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[
1
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,
[
2
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.
Ho
wev
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t
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I
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Vo
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1
7
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No
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1
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Ma
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20
2
6
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13
406
d
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[
3
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[
5
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.
Sev
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s
tr
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h
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p
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p
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t
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r
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6
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W
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o
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id
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ted
co
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h
as
b
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ad
o
p
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f
o
r
its
d
ec
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u
p
lin
g
o
f
ac
tiv
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an
d
r
ea
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p
o
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p
r
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v
id
in
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p
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f
o
r
m
an
ce
u
n
d
er
b
a
lan
ce
d
co
n
d
itio
n
s
.
Ho
wev
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its
p
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f
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ch
allen
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m
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7
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.
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r
g
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m
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p
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ar
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g
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in
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attr
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tio
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f
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t
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r
f
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y
to
h
an
d
le
s
y
s
tem
co
n
s
tr
ain
ts
,
an
d
ca
p
ac
ity
to
p
r
o
v
id
e
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t d
u
r
in
g
v
o
ltag
e
d
i
p
s
[
8
]
,
[
9
]
.
FOC
o
r
v
ec
to
r
co
n
tr
o
l
is
th
e
i
n
d
u
s
tr
y
s
tan
d
ar
d
f
o
r
R
S
C
co
n
tr
o
l
u
n
d
e
r
n
o
r
m
al
o
p
er
atio
n
,
p
r
o
v
id
in
g
d
ec
o
u
p
le
d
co
n
tr
o
l
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
.
Ho
wev
er
,
d
u
r
in
g
s
ev
er
e
an
d
asy
m
m
etr
i
ca
l
f
au
lts
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
FOC
ca
n
d
eter
io
r
ate
d
u
e
t
o
th
e
p
r
esen
ce
o
f
n
eg
ativ
e
s
eq
u
en
ce
co
m
p
o
n
en
t
s
an
d
m
ag
n
etic
s
atu
r
atio
n
,
n
ec
ess
itatin
g
m
o
r
e
r
o
b
u
s
t a
lg
o
r
ith
m
s
[
1
0
]
.
T
o
a
d
d
r
e
s
s
t
h
e
l
i
m
i
t
at
i
o
n
s
o
f
h
a
r
d
w
a
r
e
p
r
o
t
e
c
t
i
o
n
,
r
e
s
e
a
r
c
h
h
a
s
e
v
o
l
v
e
d
t
o
w
a
r
d
s
"
c
r
o
w
b
a
r
-
l
e
s
s
"
s
t
r
a
t
e
g
i
e
s
a
n
d
a
d
v
a
n
c
e
d
c
o
n
t
r
o
l
s
c
h
e
m
e
s
t
h
a
t
a
l
l
o
w
t
h
e
D
F
I
G
t
o
r
e
m
a
i
n
c
o
n
n
e
c
t
e
d
a
n
d
s
u
p
p
o
r
t
t
h
e
g
r
i
d
d
u
r
i
n
g
f
a
u
l
t
s
.
T
h
e
s
e
i
n
c
l
u
d
e
f
e
e
d
f
o
r
w
a
r
d
c
o
m
p
e
n
s
a
t
i
o
n
t
e
c
h
n
i
q
u
e
s
[
1
1
]
t
o
c
o
u
n
t
e
r
t
h
e
c
o
u
n
t
e
r
-
e
l
e
c
t
r
o
m
o
t
i
v
e
f
o
r
c
e
a
n
d
s
o
p
h
i
s
ti
c
a
t
e
d
al
g
o
r
i
t
h
m
s
l
i
k
e
f
u
z
z
y
l
o
g
i
c
c
o
n
t
r
o
l
a
n
d
M
PC
f
o
r
i
m
p
r
o
v
e
d
t
r
a
n
s
i
e
n
t
p
e
r
f
o
r
m
a
n
ce
[
1
2
]
,
[
1
3
]
.
C
o
n
cu
r
r
en
tly
,
t
h
e
r
o
le
o
f
PV sy
s
tem
s
h
as sh
if
ted
f
r
o
m
b
ein
g
m
er
e
p
ass
iv
e
p
o
wer
g
e
n
er
ato
r
s
to
ac
tiv
e
g
r
id
-
s
u
p
p
o
r
tin
g
ass
ets.
Mo
d
e
r
n
g
r
id
-
tied
in
v
er
ter
s
ar
e
ca
p
ab
le
o
f
p
r
o
v
id
i
n
g
an
cillar
y
s
er
v
ices,
in
clu
d
in
g
r
ea
ctiv
e
p
o
we
r
s
u
p
p
o
r
t
d
u
r
i
n
g
f
au
lts
.
MPC
h
as
em
er
g
ed
as
a
p
o
wer
f
u
l
f
r
am
ewo
r
k
f
o
r
i
n
v
er
ter
co
n
tr
o
l
d
u
e
t
o
its
f
ast
d
y
n
am
ic
r
esp
o
n
s
e,
in
t
u
itiv
e
h
an
d
lin
g
o
f
m
u
ltip
le
c
o
n
s
tr
ain
ts
(
e.
g
.
,
cu
r
r
en
t
a
n
d
v
o
ltag
e
lim
its
)
,
an
d
ab
ilit
y
to
b
e
tu
n
e
d
f
o
r
s
p
ec
if
ic
o
b
jectiv
es
lik
e
p
r
io
r
ity
-
b
ased
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
in
j
ec
tio
n
.
