TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5137 ~ 51
4
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.574
5
5137
Re
cei
v
ed Fe
brua
ry 5, 201
4; Revi
se
d March 21, 201
4
;
Accepte
d
April 3, 2014
dsPIC33 Based
Control for PV-Grid System with a
Buck-Boost MPPT
Slamet Riy
a
di
Dept of Electric
al Eng
i
ne
eri
ng,
Soegi
j
apr
an
ata Catho
lic Un
iv
ersit
y
Sem
a
ra
n
g
Pa
w
i
yat
an L
u
h
u
r IV-1 Semara
ng 50
23
4 Indo
nesi
a
email: s_ri
ya
d
i
672
00
3@
ya
ho
o.com
A
b
st
r
a
ct
T
he us
e of sol
a
r en
ergy is ve
ry important d
u
e
to
the fossil
b
a
sed
ener
gy cr
isis. Rap
i
d pr
o
g
ress i
n
PV techn
o
l
ogi
e
s
has
co
ntribut
ed to
its
ap
plic
ations.
T
h
ere
are many PV base
d
pow
er p
l
ants bui
lt
ar
ou
nd
the w
o
rld. M
a
xi
mu
m P
o
w
e
r Point T
r
acke
rs (MPPT
) take sig
n
ifica
n
t r
o
le
in
oper
atin
g PV
mo
dul
es
to
prod
uce
t
heir
max
i
mu
m pow
er.
T
hey are i
m
ple
m
ented
by
usin
g ch
op
pers
to
match
the
l
oad
resista
n
ce
and
the PV r
e
sista
n
ce. R
e
cently,
inte
gratio
n
be
tw
een PV
mo
dul
es a
n
d
gri
d
s is
mor
e
pop
ular
du
e to
th
ei
r
adva
n
tag
e
s. T
he PV-Grid
sys
tem c
an
be s
i
n
g
le sta
ges,
tw
o
stages
or a
n
y
other typ
e
s a
n
d
al
l of th
e
m
u
s
e
PW
M (pulse w
i
dth modu
lati
on
) converters as
their core
s. In this pap
er, a PV-Grid System
usin
g buck-
boo
s
t
chop
per
as M
PPT
is an
aly
z
ed. Pow
e
r
gen
erated
by PV
m
o
d
u
l
e
s
i
s
tran
sfe
rre
d to
th
e g
r
i
d
b
y
u
s
i
ng an
inverter th
at o
perate
d
as a
cont
rol
l
ed c
u
rr
ent sourc
e
so
the co
mpl
e
xit
y
can b
e
red
u
c
ed. F
i
na
lly, the
dsPIC33
bas
e
d
contro
l sche
m
e for s
u
ch
a PV-Grid Syst
em w
a
s
mad
e
a
s
a lab
o
ratory
scale
d-prototy
pe
t
o
verify the ana
ly
sis and si
mulat
i
ons.
Ke
y
w
ords
: bu
ck-boost cho
p
p
e
r, PV-Grid, inverter, dsPIC
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Solar en
ergy
has b
e
come
an alternative solution
sin
c
e the fossil b
a
se
d ene
rgy
cri
s
is
hit
the worl
d. By using
sola
r p
anel
s (PV), solar en
er
gy can be converted into
electrical en
ergy a
nd
an MPPT is required to maximize the o
u
tput powe
r
. An MPPT in
prin
ciple i
s
a DC-DC conv
erter
(ch
opp
er) tha
t
is capa
ble t
o
force
a PV modul
e
op
erating poi
nt n
ear it
s maxim
u
m po
we
r p
o
i
nt
(MPP) [1
-3].
There a
r
e th
ree type
s
of ch
opp
er
: b
u
ck,
boo
st a
n
d
bu
ck-b
oo
st types. A b
u
ck
cho
ppe
r ba
se
d MPPT can
be appli
ed for the output re
sista
n
ce less
than the PV resi
stan
ce at i
t
s
MPP [4] whil
e for the
out
put re
si
stan
ce greate
r
tha
n
the PV
re
si
stan
ce, a
bo
o
s
t chop
per ba
sed
MPPT ha
s to
be
used. MP
PTs h
a
ve b
e
en d
e
velop
e
d
by ma
ny re
searche
r
s e
s
p
e
cially i
n
cont
rol
method
s.
