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[
1
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e
n
th
e
f
r
eq
u
e
n
c
y
a
n
d
p
h
ase
ar
e
d
etec
ted
.
Fo
r
th
is
,
a
b
ig
a
m
o
u
n
t
o
f
s
t
u
d
ies
h
as
b
e
en
ca
r
r
ied
o
u
t
in
t
h
is
ar
ea
i
n
o
r
d
er
to
d
is
co
v
er
a
s
o
lu
tio
n
to
th
is
f
ac
t,
as
m
a
y
b
e
f
o
u
n
d
in
[
1
0
ā
1
4
]
,
th
e
m
o
s
t
o
f
th
e
m
s
h
o
w
i
n
g
a
p
er
s
p
ec
tiv
e
o
f
h
o
w
to
s
o
lv
e
th
i
s
is
s
u
e
w
h
e
n
t
h
e
d
etec
tio
n
o
f
t
h
e
f
r
eq
u
en
c
y
is
co
n
d
u
cted
.
2.
G
RI
D
CO
NNE
CT
E
D
P
H
O
T
O
VO
L
T
AIC
SYS
T
E
M
th
is
p
ap
er
f
o
cu
s
e
s
o
n
f
o
r
P
h
o
to
v
o
ltaic
g
r
id
-
co
n
n
ec
ted
s
y
s
te
m
s
is
to
co
n
tr
o
l
th
e
p
o
w
er
f
lo
w
b
et
w
ee
n
th
e
p
r
i
m
ar
y
r
e
n
e
w
ab
le
en
er
g
y
s
o
u
r
ce
an
d
th
e
u
tili
t
y
g
r
id
[
1
7
]
,
in
ad
d
itio
n
to
th
e
p
o
w
er
f
a
cto
r
o
f
th
e
in
v
er
ter
-
g
r
id
co
n
n
ec
tio
n
w
it
h
h
ig
h
p
o
w
er
q
u
al
it
y
[
1
8
]
.
T
h
e
p
o
w
er
co
n
d
itio
n
er
s
h
o
u
ld
g
u
ar
an
tee
th
e
m
a
x
i
m
u
m
ef
f
icien
c
y
b
y
i
n
j
ec
tin
g
t
h
e
m
ax
i
m
u
m
a
v
ailab
le
p
o
w
er
at
t
h
e
P
h
o
to
v
o
ltaic
m
o
d
u
le,
also
b
y
co
n
tr
o
lli
n
g
t
h
e
p
o
w
er
f
ac
to
r
o
f
t
h
e
i
n
v
er
ter
g
r
id
co
n
n
ec
t
io
n
i
n
a
f
o
u
r
q
u
ad
r
an
t
o
p
er
atio
n
,
th
e
la
s
t
m
ak
e
s
u
s
e
o
f
th
e
in
s
ta
n
ta
n
eo
u
s
r
ea
cti
v
e
p
o
w
er
th
eo
r
y
[
1
9
]
f
o
r
3
p
h
ase
s
y
s
te
m
s
w
h
ic
h
e
n
ab
le
t
h
e
co
n
tr
o
l
o
f
th
e
in
s
ta
n
ta
n
eo
u
s
act
iv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
s
in
d
ec
o
u
p
led
d
ā
q
ax
es
[
2
0
]
.
T
h
e
g
en
er
al
3
p
h
ase
P
h
o
to
v
o
lt
aic
g
r
id
co
n
n
ec
te
d
s
y
s
te
m
ca
n
b
e
d
iv
id
ed
in
to
t
w
o
s
u
b
s
y
s
te
m
s
[
1
8
]
,
th
e
co
n
tr
o
l
an
d
th
e
p
o
w
er
s
u
b
s
y
s
t
e
m
s
,
w
h
o
s
e
b
lo
ck
d
iag
r
a
m
s
ar
e
d
ep
icted
in
Fi
g
u
r
e
1
.
I
n
th
e
p
r
esen
t
s
t
u
d
y
,
t
h
e
p
o
w
er
co
n
v
er
ter
o
f
th
e
P
h
o
to
v
o
ltaic
s
y
s
te
m
s
h
o
w
n
i
n
Fi
g
u
r
e
1
w
o
r
k
s
i
n
in
v
er
ter
m
o
d
e
(
3
p
h
ase
Vo
lta
g
e
So
u
r
ce
I
n
v
er
ter
(
VSI
)
)
f
o
r
it
d
eliv
er
s
all
t
h
e
in
co
m
i
n
g
p
o
w
er
f
r
o
m
t
h
e
P
V
g
en
er
ato
r
i
n
to
th
e
3
-
p
h
ase
u
ti
lit
y
g
r
id
,
ev
e
n
th
o
u
g
h
a
n
o
p
p
o
s
ite
p
o
w
er
f
lo
w
is
also
p
o
s
s
ib
le
(
r
ec
tif
ier
m
o
d
e)
,
b
ein
g
ca
p
ab
le
to
f
ee
d
lo
ca
l d
c
lo
ad
s
f
r
o
m
th
e
u
til
it
y
g
r
id
.