T
h
is
m
a
k
es
MPC
-
co
n
tr
o
lled
PV
in
v
er
ter
s
id
ea
l
f
o
r
p
r
o
v
id
in
g
d
y
n
am
ic
v
o
ltag
e
s
u
p
p
o
r
t
d
u
r
in
g
th
e
v
o
lt
ag
e
d
ip
s
th
at
af
f
ec
t
th
e
h
y
b
r
id
s
y
s
tem
[
1
4
]
,
[
1
5
]
.
T
h
is
p
ap
er
f
ills
th
is
g
ap
b
y
p
r
o
p
o
s
in
g
a
c
o
o
r
d
i
n
ated
co
n
tr
o
l
an
d
p
r
o
tectio
n
s
tr
ateg
y
f
o
r
a
h
y
b
r
id
PV
-
DFI
G
s
y
s
tem
.
T
h
e
s
p
ec
if
ic
co
n
tr
ib
u
tio
n
s
o
f
th
is
wo
r
k
a
r
e:
-
Dev
elo
p
m
en
t
o
f
a
co
o
r
d
in
at
ed
s
tr
ateg
y
:
I
n
teg
r
atin
g
an
MPC
-
co
n
tr
o
lled
PV
s
y
s
tem
with
an
FOC
-
co
n
tr
o
lled
DFI
G
to
e
n
s
u
r
e
s
tab
le
o
p
er
atio
n
d
u
r
in
g
f
au
lts
.
-
E
n
h
an
ce
d
p
r
o
tectio
n
in
teg
r
atio
n
:
u
tili
zin
g
a
cr
o
wb
ar
cir
cu
it
to
p
r
o
tect
th
e
R
S
C
wh
ile
s
im
u
ltan
eo
u
s
ly
u
s
in
g
th
e
PV sy
s
tem
to
o
f
f
s
et
t
h
e
r
esu
ltin
g
r
ea
ctiv
e
p
o
wer
c
o
n
s
u
m
p
tio
n
.
-
C
o
m
p
ar
ativ
e
a
n
aly
s
is
:
Valid
atin
g
th
e
s
u
p
er
io
r
L
VR
T
ca
p
a
b
ilit
y
o
f
th
is
h
y
b
r
id
ap
p
r
o
ac
h
co
m
p
a
r
ed
to
is
o
lated
s
y
s
tem
s
,
d
em
o
n
s
tr
atin
g
im
p
r
o
v
ed
tr
a
n
s
ien
t p
er
f
o
r
m
a
n
ce
an
d
d
y
n
a
m
ic
v
o
ltag
e
s
u
p
p
o
r
t.
T
h
e
r
em
ain
d
er
o
f
t
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
i)
S
ec
tio
n
2
d
escr
ib
es
th
e
s
y
s
tem
co
n
f
ig
u
r
atio
n
an
d
m
o
d
elin
g
;
ii)
Sectio
n
3
d
etails
th
e
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
t
h
e
PV
s
y
s
tem
an
d
DFI
G
;
iii)
Sec
tio
n
4
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
an
d
d
is
cu
s
s
io
n
; a
n
d
iv
)
Fin
ally
,
s
ec
tio
n
5
c
o
n
clu
d
es th
e
p
ap
er
.
2.
SYST
E
M
M
O
D
E
L
I
NG
2
.
1
.
P
V
a
rr
a
y
m
o
del
T
h
e
PV a
r
r
ay
is
m
o
d
eled
u
s
in
g
th
e
s
tan
d
ar
d
s
in
g
le
-
d
io
d
e
m
o
d
el,
r
ep
r
esen
ted
b
y
(
1
)
[
1
6
]
:
=
ℎ
−
(
(
+
)
/
−
1
)
−
(
ℎ
+
)
/
(
1
)
wh
er
e
ℎ
is
th
e
p
h
o
t
o
cu
r
r
e
n
t
,
is
th
e
d
io
d
e
s
atu
r
atio
n
c
u
r
r
e
n
t,
is
th
e
id
ea
lity
f
ac
to
r
(
1
-
2
)
,
is
t
h
e
th
er
m
al
v
o
ltag
e,
an
d
an
d
ℎ
ar
e
th
e
s
er
ies an
d
s
h
u
n
t r
esis
tan
ce
s
,
r
esp
ec
tiv
ely
.
2
.
2
.
DF
I
G
wind
t
urbin
e
m
o
del
T
h
e
v
o
ltag
e
e
q
u
atio
n
s
o
f
DFI
G
s
tato
r
an
d
r
o
to
r
ca
n
b
e
d
esc
r
ib
ed
i
n
th
e
s
y
n
ch
r
o
n
o
u
s
d
-
q
f
r
am
e
[
1
7
]
as
b
elo
w
:
2
.
2
.
1
.
Sta
t
o
r
v
o
lt
a
g
e
equa
t
io
ns
T
h
e
s
tato
r
v
o
ltag
e
e
q
u
atio
n
s
in
th
e
d
-
q
f
r
a
m
e
ar
e
g
iv
en
b
y
(
2
)
an
d
(
3
)
.
=
+
−
+
−
(
2)
=
+
+
+
+
(
3
)
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
MPC a
n
d
F
OC
fo
r
LVR
T p
erf
o
r
ma
n
ce
in
h
y
b
r
id
r
en
ewa
b
le
en
erg
y
s
ystems
(
Od
a
y
S
a
a
d
F
a
r
es
)
407
2
.
