In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
5
6
4
~1
5
7
4
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1564-1574
1564
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Design and digital implementation
o
f power control strategy for
grid c
onnected pho
tovoltaic inverter
Lin
d
a Hassa
in
e, Moh
amed
R
id
a Ben
gou
r
i
n
a
C
e
ntre
de
Dé
ve
l
o
p
p
e
m
e
n
t de
s
En
e
r
g
i
es
R
enou
vel
a
bl
es,
CDER,
B
P
6
2
Ro
u
t
e
de
l
’o
b
s
erv
a
toi
r
e
16
340
Bo
uzaréah,
Algeria
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Oct
2
9
,
2
018
Re
vise
d Mar
6,
201
9
Ac
ce
p
t
ed
Ap
r
1
3
,
2
019
Th
is
p
aper
p
resen
t
s
th
e
o
p
t
i
mizat
io
n
design
a
n
d
a
d
e
t
ail
e
d
im
pl
e
m
ent
a
tion
in
FPGA
(Fiel
d
-
P
r
o
gram
m
a
bl
e
Ga
t
e
A
rray)
o
f
a
p
o
wer
cont
rol
str
a
t
e
g
y.
T
his
st
rateg
y
i
s
b
a
sed
on
t
h
e
ph
ase
shif
t
an
gl
e
of
t
he
i
nv
ert
e
r
ou
tp
u
t
volt
a
ge
w
i
t
h
resp
ect
t
o
t
h
e
gri
d
v
oltag
e
a
nd
D
S
P
WM
(
Di
gital
Sinu
soid
al
P
u
l
se
W
i
d
t
h
M
o
d
u
l
a
t
i
o
n
)
p
a
t
t
e
r
n
s
“
P
h
a
s
e
s
h
i
f
t
a
n
g
l
e
-
D
S
P
W
M
”
f
o
r
a
n
i
n
v
e
r
t
e
r
for
ph
ot
ov
olt
a
ic
s
y
s
t
e
m
conn
ected
t
o
t
h
e
gri
d
.
T
h
e
pro
p
o
s
ed
c
o
n
t
r
ol
can
sy
nch
r
oni
ze
a
s
i
nus
o
i
dal
i
nverter
o
ut
put
c
u
rre
nt
w
ith
a
g
rid
v
o
l
t
ag
e
and
con
t
ro
l
the
po
w
e
r
inj
ected
i
nto
t
h
e
gri
d
.
De
t
a
ile
d
d
e
vel
opm
en
t
of
a
d
igital
c
o
ntrol
l
e
r
w
i
t
h
lo
we
r
ha
rd
wa
re
a
nd
c
o
m
pu
ta
ti
on
r
e
q
u
i
re
me
nt
i
s
p
roposed.
De
sc
rip
tion
on
t
he
d
igi
t
a
l
i
m
p
l
e
me
nta
t
io
n
o
f
t
he
A
/D
c
o
n
v
e
rte
r
,
t
h
e
P
I
com
p
ensat
o
r
,
t
he ph
a
se s
hi
f
t
an
d
t
he D
PW
M
,
i
s
p
r
o
v
i
d
ed.
T
hi
s
d
i
gi
ta
l cont
rol
exh
i
b
i
t
sim
p
licit
y,
r
edu
c
ti
on
o
f
t
he
m
em
ory
requ
irem
ent
s
a
n
d
p
o
wer
calcu
lati
on
f
o
r
t
he
c
o
n
tro
l
.
T
h
e
f
unctio
nal
s
t
ru
cture
o
f
t
h
i
s
s
ystem
w
i
th
di
gital contro
l
has been validat
e
d
with
s
i
m
u
l
at
io
n
s
an
d
ex
p
erim
e
n
tal
re
su
lts.
K
eyw
ord
s
:
Di
gi
t
a
l
c
ont
ro
l
D
S
PW
M
Pa
t
t
e
r
n
s
FPGA
G
r
id c
on
nec
t
ed
Inver
t
e
r
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Linda Hassaine,
Ce
ntre
d
e D
é
velo
p
p
em
en
t de
s
Energie
s
R
e
n
ou
ve
lab
l
es,
CD
E
R
BP
62
Ro
u
t
e
de
l’observa
toire
16
3
40
Bo
uza
r
éa
h, A
l
g
ier
s
, A
l
g
e
r
ia.
Em
ail:
l
.
hassa
i
n
e@c
d
er.
d
z
1.
I
N
TR
OD
U
C
TI
O
N
The
o
v
er
all
effi
c
i
e
n
cy
o
f
gri
d
-co
nne
c
t
e
d
p
ho
t
o
v
o
l
ta
i
c
p
o
w
er
g
en
e
r
at
io
n
s
y
ste
m
s
de
p
e
nd
s
o
n
t
he
efficie
n
c
y
o
f
t
h
e
D
C
-
i
n
t
o-A
C
c
onve
rs
io
n
of
t
he
i
nve
rte
r
.
Im
port
an
t
i
m
p
r
ov
emen
t
s
i
n
th
e
d
e
si
gn
a
nd
implem
e
n
ta
t
i
o
n
o
f
th
is
pow
e
r
c
on
verter
d
e
v
ic
e
ca
n
b
e
c
a
rrie
d
o
u
t
[
1
–6].
Con
t
ro
l
of
a
c
t
iv
e
and
rea
c
t
i
v
e
p
o
w
e
r
in
j
e
c
t
e
d
i
n
t
o
t
h
e
gr
id;
c
o
ntro
l
of
d
c-
li
nk
v
o
lta
ge
;
g
u
a
r
ante
e
h
ig
h
q
u
a
lit
y
of
t
he
i
njec
te
d
p
o
w
e
r;
r
ed
uc
t
i
o
n
o
f
the
h
a
rm
on
i
c
d
i
s
t
o
rt
i
o
n,
e
li
m
i
na
t
i
on
of
t
h
e
D
C
com
pon
e
n
t
i
n
j
e
c
t
e
d
i
nto
t
h
e
gr
id
;
gri
d
s
y
n
c
h
r
o
n
i
z
a
t
i
o
n
a
nd
di
gita
l
impl
em
enta
t
i
o
n
o
f
t
h
e
con
t
ro
l
[7,
8].
P
u
l
s
e
w
i
dt
h
m
o
d
u
l
at
ion
(P
WM)
tec
h
n
i
que
i
s
use
d
f
or
c
on
t
r
ol
lin
g
the
v
o
lta
ge
s
o
u
r
ce
inv
e
rters,
w
hic
h
i
n
j
ec
t
s
c
urre
nts
in
to
t
he
g
r
i
d
.
T
w
o
m
e
t
h
o
d
s
o
f
P
W
M
t
e
c
h
n
i
q
u
e
s
c
a
n
b
e
a
d
opt
e
d
:
Th
e
P
W
M
t
echn
i
qu
e
c
o
nsi
s
t
on
t
h
e
c
o
m
p
a
ri
son
of
a
t
ri
an
gu
lar
ca
rrier
s
ig
nal
“
h
i
gh
fre
q
ue
ncy”
w
i
t
h
a
sinus
o
i
da
l
re
fe
renc
e
w
a
v
e
fo
r
m
“
low
freque
ncy”.
Th
e
in
tersec
ti
o
n
po
int
de
term
ines
t
he
s
w
i
t
c
h
i
n
g
w
a
ve
form
.
The
sec
ond
m
et
ho
d,
t
he
P
WM
t
e
c
h
n
i
q
u
e
base
d
o
n
g
e
n
e
r
at
e
d
s
w
itc
h
i
n
g
p
a
tter
n
s.
T
h
e
P
WM
pat
t
ern
red
u
c
e
the
l
o
w
orde
r
of
h
arm
onic
c
o
mpo
n
e
n
t
s
[
9],
[10].
In
t
hi
s
case,
t
he
s
wi
tc
hin
g
p
a
t
t
e
rns
a
r
e
c
a
l
c
u
l
a
t
e
d
a
p
r
i
o
r
i
f
o
r
c
e
r
t
a
i
n
o
p
e
r
a
t
i
n
g
c
o
n
d
i
t
i
o
n
s
a
n
d
a
r
e
t
h
e
n
s
t
o
re
d
i
n
m
emor
y
(loo
k
-
up
ta
ble)
f
or
u
se
i
n
rea
l
t
i
m
e
[1
1
–
1
3
].
D
i
g
i
t
a
l
i
m
p
le
me
nt
a
tio
n
o
f
fers
a
dva
nta
g
es
o
v
e
r
t
h
eir
a
n
al
o
gue
c
oun
te
rparts
[
14
–1
7]:
imm
uni
ty
t
o
t
h
e
n
o
i
se
a
n
d
inse
ns
iti
ve
ne
ss
i
n
t
he
c
h
a
nge
s
o
f
v
o
l
ta
g
e
a
n
d
t
e
m
pe
rature
[
13].
F
P
G
A
'
s
implem
e
n
ta
t
i
o
n
g
i
v
e
s
u
pp
le
n
e
ss
i
n
c
ha
ng
in
g
the
de
s
i
gne
d
circu
i
t
,
eas
y
a
nd
fas
t
c
irc
u
it
m
odi
fica
ti
on
w
it
hou
t
modi
fyi
n
g the
hardw
a
re
and
rapi
d pr
o
t
ot
y
p
i
n
g
[1
2].
I
n
t
h
i
s
w
o
r
k
,
t
h
e
ob
je
c
t
i
v
e
is
t
o
im
p
l
e
m
e
n
t
an
i
n
v
e
r
ter
w
ith
a
si
m
p
le
p
o
w
e
r
c
on
trol
s
trateg
y.
T
ha
t
impl
ies
to
r
ed
u
c
e
bo
th
h
ardw
a
r
e
a
nd
sof
t
w
a
re
r
e
quired
re
sour
ces
(
r
e
duc
i
ng
me
mor
y
a
n
d
c
om
put
i
ng
ne
eds
o
f
the
c
o
n
t
ro
l
sy
s
t
em
)
u
s
in
g
F
P
G
A
de
si
g
n
p
la
tform
.
