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p
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co
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Enha
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PV
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in
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d
g
rid stabili
ty us
ing
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dv
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C
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um
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nk
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m
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ev
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m
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p
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it
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e
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n
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ifi
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d
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n
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v
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c
to
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tem
p
late
g
e
n
e
ra
ti
o
n
(
M
UV
TG
),
s
u
p
p
lem
e
n
ted
b
y
a
n
a
d
d
it
i
o
n
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l
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o
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l
-
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ra
l
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d
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ri
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ti
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e
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ID)
c
o
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o
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g
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late
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h
e
to
tal
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a
rm
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n
ic
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isto
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o
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(THD)
lev
e
ls.
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e
stu
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y
a
lso
d
e
m
o
n
st
ra
tes
th
e
sy
ste
m
’s
sta
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f
o
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d
iffere
n
t
h
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rm
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o
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n
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o
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ll
,
i
n
c
o
m
p
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a
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e
with
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E
sta
n
d
a
rd
s.
T
h
e
p
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o
se
d
a
p
p
ro
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ffe
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g
th
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d
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s u
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M
ATLAB
S
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k
.
K
ey
w
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d
s
:
Mo
d
if
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u
n
it v
ec
to
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p
late
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Pro
p
o
r
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al
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-
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co
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tr
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Sy
n
ch
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o
n
o
u
s
r
ef
e
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en
ce
f
r
am
e
T
o
tal
h
ar
m
o
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ic
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is
to
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tio
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Un
if
ied
p
o
wer
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u
ality
co
n
d
itio
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er
s
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
:
Vijay
Ku
m
ar
Kala
l
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
,
Dr
.
Am
b
ed
k
ar
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
,
Vis
v
esv
ar
ay
a
T
ec
h
n
o
l
o
g
ical
Un
iv
er
s
ity
Naa
g
ar
ab
h
aa
v
i,
B
en
g
alu
r
u
,
K
ar
n
atak
a
5
6
0
0
5
6
,
I
n
d
ia
E
m
ail: v
iju
2
5
0
9
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
in
teg
r
atio
n
o
f
s
o
lar
p
h
o
t
o
v
o
ltaic
ar
r
ay
s
in
to
elec
tr
ical
g
r
id
s
h
as
s
ig
n
if
ican
tly
in
cr
ea
s
ed
d
u
e
to
th
eir
p
r
o
v
is
io
n
o
f
clea
n
,
r
en
e
wab
le
en
er
g
y
[
1
]
.
Ho
wev
e
r
,
l
ar
g
e
-
s
ca
le
s
o
lar
p
lan
ts
co
n
n
ec
ted
to
th
e
g
r
id
f
ac
e
ch
allen
g
es
in
m
ain
tain
in
g
s
tab
le
elec
tr
icity
g
en
er
atio
n
d
u
e
to
p
o
wer
q
u
ality
p
r
o
b
lem
s
,
s
u
ch
as
v
o
ltag
e
s
ag
s
,
s
wells,
an
d
h
ar
m
o
n
ic
d
is
to
r
ti
o
n
s
[
2
]
,
[
3
]
.
T
h
ese
is
s
u
es
co
m
p
r
o
m
is
e
th
e
r
eliab
ilit
y
an
d
p
er
f
o
r
m
an
ce
o
f
th
e
s
y
s
tem
s
,
u
n
d
er
s
co
r
in
g
th
e
n
ee
d
f
o
r
ef
f
ec
tiv
e
m
itig
atio
n
tech
n
o
lo
g
ies
[
4
]
.
Un
if
ied
p
o
wer
q
u
ality
co
n
d
itio
n
er
s
(
UPQC
)
h
av
e
em
er
g
e
d
as
a
p
r
o
m
is
in
g
s
o
lu
tio
n
,
ca
p
a
b
le
o
f
ad
d
r
ess
in
g
m
u
ltip
le
p
o
wer
q
u
a
lity
p
r
o
b
lem
s
[
5
]
-
[
8
]
.
I
n
teg
r
atio
n
o
f
a
1
.
5
MW so
lar
p
h
o
to
v
o
ltaic
s
y
s
tem
,
d
esi
g
n
ed
to
o
v
er
c
o
m
e
p
o
wer
q
u
ality
p
r
o
b
lem
s
[
9
]
.
UPQC
s
y
s
tem
u
tili
ze
s
a
b
le
n
d
o
f
s
y
n
c
h
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
a
m
e
(
SR
F)
th
eo
r
y
an
d
m
o
d
if
ied
u
n
it
v
ec
to
r
tem
p
late
g
en
er
atio
n
(
MU
VT
G)
,
co
m
b
in
ed
with
a
p
r
o
p
o
r
ti
o
n
al
-
in
teg
r
al
-
d
er
iv
ativ
e
(
PID
)
co
n
tr
o
ller
f
o
r
ef
f
ec
tiv
e
r
ea
ctiv
e
p
o
wer
f
lo
w
co
n
tr
o
l
[
1
0
]
,
[
1
1
]
.
