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educe
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v
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ic
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ste
m
s
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C
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Vs
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s
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ted
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n
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c
a
n
t
c
h
a
ll
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c
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larly
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re
sp
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c
t
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tal
h
a
rm
o
n
ic
d
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rt
io
n
(THD).
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is
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se
a
rc
h
is
c
o
n
c
e
rn
e
d
with
e
v
a
lu
a
t
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g
t
h
re
e
we
ll
-
k
n
o
w
n
p
u
lse
wid
t
h
m
o
d
u
lati
o
n
(P
W
M
)
tec
h
n
iq
u
e
s
-
sin
e
P
WM
(
S
P
WM
)
,
th
ird
h
a
rm
o
n
ic
in
jec
ti
o
n
P
WM
(T
HIPW
M
),
a
n
d
s
p
a
c
e
v
e
c
to
r
P
W
M
(
S
VPW
M
)
f
o
r
t
h
e
ir
e
ffe
c
ti
v
e
n
e
ss
i
n
m
it
i
g
a
ti
n
g
TH
D
in
th
re
e
-
p
h
a
se
sin
g
le
-
sta
g
e
G
CP
V
s.
Th
ro
u
g
h
e
x
ten
siv
e
sim
u
lati
o
n
s
p
e
rfo
rm
e
d
in
M
AT
LAB/S
im
u
li
n
k
,
a
c
o
m
p
r
e
h
e
n
siv
e
c
o
m
p
a
ra
ti
v
e
a
n
a
ly
sis
is
p
re
se
n
ted
th
a
t
re
v
e
a
ls
th
e
stre
n
g
th
s
a
n
d
li
m
it
a
ti
o
n
s
o
f
e
a
c
h
P
WM
stra
teg
y
.
T
h
e
re
su
lt
s
sh
o
w
t
h
a
t
S
VP
WM
is
th
e
m
o
st
e
ffe
c
ti
v
e
tec
h
n
i
q
u
e
f
o
r
THD
m
it
i
g
a
ti
o
n
a
n
d
o
u
t
p
e
rfo
rm
s it
s
c
o
u
n
ter
p
a
rts.
THI
P
WM
p
r
o
v
e
s
t
o
b
e
a
p
r
o
m
isin
g
se
c
o
n
d
-
b
e
st
o
p
ti
o
n
,
wh
il
e
S
P
WM
lag
s
b
e
h
in
d
in
term
s
o
f
h
a
rm
o
n
ic
su
p
p
re
ss
io
n
c
a
p
a
b
il
it
ies
.
T
h
is
re
se
a
rc
h
n
o
t
o
n
l
y
q
u
a
n
ti
fies
t
h
e
THD
re
d
u
c
ti
o
n
a
c
h
iev
e
d
b
y
e
a
c
h
P
WM
tec
h
n
iq
u
e
b
u
t
a
lso
d
e
lv
e
s
in
to
th
e
u
n
d
e
rly
i
n
g
m
e
c
h
a
n
ism
s
a
n
d
th
e
o
re
ti
c
a
l
u
n
d
e
rp
i
n
n
i
n
g
s
th
a
t
c
o
n
tri
b
u
te
to
t
h
e
ir
d
isti
n
c
t
p
e
rfo
rm
a
n
c
e
s.
Th
e
re
su
lt
s
a
re
fu
rth
e
r
su
p
p
o
rted
b
y
d
e
tailed
h
a
rm
o
n
ic
sp
e
c
tru
m
a
n
a
ly
se
s,
p
ro
v
id
i
n
g
v
a
l
u
a
b
le
in
si
g
h
ts
in
t
o
t
h
e
h
a
rm
o
n
ic
p
ro
fi
les
a
ss
o
c
iate
d
with
e
a
c
h
m
o
d
u
lati
o
n
stra
teg
y
.
K
ey
w
o
r
d
s
:
Gr
id
-
co
n
n
e
cted
p
h
o
to
v
o
ltaic
Po
wer
q
u
ality
Pu
ls
e
wid
th
m
o
d
u
latio
n
T
h
r
ee
-
p
h
ase
s
in
g
le
-
s
tag
e
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
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
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-
SA
li
c
e
n
se
.
C
o
r
r
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s
p
o
nd
ing
A
uth
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r
:
B
o
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led
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o
u
a
Ad
el
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
Facu
lty
o
f
T
ec
h
n
o
l
o
g
y
,
B
ad
ji M
o
k
h
tar
U
n
iv
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s
ity
An
n
ab
a
2
3
0
0
0
,
Alg
er
ia
E
m
ail: a
d
el.
b
o
u
le
d
r
o
u
a@
u
n
i
v
-
an
n
ab
a.
d
z
1.
I
NT
RO
D
UCT
I
O
N
Gr
id
-
co
n
n
e
cted
p
h
o
to
v
o
ltaic
s
y
s
tem
s
(
GC
PVs
)
h
av
e
r
ec
en
tly
g
ain
ed
c
o
n
s
id
er
ab
le
at
ten
tio
n
as
p
r
o
m
is
in
g
alter
n
ati
v
e
an
d
v
ia
b
le
en
er
g
y
s
o
u
r
ce
s
am
o
n
g
t
h
e
ex
is
tin
g
r
en
ewa
b
le
e
n
er
g
ies
to
f
u
lf
ill
th
e
e
v
er
-
g
r
o
win
g
g
lo
b
al
en
er
g
y
d
em
a
n
d
[
1
]
,
[
2
]
.
Ho
wev
er
,
GC
PV
in
teg
r
atio
n
o
f
ten
u
n
d
er
g
o
es
p
o
wer
q
u
ality
(
PQ)
is
s
u
es,
p
ar
ticu
lar
ly
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
[
3
]
,
[
4
]
.
Ma
n
y
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
m
eth
o
d
s
h
av
e
b
ee
n
s
u
g
g
ested
to
s
o
lv
e
th
is
is
s
u
e
b
y
lo
wer
in
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
th
u
s
en
h
an
cin
g
th
e
g
en
er
al
GC
PV
p
er
f
o
r
m
an
ce
.
Har
m
o
n
ic
d
is
to
r
tio
n
s
in
GC
PVs
ca
n
ca
u
s
e
PQ
p
r
o
b
lem
s
,
in
c
lu
d
in
g
v
o
ltag
e
f
lu
ctu
atio
n
s
,
h
i
g
h
er
lo
s
s
es,
an
d
in
ter
f
e
r
en
ce
with
o
th
er
e
lectr
ical
d
ev
ices
[
5
]
.