Re
cently, int
egratio
n b
e
twee
n PV mo
dule
s
a
nd
gri
d
sy
stem
s b
e
com
e
p
opul
ar
due
to
their a
d
vanta
ges, it i
s
nam
ed a
s
PV-Gri
d
System
s
.
Th
e
r
e ar
e
s
o
me
me
th
od
s to ma
ke
PV-G
r
id
,
they can u
s
e
singl
e stag
e, two stag
e or
any other typ
e
s [5-7]. An inverter i
s
a core in a PV-Grid
System for the output of PV m
odules a
r
e DC voltage/
curre
n
t while
the grid voltage is AC and
it
is also requi
red syn
c
h
r
oni
zation in
parallel co
nne
cti
on. PWM te
chniqu
e is very important to
operate inverters
with co
ntrolled
outp
u
t volt
age/cu
rre
nt [8]. A
PWM ba
se
d
voltage sou
r
ce
inverter
(VSI) will be
capable to
be
synchroni
zed to
the grid volt
age [9-11]. Some inverters
are
operated as controlled
vol
t
age sou
r
ces in
a
PV
-Gri
d System
an
d compl
e
xities are
faced du
e
to
the syn
c
h
r
oni
zation
re
quire
ments. O
pera
t
ing invert
e
r
s as cont
rolled
cur
r
e
n
t
so
ur
c
e
s
a
r
e simpl
e
r
in PV-Grid Sy
stem
s for the inverter o
u
tpu
t
volt
age is automatically l
o
cked to the
grid voltage.
In this
pap
er,
a PV-G
r
id
System u
s
ing
buck-boo
st M
PPT is d
e
scri
bed. Thi
s
MPPT ha
s
flexibility in magnitud
e
of
DC outp
u
t voltage. To
provide a
co
nsta
nt DC-lin
k volta
ge a
s
a
n
inp
u
t
of the inve
rter, such a
n
MPPT sh
ows its adva
n
tag
e
s. Th
e p
r
op
ose
d
inve
rter ope
rated
a
s
a
controlled
cu
rre
nt sou
r
ce
is ca
pabl
e to
transfe
r all
power g
ene
rated by PV module
s
. Fin
a
lly,
simulatio
n
s a
nd labo
rato
ry experime
n
ts were
done t
o
verify the analysi
s
. The
prototype u
s
es
control ci
rcuits that based
on dsPIC33.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5137 – 51
43
5138
2. Rese
arch
Metho
d
2.1. Buck
Bo
ost Choppe
r
as a Maximum Po
w
e
r P
o
int Trac
ker
(MPPT)
A photovoltaic cell can
conve
r
t sola
r energy
into
electri
c
en
ergy. Based
on its
characteri
stic curve (Fi
g
ure 1(a)),
direct
connecting a resi
stive lo
ad to this cell
will produce l
e
ss
electri
c
p
o
we
r. Some
cells can
be a
r
ra
nged
as
se
ri
al and/o
r
pa
rallel conne
cti
on to be
a PV
module.
To
maximize
the
po
wer ge
nerated by
a
PV
modul
e, an
MPPT is
nee
ded. By u
s
in
g a
buck-boo
st chopp
er, the
output vo
ltag
e of an MP
PT can
be g
r
eate
r
or less than th
e in
put
voltage. For
a PV-Gri
d
Co
nne
cted Syst
em, an inve
rter i
s
re
quired
with spe
c
ifie
d DC-lin
k volt
age
level so
su
ch a chop
pe
r
is bette
r to b
e
implem
ent
ed. In the ot
her
hand, th
e num
ber
of PV
module
s
ca
n
be m
o
re
flexible. Figu
re
1
(
b)
rep
r
e
s
ent
s a b
u
ck-bo
ost cho
ppe
r
as
an MPPT. T
h
e
relation
shi
p
b
e
twee
n input
voltage
E
, output voltage
o
V
and duty cycle
d
can b
e
stated
as:
E
d
d
V
o
1
(
1
)
L
in
i
i
L
v
ou
t
R
o
I
o
V
(a)
(b)
Figure 1. (a)
Cha
r
a
c
teri
stic cu
rve of phot
ovoltaic, (b)
A buck-b
o
o
s
t cho
ppe
r as a
n
MPPT
PV
V
PV
I
in
R
o
V
o
R
o
I
Figure 2. Con
nectin
g
an M
PPT to a PV
Module
Con
n
e
c
ting
such
a
ch
opp
er a
s
an
MPPT to a PV
module
is ai
med to
get
maximum
power. By
co
ntrolling
the
duty cycl
e, th
e op
erat
in
g p
o
int of a PV
module
s
ca
n
be
aro
und
the
MPP. This ca
n be achieve
d
if the resist
anc
e of load see
n
from th
e PV module equal
s to
MP
P
R
.
