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Dec
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er
20
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7
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7
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I
SS
N:
2252
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8
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1
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v
1
3
.
i
4
.
pp
790
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797
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ttp
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O
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ed
Sep
2
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2
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2
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R
ev
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ed
Ma
r
8
,
2
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2
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Th
is
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a
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p
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a
p
ro
p
o
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t
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a
l
-
i
n
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ra
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P
I)
c
o
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tr
o
ll
e
r
a
n
d
d
irec
t
-
q
u
a
d
ra
t
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re
(DQ
)
fra
m
e
tran
sfo
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a
ti
o
n
-
b
a
se
d
o
p
ti
m
u
m
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se
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-
c
o
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e
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ted
i
n
v
e
rt
e
r.
In
term
s
o
f
g
rid
sy
n
c
h
r
o
n
iza
ti
o
n
,
v
o
lt
a
g
e
re
g
u
latio
n
,
a
n
d
h
a
rm
o
n
ic ab
a
tem
e
n
t,
t
h
e
p
r
o
p
o
se
d
c
o
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tro
l
tec
h
n
i
q
u
e
a
tt
e
m
p
ts
to
imp
r
o
v
e
th
e
i
n
v
e
rter'
s
p
e
rfo
rm
a
n
c
e
.
By
se
p
a
ra
ti
n
g
th
e
c
o
n
tr
o
l
o
f
a
c
ti
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e
a
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re
a
c
ti
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o
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r,
th
e
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o
n
tr
o
l
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u
c
tu
re
is
m
a
d
e
sim
p
ler
a
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d
in
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e
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e
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d
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n
t
re
g
u
latio
n
o
f
th
e
se
p
a
ra
m
e
ters
is
p
o
ss
ib
le.
Th
is
imp
r
o
v
e
s
t
h
e
in
v
e
rter'
s
c
a
p
a
c
it
y
to
q
u
ick
ly
re
a
c
t
to
g
ri
d
d
isr
u
p
t
io
n
s
a
n
d
trac
k
re
fe
re
n
c
e
v
a
lu
e
s
a
c
c
u
ra
tely
.
In
o
r
d
e
r
to
lo
we
r
c
a
rb
o
n
e
m
issio
n
s
a
n
d
imp
ro
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e
g
ri
d
d
e
p
e
n
d
a
b
il
it
y
,
i
t
h
a
s
b
e
c
o
m
e
v
it
a
l
to
i
n
teg
ra
te
re
n
e
wa
b
le
e
n
e
rg
y
so
u
rc
e
s
in
to
th
e
c
u
rre
n
t
p
o
we
r
g
rid
.
G
rid
-
c
o
n
n
e
c
ted
in
v
e
rters
a
re
e
s
s
e
n
ti
a
l
in
th
i
s
situ
a
ti
o
n
b
e
c
a
u
se
th
e
y
tran
sfo
rm
DC
e
lec
tr
icity
fr
o
m
re
n
e
wa
b
le
so
u
rc
e
s
i
n
t
o
g
ri
d
-
sa
fe
AC
p
o
we
r.
Th
is
a
b
stra
c
t
o
u
tl
i
n
e
a
p
r
o
p
o
rti
o
n
a
l
-
i
n
teg
ra
l
(
P
I)
c
o
n
t
ro
ll
e
r
a
n
d
d
irec
t
-
q
u
a
d
ra
tu
re
(DQ
)
fra
m
e
-
b
a
se
d
o
p
ti
m
a
l
c
o
n
tr
o
l
m
e
th
o
d
f
o
r
a
t
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re
e
-
p
h
a
se
gr
id
-
c
o
n
n
e
c
ted
in
v
e
rter u
sin
g
a
M
ATLAB
sim
u
latio
n
.
K
ey
w
o
r
d
s
:
DQ
f
r
am
e
Gr
id
in
teg
r
atio
n
PI
co
n
tr
o
ller
R
en
ewa
b
le
en
er
g
y
T
h
r
ee
p
h
ase
in
v
er
ter
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
:
Ma
d
d
e
Saiteja
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ic
E
n
g
i
n
ee
r
in
g
,
T
ee
g
a
la
Kr
is
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n
a
R
ed
d
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n
g
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ee
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C
o
lleg
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Hy
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er
ab
ad
,
I
n
d
ia
E
m
ail:
s
aitejam
1
3
0
6
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
A
cr
u
cial
co
m
p
o
n
en
t
o
f
th
e
g
lo
b
al
s
h
if
t
to
s
u
s
tain
ab
le
en
er
g
y
s
y
s
tem
s
is
th
e
q
u
ick
d
ev
elo
p
m
en
t
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
lik
e
win
d
p
o
wer
.
T
h
e
u
s
ag
e
o
f
th
r
e
e
-
p
h
ase
L
C
L
-
ty
p
e
g
r
id
-
co
n
n
ec
ted
in
v
er
ter
s
is
o
n
e
o
f
th
e
f
av
o
r
ed
m
eth
o
d
s
f
o
r
in
t
eg
r
atin
g
r
en
ewa
b
le
e
n
er
g
y
in
s
tallatio
n
s
lik
e
win
d
tu
r
b
in
es
i
n
to
th
e
p
u
b
lic
g
r
id
.
