T
E
L
KO
MNIK
A
, V
ol
.
17
,
No.
6,
Dec
e
mb
er
20
1
9,
p
p.
3
23
2
~
324
8
IS
S
N: 1
69
3
-
6
93
0
,
accr
ed
ited
F
irst
Gr
ad
e b
y
K
em
en
r
istekdikti,
Decr
ee
No: 2
1/E/
K
P
T
/20
18
DOI:
10.12928/TE
LK
OM
N
IK
A
.v
1
7
i
6
.
13224
◼
32
32
Rec
ei
v
ed
May
29
,
20
1
9
; R
ev
i
s
ed
J
ul
y
2
, 2
01
9
; A
c
c
ep
t
ed
J
ul
y
1
8
,
20
1
9
A
ph
ot
ovo
l
taic i
nt
egr
ate
d u
n
ifie
d p
o
w
er
qu
ali
ty
c
on
dit
io
ner
w
it
h a 27
-
l
evel i
nve
rter
Kamel
S
al
eh
*
1
,
Nae
i
l Hant
o
u
li
2
El
e
c
tr
i
c
a
l
En
g
i
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ri
n
g
De
p
a
r
t
m
e
n
t
,
An
-
Naj
a
h
Na
t
i
o
n
a
l
Un
i
v
e
rs
i
t
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Na
b
l
u
e
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s
t
B
a
n
k
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Pa
l
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s
t
i
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o
rre
s
p
o
n
d
i
n
g
a
u
th
o
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e
-
m
a
i
l
:
k
a
m
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l
.
s
a
l
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h
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j
a
h
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e
d
u
1
,
n
a
e
i
l
_
h
a
n
to
u
l
i
@
y
a
h
o
o
.c
o
m
2
Ab
strac
t
Th
i
s
p
a
p
e
r
p
r
e
s
e
n
ts
a
Uni
fi
e
d
Po
wer
Q
u
a
l
i
t
y
Con
d
i
ti
o
n
e
r
(UPQ
C)
wit
h
a
2
7
-
l
e
v
e
l
i
n
v
e
rte
r
b
a
s
e
d
o
n
a
n
a
s
y
m
m
e
tri
c
H
-
b
ri
d
g
e
t
o
p
o
l
o
g
y
.
E
a
c
h
p
h
a
s
e
o
f
th
e
i
n
v
e
rt
e
r
i
s
c
o
m
p
o
s
e
d
o
f
th
re
e
H
-
b
ri
d
g
e
s
,
s
u
p
p
l
i
e
d
b
y
th
re
e
DC
s
o
u
rc
e
s
s
c
a
l
e
d
i
n
t
h
e
p
o
wer
o
f
t
h
re
e
.
T
h
e
o
u
tp
u
t
o
f
th
e
m
u
l
ti
l
e
v
e
l
i
n
v
e
r
te
r
i
s
c
o
n
n
e
c
te
d
d
i
re
c
tl
y
to
th
e
p
o
i
n
t
o
f
c
o
m
m
o
n
c
o
u
p
l
i
n
g
(PCC
)
wit
h
o
u
t
th
e
n
e
e
d
to
a
tra
n
s
fo
rm
e
r
o
r
a
f
i
l
te
r
.
Th
e
c
a
l
c
u
l
a
ti
o
n
o
f
t
h
e
Sh
u
n
t
Ac
ti
v
e
Po
wer
F
i
l
te
r
(SAPF
) c
o
m
p
e
n
s
a
t
i
o
n
c
u
rre
n
t
i
s
b
a
s
e
d
o
n
t
h
e
g
e
n
e
ra
l
i
z
e
d
t
h
e
o
r
y
o
f
s
y
n
c
h
ro
n
o
u
s
f
ra
m
e
(d
-
q
th
e
o
ry
)
whi
l
e
th
e
c
a
l
c
u
l
a
ti
o
n
o
f
a
s
e
ri
e
s
a
c
t
i
v
e
fi
l
te
r v
o
l
t
a
g
e
i
s
b
a
s
e
d
o
n
In
s
ta
n
t
a
n
e
o
u
s
Re
a
c
ti
v
e
P
o
wer
(p
-
q
t
h
e
o
r
y
).
Th
e
c
o
n
tro
l
o
f
t
h
e
SAPF
i
s
a
c
h
i
e
v
e
d
b
y
u
s
i
n
g
a
c
l
o
s
e
d
-
l
o
o
p
v
e
c
t
o
r
c
o
n
tr
o
l
fo
l
l
o
wed
b
y
a
n
e
w
m
u
l
ti
l
e
v
e
l
m
o
d
u
l
a
ti
o
n
te
c
h
n
i
q
u
e
.
In
a
d
d
i
t
i
o
n
to
th
e
c
a
p
a
b
i
l
i
ty
o
f
h
a
rm
o
n
i
c
e
l
i
m
i
n
a
ti
o
n
o
f
b
o
th
c
u
rre
n
t
a
n
d
v
o
l
t
a
g
e
d
ra
wn
fro
m
t
h
e
s
o
u
r
c
e
,
th
e
UPQ
C
c
a
n
p
ro
d
u
c
e
re
a
l
a
n
d
re
a
c
t
i
v
e
p
o
w
e
r
to
fe
e
d
t
h
e
l
o
a
d
s
d
u
ri
n
g
p
ro
l
o
n
g
e
d
v
o
l
ta
g
e
o
u
t
a
g
e
s
o
r s
o
u
r
c
e
s
h
o
rta
g
e
.
B
a
tt
e
r
i
e
s
p
a
c
k
a
re
u
s
e
d
a
s
a
d
c
l
i
n
k
,
w
h
i
c
h
i
s
c
h
a
rg
e
d
fro
m
p
h
o
to
v
o
l
ta
i
c
a
rr
a
y
c
o
n
n
e
c
te
d
t
o
th
e
b
a
t
te
ry
th
r
o
u
g
h
a
m
a
x
i
m
u
m
p
o
wer
p
o
i
n
t
tra
c
k
e
r
a
n
d
c
h
a
rg
e
c
o
n
tr
o
l
l
e
r.
Th
e
i
n
j
e
c
ti
o
n
o
f
r
e
a
l
a
n
d
re
a
c
t
i
v
e
p
o
wer
d
e
p
e
n
d
s
o
n
t
h
e
s
ta
t
e
o
f
c
h
a
r
g
e
(SO
C)
o
f
b
a
tt
e
ri
e
s
,
t
h
e
fre
q
u
e
n
c
y
o
f
th
e
s
y
s
te
m
,
r
e
a
l
a
n
d
re
a
c
t
i
v
e
p
o
wer
o
f
t
h
e
l
o
a
d
,
a
n
d
p
o
wer
f
a
c
to
r
a
t
th
e
p
o
i
n
t
o
f
PCC
.
T
h
e
p
ro
p
o
s
e
d
UPQ
C
s
tra
te
g
y
i
s
s
i
m
u
l
a
te
d
i
n
M
ATL
AB
SIM
ULI
NK
a
n
d
th
e
re
s
u
l
t
s
h
a
v
e
s
h
o
wn
a
s
i
g
n
i
fi
c
a
n
t
i
m
p
ro
v
e
d
i
n
To
ta
l
Harm
o
n
i
c
s
Di
s
to
rti
o
n
(T
HD
) o
f
b
o
th
t
h
e
v
o
l
ta
g
e
a
n
d
c
u
rr
e
n
t
s
.
Key
w
ords
:
a
c
ti
v
e
fi
l
te
r
s
,
m
u
l
t
i
l
e
v
e
l
i
n
v
e
rte
r,
s
o
l
a
r
p
o
wer
g
e
n
e
ra
ti
o
n
Copy
righ
t
©
2
0
1
9
Uni
v
e
rsi
t
a
s
Ahm
a
d
D
a
hl
a
n.
All
rig
ht
s
r
e
s
e
rve
d
.
1.
Int
r
o
d
u
ctio
n
In
l
as
t
de
c
ad
es
,
the
us
e
s
of
the
p
ower
e
l
ec
tr
o
ni
c
s
de
v
i
c
es
ha
v
e
b
ee
n
i
nc
r
ea
s
ed
s
i
gn
i
fi
c
an
tl
y
i
n
ma
ny
f
i
e
l
ds
s
uc
h
as
ad
j
us
ta
bl
e
s
pe
ed
d
r
i
v
es
[1]
,
arc
furnac
es
[
2],
e
l
ec
tr
i
c
v
eh
i
c
l
e
ba
tte
r
y
c
ha
r
g
ers
[3]
,
l
i
gh
t
i
n
g
eq
u
i
p
me
nt
s
uc
h
as
c
om
p
ac
t
fl
uo
r
es
c
en
t
an
d
L
E
D
l
a
mp
s
[4]
a
nd
i
n
r
en
ewa
bl
e e
ne
r
gy
s
ou
r
c
es
.