T
h
er
ef
o
r
e,
it
is
ess
en
tial
to
im
p
lem
en
t
ef
f
ec
tiv
e
PW
M
tech
n
iq
u
es
to
m
itig
ate
th
ese
e
f
f
ec
ts
an
d
e
n
s
u
r
e
th
e
r
eliab
le
o
p
er
atio
n
o
f
th
e
s
y
s
tem
.
T
h
r
e
e
well
-
k
n
o
wn
PW
M
tech
n
iq
u
es
th
at
h
av
e
b
ee
n
ex
t
en
s
iv
ely
s
tu
d
ied
to
r
ed
u
ce
h
ar
m
o
n
ic
cu
r
r
e
n
t
d
is
to
r
tio
n
in
GC
PV
s
ar
e
s
in
e
PW
M
(
SP
W
M
)
,
th
ir
d
h
ar
m
o
n
ic
in
jec
tio
n
PW
M
(
T
HI
PW
M
)
,
an
d
s
p
ac
e
v
ec
to
r
PW
M
(
SVPW
M
)
.
Nu
m
er
o
u
s
r
esear
c
h
ef
f
o
r
ts
h
av
e
b
ee
n
m
a
d
e
to
in
v
esti
g
ate
v
ar
io
u
s
PW
M
tech
n
iq
u
es
f
o
r
in
v
e
r
ter
s
u
s
ed
in
g
r
id
-
c
o
n
n
ec
te
d
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
,
with
th
e
aim
o
f
im
p
r
o
v
i
n
g
p
o
wer
q
u
ality
,
m
it
ig
atin
g
h
ar
m
o
n
ics,
an
d
o
p
tim
izin
g
s
y
s
tem
p
er
f
o
r
m
an
ce
.
I
n
v
esti
g
atin
g
t
h
e
h
ar
m
o
n
ic
r
ed
u
ctio
n
p
o
te
n
tial o
f
an
SP
W
M
in
v
er
ter
in
a
s
in
g
le
-
p
h
ase
g
r
id
-
co
n
n
ec
ted
PV
s
y
s
tem
[
6
]
,
wh
ile
[
7
]
d
is
cu
s
s
es
th
e
d
esig
n
an
d
a
n
aly
s
is
o
f
GC
PV
s
u
s
in
g
v
ar
io
u
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
va
lu
a
tio
n
o
f p
u
ls
e
w
id
th
mo
d
u
la
tio
n
tech
n
iq
u
es to
r
ed
u
ce
to
ta
l h
a
r
mo
n
ic
d
is
to
r
tio
n
in
…
(
B
o
u
led
r
o
u
a
A
d
el
)
565
PW
M
tech
n
iq
u
es
f
o
r
in
v
er
ter
c
o
n
tr
o
l.
T
h
e
co
n
tr
o
l
o
f
a
two
-
le
v
el
ca
s
ca
d
ed
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
f
o
r
a
GC
PVs
u
tili
zin
g
SVPW
M
an
d
a
q
u
a
d
r
atic
b
o
o
s
t c
o
n
v
e
r
ter
was stu
d
i
ed
[
8
]
,
h
ig
h
lig
h
tin
g
th
e
in
ter
p
l
ay
b
etwe
en
in
v
e
r
ter
co
n
tr
o
l
an
d
co
n
v
er
ter
to
p
o
lo
g
i
es.
A
co
m
p
ar
ativ
e
an
aly
s
is
o
f
PW
M
m
eth
o
d
s
f
o
r
a
th
r
ee
-
lev
el
NPC
in
v
er
ter
was
ca
r
r
ied
o
u
t
[
9
]
,
wh
ich
co
n
tr
i
b
u
ted
to
th
e
u
n
d
er
s
tan
d
in
g
o
f
m
u
ltil
ev
el
in
v
er
ter
co
n
tr
o
l.
A
co
m
p
r
eh
en
s
iv
e
r
e
v
iew
o
f
PW
M
tech
n
iq
u
es
in
two
-
le
v
el
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
s
is
p
r
esen
ted
,
p
r
o
v
id
in
g
a
cu
r
r
e
n
t
p
er
s
p
ec
tiv
e
an
d
f
u
tu
r
e
d
ir
ec
tio
n
s
in
th
is
ar
ea
[
1
0
]
.
T
h
is
s
tu
d
y
i
n
tr
o
d
u
ce
s
a
m
o
d
el
f
o
r
th
r
ee
-
p
h
ase,
s
in
g
le
-
s
tag
e
GC
PVs
th
at
in
co
r
p
o
r
at
es
SP
W
M,
T
HI
PW
M,
an
d
SVPW
M
tech
n
iq
u
es
.
T
h
e
aim
is
t
o
m
in
im
iz
e
cu
r
r
e
n
t
h
a
r
m
o
n
ic
d
is
to
r
tio
n
an
d
en
h
an
ce
o
v
e
r
all
s
y
s
tem
ef
f
icien
cy
.
MA
T
L
AB
Simu
lin
k
is
u
s
ed
to
m
o
d
el
th
e
b
eh
av
io
r
o
f
th
e
s
y
s
tem
u
n
d
er
v
ar
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
to
e
v
alu
ate
PW
M
m
eth
o
d
s
f
o
r
r
ed
u
cin
g
h
ar
m
o
n
i
c
d
is
to
r
tio
n
s
.
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
T
h
e
s
u
g
g
ested
GC
PV
m
o
d
el
is
illu
s
tr
ated
in
Fig
u
r
e
1
a
n
d
is
u
s
ed
to
g
en
e
r
ate
a
p
o
wer
o
f
9
5
.
9
k
W
f
o
r
s
im
u
latio
n
s
tu
d
ies.
T
h
e
s
y
s
tem
co
n
f
ig
u
r
atio
n
in
cl
u
d
es
a
PV
ar
r
ay
,
a
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P&
O)
m
a
x
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
alg
o
r
ith
m
,
a
DC
lin
k
ca
p
ac
i
to
r
,
a
th
r
ee
-
p
h
ase
two
-
lev
el
(
3
Ph
-
2
L
)
in
v
er
ter
,
a
n
d
a
p
ass
iv
e
L
C
L
f
ilter
co
n
n
ec
ted
t
o
th
e
g
r
i
d
.
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
a
rr
a
y
m
o
d
el
T
h
e
b
asic
co
m
p
o
n
en
t
o
f
a
p
h
o
t
o
v
o
ltaic
s
y
s
tem
is
a
p
h
o
to
v
o
lt
aic
ce
ll.
I
t
co
n
v
er
ts
in
cid
en
t
s
u
n
lig
h
t
in
to
co
r
r
esp
o
n
d
in
g
elec
tr
ical
en
er
g
y
u
s
in
g
t
h
e
p
h
o
to
v
o
ltaic
ef
f
ec
t
[
1
1
]
.
