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.
4, D
e
c
e
m
ber
201
9,
pp.
1863~
18
74
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1863-1874
1863
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
Track the maxim
u
m pow
er of a
photovoltaic to control a
cascade five-level inverter a sin
g
l
e-phase grid-connected with
a
fuzzy logic control
A
r
c
k
ar
a
k
it
C
haith
a
na
k
u
l
w
at
Dep
a
rtm
e
nt of Elect
rical
En
g
i
n
eer
in
g,
D
ho
nb
uri
Rajab
h
at
U
nivers
it
y,
T
ha
i
l
an
d
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Mar
15,
2
0
1
9
Re
vise
d A
p
r
20,
201
9
A
c
c
e
pte
d
J
u
n
7
,
2019
Th
is
r
esearch
p
resen
t
s
tracki
ng
th
e
max
i
m
u
m
po
wer
o
f
a
ph
otov
ol
ta
ic
t
o
con
t
ro
l
a
f
i
ve-le
v
el
i
nv
erter,
a
c
a
s
cade
t
y
p
e
c
on
necti
n
g
a
s
i
ng
le
-phase
g
rid-
con
n
ect
ed
s
ys
tem
w
i
t
h
a
f
u
z
z
y
l
og
ic
c
ont
rol
m
o
del.
M
ax
im
um
pow
e
r
tracking
cont
rol
In
t
his
research
,
t
h
e
principle
of
c
ontrolling
t
h
e
m
a
x
i
m
u
m
current
a
mpli
t
ude
o
f
the
pho
t
ov
olt
a
ic
m
ultiplied
by
t
he
s
ine
si
g
n
al
p
er
u
n
it
th
at
u
sed
as
a
r
e
f
eren
ce
curr
en
t
com
p
ared
t
o
t
h
e
grid
c
u
rrent.
Si
g
n
al
com
p
ariso
n
w
ith
th
e
P
I
D
co
nt
rol
l
er
a
l
l
o
w
s
the
cr
eatio
n
of
f
ive
le
v
e
ls
o
f
PW
M
of
cas
c
a
d
e
c
o
n
tro
l
o
f
f
i
ve
-l
evel
i
n
v
erter
con
n
ects
s
i
ngle-p
has
e
g
ri
ds
.
The
results
o
f
t
h
e
si
mulation
t
e
st
u
sing
t
he
p
ro
gram
M
ATLAB/Si
m
uli
n
k
to
com
p
are
wi
th
t
h
e
g
en
erated
p
roto
ty
pe
f
ou
nd
t
h
at
t
h
e
f
u
zzy
l
o
g
ic
p
r
i
nc
ip
le
was
used
t
o
cont
rol
t
h
e
maximu
m
power
tracking
condition
s
o
f
th
e
P&O
m
e
th
od,
w
h
e
n
th
e
am
ou
nt
o
f
radi
ati
on
lig
h
t
inten
s
it
y
d
ecrease
s
su
dd
e
n
ly
,
m
a
ki
ng
it
p
o
s
sible
to
t
rack
t
he
m
a
x
im
u
m
power
o
f
t
h
e
ph
oto
v
o
l
t
a
ic.
A
l
so,
when
th
e
i
n
v
e
rter
c
o
n
n
ected
t
o
the
gri
d
by
co
nt
rollin
g
th
e
p
o
w
e
r
ang
l
e
to
com
p
are
resu
lts
b
etween
t
he
s
im
u
l
a
t
i
o
n
and
t
h
e
p
r
ot
ot
ype-f
o
u
n
d
th
a
t
t
he
curren
t
f
lo
w
i
n
g
i
nto
the
g
r
id
i
nc
reases
acc
o
r
di
ng
t
o
th
e
p
o
w
e
r
an
gl
e
co
nt
ro
l
.
Resulting
in
a
n
earby
w
av
ef
orm,
s
i
n
e
wave
a
nd
an
o
ut
o
f
phase
a
ng
le
t
o
the
gri
d
v
o
ltag
e
b
ec
ause
t
h
e
s
yst
e
m
i
s
i
n
th
e
i
n
v
e
rter
m
o
d
e,
a
nd
t
h
e
h
a
rm
oni
c
spectrum
o
f
t
he
g
rid
currentl
y
h
a
s
total harm
o
n
i
c
di
sto
r
ti
on
(
T
H
D
)
i
s
reduced
as an
i
n
d
i
cati
on of
t
he p
rop
o
s
e
d
s
y
s
t
e
m
can
b
e d
e
velo
ped
and
ap
p
l
i
catio
ns.
K
eyw
ord
s
:
Five-
l
e
v
el c
asc
a
d
e in
ver
t
er
Fuz
z
y lo
g
i
c
co
ntr
o
l
Gri
d
-co
n
n
ect
ed
s
y
s
t
e
m
MPP
T
tec
hniq
u
e
Phot
o
v
o
lta
ic
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:
A
r
c
k
ara
k
i
t
C
ha
it
ha
na
ku
lw
a
t
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
Eng
i
ne
eri
ng,
D
h
o
n
b
u
ri Ra
j
a
bha
t
U
n
ive
r
si
ty,
S
o
i Mu
n
i
c
i
pa
l
i
t
y
P
u
1
1
9
, S
ukhumv
i
t R
o
ad,
Ba
ng P
l
a S
ub-di
st
r
i
c
t
,
Bang
Phli Dis
t
r
i
c
t
, Thail
a
n
d
Em
ail:
chai
t
h
a
n
ak
u
l
@
g
m
a
i
l
.com
1.
I
N
TR
OD
U
C
TI
O
N
F
r
om gene
r
al
r
ese
a
rc
h, solar
e
ne
rg
y c
o
n
t
r
o
l
p
r
ese
n
t
e
d wit
h
m
any
di
f
fere
nt
m
e
t
ho
d
s
,
such
a
s pe
rturb
a
nd
o
b
se
rve
c
o
nt
r
o
l
(
P
&O
),
i
nc
rem
e
nta
l
c
o
n
d
u
c
t
ance
(INC),
fuzz
y
l
o
g
i
c
c
on
tro
l
(
F
L
C)
a
nd
ge
ne
ti
c
(G
A)
,
w
h
i
c
h
a
r
e
in
depe
n
d
en
t
,
i
so
l
a
te
d
a
l
on
e
,
t
o
s
u
p
p
l
y
t
h
a
t
v
o
l
ta
ge
t
o
t
h
e
circ
ui
t
bo
os
t
c
o
nve
rter
o
r
buc
k-
bo
ost
c
o
n
v
e
r
te
r
and
t
o
s
u
p
p
l
y
fo
r
l
o
ad
i
n
g
al
one.
H
o
w
e
ver,
e
nc
ou
n
t
ere
d
c
ons
t
a
n
t
pow
er
c
on
t
r
o
l
p
ro
ble
m
s
th
a
t
w
e
r
e
quite
d
ifficu
l
t
a
nd
a
t the
sa
me
t
ime
i
f
b
ein
g
p
a
i
d
i
n
to t
h
e gri
d
or
su
p
p
ly
i
n
g
n
o
n
-l
inea
r
loa
d
s,
n
e
e
d
in
g
the
bes
t
p
ri
nci
p
les
an
d
c
ontr
o
l
m
e
th
o
d
s
[1-4]
.
F
or
t
he
p
ro
p
o
se
d
r
e
s
ea
rch,
t
he
s
imu
l
a
t
i
o
n
a
n
d
c
o
nstr
uct
i
on
o
f
t
h
e
ma
ximum
pow
e
r
t
r
acki
ng
pr
o
t
o
t
ype.
U
s
i
ng
t
h
e
pri
n
c
i
p
l
e
of
c
on
t
r
o
l
l
i
ng
t
h
e
ma
ximum
c
u
rre
nt
a
m
p
lit
u
d
e
o
f
the so
lar
ce
l
l
m
ult
i
p
lie
d
by t
h
e sin
u
s
o
i
d
a
l
s
ig
na
l pe
r un
i
t
t
ha
t is use
d as
t
he
re
f
e
r
enc
e
s
i
n
e curr
en
t c
o
m
p
ar
ed to
the
gri
d
c
urre
nt
t
hr
ou
g
h
P
ID
t
o
co
ntr
o
l
a
casc
a
de
f
ive
-
l
e
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in
ve
rter
a
s
in
g
l
e-pha
se
g
r
i
d-
con
n
ec
t
e
d
with
a
fuz
z
y
l
og
ic c
o
n
t
r
ol
w
h
i
ch is
di
ffere
n
t
from
the
o
ne
m
e
n
ti
o
n
ed
a
bov
e
.
Mo
de
ls a
n
d
co
m
pone
n
t
s of
t
h
e
P
V
system
r
e
q
u
i
re
t
he
use
o
f the
h
i
ghes
t
p
oi
n
t
t
r
a
c
k
in
g
t
e
chn
i
que
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
6
3
– 1
874
1
864
(
M
P
P
T)
t
o
tra
c
k
t
he
m
ax
im
um
p
ow
e
r
u
nde
r
di
ffe
re
nt
c
o
n
d
i
t
i
o
n
s.