Des
pi
te
i
ts
b
en
ef
i
ts
[
5],
t
he
us
es
of
po
w
er e
l
ec
tr
on
i
c
s
de
v
i
c
es
s
hi
fte
d
the
el
ec
tr
i
c
al
l
o
ad
s
fr
o
m
l
i
n
e
ar
to
no
n
-
l
i
n
ea
r
i
.e
.
pro
du
c
i
n
g
ha
r
mo
n
i
c
c
urr
en
ts
[
6].
T
he
s
e
ha
r
m
on
i
c
s
c
an
c
au
s
e
a
s
ev
er
e
ef
fe
c
t
o
n
t
he
who
l
e
po
wer
s
y
s
tem
s
uc
h
as
c
au
s
i
n
g
ov
erheat
i
n
g
i
n
tr
an
s
mi
s
s
i
o
n
l
i
ne
s
an
d
tr
an
s
former
an
d
m
al
e
fun
c
t
i
on
of
protec
t
i
on
d
ev
i
c
es
.
T
he
r
efo
r
e,
h
armon
i
c
el
i
mi
na
t
i
on
ha
s
be
e
n
of
ex
ten
s
i
v
e
c
o
nc
ern
a
nd
i
nv
es
t
i
ga
t
i
o
n.
T
o
el
i
m
i
n
ate
ha
r
m
on
i
c
p
ol
l
ut
i
o
n,
pa
s
s
i
v
e
fi
l
ters
wer
e
ap
p
l
i
ed
.
T
he
s
e
f
i
l
t
ers
ha
v
e
m
an
y
d
r
awba
c
k
s
s
uc
h
as
:
b
ul
k
y
,
o
nl
y
c
a
pa
b
l
e
of
c
om
pe
ns
ati
ng
a
l
i
mi
t
ed
r
an
ge
of
ha
r
mo
ni
c
s
an
d
the
y
c
an
prod
uc
e
r
es
on
an
c
e
p
he
no
me
na
w
he
n
c
on
ne
c
te
d
t
o
th
e
po
w
er
grid
[7]
.
O
n
t
he
oth
er
h
a
nd
(
A
c
t
i
v
e
po
w
er
fi
l
ter
(
A
P
F
)
ha
s
m
a
ny
ad
v
an
t
ag
es
,
s
uc
h
as
hi
g
h
fi
l
ter
i
ng
ac
c
urac
y
,
s
up
e
r
i
or
dy
na
mi
c
r
es
po
ns
e,
mo
du
l
ar
i
ty
a
nd
s
c
al
ab
i
l
i
ty
,
m
ak
i
n
g
i
t
an
i
de
al
de
v
i
c
e
t
o
c
o
mp
e
ns
ate
ha
r
mo
ni
c
s
an
d
i
mp
r
ov
e
p
owe
r
qu
a
l
i
ty
[8
,
9].
A
P
F
s
are
c
on
s
i
de
r
e
d
the
s
ec
on
d
s
tag
e
of
d
ev
el
op
m
e
nt
an
d
an
eff
ec
ti
v
e
s
ol
ut
i
o
n
to
ov
erc
om
e
the
l
i
m
i
tat
i
on
of
P
F
s
.
How
e
v
er,
the
s
i
z
e,
c
os
t,
an
d
r
at
i
ng
of
A
P
F
s
are
c
on
s
i
d
erab
l
y
i
nc
r
ea
s
ed
by
the
i
nc
r
ea
s
i
ng
de
ma
n
d
f
or
p
ower
s
y
s
tem
c
a
pa
c
i
ty
[10
,
1
1].
T
o
ov
erc
om
e
t
he
i
s
s
ue
s
of
s
hu
nt
A
P
F
s
,
the
th
i
r
d
s
ta
ge
of
de
v
e
l
op
m
en
t
c
on
s
i
s
ts
of
hy
brid
po
w
er
fi
l
t
er
(
HP
F
)
de
v
i
c
es
whi
c
h
c
om
pris
e
hy
brid
c
om
bi
na
t
i
on
s
o
f
P
F
s
wi
th
s
h
un
t
A
P
F
s
[12
].
F
urth
ermor
e,
HP
F
tec
h
no
l
og
y
i
s
ev
a
l
u
ate
d
i
n
t
he
f
ou
r
th
s
tag
e
of
d
ev
el
op
m
en
t
as
a
un
i
f
i
e
d
p
ower
qu
a
l
i
ty
c
on
d
i
t
i
on
er
(
U
P
Q
C)
[1
3].
S
ev
era
l
c
on
tr
ol
the
orie
s
for
A
P
F
s
ha
v
e
b
ee
n
de
v
el
o
pe
d
an
d
de
s
c
r
i
be
d
i
n
the
l
i
ter
atu
r
e,
wi
t
h
th
e
p
-
q
the
ory
[14
],
the
F
B
D
[15
],
t
he
CP
C
[
16
]
an
d
t
he
s
y
nc
hro
no
us
r
efe
r
en
c
e
fr
a
me
d
-
q
th
eo
r
y
[1
7]
be
i
ng
a
mo
n
g
the
m
ai
n m
eth
o
ds
fo
r
o
bta
i
ni
n
g t
h
e c
om
pe
ns
at
i
o
n c
urr
en
ts
for
A
P
F
s
.
Rega
r
d
i
n
g
i
ts
s
tr
uc
ture,
a
n
A
P
F
i
s
a
DC
-
A
C
p
ower
c
on
v
erter
,
w
hi
c
h
c
an
be
ei
t
he
r
of
the
v
ol
t
ag
e
s
ou
r
c
e t
y
pe
or t
he
c
urr
en
t s
ou
r
c
e t
y
pe
[
18
]
.
Mo
r
eo
v
er, a DC
-
A
C p
ower
c
on
v
erter
c
an
be
al
s
o
c
l
as
s
i
fi
ed
by
th
e
nu
mb
er
of
l
ev
e
l
s
of
the
ou
t
pu
t
v
ol
tag
e
or
c
urr
en
t,
w
he
r
eb
y
i
t
i
s
c
on
s
i
de
r
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
ph
oto
v
o
l
ta
i
c
i
nte
gra
ted
u
ni
f
i
ed
po
w
er qu
al
i
ty
c
on
d
i
ti
on
er w
i
th
a 2
7
-
l
ev
e
l
i
nv
erte
r
(
K
am
e
l
S
al
eh
)
3233
a
m
ul
t
i
l
ev
el
c
on
v
ert
er
i
f
t
h
e
n
um
b
er
o
f
l
ev
e
l
s
i
s
thre
e
or
mo
r
e
[
19
].
M
ul
t
i
l
ev
el
c
on
v
erter
s
are
ad
v
an
t
ag
e
ou
s
for
me
d
i
u
m
v
ol
tag
e
ap
p
l
i
c
ati
on
s
s
i
nc
e
t
he
y
are
c
ap
ab
l
e
of
prov
i
di
n
g
hi
g
he
r
ou
t
pu
t
v
ol
tag
es
th
an
th
e
v
o
l
ta
ge
tha
t
po
w
er
s
e
mi
c
on
du
c
tor
s
ha
v
e
to
wi
t
hs
tan
d.
B
es
i
de
s
,
mu
l
ti
l
ev
el
c
on
v
erter
s
produc
e
l
es
s
dv
/dt
an
d
h
av
e
a
be
t
ter
p
erfor
ma
nc
e
i
n
ter
ms
of
T
ota
l
H
armo
ni
c
Di
s
torti
on
(
T
HD)
when
c
o
m
pa
r
ed
to
tw
o
-
l
ev
e
l
c
on
v
erter
s
[2
0
].
T
he
r
e
are
thre
e
c
l
as
s
i
c
al
to
po
l
og
i
es
of
m
ul
t
i
l
ev
el
c
on
v
erter
s
,
n
am
e
l
y
th
e
n
eu
tr
a
l
po
i
nt
c
l
a
mp
ed
(
or
di
o
de
c
l
am
pe
d)
[
2
1
],
the
fl
y
i
ng
c
ap
ac
i
tor
(
or
c
ap
ac
i
tor
c
l
a
mp
ed
)
[
2
2
],
a
nd
t
he
c
as
c
ad
ed
mu
l
t
i
l
ev
e
l
c
on
v
erter
[
2
3
]
.
Nev
erthe
l
es
s
,
s
ev
eral
top
ol
og
i
es
ha
v
e
b
e
en
prop
os
ed
i
n
th
e
l
i
terat
u
r
e,
ai
m
i
n
g
to
ac
h
i
ev
e
h
i
g
h
er
nu
mb
ers
of
l
ev
el
s
w
i
th
r
ed
uc
e
d
s
wi
tc
h
c
ou
nts
[
24
–
2
9
].