T
he
p
ropos
ed
c
o
n
t
ro
l
stra
te
gy
im
p
l
e
m
entat
i
o
n
a
l
l
o
w
s
to
d
e
si
gn
a
n
i
nvert
e
r
w
i
t
h
lo
w
c
o
st
a
n
d
hi
gh
r
e
l
i
a
bi
li
ty
,
wh
il
e
ma
ny
o
t
h
er
i
mp
le
me
nt
a
tio
n
s
a
re
b
ased
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Desi
gn
an
d
digi
tal
i
m
pl
e
m
ent
a
tio
n
of
pow
e
r
co
nt
rol
st
ra
t
e
gy
f
o
r
g
r
i
d
c
onne
c
t
ed
…
(L
i
n
da
Ha
ssai
n
e)
1
565
c
o
mple
x
ma
th
e
m
a
t
i
c
a
l
a
lg
or
it
hm
s
tha
t
r
eq
uir
e
m
an
y
r
e
sour
ce
s
of
bo
th
s
oft
w
are
a
n
d
h
a
r
d
wa
r
e
.
F
P
GA
tec
h
n
o
lo
gy
o
f
f
e
r
s
a
f
le
xi
b
l
e
p
r
ogr
am
m
a
ble
e
n
v
i
r
o
nm
en
t
a
n
d
a
h
i
g
her
le
ve
l
of
v
er
sa
t
i
l
i
t
y.
T
h
e
c
o
de
i
s
writte
n
as b
lo
ck
s to
b
e
p
r
o
c
essed
in
p
aral
le
l
,
wh
i
ch
m
ak
es th
e
F
PG
A
i
m
p
lem
e
nta
t
io
n m
o
re
a
ttrac
tive
.
I
n
P
V
system
s
c
o
n
n
e
c
te
d
to
t
he
g
r
i
d,
s
ys
t
e
m
contr
o
l
ca
n
be
d
ivi
de
d
in
to
t
w
o
i
mpor
ta
nt
p
ar
ts.
The
MP
P
c
ont
r
o
l
,
w
hic
h
e
x
t
r
act
t
he
m
a
x
i
m
um
pow
er
f
r
o
m
t
h
e
P
V
g
ene
r
a
to
r
and
t
h
e
in
ve
r
t
e
r
c
on
t
r
o
l
,
w
h
ic
h
en
su
re
t
h
e
c
o
n
t
r
ol
o
f
act
iv
e
an
d
re
a
c
t
i
v
e
p
owe
r
g
en
erat
ed
t
o
t
h
e
gr
id,
t
h
e
c
o
n
t
r
o
l
of
D
C
-
lin
k
v
o
lta
ge
,
hi
g
h
qua
lit
y
of
t
he
i
n
j
e
c
t
ed
pow
er
a
nd
gr
i
d
s
y
n
c
h
r
o
n
i
z
a
t
i
o
n
[2,
3,
7
,
9,
1
7
–
1
9
]
.
T
he
p
r
o
pose
d
pow
e
r
c
o
n
tr
o
l
me
t
h
od
[2
0–22
]
is
b
a
s
e
d
o
n
t
h
e
ph
a
s
e
shif
t
an
gl
e
o
f
t
h
e
i
nv
e
r
t
e
r
ou
t
put
v
o
l
tage
w
it
h
r
e
spect
t
o
t
h
e
gr
id
vo
l
t
age
a
nd
D
S
PWM
pat
t
e
r
n
s
“
Phase
shift
ang
l
e-DS
PWM”.
Hi
g
h
pow
e
r
f
a
ct
o
r
c
an
b
e
ac
h
i
ev
ed
f
o
r
a
l
a
r
g
e
r
a
nge
o
f
o
u
tp
u
t
c
ur
r
e
nt.
The
m
a
in
a
dva
n
t
ag
es
a
r
e
s
im
p
l
i
c
ity,
fe
w
res
ourc
e
s,
l
ess
memor
y
,
less
c
i
r
c
uit
r
y
and
hi
g
h
a
ccur
acy.
Th
is
c
on
tro
l
s
tr
ateg
y
a
l
l
o
ws
t
he
c
on
tro
l
o
f
p
o
we
r
in
jec
t
e
d
i
nt
o
t
he
g
r
i
d.
U
si
ng
D
P
WM
p
atter
n
s
f
o
r
di
ff
er
e
n
t
m
o
du
lat
i
on
in
de
x
ma
a
nd
t
h
e
p
h
as
e
shif
t
a
n
g
l
e
o
f
t
he
in
ver
t
e
r
o
ut
p
u
t
vol
tage
a
s
con
t
r
o
l
par
a
m
e
ter
.
The
o
u
t
p
ut
c
ur
r
e
nt
a
mp
l
itu
de
a
nd
t
he
p
ow
e
r
f
ac
tor
c
a
n
be
c
on
tr
o
l
l
ed,
c
h
an
gi
ng
the
p
o
wer
fac
t
or
;
t
h
e
i
n
je
cte
d
in
d
u
ct
i
v
e
or
c
a
p
ac
it
iv
e
re
ac
t
i
ve
p
owe
r
c
a
n
b
e
d
y
n
am
ical
l
y
c
ha
n
g
ed
a
nd
c
o
nt
roll
ed
,
f
o
r
a
c
h
i
e
v
i
ng
a
n
in
v
e
r
t
er
w
i
t
h
a
dva
nce
d
a
c
c
ur
a
c
y
a
n
d
r
e
l
i
a
b
il
i
t
y.
I
n
[
2
0
–
22]
,
t
h
e
str
a
t
e
g
y
has
be
en
d
e
v
e
l
ope
d
w
i
t
h
m
et
h
o
d
ica
l
de
sc
r
i
pt
ion
a
n
d
ma
them
at
i
c
a
l
a
na
ly
sis.
T
he
t
he
or
et
ica
l
p
r
e
d
i
c
t
i
on
s
h
a
s
b
e
e
n
v
al
i
d
a
t
e
wi
th
s
i
m
ul
at
ion
an
d
f
i
rst
e
xper
i
m
e
nt
r
e
s
ults.
I
n
t
h
i
s
pa
per
a
deta
ile
d
imp
l
e
m
entat
i
o
n
in
F
P
G
A
of
t
h
i
s
p
o
w
e
r
c
o
n
t
ro
l
st
ra
t
e
g
y
,
“P
h
a
s
e
s
h
i
ft
a
n
g
l
e
-
DP
WM”
for
P
V
i
n
v
e
r
ter
s
b
a
s
e
d
o
n
t
h
e
l
o
ok
up
ta
b
l
e,
i
s
presen
te
d
.
Descr
i
pt
i
on
on
the
d
i
gita
l
imple
m
e
n
ta
ti
on
of
t
he
m
ai
n
co
ntr
o
l
b
l
oc
ks,
w
h
i
c
h
a
r
e
the
A
/
D
con
v
er
t
e
r
,
t
h
e
P
I
c
o
n
t
roll
er,
th
e
ph
a
s
e
shi
f
t
a
n
d
t
h
e
DPWM
,
i
s
pr
ovi
de
d.
T
he
p
r
o
pose
d
c
on
tr
ol
i
s
s
i
m
p
l
e
a
nd
ada
p
ted
t
o
F
P
G
A
pl
a
t
f
o
r
m
;
i
t
i
s
a
t
t
r
a
c
t
i
v
e
f
o
r
l
o
w
p
o
w
e
r
g
r
i
d
co
nn
e
c
t
e
d
ap
pli
c
at
io
ns
a
nd
a
ll
o
w
s
c
o
nt
roll
i
n
g
th
e
a
c
t
i
v
e
a
n
d
re
ac
t
i
ve
p
ow
e
r
i
njec
te
d
int
o
t
he
g
r
i
d
.
M
or
e
over
,
r
obust
n
ess
o
f
t
he
p
r
opose
d
c
o
n
t
r
ol
a
l
l
o
w
s
d
e
s
ign
i
ng
a
low
c
o
s
t
an
d
s
i
m
p
l
e
i
nve
r
t
er
w
it
h
a
r
e
duc
e
d
a
m
o
u
n
t
o
f
c
o
mpo
n
e
n
t
s
,
based
o
n
a
f
ul
l
br
id
ge
t
op
o
l
og
y
tha
t
c
a
n
b
e
imp
l
em
e
n
t
ed
w
ith
m
i
n
i
m
um
c
om
put
a
t
i
o
na
l
r
e
sour
ce
s.
2.
POWE
R
CONTRO
L S
T
RAT
EGY
I
n
pho
t
o
v
o
l
t
a
i
c
p
ow
e
r
s
ys
te
m
,
t
he
c
o
n
t
r
o
l
of
p
o
w
er
f
ac
t
o
r
is
a
c
hie
v
e
d
b
y
a
d
jus
t
ing
am
pl
itu
de
a
n
d
pha
se
a
n
g
l
e
be
t
w
een
i
n
v
er
ter
vo
l
t
age
a
n
d
g
r
id
v
o
l
tage
a
s
is
s
ho
w
n
i
n
th
e
pha
se
d
ia
gr
a
m
o
f
t
h
e
eq
u
i
vale
n
t
el
ec
t
r
i
c
al
c
i
r
c
u
i
t
of
th
e
i
n
v
e
rt
er c
o
n
n
ect
e
d
to
t
h
e g
r
i
d
Fi
g
u
r
e
1
.
F
i
gur
e
1.
P
hase
d
iagr
a
m
o
f
t
h
e
equi
va
le
nt
e
l
ectr
i
c
a
l
c
i
r
cu
it
o
f
i
n
v
e
r
ter
con
n
ec
t
e
d
t
o
t
he
g
r
i
d
i
nver
t
e
r
The
p
o
w
e
r
co
ntr
o
l
is
o
b
t
a
i
n
e
d
b
y
m
eans
o
f
t
he
p
hase
s
hi
f
t
a
ng
le
(
δ
)
o
f
t
h
e
i
n
v
e
r
t
e
r
o
u
t
p
u
t
v
o
l
t
a
g
e
,
w
i
t
h
r
espe
ct
t
o
the
gr
id
v
o
l
t
a
ge
a
n
d
t
he
u
se
o
f
S
P
WM
p
a
t
t
e
r
n
s.
The
pow
e
r
f
a
c
tor
is
d
e
t
e
r
m
i
ne
d
b
y
a
n
g
le
(
φ)
be
t
w
ee
n
t
h
e
gr
id
v
o
lta
ge
a
n
d
t
he
f
u
n
d
a
m
e
n
t
al
c
u
r
r
e
nt
c
om
p
o
ne
nt
of
i
n
v
e
r
t
e
r
o
ut
put
cu
rren
t
.