T
he
p
r
opose
d
M
P
P
T
al
g
o
ri
thm
obs
erva
ti
on
(P
&O
)
and
incre
a
sed
c
o
n
d
u
c
t
i
v
ity
(
IC)
.
A
ll
so
,
unde
r
s
u
d
d
e
n
r
a
d
i
a
tio
n
a
nd
tem
p
er
at
ure
c
h
ange
s
i
n
t
h
e
P
V
s
y
s
t
e
m
w
i
t
h
t
h
e
h
e
l
p
o
f
a
n
e
w
a
d
a
p
t
i
v
e
c
o
n
t
r
o
l
l
e
r
t
h
a
t
w
i
t
h
s
t
a
nd
t
h
ese
hea
v
y
d
i
s
t
urba
nce
s
.
The
resul
t
s
fr
om
t
h
e
c
ompa
rison
of
t
he
t
w
o
t
e
c
h
n
i
que
s,
t
he
c
har
acte
rist
ics
of
t
he
m
e
c
han
i
sm
a
n
d
t
he
p
re
vi
ou
s
lite
rat
u
re,
yie
l
d
the
resul
t
s
a
ccor
d
i
n
g
t
o
t
he
s
et
g
oals
[
5,
6
]
.
M
o
s
t
l
y
k
n
o
w
n
t
h
a
t
,
i
n
e
v
e
r
y
d
a
y
l
i
f
e
,
h
u
m
a
n
bei
n
gs
o
fte
n
i
n
v
o
l
ve
m
uc
h
e
n
ergy.
S
u
c
h
as
e
ner
gy
ob
t
a
i
n
e
d
f
r
o
m
pe
tro
l
e
u
m
foss
i
l
e
ner
gy,
w
i
n
d
pow
e
r
a
nd
so
l
a
r
e
n
erg
y
.
H
o
w
e
ver
,
t
he
e
nerg
y
ob
tai
n
e
d
f
rom
the
so
l
a
r
c
e
ll
sy
st
em
i
s
i
n
fl
u
e
n
c
e
d
b
y
t
e
mp
e
r
at
ure
a
n
d
radia
t
i
o
n,
p
rod
u
c
i
n
g
e
lec
t
r
i
ca
l
ener
gy
a
t
t
he
p
h
o
t
o
v
o
l
t
a
i
c.
T
he
refore,
to
e
nsure
that
t
he
p
h
o
t
o
v
o
l
t
a
ic
p
ro
duc
e
s
the
h
i
g
h
es
t
en
e
r
gy
a
t
a
l
l
t
i
m
es,
re
gardless
of
e
xter
nal
c
o
nd
i
t
i
o
n
s,
u
s
i
n
g
a
de
vic
e
c
al
le
d
MP
P
T
(
tr
ackin
g
th
e
ma
ximum
p
o
w
er
poi
n
t
)
t
o
m
ove
t
he
c
on
tro
l
m
o
d
e
t
o
t
he
m
o
s
t
w
i
de
l
y
use
d
s
tab
i
li
ty
b
u
t
t
h
e
re
a
r
e
di
sa
d
v
a
n
ta
ges
due
t
o
cha
t
teri
ng
p
h
en
om
en
o
n
.
The
r
efor
e,
t
hese
p
r
ob
l
e
ms
s
ho
u
l
d
be
i
m
p
rove
d.
T
h
i
s
co
n
t
ro
l
i
s
ca
l
l
e
d
A
F
S
ME
(
a
d
apt
i
ve
f
uz
z
y
s
l
i
di
n
g
m
ode
c
on
tro
l
)
and
c
o
m
p
are
w
i
t
h
t
he
S
M
C
s
c
r
ol
l
mode
c
o
n
tr
ol
le
r
to
see
the
d
i
ffe
r
enc
e
a
nd
u
s
e
o
f
P
&O
(
P
e
rturb
&
O
b
se
rve)
c
he
ck
t
h
i
s
c
ont
ro
ll
er.
Al
l
s
i
mul
a
t
i
on
re
su
lt
s
perform
ed
u
nd
er
M
A
TLA
B/
S
i
m
u
l
i
n
k
a
n
d
s
how
t
he
e
ffe
c
tive
n
e
s
s
of
A
F
S
MC
c
on
tro
l
,
c
o
n
f
irm
i
ng
t
hat
th
e
n
e
w
met
h
od
h
as
d
e
v
elo
p
e
d
en
e
r
gy
,
ef
f
i
ci
ency
a
nd
p
rod
u
cti
o
n
[7
,
8]
.
The
three
-
pha
se
l
o
a
d
co
nnec
t
e
d
t
o
t
h
e
three
-
le
ve
l
in
v
e
r
t
er,
NP
C,
i
s
pr
opose
d
t
o
c
r
ea
t
e
a
g
a
t
e
s
i
gna
l
for
m
u
l
t
i-l
e
ve
l
inve
r
t
ers.
B
oth
c
o
m
m
a
nds
a
r
e
deve
l
ope
d
a
n
d
c
o
mpa
r
ed
b
e
t
w
e
e
n
t
he
p
ha
s
e
d
i
s
p
o
s
i
tio
n
p
u
l
s
e
w
i
dt
h
m
odu
la
ti
o
n
(
P
D
PWM)
a
nd
t
h
e
spac
e
v
e
c
t
o
r
p
u
l
s
e
w
i
d
t
h
m
o
d
u
l
a
t
i
o
n
(
S
V
P
W
M
)
.
V
e
r
i
f
y
t
h
e
e
f
f
e
c
t
i
v
e
n
e
s
s
o
f
t
h
e
in
t
r
o
d
u
ced
c
o
n
t
r
oll
e
r;
i
t
c
o
mp
are
d
w
ith
t
he
f
uzz
y
l
o
g
i
c
c
ontr
o
l
l
e
r
.
W
hen
sim
u
late
d
u
s
in
g
M
A
TLA
B/S
i
m
u
lin
k
p
r
o
g
ram
,
a
na
lyse
t
he
r
es
ul
ts
o
f
the
s
e
co
ntr
o
l
s
,
show
s
t
h
a
t
N
P
C
h
a
s
s
uper
i
or
p
e
r
for
m
a
n
c
e
due
t
o
the
q
u
a
l
ity
o
f
t
h
e
o
u
tp
ut
v
olta
ge
f
or
t
h
e
ent
i
re
a
d
j
us
tm
ent
inde
x
[9,
1
0
].
T
his
p
h
o
t
o
v
o
lta
i
c
w
ater
p
umpi
n
g
s
y
ste
m
c
o
n
sis
t
s
of
t
hr
ee
m
a
in
p
ar
t
s
:
P
V
G,
d
c
-d
c
conv
e
r
t
e
r
an
d
d
c
m
ot
or
w
i
t
h
a
cen
t
r
if
ug
al
w
a
t
e
r
pump
.
H
a
s
p
ropose
d
a
n
e
w
M
P
P
T
algori
t
hm
u
sin
g
fuz
z
y
l
o
g
i
c
an
d
neura
l
n
e
t
w
o
r
k
s
(A
N
N
)
t
o
i
mpr
ove
s
ys
te
m
perform
an
c
e
.
ANN
i
s
u
se
d
t
o
p
r
e
di
ct
t
he
b
es
t
vo
lta
ge
o
f
P
V
G
unde
r
t
e
mp
e
r
ature
c
o
n
d
it
i
ons
a
n
d
s
o
l
a
r
r
adia
ti
o
n
a
nd
use
a
fuz
z
y
c
o
n
t
r
oller
t
o
c
on
tro
l
t
h
e
bo
ost
i
n
g
.
The
si
m
u
lat
i
on
r
e
sul
t
s
i
n
d
i
c
a
t
e
t
h
at
M
P
P
T
for
A
N
N
a
nd
f
u
z
z
y
l
o
g
i
c
a
r
e
p
e
r
f
o
r
m
i
n
g
w
e
l
l
.
T
h
i
s
alg
o
ri
t
h
m
has
pro
v
en
t
o
pr
ov
ide
be
tter
pe
rform
anc
e
:
fa
ste
r
r
e
s
p
ons
e
tim
e
s,
m
ore
accur
a
t
e
a
nd
r
obus
t
systems
to
c
ha
nge
[
1
1
].
T
he
e
n
e
r
gy
pai
d
b
y
ph
o
t
o
v
o
l
taic
t
hrou
g
h
t
he
d
c
-
dc
e
n
e
rgy
c
o
n
v
erter
by
t
w
o
fac
t
ors:
t
h
e
radia
t
i
o
n
of
t
h
e
s
un
a
nd
the
t
e
m
p
era
t
ure.
T
here
fore
,
im
prov
i
n
g
t
h
e
ef
fi
c
i
e
n
cy
o
f
t
h
e
PV
s
y
s
t
e
m
req
u
i
r
e
s
t
h
e
use
o
f
a
m
ec
han
i
sm
t
o
trac
k
t
h
e
m
a
x
i
m
u
m
pow
e
r
p
oint
(
MP
P
)
.
Tra
d
i
t
i
ona
l
m
a
x
i
m
u
m
pow
e
r
t
rac
k
in
g
met
h
od
s
su
ch
a
s
o
b
s
e
r
v
a
ti
o
n
a
n
d
di
s
r
upt
ive
t
e
c
hni
qu
e
s
cau
se
p
ro
b
l
em
s
in
r
e
a
l
MPP
trac
k
i
n
g
.