Referrin
g to t
he la
w
of en
e
r
gy
con
s
e
r
vation, un
der an
ideal
sy
stem
, the inp
u
t po
wer will
eq
ual
to
the output po
wer of the ch
oppe
r, then we have (whe
re
L
MPP
in
PV
R
R
V
E
and
):
out
out
o
in
out
o
o
in
o
o
in
R
E
d
d
R
V
R
E
R
V
V
R
E
E
I
.
V
I
.
E
2
2
2
2
1
out
in
R
d
d
R
2
1
(
2
)
Equation
(2
)
sho
w
s that th
e load
re
si
sta
n
ce
co
nne
cte
d
to a PV m
o
dule
can
be
greate
r
o
r
le
ss
than
MPP
R
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
dsPIC3
3 Based Co
ntrol for PV-Grid Syst
em
with a Buc
k
-Boos
t
MPPT (Slamet Riy
adi)
5139
2.2. Full-Bridge In
v
e
rter as an In
ter
f
ac
e in PV-Grid Conn
ected Sy
stem
The outp
u
t voltage of an
MPPT is DC
voltage. To transfe
r ele
c
tri
c
ene
rgy ge
n
e
rated
by
PV modules,
it is required
an inverter to
conve
r
t
DC in
to AC voltage. Conne
cting
an inverter to a
grid, the synchroni
zation require
ment
s must be regarded
so the
complex problems will be faced.
If an inverter is ope
rated
as a
controll
ed cu
rrent
source, it is si
mple to co
nstruct the
cont
rol
circuit. Fig
u
re 3
depi
cts a
PV-Gri
d
Co
nne
cted Syst
em
con
s
ist
s
of PV mod
u
l
e
s, a
bu
ck-b
oost
cho
ppe
r ba
sed MPPT a
nd a
cont
roll
ed current
source im
ple
m
ented by a
Voltage So
urce
Inverter (VSI). Two digital
sign
al co
ntrol
l
ers
im
plem
e
n
ted by dsPI
C33 a
r
e u
s
e
d
to control the
MPPT and the inverte
r
separately. The first
dsPIC33 need
s two input
sign
a
l
s (voltage a
nd
curre
n
t of the PV modules) to force the MPPT oper
at
e at its MPP.
The se
co
nd d
s
PIC33 h
a
s f
our
input sig
nal
s (refe
ren
c
e vo
ltage, cap
a
cit
o
r voltage,
te
mplate and t
he inverte
r
o
u
tput cu
rre
nt) to
operate the
i
n
verter tran
sf
erri
ng
all p
o
wer g
ene
ra
te
d
by the PV m
o
dule
s
to th
e g
r
id. Unde
r i
d
e
a
l
con
d
ition the MPPT runs o
p
timally and the elect
r
ic po
wer g
ene
rate
d by the PV
module
s
can be
stated a
s
:
MPP
MPP
PV
I
.
V
P
(
3
)
Assu
ming a
n
ideal bu
ck-b
o
o
st ch
opp
er, the output po
wer of the M
PPT.
MPP
o
o
o
MPPT
I
d
d
.
V
I
.