C
o
n
t
r
o
l
l
i
ng
the
phase
s
h
i
f
t
o
f
t
h
e
in
ver
t
e
r
o
ut
pu
t v
o
lta
ge,
th
e
o
u
t
pu
t
cur
r
e
n
t
am
p
l
itu
de
an
d
t
he pow
e
r
fact
or
c
an
b
e
c
o
n
t
ro
l
l
e
d
,
a
n
d
t
h
e
r
ef
ore
the
ma
gnit
ude
o
f
the
ac
t
i
ve
a
n
d
r
e
acti
v
e
p
o
we
r
in
jec
t
e
d
i
n
t
o
th
e
gri
d
[
2
0
]
,
[22]
.
The
ana
l
ysis
i
s
estab
l
ishe
d
us
in
g
t
h
e
i
n
d
u
ct
i
v
e
filte
r
b
e
twe
e
n
t
h
e
in
ve
r
t
er
a
nd
the
gr
id
[
24]
.
C
ons
ide
r
i
ng
t
h
e
fu
n
d
am
en
tal
ha
r
m
onic
(
p
ur
e si
nu
so
ida
l
w
ave
)
,
a
s
a first
a
ppr
oa
ch,
t
h
e
to
tal
harm
o
n
ics
(T
HD)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
5
6
4
–
1
574
1
566
of
t
he
c
ur
r
e
nt
i
n
j
e
c
t
e
d
i
nto
t
h
e
gr
id
i
s
ass
u
m
e
d
eq
ua
l
z
e
r
o
(
TH
D≈0)
.
The
r
ef
o
r
e,
t
he
power
f
act
or,
PF
,
is
de
t
e
rm
ine
d
,
on
l
y
,
by
the
d
i
s
p
l
a
cem
ent
fac
t
or
(c
o
sφ),
a
s will
be
s
h
o
w
n
i
n
(
1
)
[20
–
22]
cos
s
i
n
ad
c
ou
t
mV
PF
LI
(
1
)
To
v
ali
d
t
h
e
p
e
r
f
o
r
m
an
c
e
o
f
t
h
e
p
ropo
se
d
po
we
r
co
nt
ro
l
stra
t
e
gy
i
t
i
s
n
ec
essary,
t
o
g
uar
a
ntee
a
t
o
t
a
l
ha
r
m
onic
d
i
s
t
o
r
ti
on
no
t
h
i
ghe
r
t
h
a
n
s
pec
i
f
i
e
d
5
%
as
s
ug
ge
sts
th
e
Interna
tiona
l
S
t
anda
rd
I
EEE
Std
929-2000
[
2
,
5,
18]
.
Th
is
c
o
n
d
i
tio
n
ca
n
be
a
c
h
ie
ve
d
ca
lc
u
l
a
tin
g
a
n
d
o
p
t
i
mi
z
i
n
g
of
u
si
ng
d
i
f
f
e
r
e
nt
d
ig
it
a
l
S
PW
M
pa
t
t
e
r
n
a
nd
se
lec
t
i
n
g
an
a
p
p
r
opr
i
a
te
c
ou
p
l
i
ng
f
i
l
t
er
[
23]
a
n
d
f
r
e
q
u
e
n
c
y
m
o
d
u
l
a
t
i
o
n
inde
x
(
m
f
)
;
a
nd
the
dis
p
la
ce
m
e
nt
fact
or
(
c
o
sφ)
has
to
b
e
w
i
t
h
i
n
t
he
p
re
-ca
l
c
u
l
a
te
d
lim
its
,
to
g
u
aran
t
ee
t
h
e
sp
ecif
i
ed
o
u
t
pu
t
cu
rrent
.
T
h
i
s
m
a
gni
t
ude
c
a
n
b
e
c
ontr
o
lle
d
se
lec
t
i
n
g
an
a
d
e
qua
te
a
mpl
i
t
u
d
e
m
o
d
ul
a
tio
n
in
de
x,
m
a
,
and
a
phase
s
hi
f
t
,
,
o
f
the
i
nver
t
e
r
o
u
t
p
u
t
v
o
l
t
a
ge.
I
n
F
ig
ur
e
2,
w
hi
c
h
s
h
o
w
s
P
F
vs
,
for
tw
o
di
ffe
r
e
nt
v
a
l
u
e
s
of
m
a
a
n
d
o
f
t
h
e
in
ver
t
e
r
o
utp
u
t
v
o
l
tage
,
V
in
v
,
(
V
inv
=
m
a
.
V
dc
)
,
i
t
c
a
n
b
e
s
e
e
n
,
t
h
a
t
w
i
t
h
t
w
o
v
a
l
u
e
s
o
f
m
a
w
e
c
a
n
r
e
a
c
h
t
h
e
P
F
1
I
n
a
w
i
der
r
a
nge
o
f
.
Figure
2.
P
ower factor
(
P
F
)
acco
rd
in
g t
o
the
pha
se
s
hif
t
The
c
h
oi
c
e
o
f
i
nd
uc
tanc
e
gr
i
d
c
on
ne
ct
i
on
in
f
l
ue
nc
es
t
he
h
a
r
m
o
n
i
c
c
o
n
t
e
n
t
o
f
t
he
c
ur
r
e
nt
i
nje
c
t
ed
in
t
o
t
he
g
r
i
d
a
nd
the
m
a
xim
u
m
acti
v
e
a
n
d
r
e
a
c
tive
pow
er
t
ha
t
t
h
e
in
v
e
rt
e
r
c
a
n
d
el
iver
t
o
t
h
e
g
r
id
.
Hi
gh
i
ndu
c
t
an
ce
s
l
ead
t
o
red
u
c
ed
h
a
r
mo
ni
c
di
st
ort
i
o
n
.
H
o
w
ev
er
i
n
c
re
a
sing
t
h
e
in
duc
ta
nc
e
i
n
t
he
f
il
t
r
ate
show
s
a
num
ber
of
d
r
a
w
b
a
c
ks
:
cos
t
r
educ
t
i
o
n
a
nd
tr
ansfe
r
o
f
p
o
w
e
r
inver
t
e
r.
To a
na
lyz
e
the
b
eha
v
i
o
r
of
t
h
i
s co
n
t
r
o
l
s
t
r
a
te
gy f
o
r
sin
g
l
e
-
pha
se
i
nv
e
r
t
e
r
co
nn
e
c
t
e
d
to
t
he
g
rid
vi
a
an
L
or
L
CL
f
i
l
t
e
r
.
I
t
ha
s
bee
n
u
sin
g
t
he
e
xpr
ess
i
on
of
p
ow
er
f
a
c
t
or
m
ent
i
one
d
i
n
(
1
)
a
nd
t
o
me
as
ur
e
t
h
e
di
st
or
t
i
o
n
o
f
t
h
e
ou
tp
u
t
c
ur
r
e
nt,
t
h
e
t
o
ta
l
ha
r
m
oni
c
d
i
stor
ti
on
,
TH
D
is
o
f
t
en
u
se
d.
T
ota
l
H
ar
m
onic
D
i
stor
tio
n
is
a
m
ea
sur
e
o
f
the
pr
o
por
t
i
ona
l
ity
b
e
t
w
e
e
n
t
he
f
un
dam
e
nta
l
a
nd
t
he
s
um
o
f
a
ll
ot
he
r
fr
e
quenc
ies
i
n
t
he
c
u
r
r
e
nt
w
ave
f
o
r
m.
A
s
show
i
n
(
2
)
d
e
fi
nes
the
TH
D
used
h
e
r
e:
22
1
1
out
out
i
ou
t
II
TH
D
I
(
2
)
Where
Io
ut is
the
t
o
tal c
u
rrent
; (
R
MS)
is t
he Roo
t me
ans s
q
uar
e
a
nd I
out
1
i
s
t
h
e
f
u
nda
me
nta
l
c
u
r
r
e
n
t
(
R
MS
)
.
T
he
r
ela
t
i
o
n
s
h
i
p
be
tw
een
t
he
s
w
i
t
c
hi
n
g
f
r
e
q
u
enc
y
f
c
a
n
d
the
i
n
d
u
c
t
ance
v
al
ue
o
f
o
u
t
pu
t
fil
t
er
i
s
pr
esen
ted,
a
ssu
m
i
ng
a
pow
er
f
ac
tor
P
F
=
0.
99
6.
I
n
F
igur
e
.
3,
t
h
e
s
imula
tio
n
r
e
su
l
t
s
of
t
he
i
n
v
er
t
e
r
c
o
nnec
t
ed
t
o
the
gr
id
v
ia
a
n
L
f
i
l
t
e
r
a
nd
a
n
L
C
L
fi
lt
e
r
.
Assu
mi
ng
a
P
F
=
0
.
996,
i
t
can
b
e
con
c
l
u
d
e
t
h
a
t
fo
r
lo
w
e
r
s
wi
t
c
h
i
ng
f
r
e
qu
en
c
i
es
(
mo
d
u
l
a
t
i
on
i
nd
ex
e
s
f
o
r
l
o
w
fr
eq
ue
ncie
s)
l
ess
tha
n
5
kH
z,
t
he
i
nd
uc
tanc
e
va
l
u
e
o
f
t
h
e
L
f
ilter
i
s
h
i
gher
tha
n
t
he
v
a
l
ue
o
f
t
h
e
i
ndu
c
t
an
ce
(L
1
+
L
2
)
o
f
t
h
e LCL f
i
lter
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Desi
gn
an
d
digi
tal
i
m
pl
e
m
ent
a
tio
n
of
pow
e
r
co
nt
rol
st
ra
t
e
gy
f
o
r
g
r
i
d
c
onne
c
t
ed
…
(L
i
n
da
Ha
ssai
n
e)
1
567
F
i
gur
e
3.
I
nduc
ta
nce
o
f
L
f
i
lte
r
and
LCL
f
i
l
t
e
r
a
s
func
t
i
o
n
o
f
swit
c
h
ing
fre
q
uenc
y
fc,
for PF
=
0,996.
3.
PROPOSED
CONTRO
L
STRUCTURE
The
pr
o
p
o
s
ed
c
on
tr
o
l
s
ys
tem
,
f
or
a
phot
o
v
o
lta
i
c
s
ystem
co
nne
c
t
e
d
to
t
he
g
r
i
d
is
s
h
o
w
n
i
n
F
i
gur
e
4.
The
p
h
o
t
ov
olta
ic
g
ene
r
a
t
or
(
PV
G
)
,
D
C
/
D
C
f
o
r
a m
a
xim
u
m
pow
er
p
o
i
nt
t
r
a
c
k
in
g
(
M
P
P
T) a
nd
a
P
W
M
in
ver
t
e
r
(
DC
/AC).
F
i
gur
e
4.