There
f
ore
,
in
t
e
l
l
i
g
e
n
t
sys
t
em
s,
i
nc
lud
i
n
g
fuzz
y
l
o
g
i
c
co
ntr
o
lle
rs
(
FLC),
a
r
e
u
se
d
for
the
h
i
g
h
es
t
m
a
x
i
m
u
m
po
int
tra
c
k
in
g
system
(
MPP
T
).
A
com
p
ara
tiv
e
st
u
d
y
o
f
s
t
anda
l
one
P
V
sys
t
em
s
con
t
r
o
l
l
e
d
b
y
t
h
r
e
e
t
e
c
hni
qu
e
s
,
c
o
n
s
i
s
ti
ng
o
f
trad
it
iona
lly
b
a
s
ed
o
n
o
b
se
rva
t
i
ons
a
n
d
p
ert
u
rba
tio
n
tec
h
ni
q
u
es
,
the
o
t
he
r
are
inte
l
lige
n
t
b
a
se
d
o
n
f
uzz
y
l
og
ic
ac
cord
in
g
t
o
M
am
da
ni
a
n
d
Ta
ka
gi-S
uge
n
o
mode
l
s
.
T
h
e
inve
st
i
g
at
i
o
ns
s
how
t
ha
t
t
h
e
fuz
z
y
lo
g
i
c
c
o
n
t
ro
llers
pro
v
i
d
e
the
be
st
r
esu
lts,
an
d
Taka
gi
-
S
uge
n
o
m
ode
l
pre
s
e
n
t
s
t
he
low
e
r
o
v
e
rsho
ot
v
a
l
ue
[
12,
1
3].
The
o
v
era
l
l
perform
ance
o
f
MPP
T
,
m
a
inly
u
sed
i
n
t
h
e
a
p
p
l
i
c
a
t
i
o
n
o
f
P
V
,
i
s
a
na
l
y
se
d
f
o
r
in
ter
f
er
ence
a
nd
o
b
ser
v
a
t
io
n
alg
o
ri
t
h
ms
(
P
&
O
)
a
nd
a
dd
i
tio
na
l
c
o
nd
uc
ti
ve
m
ed
ia
(IN
C).
Re
su
lts
a
n
a
ly
si
s
for
a
l
go
r
i
t
h
m
s
i
n
t
h
e
pro
g
ra
m
MA
TLA
B/S
i
mul
i
n
k
for
var
i
ous
c
ha
nge
s
i
n
r
a
d
i
a
tio
n,
t
he
r
e
s
ear
ch
fou
n
d
tha
t
t
h
e
e
ffic
ie
nc
y
of
t
h
e
P
&O
met
h
od
i
s
hi
g
h
er
t
h
a
n
th
at
o
f
INC
.
F
o
r
t
h
e
s
ame
e
f
f
i
ci
en
cy
,
mo
r
e
i
n
t
e
n
s
i
v
e
c
a
l
c
u
l
a
t
i
ons
s
h
oul
d
a
ccoun
t
f
o
r
IN
C.
M
ea
sure
m
e
nt
o
f
o
u
t
pu
t
p
o
w
e
r
,
t
he
r
espo
nse
o
f
c
urre
n
t
a
nd
v
o
lta
ge
o
f
so
lar
c
e
l
l
s
a
t
c
o
nsta
n
t
v
a
l
u
e
s
an
d
varia
b
l
e
r
a
d
i
a
t
i
on
u
se
d
a
s
i
nput
s
f
o
r
a
l
gor
it
hm
s.
T
h
e
o
ut
p
u
t
w
a
ve
form
o
bta
i
ned
fr
om
t
he
s
imu
l
at
i
o
n
w
o
rks
ac
cord
in
g
t
o
t
h
e
s
t
a
t
e
d
o
b
j
e
c
t
i
v
es
[
14].
The
s
t
an
da
l
o
ne
p
ho
t
o
v
o
lt
a
i
c
s
y
st
e
m
i
n
ter
m
s
of
a
rc
hitec
t
ur
al
d
esi
gn,
bu
ild
i
ng
sha
p
e
a
nd
d
i
m
e
ns
io
n,
t
he
n
in
t
erm
s
o
f
e
l
ec
tric
ity.
The
b
lo
ck
d
i
a
g
r
am
p
re
se
n
t
s
t
h
e
el
e
c
t
r
i
c
al
d
e
s
ig
n.
The
s
i
m
u
la
t
i
o
n
v
er
ifi
c
a
t
io
n
pri
n
ci
p
l
e
is
m
a
d
e
for
the
s
o
la
r
pa
n
e
l
m
at
r
i
x
des
i
gn
,
bu
ck
-d
c
d
c
c
onv
ert
e
r
by
hi
ghl
i
g
h
t
i
ng
th
e
m
e
m
b
er
s
hape
a
rou
n
d
t
he
z
e
r
o
pos
it
io
n,
t
he
a
mb
i
g
uo
us
l
o
g
i
ca
l
err
o
r,
t
he
F
LC
c
o
n
t
ro
ll
e
r
,
i
s
des
i
g
n
e
d
t
o
g
u
a
r
a
ntee
t
he
d
e
s
ire
d
w
ork
i
ng
c
ond
it
i
o
n
of
t
he
m
ax
i
m
u
m
pow
er
p
o
i
nt
t
r
acki
n
g
fu
nc
ti
o
n
.
Th
e
si
m
u
lat
i
on
resul
t
s
sh
ow
t
he
e
fficie
nc
y
of
t
he
p
ro
pose
d
s
ol
u
tio
n
t
o
har
v
es
t
the
h
i
ghe
st
e
nerg
y
a
t
d
i
ffe
re
nt
radia
t
i
o
n le
v
e
ls
[
15,
16].
I
n
t
h
e
s
t
u
d
y
o
f
t
h
e
e
f
f
i
c
a
c
y
o
f
a
l
g
o
r
i
s
m
,
C
S
w
e
r
e
e
x
a
m
i
n
e
d
t
o
t
ra
ck
t
h
e
G
M
M
P
of
t
h
e
p
hot
ovo
lt
ai
c
pane
l
unde
r
P
S
C
a
nd
c
o
m
p
a
r
e
w
ith
t
he
P
&
O
a
l
g
or
i
t
hm
.
T
h
e
te
st
i
n
d
ifferent
case
s
o
f
three
cases
o
f
study.
The
P
V
m
odu
l
e
i
s
used
u
n
d
e
r
P
S
C
t
o
eva
l
u
a
te
t
he
e
ffic
ie
ncy
o
f
t
he
p
r
o
pose
d
C
S
al
g
o
r
ithm
.
W
he
n
t
e
st
a
l
l
ca
se
s,
t
he
t
ra
c
k
i
n
g
eff
i
c
i
e
n
cy
o
f
t
h
e
CS
i
s
h
i
g
h
er
t
han
99
%
w
i
t
h
i
n
3
0
0
-50
0
ms.
The
i
m
pr
o
v
e
d
C
S
al
gor
it
hm
ca
n
effec
t
i
v
e
l
y
m
a
nage
P
S
C
u
n
d
e
r
d
iffe
ren
t
s
ha
di
n
g
c
o
n
d
i
tio
ns
w
h
i
le
t
he
P
&O
a
lgor
it
hm
c
anno
t
ha
nd
le
t
h
e
P
S
C
of
p
ho
t
o
v
o
lta
ic
p
a
n
e
l
s.
T
he
r
es
ul
ts
a
l
s
o
in
dic
a
t
e
tha
t
t
he
e
n
ergy
t
rac
e
d
by
C
S
has
v
e
r
y
l
ow
s
t
a
ti
c
e
n
er
g
y
fl
uc
tua
t
io
ns
c
om
par
e
d
to
t
he
P
&O
a
lgor
it
h
m
.
P
r
ov
in
g
th
at
S
C
is
ac
cur
a
te,
dura
b
l
e
a
n
d
e
ffic
ie
n
t
i
n
e
n
erg
y
efficie
n
c
y
f
or
s
ta
nda
l
one
P
V
syst
e
m
s
[
1
7].
T
h
e
MP
P
T
c
o
n
tro
l
ler
i
s
t
he
m
ost
c
o
m
m
only
use
d
c
o
n
tro
l
alg
o
ri
t
h
m
in
t
he
p
h
o
t
o
vo
l
t
a
i
c
syst
em
b
ec
ause
i
t
is
p
rac
t
i
c
al.
W
he
n
t
h
e
MP
PT
c
ontro
l
tec
h
ni
q
u
e
re
la
tes
to
artific
ia
l
i
n
t
e
lli
genc
e
s
t
ra
t
e
g
i
e
s
,
i
t
can
b
e
impro
v
e
d
.