SR
F
th
eo
r
y
aid
s
i
n
s
y
n
c
h
r
o
n
izin
g
co
n
tr
o
l
s
ig
n
als
with
t
h
e
g
r
id
v
o
ltag
e
wav
ef
o
r
m
,
en
s
u
r
in
g
p
r
ec
is
e
co
n
tr
o
l
u
n
d
er
v
ar
iab
le
g
r
id
c
o
n
d
itio
n
s
[
1
2
]
,
[
1
3
]
.
MU
VT
G
is
em
p
lo
y
ed
t
o
g
en
e
r
ate
r
ef
er
e
n
ce
tem
p
lates
th
at
alig
n
ac
cu
r
ately
with
s
p
ec
if
ic
g
r
id
d
is
tu
r
b
an
ce
s
,
f
ac
ilit
atin
g
ef
f
ec
tiv
e
co
m
p
en
s
atio
n
[
1
4
]
,
[
1
5
]
.
T
h
e
PID
c
o
n
tr
o
ller
is
i
n
teg
r
al
to
th
e
s
y
s
tem
'
s
p
er
f
o
r
m
an
ce
,
r
e
g
u
latin
g
r
ea
ctiv
e
p
o
wer
f
lo
w
to
t
h
e
g
r
i
d
,
p
r
o
v
id
in
g
r
o
b
u
s
t a
n
d
d
y
n
a
m
ic
r
esp
o
n
s
es,
an
d
en
s
u
r
in
g
s
y
s
tem
s
tab
ilit
y
ac
r
o
s
s
v
ar
y
in
g
c
o
n
d
itio
n
s
an
d
lo
ad
s
[
1
6
]
-
[
1
8
]
.
T
h
e
in
te
g
r
atio
n
o
f
t
h
ese
tech
n
o
lo
g
ies
aim
s
to
r
ed
u
ce
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD
)
lev
els,
m
ee
t
in
d
u
s
tr
y
s
tan
d
ar
d
s
,
an
d
en
h
a
n
ce
g
r
id
p
er
f
o
r
m
a
n
ce
,
u
ltima
t
ely
p
r
o
m
o
ti
n
g
th
e
u
s
e
o
f
r
en
ewa
b
le
en
er
g
y
th
r
o
u
g
h
ad
v
an
ce
d
p
o
wer
q
u
ality
m
a
n
ag
em
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
n
h
a
n
ce
me
n
t o
f la
r
g
e
P
V
in
te
g
r
a
ted
g
r
id
s
ta
b
ilit
y
u
s
in
g
a
n
a
d
va
n
ce
d
UP
QC
(
V
ija
y
K
u
ma
r
K
a
la
l)
1185
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
A
co
m
p
r
eh
e
n
s
iv
e
liter
atu
r
e
r
ev
iew
is
ess
en
tia
l
f
o
r
ex
am
i
n
in
g
th
e
in
teg
r
atio
n
o
f
a
1
.
5
MW
s
o
lar
p
h
o
to
v
o
ltaic
ar
r
ay
with
ad
v
a
n
ce
d
p
o
wer
q
u
ality
co
n
tr
o
l
s
y
s
tem
s
to
ad
h
er
en
ce
th
e
b
e
n
ch
m
ar
k
s
lik
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T
HD
lev
els
an
d
I
E
E
E
-
5
1
9
s
tan
d
ar
d
s
is
cr
u
cial
f
o
r
m
ain
tain
i
n
g
in
d
u
s
tr
y
co
m
p
lian
ce
.
T
h
e
f
au
lt
t
r
e
e
an
al
y
s
is
[
1
9
]
is
u
ti
liz
ed
t
o
i
d
e
n
t
if
y
cr
i
tic
al
f
a
u
lts
i
n
l
ar
g
e
-
s
ca
l
e
g
r
id
-
c
o
n
n
ec
t
ed
P
V
s
y
s
te
m
s
,
s
u
c
h
as
s
o
l
d
e
r
b
o
n
d
f
ai
lu
r
es
a
n
d
in
t
er
c
o
n
n
e
ct
is
s
u
es.
A
f
a
u
l
t
d
iag
n
o
s
ti
c
t
ec
h
n
i
q
u
e
[
2
0
]
u
s
i
n
g
s
i
g
n
al
e
x
c
ita
ti
o
n
was
d
e
v
el
o
p
e
d
t
o
d
e
te
ct
an
d
id
e
n
t
if
y
d
e
f
ec
ti
v
e
m
o
d
u
les
i
n
l
ar
g
e
-
s
c
ale
PV
i
n
s
t
all
ati
o
n
s
,
i
m
p
r
o
v
i
n
g
f
a
u
l
t
d
e
tec
ti
o
n
an
d
o
p
er
ati
o
n
al
r
eli
a
b
ili
ty
.
