r
m
eth
o
d
,
Z
eig
ler
-
Nich
o
las
m
eth
o
d
,
an
d
p
ar
ticle
s
war
m
-
b
ased
ap
p
r
o
ac
h
[
3
2
]
.
3
.
2
.
P
I
t
un
ed
wit
h AN
F
I
S
ANFI
S
o
f
f
er
s
th
e
ab
ilit
y
to
co
m
b
in
e
th
e
m
er
its
o
f
n
eu
r
al
n
et
wo
r
k
an
d
f
u
zz
y
in
f
e
r
en
ce
s
y
s
tem
s
in
to
a
s
in
g
le
f
r
am
ewo
r
k
.
Ad
a
p
tiv
e
n
eu
r
o
f
u
zz
y
in
f
er
en
ce
s
y
s
tem
is
b
ased
o
n
th
e
s
et
o
f
f
u
zz
y
if
an
d
th
en
r
u
le
th
at
m
o
d
if
ies
its
s
tr
u
ctu
r
e
in
r
esp
o
n
s
e
to
in
f
o
r
m
atio
n
o
r
d
ata
p
r
e
s
en
ted
d
u
r
in
g
th
e
lear
n
in
g
p
h
a
s
e,
wh
eth
er
in
ter
n
al
o
r
e
x
ter
n
al.
T
h
e
ANFI
S
was
f
ed
with
t
h
e
d
esire
d
o
r
tar
g
et
r
esp
o
n
s
e.
T
h
e
d
is
cr
ep
a
n
cy
b
et
wee
n
th
e
p
r
ef
e
r
r
ed
r
esp
o
n
s
e
an
d
t
h
e
s
y
s
tem
o
u
t
p
u
t
r
esu
lts
in
an
er
r
o
r
.
T
h
e
s
y
s
tem
is
th
en
u
p
d
ated
with
th
is
er
r
o
r
,
a
n
d
th
e
p
ar
am
eter
s
ar
e
lo
g
ically
c
h
an
g
ed
u
n
til
t
h
e
s
y
s
tem
p
er
f
o
r
m
a
n
ce
is
d
ee
m
ed
ac
ce
p
tab
le,
th
is
p
r
o
ce
s
s
is
r
ep
ea
ted
.
T
h
e
ANFI
S c
an
b
e
tr
ain
e
d
u
s
in
g
d
if
f
er
en
t o
p
tim
izatio
n
m
eth
o
d
s
[
3
3
]
-
[
3
5
]
.
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.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
55
1
-
559
554
3
.
3
.
P
r
o
po
s
ed
m
o
del pre
dict
iv
e
co
ntr
o
ller
T
h
e
m
o
d
el
p
r
ed
ictiv
e
c
o
n
tr
o
ll
er
is
a
m
u
ltiv
ar
iab
le
c
o
n
tr
o
l
s
y
s
tem
th
at
s
im
u
ltan
eo
u
s
ly
r
eg
u
lates
th
e
o
u
tp
u
t
b
y
co
n
s
id
er
i
n
g
all
in
ter
ac
tio
n
s
b
etwe
en
s
y
s
tem
v
ar
ia
b
les
wh
ile
s
im
u
ltan
eo
u
s
ly
g
r
a
p
p
lin
g
with
s
y
s
tem
co
n
s
tr
ain
ts
.
T
h
is
ty
p
e
o
f
co
n
tr
o
ller
is
p
ar
ticu
lar
ly
u
s
ef
u
l
in
s
itu
atio
n
s
in
wh
ich
a
h
ig
h
lev
el
o
f
p
r
ec
is
io
n
a
n
d
ad
ap
tab
ilit
y
is
r
eq
u
ir
ed
.