T
h
ese
in
v
er
ter
s
m
ak
e
it e
asier
to
tr
an
s
f
o
r
m
v
ar
iab
le
r
en
ewa
b
le
en
er
g
y
o
u
tp
u
t in
to
a
f
o
r
m
at
th
at
ca
n
b
e
f
ed
in
t
o
th
e
g
r
id
.
Ne
v
er
th
eless
,
d
esp
ite
th
eir
ex
ten
s
iv
e
u
s
e,
t
h
ese
in
v
e
r
ter
s
'
in
ter
f
ac
e
wit
h
th
e
g
r
id
h
a
s
in
h
er
en
t stab
ilit
y
is
s
u
es.
As
a
r
esu
lt,
it
is
cr
itic
al
to
ca
r
e
f
u
lly
ex
am
in
e
an
d
f
i
x
th
ese
s
tab
ilit
y
is
s
u
es
[
1
]
.
T
h
e
p
u
r
s
u
it
o
f
en
er
g
y
ef
f
icien
cy
an
d
s
u
s
tain
ab
ilit
y
is
cr
itical
in
to
d
ay
's
s
o
ciety
ac
r
o
s
s
m
an
y
b
u
s
in
ess
es.
E
lev
ato
r
s
y
s
tem
s
ar
e
o
n
e
k
ey
ar
ea
wh
er
e
e
n
er
g
y
-
s
av
in
g
te
ch
n
o
lo
g
y
is
cr
u
cial,
p
ar
ticu
l
ar
ly
with
th
e
u
s
e
o
f
th
r
ee
-
p
h
ase
g
r
id
-
c
o
n
n
ec
ted
in
v
er
ter
s
.
W
ith
th
e
u
s
e
o
f
th
i
s
tech
n
o
lo
g
y
,
e
x
tr
a
DC
en
er
g
y
m
ay
b
e
c
o
n
v
er
te
d
in
to
AC
p
o
wer
an
d
ea
s
ily
in
co
r
p
o
r
ated
in
to
th
e
p
o
wer
g
r
id
,
ef
f
ec
tiv
e
ly
ac
tin
g
as
a
lo
a
d
[
2
]
.
T
h
e
in
s
tallatio
n
o
f
a
g
r
i
d
-
co
n
n
ec
ted
th
r
ee
-
p
h
ase
in
v
e
r
ter
s
y
s
tem
wh
ile
a
b
id
in
g
b
y
in
d
u
s
tr
y
n
o
r
m
s
an
d
cr
iter
ia
is
th
e
m
ain
to
p
ic
o
f
t
h
is
ar
ticle.
Av
er
ag
e
m
o
d
els
ar
e
u
s
ed
to
r
ep
r
esen
t
th
e
in
v
er
ter
an
d
L
C
L
f
ilter
,
an
d
th
e
d
esig
n
o
f
th
e
co
n
tr
o
l
s
ch
em
e
in
th
e
DQ
r
ef
er
en
ce
f
r
am
e
is
d
is
cu
s
s
ed
[
3
]
.
I
n
o
r
d
er
t
o
o
v
er
co
m
e
th
ese
d
i
f
f
icu
lties
,
a
p
r
o
p
o
r
tio
n
al
-
r
eso
n
an
t
(
PR
)
co
n
tr
o
ller
in
a
s
tatio
n
ar
y
co
o
r
d
in
ate
s
y
s
t
em
is
o
f
f
er
ed
as
a
n
o
v
el
s
o
lu
tio
n
in
th
is
s
tu
d
y
.
I
n
f
in
ite
co
n
tr
o
l
g
ain
at
a
p
ar
ticu
lar
r
eso
n
an
ce
f
r
e
q
u
en
c
y
is
o
n
e
o
f
th
e
PR
co
n
tr
o
ller
'
s
s
tan
d
o
u
t
tr
aits
.
At
th
at
f
r
eq
u
en
cy
p
o
in
t,
s
tead
y
-
s
tate
er
r
o
r
-
f
r
ee
co
n
tr
o
l
ca
n
b
e
ac
h
iev
ed
th
an
k
s
to
th
is
s
p
ec
ial
c
h
ar
ac
t
er
is
tic
[
4
]
.
T
h
is
s
tu
d
y
ad
d
r
es
s
es
th
e
ch
allen
g
in
g
p
r
o
b
lem
s
o
f
p
o
wer
co
u
p
lin
g
a
n
d
i
n
tr
icate
d
ec
o
u
p
lin
g
in
th
e
co
n
tex
t
o
f
a
th
r
ee
-
p
h
ase
g
r
id
-
c
o
n
n
ec
ted
in
v
er
ter
'
s
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
Op
timiz
ed
co
n
tr
o
l str
a
teg
y
fo
r
a
th
r
ee
-
p
h
a
s
e
g
r
id
co
n
n
ec
ted
in
ve
r
ter u
s
in
g
…
(
N
a
g
a
s
r
id
h
a
r
A
r
is
e
)
791
d
-
q
c
o
o
r
d
in
ate
s
y
s
tem
[
5
]
.
T
h
e
g
ain
s
o
f
th
e
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
(
PI)
co
n
t
r
o
ller
s
ar
e
i
m
p
r
o
v
e
d
u
tili
zin
g
a
g
en
etic
alg
o
r
ith
m
(
GA)
th
r
o
u
g
h
an
ad
ap
tiv
e
o
n
lin
e
tu
n
in
g
p
r
o
ce
d
u
r
e
to
g
u
ar
a
n
tee
th
e
a
d
ap
t
ab
ilit
y
an
d
ef
f
icac
y
o
f
th
e
co
n
tr
o
l
s
y
s
tem
[
6
]
.
