I
nt
er
na
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
,
p
p
.
1
9
3
~
2
0
6
I
SS
N:
2252
-
8
7
9
2
,
DOI
: 1
0
.
1
1
5
9
1
/ijap
e.
v
1
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.
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.
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p
1
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-
206
193
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
p
e.
ia
esco
r
e.
co
m
A
c
o
mpa
ra
tive
s
t
udy
on AC/D
C
a
n
a
ly
sis
of an
o
pera
tiona
l
l
o
w
v
o
ltag
e
d
istributi
o
n
s
y
stem
Ciha
n K
a
t
a
r
1
,
Ceng
iz
P
o
la
t
Uzuno
ğ
lu
2
1
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
De
p
a
rtme
n
t,
T
u
rk
ish
-
G
e
rm
a
n
Un
iv
e
rsity
,
Ista
n
b
u
l
,
Tu
rk
e
y
2
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
De
p
a
rtme
n
t,
Ista
n
b
u
l
Un
i
v
e
rsity
-
Ce
rra
h
p
a
sa
,
Ista
n
b
u
l,
Tu
r
k
e
y
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Sep
1
1
,
2
0
2
0
R
ev
is
ed
Dec
1
6
,
2
0
2
0
Acc
ep
ted
Feb
2
2
,
2
0
2
1
In
th
e
n
e
a
r
fu
tu
re
,
t
h
e
d
i
g
it
a
li
z
i
n
g
wo
r
ld
will
c
o
n
ti
n
u
e
t
o
imp
r
o
v
e
a
n
d
t
h
e
n
e
e
d
fo
r
DC
b
a
se
d
d
e
v
ice
s
w
il
l
b
e
in
c
re
a
se
d
b
e
y
o
n
d
d
o
u
b
t
.
To
d
a
y
’s
e
lec
tri
c
a
l
g
rid
is
strictly
d
e
p
e
n
d
e
n
t
o
n
AC
-
DC
re
c
ti
fiers
.
Eac
h
c
o
n
v
e
rsio
n
p
ro
c
e
ss
m
e
a
n
s
a
d
d
it
io
n
a
l
p
o
we
r
lo
ss
e
s
a
n
d
sig
n
a
l
q
u
a
li
t
y
d
e
terio
r
a
ti
o
n
s
fo
r
th
e
n
e
tw
o
rk
.
I
n
a
d
d
it
i
o
n
,
n
e
two
rk
s
wh
ich
a
re
fe
d
b
y
b
a
tt
e
ries
a
n
d
re
n
e
wa
b
le
so
u
rc
e
s
su
c
h
a
s
s
o
lar
p
a
n
e
ls,
a
n
d
wi
n
d
t
u
rb
i
n
e
s
a
re
su
ffe
rin
g
fro
m
c
o
n
v
e
rsio
n
-
b
a
se
d
p
o
we
r
lo
ss
e
s.
I
n
th
is
re
sp
e
c
t,
t
h
e
id
e
a
o
f
sw
it
c
h
in
g
t
o
DC
o
n
th
e
l
o
w
v
o
l
tag
e
sid
e
o
f
th
e
n
e
t
wo
rk
s
h
a
s
b
e
c
o
m
e
a
n
in
tri
g
u
i
n
g
s
u
b
jec
t.
In
th
is
stu
d
y
,
t
h
e
a
p
p
li
c
a
b
il
it
y
a
n
d
e
fficie
n
c
y
o
f
th
e
l
o
w
v
o
lt
a
g
e
d
ir
e
c
t
c
u
rre
n
t
(LVDC)
c
o
n
c
e
p
t
fo
r
lo
w
v
o
l
tag
e
d
istri
b
u
ti
o
n
sy
ste
m
s
is
d
isc
u
ss
e
d
a
n
d
a
sa
m
p
le
LVDC
d
istri
b
u
ti
o
n
sy
st
e
m
is
a
n
a
ly
z
e
d
.
I
n
th
is
o
p
e
ra
ti
o
n
a
l
re
sid
e
n
ti
a
l
a
p
p
li
c
a
ti
o
n
e
lec
tri
c
a
l
tran
si
e
n
t
a
n
a
ly
z
e
r
p
ro
g
ra
m
(ET
AP)
is
e
m
p
lo
y
e
d
f
o
r
c
o
m
p
a
riso
n
o
f
d
iffere
n
t
v
o
lt
a
g
e
l
e
v
e
ls
su
c
h
a
s
1
1
0
V
DC
,
2
5
0
V
DC
,
3
2
0
V
DC
a
n
d
c
o
n
v
e
n
ti
o
n
a
l
2
2
0
/3
8
0
V
AC
.
As
a
n
o
v
e
l
a
p
p
r
o
a
c
h
d
iffere
n
t
DC
v
o
lt
a
g
e
lev
e
ls
a
re
c
o
m
p
a
re
d
with
ty
p
ica
l
AC
sy
ste
m
in
d
e
tail.
Co
m
p
a
ra
ti
v
e
a
n
a
ly
sis
is co
n
d
u
c
ted
fo
r
sa
fe
ty
re
g
u
latio
n
s,
v
o
lt
a
g
e
d
ro
p
s,
c
u
rre
n
t
c
a
rry
i
n
g
c
a
p
a
c
it
ies
,
p
o
we
r
c
o
n
s
u
m
p
ti
o
n
a
n
d
h
a
rm
o
n
i
c
c
a
lcu
latio
n
o
f
th
e
p
r
o
p
o
se
d
sy
st
e
m
.