2
.
2
.
Ro
t
o
r
v
o
lt
a
g
e
equa
t
io
ns
T
h
e
r
o
to
r
v
o
ltag
e
eq
u
atio
n
s
in
th
e
d
-
q
f
r
am
e
a
r
e
g
iv
e
n
b
y
(
4
)
an
d
(
5
)
:
=
+
−
(
−
)
+
−
(
−
)
(
4
)
=
+
+
(
−
)
+
+
(
−
)
(
5
)
w
h
er
e,
,
,
,
ar
e
th
e
d
-
q
r
o
to
r
a
n
d
s
tato
r
v
o
ltag
es,
r
esp
ec
tiv
el
y
an
d
is
th
e
r
o
to
r
a
n
d
s
tato
r
r
esis
tan
ce
.
,
,
a
n
d
ar
e
th
e
r
o
to
r
an
d
s
tato
r
c
u
r
r
en
ts
i
n
th
e
d
an
d
q
ax
es,
r
esp
ec
tiv
ely
.
is
th
e
r
o
to
r
in
d
u
cta
n
ce
.
is
th
e
r
o
to
r
s
p
ee
d
.
is
th
e
s
tato
r
in
d
u
ctan
ce
.
is
th
e
s
y
n
ch
r
o
n
o
u
s
s
p
ee
d
o
f
t
h
e
r
o
tatin
g
f
ield
in
th
e
s
tato
r
,
is
th
e
m
u
tu
al
in
d
u
ctan
ce
b
etwe
en
th
e
s
tato
r
an
d
r
o
to
r
.
2
.
3
.
E
lect
ro
m
ec
ha
nica
l
d
y
na
m
ics
T
h
e
elec
tr
o
m
ag
n
etic
t
o
r
q
u
e
an
d
r
o
tatio
n
al
d
y
n
a
m
ics
eq
u
atio
n
s
th
at
g
o
v
er
n
th
e
in
ter
ac
tio
n
b
etwe
en
th
e
s
tato
r
,
r
o
to
r
v
o
lta
g
es,
an
d
cu
r
r
en
ts
ar
e
[
1
7
]
:
=
3
2
.
.
(
−
(
6
)
=
−
−
(
7
)
w
h
er
e
p
is
th
e
n
u
m
b
e
r
o
f
p
o
le
s
,
an
d
ar
e
th
e
d
-
q
f
r
a
m
e
f
lu
x
lin
k
ag
es
,
J
is
th
e
m
o
m
en
t
o
f
i
n
er
tia
o
f
th
e
r
o
to
r
,
is
th
e
m
ec
h
an
ical
to
r
q
u
e
,
D
is
th
e
d
am
p
in
g
co
ef
f
icien
t.
3.
CO
NT
RO
L
ST
R
AT
E
G
I
E
S
I
n
o
r
d
e
r
to
m
ax
im
ize
th
e
p
o
wer
o
u
tp
u
t,
p
r
o
p
er
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
tu
n
in
g
o
v
er
th
e
DFI
G
n
ee
d
s
to
b
e
m
ai
n
tain
ed
.
Activ
e
p
o
wer
(
P)
a
n
d
r
ea
cti
v
e
p
o
we
r
(
Q)
m
ay
b
e
r
e
p
r
esen
ted
as
(
8
)
an
d
(
9
)
.
=
3
2
⋅
⋅
(
⋅
+
⋅
)
(
8
)
=
3
2
⋅
⋅
(
⋅
−
⋅
)
(
9
)
3
.
1
.
M
P
C
f
o
r
P
V
i
nv
er
t
er
MPC
is
a
n
a
d
v
a
n
c
ed
c
o
n
tr
o
l
m
et
h
o
d
o
lo
g
y
t
h
a
t
p
er
f
o
r
m
s
o
p
tim
al
c
o
n
t
r
o
l
a
cti
o
n
s
o
n
t
h
e
P
V
in
v
e
r
t
er
b
as
ed
o
n
th
e
f
o
r
e
ca
s
t
ed
f
u
t
u
r
e
s
y
s
te
m
s
ta
te
as
t
h
e
c
o
n
tr
o
l
i
n
p
u
ts
.
I
n
t
h
e
MCS
p
r
o
b
le
m
,
MP
C
ca
lc
u
l
ates
t
h
e
b
est
in
v
e
r
t
er
s
wi
tc
h
i
n
g
s
e
q
u
e
n
ce
i
n
a
f
i
n
it
e
h
o
r
iz
o
n
i
n
o
r
d
e
r
to
m
i
n
i
m
iz
e
a
n
ass
o
ci
ate
d
c
o
s
t
f
u
n
c
tio
n
t
h
at
co
n
s
i
d
er
s
b
o
t
h
v
o
lt
ag
e
tr
ac
k
i
n
g
an
d
r
ea
ct
iv
e
p
o
we
r
in
je
cti
o
n
.
T
h
e
c
o
s
t
f
u
n
cti
o
n
J
is
f
o
r
m
u
la
te
d
as
(
1
0
)
[
1
8
]
,
[
1
9
]
.
=
∑
∥
∗
(
)
−
(
)
∥
2
=
1
+
∑
∥
Δ
(
)
∥
2
−
1
=
0
(1
0
)
W
h
er
e:
∗
(
k
)
r
ep
r
esen
ts
th
e
r
e
f
er
en
ce
v
o
ltag
e
at
th
e
m
o
m
e
n
t
k
.