Wit
h
l
e
ss
ha
ssle
t
h
a
n
phot
o
v
o
l
t
a
ic
s
ys
tem
s
w
ith
f
u
z
z
y
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
T
r
ack
t
h
e
m
a
x
i
m
u
m
powe
r
of
a
ph
o
t
ov
olt
a
ic to
co
n
t
rol
a ca
sc
ade
five
-
l
e
ve
l
… (Arc
kar
a
ki
t C
h
a
i
th
a
nak
u
l
wat)
1
865
l
o
g
i
c
c
ont
ro
ll
ers,
i
t
h
a
s
b
een
f
oun
d
t
h
at
i
t
wo
rk
s
b
e
t
t
er
t
h
a
n
t
h
e
P&
O
a
l
go
rit
h
m.
F
ro
m
t
h
e
t
e
st
r
esul
ts,
i
t
i
s
clea
r
tha
t
t
he
f
uzzy
m
et
ho
d
p
r
ovide
s
bet
t
er
p
e
r
for
m
a
n
ce
c
o
m
p
ar
e
d
t
o
o
the
r
M
PP
T
t
e
c
hni
qu
e
s
[
18
].
A
s
i
ngl
e
-
pha
se
f
i
v
e
-
le
v
e
l
p
h
o
t
ov
o
lta
ic
i
n
v
erter
top
o
l
o
gy
for
gri
d
-
c
on
nec
t
e
d
P
V
s
ystem
s
w
i
t
h
a
nove
l
pu
lse
-
w
i
dt
h-
modu
la
te
d
(
P
WM)
co
ntro
l
s
c
hem
e
,
both
re
fere
nce
s
i
gna
ls
t
ha
t
ha
v
e
t
h
e
s
a
m
e
c
ompe
nsa
tio
n
ar
e
eq
u
i
va
len
t
t
o
the
am
pl
i
t
u
d
e
of
t
he
t
ria
n
g
l
e
car
rier
s
ig
na
l
t
h
at
i
s
use
d
t
o
ge
ne
rat
e
t
he
P
WM
s
igna
l
for
the
sw
i
t
ch.
The
in
verter
o
ffe
rs
m
uch
l
e
s
s
t
ota
l
h
arm
o
n
i
c
dis
t
or
tio
n
an
d
c
a
n
o
pe
r
a
te
a
t
ne
a
r-uni
ty
p
ow
er
f
a
c
t
o
r
[1
9-2
2
].
T
he
ca
sc
ade
d
H
-brid
g
e
mu
l
tile
ve
l
s
t
a
c
ke
d
so
lar
ph
o
t
ov
o
lta
ic
m
odu
les
f
or
c
on
ne
c
tin
g
to
s
in
g
l
e
or
t
hr
ee-
pha
se
gri
d
s.
T
he
m
axim
um
pow
er
p
o
i
nt
t
ra
ck
i
ng
con
t
ro
l
a
p
pl
ied
t
o
m
u
l
t
i-le
ve
l
in
ver
t
e
r
s
i
n
b
ot
h
s
i
n
g
l
e
p
h
a
s
e
and
three
p
h
a
s
es.
A
l
l
o
w
i
ng
t
he
d
c-
li
nk
v
o
l
ta
ge
t
o
b
e
c
on
t
r
olle
d
fr
e
el
y.
F
or
a
p
p
l
i
ca
ti
ons
t
ha
t
c
o
nn
e
c
t
t
o
un
ba
lanc
e
d
t
hr
ee-
phase
g
ri
ds.
The
e
xper
i
m
e
nt
o
f
a
se
ve
n
-
le
vel
t
h
r
ee
-phas
e
h
-br
i
dge
i
n
v
e
r
t
e
r
bu
i
l
t
us
i
n
g
ni
n
e
h-bri
dge
m
od
u
l
es.
The
simu
l
a
ti
o
n
r
e
s
ul
ts
a
nd
ex
pe
rime
n
t
s
co
nfir
m
t
h
e
c
o
rre
c
t
n
es
s
of
t
h
e
p
ropo
sed
met
h
od
[2
3].
P
h
ase
an
gle
de
tec
t
i
o
n
o
f
g
ri
d
v
o
lta
ge
i
s
a
n
i
m
por
tan
t
p
ar
t
of
t
he
c
o
n
t
ro
l.
F
or
t
h
e
s
ync
hr
on
isa
tio
n
of
t
he
c
u
rre
n
t
i
n
j
ect
ed
b
y
t
h
e
i
n
v
e
rte
r
,
t
h
e
p
hot
ovol
t
a
i
c
c
o
n
n
e
c
t
ed
t
o
t
he
g
ri
d.
D
etect
i
n
g
the
p
h
a
s
e
ang
l
e,
f
re
q
u
enc
y
and
am
pl
it
ude
o
f
t
h
e
gri
d
v
o
l
t
a
ge
t
o
ge
ner
a
te
a
r
e
f
er
ence
s
i
gna
l
for
the
inverter
t
o
conn
e
c
t
t
o
t
h
a
t
g
r
i
d
.
P
h
a
s
e
loc
k
in
g
m
e
t
h
o
d
(
P
LL)
f
or
s
ing
l
e
p
h
ase
sys
t
em
s
i
s
t
o
cr
eate
or
th
og
o
n
al
v
o
lta
ge
s
yst
e
m
s
u
sin
g
t
he
s
eco
nd
in
t
e
grat
or
(
S
O
G
I).
F
ol
l
o
w
e
d
b
y
t
he
P
ar
k
t
r
ansform
a
ti
o
n
o
f
the
q
uadra
t
i
c
c
om
po
ne
nt
b
e
i
ng
f
orce
d
to
z
e
r
o
b
y
f
u
zzy
l
og
i
c
t
o
p
r
ov
i
d
e
f
a
st
d
et
e
c
ti
o
n
a
n
d
p
r
e
c
i
s
e
ph
a
s
e
a
n
gl
e
i
m
a
ge
s.
T
he
t
e
s
t
is
u
se
d
t
o
s
epar
ate
t
h
e
resu
l
t
s
and
disc
uss
the
ac
cura
cy of t
h
e
prop
osed a
lg
or
ithm
[2
4,
25].
I
n
t
h
i
s
pa
per
,
s
tud
y
t
he
t
ra
ck
i
ng
of
t
he
p
o
w
er
o
f
a
phot
ov
o
l
t
a
i
c
pane
l
t
o
c
on
tro
l
a
f
i
v
e-
l
e
vel
sta
c
k
e
d
si
n
g
l
e
-ph
a
se
i
nv
e
r
t
e
r
swi
t
c
h
co
nn
ect
e
d
t
o
a
fu
z
z
y
l
ogi
c
c
ont
rol
l
e
r.
T
he
p
r
i
nc
ip
le
o
f
c
ontr
o
l
l
in
g
t
h
e
m
a
xi
mum
c
u
rre
n
t
ampl
it
u
d
e
o
f
th
e
ph
ot
ovo
lt
ai
c
mu
lt
ip
li
ed
b
y
th
e
si
n
e
s
i
gn
al
p
e
r
u
n
i
t
t
h
a
t
u
s
e
d
as
a
r
ef
ere
n
ce
c
u
rre
n
t
com
p
are
d
t
o
t
h
e
gri
d
c
urr
e
nt.
S
i
gna
l
c
o
mpa
r
i
s
on
w
i
t
h
the
P
I
D
c
o
nt
r
o
ller
a
llow
s
t
he
c
r
eat
io
n
of
f
ive
le
v
e
ls
o
f
PWM
of
c
a
s
c
a
d
e
c
on
t
r
o
l
o
f
fi
v
e
-l
ev
e
l
i
nv
e
r
te
r
t
o
c
on
n
ect
s
i
ngl
e
-p
hase
g
r
i
ds.
The
sys
t
em
h
as
b
ee
n
tes
t
e
d
a
n
d
eva
l
ua
t
e
d usi
n
g
MA
TLA
B
/
S
i
muli
n
k
com
par
e
d to t
he
pro
t
o
t
y
p
e
c
rea
t
ed
.
2.
DESCRIPTIO
N
O
F
TH
E
P
ROPOSED S
C
HE
M
E
F
r
om
t
he
a
bo
v
e
m
enti
o
n
ed,
c
ons
i
d
eri
ng
fro
m
F
igure
1.
T
he
p
h
o
t
o
v
ol
tai
c
s
ys
tem
tha
t
c
on
tro
l
s
the
ma
ximum
p
o
w
e
r
by
us
in
g
P
&
O
a
l
g
o
r
i
t
h
m
s
,
w
h
ic
h
are
ba
si
c
c
ontro
ls
t
ha
t
a
r
e
not
c
omp
l
i
cated
a
nd
c
o
m
m
o
n
l
y
use
d
.
F
o
r
th
is
r
esea
rch,
a
n
ew
c
o
n
ce
p
t
i
ntro
d
u
ced
b
y
a
p
ply
i
ng
f
uzz
y
l
o
g
ic
p
ri
nci
p
l
e
s
to
c
on
tro
l
c
ompe
nsa
tio
n
curr
ent
(
i
Co
m
p
)
ob
ta
ine
d
from
t
h
e
c
o
n
t
ro
l
o
f
P
&O
m
etho
ds
t
o
m
a
ke
t
he
c
u
r
r
e
nt
(
*i
Co
m
p
)
m
o
r
e
s
t
a
b
l
e
.
F
o
r
t
h
e
c
o
nt
rol
of
s
e
m
i
c
ond
u
c
to
r
d
e
vi
c
e
s
witches
(IGBT).