V
P
1
(
4
)
te
mp
i
c
i
ref
V
ca
p
V
s
i
L
i
c
i
Figure 3. PV-Grid Conn
ect
ed System Consi
s
ts of PV Module
s
, Buck-b
oo
st MPPT and a
Controlled
Cu
rre
nt Source Impleme
n
t
ed
by an Voltage
Source Inverter
The voltage
o
V
is the output voltage of the MPPT, it
equals to the DC-link voltag
e (input
side of the inverter). Fo
r this inverter i
s
parall
e
l co
nn
ected to the g
r
id, so its voltage mu
st be the
same
as th
e grid voltag
e
s
v
. Operating a
n
inverter a
s
a
controlled
cu
rrent sou
r
ce
with template
cur
r
e
n
t
temp
i
take
n
from the g
r
id
voltage re
sul
t
s in si
nu
so
id
al cu
rrent flo
w
ing
at
the o
u
tput sid
e
of
the inverter.
The refe
ren
c
e cu
rre
nt is o
b
tained by
temp
i
.
k
(where
k is mult
iplying factor) then the
output
cu
rre
nt of the
in
verter
c
i
will f
l
uctuate around the re
ference current.
Under
ideal
con
d
ition, the
output power of t
he inverter can b
e
expressed a
s
:
ref
s
c
s
c
I
.
V
I
.
V
P
(
5
)
Whe
r
e
temp
ref
i
.
k
I
.
For all the po
wer g
ene
rate
d by the PV
module
m
u
st
be tran
sferre
d into the grid
, then:
MPP
PV
c
P
P
P
MPP
MPP
ref
s
I
.
V
I
V
then
s
MPP
MPP
ref
V
I
.
V
I
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5137 – 51
43
5140
Power equilibrium in the invert
er can be detected by sensin
g the capacito
r voltage. If
the inp
u
t po
wer of th
e in
verter i
s
gre
a
ter th
an th
e
output
po
wer, the
capa
citor voltage
will
increa
se, thi
s
mea
n
s that t
he inve
rter a
b
so
rb
s th
e
p
a
rt of
po
wer t
r
an
sferred.
If the in
put p
o
w
er
of the inve
rte
r
i
s
le
ss than
the o
u
tput p
o
we
r,
the
ca
pacito
r
voltag
e will
de
crea
se; it m
ean
s
that
the inverter
send
s the part
of powe
r
to the grid.
2.3. dsPIC33
Based
Con
t
rol Method
dsPIC3
3 is a family of 16-bit digital sign
al
controller t
hat provide
s
high sp
eed A
D
Cs. In
this p
ape
r, d
s
PIC33F
J16
G
S502 i
s
used
as th
e
co
re
of co
ntrol.
To fo
rce
the
PV m
odule
s
ope
rat
e
near their M
PP, the dsPI
C33
re
quires two a
nal
o
g
i
nputs th
ro
ug
h a
curre
n
t transdu
cer for
PV
curre
n
t an
d a
voltage
divider fo
r the
PV modul
es voltage
(Fig
ure
4
(
a)). Th
e flo
w
diag
ram
use
d
by the first dsPIC33 is
sho
w
n in Figu
re
5(a
)
.
Figure 4. (a)
Control sche
me of the pro
posed M
PPT usin
g dsPIC3
3, (b) Control
scheme of th
e
prop
osed inv
e
rter u
s
in
g dsPIC33
The co
ntrol
schem
e of the inverter op
erated
as a
co
ntrolled
cu
rre
nt source i
s
depi
cted
in Figure 4
(
b
)
. It requires four an
alog
input sig
nal
s. The refe
re
n
c
e voltage
a
nd the DC-Li
nk
voltage si
gna
ls a
r
e n
eed
ed
to ke
ep p
o
wer e
quilib
rium
of the invert
er. The
two
o
t
her
sign
als, t
he
inverter o
u
tpu
t
current an
d the grid volta
ge as
cu
rrent
template are
used to m
a
ke sinu
soi
dal g
r
id
curre
n
t. The flow dia
g
ra
m use
d
by the first d
s
PIC33 i
s
sh
own in Figure 5
(
b
)
.