3.
P
O
WE
R
SUB
SY
ST
E
M
T
h
e
p
o
w
er
s
u
b
s
y
s
te
m
is
f
o
r
m
ed
b
y
th
e
P
h
o
to
v
o
ltaic
m
o
d
u
l
es,
a
co
n
v
er
ter
co
n
tr
o
ller
b
y
MP
PT
,
an
d
in
v
er
ter
a
n
d
th
e
L
C
L
f
ilter
.
en
s
u
i
n
g
,
a
b
r
ief
d
esc
r
ip
tio
n
o
f
ea
ch
b
lo
ck
is
d
ev
elo
p
ed
.
3
.
1
P
ho
t
o
v
o
lt
a
ic
m
o
du
le
s
th
e
P
h
o
to
v
o
ltaic
m
o
d
u
le
s
ar
e
th
e
ai
m
p
ar
t
o
f
a
P
V
s
y
s
tem
[
2
1
]
.
T
h
er
e
ar
e
v
ar
io
u
s
k
i
n
d
s
o
f
P
V
m
o
d
u
le
tech
n
o
lo
g
ie
s
w
ith
d
if
f
er
en
t
lev
els
o
f
e
f
f
icien
c
ies
[
1
]
-
[
2
2
]
.
T
h
e
f
u
n
ctio
n
o
f
a
P
h
o
to
v
o
ltaic
m
o
d
u
le
is
to
s
u
p
p
l
y
th
e
n
ec
es
s
ar
y
p
o
w
er
f
o
r
th
e
r
en
e
w
ab
le
g
r
id
co
n
n
ec
ted
s
y
s
te
m
,
an
d
it
w
ill
d
ep
en
d
o
f
th
e
te
m
p
er
at
u
r
e
an
d
th
e
av
ailab
le
s
o
lar
ir
r
ad
ian
ce
[
2
3
]
,
s
ig
n
if
y
w
h
ile
its
s
iz
e
(
ar
r
an
g
e
o
f
p
ar
allel
-
s
er
ies
P
V
ce
lls
)
w
ill
d
ep
en
d
o
f
th
e
r
eq
u
ir
ed
p
o
w
er
o
f
t
h
e
p
h
o
to
v
o
ltaic
s
y
s
te
m
[
2
4
]
.
3
.
2
T
he
co
nv
er
t
er
co
ntr
o
ller
by
M
P
P
T
th
e
b
o
o
s
t c
o
n
v
er
ter
is
u
s
ed
n
o
t o
n
l
y
to
u
p
li
f
t t
h
e
P
h
o
to
v
o
ltaic
ar
r
ay
o
u
tp
u
t
v
o
ltag
e,
b
u
t a
l
s
o
to
r
ea
lize
P
er
tu
r
b
an
d
Ob
s
er
v
e
(
P
&
O)
s
ch
e
m
e
i
n
Ma
x
i
m
u
m
P
o
w
e
r
P
o
in
t
T
r
ac
k
in
g
(
MP
PT
)
.
T
h
e
b
o
o
s
t
co
n
v
er
ter
co
n
n
ec
ted
to
P
h
o
to
v
o
lta
ic
ar
r
ay
,
f
o
r
ev
er
w
o
r
k
s
i
n
a
co
n
ti
n
u
o
u
s
c
u
r
r
en
t
m
o
d
e
a
n
d
t
h
e
c
u
r
r
en
t r
ip
p
le
is
r
ed
u
ce
d
b
y
u
s
i
n
g
a
lar
g
e
v
a
lu
e
o
f
in
d
u
cto
r
.
A
lo
w
v
al
u
e
o
f
ca
p
ac
ito
r
at
o
u
tp
u
t a
cts a
s
f
i
lter
.
3
.
3
T
he
inv
er
t
er
T
h
e
w
o
r
k
o
f
t
h
e
i
n
v
er
ter
,
p
r
in
cip
all
y
b
u
ilt
w
it
h
s
e
m
i
-
co
n
d
u
cto
r
elec
tr
o
n
ic
d
ev
ices
[
9
]
(
I
GB
T
s
an
d
d
io
d
es),
is
to
co
n
v
er
t
th
e
g
e
n
er
ated
d
c
v
o
ltag
e
in
to
ap
p
r
o
p
r
iate
ac
cu
r
r
en
ts
to
b
e
f
ed
in
t
o
th
e
3
p
h
ase
lo
w
v
o
ltag
e
u
tili
t
y
g
r
id
[
7
,
9
]
.