C
o
n
tr
ol
s
tr
uc
tur
e
f
or
a
s
ing
l
e
pha
se
i
n
v
er
te
r
[
2
0
]
The
D
C
/
D
C
c
o
n
v
er
te
r
i
s
e
m
p
l
o
yed
t
o
b
o
o
s
t
t
he
P
V
-
ar
r
a
y
vo
l
t
age
t
o
an
a
ppr
opr
ia
te
l
e
v
el
b
a
s
e
d
o
n
the
ma
g
n
i
t
ude
o
f
gr
id
v
o
lta
ge,
w
h
ile
t
he
c
on
tr
o
l
ler
of
t
he
D
C–D
C
c
o
nver
t
e
r
i
s
de
si
gne
d
t
o
o
per
a
t
e
a
s
a
m
a
xim
u
m
pow
er
poi
nt
t
r
a
cker
(
MP
P
T
)
.
T
he
p
er
t
u
r
b
-
a
nd-
obser
ve
m
et
hod
i
s
ad
opt
ed
o
wing
t
o
it
s
si
mp
l
e
str
u
c
t
ur
e
a
n
d
i
t
r
e
quir
e
s
few
e
r
m
e
a
s
ur
ed
p
a
r
am
eter
s
[2
4,
25]
.
T
hi
s
s
t
r
a
te
gy
i
s
imple
m
e
n
te
d
to
o
pe
r
a
te
unde
r
r
a
pi
dly
c
h
a
n
g
i
ng
s
olar
r
a
d
ia
tio
n,
u
sin
g
o
n
l
y
one
v
a
r
iab
l
e.
T
he
co
ns
ta
nt
v
o
l
t
a
ge
m
e
t
ho
d
i
s
acc
omp
l
i
s
h
e
d
b
y
ke
ep
i
ng
t
h
e
vo
lta
ge
i
n
t
h
e
P
V
t
er
m
i
nals
c
o
n
s
t
an
t
a
n
d
cl
ose
t
o
t
h
e
M
PP
.
The
c
o
ntr
o
l
lo
op
f
or
t
he
P
WM
i
nver
t
e
r
i
s
a
ssur
e
d
b
y
t
he
o
u
t
put
c
u
r
r
e
n
t
c
ontr
o
l,
t
he
D
C
b
u
s
c
o
ntr
o
l
a
n
d
sy
nc
hr
o
n
i
z
in
g
to
t
he
g
r
i
d
,
t
o
inje
c
t
p
o
w
er
i
nt
o
t
h
e
g
r
id
a
t
a
ll
t
i
me
.
The
o
u
tp
ut
v
ol
t
a
ge
o
f
t
h
e
P
W
M
in
ver
t
e
r
i
s
a
l
r
e
ady
se
t
by
t
he
u
t
i
l
i
t
y
P
V
m
o
d
u
l
e
s.
T
he
r
e
f
o
r
e
,
t
he
i
n
v
er
t
e
r
i
s
c
o
n
tr
olle
d
to
e
ns
ur
e
o
n
ly
p
ow
e
r
in
jec
t
io
n
i
n
t
o
t
he
g
r
i
d.
I
n
F
i
gur
e
5,
a
r
e
r
epre
se
n
t
ed
a
n
inte
r
n
al
a
n
d
a
n
e
x
t
e
r
n
a
l
c
o
n
t
r
o
l
l
oops
o
f
a
c
o
ntr
o
ller
.
Th
e
i
n
t
e
rn
a
l
o
ne
i
n
o
r
de
r
t
o
c
on
t
r
o
l
t
h
e
i
nv
erte
r
o
u
t
put
c
u
rren
t an
d the e
x
te
rnal one
to c
o
n
t
ro
l
t
h
e D
C
b
u
s
V
dc
.
Th
e
referen
ce
o
f
t
h
e
o
u
t
pu
t
c
u
rren
t
(
I
ref
)
d
e
pen
d
s
on
t
h
e
D
C
bu
s
vo
lt
ag
e
(
V
dc
)
an
d
its
r
e
f
e
ren
c
e
(V
ref
).
A
l
o
w
pa
ss
F
ilter
is
i
nc
or
porate
in
o
rde
r
t
o
e
n
s
u
re
t
ha
t
h
i
g
h
f
r
e
que
n
c
y
s
w
i
t
c
hi
ng
noi
se
p
resen
t
i
n
t
h
e
me
a
s
u
r
e
d
in
ver
t
e
r
o
u
t
p
u
t
cur
r
ent
sig
n
a
l
doe
s
no
t
pa
ss
t
hr
o
u
g
h
t
o
the
P
I
co
n
t
roller.
The
c
ontr
o
l
st
r
u
c
t
ur
e
is
a
ss
o
c
iate
d
w
i
t
h
p
r
o
p
o
r
t
i
ona
l
–
i
n
te
gr
al
(
P
I)
c
ont
r
o
ller
s
s
i
n
ce
th
ey
h
a
v
e
a
sa
tisfa
c
t
or
y
be
ha
v
i
or
w
hen
r
e
gu
la
ti
n
g
d
c
v
a
r
i
ab
les.
T
he
g
a
i
n
a
n
d
t
i
m
e
c
ons
ta
n
t
s
has
b
e
e
n
c
a
l
cu
la
te
d
f
o
r
the
two
P
I
c
on
tro
lle
rs.
The
Gain
o
f
the
curr
en
t
PI
c
on
tr
oller
is
e
q
ua
l
to
0
.
9
81
9,
w
he
r
e
t
he
t
i
m
e
cons
tan
t
i
s
abo
u
t
0.
00
171
7.
I
n add
i
ti
on,
the
g
a
i
n o
f
t
he
v
o
l
ta
g
e
P
I c
o
n
t
r
o
lle
r
is
2
.
438
, an
d
th
e ti
me co
n
stan
t is
a
b
out
0
.02
758
. A
lo
o
k
u
p
ta
ble
to
s
tor
e
t
he
d
iffer
e
n
t
p
at
ter
n
s
an
d
t
h
e
zer
o
cr
os
si
n
g
d
e
t
e
c
tor
(
Z
C
D
)
f
o
r
sync
hr
o
n
iz
i
n
g
t
h
e
D
P
WM
w
i
t
h
t
h
e
gr
i
d
v
o
l
tage
.
V
re
f
I
MP
P
T
Di
gi
t
a
l
c
o
n
t
r
o
l
DP
W
M
ZC
D
(
V
gri
d
)
PI
Loo
k
_
u
p
Ta
b
l
e
(
δ
)
PI
V
gr
i
d
L
I
ou
t
I
re
f
I
ou
t
M
PPT
PV
G
DC/
A
C
V
dc
V
in
v
C
V
re
f
I
MP
P
T
Di
gi
t
a
l
c
o
n
t
r
o
l
DP
W
M
DP
W
M
ZC
D
(
V
gri
d
)
PI
Loo
k
_
u
p
Ta
b
l
e
(
δ
)
Loo
k
_
u
p
Ta
b
l
e
(
δ
)
PI
V
gr
i
d
L
I
ou
t
I
re
f
I
ou
t
M
PPT
PV
G
DC/
A
C
V
dc
V
in
v
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
5
6
4
–
1
574
1
568
4.
PROPOSED C
O
N
TROL
I
MPLE
M
E
N
T
ATI
O
N
The
b
l
ock
d
i
a
g
r
a
m
of
t
he
c
o
n
tr
ol
i
s
de
t
a
ile
d
i
n
F
i
g
ur
e
5
.
T
o
ea
ch
a
m
p
l
i
tu
de
m
od
u
l
at
i
o
n
i
nde
x
m
a
c
o
rre
spo
n
d
s
a
sw
i
t
c
h
in
g
pa
t
t
e
rn
SPWM
ch
ar
acte
r
ized
by
switc
h
i
n
g
a
n
g
l
e
s
(
α
1
,
α
2
,
α
3
,
α
n
,
α
n+
1
)
de
fi
ned
b
y
the
n
u
mbe
r
o
f in
ter
s
e
c
t
i
ons,
O
n
l
y
the
c
h
a
ng
e ang
l
es
a
r
e
s
t
o
r
e
d,
H
ig
h
a
c
c
u
r
a
c
y
r
e
s
ol
ut
i
o
n
ca
n be
a
c
h
ie
ved a
n
d
whe
n
u
sin
g
s
y
m
me
tric
p
at
ter
n
s
the
loo
k
u
p
ta
b
l
e
ca
n
be
r
e
duce
d
.
E
ac
h
pat
t
er
n
is
a
c
c
o
m
p
anie
d
by
a
t
t
r
ib
utes
suc
h
a
s
a
ma
ximum
and
a
m
i
nimum
p
h
ase
ang
l
e,
a
m
inim
um
a
nd
a
m
a
xim
u
m
cur
r
ent
stor
ed
i
n
t
h
e
loo
k
u
p
t
a
bl
e
(R
OM
).
On
c
e
t
h
e
d
at
a
a
r
e
st
o
r
e
d
,
th
e
DPWM
c
on
vert
s
t
h
e
d
at
a
co
d
e
p
at
t
e
rn
s
an
d
it
s
a
t
t
r
ibu
t
es
i
n
a
pu
lse
d
s
i
gna
l
tha
t
w
i
l
l
be
g
e
n
er
a
t
e
the
sw
i
t
c
h
in
g
signa
l
s
f
o
r
t
he
in
v
erte
r tra
n
sist
ors.
F
i
gur
e
5.
S
chem
e
of
t
he
p
r
o
p
o
se
d
con
t
r
o
l
i
m
pl
e
m
e
n
tat
i
on
The
co
n
t
r
o
l
a
l
gor
it
h
m
i
m
p
l
e
me
nt
e
d
i
n
F
P
G
A
is
s
how
n
in
F
ig
u
r
e
6.
T
he
r
e
f
e
r
enc
e
c
ur
r
e
nt
i
s
up
da
te
in
e
a
c
h
p
er
io
d
of
t
he
c
o
n
tr
o
l
s
ys
t
e
m
a
nd
c
o
mpa
r
ed
w
it
h
t
h
e
o
u
t
p
u
t
c
ur
r
e
nt
o
f
t
h
e
i
nve
r
t
er
.
D
e
pe
ndin
g
o
n
t
h
e
sig
n
e
rro
r,
t
h
e
c
o
n
t
r
oll
e
r
in
cre
a
s
e
s
o
r
d
e
c
r
ea
ses
t
h
e
ph
as
e
ang
l
e
δ
b
e
t
w
e
e
n
V
inv
and
V
gr
i
d
to
c
om
pe
nsa
t
e
t
h
e
erro
r.