T
h
e
s
in
g
le
-
d
io
d
e
PV
c
ell
m
o
d
el
is
wid
ely
u
s
ed
f
o
r
th
e
p
r
esen
tatio
n
o
f
P
V
ce
lls
d
u
e
t
o
its
s
im
p
licity
.
Fi
g
u
r
e
2
illu
s
tr
ates
th
e
eq
u
i
v
alen
t
cir
cu
it
o
f
th
e
s
in
g
le
d
io
d
e
PV c
ell
m
o
d
el.
=
ℎ
−
0
[
(
+
)
(
)
−
1
]
−
(
+
)
/
ℎ
(
1
)
Fig
u
r
e
1
.
C
o
n
f
ig
u
r
atio
n
o
f
a
th
r
ee
-
p
h
ase
s
in
g
le
-
s
tag
e
GC
PVs
Fig
u
r
e
2
.
s
in
g
le
-
d
io
d
e
m
o
d
el
o
f
p
h
o
to
v
o
ltaic
ce
ll
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
564
-
574
566
I
n
th
is
c
o
n
tex
t,
I
pv
r
ep
r
esen
ts
t
h
e
o
u
tp
u
t
cu
r
r
e
n
t
o
f
th
e
PV
c
ell
in
(
A)
,
V
pv
d
en
o
tes
th
e
o
u
t
p
u
t
v
o
ltag
e
(
V)
,
I
ph
d
e
n
o
tes
th
e
p
h
o
t
o
-
cu
r
r
en
t
in
(
A
)
,
I
o
d
en
o
tes
th
e
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t
in
(
A)
,
R
s
h
r
ep
r
esen
ts
th
e
s
h
u
n
t
r
esis
tan
ce
(
Ω
)
,
q
is
th
e
elec
tr
o
n
ch
ar
g
e
(
C
)
,
n
is
th
e
d
io
d
e
id
ea
lity
f
ac
to
r
in
th
e
r
an
g
e
1
to
2
,
k
r
ep
r
esen
ts
th
e
B
o
ltzm
an
n
co
n
s
tan
t
(
J
/K)
,
an
d
T
r
ep
r
esen
ts
th
e
tem
p
er
a
tu
r
e
of
th
e
PV
ce
ll
in
(
K)
.
T
h
e
in
f
lu
en
ce
o
f
s
o
la
r
r
ad
iatio
n
a
n
d
th
e
tem
p
e
r
atu
r
e
o
f
th
e
PV
ce
ll
o
n
th
e
c
u
r
r
en
t
-
v
o
ltag
e
an
d
p
o
wer
-
v
o
ltag
e
ch
a
r
ac
ter
is
tics
o
f
th
e
PV
m
o
d
u
le
is
illu
s
tr
ated
b
y
Fig
u
r
es
3
(
a)
,
3
(
b
)
,
4
(
a)
,
an
d
4
(
b
)
.
T
h
ese
illu
s
tr
atio
n
s
ar
e
b
ased
o
n
t
h
e
p
a
r
am
eter
s
p
r
o
v
id
e
d
in
T
ab
le
1
o
f
th
is
s
tu
d
y
.
A
PV
m
o
d
u
le
co
n
s
is
ts
o
f
s
ev
er
al
PV
ce
lls
ar
r
an
g
e
d
b
o
th
in
p
ar
allel
an
d
in
s
er
ies.
T
h
e
p
h
o
to
v
o
ltaic
s
y
s
tem
in
th
is
s
tu
d
y
is
m
ad
e
u
p
o
f
1
8
p
a
r
allel
-
co
n
n
e
cted
s
tr
in
g
s
,
with
ea
ch
s
tr
in
g
co
n
tain
in
g
2
5
m
o
d
u
les co
n
n
ec
ted
in
s
er
ies.
(
a)
(
b
)
Fig
u
r
e
3
.
So
lar
i
r
r
ad
ian
ce
ef
f
e
ct
with
ce
ll tem
p
T
=
2
5
°C
:
(
a)
I
-
V
cu
r
v
e
an
d
(
b
)
P
-
V
cu
r
v
e
(
a)
(
b
)
Fig
u
r
e
4
.
C
ell
tem
p
er
atu
r
e
ef
f
ec
t w
ith
s
o
lar
ir
r
ad
ian
ce
S
=
1
0
0
0
W
/m
2
:
(
a)
I
-
V
cu
r
v
e
an
d
(
b
)
P
-
V
cu
r
v
e
T
ab
le
1
.
E
lectr
ical
p
a
r
am
eter
s
f
o
r
1
STH
-
2
1
5
-
P PV
m
o
d
u
le
S
p
e
c
i
f
i
c
a
t
i
o
n
V
a
l
u
e
M
a
x
i
m
u
m
p
o
w
e
r
P
2
1
3
.
1
5
W
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
V
oc
3
6
.
3
V
V
o
l
t
a
g
e
a
t
ma
x
i
m
u
m
p
o
w
e
r
V
m
pp
2
9
V
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
I
sc
7
.
8
4
A
C
u
r
r
e
n
t
a
t
ma
x
i
mu
m
p
o
w
e
r
I
m
pp
7
.
3
5
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
t
e
m
p
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
-
0
.
3
6
0
9
9
%/
°
C
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
t
e
m
p
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
0
.
1
0
2
%/
°
C
2
.
2
.
T
he
pert
urb a
nd
o
bs
er
v
e
a
lg
o
rit
hm
(
P
&O
)
An
ex
ten
s
iv
ely
ap
p
lied
MPPT
tech
n
iq
u
e
in
GC
PV
s
is
th
e
P
&
O
m
eth
o
d
[
1
2
]
.
T
h
e
aim
o
f
th
is
m
eth
o
d
is
to
co
n
tin
u
o
u
s
ly
ch
an
g
e
th
e
o
p
er
atio
n
p
o
in
t
u
p
to
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP
)
as
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
ch
an
g
e
an
d
th
u
s
im
p
r
o
v
e
th
e
p
o
wer
o
u
tp
u
t
o
f
th
e
PV
m
o
d
u
le
[
1
3
]
.
Fig
u
r
e
5
illu
s
tr
ates
th
e
f
lo
wch
ar
t
f
o
r
th
e
P&
O
alg
o
r
ith
m
.
T
h
is
a
p
p
r
o
ac
h
in
v
o
lv
es c
o
n
tin
u
o
u
s
ly
p
er
tu
r
b
in
g
t
h
e
v
o
ltag
e
o
r
cu
r
r
en
t a
n
d
m
o
n
ito
r
in
g
th
e
ef
f
ec
ts
o
f
th
ese
ad
j
u
s
tm
en
ts
o
n
th
e
p
o
we
r
o
u
t
p
u
t.