A
c
c
ordi
n
gl
y
,
c
on
tr
ol
an
d
mo
du
l
ati
on
t
ec
hn
i
qu
es
f
or
mu
l
t
i
l
ev
el
c
on
v
erter
s
ha
v
e
be
en
al
s
o
wi
de
l
y
i
nv
es
t
i
ga
t
ed
[
30
,
31
].
T
he
ob
j
ec
t
i
v
e
of
t
hi
s
p
ap
e
r
i
s
to
s
ho
w
the
ad
v
an
tag
es
of
us
i
ng
U
P
Q
C
th
at
i
s
us
i
n
g
mu
l
t
i
l
ev
el
i
nv
erter
a
nd
b
a
tte
r
y
s
torage
.
C
om
p
ared
to
c
on
v
en
t
i
o
na
l
P
W
M
tec
hn
i
qu
es
,
t
hi
s
c
on
v
erter
,
i
n
an
y
o
f
i
ts
f
un
c
ti
on
a
l
i
t
i
es
,
a
bl
e
to
produc
e
c
urr
en
t
wav
e
forms
w
i
th
n
eg
l
i
gi
b
l
e
ha
r
mo
ni
c
c
on
ten
t
.
T
o
produc
e
ac
t
i
v
e
po
wer
,
th
e
s
y
s
tem
us
es
a
ba
tte
r
y
pa
c
k
k
ep
t
c
ha
r
ge
d
us
i
ng
ph
o
tov
ol
tai
c
arr
ay
s
.
F
urtherm
ore,
the
b
a
tte
r
i
es
c
an
al
s
o
b
e
c
h
arge
d
fr
om
t
he
m
ai
ns
wh
en
r
eq
u
i
r
ed
.
T
he
pa
pe
r
de
s
c
r
i
be
s
t
he
top
ol
o
gy
of
the
s
y
s
tem
an
d
s
ho
w
s
i
m
ul
at
i
o
ns
wi
th
a
s
ma
l
l
13
-
k
V
A
prot
oty
pe
.
T
he
r
es
ul
ts
de
m
on
s
t
r
ate
t
he
ab
i
l
i
ty
of
ac
ti
v
e
fi
l
ters
t
o
c
om
p
en
s
ate
ha
r
m
on
i
c
s
i
n
v
ol
ta
ge
s
a
nd
c
urr
en
t
i
n
a
dd
i
ti
on
t
o
c
om
p
en
s
ate
r
e
ac
ti
v
e
p
ower.
M
or
eo
v
er
,
the
pa
p
er
s
ho
ws
the
ab
i
l
i
ty
of
s
uc
h
a f
i
l
ter t
o b
e
us
ed
as
a
r
e
ne
wabl
e e
ne
r
gy
s
ou
r
c
e t
o s
up
po
r
t th
e g
r
i
d i
n
h
i
gh
-
de
m
an
d
ho
urs
.
2.
Res
ea
r
ch M
eth
o
d
2
.1.
De
sc
r
ipt
in o
f
P
V
-
U
P
Q
C S
ys
t
em
2
.1.
1
.
Ba
sic
P
r
in
ciple
T
he
p
ower c
i
r
c
ui
t
of
t
he
thr
ee
-
ph
as
e P
V
-
U
P
Q
C s
y
s
te
m i
s
s
h
own
i
n Fi
gu
r
e
1.
T
h
e A
P
F
i
s
us
i
ng
a
27
-
l
ev
el
as
y
mm
etri
c
al
i
nv
erter
.
E
ac
h
p
ha
s
e
of
thi
s
i
nv
erter
c
on
s
i
s
ts
of
th
r
ee
H
-
brid
ge
s
s
up
pl
i
ed
by
thre
e
i
n
de
p
e
nd
en
t
ph
oto
v
o
l
ta
i
c
arr
ay
s
.
A
12
5
w
p
ol
y
c
r
y
s
tal
l
i
ne
P
V
mo
d
ul
es
(
Mi
ts
ub
i
s
hi
E
l
ec
tr
i
c
P
V
-
E
E
12
5M
F
5F)
ha
v
e
be
e
n
us
e
d
to
d
es
i
gn
al
l
p
ho
tov
ol
t
ai
c
arr
ay
s
.
T
he
s
e
ph
ot
ov
ol
t
ai
c
arr
ay
s
are
de
l
i
v
erin
g
1
2.5
k
v
a
to
e
ac
h
p
ha
s
e,
10
k
v
a
for
s
h
un
t
ac
ti
v
e
f
i
l
ter
a
nd
2.5
k
v
a f
or
t
he
s
er
i
es
ac
ti
v
e
fi
l
t
er as
s
ho
w
n i
n
T
a
bl
e
1
.
S
o
l
a
r
a
r
r
a
y
M
P
P
T
3
2
4
V
1
0
8
V
3
6
V
A
C
N
o
n
l
i
n
e
a
r
L
o
a
d
N
M
P
P
T
M
P
P
T
S
e
r
i
e
s
F
i
l
e
r
A
c
t
i
v
e
F
i
l
e
r
c
o
n
t
r
o
l
l
e
r
S
o
l
a
r
a
r
r
a
y
M
P
P
T
1
0
8
V
3
6
V
1
2
V
M
P
P
T
M
P
P
T
V
i
n
v
I
i
n
v
V
l
o
a
d
I
l
o
a
d
P
W
M
P
W
M
P
W
M
c
o
n
t
r
o
l
l
e
r
V
i
n
v
I
i
n
v
V
l
o
a
d
I
l
o
a
d
P
W
M
P
W
M
P
W
M
S
O
C
S
O
C
F
i
gu
r
e
1
.
P
ow
er c
i
r
c
ui
t
s
tr
u
c
ture of
t
he
P
V
-
U
P
Q
C s
y
s
tem
B
att
ery
pa
c
k
s
are
us
e
d
as
dc
l
i
nk
an
d
c
ha
r
g
ed
fr
om
ph
ot
ov
ol
t
ai
c
arr
ay
c
on
ne
c
ted
t
o
the
b
att
ery
thro
ug
h
a
ma
x
i
mu
m
po
w
er
po
i
nt
tr
ac
k
e
r
an
d
c
ha
r
g
e
c
on
tr
o
l
l
er.
T
ab
l
e
2
s
ho
ws
the
de
ta
i
l
s
of
the
ba
tte
r
y
p
a
c
k
s
us
ed
for
t
he
s
erie
s
an
d
s
hu
nt
f
i
l
ters
.
T
h
e
o
utp
ut
o
f
t
he
s
hu
nt
ac
ti
v
e
fi
l
t
er
i
s
c
on
ne
c
ted
di
r
ec
t
l
y
to
th
e
tr
an
s
m
i
s
s
i
on
l
i
ne
at
a
P
CC
w
hi
l
e
t
he
s
eri
es
ac
ti
v
e
f
i
l
t
er
i
s
c
on
ne
c
te
d t
o
th
e
trans
m
i
s
s
i
on
l
i
n
e t
hr
ou
g
h a
c
ou
p
l
i
ng
t
r
an
s
former. I
n a
dd
i
ti
on
t
o t
h
e c
ap
a
bi
l
i
ty
of
ha
r
mo
ni
c
e
l
i
mi
na
t
i
o
n
of
bo
t
h
c
urr
en
t
an
d
v
ol
tag
e
dra
w
n
fr
om
th
e
s
ou
r
c
e,
the
c
om
bi
n
ed
s
y
s
tem
c
an
prod
uc
e
r
e
al
an
d
r
ea
c
t
i
v
e
po
w
er
to
fee
d
th
e
l
oa
ds
d
urin
g
pro
l
on
ge
d
v
ol
t
ag
e
ou
t
ag
es
or
s
o
urc
e
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
b
er 20
19
:
32
3
2
-
324
8
3234
s
ho
r
tag
e.
T
he
i
nj
ec
t
i
on
of
r
ea
l
an
d
r
ea
c
ti
v
e
po
w
er
d
ep
en
ds
on
the
s
tat
e
of
c
h
arge
(
S
O
C)
of
ba
tte
r
i
es
,
r
e
al
an
d
r
ea
c
t
i
v
e
po
wer
o
f
th
e
l
oa
d,
an
d
po
w
er
fac
tor
at
the
po
i
n
t
of
c
o
mm
on
c
ou
pl
i
ng
(
P
CC)
.
T
ab
l
e
1.
T
he
C
om
b
i
n
ati
on
s
of
P
V
Mo
d
ul
e
for
D
es
i
gn
i
n
g P
h
oto
v
o
l
ta
i
c
A
r
r
ay
s
S
ou
r
c
es
S
h
u
n
t
Fil
t
e
r
S
e
r
ies
Fil
t
e
r
C
o
mbina
t
ion
P
o
w
e
r
(
w
)
(
%
)
C
o
mbina
t
ion
P
o
w
e
r
(
w
)
P
e
r
c
e
n
t
(
%
)
A
U
X
.