Pu
ls
e
w
id
t
h
m
o
d
u
latio
n
(
P
MW
)
an
d
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
S
VM
)
[
2
5
]
tech
n
iq
u
es
ar
e
u
tili
ze
d
to
co
n
t
r
o
l
th
e
g
ate
s
i
g
n
al
s
o
f
p
o
w
er
s
w
itc
h
es
ac
co
r
d
in
g
to
th
e
cu
r
r
en
t
r
e
f
er
en
ce
s
a
n
d
av
er
ag
ed
v
o
lta
g
e.
in
Fig
u
r
e
1
,
th
e
d
c
o
f
th
e
i
n
v
er
ter
ca
n
b
e
d
escr
ib
ed
as f
o
llo
w
s
:
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
a
m
o
f
t
h
e
p
o
w
er
a
n
d
co
n
t
r
o
l su
b
s
y
s
te
m
s
f
o
r
th
e
3
-
p
h
ase
g
r
id
-
co
n
n
e
cted
P
V
s
y
s
te
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ļ²
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
622
ā
630
624
ip
=
iclin
k
+
icc
icc
=
Su
.
iu
+
Sv
.
i
v
+
S
w
.
i
w
(
1
)
iclin
k
=
cc
lin
k
(
d
Vcc
/s
t)
P
p
v
=
ip
Vp
w
h
er
e
v
p
,
ip
ar
e
th
e
v
o
lta
g
e
an
d
th
e
o
u
tp
u
t
cu
r
r
e
n
t
o
f
t
h
e
P
h
o
to
v
o
ltaic
g
en
er
ato
r
,
r
esp
ec
tiv
el
y
,
P
P
V
is
th
e
av
ailab
le
p
o
w
er
f
o
r
a
s
p
ec
if
ic
ir
r
ad
ian
ce
,
Vcc
is
th
e
d
c
b
u
s
v
o
lta
g
e,
ic
lin
k
is
th
e
cu
r
r
en
t
th
r
o
u
g
h
th
e
lin
k
ca
p
ac
ito
r
C
clin
k
,
a
n
d
icc
i
s
t
h
e
cu
r
r
en
t
is
s
u
ed
to
t
h
e
3
p
h
as
e
VSI
(
w
h
ich
is
a
f
u
n
ctio
n
o
f
th
e
li
n
e
c
u
r
r
en
t
s
i
u
,
iv
,
i
w
a
n
d
t
h
e
s
tates
o
f
t
h
e
p
o
w
er
-
p
o
les
S
u
,
S
v
,
S
w
(
1
:
ā
o
n
ā
,
0
:
ā
o
f
f
ā
,
Si
-
u
p
p
er
p
o
le,
Sā
I
lo
w
er
p
o
le
i
n
t
h
e
3
p
h
ase
VSI
)
.
T
ak
in
g
i
n
to
ac
co
u
n
t
t
h
at
t
h
e
v
o
lta
g
e
i
n
th
e
ca
p
ac
ito
r
is
ap
p
r
o
x
im
ate
l
y
t
h
e
s
a
m
e
th
a
t
th
e
v
o
ltag
e
in
th
e
t
h
r
e
e
-
p
h
ase
u
tili
t
y
g
r
id
,
th
e
d
y
n
a
m
ic
in
t
h
e
ac
o
f
t
h
e
in
v
er
ter
ex
p
r
ess
ed
in
a
v
ec
to
r
w
a
y
is
as
f
o
llo
w
s
:
(
2
)
W
h
er
e
U
is
i
n
v
er
ter
v
o
lta
g
e,
i:
in
v
er
ter
li
n
e
c
u
r
r
en
t,
Uac
:
u
tili
t
y
g
r
id
v
o
ltag
e
s
p
ac
e
v
ec
t
o
r
s
,
L
:
th
e
lin
e
i
n
d
u
cta
n
ce
,
R
: r
esi
s
ta
n
ce
.
E
x
p
r
ess
i
n
g
t
h
e
la
s
t
v
ec
to
r
eq
u
atio
n
w
it
h
its
d
a
n
d
q
co
m
p
o
n
en
t
s
i
n
d
ā
q
ax
es
u
s
i
n
g
t
h
e
P
ar
k
v
ec
to
r
tr
an
s
f
o
r
m
atio
n
[
1
8
,
2
6
]
,
th
e
in
s
tan
ta
n
eo
u
s
ac
ti
v
e
p
o
w
er
(
p
)
an
d
th
e
in
s
ta
n
tan
eo
u
s
r
ea
cti
v
e
p
o
w
er
(
q
)
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
w
s
[
1
7
,
2
5
]
:
P
=
UA
C
d
id
+
U
A
C
q
iq
(
3
)
q
=
UA
C
d
id
-
U
AC
q
iq
(
4
)
W
h
er
e
U
AC
d
,
U
A
C
q
,
id
an
d
iq
ar
e
th
e
d
ā
q
co
m
p
o
n
e
n
ts
o
f
3
-
p
h
ase
v
o
lta
g
es
an
d
cu
r
r
en
t
s
,
r
esp
ec
tiv
el
y
,
a
llo
w
in
g
a
d
ec
o
u
p
led
co
n
tr
o
l
o
f
th
e
i
n
s
tan
ta
n
eo
u
s
ac
ti
v
e
an
d
r
ea
cti
v
e
p
o
w
er
s
if
v
ec
to
r
Uac
is
a
lig
n
ed
w
i
th
t
h
e
d
ax
i
s
(
UACq
=
0
)
.