An
e
x
ter
n
al
p
o
we
r
lo
o
p
an
d
an
in
te
r
n
al
cu
r
r
e
n
t
co
n
t
r
o
l
lo
o
p
,
b
o
th
im
p
lem
en
ted
u
s
in
g
cu
s
to
m
ar
y
PI
ty
p
e
co
n
tr
o
ller
s
,
ar
e
two
cr
u
cial
p
ar
ts
o
f
th
e
s
u
g
g
ested
co
n
tr
o
l m
eth
o
d
[
7
]
.
T
h
e
p
o
wer
g
en
e
r
ated
tr
av
els
v
ia
a
th
r
ee
-
p
h
ase
in
v
er
t
er
o
n
its
way
f
r
o
m
g
en
er
atio
n
to
co
n
s
u
m
p
tio
n
,
o
p
er
atin
g
in
a
cc
o
r
d
an
ce
with
th
e
DQ
p
r
in
cip
le
to
en
s
u
r
e
s
m
o
o
th
co
m
m
u
n
icatio
n
with
th
e
g
r
id
.
T
h
is
in
teg
r
atio
n
n
o
t
o
n
ly
m
ak
e
s
it
ea
s
ier
to
ex
p
o
r
t
ex
ce
s
s
en
er
g
y
,
b
u
t
it
also
d
ea
ls
with
th
e
cr
u
cial
p
r
o
b
lem
o
f
p
o
o
r
p
o
wer
q
u
ality
,
w
h
ich
c
an
d
ev
elo
p
in
s
u
ch
in
tr
icate
s
y
s
tem
s
[
8
]
.
T
h
ese
co
n
tr
o
l
tech
n
iq
u
es'
m
ain
g
o
al
is
t
o
s
m
o
o
th
ly
tr
an
s
f
er
all
ac
tiv
e
p
o
wer
p
r
o
d
u
ce
d
b
y
non
-
r
e
n
ewa
b
le
s
o
u
r
ce
s
in
to
t
h
e
g
r
i
d
u
tili
ty
wh
ile
m
ain
tai
n
in
g
t
h
e
h
i
g
h
est
s
tan
d
ar
d
s
o
f
p
o
wer
q
u
ality
an
d
ac
h
iev
in
g
a
u
n
ity
p
o
wer
f
ac
t
o
r
[
9
]
.
T
h
is
p
a
p
er
n
o
t
o
n
ly
e
x
p
lai
n
s
th
e
c
o
m
p
lex
d
esig
n
o
f
th
e
c
o
n
tr
o
ller
b
u
t
also
g
o
es
in
to
g
r
ea
t
d
etail
o
n
h
o
w
it
is
im
p
lem
e
n
ted
an
d
ev
alu
ates
h
o
w
well
it
wo
r
k
s
u
s
in
g
a
n
u
m
b
er
o
f
s
im
u
latio
n
s
[
1
0
]
.
T
h
e
v
o
ltag
e
s
o
u
r
ce
i
n
v
er
ter
(
VSI
)
th
at
p
o
wer
s
th
e
DVR
u
s
es
two
PI
c
o
n
tr
o
ller
s
t
o
ca
r
e
f
u
lly
co
n
tr
o
l
th
e
in
s
u
lated
g
ate
b
ip
o
lar
tr
a
n
s
is
to
r
(
I
GB
T
)
p
u
ls
es.
T
h
ese
c
o
n
tr
o
ller
s
ac
co
m
p
lis
h
th
is
b
y
f
in
e
-
tu
n
in
g
th
e
D
-
Q
ax
is
v
o
ltag
e
s
ig
n
als,
with
ea
c
h
co
n
t
r
o
ller
h
an
d
lin
g
a
s
in
g
le
ax
is
co
m
p
o
n
en
t
o
f
th
e
lo
a
d
v
o
ltag
e
as
in
p
u
t
an
d
o
u
tp
u
t
[
1
1
]
.
A
DC
-
lin
k
v
o
ltag
e
co
n
tr
o
l
lo
o
p
u
s
in
g
a
PI
co
n
tr
o
l
ler
is
ca
s
ca
d
ed
with
an
in
ter
n
al
cu
r
r
en
t
lo
o
p
u
s
in
g
PI
an
d
p
r
o
p
o
r
tio
n
al
-
r
eso
n
an
t
(
PR
)
co
n
tr
o
ller
s
i
n
th
e
s
u
g
g
e
s
ted
to
p
o
lo
g
y
.
Fo
r
n
o
n
-
r
e
n
ewa
b
le
s
y
s
tem
s
,
th
ese
co
n
tr
o
l
tech
n
i
q
u
es
ar
e
f
r
e
q
u
en
tly
u
s
ed
in
a
v
ar
iety
o
f
r
ec
o
g
n
ized
r
ef
er
e
n
ce
f
r
am
es.
T
h
e
s
tead
y
-
s
tate
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
tem
was
d
eter
m
in
ed
b
y
ev
alu
atin
g
k
ey
p
e
r
f
o
r
m
an
ce
in
d
icato
r
s
,
s
u
ch
as
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
1
2
]
.