U
se
t
he
p
rinci
ple
of
d
e
t
e
c
t
i
ng
th
e
vo
lta
ge
s
ig
na
l
fr
om
t
he
grid
t
hr
ough
l
ow-frequenc
y
f
i
l
t
er
ing
(
L
PF)
i
nto
the
PLL
process
.
T
o
b
r
i
n
g
t
h
e
t
i
m
e
s
i
g
n
a
l
(
t
)
toget
h
e
r
w
ith
the
pow
er
a
ngl
e
(
),
t
o
c
r
ea
te
a
c
urr
e
nt
t
ha
t
is
a
s
i
n
us
oi
da
l
sig
n
a
l
(
i
S.pu
)
mul
tip
l
i
e
d
by
t
h
e
fuz
z
y
c
urr
e
nt
l
o
g
i
c
com
p
en
sat
i
on
(
*i
Co
m
p
)
to
b
e
a
reference
grid
s
tream
(
i
S.
r
e
f
)
c
o
mpa
r
ed
t
o
t
h
e
curr
ent
th
at
e
n
t
er
s
the
gr
id
i
n
t
o
t
h
e
curr
ent
PID
process
(
i
S.m
o
d
)
to
c
on
t
r
ol
P
DP
WM
m
ak
e
s
I
GBT
w
o
rk
a
c
c
o
r
d
i
ng
t
o
c
ond
i
tio
n
s
.
In
t
h
e
m
u
lti
lev
e
l
c
a
s
c
a
d
e
i
n
v
e
rte
r
,
wh
en
c
onne
ct
ed
t
o
th
e
g
r
i
d
,
it
w
i
l
l
t
e
st
t
h
e
m
e
c
h
an
ism
of
t
he
m
ec
ha
ni
sm
b
y
a
d
j
u
st
in
g
the
pow
er
a
ng
le
t
o
o
b
ser
v
e
cha
n
g
e
s
i
n
t
he
e
lec
t
r
i
c
i
t
y
s
up
pl
y
to t
h
e
g
r
i
d.
B
y
si
m
u
l
a
ti
on
usi
n
g
M
A
TLA
B/S
i
m
u
lin
k
pro
g
ra
m
com
p
are
w
ith the
p
r
o
t
o
ty
pe
cr
eate
d
,
w
h
ic
h d
i
sc
usse
d in
d
e
ta
i
l
in
e
a
c
h
s
e
c
t
io
n
.
F
i
gure
1.
T
he struc
t
u
r
e
of t
h
e
pow
er
t
r
a
nsm
i
s
s
i
on co
n
t
rol sc
hem
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
6
3
– 1
874
1
866
2.1.
C
o
nt
rol of
p
o
w
e
r
d
istrib
uti
o
n
system
C
ons
ide
r
from
F
i
gure
1,
F
uzz
y
l
o
g
i
c
c
on
t
r
ol
s
c
h
em
e
o
f
c
a
s
c
a
de
m
u
lti-l
e
v
e
l
in
v
e
r
t
er
c
o
n
t
r
ol
f
o
r
ph
o
t
o
v
o
l
t
a
i
c
gr
i
d
-
c
o
nnec
t
e
d
s
ys
t
e
ms
i
n
t
h
is
r
e
s
ear
ch.
F
o
r
the
c
l
o
sed-
lo
o
p
f
ee
dba
c
k
c
o
n
t
r
ol
s
y
s
tem
(P
ID
),
i
t
must
c
o
n
tr
ol
t
he
c
urr
e
nt
s
yst
e
m
netw
ork
a
m
pli
t
ude
.
B
y
b
ringi
n
g
t
h
e
rea
l
c
u
rren
t
i
n
th
e
n
e
t
w
o
r
k
sy
st
em
b
ack
to
t
he
n
e
g
at
i
v
e
w
ith
t
he
r
efer
e
n
ce
ne
t
w
ork
s
t
r
eam
t
hro
u
g
h
t
h
e
P
I
D
c
ontro
ller
t
o
c
o
n
t
ro
l
the
e
l
ec
trici
t
y
i
n
t
he
netw
ork
s
y
ste
m
c
oncer
n
i
n
g
t
he
p
ow
e
r
t
o
t
h
e
ph
ot
o
v
o
l
t
a
ic
i
nte
n
si
ty
,
and
mu
st
m
ai
nt
ai
n
th
e
vol
t
a
g
e
a
t
th
e
ca
paci
t
o
r
to t
he
h
ig
hes
t
vol
ta
ge
l
eve
l
.
F
o
r
cre
a
ti
ng on
e
s
i
n
u
s
o
i
d
al
s
ig
n
a
l
,
i
t
d
e
t
ect
s
t
h
e
si
gn
al
f
ro
m
t
h
e
vo
lt
ag
e
in
t
he
g
ri
d
s
y
st
e
m
t
hro
u
g
h
a
lg
ori
t
hm
pha
se
l
ocke
d
l
o
o
p
a
nd
c
o
m
b
i
n
ed
w
i
t
h
po
wer
an
gl
e,
r
ec
re
a
t
e
t
h
e
sinus
o
i
da
l
si
g
n
a
l
w
i
t
h
t
he
a
l
g
ori
t
hm
s
i
n
e
as
one
s
i
n
e
sig
n
a
l
in
o
ne
s
i
n
e
curr
ent
va
r
i
ab
l
e
.
There
is
a
n
in
i
t
ia
l
a
n
gl
e
c
o
rre
s
pon
di
n
g
t
o
t
h
e
vo
lt
ag
e
a
n
g
l
e
of
t
h
e
g
ri
d
sy
s
t
e
m
t
o
g
i
ve
t
he
f
a
c
t
or
o
f
po
w
e
r
appr
oa
ch
i
n
g
o
n
e
.
F
r
om
t
he
a
b
o
v
e
m
e
nt
ione
d,
t
he
a
m
p
li
tu
d
e
o
f
t
h
e
com
p
en
sat
i
on
c
u
r
ren
t
(
i
Co
m
p
)
ch
an
g
e
a
cco
rdi
ng
t
o
t
h
e
rela
tio
ns
hip
t
h
e
am
ou
n
t
o
f
p
o
w
e
r.
T
ha
t
is
o
b
t
a
i
ne
d
from
t
he
p
h
o
t
o
vo
lta
ic
i
n
t
h
e
m
a
x
i
mum
po
w
e
r
trac
kin
g
tech
n
i
q
u
e
of
t
he
P
&O
m
eth
od,
t
hro
u
gh
t
h
e
cre
a
ti
on
o
f
a
c
on
d
i
t
i
o
n
o
f
t
h
e
f
u
z
z
y
l
o
g
i
c
c
o
n
t
r
o
l
,
t
h
e
s
y
s
t
e
m
incre
a
se
t
he
o
r
d
er
f
low
a
m
pli
t
u
d
e
m
o
re
w
he
n
t
h
e
i
n
t
e
ns
i
t
y
of
t
h
e
s
unli
ght
i
n
c
re
a
s
es
a
nd
s
i
m
il
a
r
l
y
,
wh
en
t
h
e
lig
ht
i
n
t
e
n
s
i
t
y
d
ec
rea
s
es,
the
order
fl
ow
r
educ
ed
i
n
the
p
o
w
er
of
t
he
p
h
o
t
o
vo
l
t
a
i
c
.
T
hat
rec
h
arge
d
i
n
t
o
t
he
e
l
e
c
t
r
i
c
a
l
n
e
t
w
o
r
k
s
y
s
t
e
m
v
a
r
i
e
s
a
c
c
o
r
d
i
n
g
t
o
t
h
e
a
m
p
l
i
t
u
d
e
o
f
t
h
e
order
fl
ow
.
Crea
tin
g
a
re
fer
e
nce
c
u
rrent
gri
d
s
ys
tem
(
i
S
,
re
f
)
from
in
F
i
g
ure
1,
t
he
r
efer
e
n
ce
cur
r
en
t
gr
i
d
s
ys
t
e
m,
t
he
p
r
o
d
uc
t
o
f
b
r
i
n
g
i
ng
o
n
e
s
i
ne
s
ig
na
l
(
i
S,pu
)
tha
t
i
s
a
cons
ta
nt
m
u
l
t
i
p
l
ied
by
t
h
e
com
p
en
sat
i
on
c
u
rre
nt
(
i
Co
m
p
)
a
c
c
o
r
d
i
n
g
t
o
t
h
e
r
e
l
a
tio
ns
hi
p
of
t
h
e
ma
ximum
pow
e
r
tra
ckin
g a
b
o
v
e. The resul
t i
s
a
re
f
er
ence
sine st
r
eam
tha
t is a pure sine
s
ig
na
l t
h
at is eq
ual to
the
a
m
pl
i
t
u
d
e of t
he c
urr
e
nt
c
omm
a
nd c
o
n
t
rol
lin
g t
h
e
cur
r
e
n
t
in
t
he
g
r
i
d s
y
stem
.