3
.
4
L
CL
F
ilte
r
I
n
ad
d
itio
n
o
f
g
u
ar
an
tee
in
g
a
co
n
s
tan
t
p
o
w
er
d
eliv
er
y
to
th
e3
-
p
h
a
s
e
u
tili
t
y
g
r
id
,
r
en
e
w
a
b
le
ag
en
t
s
m
u
s
t
f
u
l
f
ill
t
h
e
p
o
w
er
q
u
alit
y
r
eg
u
latio
n
s
.
T
h
e
m
a
x
i
m
u
m
t
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
f
o
r
th
e
3
-
p
h
ase
cu
r
r
en
t
s
m
u
s
t
b
e
ar
o
u
n
d
5
%
[
2
8
]
ac
co
r
d
in
g
to
h
eter
o
n
o
r
m
ativ
e
[
6
,
2
9
]
,
w
h
er
ea
s
t
h
e
n
o
r
m
ati
v
e
f
o
r
th
e
lo
w
o
r
d
er
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
is
in
d
ee
d
m
o
r
e
r
estrictiv
e.
A
n
a
b
s
tr
ac
t
o
f
d
if
f
er
e
n
t
s
ta
n
d
ar
d
s
ab
o
u
t
p
o
w
er
q
u
ali
t
y
f
o
r
p
h
o
to
v
o
ltaic
s
y
s
te
m
s
ca
n
b
e
f
o
u
n
d
in
[
3
0
]
.
R
ip
p
les
ar
e
p
r
o
d
u
ce
d
in
th
e
o
u
tp
u
t
cu
r
r
en
t
s
o
f
th
e
in
v
er
ter
d
u
e
to
th
e
h
i
g
h
f
r
eq
u
e
n
c
y
co
m
m
u
t
atio
n
o
f
t
h
e
I
GB
T
s
,
m
ea
n
w
h
il
e
th
e
lo
w
o
r
d
er
h
ar
m
o
n
ic
s
ar
e
p
r
o
d
u
ce
d
b
y
n
o
n
-
lin
ea
r
lo
ad
s
.
T
h
e
g
o
o
d
s
o
lu
tio
n
f
o
r
co
r
r
ec
tin
g
t
h
e
h
ig
h
f
r
eq
u
en
c
y
r
ip
p
les is
b
y
u
t
ilizi
n
g
a
n
L
C
o
r
an
L
C
L
f
il
ter
in
th
e
ac
s
id
e
o
f
th
e
i
n
v
er
ter
[
3
1
]
.
3
.
5
E
M
I
f
ilte
r
I
n
a
g
r
id
-
co
n
n
ec
ted
r
en
e
w
ab
l
e
ag
e
n
t,
it
i
s
es
s
en
tial
to
ta
k
e
in
to
ac
co
u
n
t
t
h
e
h
ar
m
o
n
ic
p
o
l
lu
tio
n
d
u
e
to
th
e
E
lectr
o
m
a
g
n
et
ic
I
n
ter
f
e
r
en
ce
(
E
MI
)
.
T
h
ese
E
MI
s
ar
e
p
r
o
d
u
ce
d
b
y
th
e
co
m
m
u
tatio
n
o
f
s
e
m
ico
n
d
u
cto
r
elec
tr
o
n
ic
d
ev
ice
s
(
I
GB
T
s
an
d
d
io
d
es)
[
3
0
]
an
d
an
E
MI
f
ilter
is
r
eq
u
ir
ed
to
r
ed
u
ce
it.
T
h
er
e
ar
e
v
ar
io
u
s
m
et
h
o
d
o
lo
g
ies
to
d
es
ig
n
a
n
a
p
p
r
o
p
r
iate
E
MI
f
ilter
,
s
o
m
e
o
f
t
h
e
m
ar
e
f
o
u
n
d
ed
o
n
tr
ial
a
n
er
r
o
r
[
3
0
,
3
1
]
,
an
d
s
o
m
e
n
o
v
el
m
eth
o
d
o
lo
g
ies ar
e
cited
in
s
ev
er
al
p
u
b
lica
tio
n
s
,
i
n
clu
d
i
n
g
[
3
3
,
3
4
]
.
4.
CO
NT
RO
L
SUB
SYS
T
E
M
T
h
e
co
n
tr
o
l
s
u
b
s
y
s
te
m
i
s
f
o
r
m
ed
b
y
th
e
P
I
r
eg
u
lato
r
s
,
P
SD
s
y
n
ch
r
o
n
izatio
n
,
an
d
t
h
e
an
d
th
e
Uu
v
w
g
en
er
atio
n
.
4
.
1
P
I
Reg
ula
t
o
rs
r
eg
u
lato
r
s
T
h
e
i
m
p
le
m
en
ted
c
o
n
tr
o
l
s
tr
ateg
y
u
tili
ze
s
a
ca
s
ca
d
ed
co
n
tr
o
l:
an
o
u
ter
v
o
ltag
e
r
eg
u
lato
r
an
d
an
in
n
er
cu
r
r
en
t
r
eg
u
lato
r
.