1
1
in
s
e
r
ies
*4
in
p
a
r
a
ll
e
l
500
5%
1
in
s
e
r
ies
*1
in
p
a
r
a
ll
e
l
125
5%
A
U
X
.
2
3
in
s
e
r
ies
*4
in
p
a
r
a
ll
e
l
1500
15%
1
in
s
e
r
ies
*3
in
p
a
r
a
ll
e
l
375
15%
MA
I
N
1
1
in
s
e
r
ies
*6
in
p
a
r
a
ll
e
l
8000
80%
4
in
s
e
r
ies
*4
in
p
a
r
a
ll
e
l
2000
80%
Total
(w)
10
kw
2
.
5
kw
T
ab
l
e
2
.
T
he
P
er P
ha
s
e
Co
mb
i
na
t
i
on
s
of
B
att
ery
P
ac
k
s
S
h
u
n
t
Fil
t
e
r
S
e
r
ies
Fil
t
e
r
C
o
mbina
t
ion
AH
V
o
lt
a
g
e
(
v
)
C
o
mbina
t
ion
AH
V
o
lt
a
g
e
(
v
)
A
U
X
.
1
3
in
s
e
r
ies
*4
in
p
a
r
a
ll
e
l
400
36
1
in
s
e
r
ies
*1
in
p
a
r
a
ll
e
l
100
12
A
U
X
.
2
9
in
s
e
r
ies
*4
in
p
a
r
a
ll
e
l
400
108
1
in
s
e
r
ies
*3
in
p
a
r
a
ll
e
l
100
36
MA
I
N
2
7
in
s
e
r
ies
*7
in
p
a
r
a
ll
e
l
700
324
4
in
s
e
r
ies
*4
in
p
a
r
a
ll
e
l
175
108
Total
(w)
10
kw
2
.
5
kw
2
.1.
2
.
Mult
i
-
l
e
ve
l In
ve
r
t
er
A
s
y
mm
etri
c
c
as
c
ad
ed
m
ul
t
i
-
l
ev
e
l
i
nv
erter
i
s
us
e
d
i
n
th
i
s
r
es
ea
r
c
h
[31
].
E
ac
h
l
e
g
o
f
the
i
nv
ert
er
c
on
s
i
s
ts
of
thre
e
H
-
br
i
dg
es
c
on
ne
c
ted
i
n
s
erie
s
an
d
s
up
pl
i
ed
by
thre
e
i
n
de
pe
n
de
nt
ph
ot
ov
ol
t
ai
c
arr
ay
s
s
c
al
e
d
i
n
t
he
po
wer
of
t
hree
as
s
ho
wn
i
n
F
i
gu
r
e
2.
T
h
i
s
c
on
fi
gu
r
at
i
o
n
of
the
mu
l
ti
-
l
ev
el
i
nv
ert
er
h
el
ps
to
g
en
erate
27
-
l
ev
el
at
the
ou
tp
ut
o
f
th
e
i
nv
erter
i
ns
te
a
d
of
ge
ne
r
at
i
ng
7 l
ev
el
s
w
he
n
us
i
n
g s
y
mm
e
tr
i
c
s
ou
r
c
es
. The
ou
t
pu
t
of
ea
c
h H
-
br
i
dg
e i
s
s
h
own
i
n
F
i
gu
r
e
2.
I
t c
an
be
no
te
d
t
ha
t
th
e
s
w
i
tc
hi
ng
fr
eq
u
en
c
y
o
f
t
he
ma
i
n
H
-
b
r
i
dg
e,
w
hi
c
h
ma
na
g
es
m
ore
th
an
80
%
of
the
tot
a
l
po
w
er,
i
s
t
he
s
a
m
e
fr
e
qu
e
nc
y
of
the
s
y
s
tem
,
i
n
thi
s
c
as
e,
on
l
y
5
0
Hz
.
T
h
e
fr
e
qu
e
nc
y
of
the
au
x
i
l
i
ary
H
-
B
r
i
dg
es
are
al
s
o
l
ow
bu
t
i
nc
r
e
as
es
as
the
v
ol
t
ag
e
l
ev
e
l
of
t
he
i
n
v
erter
be
c
om
e
l
ower
i
n
th
e
c
ha
i
n.
T
he
t
ota
l
ha
r
m
on
i
c
d
i
s
torti
on
of
t
he
ou
tp
ut
wav
ef
orm
of
th
e
mu
l
ti
l
ev
el
i
nv
erter
i
s
on
l
y
1.
8
% wh
i
l
e i
t i
s
i
n
th
e c
as
e o
f
us
i
ng
2
-
l
ev
e
l
i
nv
e
r
ter i
s
5.
4%. Th
i
s
l
ow THD
at
th
e o
utp
u
t o
f
the
mu
l
t
i
-
l
ev
e
l
he
l
ps
to
g
et
r
i
de
o
f
the
n
ee
d
for
an
y
k
i
n
d
of
f
i
l
teri
ng
at
t
he
o
utp
u
t
of
t
he
ac
ti
v
e
f
i
l
t
er.
S
o
l
a
r
a
r
r
a
y
M
P
P
T
3
2
4
V
1
0
8
V
3
6
V
N
S
o
l
a
r
a
r
r
a
y
M
P
P
T
S
o
l
a
r
a
r
r
a
y
M
P
P
T
A
c
t
i
v
e
F
i
l
e
r
F
i
gu
r
e
2.
A
s
y
mm
etr
i
c
27
-
l
e
v
el
i
nv
erter
2
.
2
.
Co
n
t
r
o
l
S
cheme
Ma
ny
tec
h
ni
q
ue
s
wer
e i
ntro
du
c
ed
i
n
the
l
i
t
eratur
e
to
c
al
c
ul
ate
t
he
r
ef
erenc
e
c
urr
en
t
s
an
d
v
ol
tga
es
for
ac
ti
v
e
fi
l
ters
[1
4,
1
5
,
1
7].
T
he
s
e
c
urr
e
nts
an
d
v
o
l
ta
ge
s
w
i
l
l
ha
v
e
al
l
t
he
c
o
mp
o
ne
nts
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
ph
oto
v
o
l
ta
i
c
i
nte
gra
ted
u
ni
f
i
ed
po
w
er qu
al
i
ty
c
on
d
i
ti
on
er w
i
th
a 2
7
-
l
ev
e
l
i
nv
erte
r
(
K
am
e
l
S
al
eh
)
3235
of
th
e
c
urr
en
t
an
d
v
o
l
ta
ge
tha
t
ne
e
de
d
to
be
c
om
pe
n
s
ate
d
by
the
ac
t
i
v
e
f
i
l
t
er
to
ac
hi
ev
e
u
ni
ty
po
wer
f
ac
tor an
d m
i
n
i
m
um
di
s
torti
on
i
n
bo
t
h v
ol
t
ag
e
an
d c
urr
en
t o
f th
e s
ou
r
c
e.
2.2
.1
.
Ref
er
en
ce
Cu
r
r
ent
C
alc
u
l
atio
n
f
o
r
S
h
u
n
t
Activ
e Filt
er
S
y
nc
hrono
us
Re
ferenc
e
d
-
q
m
eth
o
d
w
as
a
do
pt
e
d
i
n
t
hi
s
r
es
e
arc
h
to
c
al
c
ul
ate
the
c
urr
en
t
r
e
ferenc
e
for
ac
ti
v
e
fi
l
ter
[
14
].
T
he
a
l
g
orit
h
m
of
t
hi
s
m
eth
o
d
i
s
i
l
l
us
tr
at
ed
i
n
F
i
g
ure
3.
T
hi
s
me
tho
d
b
as
ed
on
tr
a
ns
formi
ng
t
he
l
o
ad
c
urr
en
t
i
nt
o
th
e
l
oa
d
v
ol
tag
e
s
y
nc
hrono
us
fr
am
e
d
-
q
fr
am
e.
I
n
s
uc
h
a
c
as
e
the
c
urr
en
t
w
i
l
l
ha
v
e
tw
o
c
om
po
ne
nts
Id
an
d
Iq.
T
h
e
Id
c
urr
en
t
i
s
i
n
the
di
r
ec
ti
o
n o
f th
e
l
oa
d v
ol
t
ag
e a
n
d s
o i
t i
s
th
e real
p
o
wer
c
urr
en
t c
om
po
ne
nt
. Th
e I
q c
urr
en
t wi
l
l
be
p
erpen
di
c
u
l
ar t
o t
h
e l
oa
d v
ol
t
ag
e
an
d
he
n
c
e i
t
i
s
th
e reac
ti
v
e
po
w
er c
urr
en
t c
o
mp
on
en
t.