Wil
l
bri
ng the
re
fe
renc
e
gr
id
curr
ent
to
t
he
a
ctua
l
c
u
r
r
ent
i
n
t
he
g
r
i
d
s
y
s
t
em
(
*
i
S
)
and
e
n
t
e
r
t
h
e
e
xpe
c
t
ed
v
a
l
ue
f
o
r
t
h
e
g
ai
n
co
n
t
ro
l
P
I
D
in
order
t
o
c
o
n
t
r
o
l
t
he
c
urre
n
t
a
mpli
t
ude
s
ine
i
n
m
od
ula
t
i
on
(
i
S,mod
)
is
t
he
a
mpli
t
ude
o
f
on
e
un
it
for
m
o
d
u
l
a
t
i
o
n
to
ge
ther
w
ith
t
he
P
D trian
g
le
s
igna
l
sh
ow
n i
n
F
i
gur
e 2.
2
F
i
gure
2.
D
isp
o
sit
i
on
pu
l
se
-w
id
t
h
-mod
ula
t
e
d
o
f
casc
a
de
f
i
v
e-lev
el
i
n
v
e
r
t
e
r.
2.2.
Perturb
a
n
d o
b
serv
e;
P&O meth
o
d
F
o
r
F
i
gure
3
,
t
he
m
a
x
i
m
um
pow
er
t
rac
k
in
g
o
f
t
he
p
hot
o
v
o
l
t
a
i
c
c
a
n
w
r
it
e
t
h
e
w
o
r
k
in
g
pr
inc
i
p
l
e
of
the
sys
t
e
m
.
F
i
nd
t
h
e
m
a
xim
u
m
pow
er
by
br
i
n
g
i
n
g
c
urr
e
nt
t
o
c
o
m
p
a
re
w
i
t
h
t
h
e
prev
io
us
c
urr
e
nt
t
o
ma
inta
i
n
the
vo
lta
ge
l
ev
el
a
t
t
h
e
c
a
p
ac
itor
a
n
d
a
d
just
t
he
c
u
r
rent
v
a
l
u
e
t
o
th
e
ma
xi
mu
m
po
we
r
ra
ng
e
a
c
c
o
r
di
ng
t
o
th
e
rela
tio
ns
hip
o
f
t
he
p
ow
er
a
n
d
p
h
o
t
o
v
o
l
t
a
i
c
in
ten
s
i
t
y.
C
ons
ide
r
i
ng
th
e
r
e
lati
o
n
shi
p
g
rap
h
,
F
i
gure
4,
w
hen
t
h
e
t
o
ta
l
p
o
w
e
r
ou
tpu
t
i
s
zer
o,
t
he
m
ean
v
o
lta
ge
and
c
u
rre
n
t
a
re
i
n
the
h
i
ghe
st
pow
e
r
p
o
i
n
t
.
H
o
w
e
ver
,
on
the
ot
h
er
h
a
n
d,
w
hen
t
h
e
s
u
m
of
t
he
p
ow
er
i
s
no
t
equa
l
t
o
z
ero,
it
i
s
c
o
n
s
i
de
re
d
w
i
t
h
t
he
s
u
m
o
f
the
v
o
lta
ge
i
n
t
h
e
ra
ng
e
gre
a
ter
tha
n
o
r
le
ss
t
ha
n
zer
o.
I
f
the
t
o
t
a
l
v
o
lt
ag
e
i
s
m
o
r
e
si
gni
fi
can
t
th
an
z
e
r
o
,
i
nd
i
c
at
es
t
h
a
t
i
n
the
calc
u
la
ti
on
p
eri
od,
t
he
d
irec
t
vo
l
t
a
g
e
is
h
ig
he
r
tha
n
t
he
m
a
x
i
m
um
volta
ge.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
T
r
ack
t
h
e
m
a
x
i
m
u
m
powe
r
of
a
ph
o
t
ov
olt
a
ic to
co
n
t
rol
a ca
sc
ade
five
-
l
e
ve
l
… (Arc
kar
a
ki
t C
h
a
i
th
a
nak
u
l
wat)
1
867
F
i
gure
3.
A
lgo
r
it
hm
f
low
c
h
a
r
t dia
g
r
a
m
F
i
gure
4.
M
ax
i
m
um
pow
e
r
tr
a
cki
n
g w
i
t
h
P&O met
h
od
.
2.3.
T
h
e
fuz
z
y
l
o
g
i
c
MPPT c
ontrolle
r
A
typ
i
c
a
l
P
I
D
c
o
n
t
rol
is
f
ix
e
d
f
ee
d
b
ac
k.
T
her
e
for
e
c
an
no
t
com
p
e
nsa
t
e
for
va
ri
at
i
ons
i
n
proce
s
s
para
me
ters
a
n
d
c
a
n
n
o
t
a
d
jus
t
t
o
cha
nge
s
i
n
t
he
e
nv
iro
n
m
e
nt.
P
I
D
c
on
trol
l
e
d
sy
ste
m
s
do
n
o
t
re
sp
ond
t
o
r
e
a
l
cha
nge
s
a
n
d
a
r
e
qui
t
e
f
ast
i
n
t
he
s
ys
tem
so
t
ha
t
the
s
y
s
t
e
m
d
ec
re
ase
d
a
t
th
e
set
poi
nt
.
On
t
he
o
t
h
er
h
and
,
stim
ula
t
i
o
n
a
n
d
ob
serva
t
i
o
n
(P
&O
)
for
t
r
ack
in
g
MP
P
T
.
Th
e
respo
n
s
e
r
e
s
u
l
t
s
a
r
e
n
o
t
f
a
s
t
f
o
r
r
a
p
i
d
c
h
a
n
g
e
s
i
n
tem
p
era
t
ur
e
o
r
r
a
d
i
a
tio
n.
T
her
e
for
e
t
he
f
uzz
y
c
ontr
o
l
alg
o
ri
thm
i
s
c
a
pa
ble
o
f
i
mp
rov
i
n
g
t
he
t
ra
c
k
in
g
perform
ance
a
s
com
p
ar
e
d
w
it
h the
c
l
a
ssic
a
l
m
etho
ds
f
or
b
o
t
h
li
n
ea
r
a
n
d
n
on-
li
near
l
oa
ds
.
A
l
so,
fuzz
y
l
o
g
i
c
i
s
appr
opr
i
a
t
e
f
or
non-
line
a
r
c
o
nt
r
o
l
be
ca
u
s
e
it
d
o
e
s
n
ot
u
se
a
c
o
m
p
le
x
m
a
t
h
em
ati
c
a
l
e
qua
ti
o
n
.
Bloc
k
d
i
a
g
ram
of
t
h
e
f
uzzy
l
ogic
c
ontro
l
l
er
s
how
n
in
F
i
g
ure
5,
t
w
o
f
uz
zy
l
o
g
i
c
i
n
p
u
t
v
a
r
ia
bles
a
re
e
r
r
or
pow
er
a
nd
er
ror
vo
lta
ge.
The
fu
zz
y lo
g
i
c
be
ha
vio
u
r
depe
nds
on t
h
e
sha
p
e
o
f
the
fu
nc
ti
o
n
and
t
h
e
ba
sic
rul
e
s.
F
i
gure
5.
F
uzz
y
lo
g
i
c bl
oc
k
d
i
a
g
ram
.
F
r
om
F
igure
5,
t
o
fi
n
d
t
he
e
rror
of
p
ow
e
r
a
nd
v
o
lta
ge,
use
t
h
e
o
l
d
va
lue
m
i
n
u
s
t
h
e
new
v
a
lue
t
o
f
in
d
the c
h
an
ge o
f pow
er and vo
l
t
a
ge
w
hic
h
has the e
qua
t
i
o
n
t
o
find
t
h
e c
h
a
n
g
e
as t
h
e
e
qua
ti
on (1) and (
2
). Whe
re
)
(
k
dE
is
t
he
c
ha
n
g
e
r
a
te
o
f
t
h
e
err
o
r
va
l
u
e
a
t
t
he
t
ime
k
,
)
(
k
E
is
t
he
e
r
r
or
v
a
l
ue
a
t
t
h
e
t
i
m
e
k
,
)
1
(
k
E
is
t
he
err
o
r va
lu
e
a
t
t
he tim
e of
k-
1
.
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
6
3
– 1
874
1
868
(
2
)
The
u
s
e
o
f
f
u
z
zy
l
ogic
to
c
ontro
l
t
h
e
m
a
x
i
mum
pow
er
t
r
acki
ng
is
u
s
e
d
t
o
d
e
t
e
c
t
c
h
a
n
g
e
s
i
n
t
h
e
pow
er
o
f
a
p
h
o
t
ovo
l
t
ai
c
a
n
d
vo
l
t
a
g
e
c
h
an
ge
t
hr
oug
h
proce
ssi
ng
i
n
a
fuzz
y
lo
gic
bl
oc
k.
T
o
cr
eat
e,
c
alc
u
la
te
and
c
o
m
p
are
as
a
d
u
t
y
c
y
c
l
e
for
co
n
t
rol
l
ing
the
v
o
lta
ge
D
C-
DC
b
o
o
s
t
c
o
n
v
e
r
t
e
r
c
i
r
c
u
i
t
.
T
h
e
f
u
z
z
y
p
a
r
t
i
s
t
h
e
in
put
v
a
r
iab
l
e
for
da
ta
c
han
g
e
s
i
n
p
ow
er
a
nd
v
o
l
t
a
ge
a
nd
dut
y
c
yc
le
v
alue
s.