T
h
is
co
n
tr
o
l
h
as
b
ee
n
p
er
f
o
r
m
ed
u
tili
z
in
g
P
I
co
n
tr
o
ller
s
[
1
7
]
:
th
e
o
u
ter
lo
o
p
r
eg
u
lato
r
co
m
p
ar
es
t
h
e
d
c
b
u
s
v
o
lta
g
e
i
n
th
e
l
in
k
ca
p
ac
ito
r
w
i
th
t
h
e
r
e
f
er
en
ce
w
h
ic
h
ar
r
iv
es
f
r
o
m
t
h
e
b
lo
c
k
Vd
c
r
eg
u
lato
r
k
ee
p
in
g
a
co
n
s
t
an
t
d
c
v
o
ltag
e
an
d
m
a
k
in
g
th
e
p
o
w
er
b
alan
ce
b
et
w
ee
n
th
e
P
h
o
to
v
o
ltaic
s
y
s
te
m
an
d
th
e
u
til
it
y
g
r
id
,
w
h
er
ea
s
th
e
in
n
er
co
n
tr
o
l
lo
o
p
u
tili
ze
s
t
w
o
co
n
tr
o
ller
s
to
r
eg
u
late
t
h
e
d
ā
q
c
o
m
p
o
n
e
n
ts
o
f
th
e
li
n
e
cu
r
r
en
t
s
p
er
m
it
th
e
s
y
n
ch
r
o
n
izatio
n
o
f
t
h
e
3
p
h
ase
i
n
v
er
ter
li
n
e
cu
r
r
en
t
s
w
it
h
th
e
3
p
h
ase
u
tili
t
y
g
r
id
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I
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a
m
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s
eq
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m
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p
h
ase
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ed
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o
r
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h
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ltaic
s
y
s
te
m
s
is
d
ep
icted
in
Fi
g
u
r
e
2
.
(
a)
(
b
)
(
c)
b
lo
c
d
iag
r
a
m
o
f
cu
r
r
e
n
t r
eg
u
la
to
r
Fig
u
r
e
2
.
(
a,
b
,
c,
)
b
lo
c
d
iag
r
a
m
o
f
co
n
tr
o
ller
f
o
r
3
-
p
h
ase
VSI
f
o
r
P
V
s
y
s
te
m
T
h
e
s
y
n
ch
r
o
n
iza
tio
n
a
lg
o
r
it
h
m
f
o
r
ar
r
iv
i
n
g
a
co
n
tr
o
llab
le
p
o
w
er
f
ac
to
r
in
th
e
co
n
n
ec
t
io
n
s
h
o
u
ld
d
etec
t
th
e
p
h
ase
an
g
le
o
f
th
e
3
p
h
ase
u
tili
t
y
g
r
id
v
o
lta
g
es
w
it
h
o
p
ti
m
al
d
y
n
a
m
ic
r
esp
o
n
s
e
an
d
r
eliab
ilit
y
in
o
r
d
er
to
g
et
th
e
s
y
n
c
h
r
o
n
izati
o
n
o
f
t
h
e
co
n
tr
o
lled
3
p
h
ase
i
n
v
er
ter
c
u
r
r
en
ts
a
n
d
as
s
u
r
e
t
h
e
p
r
o
p
er
b
eh
av
io
r
o
f
th
e
in
v
er
ter
co
n
tr
o
l
s
tr
ate
g
y
.
T
h
er
e
ar
e
v
ar
io
u
s
s
tu
d
ies
w
h
i
ch
s
h
o
w
d
i
f
f
er
en
t
s
tr
u
ct
u
r
es
f
o
r
s
y
n
c
h
r
o
n
izatio
n
alg
o
r
ith
m
s
[
1
2
]
,
ex
is
ten
ce
t
h
e
P
h
ase
L
o
ck
ed
L
o
o
p
th
e
class
ical
o
n
e.
A
3
p
h
ase
P
h
ase
L
o
ck
ed
L
o
o
p
(
P
L
L
)
s
tr
u
ct
u
r
e
is
s
h
o
w
n
i
n
Fi
g
u
r
e
3
,
w
h
ich
i
s
m
ad
e
b
y
t
h
e
C
lar
k
e
an
d
P
ar
k
tr
an
s
f
o
r
m
a
tio
n
s
(
al
s
o
k
n
o
w
n
a
s
ab
c
ā
d
q
tr
an
s
f
o
r
m
atio
n
)
,
th
e
P
I
r
e
g
u
la
to
r
as
th
e
lo
o
p
f
ilter
,
an
d
an
in
te
g
r
ato
r
as
th
e
v
o
lta
g
e
-
co
n
tr
o
lled
o
s
cillato
r
(
VC
O)
.