T
he
s
e
d
-
q
c
urr
e
nt
c
om
po
n
en
ts
wi
l
l
ha
v
e
two
c
o
mp
o
n
en
ts
.
T
he
fi
r
s
t
c
om
po
ne
nt
i
s
the
dc
c
om
po
n
en
t
t
ha
t
r
ep
r
es
e
nts
the
fun
d
am
en
ta
l
c
om
p
on
e
nt
of
the
r
ea
l
an
d
r
ea
c
ti
v
e
c
om
po
n
en
ts
.
T
he
ac
c
o
mp
o
ne
n
t
r
ep
r
es
e
nts
the
ha
r
mo
n
i
c
s
i
n
the
c
urr
en
t.
M
oreov
er,
the
i
nj
ec
ti
o
n
of
r
ea
l
po
wer
fr
om
th
e P
V
s
c
an
be
do
n
e
by
ad
d
i
ng
a
c
o
mp
o
ne
nt
to
I
d a
s
s
ho
w
n i
n
F
i
gu
r
e
3
.
P
h
a
s
e
l
o
c
k
e
d
l
o
o
p
V
L
a
b
c
Ɵ
I
L
a
b
c
I
d
_
r
e
f
a
b
c
d
q
H
i
g
h
p
a
s
s
f
i
l
t
t
e
r
I
q
_
r
e
f
R
e
a
l
p
o
w
e
r
i
n
j
e
c
t
i
o
n
+
+
F
i
gu
r
e
3.
P
r
i
nc
i
pl
e o
f
i
ns
ta
n
tan
e
ou
s
ac
ti
v
e
an
d reac
t
i
v
e
po
wer
t
he
ory
(
d
-
q
me
t
ho
d)
2
.
2
.
2.
Ref
r
enc
e V
o
lt
age
V
alc
u
l
a
t
ion
f
o
r
S
er
ies
Activ
e Filt
er
T
he
i
ns
ta
nta
ne
o
us
r
ea
l
a
n
d
r
ea
c
ti
v
e
m
eth
o
d
(
P
Q
me
tho
d)
i
s
ad
op
t
ed
i
n
th
i
s
r
es
ea
r
c
h
to
c
al
c
ul
ate
t
he
r
ef
erenc
e
v
ol
tag
es
for
the
s
eri
es
ac
ti
v
e
fi
l
t
er
[17
].
T
hi
s
tec
hn
i
q
u
e
i
s
i
l
l
us
tr
at
ed
in
F
i
gu
r
e
4.
T
he
ou
tp
ut
c
om
po
n
en
ts
V
α_re
f
a
nd
V
β
_ref
are
t
he
ha
r
mo
ni
c
c
om
po
n
en
ts
i
n
the
v
o
l
tag
es
th
a
t
are
ne
e
de
d t
o f
i
l
ter ou
t u
s
i
ng
t
he
s
eri
es
ac
ti
v
e f
i
l
t
er.
V
L
a
b
c
I
α
a
b
c
α
β
P
_
r
e
f
-
I
L
a
b
c
a
b
c
α
β
I
β
V
β
V
α
X
X
X
X
+
+
X
X
X
X
-
-
+
P
Q
_
r
e
f
X
X
X
X
+
+
+
+
I
α
2
+
I
β
2
X
X
X
X
X
X
X
X
I
α
I
β
+
+
+
-
-
÷
÷
V
β
_
r
e
f
V
α
_
r
e
f
H
i
g
h
p
a
s
s
f
i
l
t
t
e
r
H
i
g
h
p
a
s
s
f
i
l
t
t
e
r
F
i
gu
r
e
4.
P
r
i
nc
i
pl
e o
f
i
ns
ta
n
tan
e
ou
s
ac
ti
v
e
an
d rea
c
t
i
v
e
po
wer
t
he
ory
(
P
-
Q
me
th
od
)
2
.
2
.
3.
Co
n
t
r
o
l of
Active
P
o
w
e
r
I
n
jec
t
ion
f
o
r
S
h
u
n
t
A
ctive
F
ilter
T
he
i
nj
ec
t
i
on
of
th
e
ac
ti
v
e
po
wer
(
P
)
i
nj
ec
ted
t
o
th
e
po
i
nt
of
c
o
mm
o
n
c
ou
p
l
i
ng
(
P
CC)
de
pe
nd
s
on
th
e
S
O
C
of
a
l
l
ba
tt
ery
pa
c
k
s
an
d
the
s
y
s
tem
fr
eq
u
en
c
y
to
en
s
ure
the
s
tab
i
l
i
ty
of
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
b
er 20
19
:
32
3
2
-
324
8
3236
the
el
ec
tr
i
c
al
ne
t
wor
k
as
s
h
own
i
n
F
i
g
ure
5.
T
he
c
o
ntro
l
s
y
s
tem
wi
l
l
me
as
ure
t
he
s
tat
e
of
c
h
arge
(
S
O
C)
of
a
l
l
b
att
er
i
es
an
d
the
n
etwo
r
k
fr
eq
ue
nc
y
th
e
n
ou
t
pu
t
a
s
i
gn
al
t
o
a
mu
l
ti
l
ev
el
i
nv
erter
c
on
tr
ol
l
er
c
on
ta
i
ns
th
e
o
pti
mu
m
v
al
u
e
o
f
r
ea
l
po
w
er
ne
ed
t
o
b
e
i
nj
ec
ted
.
If
the
S
O
C
of
an
y
b
att
ery
l
es
s
tha
n
or
eq
ua
l
0.
28
,
th
i
s
s
tat
e
c
a
l
l
e
d
em
pty
or
fa
ul
t
ba
tt
ery
s
tat
e,
th
en
t
he
s
y
s
t
em
w
i
l
l
c
h
arge
the
b
att
eri
es
at
a
ma
x
i
mu
m
r
ate
t
o
pu
s
h
t
he
s
tat
e
o
f
c
ha
r
ge
(
S
O
C)
fr
o
m
an
e
mp
ty
r
eg
i
on
t
o
c
ha
r
gi
n
g
r
e
gi
o
n.
A
n
d
If
t
he
s
tat
e
of
c
h
arge
(
S
O
C)
of
al
l
ba
tt
erie
s
great
er
t
ha
n
0.3
5,
an
d
the
fr
e
qu
en
c
y
of
t
he
s
y
s
tem
i
s
n
orma
l
i
.e
.
be
t
wee
n
4
9.5
an
d
50
.5,
thi
s
s
tat
e
i
s
c
a
l
l
e
d
no
r
ma
l
s
tat
e
an
d
th
e
s
y
s
tem
wi
l
l
c
ha
r
g
e
t
he
ba
t
teri
es
at
a
r
ate
th
at
g
ua
r
an
t
ee
fu
l
l
y
c
ha
r
g
ed
ba
tt
erie
s
at
th
e
en
d
of
s
un
s
e
t.
D
urin
g
t
he
c
ha
r
g
i
ng
proc
es
s
,
t
he
ex
c
es
s
i
v
e
po
wer
fr
om
P
V
arr
ay
s
wi
l
l
be
i
nj
ec
ted
t
o
th
e
e
l
ec
tr
i
c
a
l
d
i
s
tr
i
bu
t
i
o
n
ne
t
wor
k
di
r
ec
tl
y
by
s
ett
i
ng
the
r
ea
l
po
wer
r
ef
erenc
e
c
urr
en
t
(
i
d)
ac
c
ordi
n
g
to
th
e e
x
c
es
s
i
v
e p
o
wer
fro
m t
he
c
ha
r
g
i
ng
proc
es
s
.
W
he
n
the
s
tat
e
of
c
ha
r
ge
(
S
O
C)
i
s
greate
r
tha
n
0.5
a
nd
the
fr
e
qu
e
nc
y
of
the
s
y
s
tem
i
s
l
es
s
tha
n
49
.5
,
th
i
s
s
tat
e
c
al
l
ed
u
ns
tab
l
e
n
etwo
r
k
s
tat
e.
T
he
s
y
s
tem
w
i
l
l
s
top
c
h
argi
n
g
ba
t
teri
es
an
d
i
nj
ec
t
al
l
po
w
er
t
ha
t
c
o
me
s
fr
o
m
P
V
arr
ay
s
,
a
l
s
o
di
s
c
ha
r
ge
s
th
e
b
att
er
i
es
at
r
at
ed
di
s
c
ha
r
g
i
ng
c
urr
en
t,
by
s
ett
i
ng
t
he
r
e
al
po
w
er
r
efe
r
en
c
e
c
urr
en
t
(
i
d)
ac
c
ordi
ng
to
t
he
m
a
x
i
mu
m
po
w
er
av
ai
l
ab
l
e.