I
n
teg
r
atin
g
a
UPQC
with
a
P
V
s
y
s
tem
[
2
1
]
,
was
p
r
o
p
o
s
ed
u
s
in
g
a
h
y
b
r
i
d
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
tech
n
i
q
u
e
a
n
d
d
-
q
c
o
n
tr
o
l
to
en
h
a
n
ce
p
o
wer
q
u
alit
y
an
d
clea
n
en
e
r
g
y
g
en
er
atio
n
.
UPQC
l
in
k
ed
with
PV a
n
d
b
atter
y
en
er
g
y
s
y
s
tem
s
,
to
s
tab
ilize
v
o
ltag
e
an
d
m
in
im
ize
d
is
to
r
tio
n
s
,
s
ig
n
if
ican
tly
r
ed
u
cin
g
T
HD
an
d
im
p
r
o
v
in
g
p
o
we
r
f
ac
to
r
[
2
2
]
.
Po
wer
q
u
ality
co
n
ce
r
n
s
ar
e
ad
d
r
ess
ed
in
g
r
id
-
co
n
n
ec
ted
PV
s
y
s
tem
s
with
a
UPQC
,
ac
h
iev
in
g
ef
f
ec
tiv
e
v
o
ltag
e
h
ar
m
o
n
ic
m
itig
ati
o
n
an
d
g
r
id
s
y
n
ch
r
o
n
izatio
n
[
2
3
]
.
E
n
h
a
n
ce
d
UPQC
[
2
4
]
,
u
tili
ze
s
d
is
tr
ib
u
t
ed
g
en
er
atio
n
t
o
s
u
p
p
ly
r
ea
cti
v
e
p
o
wer
ass
is
tan
ce
to
th
e
g
r
id
,
u
s
in
g
ad
v
an
ce
d
co
n
tr
o
l
m
eth
o
d
s
f
o
r
b
etter
lo
a
d
m
an
ag
em
e
n
t
an
d
s
y
s
tem
s
tab
ilit
y
to
im
p
r
o
v
e
r
esis
tan
ce
ag
ain
s
t
v
o
ltag
e
s
ag
s
,
v
er
if
ied
th
r
o
u
g
h
s
im
u
lati
o
n
s
in
MA
T
L
AB
-
Simu
lin
k
[
2
5
]
.
T
h
ese
s
tu
d
ies
co
llectiv
ely
co
n
tr
ib
u
te
to
ad
v
a
n
cin
g
PV sy
s
tem
r
eliab
ilit
y
an
d
p
o
w
er
q
u
ality
m
a
n
ag
em
e
n
t,
cr
u
cia
l f
o
r
s
u
s
tain
ab
le
en
er
g
y
d
ev
elo
p
m
en
t.
As
o
f
J
u
n
e
3
0
,
2
0
2
3
,
th
e
Natio
n
al
So
lar
Miss
io
n
is
an
in
iti
ativ
e
b
y
I
n
d
ia
to
p
r
o
m
o
te
s
o
l
ar
en
er
g
y
,
ac
h
iev
in
g
7
0
.
1
0
GW
o
f
in
s
talled
ca
p
ac
ity
,
wh
ich
ca
n
s
u
r
p
a
s
s
5
0
0
GW
ac
c
o
r
d
in
g
to
th
e
m
in
is
tr
y
o
f
n
ew
an
d
r
en
ewa
b
le
en
er
g
y
I
n
d
ia.
T
h
e
in
ter
m
itten
t
n
atu
r
e
o
f
s
o
lar
e
n
er
g
y
ca
n
ca
u
s
e
s
tab
ilit
y
is
s
u
es
wh
en
in
teg
r
ated
with
th
e
co
n
v
en
tio
n
al
elec
tr
i
c
g
r
id
.
Ph
o
to
v
o
ltaic
s
y
s
tem
s
m
u
s
t
ad
h
er
e
to
g
r
id
in
te
g
r
ati
o
n
I
E
E
E
s
tan
d
ar
d
s
en
s
u
r
in
g
s
af
e
an
d
ef
f
icie
n
t p
h
o
to
v
o
ltaic
s
y
s
tem
in
teg
r
atio
n
i
n
to
th
e
g
r
id
.
T
h
e
l
i
t
e
r
a
t
u
r
e
r
e
v
i
e
w
p
r
i
m
a
r
ily
f
o
c
u
s
e
s
o
n
p
o
w
e
r
q
u
a
l
i
t
y
e
n
h
a
n
c
e
m
e
n
t
,
w
i
t
h
l
i
m
it
e
d
c
o
n
s
id
e
r
a
t
i
o
n
o
f
vo
l
t
a
g
e
s
t
a
b
il
i
t
y
u
n
d
e
r
d
y
n
a
m
i
c
g
r
i
d
c
o
n
d
i
t
i
o
n
s
.