O
n
c
e
t
h
e
o
u
t
p
ut
c
u
rren
t
i
s
equ
a
l
to
t
h
e
r
ef
ere
n
ce
c
u
rren
t,
t
he
c
on
t
r
ol
k
ee
ps t
he
c
ur
r
e
nt
p
hase
a
n
g
l
e
.
T
he
de
sig
n
m
e
t
ho
d
of
i
nver
t
er
p
r
o
p
o
se
d
i
n
t
hi
s
w
o
r
k
i
s
a
t
tr
a
c
t
i
ve
t
o
m
e
d
i
um
a
nd
l
o
w
p
o
w
e
r
P
V
s
ystem
,
w
hic
h
c
a
n c
o
n
t
ro
l
ac
tive
an
d
rea
c
ti
ve
powe
r
for r
el
ati
v
e
low
cost.
F
i
gur
e
6.
C
o
n
tr
ol
a
lg
or
ithm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Desi
gn
an
d
digi
tal
i
m
pl
e
m
ent
a
tio
n
of
pow
e
r
co
nt
rol
st
ra
t
e
gy
f
o
r
g
r
i
d
c
onne
c
t
ed
…
(L
i
n
da
Ha
ssai
n
e)
1
569
I
n
t
h
i
s
c
o
ntr
o
l
sc
hem
e
,
t
h
e
c
o
ntr
o
l
l
e
r
i
s
i
m
p
l
em
ented
by
s
p
e
c
i
f
i
c
h
a
r
d
w
a
r
e
i
n
F
P
G
A
.
T
h
e
s
e
d
e
v
i
c
e
s
a
r
e
particu
l
arl
y
s
u
i
tab
l
e
f
o
r
t
h
e
d
i
re
ct
g
e
n
era
t
i
o
n
o
f
t
r
i
gge
r
signa
ls
f
or
t
he
s
w
itc
hes,
s
o
the
D
P
WM
b
l
o
ck
i
s
a
c
tua
l
l
y
e
mbe
dde
d
w
ith
in
t
he
c
on
tr
o
lle
r
;
i
t
is
one
o
f
t
h
e
a
dva
n
ta
g
e
s
of
t
he
s
pe
c
i
f
i
c
har
d
w
a
r
e
f
eatur
e
s
.
H
o
w
e
ver
,
t
he
s
pe
ci
f
i
c
har
d
w
a
r
e
f
ea
tur
e
s
t
w
o
d
i
s
tinc
t
i
v
e
a
d
van
t
a
ges
:
g
r
e
a
t
e
r
a
c
c
ur
a
c
y
a
n
d
fle
x
ib
i
l
i
t
y
i
n
bl
oc
k
D
P
WM,
i
t
i
s
r
e
a
c
hed
a
n
d
i
t
i
s
p
oss
i
ble
to
g
ener
ate
a
n
y
n
u
m
ber
o
f
t
r
i
g
g
e
r
si
gn
a
l
s,
w
hi
ch
i
s
i
m
po
ssi
b
le
i
n
a
D
S
P
bec
a
use
t
h
ey
h
a
v
e
on
e
o
r
a
s
m
a
ny
t
w
o
D
P
WM
b
loc
k
.
N
o
r
m
ally,
al
l
si
gn
al
s
i
nvo
lv
ed
i
n
th
e
co
nt
rol
l
oop
a
r
e
cont
inu
o
u
s
.
H
ow
eve
r
,
w
h
en
u
s
i
ng
a
d
i
g
ital
c
o
nt
r
o
lle
r
som
e
o
f
t
h
e
c
o
nti
n
u
o
u
s
f
unc
t
i
ons
a
r
e
r
eplac
e
d
b
y
di
scr
e
te
s
e
q
ue
nc
es,
t
h
us
t
w
o
d
is
t
i
nc
t
d
o
ma
in
s
a
ppear
t
he
c
o
n
ti
n
ued
d
o
m
ina
n
ce
(
A
n
a
l
og)
c
o
nnec
t
or
o
n
t
h
e
pr
o
c
ess
si
de
a
nd
t
he
(
d
i
g
ita
l
)
d
i
s
c
r
e
t
e
dom
a
i
n
o
n
t
he
s
i
d
e
of
t
he
r
e
g
u
l
a
t
or
.
To
c
on
nec
t
b
ot
h
d
o
m
a
in
s
som
e
ki
n
d
o
f in
terfa
ce
i
s
ne
ede
d
.
U
s
ua
l
l
y the
s
e in
t
e
r
f
ac
es
a
re
a
na
lo
g / di
g
i
t
a
l
c
onve
r
t
er
s (
D
A
C
)
and dig
i
t
a
l
/ a
n
al
o
g
c
o
n
v
erter
s
(
DAC).
The
f
o
ll
ow
in
g
de
scr
i
bes
a
nd
r
e
qu
ir
e
m
e
n
ts
f
or
e
ach
o
f
the
di
g
i
t
a
l
bloc
ks
t
ha
t
ar
e
par
t
o
f
the
c
ontr
o
l
lo
o
p
t
o
ens
u
re
c
ertain
d
es
ign
spec
if
i
c
at
i
ons
a
r
e
d
i
s
c
u
sse
d
:
fi
l
t
e
r
,
P
I
c
ontr
o
lle
r
,
m
odu
la
tor
D
P
WM,
lo
ok
up
t
a
bl
e,
z
ero
c
r
o
ssin
g
d
et
e
c
t
o
r
Z
C
D.
I
t
i
s
c
l
ear
t
h
a
t
e
ach
o
f
th
e
b
lo
ck
s
f
o
rmi
n
g
t
h
e
co
nt
rol
l
o
op
,
d
i
re
c
tly
a
f
f
e
c
t
the
s
y
ste
m
r
espo
nse.
5.
DIGIT
A
L
CO
NTROLLER
The
pr
o
p
o
r
t
i
o
nal
i
n
te
gr
al
c
o
n
tr
olle
r
s
P
I
s
a
r
e
a
g
o
o
d
c
om
pr
om
i
s
e
b
e
t
we
en
t
he
s
im
p
l
ic
i
t
y
in
d
i
g
i
t
a
l
im
pl
e
m
e
n
ta
t
i
o
n
a
n
d
t
he
obta
i
ne
d
per
f
o
r
m
a
n
ces.
The
P
I
c
om
pen
s
at
o
r
de
si
gne
d
i
n
t
his
st
ud
y
g
u
ar
a
n
t
e
e
the
sta
b
i
l
i
t
y
o
f
th
e
ou
t
put-
r
egu
l
ated
v
ar
ia
b
l
e,
t
he
p
hase
s
hi
ft.
Th
e
har
d
w
a
r
e
r
e
a
lizat
i
on
of
t
he
c
om
pe
nsa
t
o
r
tran
sfer
f
u
n
c
tion
in
th
e FP
G
A
p
l
a
tfo
r
m is ach
iev
e
d
by
u
s
i
ng
th
e
c
or
r
e
sp
ond
in
g
d
i
f
f
e
r
e
nce
equa
tio
n
:
[1
]
[
]
[
]
pi
i
Dn
k
e
n
k
D
n
(
3
)
Where
:
k
p
a
nd
k
i
a
r
e
the
c
o
e
f
f
i
c
i
e
n
ts
t
hat
d
e
te
rmine
t
h
e
pr
op
ortio
na
l
,
d
e
r
iva
tive
a
n
d
in
t
e
gra
l
g
ai
n,
r
e
spec
tive
l
y.
D
[
n
]
is
t
h
e
v
a
l
u
e
o
f
t
h
e
dut
y
cy
cl
e
at
d
i
s
c
r
et
e
ti
me
n
;
e
[
n
]
is
t
he
d
i
g
it
iz
ed
v
a
l
ue
o
f
th
e
e
rror;
D
i
[
n
]
,
i
s
the
st
ate
o
f
t
he
i
nte
g
r
a
tor
;
O
nce
the
di
gi
ta
l
co
de
o
f
the
e
r
r
or
,
e
[
n]
i
s
ob
ta
i
n
ed,
th
e
va
lue
o
f
t
he
p
ha
se
sh
ift a
n
g
l
e
[
n
] i
s
g
e
n
era
t
ed
f
ol
lo
wi
ng
t
h
e
scheme sh
o
w
n
i
n
F
i
g
u
r
e 8
.
T
h
e
c
o
ef
fi
c
i
ent
s
o
f
e
ach
g
a
i
n
s
(
K
p
a
nd
K
i
)
,
m
ay
b
e
r
o
un
de
d
t
o
pow
e
r
s
of
2
i
n
pr
a
c
t
i
ce.
T
h
i
s
ma
kes
it
im
pl
e
m
e
n
ta
t
i
o
n
e
a
s
y
us
i
ng
b
i
nar
y
s
h
i
fts.
T
his
co
n
t
r
o
l
la
w
c
a
n
b
e
impl
em
ented
us
i
ng
di
ffe
r
e
nc
e
eq
uat
i
o
n
s
,
lo
o
k
-
u
p
ta
b
l
e
s
o
r
c
a
lc
u
l
ate
d
d
ir
e
c
tl
y
us
ing
mic
r
o
p
r
o
ce
s
s
or
s
w
i
t
h
h
i
g
h
p
e
r
for
m
a
n
ce
.
I
n
t
h
i
s
pa
pe
r
,
t
he
pr
opose
d
p
ha
se
s
h
i
f
t
c
on
tr
o
l
i
s
ba
se
d
o
n
t
ha
t
for
a
de
ter
m
ined
vo
l
t
a
g
e
of
t
he
D
C
bus
a
nd
c
u
r
r
e
nt
m
o
d
u
l
a
tio
n
in
de
x,
m
a,
it
c
a
n
i
njec
t
c
u
r
r
e
nt
i
nt
o
t
h
e
g
r
id
by
var
y
in
g
t
h
e
phase
a
ng
l
e
b
e
t
wee
n
t
h
e
i
nvert
e
r
o
u
t
put
vol
t
a
g
e
a
nd
t
h
e
gr
i
d
v
o
l
t
a
ge.
The
c
o
n
t
r
o
l
pa
r
a
m
e
ter
i
n
t
hi
s
c
a
se,
is
t
h
e
a
ng
le
phas
e
δ
g
ene
r
a
ted
be
t
w
e
e
n
o
u
t
put
v
ol
t
a
ge
o
f
t
h
e
in
ver
t
e
r
a
n
d
t
h
e
g
r
i
d
vo
lta
ge
.