B
y
co
n
s
id
er
in
g
th
e
r
elatio
n
s
h
ip
s
b
et
wee
n
all
r
elev
a
n
t
v
ar
ia
b
les,
th
e
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
ller
is
ab
le
to
m
ak
e
m
o
r
e
in
f
o
r
m
ed
d
ec
is
io
n
s
an
d
ac
h
iev
e
m
o
r
e
ac
cu
r
ate
r
esu
lts
wh
ich
ar
e
g
en
er
ally
d
if
f
icu
lt
to
co
n
tr
o
l
u
s
in
g
co
n
v
en
tio
n
al
tech
n
iq
u
es.
T
h
e
r
e
a
r
e
s
ev
er
al
v
ar
iatio
n
s
o
f
th
e
M
PC
tech
n
iq
u
e
,
with
th
e
m
ain
d
if
f
er
e
n
ce
b
ein
g
h
o
w
th
e
o
b
jectiv
e
f
u
n
ctio
n
ca
n
b
e
f
o
r
m
u
lated
o
r
h
o
w
s
y
s
tem
m
o
d
el
is
o
b
tain
ed
.
Nev
er
th
eless
,
all
th
ese
s
tr
ate
g
ies
u
tili
ze
s
y
s
tem
m
o
d
el
f
o
r
g
en
er
atin
g
a
co
n
tr
o
l
s
ig
n
al
to
m
in
im
ize
th
e
o
b
jectiv
e
f
u
n
ctio
n
[
3
6
]
,
[
3
7
]
.
T
h
e
s
tr
u
ctu
r
e
o
f
m
o
d
el
p
r
e
d
ictiv
e
co
n
tr
o
l is sh
o
wn
in
Fig
u
r
e
3
.
Fig
u
r
e
3
.
Mo
d
el
p
r
e
d
ictiv
e
co
n
tr
o
l
T
h
e
s
tates
o
f
th
e
s
y
s
tem
h
ad
b
ee
n
esti
m
ated
b
ased
o
n
th
e
o
b
s
er
v
er
-
b
ased
c
o
n
tr
o
l
a
p
p
r
o
ac
h
Kalm
an
f
ilter
.
T
h
e
Kalm
an
f
ilter
is
an
iter
ativ
e
p
r
o
ce
s
s
f
o
r
esti
m
atin
g
th
e
s
tate
o
f
th
e
s
y
s
tem
wh
en
in
p
u
ts
ar
e
u
n
ce
r
tain
an
d
its
q
u
ick
ly
esti
m
ates
th
e
tr
u
e
v
alu
es.
I
t
is
a
r
ec
u
r
s
iv
e
m
eth
o
d
th
at
u
s
es
s
y
s
tem
p
r
io
r
s
tate
m
ea
s
u
r
em
en
ts
an
d
co
n
tr
o
l
in
p
u
ts
to
esti
m
ate
th
e
p
r
esen
t
s
y
s
tem
s
tate
[
3
8
]
.
T
h
e
s
tate
s
p
ac
e
r
ep
r
esen
tatio
n
an
d
o
b
jectiv
e
f
u
n
ctio
n
wh
ich
is
co
m
b
in
atio
n
o
f
th
e
lin
ea
r
q
u
ad
r
atic
an
d
th
e
Kalm
a
n
f
ilter
in
g
ap
p
r
o
ac
h
is
r
ep
r
esen
ted
b
y
(
3
)
-
(
6
)
.
̇
=
(
)
+
(
)
+
(
3
)
W
h
er
e
w
r
ep
r
esen
ts
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
ch
an
g
e
in
p
o
wer
d
u
e
to
en
er
g
y
s
to
r
ag
e
d
ev
ices
an
d
lo
ad
d
em
an
d
a
n
d
u
(
t)
r
ep
r
esen
ts
th
e
in
p
u
t
co
n
tr
o
l
s
ig
n
al.
A
is
s
tate
m
atr
ix
,
C
is
co
n
tr
o
l
o
u
t
p
u
t v
ec
to
r
,
an
d
B
an
d
D
ar
e
co
ef
f
icien
t
m
atr
ix
.