A
d
d
i
t
i
o
n
a
l
ly
,
t
h
e
r
e
i
s
l
i
m
i
t
e
d
r
e
s
ea
r
c
h
o
n
t
h
e
i
n
t
e
g
r
a
t
i
o
n
o
f
l
a
r
g
e
-
s
c
al
e
PV
s
y
s
te
m
s
i
n
t
o
t
h
e
g
r
i
d
.
T
h
i
s
p
a
p
e
r
a
d
d
r
e
s
s
es
p
o
w
e
r
q
u
a
l
i
t
y
d
i
s
t
u
r
b
a
n
c
e
s
i
n
t
h
e
d
i
s
t
r
i
b
u
t
i
o
n
s
y
s
t
e
m
a
n
d
r
e
g
u
l
a
t
e
s
t
h
e
r
e
a
c
t
i
v
e
p
o
we
r
f
l
o
w
i
n
t
o
t
h
e
g
r
i
d
.
T
h
e
m
ai
n
f
e
a
t
u
r
e
s
o
f
t
h
e
p
r
o
p
o
s
e
d
m
e
t
h
o
d
i
n
c
l
u
d
e
:
˗
R
ed
u
ctio
n
o
f
p
o
wer
q
u
ality
is
s
u
es:
M
itig
ates
v
o
ltag
e
s
ag
,
s
well,
an
d
h
ar
m
o
n
ic
d
is
tu
r
b
a
n
ce
s
ca
u
s
ed
b
y
b
o
th
lin
ea
r
,
n
o
n
-
lin
ea
r
lo
a
d
s
a
n
d
d
if
f
er
en
t f
a
u
lts
u
n
d
er
v
ar
io
u
s
s
ce
n
ar
io
s
u
s
in
g
UPQC
.
˗
I
n
teg
r
ates
th
e
1
.
5
MW
p
h
o
to
v
o
ltaic
s
y
s
tem
in
to
th
e
g
r
id
u
s
in
g
th
e
UPQC
,
en
s
u
r
in
g
a
co
n
s
tan
t
DC
v
o
ltag
e
d
esp
ite
v
o
ltag
e
p
o
wer
q
u
ality
is
s
u
es a
n
d
h
ar
m
o
n
ics.
˗
Stead
y
p
o
wer
s
u
p
p
ly
:
E
n
s
u
r
e
s
co
n
s
is
ten
t
p
o
wer
d
eliv
er
y
to
th
e
g
r
id
,
ev
e
n
d
u
r
in
g
PV
p
o
wer
g
en
er
atio
n
an
d
v
o
lta
g
e
f
lu
ctu
atio
n
s
,
en
h
a
n
cin
g
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
tab
ilit
y
.
˗
Ma
in
tain
s
a
T
HD
b
elo
w
5
% a
t th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
.
3.
P
RO
P
O
SE
D
M
E
T
H
O
DO
L
O
G
Y
T
h
e
r
esear
ch
f
o
cu
s
es
o
n
lar
g
e
-
s
ca
le
1
.
5
MW
s
o
lar
p
h
o
to
v
o
l
taic
ar
r
ay
th
at
is
in
teg
r
ated
wi
th
th
e
g
r
i
d
u
s
in
g
UPQC
to
ad
d
r
ess
s
ev
er
al
p
o
wer
q
u
alities
co
n
ce
r
n
s
th
at
ar
e
o
f
ten
en
co
u
n
ter
ed
i
n
g
r
id
-
in
teg
r
ated
s
o
lar
en
er
g
y
s
y
s
tem
s
wh
ich
in
clu
d
es
v
o
ltag
e
s
ag
s
,
v
o
ltag
e
s
wells
,
an
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
.
Fi
g
u
r
e
1
s
h
o
ws
th
e
s
im
u
latio
n
m
o
d
el
o
f
p
r
o
p
o
s
ed
s
y
s
tem
.
3
.
1
.
Sy
s
t
e
m
des
ig
n
T
h
e
d
esig
n
o
f
th
e
UPQC
is
es
s
en
tial,
as
it
r
eq
u
ir
es
c
o
n
n
ec
ti
n
g
th
e
s
o
lar
p
h
o
to
v
o
ltaic
ar
r
a
y
s
y
s
tem
to
a
co
m
m
o
n
DC
lin
k
.
T
h
is
in
v
o
lv
es
ch
o
o
s
in
g
th
e
co
r
r
ec
t
r
ati
n
g
s
f
o
r
th
e
DC
ca
p
ac
ito
r
an
d
v
o
ltag
e
f
o
r
th
e
DC
bus
.
T
h
e
d
etails
f
o
r
th
e
1
.