The
u
pda
t
i
n
g
o
f
t
he
c
ur
r
e
n
t
v
alu
e
of
t
he
p
ha
se
s
h
i
ft
a
c
c
o
r
d
i
n
g
to
t
he
l
aw
o
f
th
e
im
pl
e
m
e
n
te
d
c
o
n
t
r
o
l
i
s
r
e
a
liz
e
d
.
I
t
is
c
le
ar
t
hat
t
h
e
m
e
th
od
u
se
d
i
s
t
o
ave
r
ag
e
t
h
e
erro
r
b
e
t
w
ee
n
t
h
e
re
f
e
re
n
ce
c
u
r
r
e
nt
a
n
d
t
he
a
c
t
ua
l
me
asur
ed
v
a
l
ue
i
n
se
ver
a
l
cyc
l
e
s
o
f
gr
id
v
o
l
t
a
ge,
so
t
ha
t
r
e
g
u
la
t
o
r
y
r
e
qui
r
e
m
e
n
t
s
w
i
ll
en
su
re
s
t
a
bi
li
ty
o
f
th
e
sy
st
em
[
19
],
[
3
6
]
.
Di
re
ct
r
e
p
resen
t
ati
o
n
o
f
d
if
fe
r
e
nt
ials
e
q
u
a
t
i
on
an
d
o
p
er
a
t
ing
m
ode
s
of
L
i
n
ea
r
Reg
u
l
at
or
f
or
t
h
i
s
c
a
s
e
ar
e
show
n
r
e
spec
t
i
ve
l
y
i
n
F
i
g
ur
e
7(
a
)
a
nd
F
i
gur
e
7(
b)
.
(a)
(b
)
F
i
gur
e.
7.
(
a).
D
i
r
ect
r
epr
e
sentat
i
on
o
f
d
i
f
fer
e
nt
i
a
ls
e
q
u
a
t
i
o
n
a
nd
(
b
)
.
O
pera
t
i
n
g
m
odes
Line
ar
Reg
ula
t
or
T
h
e
A/
D
c
onv
ert
e
r
n
e
ed
ed
t
o
i
m
p
l
ement
t
h
e
con
t
ro
l
l
e
r
mu
st
h
a
v
e
b
etter
p
e
rfo
rman
ce
(
r
e
so
lu
tion
)
w
i
t
h
g
r
e
a
t
e
r
n
u
m
b
e
r
o
f
b
i
t
s
(
n
+
1
)
.
T
h
i
s
i
s
d
u
e
a
g
r
e
a
t
e
r
n
u
m
b
e
r
o
f
l
e
v
e
ls
o
f
q
u
a
nt
i
f
i
cati
o
n
are
n
eed
ed.
T
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
5
6
4
–
1
574
1
570
vo
l
t
age
s
t
hat
d
e
fi
ne
t
he
t
o
l
e
r
anc
e
b
a
nd
li
m
i
t
the
s
e
le
vels.
O
n
c
e
t
h
e
e
r
r
o
r
signa
l
e
[
n
]
is
o
b
t
a
i
ne
d,
t
he
v
a
l
ue
o
f
pha
se
s
hi
f
t
δ
[
n
]
i
s
ge
ner
a
t
e
d
a
ccor
d
i
n
g
to
F
ig
ur
e
7.
01
2
1[
]
[
1
]
[
2
]
nn
b
e
n
b
e
n
b
e
n
(
4
)
To
a
vo
id
e
xce
s
si
ve
F
P
G
A
r
e
sour
ce
c
o
n
sum
p
t
i
on,
f
i
x
e
d
-
p
o
i
n
t
f
or
m
a
t
is
u
sed
in
t
he
r
o
u
n
d
i
ng
o
f
the
di
ff
er
e
n
ce
e
qua
tio
n
c
o
ef
fic
i
e
n
ts
(
b
0
,
b
1
a
n
d
b2)
w
he
n
i
m
pl
e
m
e
n
t
ing
th
e
co
mp
e
n
sa
tor
t
r
an
sf
e
r
f
un
ct
io
n
i
n
ha
r
d
w
a
r
e
.
Mo
r
e
ove
r
,
i
n
or
d
e
r
to
i
m
p
r
o
ve
t
he
t
r
a
ns
ien
t
r
e
s
ponse
o
f
t
h
e
c
o
n
v
e
r
t
e
r
,
t
h
e
t
i
m
e
d
e
l
a
y
o
f
t
h
e
a
n
al
o
g
/d
ig
i
t
a
l
(
A
/
D
)
c
onve
r
t
er
s
houl
d
be
m
in
imize
d
.
Ther
e
f
or
e,
a
hig
h
-
s
pe
e
d
A
/D
c
onver
t
e
r
i
s
ne
ede
d
.
6.
DIGIT
A
L
SP
WM
I
n
t
his
w
o
r
k
,
the
P
W
M
ge
ne
r
a
tor
is
b
ase
d
on
o
n
l
y
one
c
o
u
n
t
er
w
i
t
c
h
g
u
a
r
a
nt
e
e
t
he
s
y
n
c
hr
onism
o
f
a
l
l
si
g
n
al
s,
t
he
a
ddr
ess
si
g
n
a
l
,
sy
ncr
o
-
s
ig
na
l
a
nd
the
c
o
n
t
r
o
l
s
i
gna
l.
I
n
F
i
gu
r
e
8
,
i
s
s
how
n
t
h
e
s
i
m
u
l
a
tio
n
r
e
sults
o
f
DPWM
s
i
g
na
ls
i
m
p
lem
e
n
t
ed
i
n
M
ode
lSim
.
(Vg1,
V
g2,
V
g
3
,
a
n
d
V
g
4)
w
hic
h
r
e
p
r
e
se
nt
t
he
P
WM
si
gna
l for e
ach
I
GT
o
f the
sin
g
le
-p
hase
i
n
v
ert
e
r
.
F
i
gur
e
8.
D
P
W
M
si
gna
ls
7.
D
I
G
I
TA
L
P
H
A
S
E
S
H
I
F
T
I
M
P
L
EM
EN
T
A
T
I
ON
F
i
gur
e
7
(
4
s
e
c
t
i
o
n)
,
show
s
t
h
e
c
o
n
t
r
o
l
a
l
g
o
r
ithm
o
f
t
he
i
n
v
e
r
t
er
o
utp
u
t
c
u
r
r
e
nt
b
a
s
e
d
on
t
h
e
phas
e
sh
ift
o
f
t
he
i
n
v
erter
out
p
u
t
vo
ltage
.
The
p
h
a
s
e
sh
ift
is
d
esi
g
n
e
d
t
o
pr
o
v
i
d
e
f
l
e
x
i
b
il
i
t
y
in
o
r
d
er
t
o
pr
od
uc
e
e
i
t
h
e
r
l
ag
g
i
n
g
,
lead
i
ng
or
i
n
p
h
ase
,
i
n
or
der
t
o
a
dj
us
t
t
h
e
po
w
er
f
ac
tor.
In
it
i
a
ll
y
t
h
e
phas
e
c
o
unt
er
i
s
l
o
a
d
e
d
t
o
th
e
sh
i
f
t
ph
a
s
e
a
ngle
val
u
e
e
q
ua
l
z
e
r
o
(
δ
=
0)
.
The
co
n
t
r
o
l
ha
ve
t
o
ma
i
n
t
a
i
n
t
he
a
de
qua
t
e
s
h
i
f
t
p
ha
se
a
n
g
l
e
w
hic
h
a
cco
m
p
lis
h
tha
t
t
he
i
nve
r
t
er
o
ut
p
u
t
c
u
r
r
ent
I
out
e
qu
a
l
t
o
th
e
referen
c
e I
ref
.
The
sign
of
t
he
pha
se
a
ngle
depe
n
d
s
o
n
t
he
pow
er
f
a
c
tor
c
h
ar
a
cter
(ind
u
c
t
i
v
e
or c
apac
it
i
v
e)
.
F
r
om
t
he r
esol
ut
ion w
i
t
h
w
h
i
ch the
m
agn
i
tu
de of
t
h
e o
u
t
p
u
t cur
r
en
t
I
out
i
s
r
e
pr
e
s
ente
d,
th
e
r
esol
uti
on (
n
umbe
r
of
b
i
t
s)
o
f
the
pha
se
s
hif
t
,
I
AD
C
r
esol
u
tio
n
o
f
t
h
e
a
na
lo
g
d
i
gita
l
A
/
D
conver
t
e
r
,
expr
e
s
sed
i
n
c
u
r
r
e
n
t
,
w
i
l
l
de
pe
n
d
on
ma
x
i
m
u
m
out
p
u
t
c
ur
r
e
nt
I
ma
x
a
n
d
i
n
cremen
t
c
u
rre
n
t
I
q:
The
r
e
solu
ti
o
n
o
f
the
c
o
n
v
e
r
t
e
r
A
/
D
de
pen
d
on
the
m
a
gn
i
t
u
d
e
of
t
h
e
curre
nt t
o stea
dy
q
I
I
ma
x
2
AD
C
log
N
(
9
)
F
r
om
d
e
s
ign
t
o
p
o
lo
g
y
,
t
h
e
s
e
lec
t
ed
a
p
p
roa
c
h
h
as
b
ee
n
t
h
e
regu
la
t
i
on
o
f
t
h
e
ou
tpu
t
c
urren
t
o
f
th
e
in
ver
t
e
r
(
I
out
)
a
s
a
fu
n
c
tio
n
of
t
h
e
δ of
f
set [2
]
-
[
4
].
22
2
2
2
1
co
s
2
in
v
r
e
d
s
inv
r
e
d
VV
L
I
VV
(
10)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Desi
gn
an
d
digi
tal
i
m
pl
e
m
ent
a
tio
n
of
pow
e
r
co
nt
rol
st
ra
t
e
gy
f
o
r
g
r
i
d
c
onne
c
t
ed
…
(L
i
n
da
Ha
ssai
n
e)
1
571
F
r
om
(
9)
,
eac
h
val
u
e
of
t
he
a
ng
les
c
an
b
e
ca
l
c
ul
at
ed
f
o
r
e
ac
h
out
put
c
u
rren
t
v
alu
e
o
f
t
h
e
in
v
e
r
t
e
r
I
out
c
or
r
e
spo
n
d
i
n
g
t
o
t
h
e
c
u
r
r
ent
of
t
he
m
a
x
imum
pow
er
p
oin
t
o
n
t
h
e
s
id
e
of
t
he
p
hot
o
v
o
l
t
a
ic
s
ys
tem
.