(
)
=
∆
=
(
)
(
4
)
(
1
,
2
,
)
=
∑
[
2
=
1
∆
(
+
,
)
]
2
+
1
∑
∆
1
(
+
−
1
)
2
+
2
∑
∆
2
(
+
−
1
)
2
=
0
=
0
(
5
)
1
an
d
2
ar
e
th
e
weig
h
in
g
f
ac
to
r
;
N1
an
d
N2
ar
e
th
e
m
in
i
m
u
m
an
d
m
a
x
im
u
m
co
s
tin
g
h
o
r
izo
n
;
Nc
r
ep
r
esen
ts
th
e
co
n
tr
o
l
h
o
r
izo
n
;
∆
1
an
d
∆
2
ar
e
t
h
e
c
o
n
tr
o
l
s
ig
n
a
ls
to
th
e
DG
an
d
f
u
el
ce
ll
,
r
e
s
p
ec
tiv
ely
;
an
d
w(
t+j)
r
ep
r
esen
ts
th
e
r
ef
er
en
ce
o
v
er
th
e
f
u
tu
r
e
h
o
r
izo
n
N
.
C
o
n
tr
o
l
s
ig
n
al
co
n
s
tr
ain
ts
f
o
r
th
e
o
u
t
p
u
t
ar
e
ad
d
e
d
to
t
h
e
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
ese
co
n
s
tr
ain
ts
ar
e
r
ep
r
esen
ted
b
y
(
7
)
to
(
9
).
≤
(
+
)
≤
(
6
)
≤
(
+
)
≤
(
7
)
W
h
er
e
:
(
)
=
(
−
1
)
+
∆
(
)
(
+
1
)
=
(
−
1
)
+
∆
(
)
+
∆
(
+
1
)
(8
)
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
Mo
d
el
p
r
ed
ictive
co
n
tr
o
l b
a
s
e
d
fr
eq
u
en
cy
r
eg
u
l
a
tio
n
o
f m
icr
o
g
r
id
w
ith
in
teg
r
a
tio
n
o
f
…
(
S
a
r
b
jeet
K
a
u
r
)
555
So
lu
tio
n
o
f
th
e
o
b
jectiv
e
f
u
n
ctio
n
(
5
)
g
i
v
es
th
e
o
p
tim
al
r
esu
lt
o
v
er
th
e
h
o
r
iz
o
n
N
wh
i
le
s
u
b
jecte
d
to
th
e
co
n
s
tr
ain
ts
s
p
ec
if
ied
b
y
(
6
)
a
n
d
(
7
)
.
T
h
e
p
e
r
f
o
r
m
an
ce
i
n
d
e
x
o
f
th
e
f
r
eq
u
e
n
cy
c
h
an
g
es
w
h
ich
is
in
teg
r
al
tim
e
s
q
u
ar
e
o
f
t
h
e
er
r
o
r
in
t
h
e
f
r
e
q
u
en
cy
s
ig
n
al
ca
n
b
e
e
x
p
r
ess
ed
b
y
(
9
)
,
wh
ic
h
d
eter
m
in
es
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
co
n
tr
o
ller
.
T
h
e
d
etailed
s
tep
b
y
s
tep
alg
o
r
ith
m
o
f
MPC
is
d
ep
icted
th
r
o
u
g
h
Fig
u
r
e
4
.
=
∫
|
∆
|
2
0
(
9
)
Fig
u
r
e
4
.
Flo
wch
ar
t
o
f
MPC
co
n
tr
o
ller
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
m
icr
o
g
r
id
d
ep
icted
i
n
Fig
u
r
e
1
was
d
ev
elo
p
ed
u
s
in
g
MA
T
L
AB
Simu
lin
k
2
0
2
2
.
T
h
e
n
atu
r
e
o
f
th
e
win
d
an
d
s
o
lar
en
er
g
y
p
r
o
f
iles
was
as
s
u
m
ed
to
b
e
s
to
ch
asti
c,
wh
er
ea
s
th
e
v
ar
iatio
n
in
lo
ad
d
em
an
d
was
r
eg
ar
d
e
d
as
a
s
tep
ch
an
g
e
wit
h
an
am
p
litu
d
e
o
f
1
p
.
u
.