5
MW
p
h
o
to
v
o
ltaic
m
o
d
u
les
an
d
m
ath
e
m
atica
l
m
o
d
el
o
f
UPQC
with
g
r
id
ar
e
co
n
s
id
er
ed
i
n
th
e
p
r
o
p
o
s
ed
s
y
s
tem
[
2
6
]
.
T
h
e
c
o
n
tr
o
l
tech
n
i
q
u
e
f
o
r
th
e
UPQC
s
y
s
tem
co
m
b
in
es
SR
F
th
eo
r
y
an
d
MU
VT
G
.
3
.
2
.
Sy
nch
ro
no
us
re
f
er
ence
f
ra
m
e
t
heo
ry
Usi
n
g
th
e
SR
F
-
b
ased
co
n
tr
o
l
s
tr
ateg
y
,
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
ler
m
an
ag
es
t
h
e
s
h
u
n
t
APF,
a
s
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
SR
F
m
eth
o
d
ca
l
cu
lates
th
e
d
esire
d
s
o
u
r
ce
cu
r
r
en
ts
f
r
o
m
th
e
lo
ad
cu
r
r
en
ts
b
y
ap
p
ly
in
g
a
d
q
0
-
to
-
ab
c
tr
an
s
f
o
r
m
atio
n
[
2
4
].
˗
Sy
n
ch
r
o
n
izatio
n
with
g
r
id
v
o
ltag
e
:
SR
F
th
eo
r
y
en
s
u
r
es
th
at
co
n
tr
o
l
s
ig
n
als
m
atch
th
e
g
r
id
’
s
v
o
ltag
e
wav
ef
o
r
m
.
T
h
is
m
ea
n
s
th
at
th
e
co
n
tr
o
l
s
ig
n
als
Vr
ef
an
d
I
r
e
f
ar
e
in
s
y
n
c
h
r
o
n
izatio
n
with
th
e
g
r
id
v
o
ltag
e
Vg
r
id
.
Ma
th
em
atica
lly
,
th
is
ca
n
b
e
r
e
p
r
esen
ted
as (
1
)
an
d
(
2
)
.
(
)
=
(
)
(
1
)
(
)
=
(
)
(
2
)
˗
R
ef
er
en
ce
s
ig
n
al
g
en
er
ati
o
n
:
M
ath
em
atica
lly
,
th
e
r
ef
er
e
n
ce
s
ig
n
als ca
n
b
e
r
ep
r
esen
ted
as (
3
)
an
d
(
4
)
.
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.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
8
4
-
1195
1186
(
)
=
(
)
+
(
3
)
(
)
=
(
)
+
(
4
)
˗
E
n
h
an
ce
d
c
o
n
tr
o
l
ac
cu
r
ac
y
:
B
y
tr
an
s
f
o
r
m
in
g
AC
q
u
an
titi
es
in
to
a
r
o
tatin
g
r
ef
er
en
ce
f
r
a
m
e
(
d
-
q
f
r
am
e
)
,
SR
F th
eo
r
y
s
im
p
lifie
s
th
e
co
n
tr
o
l o
f
AC
s
ig
n
als
.
T
h
is
tr
an
s
f
o
r
m
atio
n
is
r
ep
r
esen
ted
b
y
(
5
)
a
n
d
(
6
)
.
=
(
)
+
(
)
(
5
)
=
−
(
)
+
(
)
(
6
)
˗
Har
m
o
n
ic
m
itig
atio
n
:
T
h
e
th
eo
r
y
aid
s
in
th
e
d
etec
tio
n
an
d
co
m
p
en
s
atio
n
o
f
h
ar
m
o
n
ic
s
in
th
e
p
o
wer
s
y
s
tem
.
T
h
is
co
m
p
en
s
atio
n
ca
n
b
e
r
e
p
r
esen
ted
m
ath
e
m
atica
lly
as (
7
)
.
=
−
ℎ
(
7
)
˗
Vo
ltag
e
an
d
cu
r
r
e
n
t
r
eg
u
latio
n
:
SR
F
th
eo
r
y
en
s
u
r
es
p
r
ec
is
e
r
eg
u
latio
n
o
f
v
o
ltag
e
an
d
cu
r
r
en
t
wav
ef
o
r
m
s
.
T
h
is
r
eg
u
latio
n
is
r
ep
r
esen
ted
m
ath
em
atica
lly
as (
3
)
a
n
d
(
4
)
.
Fig
u
r
e
1
.
Simu
latio
n
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
3
.
3
.
M
o
dified
un
it
v
ec
t
o
r
t
e
m
pla
t
e
g
ener
a
t
i
o
n (
M
UVTG
)
MU
VT
G
is
a
tech
n
iq
u
e
e
m
p
l
o
y
ed
in
UPQC
,
aim
ed
at
r
ef
i
n
in
g
t
h
e
c
o
n
tr
o
l
o
f
elec
tr
ical
p
ar
am
eter
s
s
u
ch
as
v
o
ltag
e
a
n
d
cu
r
r
en
t
.