Figure 5. (a)
Flow dia
g
ram
of the propo
sed MPPT
con
t
rol, (b) Flo
w
diagram of the prop
osed
inverter control
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
dsPIC3
3 Based Co
ntrol for PV-Grid Syst
em
with a Buc
k
-Boos
t
MPPT (Slamet Riy
adi)
5141
3. Results a
nd Analy
s
is
To verify the analysi
s
, sim
u
lation
s and l
aboa
rtory ex
perim
ents
we
re do
ne ba
se
d on the
circuit de
pict
ed in Figu
re
3. The sim
u
l
a
tions
we
re
done by u
s
in
g the PSIM software a
n
d
the
laboa
rtory ex
perim
ents
we
re te
sted by u
s
ing th
e
p
r
oto
t
ype desi
gne
d.The
simulat
i
ons fo
r the P
V
-
Grid System
were don
e wi
th the MPPT
operated
a
s
a boo
st chop
per an
d a bu
ck
cho
ppe
r u
nder
two p
o
wer co
ndition,
whe
n
the the
lo
ad
power (
P
L
) i
s
greater o
r
le
ss than
the
p
o
we
r
gene
rat
e
d
by the PV mo
dule
s
(
P
PV
). Figure 6
and
Figure 7
sh
o
w
the
sim
u
lati
on results
wh
en the
MPPT
is
operated a
s
a boo
st ch
op
per. The
outp
u
t voltage of
the MPPT is g
r
eate
r
than th
e voltage of the
PV modules (Figure 6(a) and 6(b
)).
The inverte
r
is also cap
a
b
le to transf
e
r all the po
wer
gene
rated
by
the PV mo
d
u
les to the
g
r
id b
e
cau
s
e t
he ave
r
ag
e
power
of the
inverte
r
o
u
tput
equal
s to
P
PV
(Figu
r
e 6
c
a
nd 6d
). Whe
n
P
L
is gre
a
ter than
P
PV
, the load
current equal
s to
the
sum of the g
r
i
d
cu
rre
nt and
the in
verter o
u
tput cu
rre
nt while if
P
L
is less than
P
PV
, the part of the
power g
ene
rated by the
PV module
s
will ente
r
int
o
the g
r
id
si
de. Thi
s
me
ans th
at the
grid
curre
n
t ha
s t
he o
ppo
site
polarity
with
respe
c
t to
th
e gri
d
voltag
e or inverte
r
output
cu
rre
n
t
(Figu
r
e 7
)
. O
peratin
g the
MPPT of the PV-Grid Syst
em as
a bu
ck cho
ppe
r re
sults in the M
PPT
output voltag
e less than t
he PV modul
es volt
age
(Figure 8). Th
e cu
rrents u
nder t
w
o p
o
w
er
con
d
ition are depi
cted in Fi
gure 9.
Figure 6. Simulation Results of the PV-G
r
id
Co
nne
cte
d
System with MPPT Operated as a
Boost-ch
opp
er (a
) MPPT voltage (b
) PV voltage
(c) powe
r
gen
erated by PV module
s
(d
) po
wer
transfe
rred b
y
the inverter to the grid
Figure 7. Simulation Results of the PV-G
r
id
Co
nne
cte
d
System with MPPT Operated as a
Boost-ch
opp
er (lo
ad curre
n
t I
L
, grid current I
s
, inverter output curre
n
t I
c
) (a) whe
n
the load
power is g
r
e
a
t
er than the p
o
we
r gen
erated by PV
(b) whe
n
the loa
d
power is le
ss than the
power ge
ne
ra
ted by PV
Figure 8. Simulation Results of the PV-G
r
id Co
nne
cte
d
System with MPPT Operated as a Bu
ck-
cho
ppe
r (a
) MPPT voltage (b) PV voltage (c) po
wer
gene
rated by
PV (d) po
wer
transfe
rred b
y
the inverter to
the grid
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5137 – 51
43
5142
Figure 9. Simulation Results of the PV-G
r
id Co
nne
cte
d
System with MPPT Operated as a Bu
ck-
cho
ppe
r (lo
a
d
current I
L
, grid c
u
rrent I
s
, i
n
verter output c
u
rrent I
c
) (a) wh
en the l
oad po
we
r is
greate
r
than t
he po
wer g
e
n
e
rated by PV (b)
when the
load po
we
r is less tha
n
the
powe
r
gene
rated by
PV
To do the la
b
o
rato
ry experiments, the P
V
-G
rid Sy
ste
m
wa
s de
sig
ned by u
s
ing
dsPIC3
3
based
control
schem
e a
s
p
r
esented i
n
Fi
gure
10. Th
e
gird voltag
e a
pplie
s 32 Volt
RMS an
d th
e
resi
stive
lo
ad
s
of 3.3 Ohm and 9
O
h
m. The
l
oad
cu
rrent, the g
r
id
current a
nd th
e inverte
r
out
put
curre
n
t are d
epicte
d
in Fi
gure
11 an
d Figure 12.