I
f
th
e
fr
eq
ue
nc
y
of
th
e
s
y
s
tem
i
s
gr
ea
ter
tha
n
0.5
,
or
n
o
r
ea
l
p
ower
l
oa
d
at
di
s
tr
i
b
ut
i
on
ne
twork
th
en
th
i
s
s
tat
e c
a
l
l
ed
no
n
-
r
ea
l
po
w
er l
o
ad
s
tat
e,
the
s
y
s
tem
w
i
l
l
s
top
po
w
er i
nj
ec
ti
o
n a
nd
c
ha
r
ge
s
the
ba
t
teri
es
on
l
y
,
by
s
ett
i
ng
t
he
r
e
al
po
w
er
r
efe
r
en
c
e
c
urr
e
nt
(
i
d)
t
o
z
ero.
T
h
es
e
r
efe
r
en
c
e c
urr
en
ts
Id
_re
f a
nd
Iq
_ref w
i
l
l
b
e u
s
e
d t
h
en
by
th
e c
o
ntrol
l
er.
S
t
a
r
t
P
l
o
a
d
r
e
f
>
0
Y
e
s
I
d
=
0
N
O
p
f
>
0
.
8
5
Y
e
s
N
O
N
O
I
d
=
0
Y
e
s
I
d
=
c
u
r
r
e
n
t
f
r
o
m
P
V
a
r
r
a
y
s
+
r
a
t
e
d
d
i
s
c
h
a
r
g
e
c
u
r
r
e
n
t
o
f
b
a
t
t
e
r
i
e
s
F
r
e
q
<
4
9
.
5
&
S
O
C
V
D
C
,
3
V
D
C
,
9
V
D
C
b
a
t
t
e
r
i
e
s
>
0
.
5
I
d
=
c
u
r
r
e
n
t
o
f
e
x
c
e
s
s
i
v
e
p
o
w
e
r
f
r
o
m
c
h
a
r
g
e
c
o
n
t
r
o
l
l
e
r
p
f
>
0
.
8
5
F
r
e
q
>
=
4
9
.
5
&
F
r
e
q
<
=
5
0
.
5
&
S
O
C
V
D
C
,
3
V
D
C
,
9
V
D
C
b
a
t
t
e
r
i
e
s
>
0
.
3
5
F
i
gu
r
e
5.
T
h
e f
l
owc
ha
r
t
di
a
gram o
f
ac
ti
v
e
po
w
er c
on
tr
ol
a
l
g
orit
h
m
2
.
2
.
4.
Co
n
t
r
o
l of
Rea
cti
ve
P
o
w
e
r
Inje
ctio
n
f
o
r
S
h
u
n
t
Act
i
v
e Filt
er
T
he
i
nj
ec
ti
o
n
of
r
e
ac
ti
v
e
po
wer
(
Q
)
i
s
o
nl
y
ne
c
es
s
ary
w
he
n
the
l
oa
d
draws
r
e
ac
ti
v
e
po
w
er
fr
om
the
s
o
urc
e.
In
th
e
c
a
s
e
of
em
p
ty
ba
tte
r
i
es
,
th
e
s
y
s
tem
wi
l
l
di
s
c
on
ne
c
t
th
e
ba
tte
r
i
es
fr
om
the
dc
l
i
nk
an
d
c
on
t
i
nu
e
r
e
ac
ti
v
e
po
w
er
c
om
p
en
s
at
i
on
by
i
ns
erti
n
g
of
c
ap
ac
i
t
or
b
an
k
s
at
the
dc
l
i
nk
o
f
ea
c
h
“
H”
br
i
dg
e
i
nv
erter
.
S
o
th
e
r
ea
c
t
i
v
e
po
w
er
i
nj
ec
ti
on
d
i
d
n
ot
de
pe
n
d
on
the
s
t
ate
of
c
ha
r
g
e
(
S
O
C)
of
b
att
erie
s
,
th
i
s
w
i
l
l
i
nc
r
ea
s
e
th
e
r
e
l
i
ab
i
l
i
ty
o
f
t
he
hy
bri
d
ac
t
i
v
e
fi
l
ter
to
s
up
po
r
t
the
r
e
ac
ti
v
e
po
w
er
l
oa
d
ev
e
n
i
f
no
p
ow
er
ge
ne
r
at
ed
fr
om
p
ho
t
o
v
ol
ta
i
c
arr
ay
s
.
T
he
f
l
owc
h
art
d
i
a
gram
of
t
he
c
o
ntrol
a
l
go
r
i
th
m
i
s
s
h
own
i
n
F
i
g
ure
6.
W
h
en
th
ere
i
s
no
l
oa
d
c
on
ne
c
te
d t
o
th
e s
ou
r
c
e t
h
e reac
ti
v
e
po
wer
c
urr
en
t
r
ef
erenc
e
(
i
q_
r
ef) s
e
t to
z
ero
an
d
no
r
e
ac
ti
v
e
po
wer
i
nj
ec
ted
to
t
he
po
i
n
t
of
c
om
mo
n
c
ou
p
l
i
ng
(
P
C
C)
.
A
n
d
i
f
r
ea
c
ti
v
e
l
o
ad
i
s
c
on
ne
c
te
d
to
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
ph
oto
v
o
l
ta
i
c
i
nte
gra
ted
u
ni
f
i
ed
po
w
er qu
al
i
ty
c
on
d
i
ti
on
er w
i
th
a 2
7
-
l
ev
e
l
i
nv
erte
r
(
K
am
e
l
S
al
eh
)
3237
the
d
i
s
tr
i
b
uti
on
n
etwo
r
k
,
t
h
e
s
y
s
tem
wi
l
l
au
to
ma
t
i
c
al
l
y
ge
ne
r
ate
i
q
-
r
ef
r
e
qu
i
r
ed
f
or
al
l
r
ea
c
ti
v
e
po
wer
l
oa
ds
c
on
n
ec
ted
,
an
d
t
he
s
ou
r
c
e
w
i
l
l
s
e
e
a
un
i
t
y
po
wer
f
ac
tor
i
nd
e
pe
nd
e
nt
on
t
he
ty
pe
of
c
on
tam
i
n
ati
ng
t
he
l
oa
d.
T
he
s
pe
e
d
of
c
o
mp
e
ns
ati
on
of
r
e
ac
ti
v
e
p
ower
d
ep
en
d
i
ng
on
th
e
p
ower
fac
t
or
of
the
el
ec
tr
i
c
al
ne
twork
,
s
o
i
f
th
e
p
ower
fac
tor
(
P
F
)
i
s
l
es
s
t
ha
n
0.
85
(
l
ag
gi
n
g),
th
e
s
y
s
tem
c
om
pe
ns
ate
s
at
m
ax
i
m
um
av
ai
l
ab
l
e
r
ea
c
ti
v
e
po
wer
,
el
s
e
t
he
s
y
s
tem
wi
l
l
i
nj
ec
t
the
ex
c
es
s
i
v
e
po
wer
fr
o
m
c
ha
r
gi
ng
proc
es
s
.
A
c
c
ordi
ng
t
o
the
ab
ov
e
ex
pl
a
na
t
i
o
n,
the
s
y
s
tem
wor
k
s
l
i
k
e
a
s
y
nc
hronou
s
ma
c
h
i
ne
,
where
t
he
r
e
ac
ti
v
e
po
w
er
i
s
c
on
tr
o
l
l
ed
t
hrou
gh
t
h
e
ex
c
i
tat
i
on
c
oi
l
.
In
th
i
s
c
as
e,
i
t i
s
c
on
tr
ol
l
ed
throug
h i
q_
r
ef.
S
t
a
r
t
Q
l
o
a
d
r
e
f
>
0
(
R
e
a
c
t
i
v
e
l
o
a
d
)
Y
e
s
I
q
=
0
N
O
p
f
>
0
.
8
5
Y
e
s
N
O
P
f
<
1
N
O
I
q
=
0
Y
e
s
I
q
=
r
a
t
e
d
d
i
s
c
h
a
r
g
e
c
u
r
r
e
n
t
o
f
b
a
t
t
e
r
i
e
s
I
q
=
1
1
.
5
%
r
a
t
e
d
d
i
s
c
h
a
r
g
e
c
u
r
r
e
n
t
o
f
b
a
t
t
e
r
i
e
s
F
i
gu
r
e
6.
T
h
e f
l
owc
ha
r
t
di
a
gram o
f r
ea
c
ti
v
e
po
wer
c
on
tr
ol
a
l
go
r
i
th
m
2
.
2
.
5
. M
o
d
el
ling
and
Co
n
t
r
o
l of
S
h
u
n
t
Activ
e Filt
e
r
A
s
s
um
e
th
at
the
ac
t
i
v
e
fi
l
ter
i
s
c
on
ne
c
ted
to
t
he
P
CC
thr
ou
gh
a
r
es
i
s
t
an
c
e
an
d
i
n
du
c
tan
c
e
as
s
ho
wn
i
n
F
i
gu
r
e
7.