T
h
e
in
co
r
p
o
r
atio
n
o
f
m
icr
o
-
s
o
u
r
ce
s
in
to
m
icr
o
g
r
id
s
,
h
o
w
ev
er
,
also
p
r
esen
ts
d
if
f
icu
lties
,
p
ar
ticu
lar
ly
in
r
es
o
lv
in
g
p
r
o
b
lem
s
with
p
o
wer
q
u
ality
.
No
n
-
lin
ea
r
a
n
d
u
n
b
al
an
ce
d
lo
a
d
s
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
m
ig
h
t
ca
u
s
e
d
is
tu
r
b
an
ce
s
th
at
d
eg
r
a
d
e
t
h
e
m
icr
o
g
r
i
d
'
s
o
v
er
all
p
o
wer
q
u
ality
.
T
h
is
p
ap
er
ev
alu
ates
th
e
ef
f
icien
cy
o
f
th
e
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
(
VSI
)
to
p
o
l
o
g
y
a
n
d
s
u
g
g
ests
a
m
eth
o
d
f
o
r
im
p
r
o
v
in
g
s
tab
ilit
y
in
th
e
co
n
tex
t
o
f
cu
r
r
en
t
s
to
ch
asti
c
g
r
id
s
y
s
tem
s
b
y
em
p
lo
y
in
g
a
p
r
o
p
o
r
tio
n
al
-
in
t
eg
r
al
(
PI)
co
n
tr
o
ller
[
1
3
]
.
Po
wer
q
u
ality
is
s
u
es
in
s
m
ar
t
m
icr
o
g
r
id
n
etwo
r
k
s
ar
e
ca
u
s
ed
b
y
th
e
s
u
b
s
tan
tial
v
o
l
tag
e
v
ar
iatio
n
s
th
at
th
ese
g
r
id
s
y
s
tem
s
f
r
eq
u
e
n
tly
s
u
f
f
er
[
1
4
]
.
T
h
e
p
e
r
f
o
r
m
an
ce
o
f
th
ese
tech
n
i
q
u
es
is
th
en
c
ar
ef
u
lly
co
m
p
ar
ed
,
tak
in
g
in
to
ac
co
u
n
t
elem
en
ts
li
k
e
g
r
id
v
o
ltag
e
d
is
tu
r
b
an
c
e
r
ej
ec
tio
n
an
d
s
tab
ilit
y
u
n
d
e
r
v
ar
i
o
u
s
g
r
id
s
h
o
r
t
cir
cu
it
lev
els
[
1
5
]
.
Vo
ltag
e
s
tab
ilit
y
h
as
b
ee
n
s
ig
n
if
ican
tly
ch
allen
g
ed
b
y
th
e
r
ap
id
ex
p
an
s
io
n
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
n
o
tab
ly
s
o
lar
en
er
g
y
s
y
s
tem
s
co
n
n
ec
ted
to
lo
w
an
d
m
ed
iu
m
v
o
ltag
e
n
etwo
r
k
s
[
1
6
]
.
T
h
r
ee
cr
u
cial
p
er
f
o
r
m
an
ce
i
n
d
ices
ar
e
u
s
ed
to
ass
ess
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
s
u
g
g
ested
m
et
h
o
d
:
th
e
ele
ctr
ical
s
ig
n
al'
s
r
o
o
t
m
ea
n
s
q
u
a
r
e
(
R
MS)
v
alu
e,
to
t
al
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
an
d
v
o
ltag
e
s
ag
co
m
p
en
s
atio
n
[
1
7
]
-
[
1
9
]
.
T
h
e
f
o
r
m
o
f
a
m
o
d
u
lar
tr
a
n
s
f
o
r
m
e
r
less
g
r
id
-
co
n
n
ec
ted
p
h
o
t
o
v
o
ltaic
m
u
ltil
ay
er
in
v
er
te
r
,
a
n
o
v
el
ap
p
r
o
ac
h
is
p
r
esen
ted
in
th
is
wo
r
k
[
2
0
]
-
[
2
2
]
.
I
n
t
h
is
s
tu
d
y
,
we
i
n
d
ep
e
n
d
en
tly
s
et
lim
its
f
o
r
th
e
d
-
ax
is
an
d
q
-
ax
is
g
r
id
c
u
r
r
en
ts
u
s
in
g
a
th
o
r
o
u
g
h
n
o
n
lin
ea
r
clo
s
ed
-
lo
o
p
s
y
s
tem
an
aly
s
is
th
at
is
b
ased
o
n
i
n
p
u
t
-
to
-
s
tate
s
tab
ilit
y
th
eo
r
y
[
2
3
]
-
[
2
4
]
.
Ou
r
s
tu
d
y
'
s
s
im
u
latio
n
r
esu
lts
wi
ll
b
e
p
r
esen
ted
an
d
d
is
cu
s
s
ed
,
s
h
ed
d
in
g
lig
h
t
o
n
th
e
p
o
s
s
ib
ilit
ies
o
f
in
teg
r
ated
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
as a
s
u
s
tain
ab
le
an
d
f
o
r
war
d
-
th
i
n
k
in
g
s
tr
ateg
y
to
f
u
lf
il o
u
r
ex
p
a
n
d
in
g
en
e
r
g
y
n
ee
d
s
wh
ile
p
r
eser
v
in
g
o
u
r
p
lan
et'
s
v
u
ln
er
ab
le
ec
o
s
y
s
tem
s
[
2
5
]
.
2.