T
h
e
a
lg
o
r
ith
m
ad
j
u
s
ts
th
e
o
p
er
atin
g
p
o
in
t
to
i
n
cr
ea
s
e
p
o
wer
o
u
tp
u
t b
y
co
m
p
a
r
in
g
th
e
p
o
we
r
o
u
tp
u
t a
t th
e
d
is
tu
r
b
e
d
o
p
er
atin
g
p
o
in
t w
ith
th
e
p
r
ev
io
u
s
p
o
wer
o
u
tp
u
t.
T
h
e
v
o
ltag
e
(
V)
an
d
c
u
r
r
en
t
(
I
)
r
ea
d
in
g
s
f
r
o
m
th
e
PV
s
y
s
tem
s
er
v
e
as
th
e
alg
o
r
ith
m
'
s
in
p
u
ts
in
th
is
ca
s
e,
an
d
th
e
r
ef
er
en
ce
v
o
ltag
e
(
Vr
ef
)
,
wh
ich
r
eg
u
lates th
e
s
y
s
tem
'
s
p
o
wer
co
n
v
er
t
er
,
s
er
v
es a
s
th
e
o
u
tp
u
t [
1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
va
lu
a
tio
n
o
f p
u
ls
e
w
id
th
mo
d
u
la
tio
n
tech
n
iq
u
es to
r
ed
u
ce
to
ta
l h
a
r
mo
n
ic
d
is
to
r
tio
n
in
…
(
B
o
u
led
r
o
u
a
A
d
el
)
567
Fig
u
r
e
5
.
Flo
wch
ar
t
o
f
P&
O
MPPT
alg
o
r
ith
m
2
.
3
.
T
hree
ph
a
s
e
t
wo
-
lev
el
(
3
P
h
-
2
L
)
po
wer
inv
er
t
er
2
.
3
.
1
.
Co
nfig
ura
t
io
n a
nd
ro
l
e
T
h
e
3
Ph
-
2
L
in
v
e
r
ter
d
ep
icte
d
in
Fig
u
r
e
1
is
co
m
p
o
s
ed
o
f
s
ix
p
o
wer
s
em
ico
n
d
u
cto
r
s
witch
es
,
s
p
ec
if
ically
in
s
u
lated
g
ate
b
ip
o
lar
tr
an
s
is
to
r
s
(
I
GB
T
s
)
,
co
n
f
i
g
u
r
ed
i
n
th
r
ee
-
p
h
ase
b
r
id
g
e
ar
m
s
.
E
ac
h
o
f
th
e
a
r
m
s
en
co
m
p
ass
es two
s
witch
es
an
d
two
f
r
ee
-
wh
ee
lin
g
d
io
d
es set in
an
a
n
tip
ar
allel
ar
r
a
n
g
em
en
t
with
r
esp
ec
t to
th
e
s
witch
es.
T
h
e
DC
lin
k
ca
p
ac
ito
r
C
dc
to
wh
ich
th
e
in
v
er
ter
is
co
n
n
ec
ted
s
er
v
es
as
an
en
er
g
y
b
u
f
f
er
an
d
k
ee
p
s
th
e
DC
lin
k
v
o
ltag
e
co
n
s
tan
t
at
th
e
in
v
er
ter
in
p
u
t
ter
m
in
als.
T
h
e
PV
s
y
s
tem
is
co
n
n
ec
ted
to
th
e
in
ter
m
ed
iate
cir
cu
it
ca
p
ac
ito
r
,
wh
er
e
th
e
d
ir
ec
t
cu
r
r
en
t
p
r
o
d
u
ce
d
b
y
th
e
s
o
l
ar
m
o
d
u
les
is
r
ec
eiv
ed
[
1
5
]
.
Usu
ally
em
p
lo
y
ed
at
th
e
in
v
er
ter
o
u
tp
u
t,
an
L
C
L
f
il
ter
r
ed
u
ce
s
h
ig
h
-
f
r
e
q
u
en
c
y
s
witch
in
g
h
ar
m
o
n
ic
g
e
n
er
atio
n
a
n
d
im
p
r
o
v
e
s
o
u
t
p
u
t
wav
ef
o
r
m
q
u
ality
d
u
r
in
g
g
r
id
co
n
n
ec
tio
n
[
1
6
]
.
2
.
3
.
2
.
Co
ntr
o
l st
ra
t
e
g
ies inv
er
t
er
s
Fig
u
r
e
6
d
e
p
icts
th
e
p
r
o
p
o
s
ed
two
-
lo
o
p
ca
s
ca
d
ed
PI
co
n
tr
o
ll
er
.
T
y
p
ically
,
t
h
e
c
o
n
tr
o
l
s
y
s
tem
co
n
s
is
ts
o
f
two
lo
o
p
s
:
an
i
n
n
er
cu
r
r
en
t c
o
n
tr
o
l
l
o
o
p
an
d
an
o
u
ter
v
o
lt
ag
e
co
n
tr
o
l
l
o
o
p
.
W
ith
th
e
aim
o
f
k
ee
p
i
n
g
t
h
e
DC
lin
k
v
o
ltag
e
(
Vd
c
)
at
th
e
s
p
ec
i
f
ied
r
ef
e
r
en
ce
v
alu
e
(
Vd
cr
e
f
)
,
it is
co
n
tr
o
lled
b
y
th
is
ex
te
r
n
al
lo
o
p
.
T
h
e
DC
-
lin
k
v
o
ltag
e
er
r
o
r
(
Vd
c
r
ef
-
Vd
c
)
is
f
ed
to
a
PI
co
n
tr
o
ller
,
wh
ic
h
g
en
er
ates
th
e
ac
tiv
e
cu
r
r
e
n
t
r
ef
e
r
en
ce
(
I
r
e
f
)
f
o
r
th
e
in
n
er
c
u
r
r
en
t
co
n
tr
o
l
lo
o
p
,
an
d
th
e
MPPT
c
o
n
tr
o
ller
d
eter
m
in
es
th
e
v
o
l
tag
e
r
e
f
er
en
ce
(
Vd
cr
ef
)
b
ased
o
n
th
is
d
ep
en
d
i
n
g
o
n
th
e
e
n
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
o
f
th
e
PV
ar
r
ay
to
ex
tr
ac
t
m
ax
im
u
m
p
o
wer
[
1
7
]
.
T
h
e
Par
k
tr
an
s
f
o
r
m
is
u
s
ed
to
co
n
v
er
t
t
h
e
th
r
ee
-
p
h
ase
v
o
ltag
es
Vab
c
an
d
cu
r
r
en
ts
I
ab
c
f
r
o
m
th
e
n
atu
r
al
AB
C
to
th
e
s
y
n
ch
r
o
n
o
u
s
d
q
f
r
am
e
.