(
k
)
is
th
e
ap
p
lied
v
o
ltag
e
f
o
r
k
-
th
tim
e
s
tep
.
is
th
e
n
u
m
b
er
o
f
p
r
e
d
i
cted
s
tep
s
.
d
en
o
tes
th
e
co
n
tr
o
l
h
o
r
izo
n
.
λ
is
th
e
weig
h
t.
Δ
u
(
k
)
is
th
e
v
ar
iatio
n
o
f
th
e
s
witch
in
g
a
c
tio
n
s
(
co
n
tr
o
l
in
p
u
ts
)
at
t
h
e
k
-
th
s
am
p
le
in
s
tan
t.
T
h
e
f
ir
s
t
ter
m
o
f
t
h
e
co
s
t
f
u
n
ctio
n
is
th
e
v
o
ltag
e
tr
ac
k
in
g
er
r
o
r
,
wh
ich
g
u
ar
a
n
tees
th
at
th
e
in
v
er
ter
tr
ac
k
s
th
e
r
ef
e
r
en
ce
v
o
ltag
e
clo
s
ely
.
T
h
e
s
ec
o
n
d
ter
m
is
ad
d
ed
t
o
av
o
id
ex
ce
s
s
iv
e
ch
an
g
es
in
co
n
tr
o
l
co
m
m
an
d
s
,
wh
ich
g
u
ar
an
tees
th
at
th
e
co
n
v
er
ter
co
m
p
o
n
en
ts
will wo
r
k
at
a
lo
wer
tem
p
er
atu
r
e
.
At
e
ac
h
co
n
tr
o
l step
as in
F
ig
u
r
e
1
.
T
h
e
o
p
tim
al
co
n
tr
o
l
also
tak
es
in
to
ac
co
u
n
t
s
y
s
tem
d
y
n
am
ics
an
d
o
p
er
atio
n
al
co
n
s
tr
ain
t
s
.
C
er
tain
co
n
s
tr
ain
ts
f
o
r
th
e
in
v
er
ter
s
u
ch
as
m
ax
im
u
m
o
u
tp
u
t
p
o
wer
,
v
o
ltag
e,
an
d
cu
r
r
en
t
s
h
o
u
l
d
b
e
m
ain
tain
ed
.
Su
c
h
co
n
s
tr
ain
ts
ca
n
b
e
wr
itten
as
(
1
1
)
an
d
(
1
2
)
.
≤
(
)
≤
(
1
1
)
≤
(
)
≤
(
1
2
)
W
h
er
e
an
d
d
ef
in
e
t
h
e
b
o
u
n
d
s
o
n
co
n
tr
o
l
in
p
u
ts
,
an
d
s
et
th
e
p
er
m
is
s
ib
le
v
o
ltag
e
le
v
els
f
o
r
th
e
i
n
v
er
ter
o
u
tp
u
t [
8
]
.
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
:
405
-
4
13
408
Fig
u
r
e
1
.
Mo
d
el
p
r
e
d
ictiv
e
co
n
tr
o
l stra
teg
y
o
f
PV a
r
r
ay
3
.
2
.
F
O
C
f
o
r
DF
I
G
ro
t
o
r
c
o
nv
er
t
er
I
n
L
VR
T
ev
en
ts
,
th
e
d
ec
o
u
p
led
co
n
t
r
o
l
o
f
th
e
r
o
to
r
c
u
r
r
en
ts
an
d
is
n
ec
ess
ar
y
to
c
o
n
tr
o
l
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
an
d
th
e
r
ea
ctiv
e
p
o
wer
o
f
t
h
e
DFI
G
as
illu
s
tr
ated
in
F
ig
u
r
e
2
.
T
h
e
to
r
q
u
e
r
ef
e
r
en
c
e
u
n
d
er
v
o
ltag
e
d
ip
is
b
ased
o
n
MPPT
o
f
win
d
tu
r
b
in
e
m
o
d
el
s
u
ch
t
h
at
th
e
DFI
G
o
p
e
r
ates
in
an
e
f
f
icien
t
m
an
n
er
d
esp
ite
th
e
p
o
o
r
co
n
d
i
tio
n
o
f
g
r
id
[
2
0
]
.
Fig
u
r
e
2
.
Field
-
o
r
ien
ted
c
o
n
tr
o
l stra
teg
y
(
FOC
)
f
o
r
R
SC
o
f
DFI
G
win
d
tu
r
b
in
e
3
.
2
.
1
.
Co
ntr
o
l
la
ws f
o
r
ro
t
o
r
curr
ent
s
T
h
e
r
o
to
r
co
n
v
er
ter
c
o
n
tr
o
l la
ws f
o
r
th
e
DFI
G
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
ws:
˗
Qu
ad
r
atu
r
e
c
u
r
r
e
n
t r
ef
er
e
n
ce
a
n
d
d
ir
ec
t c
u
r
r
en
t
r
ef
er
e
n
ce
:
∗
=
∗
3
2
=
(
1
3
)
∗
=
∗
3
2
−
(
1
4
)
W
h
er
e:
∗
∗
is
th
e
r
ef
er
en
ce
s
ig
n
a
l
f
o
r
th
e
q
u
a
d
r
atu
r
e
an
d
d
ir
ec
t
ax
is
cu
r
r
en
t,
r
esp
ec
tiv
ely
.