D
iv
ide
d
i
nto
5
v
a
riab
l
e
s
a
s
fo
l
l
ow
s:
N
B
(N
ega
t
i
v
e
Big),
N
S
(
N
e
gative
S
m
all),
ZE
(
Z
ero)
,
PS
(P
osit
i
v
e
S
m
all)
a
nd
P
B
(
P
o
si
t
i
ve
B
i
g
)
.
I
n
th
i
s
r
esea
rch,
the
t
ria
n
g
l
e use
d
, a
s show
n in
F
igure
6.
(a)
(
b
)
F
i
gure
6.
T
he tria
ngle
fuz
z
y
l
og
ic
c
hara
cter
ist
i
cs.
(a)
Input variable error
power
(
b)
Inpu
t va
ri
able
e
rr
or vol
ta
ge
I
n
t
e
r
ms
o
f
dete
rm
i
n
in
g
the
w
o
rking
c
o
ndi
t
i
o
n
s
o
f
t
he
F
uz
zy
R
ul
e,
i
t
i
s
n
ec
es
sary
t
o
u
s
e
t
h
e
expe
r
t
i
s
e
i
n
t
h
a
t
s
y
st
em
.
D
e
sig
n
o
f
o
u
t
p
ut
u
se
d
f
o
r
s
y
stem
c
on
t
ro
l
w
h
e
n
e
rr
or
v
alue
s
are
di
sp
la
yed,
a
s
sho
w
n
in Ta
b
le
1.
Ta
bl
e
1
.
Th
e
co
ndi
tio
n
s o
f
fuz
zy
l
ogi
c.
E
r
ro
r
Volta
g
e
/
E
r
r
o
r Pow
e
r
NB
NS
ZE
PS
PB
NB
N
B
NS
Z
E
P
S
P
B
NS
N
B
N
S
ZE
PS
P
B
Z
E
P
B
PS
ZE
N
S
N
B
P
S
P
B
PS
ZE
N
S
N
B
PB
P
B
PS
ZE
N
S
N
B
3.
RESULT
S
A
N
D
DISCU
SSIO
N
The
resu
lt
s
of
t
he
s
imula
t
io
n
te
st
u
s
i
ng
t
h
e
pro
g
ra
m
MA
TLA
B
/
S
i
m
ul
i
nk
t
o
c
om
p
a
r
e
w
it
h
t
h
e
gene
ra
ted
pr
ot
oty
p
e
,
t
he
m
a
x
i
m
um
p
ow
e
r
t
r
acki
n
g
of
a
p
h
o
t
o
vo
l
t
a
i
c
t
o
co
nt
rol
a
c
a
s
cade
fi
v
e
-
l
ev
el
i
nve
rt
er
a
sing
le-
p
hase
g
rid-co
nnec
t
e
d
w
it
h
a
fuzz
y
log
i
c
co
n
t
ro
l.
F
r
o
m
t
h
e
tes
t
o
f
the
work
o
f
t
h
e
so
l
a
r
cell
s
y
s
t
em
,
c
o
nn
e
c
t
t
h
e
con
v
e
rt
ers
wit
h
t
h
e
g
ri
d
,
w
i
t
h
th
e
maxi
mu
m
po
we
r
mo
ni
t
o
ri
n
g
i
n
av
era
g
e
t
e
mp
era
t
u
r
e
and
l
i
gh
t
in
t
e
nsit
y
c
ond
i
t
i
ons,
t
h
e
te
st
i
n
the
tem
p
era
t
ur
e
a
n
d
l
i
gh
t
i
n
t
en
sit
y
c
ond
it
i
o
n
s
s
udd
en
ly
r
ed
u
c
ed
t
o
v
i
e
w
t
he
resul
t
s of
t
he
p
he
nom
ena
o
f
p
ara
m
e
t
ers
of t
h
e
r
esults as
fo
l
l
ow
s.
F
o
r
F
i
gure
7,
t
he
s
i
m
ula
t
i
on
of
m
a
x
im
um
p
ow
e
r
t
rac
k
i
n
g
i
n
a
ver
a
ge
t
em
per
a
t
u
re
a
nd
li
gh
t
i
n
te
ns
i
t
y
con
d
i
t
i
on
s
by
s
et
tin
g
t
h
e
c
o
m
m
a
nd
fl
ow
(
i
Comp
).
T
he
v
o
l
t
a
ge
a
n
d
c
ur
rent
o
bta
i
ne
d
fr
om
t
ra
ck
i
n
g
t
h
e
ma
ximum
pow
er
o
f
p
h
o
to
vo
l
t
aic
from
the
s
i
m
u
lat
i
on
us
i
n
g
the
pro
gra
m
M
A
TLA
B/S
i
m
u
li
nk
a
n
d
t
h
e
p
o
w
e
r
and
c
u
rrent
t
h
a
t
is
p
a
i
d
ou
t
from
m
any
i
n
verter
s
p
a
i
d
t
o
t
h
e
lo
a
d
a
nd
g
ri
d
ca
n
be
p
a
i
d
a
c
c
o
r
d
in
g
t
o
t
he
conditions spe
c
ified.
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
T
r
ack
the m
a
xi
m
u
m
pow
e
r
of a
ph
o
t
ov
o
l
t
a
i
c
to
c
o
n
t
r
o
l
a ca
sca
d
e
fi
v
e
-
l
e
v
e
l
…
(
A
rck
a
rak
i
t
Cha
i
th
a
nak
u
l
w
a
t)
1
869
F
i
gur
e
7.
T
h
e
s
im
ul
a
t
i
on
us
i
n
g
the
pr
ogr
a
m
M
A
TLA
B/S
i
m
u
l
i
nk.
F
o
r
in
F
i
gur
e
8
,
t
he
s
i
m
ula
t
i
on
at
v
ar
i
o
us
l
i
g
ht
i
n
t
ens
i
t
y
c
o
n
s
i
s
t
s
o
f
ab
out
4
00
,
60
0
,
1
000
W
/
m
2
.
It
i
s
f
o
und
t
h
a
t
w
h
e
n
de
ter
m
in
ing
t
h
e
sam
e
c
o
n
d
it
io
ns
a
s
F
i
gu
r
e
7
,
th
e
ma
xi
mum
powe
r
t
ra
cin
g
c
a
n
b
e
t
r
acke
d
,
w
h
ic
h
pr
o
v
es
t
ha
t
t
h
e
f
u
zzy
l
ogic
co
ntr
o
l
mode
l
w
o
r
k
s
a
ccor
d
i
n
g
t
o
the
s
p
e
c
i
f
ied
o
b
j
ec
t
i
ve
s.
F
i
gur
e
8.
T
he
r
elat
i
o
n
s
hi
p
bet
w
ee
n
vo
lt
a
g
e
a
nd
m
a
xim
u
m
p
o
w
e
r
tr
ac
ki
n
g
.
S
i
m
i
l
a
r
l
y,
w
hen
te
st
in
g
co
n
d
i
tio
ns
i
n
w
h
ic
h
lig
h
t
i
n
t
e
n
si
ty
a
nd
t
em
p
e
r
a
tur
e
c
h
a
n
g
e
s
s
ud
de
nl
y,
sim
u
la
ti
on r
e
s
u
l
t
s
us
i
n
g t
h
e p
r
ogr
am
M
A
TLA
B/S
i
m
u
lin
k.
F
r
o
m obse
r
v
i
n
g the
fe
a
t
ur
e
s
of
vo
ltag
e
a
n
d
cur
r
e
nt
ch
a
n
g
e
s
and
mo
nit
o
ri
ng
o
f
the
max
i
mu
m
power
o
f
t
h
e
sy
ste
m
,
a
s
w
e
l
l
as
t
h
e
g
rid
con
n
ect
ion
s
,
th
e
re
sul
t
s
a
r
e
a
ccor
d
i
n
g
to
t
h
e
t
er
ms
s
et.
C
a
n
be
c
on
si
der
e
d
as
F
igur
e
9.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
6
3
– 1
874
1
870
F
i
gur
e 9.
The
ligh
t
c
han
g
e
s
s
udde
nly.
Ba
se
d
on
F
i
gure
9,
t
h
e
o
p
e
ra
ti
on
o
f
th
e
ma
xi
mu
m
p
hot
ovo
l
t
a
i
c
p
o
w
e
r
t
r
a
c
k
i
n
g
s
y
s
t
e
m
w
h
e
n
a
l
i
g
h
t
inc
i
den
t
o
cc
urre
d
o
n
t
he
p
h
o
tov
o
lta
ic
s
udde
nly
dro
ppe
d
n
a
tura
ll
y
cau
si
ng
t
h
e
p
o
w
er
o
f
t
h
e
pho
t
o
v
o
lt
ai
c
t
o
dec
r
ea
se
,
re
sulti
n
g
i
n
t
h
e
c
o
m
m
a
nd
curr
ent
(
i
Comp
)
ha
s
r
e
d
u
ced
a
mpl
i
t
ud
e
.