T
h
is
P
L
L
s
tr
u
ct
u
r
e
i
s
e
v
en
l
y
k
n
o
w
n
as
S
y
n
c
h
r
o
n
o
u
s
R
e
f
er
en
ce
Fra
m
e
P
L
L
o
r
d
q
P
L
L
:
th
e
i
n
p
u
t
v
ar
iab
les
ar
e
th
e
3
p
h
ase
u
tili
t
y
g
r
id
v
o
lta
g
es(u
a,
u
b
,
u
c)
,
an
d
th
e
o
u
tp
u
t
v
ar
iab
le
is
th
e
p
h
ase
an
g
le
(
Oo
b
s
)
.
T
h
e
d
esig
n
o
f
t
h
e
P
h
ase
L
o
c
k
ed
L
o
o
p
g
ain
i
s
a
cr
itical
p
o
in
t
w
it
h
in
t
h
i
s
p
r
o
ce
s
s
.
T
h
e
clo
s
ed
lo
o
p
t
r
an
s
f
er
f
u
n
ctio
n
o
f
t
h
e
d
q
P
L
L
is
g
i
v
i
n
g
b
y
:
H(
s
)
=
(
Kp
S+Ki)
/ (
SĀ² +
Kp
S+Ki)
(
5
)
w
h
er
e
Kp
i
s
t
h
e
p
r
o
p
o
r
tio
n
al
g
ain
s
e
m
p
lo
y
ed
P
I
r
eg
u
lato
r
,
Ki:
i
n
te
g
r
al
g
a
in
s
o
f
t
h
e
e
m
p
l
o
y
ed
P
I
r
eg
u
lato
r
.
E
q
.
(
5
)
is
a
s
ec
o
n
d
o
r
d
er
tr
an
s
f
er
f
u
n
c
tio
n
,
s
i
m
ilar
to
(
6
)
.
G(
s
)
=
(
2
Ī¾
Ļ
0
S
+
Ļ
0
Ā²
)
/
(
SĀ²
+2
Ī¾
Ļ
0
S
+
Ļ
0
Ā²)
(
6
)
w
h
er
e
Ļ
0
is
th
e
n
atu
r
al
a
n
g
u
la
r
f
r
eq
u
en
c
y
,
Ī¾: is t
h
e
d
a
m
p
i
n
g
f
ac
to
r
.
f
r
o
m
eq
u
ati
n
g
(
5
)
an
d
(
6
)
:
Kp
=
9
.
2
/
T
s
(
7
)
Ļ
0
=
Kp
/ 2
Ī¾
(
8
)
Ki
=
Ļ
0
Ā²
(
9
)
I
n
th
is
w
o
r
k
,
th
e
d
q
P
L
L
g
ai
n
s
ar
e
ca
lcu
lated
s
o
a
s
to
o
b
tain
T
S=
0
.
0
5
m
s
(
o
n
e
5
0
Hz
c
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cle
)
allo
w
i
n
g
a
f
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s
t
r
esp
o
n
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e
o
f
t
h
e
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g
o
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ith
m
w
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e
n
a
v
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iatio
n
o
f
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h
e
n
o
m
i
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f
r
eq
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n
c
y
o
cc
u
r
,
a
n
d
a
d
am
p
i
n
g
f
ac
to
r
Ī¾=
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id
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n
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[
8
]
,
w
h
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also
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o
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3
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tili
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ar
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o
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d
a
m
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ta
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en
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lu
tio
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p
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m
s
ca
u
s
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y
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n
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ala
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h
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t
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y
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lo
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,
w
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is
f
o
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d
ed
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th
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s
y
m
m
etr
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m
p
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ts
m
et
h
o
d
[
1
5
]
.
it
is
p
o
s
s
ib
le
to
d
ec
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m
p
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e
t
h
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d
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ase
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tili
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r
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s
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n
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e,
p
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s
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e
q
u
en
ce
s
,
allo
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i
n
g
a
g
o
o
d
p
er
f
o
r
m
a
n
ce
o
f
th
e
P
L
L
al
g
o
r
ith
m
.
I
n
ti
m
e
d
o
m
ai
n
,
th
e
in
s
ta
n
tan
eo
u
s
p
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s
iti
v
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e
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en
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co
m
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V+
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c
o
f
a
v
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e
v
ec
to
r
is
g
iv
en
b
y
[
1
0
]
:
Fig
u
r
e
3
.
B
lo
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d
iag
r
a
m
o
f
t
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e
P
SD +
d
q
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L
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y
n
c
h
r
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n
iza
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o
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ith
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a
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izatio
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ase
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o
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I
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5.
CASE
O
F
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A
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ith
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s
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n
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2
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k
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g
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a
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Ob
s
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tech
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o
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clu
d
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th
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f
o
llo
w
i
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g
co
m
p
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e
n
ts
:
1.
P
h
o
to
v
o
ltaic
ar
r
ay
d
eli
v
er
in
g
a
m
ax
i
m
u
m
o
f
5
k
W
at
1
0
0
0
W
/
m
^2
s
u
n
ir
r
ad
ian
ce
.
2.