∗
is
th
e
elec
tr
o
m
ag
n
etic
t
o
r
q
u
e
r
e
f
er
e
n
ce
,
∗
is
th
e
r
ea
ctiv
e
p
o
wer
r
e
f
e
r
en
ce
?
I
n
t
h
e
(
FOC
)
s
tr
ateg
y
,
th
e
r
o
t
o
r
c
u
r
r
e
n
t
r
ef
er
en
ce
s
ar
e
d
e
f
in
ed
as
i
rd
∗
an
d
i
rq
∗
wh
ich
r
ep
r
esen
t
th
e
d
ir
ec
t
an
d
q
u
a
d
r
atu
r
e
a
x
is
s
ig
n
als
,
r
esp
ec
tiv
ely
.
T
h
ese
ar
e
d
er
iv
ed
f
r
o
m
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
r
ef
er
e
n
c
e
(
T
e
∗
)
an
d
th
e
r
ea
ctiv
e
p
o
wer
r
e
f
er
en
ce
(
Q
∗
)
.
As
illu
s
tr
ated
in
Fig
u
r
e
2
,
t
h
e
FOC
alg
o
r
ith
m
ex
ec
u
tes th
e
f
o
llo
win
g
co
r
e
f
u
n
ctio
n
s
:
-
Dec
o
u
p
led
c
o
n
tr
o
l
:
T
h
e
s
tr
ateg
y
in
d
ep
en
d
en
tly
r
eg
u
lates
th
e
d
-
ax
is
c
u
r
r
en
t
f
o
r
r
ea
ctiv
e
p
o
wer
an
d
th
e
q
-
ax
is
cu
r
r
e
n
t
f
o
r
to
r
q
u
e.
T
h
is
d
ec
o
u
p
lin
g
is
ess
en
tial f
o
r
s
y
s
tem
s
tab
ilit
y
[
2
0
]
.
-
T
o
r
q
u
e
r
ef
e
r
en
ce
(
MPPT)
:
T
e
∗
i
s
ca
lcu
lated
v
ia
a
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
alg
o
r
ith
m
to
ex
tr
ac
t m
ax
im
u
m
en
er
g
y
b
ase
d
o
n
r
ea
l
-
tim
e
win
d
v
elo
city
.
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
MPC a
n
d
F
OC
fo
r
LVR
T p
erf
o
r
ma
n
ce
in
h
y
b
r
id
r
en
ewa
b
le
en
erg
y
s
ystems
(
Od
a
y
S
a
a
d
F
a
r
es
)
409
-
R
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t
:
Q
∗
is
s
et
ac
co
r
d
in
g
to
g
r
i
d
r
eq
u
ir
em
en
ts
,
en
s
u
r
in
g
th
e
DFI
G
p
r
o
v
id
es
v
o
ltag
e
s
u
p
p
o
r
t d
u
r
in
g
an
o
m
alies
-
a
cr
itical
f
ac
to
r
f
o
r
g
r
id
s
tab
ilit
y
d
u
r
in
g
lo
w
-
v
o
ltag
e
e
v
en
ts
.
-
C
r
o
wb
ar
p
r
o
tectio
n
:
T
o
s
af
e
g
u
ar
d
th
e
r
o
to
r
s
id
e
co
n
v
er
ter
(
R
S
C
)
f
r
o
m
o
v
er
-
c
u
r
r
en
ts
d
u
r
i
n
g
d
ee
p
v
o
ltag
e
s
ag
s
,
a
cr
o
wb
ar
cir
c
u
it is
ac
tiv
ated
if
r
o
to
r
cu
r
r
en
t c
o
m
p
o
n
e
n
ts
ex
ce
ed
a
th
r
esh
o
ld
I
m
ax
:
|
i
rd
|
>
I
m
ax
o
r
|
i
rq
|
>
(
1
5
)
-
L
VR
T
e
n
h
an
ce
m
en
t:
T
h
is
in
teg
r
ated
s
ch
em
e
en
s
u
r
es
th
at
b
o
th
PV
in
v
er
ter
s
an
d
DFI
Gs
m
ain
tain
s
tab
le
o
p
er
atio
n
d
u
r
in
g
g
r
id
f
a
u
lts
,
p
r
o
v
id
in
g
cr
itical
g
r
id
ass
is
tan
c
e
wh
ile
p
r
o
tectin
g
in
ter
n
al
p
o
wer
elec
tr
o
n
ics
[
2
1
]
.
I
n
th
e
ev
e
n
t
o
f
a
g
r
id
f
au
lt,
th
e
s
y
s
tem
em
p
lo
y
s
a
m
u
lti
-
s
tag
ed
o
p
er
atio
n
al
s
tr
ateg
y
s
tar
tin
g
with
MPC
-
b
ased
f
ast
r
esp
o
n
s
e
s
u
p
p
o
r
t
[
2
2
]
,
wh
er
e
th
e
PV
in
v
er
t
er
q
u
ick
ly
in
jects
r
ea
ctiv
e
p
o
wer
Q
PV
=
K
MPC
*(
V
r
ef
-
V)
to
s
tab
ilize
th
e
DC
-
lin
k
an
d
m
itig
ate
v
o
ltag
e
d
r
o
p
s
.
Simu
ltan
eo
u
s
ly
,
to
r
q
u
e
c
o
n
t
r
o
l
v
ia
FOC
m
ain
tain
s
co
n
s
tan
t
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
(
T
e
)
b
y
d
ec
o
u
p
lin
g
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
,
allo
win
g
th
e
DFI
G
to
r
em
ain
s
tab
le
d
esp
ite
g
r
id
p
er
tu
r
b
atio
n
s
[
2
3
]
.