O
nc
e
the
ph
ase
sh
ift
a
ngle
h
as
b
e
e
n
c
a
lc
u
l
ate
d
,
the
pha
se
s
h
i
ft
a
n
g
l
e
φ
betw
ee
n
t
h
e
i
n
ver
te
r
o
u
t
pu
t
cu
rren
t
a
nd
the
gr
i
d
v
o
l
t
a
g
e
(
1)
,
i
s
d
e
t
er
m
i
ned,
w
h
i
ch
a
l
l
ow
s
t
o
d
e
t
e
r
m
i
ne
an
d
to
c
on
tr
o
l
t
he
a
c
t
i
v
e
p
o
w
e
r
a
nd
r
e
a
c
ti
ve
pow
e
r
i
n
j
ec
t
e
d
int
o
t
he
g
r
i
d
b
y
t
he
i
n
v
e
r
ter
.
S
i
nc
e the
ou
t
p
ut
c
ur
r
e
n
t
I
out
i
s
a
fu
nc
ti
o
n
o
f
the
o
u
t
pu
t v
o
lt
age
of
t
he i
n
v
e
r
ter
V
inv
a
n
d
th
e
ph
ase
shi
f
t
,
t
hen
V
in
v
c
a
n
b
e
e
xpr
esse
d
as
a
f
un
c
t
ion
o
f
t
he
d
u
t
y
cyc
l
e
(
d
)
(
10)
.
dc
V
d
inv
V
(
11)
The
pr
inc
i
ple
ope
r
a
ti
o
n
o
f
t
h
is
c
o
n
t
r
o
l
str
a
t
e
gy,
b
a
s
e
d
on
t
h
e
P
W
M
co
n
t
r
o
l
a
nd
pha
se
s
hi
f
t
,
cons
is
ts
o
f
s
e
n
sing
t
he
c
u
r
r
e
n
t
a
nd
c
a
l
cu
l
a
ti
ng
th
e
phas
e
s
hif
t
.
Th
e
ou
t
pu
t
cu
rren
t
can
b
e
re
p
r
e
s
ent
e
d
by
a
s
ing
l
e
PW
M
swi
t
c
hi
ng
p
a
t
t
e
r
n
(
d
=
co
n
s
t
a
nt
) a
s
a
f
un
ct
ion
o
f
a
s
i
ngl
e
st
at
e varia
b
le
:
p
h
a
s
e sh
i
f
t
an
g
l
e δ betwee
n t
h
e o
u
tp
ut
vo
l
t
age
o
f
t
he
i
nver
t
er
V
inv
a
nd
t
h
e
v
o
lta
ge
o
f
the
gr
i
d
V
gr
i
d
.
)
(
f
out
I
(
12)
Th
is
i
s
a
ve
r
y
i
mpor
ta
nt
f
u
n
c
tio
n
sinc
e
i
t
g
r
e
atl
y
s
im
p
l
i
f
i
e
s
t
he
h
a
r
dwar
e
com
p
le
x
ity
b
y
t
r
ansfe
rrin
g
the
p
r
evi
o
us
c
alc
u
l
a
tio
ns
t
o
a
P
C
o
f
t
h
e
S
P
W
M
s
w
itc
h
i
n
g
pa
t
t
er
n
.
In
a
"
l
ook
u
p
t
a
bl
e
"
w
e
sto
r
e
ea
ch
p
h
a
se
shi
f
t
an
gl
e
v
a
lu
e
s
b
y
e
t
h
e
i
r
c
o
r
re
sp
ond
ing
cu
rr
e
n
t
ma
gn
it
ud
e
I
ou
t
.
U
s
ing
as
a
d
es
ig
n
pla
t
f
o
r
m
a
n
F
P
GA
,
the
pha
se
s
hi
f
t
a
ng
l
e
c
a
n
b
e
ge
ne
r
a
te
d
ac
c
o
r
d
i
n
g
to
t
he
c
l
o
c
k
a
n
d
t
he
g
r
i
d
f
r
e
q
u
e
n
c
y
(
t
s
co
rre
s
p
ondi
ng
to
f
s
).
N
q
2
max
(
13)
Ta
k
i
n
g
t
he
m
axim
um
n
um
be
r
of
p
u
l
se
s
cor
r
e
s
po
ndi
ng
to
t
he
m
aximu
m
ph
a
s
e
s
h
i
f
t
an
gle
f
o
r
a
n
I
ou
t
m
a
x,
t
he
c
ou
nt
er
o
f
the
pha
se
s
h
i
f
t
a
ng
le
c
a
n
b
e
si
z
e
d
.
q
N
ma
x
2
log
q
N
ma
x
2
(
14)
The
de
si
gn
of
t
he
l
oo
k
up
tab
l
e
w
ill
b
e
de
te
r
m
ine
d
by
the
m
a
xim
um
a
ng
l
e
o
f
p
h
ase
s
h
i
f
t
ma
x
an
d
b
y
the
r
e
so
l
u
t
i
on
of
t
he
o
u
t
p
u
t
c
ur
r
e
nt
I
out
.
F
i
gur
e
.
9,
s
how
s
t
h
e
inve
r
t
er
o
u
t
pu
t
c
u
r
r
e
n
t
I
out
a
s
a
func
ti
on
of
t
he
pha
se
a
ng
le
δ
.
Th
is
f
igur
e
r
e
pr
esen
ts
t
he
o
utp
u
t
c
u
r
r
ent
I
out1
f
or
a
n
inv
e
r
t
er
o
ut
p
u
t
vol
ta
ge
V
in
v
1
=
3
4
2
V
(m
a1
=
0.
91
0)
a
nd
t
he
o
ut
p
u
t
c
ur
r
e
nt
I
ou
t
2
fo
r
V
inv2
=
3
7
0
V
(
ma
2
=
0.
9
8
6
)
,
e
ns
ur
in
g
a
p
o
w
e
r
f
ac
t
o
r
P
F
>
0.
9
9.
O
n
l
y
t
w
o
p
a
t
te
r
n
s
a
r
e
ne
ce
ssa
r
y
to
c
o
v
e
r
r
ange
f
r
o
m
3.
5
A
to
3
3
.4
A
,
wh
i
l
e
PF
re
mai
n
s
al
wa
y
s
h
i
g
h
e
r
t
h
an
0.
99.
T
he
r
e
f
o
r
e
,
t
h
e
n
u
mbe
r
o
f
D
S
P
W
M
pa
tter
n
s
is
d
e
t
e
r
mina
t
e
b
y
t
h
e
m
a
,
an
d
t
h
e
min
i
mu
m
aff
o
rd
ab
l
e
P
F
(
w
i
t
h
r
e
spec
t
t
o
t
he
q
ua
lit
y
of
i
njec
te
d
cur
r
ent)
.
F
i
gur
e
9.
I
nve
r
t
er
o
u
t
p
u
t
c
ur
r
e
nt,
I
out
vs
a
n
g
l
e
phase
δ
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
5
6
4
–
1
574
1
572
I
n
F
ig
ur
e
9,
i
t
is
p
oss
i
b
l
e
t
o
obs
er
v
e
how
t
he
c
ur
r
e
nt
I
ou
t
c
han
g
e
s
a
s
a
f
u
nc
t
i
o
n
o
f
the
pha
se
s
hi
f
t
.
A
s
a
r
e
s
u
l
t
,
t
h
e
o
u
t
p
u
t
c
u
r
r
e
n
t
I
out
.
Discr
e
tized
i
n
N
2
i
nter
va
ls
a
s
a
fu
nc
ti
on
o
f
t
he
p
ha
se
s
h
i
f
t
r
e
p
r
e
s
e
n
t
e
d
by
a
f
i
nite
n
umbe
r
N
CD
b
it
s
f
o
r
eac
h
value
s
o
f
t
h
e
cur
r
en
t
of
t
he
s
ystem
.
The
co
nd
i
t
i
on
of
t
he
l
imite
d
dut
y
cyc
l
e
t
o
b
e
hap
p
e
n
e
d
:
q
N
ma
x
2
log
(
15)
The
n
:
N
= N
AD
C
+1
(
16)
qA
DC
q
I
I
(
17)
I
t
m
e
a
ns
t
ha
t
the
r
e
solut
i
on
e
xpr
esse
d
in
c
ur
r
e
nt
m
ust
be
g
r
e
a
t
e
r
t
ha
n
tha
t
o
f
t
h
e
A
/
D
conve
r
t
e
r
.
The
F
P
GA
u
sed
i
n
t
hi
s
w
o
r
k
i
s
X
i
l
i
n
x
S
PA
RTA
N
-
3
X
C
3S
20
0
F
P
G
A
fa
m
i
l
y
bo
ard
pr
o
c
e
s
so
r.
T
o
im
pl
e
m
e
n
t
t
h
e
pr
op
ose
d
c
on
tr
o
l
s
tr
a
t
eg
y,
X
C
3
S
2
00
pr
o
c
essor
is
u
se
d
as
a
P
WM
g
e
n
er
a
t
or
t
o
b
u
i
l
d
t
he
a
ppr
opr
ia
te
g
a
t
i
n
g
s
i
gna
l
s
t
o
t
h
e
in
v
e
r
t
er
s
w
itc
he
s.
F
ig
ur
e
1
0
,
s
ho
ws
t
h
e
s
i
m
ul
a
t
i
o
n
resu
l
t
s
o
f
th
e
c
o
nt
rol
St
r
a
t
e
g
y
“
P
h
as
e
s
h
i
f
t
a
n
g
l
e
-
DPW
M
”;
t
h
e
D
PW
M
s
i
g
n
al
s
,
t
h
e
a
n
g
l
e
p
h
ase
a
nd
the
DZC.
.
F
i
gure
10. Propos
ed
h
igh-
resolut
i
on
c
ontrol
s
t
r
ategy
base
d on
F
P
G
A
r
e
sour
c
e
s
The
pr
o
p
o
se
d
D
i
g
ita
l
P
u
l
s
e
Wi
dth
M
o
d
u
l
a
t
or
(
D
P
WM)
takes
a
d
va
nta
ge
o
f
th
e
ca
p
a
bil
i
t
y
of
FPGA
to
s
h
i
ft
t
he
p
h
a
se
o
f
t
h
e
c
l
oc
k
in
s
m
a
ll
i
ncr
e
me
nts.
A
S
pa
r
t
an-
3E
d
e
v
ice
fr
om
X
i
l
i
n
x
ha
s
be
e
n
u
se
d
i
n
t
h
e
e
xper
i
m
e
nta
l
r
e
s
u
l
ts.