T
he
f
ol
l
owi
ng
eq
u
ati
on
s
h
ol
d
tru
e:
=
+
+
(
1)
=
+
+
(
2)
=
+
+
(
3)
A
l
l
(1
)
,
(
2
)
,
an
d
(
3)
ar
e
tr
an
s
formed
i
n
ter
ms
of
t
he
d
-
q
v
aria
b
l
es
us
i
ng
th
e
r
efe
r
en
c
e
fr
am
e
tr
an
s
format
i
o
n
as
f
ol
l
ows
:
Lf
d
i
f
d
dt
=
−
ifd
R
f
+
(
Vin
vd
−
Vp
c
c
d
)
−
ω
Lf
ifq
(
4)
Lf
d
i
f
q
dt
=
−
ifq
R
f
+
(
Vin
vq
−
Vp
c
c
q
)
+
ω
Lf
ifd
(
5)
both
(
4
)
an
d
(
5
)
c
an
b
e rew
r
i
tte
n
as
:
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
b
er 20
19
:
32
3
2
-
324
8
3238
vd
=
ifd
R
f
+
Lf
d
i
f
d
dt
(
6)
vq
=
iq
fR
f
+
Lf
d
i
f
q
dt
(
7)
where
vd
=
(
Vin
vd
−
Vp
c
c
d
)
−
ω
Lf
iq
(
8)
vq
=
(
Vin
vq
−
Vp
c
c
q
)
+
ω
Lf
id
(
9)
both
(
8
)
and
(
9
)
are
us
e
d
th
en
to
de
s
i
gn
a
prop
orti
o
na
l
-
i
nte
gral
c
o
ntro
l
l
er
(
P
I)
to
c
o
ntrol
t
he
i
d
a
nd
i
q
c
om
po
n
en
ts
of
t
he
i
nv
ert
er
c
urr
en
ts
as
s
ho
wn
i
n
F
i
g
ure
8.
T
he
ou
tp
ut
of
t
he
c
o
ntrol
l
ers
(
V
dq
)
i
s
th
e
n u
s
ed
to
ge
n
erate
pu
l
s
es
fo
r
th
e I
G
B
T
s
i
n t
he
m
ul
t
i
-
l
ev
e
l
i
nv
erte
r
as
s
ho
wn
i
n
F
i
gu
r
e
9.
N
o
n
l
i
n
e
a
r
l
o
a
d
I
n
v
e
r
t
e
r
P
C
C
V
i
n
v
V
p
c
c
R
f
L
f
I
f
P
I
C
o
n
t
r
o
l
l
e
r
1
R
f
+
L
f
s
I
d
q
_
r
e
f
V
d
q
I
d
q
+
-
F
i
gu
r
e
7.
Dy
n
am
i
c
mo
d
el
l
i
n
g
of
th
e s
hu
n
t a
c
ti
v
e
fi
l
ter
F
i
gu
r
e
8
.
C
l
os
ed
l
o
op
c
o
ntr
ol
b
l
oc
k
d
i
ag
r
a
m f
or
s
hu
nt
ac
t
i
v
e f
i
l
t
er
N
o
n
l
i
n
e
a
r
l
o
a
d
P
C
C
M
u
l
i
t
_
l
e
v
e
l
i
n
v
e
r
t
e
r
V
p
c
c
R
f
L
f
I
f
I
L
a
b
c
V
L
a
b
c
P
L
L
Ɵ
a
b
c
d
q
V
q
_
r
e
f
P
I
C
o
n
t
r
o
l
l
e
r
V
d
_
r
e
f
+
-
+
-
H
i
g
h
P
a
s
s
F
i
l
t
r
+
R
e
a
l
p
o
w
e
r
i
n
j
e
c
t
i
o
n
a
b
c
d
q
Ɵ
a
b
c
d
q
+
+
+
+
+
L
f
*
w
L
f
*
w
-
I
d
I
q
+
a
b
c
d
q
Ɵ
M
o
d
u
l
a
t
i
o
n
T
e
c
h
n
i
q
u
e
P
I
C
o
n
t
r
o
l
l
e
r
P
I
C
o
n
t
r
o
l
l
e
r
F
i
gu
r
e
9.
T
h
e c
on
tr
o
l
s
tr
uc
t
ure of
ac
ti
v
e f
i
l
t
er
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
ph
oto
v
o
l
ta
i
c
i
nte
gra
ted
u
ni
f
i
ed
po
w
er qu
al
i
ty
c
on
d
i
ti
on
er w
i
th
a 2
7
-
l
ev
e
l
i
nv
erte
r
(
K
am
e
l
S
al
eh
)
3239
3
. Re
sult
s
a
n
d
An
aly
s
is
T
he
prop
os
ed
s
y
s
tem
i
s
s
i
mu
l
ate
d
i
n
M
A
T
L
A
B
S
IMU
LIN
K
en
v
i
r
on
m
en
t
t
o
c
he
c
k
the
pe
r
form
an
c
e
an
d
th
e
c
o
r
r
ec
t
wor
k
i
ng
of
the
c
om
p
l
et
e
s
y
s
tem
.
T
h
e
s
i
mu
l
at
i
on
of
Uni
f
i
ed
P
ower
Q
ua
l
i
ty
Co
nd
i
ti
on
er
(
U
P
Q
C)
i
s
tes
t
ed
to
i
ns
ure
th
e
c
orr
ec
t
wor
k
i
ng
of
al
l
s
y
s
tem
pa
r
ts
c
om
po
s
e
d t
o
ge
th
er.
3.1.
S
imu
latio
n
R
es
u
lt
s fo
r
S
h
u
n
t
Act
i
ve
F
ilte
r
F
i
gu
r
e
10
s
h
ows
th
e
s
ou
r
c
e
c
urr
en
t
be
for
e
a
nd
po
s
t
the
o
pe
r
at
i
o
n
of
th
e
ac
t
i
v
e
fi
l
ter.
A
t
t
=
0.
4
s
t
he
ac
ti
v
e
po
w
er
fi
l
ter
s
tarts
wor
k
i
n
g
to
m
i
t
i
g
ate
t
he
ha
r
m
on
i
c
s
an
d
th
e
s
ou
r
c
e
c
urr
en
t
be
c
am
e
p
ure
s
i
nu
s
o
i
d
al
.
T
h
e
t
ota
l
ha
r
mo
ni
c
di
s
t
orti
o
n
(
T
HD)
r
ed
uc
e
d
fr
om
1
8%
t
o
0.4
%.
T
he
n
at
t
=
0.7
s
,
the
ac
ti
v
e
po
wer
i
nj
ec
ti
on
s
tarts
wi
t
h
6
A
c
urr
en
t
as
s
i
s
tan
t
as
s
ee
n
i
n
F
i
gu
r
e
10
a
nd
the
t
ota
l
ha
r
mo
n
i
c
di
s
t
orti
o
n rema
i
n
ed
v
ery
l
ow (0.
5%)
du
r
i
n
g a
c
t
i
v
e p
ower i
nj
ec
ti
on
.
3.
2
.
S
imu
latio
n
R
es
u
lt
s fo
r
S
er
ie
s Ac
t
i
ve
f
ilte
r
T
he
t
hree
-
p
ha
s
e
s
o
urc
e
v
ol
ta
ge
s
i
gn
al
i
s
s
ho
w
n
b
efo
r
e
an
d
p
os
t
t
he
op
era
ti
on
of
the
s
erie
s
ac
t
i
v
e
fi
l
ter
i
s
s
h
own
i
n
F
i
g
ure
11
.
A
t
t
=
0.4
s
the
s
erie
s
ac
ti
v
e
fi
l
ter
s
ta
r
ted
to
m
i
ti
ga
t
e
the
v
o
l
ta
ge
ha
r
mo
n
i
c
s
.
T
h
en
A
t
t
=
0.7
s
,
t
he
s
y
s
tem
s
tep
s
up
th
e
s
o
urc
e
v
o
l
tag
e
to
23
0
v
an
d
m
ad
e
the
el
ec
tr
i
c
al
ne
twork
i
de
al
w
i
th
tot
a
l
h
arm
on
i
c
d
i
s
to
r
ti
on
1
%
i
n
s
o
urc
e
v
ol
ta
ge
.
I
t
i
s
c
l
ea
r
fr
o
m
t
he
ab
ov
e
r
es
u
l
ts
,
the
be
ha
v
i
or
of
S
erie
s
A
P
F
be
c
a
me
be
t
ter
a
nd
th
e
c
ap
ab
i
l
i
ty
of
ha
r
mo
ni
c
m
i
ti
ga
t
i
on
a
nd
v
ol
ta
ge
c
om
pe
ns
a
t
i
o
n
be
c
a
me
i
d
ea
l
be
c
a
us
e
of
th
e
po
s
i
t
i
v
e
eff
ec
t
of
s
hu
n
t A
P
F
.