SYNCH
RO
NO
US R
E
F
E
RE
NCE F
RA
M
E
T
H
E
O
RY
I
n
F
ig
u
r
e
1
s
h
o
ws
P
-
Q
co
n
tr
o
l
s
ch
em
es
o
f
a
th
r
ee
-
p
h
ase
g
r
id
co
n
n
ec
ted
in
v
e
r
ter
in
a
m
icr
o
g
r
id
.
I
n
F
ig
u
r
e
1
,
L
f
s
tan
d
s
f
o
r
th
e
eq
u
i
v
alen
t
in
d
u
ctan
ce
o
f
t
h
e
L
C
f
il
ter
,
R
f
is
th
e
e
q
u
iv
ale
n
t
r
esis
tan
ce
o
f
th
e
L
C
f
ilter
,
an
d
Vd
c
is
th
e
DC
v
o
ltag
e
s
u
p
p
lied
b
y
a
d
is
tr
ib
u
tio
n
g
en
e
r
atio
n
u
n
it.
C
d
an
d
C
f
ar
e
th
e
ca
p
ac
itan
ce
o
f
th
e
DC
s
id
e
an
d
th
e
L
C
f
ilter
,
r
esp
ec
ti
v
ely
.
T
h
e
g
r
id
-
s
id
e
v
o
ltag
e
,
a
c
u
r
r
en
t
a
n
d
p
h
ase
d
etec
to
r
,
an
i
n
v
er
ter
-
s
id
e
v
o
ltag
e
an
d
cu
r
r
en
t
d
etec
to
r
,
a
ca
lcu
latio
n
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
,
an
ac
tiv
e
p
o
wer
PI
co
n
tr
o
ll
er
,
a
r
ea
ctiv
e
p
o
wer
PI
co
n
tr
o
ller
,
a
cu
r
r
e
n
t
PI
co
n
tr
o
ller
,
ab
c/d
q
an
d
d
q
/ab
c
tr
an
s
f
o
r
m
atio
n
s
,
an
d
s
p
ac
e
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SVPW
M)
ar
e
th
e
k
ey
o
p
er
atio
n
s
th
at
m
a
k
e
u
p
th
e
P
-
Q
co
n
tr
o
l sch
em
e.
A
co
n
tr
o
l m
eth
o
d
u
s
ed
i
n
pow
er
elec
tr
o
n
ics
to
m
an
a
g
e
th
e
f
lo
w
o
f
elec
tr
ical
en
e
r
g
y
b
etwe
en
a
m
icr
o
g
r
id
(
a
lo
c
alize
d
co
llectio
n
o
f
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
)
an
d
th
e
p
r
im
ar
y
u
tili
ty
g
r
id
is
k
n
o
wn
as
th
e
P
-
Q
c
o
n
tr
o
l
s
y
s
t
em
o
f
a
th
r
ee
-
p
h
ase
g
r
id
-
co
n
n
ec
ted
in
v
er
ter
.
T
h
e
ac
tiv
e
p
o
wer
(
P)
an
d
r
ea
ctiv
e
p
o
wer
(
Q)
ex
ch
a
n
g
ed
b
etwe
en
th
e
u
tili
ty
g
r
id
an
d
th
e
m
icr
o
g
r
id
a
r
e
th
e
two
m
ai
n
p
ar
am
eter
s
th
at
ar
e
th
e
s
u
b
je
ct
o
f
th
is
co
n
tr
o
l sch
em
e'
s
atte
n
tio
n
.
An
o
v
e
r
v
iew
o
f
th
e
P
-
Q
co
n
tr
o
l te
ch
n
iq
u
e
i
s
p
r
o
v
id
ed
b
elo
w:
-
Activ
e
p
o
wer
c
o
n
tr
o
l
(
P):
T
h
e
ac
tu
al
wo
r
k
ca
r
r
ied
o
u
t
b
y
el
ec
tr
ical
en
er
g
y
is
r
ef
e
r
r
ed
to
a
s
ac
tiv
e
p
o
wer
,
also
k
n
o
wn
as
r
ea
l
p
o
wer
.
T
h
e
P
co
n
tr
o
l
in
a
m
icr
o
g
r
i
d
m
a
k
e
s
s
u
r
e
th
at
th
e
in
v
e
r
ter
ca
n
co
n
tr
o
l
th
e
tr
an
s
f
er
o
f
ac
tu
al
p
o
wer
with
th
e
u
tili
ty
g
r
id
.
T
h
e
in
v
e
r
ter
m
o
d
if
ies
its
o
u
tp
u
t
to
d
eliv
er
ac
tiv
e
p
o
wer
to
th
e
m
icr
o
g
r
id
wh
en
th
e
m
icr
o
g
r
i
d
n
ee
d
s
to
im
p
o
r
t
p
o
wer
(
f
o
r
in
s
tan
c
e,
d
u
r
in
g
a
d
ef
icit)
.
On
th
e
o
th
e
r
h
an
d
,
th
e
in
v
er
te
r
ca
n
ex
p
o
r
t
ex
tr
a
elec
tr
icity
to
t
h
e
u
tili
ty
g
r
i
d
wh
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I
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2
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SYST
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F
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R
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r
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d
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ts
3
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p
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ase
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p
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ase
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b
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α
a
n
d
β
c
u
r
r
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ts
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k
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tr
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s
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m
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s
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tr
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e
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f
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tr
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ter
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it c
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to
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p
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co
m
p
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n
ts
.