Fig
u
r
e
3
illu
s
tr
ates
a
b
asic
co
n
t
r
o
l
s
ch
em
e
f
o
r
MU
VT
G
i
n
a
s
er
ies
ac
tiv
e
p
o
wer
f
ilte
r
(
APF
)
[
24
]
.
T
h
is
m
eth
o
d
is
u
s
ed
to
g
en
er
ate
th
e
r
eq
u
ir
ed
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
PW
M
)
p
u
ls
es
f
o
r
APF co
n
tr
o
l.
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
E
n
h
a
n
ce
me
n
t o
f la
r
g
e
P
V
in
te
g
r
a
ted
g
r
id
s
ta
b
ilit
y
u
s
in
g
a
n
a
d
va
n
ce
d
UP
QC
(
V
ija
y
K
u
ma
r
K
a
la
l)
1187
Fig
u
r
e
2
.
E
n
h
an
ce
d
g
r
i
d
s
u
p
p
o
r
t v
ia
UPQC
-
DG
co
n
tr
o
ller
Fig
u
r
e
3
.
Per
f
o
r
m
an
c
e
o
f
a
UPQC
d
u
r
in
g
0
.
3
p
.
u
.
v
o
ltag
e
s
ag
an
d
s
well
co
n
d
itio
n
s
T
h
e
r
ef
er
en
ce
v
o
ltag
e
wav
ef
o
r
m
is
r
ep
r
esen
ted
as
Vr
ef
(
t
)
an
d
th
e
ac
tu
al
g
r
id
v
o
ltag
e
w
av
ef
o
r
m
as
Vg
r
id
(
t
)
.
Similar
ly
,
th
e
r
e
f
er
en
ce
cu
r
r
e
n
t
wav
ef
o
r
m
is
d
en
o
ted
as
I
r
ef
(
t
)
an
d
t
h
e
ac
tu
al
g
r
id
cu
r
r
en
t
wav
ef
o
r
m
as I
g
r
id
(
t
)
.
MU
VT
G
ca
n
b
e
ex
p
r
e
s
s
ed
b
y
(
8
)
a
n
d
(
9
)
.
(
)
=
(
)
+
(
8
)
(
)
=
(
)
+
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
8
4
-
1195
1188
W
h
er
e,
V_
tem
p
late
(
t
)
an
d
I
_
tem
p
late
(
t
)
ar
e
t
h
e
id
ea
l
r
ef
er
en
ce
tem
p
lates
f
o
r
v
o
ltag
e
an
d
cu
r
r
e
n
t,
r
esp
ec
tiv
ely
.
∆
V
an
d
∆
I
ar
e
a
d
ju
s
tm
en
ts
m
ad
e
to
th
e
r
ef
er
e
n
ce
tem
p
lates
b
ased
o
n
th
e
s
p
ec
if
ic
co
n
d
itio
n
s
o
f
th
e
p
o
wer
s
y
s
tem
.
V_
r
e
f
(
t
)
a
n
d
I
_
r
e
f
(
t
)
a
r
e
th
e
m
o
d
if
ied
r
ef
er
en
ce
s
ig
n
als u
s
ed
b
y
th
e
co
n
tr
o
l sy
s
tem
.
3
.
4
.
Rea
c
t
iv
e
po
wer
co
ntr
o
l
T
h
e
in
teg
r
atio
n
o
f
a
PID
co
n
tr
o
ller
in
to
a
UPQC
s
y
s
tem
s
ig
n
if
ican
tly
en
h
an
ce
s
its
ca
p
ab
ilit
y
to
r
eg
u
late
r
ea
ctiv
e
p
o
wer
,
r
esp
o
n
d
d
y
n
a
m
ically
to
g
r
id
c
h
a
n
g
es,
an
d
m
ain
tain
o
v
e
r
all
s
y
s
tem
s
tab
ilit
y
.
I
ts
s
im
p
licity
an
d
ef
f
ec
tiv
e
n
ess
m
ak
e
it
a
cr
itical
co
m
p
o
n
en
t
in
th
e
p
u
r
s
u
it
o
f
h
i
g
h
-
p
er
f
o
r
m
an
ce
p
o
wer
q
u
ality
m
an
ag
em
en
t
.
T
h
e
o
u
tp
u
t
o
f
a
PID
co
n
tr
o
ller
,
u
(
t
)
,
ca
n
b
e
e
x
p
r
ess
ed
as (
1
0
)
.