T
h
is
tr
an
s
f
o
r
m
atio
n
is
n
ec
ess
ar
y
f
o
r
d
ec
o
u
p
li
n
g
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
co
m
p
o
n
en
ts
an
d
s
im
p
lify
in
g
th
e
co
n
tr
o
l
p
r
o
ce
s
s
an
d
in
v
o
lv
es
th
e
u
s
e
o
f
th
e
lin
e
v
o
ltag
e
an
g
le
(
θ)
,
wh
ich
is
ty
p
ically
o
b
tain
e
d
f
r
o
m
a
p
h
as
e
-
lo
ck
ed
l
o
o
p
s
y
n
ch
r
o
n
izatio
n
b
lo
ck
(
PLL
)
[
1
8
]
.
T
h
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
c
u
r
r
e
n
ts
I
d
a
n
d
I
q
in
th
e
d
q
f
r
am
e
ar
e
c
o
n
tr
o
lled
b
y
th
e
in
n
e
r
c
o
n
tr
o
l
.
T
h
e
o
u
ter
v
o
ltag
e
co
n
t
r
o
l
l
o
o
p
p
r
o
v
id
es
th
e
ac
tiv
e
cu
r
r
en
t
r
e
f
er
en
ce
I
d
r
e
f
.
Fo
r
u
n
ity
p
o
wer
f
ac
t
o
r
o
p
er
atio
n
,
th
e
r
ea
ctiv
e
cu
r
r
en
t
r
ef
e
r
en
ce
I
q
r
ef
is
u
s
u
ally
s
et
to
ze
r
o
[
1
9
]
.
T
h
e
cu
r
r
e
n
t
er
r
o
r
s
(
I
d
r
ef
-
I
d
)
an
d
(
I
q
r
ef
-
I
I
q
)
ar
e
f
ed
to
s
ep
ar
ate
PI
co
n
tr
o
ller
s
,
wh
ich
g
en
er
ate
th
e
r
esp
ec
tiv
e
v
o
ltag
e
r
ef
e
r
en
ce
s
(
Vd
r
ef
an
d
Vq
r
ef
)
in
th
e
d
q
f
r
a
m
e.
Usi
n
g
th
e
in
v
er
s
e
Par
k
tr
a
n
s
f
o
r
m
,
th
e
v
o
ltag
e
r
ef
er
en
ce
s
(
V
d
r
ef
an
d
Vq
r
ef
)
in
th
e
d
q
f
r
am
e
ar
e
r
eset
to
th
e
n
atu
r
al
AB
C
f
r
am
e,
g
en
er
at
in
g
th
e
th
r
ee
-
p
h
ase
v
o
ltag
e
r
ef
er
e
n
ce
s
f
o
r
Vab
c
r
ef
.
T
h
ese
v
o
ltag
e
r
ef
e
r
en
ce
s
ar
e
ad
o
p
ted
as
in
p
u
ts
to
th
e
PW
M
b
lo
ck
th
at
g
e
n
er
ates
th
e
s
witch
in
g
s
ig
n
als f
o
r
th
e
3
Ph
-
2
L
in
v
e
r
ter
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
564
-
574
568
2
.
4
.
P
WM
t
ec
hn
iqu
e
PW
M
is
ex
ten
s
iv
ely
u
tili
ze
d
in
p
o
wer
co
n
v
er
ter
s
s
u
ch
as
th
r
ee
-
p
h
ase,
two
-
lev
el
in
v
er
te
r
s
.
Po
wer
elec
tr
o
n
ic
d
ev
ices
ar
e
s
witch
ed
at
h
ig
h
f
r
e
q
u
en
cies
to
p
r
o
d
u
ce
a
m
o
d
u
lated
s
ig
n
al,
wh
ic
h
is
th
en
f
ilter
e
d
to
o
b
tain
th
e
d
esire
d
AC
o
u
tp
u
t
[
2
0
]
.
2
.
4
.
1
.
SPWM t
ec
hn
iq
ue
T
h
e
p
r
im
ar
y
g
o
al
o
f
th
e
SP
W
M
tech
n
iq
u
e
in
GC
PVs
is
to
tr
an
s
f
o
r
m
th
e
s
o
lar
p
a
n
el'
s
d
ir
ec
t
cu
r
r
e
n
t
(
DC
)
in
to
alter
n
atin
g
cu
r
r
en
t
(
AC
)
s
u
itab
le
f
o
r
f
ee
d
in
g
in
to
th
e
elec
tr
ical
g
r
i
d
[
2
1
]
,
[
2
2
]
.
Fig
u
r
e
7
illu
s
tr
ates
th
e
o
p
e
r
atio
n
o
f
SP
W
M
b
y
c
o
m
p
ar
in
g
a
h
ig
h
-
f
r
eq
u
en
cy
tr
i
an
g
u
lar
ca
r
r
ier
s
ig
n
al
with
a
s
in
u
s
o
id
al
r
ef
e
r
en
ce
s
ig
n
al,
s
o
d
ep
ictin
g
th
e
in
te
n
d
ed
o
u
tp
u
t
v
o
ltag
e
[
2
3
]
.
As
th
e
r
ef
er
en
ce
s
ig
n
al
s
u
r
p
ass
es
th
e
ca
r
r
ier
wav
e,
th
e
ass
o
ciate
d
s
witch
in
th
e
in
v
er
t
er
is
ac
tiv
ated
,
an
d
wh
e
n
th
e
r
ef
er
en
ce
s
ig
n
al
d
r
o
p
s
b
elo
w
t
h
e
ca
r
r
ie
r
wav
e
,
th
e
s
witch
is
d
ea
ctiv
ated
.
T
h
is
p
r
o
ce
s
s
p
r
o
d
u
ce
s
a
s
er
ies
o
f
p
u
ls
es
with
d
if
f
er
e
n
t
wid
th
s
f
o
r
ea
c
h
p
h
ase,
ef
f
ec
tiv
el
y
p
r
o
d
u
cin
g
a
n
o
u
t
p
u
t w
av
ef
o
r
m
th
at
is
clo
s
e
to
th
e
s
in
u
s
o
id
a
l r
ef
er
en
ce
s
ig
n
al
[
2
4
]
,
[
2
5
]
.
T
h
e
th
r
ee
s
in
u
s
o
id
al
r
ef
er
e
n
c
e
wav
ef
o
r
m
s
p
r
o
p
o
s
ed
in
th
e
p
r
esen
t
m
o
d
el
(
Vr
ef
Sa
,
Vr
e
f
Sb
,
Vr
ef
Sc
)
r
ep
r
esen
t
th
e
d
esire
d
o
u
t
p
u
t
v
o
ltag
e
f
o
r
ea
ch
p
h
ase
ab
c
,
with
ea
ch
p
h
ase
s
h
if
ted
b
y
1
2
0
d
e
g
r
ee
s
,
an
d
ar
e
g
iv
en
b
y
(
2
)
.