3
.
1
.
P
I
co
ntr
o
ller
Gr
id
in
v
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ter
s
an
d
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th
er
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t
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l
s
y
s
tem
s
f
r
eq
u
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tly
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s
e
th
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p
r
o
p
o
r
tio
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al
-
in
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g
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al
(
PI
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c
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n
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r
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ller
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a
co
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tr
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h
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m
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c
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n
tr
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ller
is
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r
eq
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n
tly
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th
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tex
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o
f
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ter
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tr
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l
th
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tr
icity
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win
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d
th
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g
r
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ce
er
r
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r
s
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d
k
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p
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u
tp
u
t th
at
is
ac
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ate
an
d
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s
is
ten
t,
it m
ak
es u
s
e
o
f
b
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p
r
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p
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r
tio
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an
d
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r
a
l c
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m
p
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n
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co
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tr
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m
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t b
e
p
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p
er
ly
tu
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ed
to
wo
r
k
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b
est u
n
d
e
r
v
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u
s
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atin
g
s
ettin
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s
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d
g
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s
.
-
Pro
p
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tio
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co
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p
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n
t
(
P):
T
h
e
cu
r
r
en
t
e
r
r
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r
,
o
r
t
h
e
d
is
cr
ep
an
cy
b
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h
e
p
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n
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etp
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t
an
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th
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tu
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p
r
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ce
s
s
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ar
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is
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t th
e
p
r
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p
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tio
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co
m
p
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n
e
n
t
o
f
th
e
co
n
tr
o
ller
r
ea
cts to
.
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t a
t
tem
p
ts
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less
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th
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er
r
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b
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p
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d
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t th
at
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p
r
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p
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tio
n
ate
to
th
e
e
r
r
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r
.
T
h
e
m
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g
n
itu
d
e
o
f
th
is
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s
e
d
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p
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p
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(
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.
-
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co
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p
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(
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co
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p
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n
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s
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tead
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s
tate
o
r
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g
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ter
m
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r
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s
b
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ac
c
u
m
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l
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g
th
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p
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r
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tim
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t
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cr
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r
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r
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s
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in
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Ho
w
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r
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th
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co
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d
s
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in
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g
ain
(
Ki)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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o
v
id
ed
b
y
th
e
s
o
u
r
ce
,
an
d
lo
ad
b
alan
cin
g
is
ac
co
m
p
lis
h
ed
.
T
h
r
o
u
g
h
b
alan
cin
g
th
e
s
o
u
r
ce
r
ef
er
e
n
ce
cu
r
r
e
n
t.
R
ef
er
en
ce
s
o
u
r
ce
cu
r
r
en
t
u
s
ed
to
d
eter
m
in
e
wh
en
th
e
DSTA
T
C
OM
will
s
witch
on
th
e
lo
ad
cu
r
r
en
t
ac
t
u
ally
h
as
a
f
u
n
d
a
m
en
tal
f
r
eq
u
e
n
cy
c
o
m
p
o
n
e
n
t
wh
er
e
b
y
t
h
ese
ap
p
r
o
ac
h
es
ar
e
u
s
ed
t
o
ex
tr
ac
ted
b
y
ANFI
S
co
n
tr
o
ller
.
I
R
P
th
eo
r
y
is
b
ased
o
n
th
e
ca
l
cu
latio
n
o
f
in
s
tan
tan
e
o
u
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
in
th
e
-
f
r
am
e
an
d
th
e
tr
an
s
f
er
o
f
th
r
ee
-
p
h
ase
q
u
a
n
titi
es
to
two
-
p
h
ase
q
u
a
n
titi
es
[
3
]
,
[
4
]
.
Fig
u
r
es
2
d
is
p
lay
s
a
b
l
o
ck
d
iag
r
am
o
f
th
e
r
ef
er
en
ce
e
x
tr
ac
tio
n
o
f
u
s
in
g
ANFI
S
co
n
tr
o
ller
with
I
R
P
th
e
o
r
y
.
He
co
n
tr
o
ller
r
ec
eiv
es
s
en
s
ed
in
p
u
ts
VR
,
VY,
an
d
VB
as
well
as
iLR,
iLY
,
an
d
iLB.
T
h
ese
q
u
an
titi
es
ar
e
th
e
n
p
r
o
ce
s
s
ed
to
cr
ea
te
r
ef
er
e
n
ce
cu
r
r
e
n
t
co
m
m
a
n
d
s
(
iSR
,
iS
Y,
an
d
iSB
)
,
wh
ich
ar
e
th
en
f
ed
to
a
h
y
s
ter
esis
-
b
ased
p
u
ls
e
wid
th
modu
lated
(
PW
M)
s
ig
n
al
g
en
er
ato
r
(
s
h
o
wn
in
Fig
u
r
e
2
)
t
o
p
r
o
d
u
c
e
f
in
al
s
witch
in
g
s
ig
n
als f
ed
to
th
e
DSTA
T
C
OM
.
T
h
e
s
y
s
tem
o
f
th
e
v
o
ltag
es
is
g
iv
en
b
y
(
1
)
.
=
(
)
=
(
−
2
3
)
=
(
−
4
3
)
(
1
)
T
h
e
lo
ad
c
u
r
r
en
ts
ar
e
s
h
o
wn
i
n
(
2
)
.