(
)
=
∗
(
)
+
∗
∫
[
0
]
(
)
+
(
(
)
⁄
)
(
1
0
)
Her
e,
u
(
t)
s
tan
d
s
f
o
r
th
e
c
o
n
t
r
o
l
o
u
tp
u
t,
K
p
,
K
i
,
an
d
K
d
ar
e
th
e
p
r
o
p
o
r
tio
n
al,
in
teg
r
al,
an
d
d
er
iv
ativ
e
g
ain
s
,
r
esp
ec
tiv
ely
,
an
d
e
(
t
)
is
th
e
er
r
o
r
s
ig
n
al,
wh
ich
is
th
e
d
if
f
e
r
en
ce
b
etwe
en
th
e
d
esire
d
s
etp
o
in
t
an
d
th
e
ac
tu
al
m
ea
s
u
r
ed
p
r
o
ce
s
s
v
ar
iab
le.
˗
E
r
r
o
r
s
ig
n
al
:
T
h
e
er
r
o
r
s
ig
n
al
e
(
t
)
is
ex
p
r
ess
ed
as (
1
1
)
.
(
)
=
(
)
−
(
)
(
1
1
)
W
h
er
e
r
(
t
)
is
th
e
r
ef
e
r
en
ce
v
al
u
e
(
s
et
p
o
in
t
)
;
y
(
t
)
is
th
e
m
ea
s
u
r
ed
p
r
o
ce
s
s
v
ar
iab
le
.
˗
Pro
p
o
r
tio
n
al
ter
m
:
T
h
e
p
r
o
p
o
r
tio
n
al
ter
m
p
r
o
v
id
es a
n
o
u
tp
u
t th
at
is
p
r
o
p
o
r
tio
n
al
to
t
h
e
cu
r
r
en
t e
r
r
o
r
v
alu
e:
(
)
=
∗
(
)
(
1
2
)
˗
I
n
teg
r
al
ter
m
:
T
h
e
in
teg
r
al
ter
m
p
r
o
v
id
es
a
n
o
u
tp
u
t
t
h
at
is
p
r
o
p
o
r
tio
n
al
to
t
h
e
cu
m
u
lati
v
e
s
u
m
o
f
p
ast
er
r
o
r
s
,
th
u
s
a
d
d
r
ess
in
g
th
e
ac
c
u
m
u
lated
o
f
f
s
et
:
(
)
=
∗
∫
[
0
]
(
)
(
1
3
)
˗
Der
iv
ativ
e
ter
m
:
T
h
e
d
er
iv
ati
v
e
ter
m
p
r
o
v
id
es
an
o
u
tp
u
t
th
at
is
p
r
o
p
o
r
tio
n
al
to
th
e
r
ate
o
f
ch
an
g
e
o
f
th
e
er
r
o
r
,
p
r
ed
ictin
g
f
u
tu
r
e
er
r
o
r
b
ased
o
n
its
cu
r
r
e
n
t r
ate
o
f
ch
an
g
e
:
(
)
=
∗
(
(
(
)
)
⁄
)
(
1
4
)
˗
C
o
m
b
in
ed
PID
o
u
t
p
u
t
:
C
o
m
b
i
n
in
g
th
ese
th
r
ee
ter
m
s
g
iv
es th
e
to
tal
o
u
tp
u
t
o
f
th
e
PID
c
o
n
tr
o
ller
:
(
)
=
(
)
+
(
)
+
(
)
(
1
5
)
T
h
ese
eq
u
atio
n
s
co
llectiv
ely
d
escr
ib
e
h
o
w
th
e
PID
co
n
t
r
o
ll
er
ca
lcu
lates
its
co
n
tr
o
l
o
u
tp
u
t
b
ased
o
n
th
e
er
r
o
r
s
ig
n
al,
aim
in
g
to
m
i
n
im
ize
th
e
er
r
o
r
an
d
th
u
s
m
ai
n
tain
th
e
s
tab
ilit
y
an
d
p
er
f
o
r
m
an
ce
o
f
th
e
UPQ
C
s
y
s
tem
.
C
o
m
b
in
in
g
SR
F
th
eo
r
y
an
d
MU
VT
G,
s
u
p
p
lem
en
t
ed
b
y
a
PID
co
n
tr
o
ller
,
en
h
a
n
ce
s
r
ea
ctiv
e
p
o
wer
f
lo
w
co
n
tr
o
l
in
lar
g
e
-
s
ca
le
s
o
lar
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Simu
latio
n
r
esu
lts
f
r
o
m
th
e
MA
T
L
AB
/Si
m
u
lin
k
en
v
ir
o
n
m
en
t
s
h
o
ws
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
UPQC
-
DG
co
n
tr
o
ller
.
T
h
is
s
y
s
tem
p
r
o
v
id
es
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t
to
th
e
g
r
id
.