T
h
e
p
ar
am
eter
s
o
f
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
f
o
r
th
e
m
icr
o
g
r
id
d
esig
n
ar
e
d
e
p
icted
in
T
ab
le
1
.
Fig
u
r
e
5
illu
s
tr
ates
th
e
PV
o
u
tp
u
t,
win
d
p
o
wer
f
lu
ctu
atio
n
s
,
an
d
lo
ad
d
em
a
n
d
d
is
r
u
p
tio
n
.
T
h
e
f
r
eq
u
en
cy
r
esp
o
n
s
e
o
f
t
h
e
m
icr
o
g
r
id
was
an
aly
ze
d
with
an
d
with
o
u
t
en
e
r
g
y
s
to
r
ag
e
d
ev
ices
eq
u
ip
p
e
d
with
PI
co
n
tr
o
ller
s
s
h
o
wn
in
F
ig
u
r
e
6
(
a)
.
T
h
e
r
esp
o
n
s
e
f
r
o
m
t
h
e
f
ig
u
r
e
in
d
icate
s
th
at
th
e
f
r
eq
u
en
cy
d
ev
iatio
n
o
v
er
s
h
o
o
t
an
d
u
n
d
e
r
s
h
o
o
t
ar
e
m
o
r
e
p
r
o
n
o
u
n
ce
d
wh
en
th
e
b
atter
y
an
d
f
ly
wh
ee
l
en
er
g
y
s
to
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e
ar
e
n
o
t
co
n
s
id
er
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d
,
an
d
th
e
s
y
s
tem
'
s
r
esp
o
n
s
e
is
s
lo
wer
o
win
g
to
its
lo
n
g
er
s
ettlin
g
tim
e.
H
o
wev
er
,
th
e
r
esu
lts
s
h
o
w
th
at
th
e
in
c
o
r
p
o
r
atio
n
o
f
e
n
er
g
y
s
to
r
ag
e
d
e
v
ices
in
m
icr
o
g
r
id
p
r
o
v
id
es
th
e
f
r
e
q
u
en
cy
s
u
p
p
o
r
t
a
n
d
im
p
r
o
v
es
th
e
r
esp
o
n
s
e
.
Fu
r
th
e
r
m
o
r
e,
Fig
u
r
e
6
(
b
)
p
r
esen
ts
a
co
m
p
ar
ativ
e
an
al
y
s
is
o
f
th
e
f
r
eq
u
en
cy
d
ev
iatio
n
u
s
in
g
co
n
tr
o
ller
PI,
PI
ad
ju
s
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ed
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ANFI
S,
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d
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o
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el
p
r
ed
ictiv
e
co
n
tr
o
l
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ile
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co
r
p
o
r
atin
g
th
e
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atter
y
en
er
g
y
s
to
r
a
g
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tem
(
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E
SS
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d
f
ly
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h
ee
l
en
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to
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g
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s
tem
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ich
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r
ly
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ep
icts
th
at
th
e
m
o
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el
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r
ed
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e
c
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n
tr
o
ller
o
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ts
h
in
es
th
e
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
a
n
d
PI
tu
n
e
d
-
ANFI
S.
I
n
co
m
p
ar
is
o
n
,
th
e
PI
co
n
tr
o
ller
with
o
u
t
tu
n
i
n
g
ex
h
ib
its
p
o
o
r
r
esp
o
n
s
e,
as
in
d
icate
d
b
y
its
lar
g
e
r
o
s
cillati
o
n
s
in
th
e
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
in
Fig
u
r
e
6
(
b
)
.
Fo
r
PI
co
n
tr
o
ller
,
t
h
e
tr
an
s
ien
t tim
e
is
r
elativ
ely
lar
g
er
wh
ich
s
h
o
ws its
p
o
o
r
r
esp
o
n
s
e
as it ta
k
es a
p
p
r
o
x
im
ately
7
.