5
k
Hz
b
o
o
s
t
co
n
v
er
ter
in
cr
ea
s
in
g
v
o
ltag
e
f
r
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m
P
h
o
to
v
o
lta
ic
n
at
u
r
al
v
o
lta
g
e
(
2
7
3
V
DC
at
m
a
x
i
m
u
m
p
o
w
er
)
to
5
0
0
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DC
.
S
w
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i
n
g
D
is
o
p
ti
m
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b
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a
MP
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c
o
n
tr
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ller
th
at
u
t
ilizi
n
g
t
h
e
ā
P
&
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tec
h
n
iq
u
e.
3.
1980
-
Hz
3
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el
3
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h
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b
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s
t
co
n
v
er
ter
.
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ltag
e
s
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r
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co
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v
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ter
co
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v
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ts
th
e
5
0
0
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DC
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k
v
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to
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6
0
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a
n
d
k
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s
u
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it
y
p
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w
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f
ac
to
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.
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h
e
Vo
ltag
e
s
o
u
r
ce
co
n
v
e
r
ter
co
n
tr
o
l
s
y
s
te
m
u
ti
lizi
n
g
t
w
o
co
n
tr
o
l
lo
o
p
s
: a
n
e
x
ter
n
a
l c
o
n
tr
o
l lo
o
p
w
h
ic
h
co
n
tr
o
l D
C
l
in
k
v
o
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a
n
d
an
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ter
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tr
o
l lo
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u
late
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d
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r
r
en
ts
.
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d
cu
r
r
en
t
r
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er
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n
ce
r
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t
t
h
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o
u
tp
u
t
o
f
th
e
D
C
v
o
lta
g
e
e
x
ter
n
a
l
co
n
tr
o
ller
.
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q
cu
r
r
en
t
r
e
f
er
en
c
e
is
f
i
x
e
to
ze
r
o
in
o
r
d
er
to
m
ai
n
tai
n
u
n
it
y
p
o
w
er
f
ac
to
r
.
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an
d
Vq
v
o
lta
g
e
o
u
tp
u
ts
o
f
th
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c
u
r
r
en
t
co
n
tr
o
ller
ar
e
tr
an
s
f
o
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m
ed
to
t
h
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ee
m
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u
lati
n
g
s
i
g
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a
ls
U
u
v
w
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r
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f
u
s
ed
b
y
t
h
e
P
W
M
Gen
er
ato
r
.
T
h
e
co
n
tr
o
l
s
y
s
te
m
u
tili
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a
s
a
m
p
le
ti
m
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f
1
0
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s
ec
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d
s
f
o
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v
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a
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d
cu
r
r
en
t
co
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tr
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s
as
w
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as
f
o
r
th
e
P
L
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s
y
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c
h
r
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n
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n
u
n
it.
P
u
l
s
e
g
e
n
er
ato
r
s
o
f
DC
-
D
C
an
d
V
SC
c
o
n
v
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ter
s
u
s
e
a
f
as
t
s
a
m
p
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ti
m
e
o
f
o
n
e
m
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o
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in
o
r
d
er
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b
tain
an
ap
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r
o
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r
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r
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lu
tio
n
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f
P
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M
w
a
v
ef
o
r
m
s
.
6.
RE
SU
L
T
S
A
ND
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AL
Y
SI
S
Fig
u
r
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5
s
h
o
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m
o
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s
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m
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s
.
Fig
u
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5
.
SIM
UL
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m
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]
A
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B.
Re
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.
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A
n
in
te
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p
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n
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H.
A
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Hiro
k
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2
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G
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1
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In
f
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Kin
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p
p
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.
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teristics
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3
5
(2
0
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4
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ā
5
5
4
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[2
2
]
V
.
S
c
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rp
a
,
S
.
Bu
so
,
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.
S
p
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lex
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.
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tro
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6
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2
0
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ā
1
5
3
8
.
[2
3
]
N.
M
u
t
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h
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M
.
Oh
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o
,
T
.
In
o
u
e
,
A
m
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f
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P
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o
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tr
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rc
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f
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ra
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sy
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m
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:
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2
0
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n
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p
p
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0
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9
9
.
[2
4
]
K.
Zh
o
u
,
D.
W
a
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g
,
Re
latio
n
sh
ip
b
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tw
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a
c
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to
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P
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:
a
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siv
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l
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sis [
th
re
e
-
p
h
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se
in
v
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]
,
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T
ra
n
s.
In
d
.
El
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c
tro
n
.
4
9
(
2
0
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)
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8
6
ā
1
9
6
.
[2
5
]
R.
H.
P
a
rk
,
Tw
o
re
a
c
ti
o
n
th
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rt
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n
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.
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IEE
,
1
9
2
9
,
p
p
.
7
1
6
ā
7
3
0
.
[2
6
]
A
.
F
e
rre
ro
,
G
.
S
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p
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rti
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F
u
rg
a
,
A
n
e
w
a
p
p
ro
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th
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d
e
f
in
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o
f
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m
-
p
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ts
in
th
re
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-
p
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se
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it
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IEE
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m
.