I
f
r
o
to
r
cu
r
r
en
ts
ex
ce
e
d
s
af
e
th
r
e
s
h
o
ld
s
,
cr
o
wb
ar
en
g
ag
em
e
n
t
tr
ig
g
er
s
to
r
ed
ir
ec
t
cu
r
r
en
t
th
r
o
u
g
h
r
esis
to
r
s
,
p
r
o
tectin
g
th
e
r
o
t
o
r
-
s
id
e
co
n
v
er
te
r
f
r
o
m
d
am
ag
e
d
u
r
in
g
s
ev
e
r
e
s
ag
s
.
Fin
ally
,
o
n
ce
th
e
g
r
id
v
o
ltag
e
r
ec
o
v
er
s
to
ab
o
v
e
0
.
7
V
n
o
m
,
th
e
s
y
s
tem
tr
an
s
itio
n
s
to
r
esu
m
in
g
r
ea
ctiv
e
in
jectio
n
,
p
r
o
v
id
i
n
g
n
e
g
ativ
e
r
ea
ctiv
e
p
o
wer
b
ac
k
in
to
th
e
g
r
id
to
e
n
s
u
r
e
a
s
m
o
o
th
r
etu
r
n
to
n
o
r
m
al
o
p
e
r
atio
n
an
d
co
n
tin
u
o
u
s
r
en
ewa
b
le
e
n
er
g
y
in
teg
r
atio
n
[
2
4
]
.
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
4
.
1
.
Sim
ula
t
i
o
n
r
esu
lt
s
T
h
e
h
y
b
r
i
d
PV
-
DFI
G
s
y
s
tem
was
m
o
d
eled
in
MA
T
L
AB
/
Simu
lin
k
(
R
2
0
2
4
b
)
to
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[
2
5
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-
[
2
7
]
,
e
n
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ased
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4
.
2
.
No
v
elt
y
a
nd
d
is
t
inct
io
n
T
h
is
p
ap
er
in
tr
o
d
u
ce
s
a
c
o
o
r
d
in
ated
m
u
lti
-
o
b
jectiv
e
co
n
tr
o
l stra
teg
y
th
at
tr
an
s
f
o
r
m
s
th
e
h
y
b
r
id
s
y
s
tem
f
r
o
m
a
p
ass
iv
e
f
au
lt su
r
v
iv
o
r
t
o
an
ac
tiv
e
g
r
id
s
u
p
p
o
r
ter
.
T
h
e
n
o
v
elty
m
a
n
if
ests
in
th
r
ee
k
ey
asp
ec
ts
:
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
MPC a
n
d
F
OC
fo
r
LVR
T p
erf
o
r
ma
n
ce
in
h
y
b
r
id
r
en
ewa
b
le
en
erg
y
s
ystems
(
Od
a
y
S
a
a
d
F
a
r
es
)
411
-
Prio
r
ity
-
b
ased
r
ea
ctiv
e
p
o
we
r
o
r
c
h
estra
tio
n
:
MPC
-
co
n
tr
o
l
led
PV
in
v
er
te
r
s
p
r
o
v
id
e
o
p
tim
ized
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t
th
r
o
u
g
h
co
n
s
tr
ain
t
-
awa
r
e
c
o
s
t
f
u
n
ctio
n
s
,
e
n
ab
lin
g
n
et
r
ea
ctiv
e
p
o
wer
c
o
n
tr
ib
u
tio
n
d
u
r
in
g
f
au
lts
-
o
v
er
c
o
m
in
g
th
e
tr
ad
iti
o
n
al
cr
o
wb
a
r
'
s
r
ea
ctiv
e
p
o
wer
co
n
s
u
m
p
tio
n
lim
itatio
n
.
-
D
e
c
o
u
p
l
e
d
c
o
n
t
r
o
l
a
r
c
h
i
t
e
c
t
u
r
e
:
T
h
e
s
t
r
a
t
e
g
y
c
r
e
a
t
es
d
i
s
ti
n
c
t
c
o
n
t
r
o
l
r
o
l
e
s
:
P
V
h
a
n
d
l
es
r
e
a
c
ti
v
e
s
u
p
p
o
r
t
w
h
i
l
e
D
F
I
G
f
o
c
u
s
e
s
o
n
t
o
r
q
u
e
/s
p
e
e
d
s
t
a
b
il
i
t
y
,
p
r
e
v
e
n
t
i
n
g
F
OC
p
e
r
f
o
r
m
a
n
c
e
d
e
g
r
a
d
a
t
i
o
n
d
u
r
i
n
g
a
s
y
m
m
e
t
r
i
c
a
l
f
a
u
l
t
s
.
-
Gr
id
-
co
d
e
c
o
m
p
lian
t p
o
wer
q
u
ality
:
T
h
e
co
o
r
d
in
ate
d
co
n
tr
o
l
m
ain
tain
s
s
in
u
s
o
id
al
wav
ef
o
r
m
s
an
d
lo
w
T
HD
d
u
r
in
g
s
ev
er
e
f
a
u
lts
,
ac
h
iev
in
g
co
m
p
lia
n
t
p
o
wer
q
u
ality
r
at
h
er
th
an
m
er
e
s
tab
ilit
y
s
u
r
v
iv
al.