2
s
ec
o
n
d
s
to
s
ettle
d
o
wn
t
o
s
tead
y
s
tate.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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2
2
5
2
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9
2
I
n
t J Ap
p
l Po
wer
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n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
55
1
-
559
556
T
ab
le
1
.
Data
f
o
r
th
e
d
is
tr
ib
u
ted
en
er
g
y
r
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u
r
ce
s
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r
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me
t
e
r
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TG
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ESS
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ESS
LO
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a
t
e
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o
w
e
r
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kW
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1
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0
30
70
1
6
0
45
45
2
1
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(
a)
(
b
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(
c)
Fig
u
r
e
5
.
Per
u
n
it v
ar
iatio
n
in
s
o
lar
,
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d
,
an
d
lo
ad
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em
an
d
:
(
a)
s
to
ch
asti
c
v
ar
iatio
n
o
f
s
o
l
ar
,
(
b
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v
ar
iatio
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in
win
d
o
u
tp
u
t
,
an
d
(
c)
s
tep
c
h
an
g
e
in
lo
ad
(
a)
(
b
)
Fig
u
r
e
6
.
Fre
q
u
en
cy
r
esp
o
n
s
e
:
(
a)
ef
f
ec
t
o
f
en
e
r
g
y
s
to
r
ag
e
an
d
(
b
)
p
er
f
o
r
m
an
ce
with
d
if
f
e
r
e
n
t
co
n
tr
o
ller
s
T
h
e
r
esp
o
n
s
e
o
f
t
h
e
PI
co
n
tr
o
l
ler
is
en
h
an
ce
d
wh
en
it
is
tr
ain
ed
u
s
in
g
ANFI
S
as
its
s
tead
y
s
tate
er
r
o
r
r
ed
u
ce
s
an
d
th
e
tr
an
s
ien
t
tim
e
r
ed
u
ce
s
t
o
ab
o
u
t
3
s
ec
o
n
d
s
.
T
h
e
p
ar
a
m
eter
s
s
elec
ted
f
o
r
t
h
e
ANFI
S
-
b
ased
PI
ar
e
lis
ted
in
T
a
b
le
2
.
T
h
e
v
ar
i
atio
n
in
t
r
ain
in
g
er
r
o
r
with
m
a
x
im
u
m
e
p
o
ch
s
a
n
d
test
in
g
o
f
o
u
tp
u
t
v
er
s
u
s
in
p
u
t
is
r
ep
r
esen
ted
in
Fig
u
r
e
7
.
Alth
o
u
g
h
PI
tu
n
ed
with
ANFI
S
r
ep
r
esen
ts
a
s
m
aller
tr
an
s
ien
t
tim
e
b
u
t
th
e
d
ev
iatio
n
in
f
r
eq
u
en
cy
is
n
o
t
co
m
p
letely
elim
in
ate
d
.
Mo
r
eo
v
er
,
tr
ain
i
n
g
with
n
e
u
r
al
n
etwo
r
k
s
h
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ce
r
tain
lim
itatio
n
s
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h
o
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r
o
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iate
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em
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er
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ip
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n
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tio
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im
en
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io
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ality
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es
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wh
ich
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n
s
o
m
etim
es
af
f
ec
t
t
h
e
p
e
r
f
o
r
m
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ce
.
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n
co
n
tr
ast,
th
e
MPC
r
esu
lts
in
alm
o
s
t
ze
r
o
f
r
eq
u
e
n
cy
d
ev
iat
io
n
an
d
th
e
o
s
cillatio
n
s
in
f
r
eq
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en
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ev
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n
r
esp
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n
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e
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u
ch
less
tim
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ettle
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n
o
m
i
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l
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ter
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p
e
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s
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g
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tr
an
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ien
t
tim
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less
th
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as
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m
p
ar
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to
o
th
er
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n
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r
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ller
s
as
d
ep
icted
in
F
ig
u
r
e
6
(
b
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,
it
d
am
p
en
s
th
e
o
s
cillatio
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s
q
u
ick
ly
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d
t
h
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r
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ettles
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o
m
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al
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u
e
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tab
le
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r
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e.