=
∑
{
(
=
1
)
−
}
=
∑
{
(
−
2
3
)
−
}
=
∑
{
−
4
3
)
−
}
(
2
)
T
h
e
R
,
Y,
an
d
B
ax
es
ar
e
f
ix
e
d
o
n
th
e
s
am
e
p
lan
e
an
d
s
p
ac
e
d
o
u
t
b
y
2
/3
in
R
-
Y
-
B
co
o
r
d
in
at
es.
T
h
e
"R"
ax
is
i
s
th
e
lo
ca
tio
n
o
f
th
e
in
s
tan
tan
eo
u
s
s
p
ac
e
v
ec
to
r
s
VR
an
d
iLR,
wh
o
s
e
am
p
litu
d
es
ch
a
n
g
e
with
tim
e
in
b
o
th
p
o
s
itiv
e
an
d
n
e
g
ativ
e
d
ir
ec
tio
n
s
.
T
h
is
lik
ewis
e
ap
p
lies
to
th
e
o
th
er
two
p
h
ases
.
Usi
n
g
C
lar
k
'
s
tr
an
s
f
o
r
m
atio
n
,
th
ese
p
h
aso
r
s
ca
n
b
e
co
n
v
er
ted
in
t
o
-
co
o
r
d
in
ates a
s
s
h
o
wn
in
(
3
)
an
d
(
4
)
.
[
]
=
√
2
3
(
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
)
[
]
(
3
)
[
]
=
√
2
3
(
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
)
[
]
(
4
)
W
h
er
e
α
an
d
β ar
e
o
r
th
o
g
o
n
al
co
o
r
d
in
ates.
T
h
e
p
o
we
r
o
f
c
o
n
v
en
tio
n
al
is
d
ef
in
e
d
as
(
5
)
,
=
+
(
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.
1
3
,
No
.
4
,
Dec
em
b
er
20
2
4
:
7
9
0
-
797
794
wh
er
e
p
eq
u
als th
e
s
tan
d
ar
d
e
q
u
atio
n
as sh
o
wn
i
n
(
6
)
.
=
+
+
(
6
)
S
im
ilar
ly
,
th
e
I
R
P q
is
d
ef
in
ed
b
y
(
7
)
.
=
−
+
(
7
)
A
ctiv
e
an
d
r
ea
l p
o
wer
ca
n
b
e
wr
itten
as
(
8
)
.
[
]
=
(
−
)
[
]
(
8
)
To
f
in
d
th
e
cu
r
r
en
ts
,
r
ef
e
r
to
(
9
)
,
[
]
=
1
(
−
)
[
]
(
9
)
w
h
er
e
is
d
ef
in
ed
as sh
o
wn
in
(
1
0
)
.
=
2
+
2
(
1
0
)
I
t
is
p
o
s
s
ib
le
to
s
ep
ar
ate
th
e
in
s
tan
tan
eo
u
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
p
an
d
q
in
t
o
an
o
s
cillato
r
y
an
d
a
n
av
er
ag
e
(
DC
)
co
m
p
o
n
e
n
t.
=
+
̃
q
q
q
=+
(
1
1
)
T
h
e
r
ef
e
r
en
ce
o
f
cu
r
r
e
n
ts
in
R
,
Y
,
an
d
B
co
o
r
d
in
ates
u
s
in
g
r
e
v
er
s
e
C
lar
k
’
s
tr
an
s
f
o
r
m
atio
n
a
s
d
escr
ib
ed
in
(
1
2
)
.
[
∗
∗
]
=
1
(
−
−
)
[
0
]
(
1
2
)
T
h
e
th
r
ee
p
h
ase
cu
r
r
e
n
ts
o
f
R
,
Y
,
an
d
B
ar
e
s
h
o
w
n
in
(
1
3
)
,
[
∗
∗
∗
]
=
√
2
3
(
1
√
2
1
0
1
√
2
−
1
2
√
3
2
1
√
2
−
1
2
−
√
3
2
)
[
0
∗
∗
∗
]
(
1
3
)
w
h
er
e
0
∗
is
th
e
ze
r
o
-
s
eq
u
en
ce
c
o
m
p
o
n
e
n
t
.
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
h
e
F
ig
u
r
e
3
s
h
o
ws
it
is
a
s
u
p
p
ly
v
o
ltag
e
f
r
o
m
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
th
at
m
ea
n
s
we
g
i
v
e
a
s
u
p
p
ly
f
r
o
m
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
c
es
to
g
r
id
th
r
o
u
g
h
th
r
ee
p
h
ase
in
v
er
ter
s
.
I
n
v
e
r
ter
co
n
v
er
ts
DC
to
AC
.
Vo
ltag
e.
T
h
e
b
elo
w
f
ig
u
r
e
s
u
p
p
ly
v
o
lt
ag
e
p
ea
k
v
o
ltag
e
is
6
0
0
V
is
s
u
p
p
lied
v
o
ltag
e,
R
,
Y
,
an
d
B
p
h
ase
s
h
o
u
ld
b
e
am
p
litu
d
e
is
a
6
0
0
V.
T
h
e
p
h
a
s
e
s
h
if
t b
etwe
en
th
r
ee
p
h
ases
s
h
o
u
ld
b
e
at
1
2
0
d
e
g
r
ee
s
ap
ar
t.
An
d
th
e
b
elo
w
t
h
e
s
u
p
p
ly
cu
r
r
en
t
is
s
h
o
wn
f
i
g
u
r
e
.