T
h
e
in
n
o
v
atio
n
lies
n
o
t
in
in
d
i
v
id
u
al
c
o
m
p
o
n
en
ts
b
u
t
in
th
eir
s
y
s
tem
-
lev
el
in
teg
r
atio
n
,
cr
ea
tin
g
a
s
y
n
er
g
is
tic
g
r
id
-
s
u
p
p
o
r
tin
g
ass
et
d
u
r
in
g
tr
a
n
s
ien
ts
.
(
a)
(
b
)
Fig
u
r
e
6
.
C
o
m
p
a
r
ativ
e
p
e
r
f
o
r
m
an
ce
o
f
m
ec
h
an
ical
s
p
ee
d
d
u
r
in
g
a
g
r
id
f
a
u
lt: (
a)
u
n
d
er
t
h
e
co
n
v
en
tio
n
al
co
n
tr
o
l stra
teg
y
a
n
d
(
b
)
u
n
d
e
r
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
PV
-
DFI
G
s
tr
ateg
y
T
ab
le
2
.
C
o
m
p
a
r
ativ
e
a
n
aly
s
is
o
f
L
VR
T
en
h
an
ce
m
en
t stra
te
g
ies
F
e
a
t
u
r
e
C
o
n
v
e
n
t
i
o
n
a
l
D
F
I
G
P
r
o
p
o
se
d
M
P
C
-
F
O
C
C
r
o
w
b
a
r
-
l
e
s
s
AI
-
b
a
se
d
c
o
n
t
r
o
l
F
a
u
l
t
r
e
sp
o
n
se
D
i
sco
n
n
e
c
t
s fr
o
m
t
h
e
g
r
i
d
(
f
a
i
l
s
LV
R
T)
S
t
a
y
s c
o
n
n
e
c
t
e
d
;
v
e
r
y
f
a
st
r
e
a
c
t
i
o
n
S
t
a
y
s c
o
n
n
e
c
t
e
d
;
sea
ml
e
ss
c
o
n
t
r
o
l
S
t
a
y
s c
o
n
n
e
c
t
e
d
;
p
e
r
f
o
r
ma
n
c
e
v
a
r
i
e
s
C
o
n
t
r
o
l
d
u
r
i
n
g
f
a
u
l
t
U
n
c
o
n
t
r
o
l
l
e
d
(
c
r
o
w
b
a
r
a
c
t
i
v
a
t
e
d
)
Ex
c
e
l
l
e
n
t
c
o
n
t
r
o
l
a
f
t
e
r
c
r
o
w
b
a
r
u
se
F
u
l
l
,
c
o
n
t
i
n
u
o
u
s c
o
n
t
r
o
l
A
d
a
p
t
i
v
e
,
b
u
t
c
a
n
b
e
sl
o
w
/
u
n
p
r
e
d
i
c
t
a
b
l
e
(
TH
D
)
V
e
r
y
h
i
g
h
(
>
2
0
%)
Lo
w
(
<
5
%)
V
e
r
y
l
o
w
(
<
2
%)
V
a
r
i
a
b
l
e
4
.
3
.
Ro
bu
s
t
nes
s
,
g
rid c
o
m
pli
a
nce,
a
nd
f
a
ult
ma
na
g
em
ent
W
h
ile
th
e
p
r
o
p
o
s
ed
s
tr
ateg
y
d
em
o
n
s
tr
ates
ex
ce
llen
t
s
im
u
lated
p
er
f
o
r
m
an
ce
,
s
u
cc
ess
f
u
l
p
r
ac
tical
d
ep
lo
y
m
e
n
t
n
ec
ess
itates
ad
d
r
ess
in
g
p
ar
am
etr
ic
s
en
s
itiv
ity
,
g
r
id
c
o
d
e
co
m
p
lian
ce
,
a
n
d
a
d
v
an
ce
d
f
a
u
lt
m
an
ag
em
en
t.
Par
am
etr
ic
s
en
s
itiv
ity
r
em
ain
s
a
c
h
allen
g
e
as
b
o
th
FOC
an
d
MPC
r
ely
o
n
p
r
ec
is
e
m
o
d
elin
g
;
FOC
i
s
n
o
tab
ly
s
en
s
itiv
e
to
r
o
to
r
r
esis
tan
ce
an
d
m
u
tu
al
in
d
u
ctan
ce
v
ar
iatio
n
s
,
wh
ich
ca
n
lead
to
d
ec
o
u
p
lin
g
lo
s
s
,
wh
ile
MPC
p
er
f
o
r
m
an
ce
ca
n
d
eg
r
ad
e
d
u
e
to
p
r
ed
ictio
n
m
o
d
el
in
ac
c
u
r
ac
ies,
s
u
g
g
esti
n
g
a
n
ee
d
f
o
r
f
u
tu
r
e
in
teg
r
atio
n
o
f
ad
ap
tiv
e
tec
h
n
iq
u
es
lik
e
m
o
d
el
r
ef
e
r
en
ce
ad
ap
tiv
e
s
y
s
tem
(
MRAS
)
o
r
r
o
b
u
s
t
MPC
f
o
r
m
u
latio
n
s
[
2
5
]
.