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h
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m
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ar
ativ
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e
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g
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atu
r
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ased
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m
eth
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d
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u
s
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o
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r
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o
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en
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r
atio
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p
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r
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le
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w
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e
f
f
ec
tiv
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ess
o
f
th
e
p
r
o
p
o
s
ed
wo
r
k
.
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
Mo
d
el
p
r
ed
ictive
co
n
tr
o
l b
a
s
e
d
fr
eq
u
en
cy
r
eg
u
l
a
tio
n
o
f m
icr
o
g
r
id
w
ith
in
teg
r
a
tio
n
o
f
…
(
S
a
r
b
jeet
K
a
u
r
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557
T
ab
le
2
.
ANFI
S
p
ar
am
eter
s
S
.
N
o
P
a
r
a
me
t
e
r
s
M
e
m
b
e
r
s
h
i
p
f
u
n
c
t
i
o
n
Tr
i
a
n
g
u
l
a
r
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u
z
z
y
r
u
l
e
s
10
N
o
d
e
s
44
Tr
a
i
n
i
n
g
sam
p
l
e
1
3
8
9
M
a
x
i
m
u
m
e
p
o
c
h
50
T
ab
le
3
.
C
o
m
p
a
r
is
o
n
with
th
e
r
elate
d
wo
r
k
R
e
f
e
r
e
n
c
e
C
o
n
f
i
g
u
r
a
t
i
o
n
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o
u
r
c
e
s
o
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e
n
e
r
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M
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h
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u
se
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P
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f
o
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ma
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[
3
1
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A
C
mi
c
r
o
g
r
i
d
M
i
c
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t
u
r
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i
n
e
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PSO
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u
z
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[
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sl
a
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PSO
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[
4
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t
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n
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[
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H
y
b
r
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t
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G
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P
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0
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2
Fig
u
r
e
7
.
ANFI
S r
esu
lts
:
(
a)
tr
ain
in
g
er
r
o
r
an
d
(
b
)
FIS
o
u
tp
u
t
5.
CO
NCLU
SI
O
N
I
n
th
is
s
tu
d
y
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th
e
d
y
n
a
m
ic
b
eh
av
io
r
o
f
th
e
m
icr
o
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id
was
an
aly
ze
d
with
d
if
f
e
r
en
t
ty
p
es
o
f
co
n
tr
o
ller
s
w
h
ile
s
im
u
ltan
eo
u
s
ly
co
n
s
id
er
in
g
th
e
v
ar
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le
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atu
r
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f
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en
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le
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o
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atin
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er
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lik
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atter
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g
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ly
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ee
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en
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a
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h
e
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o
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n
er
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d
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ad
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e
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o
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le
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y
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o
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r
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s
.
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o
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elec
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f
icien
t
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ller
is
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f
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ar
a
m
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im
p
o
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ce
.
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n
t
h
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r
eg
ar
d
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th
e
m
o
d
el
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r
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e
co
n
tr
o
ller
(
MPC
)
o
f
f
er
s
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o
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tim
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s
o
lu
tio
n
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an
d
t
h
e
Ka
lm
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ilter
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u
r
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ce
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th
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er
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o
r
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a
n
ce
o
f
t
h
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MPC
co
n
tr
o
ller
b
y
p
r
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m
p
tl
y
esti
m
atin
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its
s
tate
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ec
to
r
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
m
icr
o
g
r
id
with
th
e
Kalm
a
n
f
ilter
-
b
ased
MPC
o
u
tp
er
f
o
r
m
s
b
o
th
PI
an
d
PI
tr
ain
ed
with
ANFI
S.
F
UNDING
I
NF
O
R
M
A
T
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N
Au
th
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