M
oreo
ve
r,
t
he
c
urrent
a
n
d
v
o
l
tage
and
m
a
x
i
mum
pow
er
w
hen
t
h
e
syst
e
m
i
s
run
n
i
n
g
at
a
s
ud
d
e
n
l
i
gh
t
i
n
te
ns
ity
b
etw
e
e
n
4
0
0
,
10
00
W/m
2
w
h
e
n
the m
a
xim
u
m pow
er
t
rac
k
ed.
S
how
r
esul
ts, a
s show
n i
n
F
igure
1
0
.
F
i
gure
1
0
.
The r
e
lati
onsh
i
p b
e
t
w
een
v
olta
ge
a
n
d
pow
er
w
hen
a
su
dd
en
c
han
g
e
.
F
i
gure
1
1
,
fro
m
t
he
s
a
m
e
co
nd
i
t
i
o
ns
a
s
the
si
m
u
la
tio
n
res
u
l
t
s
b
y
t
h
e
pro
g
ram
MA
TLA
B
/
S
i
mul
i
nk.
Whe
n
t
e
s
ti
ng
t
h
e
pro
t
o
t
ype
b
ui
l
t
,
it
c
o
n
c
l
u
d
e
d
t
h
at
v
o
l
tage
,
el
ec
t
r
ici
t
y,
a
nd
tra
c
k
i
n
g
t
he
m
aximum
pow
er
o
f
P
&
O
w
h
e
n
c
on
t
r
o
lle
d
b
y
f
uz
zy
l
o
g
i
c
a
s
w
e
ll
a
s
gri
d
c
o
nnec
tio
ns.
T
he
r
es
ul
t
s
a
r
e
c
ons
iste
n
t
w
i
t
h
the
si
m
u
lat
i
on an
d
can
c
onfirm
th
at
s
uc
h princ
i
p
l
es
a
p
p
l
i
e
d
to t
h
e
des
i
red
pur
pos
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
T
r
ack
t
h
e
m
a
x
i
m
u
m
powe
r
of
a
ph
o
t
ov
olt
a
ic to
co
n
t
rol
a ca
sc
ade
five
-
l
e
ve
l
… (Arc
kar
a
ki
t C
h
a
i
th
a
nak
u
l
wat)
1
871
F
i
gure
1
1
. L
i
g
ht i
s tra
c
ki
n
g
t
he
r
adia
ti
o
n
sy
s
tem
of
t
he
pr
o
to
t
ype.
F
o
r
F
i
gure
1
2
,
sim
ilar
l
y
,
w
he
n
te
sti
n
g
for
t
h
e
ma
xi
m
u
m
p
o
w
e
r
o
f
t
he
p
r
o
t
o
t
y
pe
t
o
c
o
mp
a
r
e
w
ith
t
he
si
m
u
lat
i
on
us
ing
M
A
TLA
B/
S
i
m
u
lin
k
pr
o
g
r
a
m
a
ccordin
g
t
o
t
he
r
e
s
u
l
ts
s
how
n
a
b
o
v
e
.
T
he
m
ax
imum
p
ow
e
r
t
r
a
c
ki
ng
r
e
s
ults
w
h
e
n
t
h
e
n
a
t
u
ral
li
ght
i
n
t
e
n
si
ty
a
nd
a
n
a
v
era
g
e
t
e
m
p
e
r
a
t
ur
e
of
t
he
w
orki
n
g
m
ec
hani
sm
respo
nd
to
t
he
s
pec
i
fied
c
o
n
d
it
io
ns
a
n
d
c
a
n
s
ubsta
nt
ia
l
l
y
c
o
n
f
i
r
m
t
he
a
cc
u
r
acy
b
etwe
e
n
t
he
s
i
m
u
l
at
i
o
n
a
n
d
the pr
oto
t
y
p
e
as a
ccur
a
te
a
s stated
i
n pri
n
c
i
p
l
e.
F
i
gure
1
2
. Ma
x
i
m
um
pow
e
r
t
est from
the tr
a
c
ki
n
g
sys
tem
of
t
he
p
roto
typ
e
.
C
ons
ide
r
r
eversi
n
g
,
se
e
F
i
g
u
re
9
a
nd
F
i
gure
1
0
i
n
con
d
i
t
i
on
s
w
h
e
r
e
the
l
i
g
h
t
i
n
te
ns
i
t
y
an
d
tem
p
era
t
ur
e
ch
ange
s
su
dde
n
l
y
due
t
o
cl
ou
d
cover
a
n
d
o
t
h
e
r
fa
cto
rs.
Wh
en
c
om
pari
n
g
t
he
r
esu
lts
w
i
t
h
t
h
e
sam
e
c
ond
iti
o
n
s,
t
he
r
esu
l
t
s
a
re
c
onsi
s
t
e
n
t
a
nd
in
t
he
s
a
m
e
dir
ec
ti
on,
a
s
show
n
i
n
F
i
g
u
r
e
13
a
n
d
F
i
g
u
r
e
14.
Wh
ic
h
c
o
nf
i
r
ms
t
ha
t
the
re
sea
r
ch
t
ar
gete
d
to
p
r
ove
t
he
m
a
x
imum
p
o
w
e
r
t
rac
k
ing
pri
n
c
i
pl
e
of
t
h
e
c
ont
rol
me
cha
n
ism
is
a
f
e
a
t
u
re
t
ha
t
m
a
ke
s
t
h
e
pow
er
f
low
i
n
g
i
nt
o
th
e
n
o
n
l
in
ea
r
l
o
ad
a
nd
t
h
e
g
ri
d
supp
l
y
c
on
tro
l
l
e
d
due
t
o
the
pow
e
r
supp
li
e
d
b
y
sta
b
le
p
h
o
t
ovo
l
t
aic.
F
i
gure
1
3
.
P
a
ra
m
e
te
r va
l
u
e
s
w
hen
t
h
e
l
i
g
h
t
c
ha
nge
s su
d
d
en
l
y
on
t
h
e
pro
t
ot
yp
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
P
o
w
Elec &
D
r
i S
y
st
V
o
l
. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
1
863
–
1
874
1
872
F
i
gur
e
1
4
.
Maximum
pow
e
r
t
e
s
t
fr
om
t
he
t
r
a
c
k
in
g
sys
t
em
.
Th
is
r
e
s
ear
ch,
whe
n
t
est
i
ng
t
h
e
pro
t
ot
y
p
e
ma
chi
n
e
by
su
pp
ly
i
ng
e
x
cess
e
n
er
g
y
t
o
the
g
r
i
d
t
o
t
e
st
t
he
c
u
r
r
e
nt
c
o
n
t
r
o
l
m
ec
han
i
sm,
pow
er
a
ng
l
e
c
o
n
tr
ol
a
n
d
c
om
pen
s
a
t
i
o
n
m
ec
ha
n
i
sm
,
ha
r
m
oni
c
,
b
o
t
h
s
i
m
u
late
d
w
i
t
h
M
A
TLA
B
/
S
i
mul
i
nk
pr
ogr
a
m
c
om
par
e
w
it
h
t
h
e
pr
ot
oty
p
e
.
T
he
r
e
sul
t
i
s
as
s
how
n
i
n
t
he
F
ig
ur
e.
15
(
a
)
a
n
d
(
b
)
f
o
r
t
h
e
s
i
m
u
l
a
t
i
o
n
a
n
d
F
i
g
u
r
e
1
6
(
a
)
a
n
d
(
b
)
f
r
o
m
b
o
t
h
fig
u
re
,
it
c
an
b
e
seen
t
h
a
t
th
e
wa
ve
f
o
rms
sup
p
l
i
e
d
t
o
t
he
g
r
i
d
a
r
e
close
to
t
he
s
ine
w
a
v
e
a
nd
p
h
ase
a
n
gl
e
f
r
o
m
the
gr
id
v
o
l
tage
b
e
c
a
u
se
t
he
s
ys
t
e
m
is
i
n
in
ver
t
e
r
m
ode
.
M
o
r
e
o
v
e
r
,
t
h
e
har
m
on
ic
s
pec
t
r
u
m
o
f
t
he
c
ur
r
e
nt
p
a
i
d
to
t
he
g
r
i
d
has
t
o
ta
l
ha
r
m
on
ic
d
i
s
t
o
r
tio
n
(
T
HD
) red
u
c
ed.
(a)
(b
)
F
i
gur
e
1
5
.
The
si
m
u
la
ti
on
of
h
ar
m
o
n
i
c
c
u
r
r
e
nt
c
om
pe
nsa
t
io
n
(
a
)
vol
ta
ge
a
n
d
c
u
r
r
e
nt
s
up
ply
i
n
g
t
o
gr
id-
c
on
nec
t
i
on
(
b
)
H
a
rm
on
ic s
pe
ctr
u
m
(a)
(b
)
F
i
gur
e
1
6
.
The
e
xper
i
m
e
n
t
o
f
har
m
on
ic
c
ur
r
e
nt
c
ompe
nsa
tio
n
on
t
he
p
r
o
tot
ype.
(
a
)
vol
ta
ge
a
n
d
cur
r
e
nt
s
up
p
l
y
i
n
g
e
xce
s
s
ener
gy
t
o
t
he
g
r
i
d
(b)
H
a
r
monic
s
p
ec
t
r
um
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