Fu
r
th
er
m
o
r
e,
en
s
u
r
in
g
ex
p
licit
c
o
m
p
lia
n
ce
with
i
n
ter
n
atio
n
al
s
tan
d
a
r
d
s
s
u
ch
as
NE
R
C
PR
C
-
0
2
4
an
d
th
e
Ger
m
an
g
r
id
co
d
e
is
ess
en
tial,
r
eq
u
ir
in
g
f
u
tu
r
e
co
n
tr
o
l
lo
g
ic
to
e
m
b
ed
s
p
ec
if
ic
L
VR
T
cu
r
v
es
an
d
s
tan
d
ar
d
ized
r
ea
ctiv
e
cu
r
r
e
n
t
r
eq
u
ir
em
en
ts
(
I
q
∗
=
k
*
(
0
.
9
-
V
g
)*
I
r
at
ed
)
d
ir
ec
tly
in
to
th
e
MPC
co
s
t
f
u
n
ctio
n
[
2
6
]
,
[
2
7
]
.
Fin
ally
,
tr
an
s
itio
n
in
g
f
r
o
m
b
asic
o
v
er
c
u
r
r
en
t
p
r
o
tectio
n
to
ad
v
an
ce
d
f
au
lt
m
an
ag
em
en
t
u
s
in
g
FF
T
o
r
wav
elet
-
b
ased
d
etec
tio
n
wo
u
ld
allo
w
f
o
r
m
illi
s
ec
o
n
d
-
lev
el
f
a
u
lt
class
if
icati
o
n
an
d
co
n
d
itio
n
ed
r
esp
o
n
s
es
b
ased
o
n
f
au
lt
ty
p
e
an
d
lo
ca
tio
n
,
u
ltima
tely
o
p
ti
m
izin
g
cr
o
wb
ar
e
n
g
ag
em
e
n
t
an
d
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t to
e
n
h
an
ce
o
v
e
r
all
s
y
s
tem
r
esil
ien
ce
an
d
av
ailab
ilit
y
[
2
8
]
,
[
2
9
]
.
5.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
d
em
o
n
s
tr
ates
th
at
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
s
y
s
tem
,
co
m
b
in
in
g
a
DFI
G
win
d
tu
r
b
in
e
with
a
PV
ar
r
ay
u
s
in
g
c
o
o
r
d
in
ated
MPC
an
d
FOC
,
s
ig
n
if
ican
tly
o
u
tp
er
f
o
r
m
s
a
co
n
v
en
tio
n
al
DFI
G
s
y
s
tem
d
u
r
in
g
g
r
id
f
au
lts
.
T
h
e
k
ey
f
in
d
i
n
g
s
ar
e
i)
Su
p
er
io
r
g
r
id
s
u
p
p
o
r
t
:
T
h
e
s
y
s
tem
s
u
cc
ess
f
u
ll
y
ac
h
iev
ed
L
VR
T
,
m
ain
tain
in
g
a
s
tab
le
s
tato
r
v
o
l
tag
e
(
7
0
%
o
f
n
o
m
i
n
al)
d
u
r
in
g
a
s
ev
er
e
f
au
lt,
wh
er
ea
s
th
e
c
o
n
v
en
tio
n
al
s
y
s
tem
co
llap
s
ed
(
2
0
%
o
f
n
o
m
in
al)
;
ii)
E
f
f
ec
tiv
e
co
m
p
o
n
en
t
p
r
o
tec
tio
n
:
T
h
e
co
o
r
d
in
ated
co
n
tr
o
l
d
r
asti
ca
lly
lim
ited
d
an
g
er
o
u
s
cu
r
r
e
n
t
s
u
r
g
es
in
th
e
s
tato
r
an
d
r
o
to
r
,
p
r
o
tec
tin
g
th
e
v
u
l
n
er
ab
le
p
o
wer
e
lectr
o
n
ics
;
an
d
iii)
I
m
p
r
o
v
ed
s
y
s
tem
s
tab
ilit
y
:
T
h
e
p
r
o
p
o
s
ed
s
tr
ateg
y
r
esu
lted
i
n
a
m
o
r
e
s
tab
le
r
o
to
r
s
p
ee
d
an
d
elim
in
ated
h
ea
v
y
to
r
q
u
e
o
s
cillatio
n
s
,
en
s
u
r
in
g
s
m
o
o
th
er
m
ec
h
a
n
ical
o
p
er
atio
n
.
I
n
ess
en
ce
,
th
is
h
y
b
r
id
MPC
-
FOC
s
tr
ateg
y
is
a
h
ig
h
ly
ef
f
ec
tiv
e
s
o
lu
tio
n
f
o
r
m
ain
tain
in
g
g
r
i
d
co
n
n
ec
tio
n
a
n
d
s
tab
ilit
y
d
u
r
in
g
f
au
lts
,
p
r
o
v
in
g
ess
en
tial
f
o
r
th
e
r
eliab
le,
lar
g
e
-
s
ca
le
in
teg
r
atio
n
o
f
r
e
n
ewa
b
le
en
e
r
g
y
.
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
:
405
-
4
13
412
ACK
NO
WL
E
DG
E
M
E
NT
T
h
e
au
th
o
r
s
wo
u
l
d
lik
e
to
e
x
p
r
ess
th
eir
g
r
atitu
d
e
to
Mu
s
tan
s
ir
iy
ah
Un
iv
e
r
s
ity
f
o
r
its
s
u
p
p
o
r
t.
A
ls
o
,
th
an
k
th
e
r
ev
iewe
r
s
f
o
r
th
eir
v
alu
ab
le
co
m
m
e
n
ts
th
at
h
elp
ed
im
p
r
o
v
e
t
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