3.
3
.
P
o
w
er
F
ac
t
o
r
Co
r
r
e
ctio
n
F
i
gu
r
e
12
prov
es
th
e
c
ap
a
bi
l
i
ty
of
s
h
un
t
ac
t
i
v
e
po
wer
fi
l
t
er
(
S
A
P
F
)
of
k
ee
pi
ng
a
un
i
ty
po
wer
f
ac
tor
a
t
th
e
s
ou
r
c
e.
A
t
t
=
0.
4
s
,
t
he
s
h
un
t
ac
ti
v
e
fi
l
ter
s
tarts
t
o
i
nj
ec
t
r
ea
c
ti
v
e
p
ower
an
d
the
po
w
er
fac
tor
ha
s
be
en
i
mp
r
ov
ed
fr
o
m
0.7
8
to
0.
97
.
T
he
n
at
t
=
0.7
s
the
ac
ti
v
e
fi
l
ter
s
tarts
to
i
nj
ec
t
r
ea
l
po
w
er
the
r
es
u
l
t
s
i
n
F
i
gu
r
e
12
d
em
on
s
tr
ate
tha
t
th
e
po
w
er
fac
tor
c
orr
ec
ti
on
proc
es
s
ha
s
n’
t
be
en
i
nte
r
r
u
pte
d b
y
t
he
r
ea
l
p
ower
i
nj
ec
ti
on
proc
es
s
.
3.4.
Real
P
o
w
er
Injectio
n
T
he
ac
ti
v
e
po
wer
(
P
)
was
c
on
tr
ol
l
e
d
by
ad
j
us
ti
n
g
the
v
al
u
e
of
i
d
-
r
ef
c
urr
en
t
,
wher
e
i
d
-
r
ef
c
urr
en
t
d
ep
e
nd
s
on
the
S
O
C
of
a
l
l
b
att
ery
pa
c
k
s
an
d
t
he
fr
eq
u
en
c
y
of
th
e
s
y
s
tem
.
T
he
i
nj
ec
ti
o
n
of
r
ea
c
ti
v
e
p
ower
(
Q
)
de
pe
nd
s
on
th
e
tun
i
ng
of
i
q
-
r
ef
c
urr
en
t,
wh
ere
i
q
-
r
ef
s
et
t
o
ma
i
nta
i
n
a
u
ni
ty
po
wer
fac
tor.
F
i
gu
r
e
1
3
s
ho
ws
the
c
ha
ng
i
ng
i
n
s
ou
r
c
e
c
urr
en
t
whe
n
the
s
y
s
tem
s
tar
ts
ac
ti
v
e
po
wer
i
nj
ec
ti
o
n
at
t
=
0.7
s
ec
.
T
he
i
nj
ec
t
i
on
o
f
r
ea
l
po
w
er
ha
s
be
e
n
s
top
p
ed
at
t
=
0.9
s
an
d
the
s
ou
r
c
e c
urr
e
nt
r
etu
r
ns
t
o i
ts
prev
i
ou
s
v
a
l
ue
be
f
ore t
he
r
ea
l
p
owe
r
i
nj
ec
ti
on
.
3.5. F
r
equ
enc
y V
ar
i
atio
n
E
f
f
ec
t
F
i
gu
r
e
s
14
a
nd
15
de
mo
n
s
tr
ate
t
he
eff
ec
t
of
t
he
fr
eq
ue
nc
y
v
ari
ati
on
on
th
e
am
ou
nt
of
the
r
ea
l
p
ower
i
nj
ec
ted
by
t
he
f
i
l
ter.
A
t
t
=
0.
5
s
W
he
n
t
he
ne
tw
ork
fr
eq
ue
nc
y
be
tw
ee
n
th
e
n
orma
l
l
i
m
i
ts
(
be
tw
ee
n
49
.5
Hz
an
d
50
Hz
)
,
the
s
y
s
tem
ad
j
us
ts
id
-
r
ef
to
i
nj
ec
t
r
ea
l
p
ower
wi
th
a
c
erta
i
n
v
al
ue
de
p
en
d
i
n
g
on
t
he
s
t
ate
of
c
h
arge
(
S
O
C)
of
ba
tte
r
i
es
as
s
ho
w
n
i
n
F
i
g
ure
14
.
F
i
gu
r
e
1
5
de
mo
ns
tr
ate
s
th
e
c
urr
en
t
i
n
j
ec
ti
on
wh
en
t
he
fr
e
qu
e
nc
y
i
n
th
e
n
orma
l
r
eg
i
on
,
i
d
-
r
ef
i
s
s
et
to
1
5%
of
the
r
ate
d
i
d
.
O
n
th
e
ot
he
r
ha
nd
,
i
f
the
S
O
C
i
s
s
et
to
0
.
9
(
for
ex
am
pl
e)
an
d
the
ne
t
wor
k
fr
eq
ue
nc
y
do
wn
s
ud
d
en
l
y
to
48
Hz
at
t
=
0.7
s
,
th
e
c
on
tr
ol
l
er
w
i
l
l
a
dj
us
t
i
d
-
r
ef
to
i
ts
ma
x
i
mu
m
v
al
u
e
a
nd
pu
s
h
the
ne
tw
ork
fr
eq
u
en
c
y
to
th
e
no
r
ma
l
r
eg
i
on
as
s
ho
wn
i
n
F
i
g
ure
s
1
4
a
nd
15.
T
he
t
ota
l
ha
r
mo
n
i
c
di
s
torti
on
(
T
HD)
i
s
r
ed
uc
e
d
fr
om
16
.5%
to
1%
an
d
d
i
d
no
t
c
ha
n
ge
wh
en
th
e
c
o
ntrol
l
er
i
nj
ec
ts
di
ff
erent
l
ev
el
s
of
c
urr
en
t
t
o
the
po
i
nt
of
c
om
m
on
c
ou
pl
i
ng
.
He
nc
e
the
s
y
s
tem
i
s
tr
u
s
ted
an
d
s
ta
bl
e
for al
l
i
ts
ta
s
k
s
.
3.6
.
S
t
ate o
f
Ch
a
r
g
e (
S
O
C
)
V
ar
i
atio
n
E
f
f
ec
t
F
i
gu
r
e
s
16
an
d
17
s
ho
w
t
h
e
eff
ec
t
of
c
h
an
g
i
n
g
the
S
O
C
on
i
d
-
r
ef
an
d
t
he
a
mo
u
nt
of
r
ea
l
po
wer
i
nj
ec
t
ed
by
t
he
ac
ti
v
e
f
i
l
t
er.
F
i
gu
r
e
1
6
s
h
ows
t
h
at
t
he
s
tat
e
of
c
ha
r
ge
ha
s
be
en
d
ec
l
i
ne
d
fr
om
0.8
t
o
0.
25
at
t=
0
.7
s
.
T
he
three
-
p
ha
s
e
s
ou
r
c
e
c
urr
en
t
wav
ef
o
r
ms
are
s
ho
w
n
i
n
F
i
gu
r
e
1
7.
A
t
t=
0.
5
s
th
e
S
O
C
w
as
0.8
s
o
the
c
on
tr
o
l
l
er
s
et
t
he
v
a
l
ue
of
i
d
_ref
t
o
th
e
m
ax
i
m
u
m
as
s
ho
wn
i
n
F
i
gu
r
e
17
.
T
he
n
at
t=
0.
7
s
t
he
S
O
C
was
de
c
l
i
ne
d
t
o
0.
25
an
d
h
en
c
e
t
he
c
on
tr
ol
l
er
s
et
i
d
_ref
to
0
as
s
ho
wn
i
n
F
i
gu
r
e
17.
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
b
er 20
19
:
32
3
2
-
324
8
3240
F
i
gu
r
e
10
.
S
o
urc
e c
urr
en
t
wav
efo
r
ms
a
fte
r
o
pe
r
at
i
on
of
ac
ti
v
e
fi
l
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
ph
oto
v
o
l
ta
i
c
i
nte
gra
ted
u
ni
f
i
ed
po
w
er qu
al
i
ty
c
on
d
i
ti
on
er w
i
th
a 2
7
-
l
ev
e
l
i
nv
erte
r
(
K
am
e
l
S
al
eh
)
3241
F
i
gu
r
e
11
.
S
o
urc
e v
ol
t
ag
e
wav
efo
r
ms
a
fte
r
o
pe
r
at
i
on
of
s
erie
s
ac
t
i
v
e f
i
l
t
er
Evaluation Warning : The document was created with Spire.PDF for Python.