=
s
in
(
)
=
s
in
(
−
2
3
)
=
s
in
(
+
2
3
)
(
2
)
W
h
er
e:
ω
d
en
o
tes th
e
an
g
u
la
r
f
r
eq
u
e
n
cy
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
an
d
t r
e
p
r
esen
ts
tim
e.
Fig
u
r
e
6
.
C
o
n
tr
o
l b
lo
c
k
d
iag
r
a
m
Fig
u
r
e
7
.
T
h
e
f
u
n
ctio
n
p
r
in
cip
le
o
f
SP
W
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
va
lu
a
tio
n
o
f p
u
ls
e
w
id
th
mo
d
u
la
tio
n
tech
n
iq
u
es to
r
ed
u
ce
to
ta
l h
a
r
mo
n
ic
d
is
to
r
tio
n
in
…
(
B
o
u
led
r
o
u
a
A
d
el
)
569
2
.
4
.
2
.
T
hird ha
rm
o
nic inj
ec
t
ed
P
WM
Fig
u
r
e
8
d
ep
icts
th
e
p
r
in
cip
al
f
u
n
ctio
n
o
f
t
h
e
T
HI
PW
M
tech
n
iq
u
e
.
I
n
th
is
ap
p
r
o
ac
h
,
two
s
in
e
wav
ef
o
r
m
s
ar
e
m
e
r
g
ed
to
c
r
ea
t
e
a
r
ef
er
en
ce
s
ig
n
al,
with
o
n
e
s
in
e
wav
e
s
elec
ted
to
h
av
e
a
f
r
e
q
u
en
cy
t
h
r
ee
tim
es
g
r
ea
ter
th
an
t
h
e
o
th
er
.
Su
b
s
eq
u
en
tly
,
tr
ig
g
er
p
u
ls
e
s
ig
n
als
ar
e
g
en
er
ated
b
y
co
m
p
ar
in
g
th
e
r
ef
er
en
ce
wav
e
f
o
r
m
with
th
e
ca
r
r
ier
s
ig
n
al.
T
h
e
T
HI
r
ef
er
en
ce
s
ig
n
al
ev
alu
ates
th
e
m
ag
n
itu
d
e
o
f
th
e
th
ir
d
h
a
r
m
o
n
ic
co
m
p
o
n
en
t
to
v
er
if
y
t
h
e
d
esire
d
o
u
tp
u
t
q
u
al
ity
.
T
h
is
tech
n
i
q
u
e,
alo
n
g
with
th
e
f
latten
ed
s
tr
u
ct
u
r
e
o
f
t
h
e
r
ef
er
e
n
ce
s
ig
n
al,
m
in
im
izes
s
witch
in
g
lo
s
s
es.
B
y
elim
in
atin
g
t
h
ir
d
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
,
th
is
ap
p
r
o
ac
h
en
a
b
les
m
o
r
e
ef
f
ec
tiv
e
u
tili
za
tio
n
o
f
DC
s
o
u
r
ce
s
[
2
6
]
.
T
h
e
T
HI
r
ef
er
e
n
ce
s
ig
n
al
d
esc
r
ib
ed
in
(
3
)
is
cr
ea
ted
b
y
c
o
m
b
in
in
g
th
e
r
ef
e
r
en
ce
s
in
e
wav
e
with
a
th
ir
d
h
a
r
m
o
n
ic
s
ig
n
al
atten
u
ated
b
y
1
3
√
3
.
T
h
is
m
eth
o
d
r
esu
lts
in
a
1
5
%
en
h
an
ce
m
en
t
o
f
th
e
s
in
e
wav
e'
s
f
u
n
d
am
en
tal
co
m
p
o
n
en
t.
Fig
u
r
e
8
.
T
h
e
f
u
n
ctio
n
p
r
in
cip
le
o
f
T
HI
PW
M
T
h
e
eq
u
atio
n
f
o
r
t
h
e
th
r
ee
r
e
f
er
en
ce
wav
ef
o
r
m
s
with
th
e
th
ir
d
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t
in
jec
ted
ca
n
b
e
ex
p
r
ess
ed
as (
3
)
[
2
7
]
,
[
2
8
]
.
=
2
√
3
s
in
(
)
+
1
3
√
3
s
in
(
3
)
=
2
√
3
s
in
(
−
2
/
3
)
+
1
3
√
3
s
in
(
3
)
=
2
√
3
s
in
(
+
2
/
3
)
+
1
3
√
3
s
in
(
3
)
}
(
3
)
W
h
er
e
ω
is
th
e
o
u
tp
u
t v
o
ltag
e
’
s
an
g
u
lar
f
r
eq
u
e
n
cy
a
n
d
t d
e
n
o
te
tim
e.
2
.
4
.
3
.
Sp
a
ce
v
ec
t
o
r
P
WM
SVP
W
M
is
an
ad
v
an
ce
d
tec
h
n
iq
u
e
f
o
r
co
n
tr
o
llin
g
th
r
ee
-
p
h
ase,
two
-
lev
el
in
v
er
ter
s
b
y
o
p
tim
izin
g
s
witch
in
g
s
tates
to
m
in
im
ize
h
ar
m
o
n
ic
d
is
to
r
tio
n
an
d
im
p
r
o
v
e
o
u
tp
u
t
v
o
ltag
e
q
u
ality
.
I
t
e
f
f
ec
tiv
ely
u
tili
ze
s
th
e
av
ailab
le
v
o
ltag
e
s
p
ac
e
v
ec
to
r
s
to
g
en
er
ate
a
d
esire
d
o
u
tp
u
t
v
o
ltag
e
to
im
p
r
o
v
e
th
e
p
er
f
o
r
m
an
ce
o
f
m
o
t
o
r
d
r
iv
es
an
d
p
o
wer
co
n
v
er
ter
s
.
T
o
b
eg
in
im
p
lem
en
tin
g
SVPW
M,
it
is
n
ec
ess
ar
y
to
d
eter
m
in
e
th
e
v
ec
to
r
o
f
r
e
f
er
en
ce
v
o
ltag
e
̅
in
th
e
α
–
β
s
tatio
n
ar
y
f
r
am
e,
u
tili
zin
g
th
e
s
tan
d
a
r
d
C
lar
k
e
tr
an
s
f
o
r
m
as d
e
s
cr
ib
e
d
in
(
4
)
[
2
7
]
,
[
2
9
]
.