Base
d on the
results, it is
proved th
at the
prop
osed
system is
cap
abl
e to tran
sfer
all the
po
we
r
gene
rated
by the PV mod
u
les i
n
to the
grid
without syn
c
hroni
zatio
n
requireme
nts.
Taking
a te
mplate from t
he grid volta
ge as the
cu
rre
nt
referen
c
e
will
force the inv
e
rter t
r
an
smit
the re
al po
wer. The
outpu
t voltage of the inverte
r
th
at
operated a
s
a cont
rolle
d current so
urce
is automati
c
ally locked to
the grid volt
age. The u
s
e
of
dsP
I
C
s
a
s
co
res
of
t
he co
nt
rol s
c
h
e
me
make
s t
he
system si
mple,
they also p
r
o
v
ide high
spe
e
d
ADC. F
o
r the
DC-lin
k volta
ge of th
e inv
e
rter mu
st be
set
on
co
m
m
on valu
e, th
e u
s
e
of a
bu
ck-
boos
t
MPPT is
more attrac
tive.
Figure 10.
The Prototyp
e use
d
for La
borato
r
y Experime
n
ts
Figure 11. Experim
ental Result
s of the PV-
Grid
Con
necte
d System for Load
Current I
L
, Grid
Cur
r
e
n
t I
s
and Inverter Current I
c
when the Loa
d Power is G
r
eate
r
than the Powe
r Gene
rate
d
by PV Modules [scale : 5A
/div – 5ms/div]
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
dsPIC3
3 Based Co
ntrol for PV-Grid Syst
em
with a Buc
k
-Boos
t
MPPT (Slamet Riy
adi)
5143
Figure 12. Experim
ental Result
s of the PV-
Grid
Con
necte
d System for Load
Current I
L
, Grid
Cur
r
e
n
t I
s
and Inverter Current I
c
when t
he Loa
d Power is Le
ss tha
n
the Powe
r Gene
rated by
PV Modules [
s
cale : 5A/div – 5ms/div]
4. Conclusio
n
A PV-Grid Co
nne
cted System with a bu
ck-bo
o
st MP
PT has be
en pre
s
ente
d
. By using a
dsPIC3
3 ba
sed co
ntrol, such a
PV-Gri
d
System is cap
able to transmit all the
maximum p
o
we
r
gene
rated by
the PV modules into the
grid. The d
s
P
I
C33 is
suita
b
le for the co
re of the cont
rol
circuit b
e
cau
s
e it ha
s
high
spe
ed A
D
Cs.
Dete
ction
of
the DC-li
n
k voltage
ca
n b
e
used to
ide
n
tify
the behavio
r of the power tran
sferre
d. By keeping its volt
age nearly con
s
tant, the power
equilib
rium i
s
achi
eved. T
h
is
con
c
e
p
t is then
used
as the
ba
sic to co
ntrol th
e
magnitud
e
of
the
inverter outp
u
t cu
rrent. In
the oth
e
r
h
and, the
tem
p
late
curre
n
t take
n fro
m
the gri
d
volt
age
results in the
inverter o
u
tpu
t
current in
ph
ase
with re
sp
ect to the grid
voltage.
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a
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e
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n
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r
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taic Ar
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s
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g Ri
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le C
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rrel
a
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n
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06;
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Brito MAG, Galotto L, Sampa
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