At
th
e
s
tar
tin
g
cu
r
r
en
t
th
e
f
lu
ctu
atio
n
s
ar
e
o
cc
u
r
r
ed
at
0
to
0
.
0
1
s
ec
af
ter
0
.
0
1
s
ec
th
e
cu
r
r
en
ts
will
co
n
tin
u
e
with
o
u
t
f
lu
ctu
atio
n
with
h
elp
o
f
L
C
L
f
ilter
an
d
PI
co
n
tr
o
ller
.
T
h
e
s
u
p
p
ly
cu
r
r
e
n
t
will
ch
an
g
e
with
h
elp
o
f
co
n
t
r
o
l
s
ch
em
es
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
e
n
t
c
o
n
tr
o
l
s
ch
em
es.
I
f
we
k
ee
p
2
0
5
at
Activ
e
cu
r
r
en
t
an
d
r
ea
ctiv
e
cu
r
r
en
t
is
0
th
e
cu
r
r
en
t
s
tar
t
f
r
o
m
0
an
d
th
e
am
p
litu
d
e
o
f
c
u
r
r
en
t
is
2
0
5
A.
An
d
if
we
k
ee
p
ac
tiv
e
cu
r
r
en
t
0
an
d
r
ea
ctiv
e
cu
r
r
en
t is 1
5
0
th
e
n
g
r
a
p
h
s
tar
t a
t n
eg
ativ
e
a
n
d
am
p
litu
d
e
is
1
5
0
A.
T
h
e
Fig
u
r
e
4
s
h
o
ws
th
e
ac
tiv
e
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
.
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
f
r
o
m
t
h
e
s
u
p
p
l
y
.
Fro
m
Fig
u
r
e
4
p
o
wer
s
f
r
o
m
0
to
clo
s
e
0
.
0
2
s
ec
wil
l
co
n
s
tan
t
an
d
af
ter
0
.
0
2
will
g
et
s
in
u
s
o
id
al
wav
e
f
o
r
m
o
f
th
r
ee
p
h
ase.
T
h
e
R
ea
ctiv
e
p
o
wer
af
ter
0
.
0
2
s
ec
wi
ll
f
lo
w
u
p
an
d
m
o
v
e
c
o
n
s
tan
t
till
en
d
an
d
R
an
d
Y
p
h
ases
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
Op
timiz
ed
co
n
tr
o
l str
a
teg
y
fo
r
a
th
r
ee
-
p
h
a
s
e
g
r
id
co
n
n
ec
ted
in
ve
r
ter u
s
in
g
…
(
N
a
g
a
s
r
id
h
a
r
A
r
is
e
)
795
will
g
et
p
ea
k
b
ec
a
u
s
e
o
f
PI
co
n
tr
o
ller
.
T
h
e
Fig
u
r
e
5
is
an
i
n
v
er
ter
cu
r
r
en
t.
T
h
e
in
v
er
ter
a
n
d
s
u
p
p
ly
cu
r
r
e
n
t
ar
e
s
am
e.
T
h
e
am
p
litu
d
e
o
f
cu
r
r
en
t
is
co
n
tr
o
lled
b
y
t
h
e
c
u
r
r
en
t
c
o
n
tr
o
l
s
ch
em
es.
At
th
e
s
tar
tin
g
th
e
p
h
ases
ar
e
g
et
f
lu
ctu
atio
n
s
af
ter
it c
o
n
tin
u
es
with
o
u
t f
lu
ctu
atio
n
s
.
Fig
u
r
e
3
.
Su
p
p
ly
c
u
r
r
en
t a
n
d
s
u
p
p
ly
v
o
ltag
e
with
r
esp
ec
t to
tim
e
Fig
u
r
e
4
.
Activ
e
a
n
d
r
ea
ctiv
e
p
o
wer
with
r
esp
ec
t to
tim
e
Fig
u
r
e
5
.
I
n
v
er
te
r
cu
r
r
en
t w
ith
r
esp
ec
t to
tim
e
5.
CO
NCLU
SI
O
N
I
n
c
o
n
clu
s
io
n
,
a
th
r
ee
-
p
h
ase
g
r
id
-
co
n
n
ec
ted
i
n
v
er
ter
u
s
in
g
a
n
o
p
tim
al
co
n
tr
o
l
s
tr
ateg
y
in
cl
u
d
in
g
a
P
I
co
n
tr
o
ller
an
d
th
e
d
ir
ec
t
-
q
u
a
d
r
atu
r
e
(
DQ
)
f
r
am
e
o
f
f
er
s
a
r
eliab
le
an
d
ef
f
ec
tiv
e
s
o
lu
tio
n
f
o
r
c
o
n
tem
p
o
r
ar
y
p
o
wer
g
r
id
in
te
g
r
atio
n
.
W
ith
th
e
h
el
p
o
f
th
is
s
o
p
h
is
ticated
co
n
tr
o
l
s
y
s
tem
,
v
o
ltag
e
an
d
c
u
r
r
en
t
wav
ef
o
r
m
s
m
a
y
b
e
p
r
ec
is
ely
r
eg
u
lated
,
r
esu
ltin
g
in
s
m
o
o
th
co
m
m
u
n
icatio
n
b
et
wee
n
u
tili
ty
g
r
id
s
an
d
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
lik
e
s
o
lar
o
r
win
d
tu
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Evaluation Warning : The document was created with Spire.PDF for Python.