[
]
=
2
3
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
[
]
(
4
)
V
a
, V
b
,
an
d
V
c
ar
e
t
h
e
th
r
ee
c
o
o
r
d
in
ate
r
e
f
er
en
ce
v
o
ltag
es.
A
d
d
itio
n
ally
,
th
e
v
ec
to
r
̅
ca
n
b
e
ex
p
r
ess
ed
in
th
e
f
o
llo
win
g
co
m
p
lex
f
o
r
m
,
as (
5
)
.
̅
=
+
(
5
)
C
o
n
s
eq
u
en
tly
,
th
e
m
ag
n
itu
d
e
|
|
an
d
th
e
p
h
ase
θ
o
f
̅
ca
n
b
e
d
ete
r
m
in
ed
as (
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
564
-
574
570
{
|
|
=
√
2
+
2
=
−
1
(
)
(
6
)
Du
e
to
th
e
co
m
p
lem
en
tar
y
co
m
m
u
tatio
n
o
f
th
e
u
p
p
er
an
d
lo
wer
s
witch
es,
eith
er
th
e
u
p
p
er
o
r
lo
wer
ar
m
s
witch
s
tatu
s
ca
n
b
e
r
ep
r
e
s
en
ted
.
T
h
e
s
witch
es
ar
e
m
ar
k
ed
"1
"
f
o
r
ON
an
d
"0
"
f
o
r
OF
F.
Six
ac
tiv
e
v
ec
to
r
s
an
d
two
ze
r
o
v
ec
to
r
s
r
e
p
r
esen
t
th
e
eig
h
t p
o
ten
tial
s
witch
in
g
s
tates o
f
th
e
in
v
er
ter
.
T
ab
le
2
d
is
p
lay
s
th
e
v
ar
io
u
s
r
ef
er
en
ce
v
o
ltag
es c
o
r
r
esp
o
n
d
i
n
g
to
ea
c
h
o
f
t
h
ese
eig
h
t states
.
I
n
Fig
u
r
e
9
(
a)
,
th
e
h
ex
ag
o
n
al
d
iag
r
am
d
is
p
lay
s
ac
tiv
e
v
o
ltag
es
(
V
1
−
V
6
)
alo
n
g
its
ax
es,
w
h
ile
th
e
two
ze
r
o
v
ec
t
o
r
s
(
V
0
–
V
7
)
r
ep
r
es
en
t
ze
r
o
v
o
ltag
e
ap
p
licatio
n
s
.
T
h
e
SVPW
M
m
eth
o
d
u
s
es
th
ese
eig
h
t
s
witch
in
g
co
n
f
ig
u
r
atio
n
s
to
esti
m
ate
th
e
r
ef
er
en
ce
v
o
ltag
e
v
ec
t
o
r
V
r
.
Fo
r
th
e
p
u
r
p
o
s
e
o
f
illu
s
tr
atio
n
,
ass
u
m
e
th
at
th
e
s
ec
to
r
1
co
n
tain
s
th
e
r
e
f
er
en
ce
v
ec
to
r
,
as
s
h
o
wn
in
Fig
u
r
e
9
(
a
)
.
V
1
an
d
V
2
ar
e
th
e
two
v
o
ltag
e
v
ec
to
r
s
clo
s
est
to
th
e
r
ef
er
en
ce
v
ec
to
r
,
an
d
V
0
o
r
V
7
is
th
e
ze
r
o
-
v
o
ltag
e
v
ec
to
r
.
T
1
,
T
2
,
an
d
T
0
r
ep
r
esen
t
th
e
r
esp
ec
tiv
e
ap
p
licatio
n
tim
es
f
o
r
th
e
r
ef
er
e
n
ce
v
ec
to
r
s
.
Allo
ca
tin
g
th
ese
v
ec
to
r
s
d
u
r
in
g
a
s
witch
in
g
p
er
io
d
c
o
n
s
id
er
s
th
e
f
o
llo
win
g
r
estrictio
n
s
,
as sh
o
wn
in
Fig
u
r
e
9
(
b
)
.
‐
I
n
a
s
in
g
le
s
witch
in
g
p
er
io
d
,
th
e
p
o
wer
s
em
ico
n
d
u
cto
r
s
s
h
o
u
ld
n
o
t
s
witch
b
etwe
en
th
eir
ON
an
d
OFF
s
ta
tes
m
o
r
e
th
an
twice.
‐
T
h
e
v
o
ltag
e
at
n
eu
tr
al
p
o
in
t sh
o
u
ld
b
e
k
ep
t c
lo
s
e
to
ze
r
o
.
T
h
e
v
o
lt
-
s
ec
o
n
d
eq
u
atio
n
is
u
t
ilized
to
d
eter
m
in
e
t
h
e
ap
p
lica
tio
n
tim
es a
n
d
is
ex
p
r
ess
ed
as
(
7
)
.
{
.
̅
=
1
.
1
̅
+
2
.
2
̅
+
0
̅
.
0
̅
=
1
+
2
+
0
(
7
)
T
s
is
th
e
s
am
p
lin
g
tim
e
in
t
h
is
ca
s
e.
B
y
em
p
lo
y
in
g
th
e
s
p
ac
e
v
ec
to
r
d
iag
r
am
an
d
(
7
)
,
we
ca
n
ex
p
r
ess
as
(
8
)
.
{
|
|
=
1
|
1
|
+
2
|
2
|
60°
|
|
=
2
|
2
|
60°
(
8
)
T
ab
le
2
.
Switch
s
tates a
n
d
o
u
t
p
u
t
v
ec
to
r
s
S
p
a
c
e
v
e
c
t
o
r
V
an
V
bn
V
cn
|V
r
|
θ
V
0
(
0
0
0
)
0
0
0
0
0°
V
1
(
1
0
0
)
2
3
−
1
3
−
1
3
V
dc
0°
V
2
(
1
1
0
)
1
3
−
1
3
−
2
3
V
dc
60°
V
3
(
0
1
0
)
−
1
3
2
3
1
3
V
dc
1
2
0
°
V
4
(
0
1
1
)
−
2
3
1
3
1
3
V
dc
1
8
0
°
V
5
(
0
0
1
)
−
1
3
−
1
3
2
3
V
dc
2
4
0
°
V
6
(
1
0
1
)
1
3
−
2
3
1
3
V
dc
3
0
0
°
V
7
(
1
1
1
)
0
0
0
0
0°
(
a)
(
b
)
Fig
u
r
e
9
.