T
h
e
so
l
u
t
i
on
ha
s
bee
n
i
mplem
e
nte
d
by
m
ean
s
o
f
a
c
ou
n
t
er
b
ase
d
D
P
W
M
a
r
chi
t
e
c
t
ur
e
a
nd
a
s
p
ec
if
ic
b
l
o
c
k
a
va
i
l
a
b
le
i
n
the
F
P
G
A
[
3
7
]
.
T
he
t
i
m
e
pe
r
i
o
d
of
t
he
s
ys
tem
cloc
k
is
s
lice
d
by
m
e
a
n
s
o
f
the
pr
oper
pha
se
s
hi
ft
ing
o
f
t
he
c
loc
k
s
ig
na
l.
T
his
sol
u
tio
n
pr
o
v
ide
s
a
l
ow
er
e
qui
vale
n
t
F
P
G
A
cloc
k
per
i
o
d
.
8.
EX
PERIMEN
T
AL
RESULT
S
F
i
gur
e
11
s
h
ow
s
a
pr
ot
o
t
y
p
e
o
f
s
i
ng
le-
p
h
a
se
i
nver
t
e
r
w
ith
t
he
d
i
g
it
a
l
c
o
n
t
r
ol
“
Ph
as
e
sh
i
f
t
angl
e-
D
S
P
W
M”
i
m
p
l
e
me
nt
ed
i
n
a
F
P
G
A
plat
f
o
r
m
(
S
p
a
r
tan-
3
of
X
il
in
x)
r
ea
liz
e
d
and
te
st
e
d
V
gr
i
d
=
2
30
V
,
a
nd
co
u
p
l
i
n
g
i
n
du
c
t
a
n
ce
L
=
2
0
mH
.
F
i
gur
e
1
1
.
S
i
ngl
e
-
phase
i
n
v
er
ter
pr
ot
ot
y
p
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Desi
gn
an
d
digi
tal
i
m
pl
e
m
ent
a
tio
n
of
pow
e
r
co
nt
rol
st
ra
t
e
gy
f
o
r
g
r
i
d
c
onne
c
t
ed
…
(L
i
n
da
Ha
ssai
n
e)
1
573
F
i
g
u
r
e
12(a
)
s
hows
the
P
W
M
Pa
tte
rn,
the
in
verte
r
o
u
t
p
u
t
c
u
r
r
ent
I
ou
t
a
nd
i
nver
t
e
r
o
ut
p
u
t
v
o
l
t
a
g
e
V
inv
.
F
i
gur
e
12
(
b
)
show
s
the
I
nver
t
er
out
p
u
t
cur
r
ent
a
nd
gr
i
d
v
o
l
ta
g
e
a
n
d
PW
M
P
a
t
t
e
rn
s
.
(a)
(b
)
F
i
gur
e
1
2
.
(
a
)
.
P
W
M
P
a
tt
e
r
n,
i
nve
r
t
er
o
u
t
put
c
ur
r
e
nt
a
nd
i
nve
r
t
er
o
u
t
p
u
t
v
o
lta
ge
,
(
b
).
I
nv
e
r
ter
outpu
t
c
u
r
r
e
nt
and
gr
id
v
o
l
t
a
g
e
.
Th
e
ex
pe
r
i
men
t
a
l
r
e
s
u
l
t
s
s
ho
w
t
h
e
v
i
a
b
il
it
y
of
t
h
e
SPWM
me
t
hod
pr
o
pose
d
a
nd
v
a
lida
t
e
th
e
the
o
r
i
c
a
l
p
r
e
d
i
cti
o
ns.
The
c
u
r
r
e
nt
t
o
t
a
l
h
a
r
m
oni
c
d
i
s
t
or
ti
on
(
T
H
D
)
i
s
3
.
5%,
w
h
i
c
h
i
s
b
el
ow
t
he
s
u
g
g
es
ted
va
lue
b
y
S
tand
ar
d
I
EEE
S
t
d
929-
200
0.
9.
CONCLUSION
The
p
a
per
ha
s
foc
u
se
d
o
n
t
he
d
e
t
a
i
l
e
d
imp
l
e
m
entat
i
o
n
o
f
t
he
p
ow
e
r
c
on
tr
ol
s
tr
ate
g
y
o
f
P
V
inver
t
e
r
c
o
n
n
ec
ted
t
o
t
he
g
r
i
d.
T
he
p
r
opose
d
s
t
r
a
t
e
g
y
base
d
o
n
a
“
P
h
ase
shift
a
n
g
l
e
–
DSP
W
M”
p
a
t
t
e
rn
i
s
able
t
o
c
o
n
t
r
o
l
bo
t
h
t
h
e
a
ct
ive
a
n
d
r
e
a
c
ti
ve
p
ow
er
a
nd
r
e
duce
b
o
t
h
har
d
w
a
r
e
a
n
d
s
of
tw
ar
e
r
e
qu
ir
ed
r
e
s
our
ce
s
usin
g
F
P
GA
de
si
g
n
p
la
t
f
orm
.
D
i
g
i
t
a
l
imp
l
em
en
ta
t
i
o
n
o
f
th
e
ma
i
n
c
o
n
t
r
o
l
b
l
oc
ks,
w
h
ic
h
a
r
e
t
h
e
A
/
D
c
o
nver
t
er
,
the
c
o
mpe
n
sa
t
o
r
P
I
,
the
phase
shi
ft
an
d
t
he
D
P
W
M,
has be
e
n
p
r
o
vide
d
.
H
o
w
e
ve
r
,
the
p
r
o
p
o
se
d
c
ontr
o
l a
l
g
o
r
i
t
h
m
pr
ovi
de
f
lex
i
bili
t
y
t
o
a
d
j
u
s
t
t
he
pow
e
r
f
a
c
t
o
r
a
n
d
r
e
gu
la
t
e
t
he
r
ea
c
t
i
v
e
powe
r
.
Th
is
d
i
g
ita
l
p
o
we
r
c
ontr
o
l
str
a
t
e
gy
h
a
s
b
e
e
n
imple
m
e
n
t
e
d
in
F
P
G
A
pla
t
f
o
r
m
a
nd
va
l
i
date
d
w
i
t
h
e
xp
er
i
m
enta
l
r
e
su
lts.
The
e
x
per
i
m
e
nta
l
r
e
sults
s
how
t
he
v
ia
b
i
l
ity
o
f
t
h
e
S
P
WM
m
e
t
hod
pr
o
p
o
s
ed,
th
e
si
m
p
l
i
c
it
y
o
f
t
he
d
i
g
ita
l
i
m
p
l
em
e
n
ta
t
i
o
n
,
r
e
duc
ti
o
n
o
f
th
e
m
e
m
o
r
y
r
equir
e
me
nt
s
an
d
p
o
w
e
r
c
a
lcula
t
io
n
f
o
r
t
h
e
p
r
o
pose
d
con
t
r
ol
.
Th
is
t
e
c
h
n
i
qu
e
is
s
im
ple
and
a
d
ap
te
d
t
o
F
P
G
A
plat
fo
r
m
,
i
t
i
s
a
t
tr
acti
v
e
f
o
r
low
powe
r
g
r
i
d
co
nn
e
c
t
e
d
appl
i
c
a
t
i
o
ns
a
n
d
all
o
ws
t
o
c
ont
ro
l
t
h
e
a
c
tiv
e
a
nd
rea
c
t
i
v
e
p
o
w
e
r
in
jec
t
e
d
i
n
t
o
the
gr
i
d
.
Mor
e
over
,
r
obust
n
ess
o
f
t
he
p
r
opose
d
c
o
n
t
r
ol
a
l
l
o
w
s
d
e
s
ign
i
ng
a
low
c
o
s
t
an
d
s
i
m
p
l
e
i
nve
r
t
er
w
it
h
a
r
e
duc
e
d
a
m
o
u
n
t
o
f
c
o
mpo
n
e
n
t
s
,
based
o
n
a
f
ul
l
br
id
ge
t
op
o
l
og
y
tha
t
c
a
n
b
e
imp
l
em
e
n
t
e
d
w
i
t
h
m
i
n
i
m
u
m
c
o
m
p
u
t
a
t
i
o
n
a
l
r
e
sour
ce
s.
REFERE
NC
E
S
[1]
M
.
C
al
ais,
J
.
My
rz
i
k
,
an
d
T
.
S
po
oner,
‘Invert
ers
f
o
r
Singl
e
-pha
se
G
ri
d
Co
nnect
ed
P
ho
to
vo
lt
aic
S
y
s
t
em
s
-
A
n
O
v
ervi
ew’, in
P
r
oc. IE
EE,
PESC
’
02
,
vol.
2
p
p
.
1
9
95–
20
00
,
2
0
02
[2]
S. B.
K
j
aer,
J.
K
.
P
ed
ersen
, an
d
F
.
B
laabjerg,
‘A Re
v
iew
of
S
in
g
l
e-P
h
ase G
r
id
-Co
n
n
ected Inv
erter
s
fo
r
P
hoto
v
o
l
t
a
ic
M
o
dul
es’,
IEEE T
r
ans
actio
ns
on
Ind
u
s
t
r
y
Ap
p
l
i
c
a
t
io
n
s
,
vo
l
.
4
1
, no
.
5
,
20
05
.
[3]
L
.
H
as
sa
i
n
e,
E
.
Olías
,
J
.
Qui
n
t
e
ro,
an
d
V
.
S
alas
,
‘Ov
e
rview
of
P
o
we
r
In
ve
rte
r
T
op
olog
ie
s
a
n
d
Co
ntro
l
S
t
ruc
t
ure
s
f
o
r
Grid
c
on
nected
P
ho
to
voltai
c
S
yst
e
m
s
’,
R
e
newa
ble &
S
u
stai
n
a
bl
e
Ener
gy
R
eviews
,
v
o
l
.
30,
p
p
.
7
96
–80
7,
F
eb
.
20
14
.
[4]
Y
.
Y
ang
an
d
F.
b
l
aabjerg
,
‘Ov
e
rv
iew
of
s
in
g
l
e-phas
e
g
rid
co
nn
ec
ted
p
hot
ovol
ta
i
c
s
yst
e
ms’,
Electric Po
wer
Co
mpo
n
en
ts
System
s
,
v
o
l
.
4
3,
n
o
.
1
2
,
p
p.
135
2–
1
3
63
,
J
ul.
20
15.
Evaluation Warning : The document was created with Spire.PDF for Python.