I
t
in
v
o
lv
es
m
o
d
elin
g
an
d
test
in
g
a
th
r
ee
-
p
h
ase,
s
in
g
le
-
s
tag
e
UPQC
-
DG
s
y
s
tem
u
n
d
er
v
ar
io
u
s
d
y
n
a
m
ic
co
n
d
itio
n
s
,
s
u
ch
as g
r
id
v
o
ltag
e
s
ag
,
v
o
ltag
e
s
well,
lo
ad
u
n
b
alan
cin
g
,
an
d
ch
a
n
g
es in
s
o
lar
ir
r
a
d
iatio
n
.
4
.
1
.
Ca
s
e
-
1
Fig
u
r
e
3
d
em
o
n
s
tr
ates
th
e
ca
p
ab
ilit
ies
o
f
a
UPQC
in
m
an
ag
in
g
g
r
i
d
v
o
ltag
e
f
l
u
ctu
atio
n
s
.
I
t
s
h
o
ws
h
o
w
th
e
UPQC
s
tab
ilizes
th
e
lo
ad
v
o
ltag
e
b
y
r
ap
id
l
y
a
d
ju
s
tin
g
its
in
jecte
d
v
o
ltag
e
in
r
es
p
o
n
s
e
to
a
0
.
3
p
.
u
.
v
o
ltag
e
s
ag
an
d
s
well.
Sp
ec
if
ically
,
th
e
UPQC
q
u
ick
l
y
in
c
r
ea
s
es
its
v
o
ltag
e
o
u
tp
u
t
to
c
o
u
n
ter
ac
t
s
ag
s
,
an
d
d
ec
r
ea
s
es it to
m
itig
ate
s
wells.
4
.
2
.
Ca
s
e
-
2
Fig
u
r
e
4
illu
s
tr
ates
th
e
p
er
f
o
r
m
an
ce
o
f
a
UPQC
in
ad
d
r
ess
in
g
a
0
.
5
p
.
u
.
v
o
lta
g
e
s
ag
a
n
d
s
well
o
n
th
e
p
o
wer
g
r
id
.
T
h
e
UPQC
ex
h
ib
its
r
o
b
u
s
t
co
n
tr
o
l.
Sp
ec
if
ically
,
it
in
jects
ad
d
itio
n
al
v
o
ltag
e
at
ar
o
u
n
d
1
.
2
s
ec
o
n
d
s
to
c
o
u
n
ter
ac
t
th
e
s
ag
,
an
d
r
ed
u
ce
s
th
e
in
jecte
d
v
o
ltag
e
at
ap
p
r
o
x
im
ately
1
.
6
s
ec
o
n
d
s
to
m
itig
ate
th
e
s
well.
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
E
n
h
a
n
ce
me
n
t o
f la
r
g
e
P
V
in
te
g
r
a
ted
g
r
id
s
ta
b
ilit
y
u
s
in
g
a
n
a
d
va
n
ce
d
UP
QC
(
V
ija
y
K
u
ma
r
K
a
la
l)
1189
4
.
3
.
Ca
s
e
-
3
Fig
u
r
e
5
s
h
o
wca
s
es
th
e
ca
p
ab
ilit
ies
o
f
a
UPQC
in
m
an
ag
in
g
a
0
.
6
p
.
u
.
v
o
ltag
e
s
ag
a
n
d
s
well
ac
r
o
s
s
th
r
ee
p
h
ases
o
f
a
p
o
wer
g
r
i
d
.
At
a
r
o
u
n
d
1
.
2
s
ec
o
n
d
s
,
i
t
in
cr
ea
s
es
th
e
v
o
ltag
e
to
c
o
u
n
ter
ac
t
th
e
s
ag
,
m
ain
tain
in
g
th
e
lo
a
d
v
o
ltag
e
alm
o
s
t
co
n
s
tan
t.
C
o
n
v
e
r
s
ely
,
at
a
b
o
u
t
1
.
6
s
ec
o
n
d
s
,
it
r
e
d
u
ce
s
th
e
in
jecte
d
v
o
ltag
e
to
m
itig
ate
th
e
s
well,
m
in
im
izin
g
d
is
r
u
p
tio
n
to
t
h
e
l
o
ad
.
Fig
u
r
e
4
.
Per
f
o
r
m
an
c
e
o
f
a
UPQC
d
u
r
in
g
0
.
5
p
.
u
.
v
o
ltag
e
s
ag
an
d
s
well
co
n
d
itio
n
s
Fig
u
r
e
5
.
Per
f
o
r
m
an
c
e
o
f
a
UPQC
d
u
r
in
g
0
.
6
p
.
u
.
v
o
ltag
e
s
ag
an
d
s
well
co
n
d
itio
n
s
4
.
4
.
Ca
s
e
4
Fig
u
r
e
6
h
i
g
h
lig
h
ts
th
e
p
e
r
f
o
r
m
an
ce
o
f
a
UPQC
in
m
a
n
ag
in
g
a
0
.
7
p
.
u
.
v
o
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