2
L
-
SVPW
M
p
atter
n
: (
a)
v
ec
to
r
d
iag
r
am
an
d
s
ec
to
r
s
n
u
m
b
er
in
g
an
d
(
b
)
s
witch
in
g
s
tates
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
va
lu
a
tio
n
o
f p
u
ls
e
w
id
th
mo
d
u
la
tio
n
tech
n
iq
u
es to
r
ed
u
ce
to
ta
l h
a
r
mo
n
ic
d
is
to
r
tio
n
in
…
(
B
o
u
led
r
o
u
a
A
d
el
)
571
T
h
ese
ap
p
licatio
n
tim
es c
an
b
e
f
o
u
n
d
b
y
s
o
lv
in
g
(
8
)
.
{
1
=
√
3
⌈
⌉
s
in
(
3
−
)
2
=
√
3
⌈
⌉
s
in
(
)
0
=
1
−
(
1
+
2
)
(
9
)
Fo
r
th
e
two
-
lev
el
i
n
v
er
ter
s
h
o
wn
in
Fig
u
r
e
1
,
th
e
g
en
er
al
ex
p
r
ess
io
n
s
f
o
r
th
e
a
p
p
licatio
n
ti
m
es
ar
e
d
er
iv
e
d
b
y
ap
p
ly
in
g
th
is
p
r
in
cip
le
to
th
e
s
ix
o
p
er
atin
g
s
ec
to
r
s
,
as in
(
1
0
)
.
{
1
=
√
3
⌈
⌉
s
in
(
3
−
)
2
=
√
3
⌈
⌉
s
in
(
−
(
−
1
)
3
)
0
=
1
−
(
1
+
2
)
(
1
0
)
W
h
er
e
,
k
sn
r
ep
r
esen
ts
th
e
s
e
cto
r
n
u
m
b
er
.
T
h
e
s
witch
in
g
s
eq
u
en
ce
s
f
o
r
all
o
p
er
atin
g
r
an
g
es
ar
e
lis
ted
in
T
ab
le
3
.
T
ab
le
3
.
C
o
n
v
en
tio
n
al
SVPW
M
v
ec
to
r
s
eq
u
e
n
ce
S
e
c
t
o
r
N
°
S
w
i
t
c
h
i
n
g
se
q
u
e
n
c
e
1
V
0
_
V
1
_
V
2
_
V
7
_
V
2
_
V
1
_
V
0
2
V
0
_
V
3
_
V
2
_
V
7
_
V
2
_
V
3
_
V
0
3
V
0
_
V
3
_
V
4
_
V
7
_
V
4
_
V
3
_
V
0
4
V
0
_
V
5
_
V
4
_
V
7
_
V
4
_
V
5
_
V
0
5
V
0
_
V
5
_
V
6
_
V
7
_
V
6
_
V
5
_
V
0
6
V
0
_
V
1
_
V
6
_
V
7
_
V
6
_
V
1
_
V
0
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
is
d
ev
o
ted
to
ass
ess
in
g
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
s
u
g
g
ested
PW
M
an
d
s
u
m
m
a
r
iz
es
th
e
k
ey
f
in
d
in
g
s
o
f
th
e
s
tu
d
y
.
Fo
r
th
is
p
u
r
p
o
s
e,
an
aly
s
es
o
f
th
e
T
HD
cu
r
r
en
t
f
e
d
in
u
n
d
er
d
if
f
e
r
en
t
o
p
er
atin
g
co
n
d
itio
n
s
an
d
co
m
p
a
r
is
o
n
s
with
SP
W
M,
T
HI
PW
M,
an
d
SV
PW
M
ar
e
ca
r
r
ied
o
u
t
f
o
r
g
r
id
-
c
o
n
n
ec
ted
o
p
er
atio
n
.
T
h
e
p
r
o
p
o
s
ed
PW
M
tech
n
iq
u
es
ar
e
ev
alu
ated
u
n
d
er
r
a
p
id
ly
ch
an
g
in
g
ir
r
a
d
ian
ce
co
n
d
itio
n
s
.
T
o
im
p
lem
en
t
th
e
p
r
o
p
o
s
ed
m
o
d
el
s
h
o
wn
in
Fig
u
r
e
1
,
th
e
MA
T
L
AB
/
Simu
lin
k
s
o
f
twar
e
p
ac
k
a
g
e
was
u
s
ed
.
T
h
e
v
alu
es
co
n
s
id
er
e
d
f
o
r
th
e
s
im
u
latio
n
ar
e
lis
ted
in
T
ab
le
4
.
T
h
e
lev
el
o
f
ir
r
ad
iat
io
n
d
eter
m
i
n
es
th
e
o
u
t
p
u
t
p
o
wer
o
f
a
PV
s
y
s
tem
an
d
th
u
s
th
e
cu
r
r
en
t
th
at
f
l
o
ws
th
r
o
u
g
h
th
e
in
v
er
te
r
.
As
ir
r
ad
ian
ce
in
cr
ea
s
es,
th
e
cu
r
r
en
t
in
cr
ea
s
es,
p
o
ten
tially
af
f
ec
tin
g
h
a
r
m
o
n
ic
c
o
n
ten
t a
n
d
T
HD.
T
h
e
ir
r
ad
ian
ce
p
r
o
f
ile
d
ep
icte
d
in
Fig
u
r
e
1
0
illu
s
tr
ates
an
in
itial
ir
r
ad
ian
ce
o
f
5
5
0
W
/m
2
f
r
o
m
0
to
0
.
5
s
ec
o
n
d
s
,
f
o
llo
wed
b
y
a
n
ab
r
u
p
t in
cr
ea
s
e
to
1
0
0
0
W
/m
2
at
0
.
5
s
,
an
d
a
s
u
b
s
eq
u
en
t d
ec
r
ea
s
e
to
7
5
0
W
/m
2
at
1
s
,
co
n
tin
u
in
g
u
n
til
1
.
5
s
.
T
h
r
o
u
g
h
o
u
t
t
h
e
s
im
u
latio
n
,
th
e
tem
p
e
r
atu
r
e
r
em
ain
s
co
n
s
tan
t
at
2
5
°C
.
Fig
u
r
es
1
1
,
1
2
,
an
d
1
3
p
r
esen
t
th
e
g
r
id
cu
r
r
en
t
wav
ef
o
r
m
a
n
d
its
co
r
r
esp
o
n
d
i
n
g
h
ar
m
o
n
ic
s
p
ec
tr
u
m
f
o
r
SP
W
M,
T
HI
PW
M,
an
d
SVP
W
M,
r
esp
ec
tiv
ely
,
at
th
r
e
e
d
is
tin
ct
ir
r
ad
ian
ce
lev
els.
T
ab
le
4
.
Sp
ec
if
icatio
n
s
v
al
u
es f
o
r
th
e
p
r
o
p
o
s
ed
m
o
d
el
S
p
e
c
i
f
i
c
a
t
i
o
n
s
V
a
l
u
e
R
a
t
e
d
p
o
w
e
r
o
f
P
V
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5
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6
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S
.
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