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e
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su
re
.
4
0
(1
9
9
1
)
5
6
8
ā
5
7
7
.
[2
7
]
R.
Ek
stro
m
,
M
.
L
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ij
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n
,
L
o
w
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r
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rd
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r
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rid
c
u
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rm
o
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f
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r
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o
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n
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c
ted
to
a
d
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rte
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g
rid
,
El
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c
tr.
P
o
w
e
r
S
y
st.
Re
s.
1
0
6
(2
0
1
4
)
2
2
6
ā
2
3
1
.
[2
8
]
[2
7
]
S
tan
d
a
r
d
f
o
r
In
terc
o
n
n
e
c
ti
n
g
Distrib
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ted
Re
so
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rc
e
s w
it
h
El
e
c
tri
c
P
o
w
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r
S
y
s
-
te
m
s,
2
0
0
3
.
[2
9
]
J.C.
He
rn
Ć”
n
d
e
z
,
J.
Orte
g
a
,
De
la
Cru
z
,
D.
V
e
ra
,
G
u
id
e
li
n
e
s
f
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th
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tec
h
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ica
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a
ss
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-
me
n
t
o
f
h
a
r
m
o
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ic,
f
li
c
k
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r
a
n
d
u
n
b
a
la
n
c
e
e
m
is
sio
n
li
m
it
s f
o
r
P
V
-
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
,
El
e
c
tr.
P
o
w
e
r
S
y
st.
Re
s.
8
1
(
2
0
1
1
)
1
2
4
7
ā
1
2
5
7
.
[3
0
]
E.
J.
Bu
e
n
o
,
F
.
Es
p
in
o
sa
,
F
.
J.
Ro
d
rig
u
e
z
,
J.
Ure
f
i,
S
.
Co
b
re
c
e
,
Cu
rre
n
t
c
o
n
tr
o
l
o
f
v
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lt
a
g
e
so
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rc
e
c
o
n
v
e
rters
c
o
n
n
e
c
ted
t
o
th
e
g
rid
th
r
o
u
g
h
a
n
L
C
L
-
f
il
ter,
in
:
P
o
w
e
rEl
e
c
tro
n
ics
S
p
e
c
ialists
Co
n
f
e
re
n
c
e
,
2
0
0
4
IEE
E
3
5
t
h
A
n
n
u
a
l
,
v
o
l.
1
,
2
0
0
4
,
p
p
.
6
8
ā
7
3
.
[3
1
]
D.
Ha
m
z
a
,
Q.
M
e
i,
P
.
K.
Ja
in
,
Im
p
lem
e
n
tatio
n
o
f
a
n
E
M
I
a
c
ti
v
e
f
i
lt
e
r
in
g
ri
d
-
ti
e
d
P
V
m
icro
-
in
v
e
rter
c
o
n
tr
o
ll
e
r
a
n
d
sta
b
il
it
y
v
e
ri
f
ica
ti
o
n
,
in
:
I
ECON,
2
5
t
h
Oc
to
b
e
r,
2
0
1
2
,
p
p
.
4
7
7
ā
4
8
2
.
[3
2
]
S
.
W
a
n
g
,
C.
X
u
,
H.
Qin
,
De
sig
n
th
e
o
ry
a
n
d
im
p
le
m
e
n
tatio
n
o
f
p
lan
a
r
EM
I
f
il
-
ter
b
a
se
d
o
n
a
n
n
u
lar
in
teg
ra
te
d
in
d
u
c
to
r
-
c
a
p
a
c
it
o
r
u
n
it
,
E
lec
tro
m
a
g
n
.
Co
m
p
a
t.
(A
P
EM
C)
(2
0
1
3
)
1
2
9
ā
1
3
2
.
[3
3
]
C.
P
o
-
S
h
e
n
,
L
.
Ye
n
-
S
h
i
n
,
Ef
f
e
c
t
iv
e
EM
I
f
il
ter
d
e
sig
n
m
e
th
o
d
f
o
r
th
re
e
-
p
h
a
se
in
v
e
rter
b
a
se
d
u
p
o
n
so
f
t
w
a
re
n
o
ise
se
p
a
ra
ti
o
n
,
IE
EE
T
ra
n
s.
P
o
w
e
r
El
e
c
tro
n
.
2
5
(
2
0
1
0
)
2
7
9
7
ā
2
8
0
6
.
[3
4
]
N.S
.
Dā
S
o
u
z
a
,
L
.
A
.
C
L
o
p
e
s,
X.
L
iu
,
Co
m
p
a
ra
ti
v
e
stu
d
y
o
f
v
a
ri
a
b
le
siz
e
p
e
rtu
r
b
a
ti
o
n
a
n
d
o
b
se
rv
a
ti
o
n
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
tra
c
k
e
rs f
o
r
P
V
sy
ste
m
s,
El
e
c
tr.
P
o
w
e
r
S
y
st.
Re
s 8
0
(2
0
1
0
)
2
9
6
-
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