In
th
is
re
sp
e
c
t
a
p
p
li
c
a
b
il
i
ty
,
p
o
ss
ib
le
d
ra
wb
a
c
k
s
a
n
d
fu
tu
re
a
sp
e
c
ts
o
f
LVDC
sy
ste
m
s a
re
in
terp
re
ted
.
K
ey
w
o
r
d
s
:
L
o
w
v
o
ltag
e
DC
s
y
s
tem
s
Po
wer
d
is
tr
ib
u
tio
n
Po
wer
m
an
ag
em
e
n
t
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
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
C
en
g
iz
Po
lat
Uzu
n
o
ğ
lu
E
lectr
ic
al
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
in
g
Dep
a
r
tm
en
t
I
s
tan
b
u
l U
n
iv
er
s
ity
-
C
er
r
ah
p
aşa
3
4
3
2
0
Av
cılar
/İ
s
tan
b
u
l
,
T
u
r
k
e
y
E
m
ail:
p
o
lat@
is
tan
b
u
l.e
d
u
.
tr
1.
I
NT
RO
D
UCT
I
O
N
A
b
ig
d
eb
ate
was
p
r
esen
ted
a
ce
n
tu
r
y
ag
o
b
y
E
d
is
o
n
an
d
T
e
s
la,
wh
ich
was
b
ased
o
n
th
e
d
is
cu
s
s
io
n
ab
o
u
t
t
h
e
i
d
ea
o
f
E
d
is
o
n
'
s
d
ir
ec
t
cu
r
r
en
t
(
DC
)
an
d
th
e
id
ea
o
f
T
esla’
s
alter
n
a
tin
g
cu
r
r
e
n
t
(
AC
)
f
o
r
tr
an
s
m
is
s
io
n
o
f
elec
tr
ical
en
er
g
y
[
1
]
,
[
2
]
.
At
th
e
tim
e
,
th
e
AC
-
DC
d
is
cu
s
s
io
n
r
esu
lted
in
s
u
p
er
io
r
ity
o
f
AC
,
s
in
ce
elec
tr
ical
en
er
g
y
co
n
v
er
s
io
n
in
te
r
m
s
o
f
h
i
g
h
v
o
ltag
e
(
HV)
an
d
lo
w
v
o
ltag
e
(
L
V)
ca
n
b
e
ea
s
ily
ad
j
u
s
ted
b
y
th
e
ai
d
o
f
tr
an
s
f
o
r
m
er
s
in
th
e
AC
s
y
s
tem
b
r
illi
an
tly
.
As
a
r
esu
lt
o
f
ad
v
a
n
tag
es
s
u
ch
a
s
v
o
ltag
e
d
r
o
p
a
n
d
o
p
tim
u
m
ca
b
le
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
,
th
e
elec
tr
ical
g
r
id
is
d
o
m
in
an
tly
d
e
p
en
d
e
n
t
o
n
th
e
AC
s
y
s
tem
[
3
]
.
So
,
AC
-
b
ased
d
is
tr
ib
u
tio
n
s
y
s
tem
s
h
av
e
b
ee
n
in
s
talled
an
d
u
s
ed
f
o
r
a
ce
n
tu
r
y
ef
f
icien
tly
.
W
ith
th
e
in
cr
ea
s
ed
im
p
r
o
v
em
e
n
ts
in
p
o
wer
elec
t
r
o
n
ics,
AC
-
DC
d
eb
ate
in
th
e
p
o
wer
tr
a
n
s
m
is
s
io
n
o
f
elec
tr
icity
n
etwo
r
k
s
h
as
b
ee
n
r
eiss
u
ed
d
u
e
to
in
cr
ea
s
in
g
n
ee
d
f
o
r
b
atter
ies,
th
e
ex
p
an
s
io
n
o
f
elec
tr
ic
v
eh
icles
an
d
th
e
ad
v
an
ce
m
en
ts
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
[
4
]
-
[
6
]
.
Ma
n
y
ad
v
an
tag
es
o
f
DC
s
y
s
tem
s
co
m
p
ar
e
d
to
AC
s
y
s
tem
s
ca
n
b
e
u
n
d
e
r
lin
ed
wh
e
r
e
th
e
i
d
ea
o
f
DC
d
is
tr
ib
u
tio
n
d
r
aws
atten
tio
n
.
Sin
ce
th
e
AC
ca
u
s
es
ex
ce
s
s
iv
e
m
u
s
cle
co
n
tr
ac
tio
n
wh
e
n
elec
tr
ical
co
n
tact
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
1
9
3
–
206
194
estab
lis
h
ed
with
liv
in
g
b
ei
n
g
s
,
it
is
m
u
ch
m
o
r
e
d
an
g
er
o
u
s
t
h
an
th
e
DC
wh
ich
h
as
th
e
s
a
m
e
elec
tr
ical
s
tr
ess
with
AC
[
7
]
.
E
lectr
ical
in
s
tallatio
n
m
alf
u
n
ctio
n
s
m
a
y
r
esu
lt
in
d
ea
th
o
r
s
ev
er
e
i
n
ju
r
y
,
wh
ich
ar
e
o
b
s
er
v
e
d
f
r
eq
u
e
n
tly
in
AC
n
etwo
r
k
s
.
A
m
o
r
e
s
ec
u
r
e
in
s
tallatio
n
ca
n
b
e
f
u
lf
illed
b
y
r
ed
u
cin
g
th
e
v
o
ltag
e
lev
el
with
t
h
e
DC
s
y
s
tem
[
8
]
.
Ma
n
y
eq
u
ip
m
en
t
th
at
r
eq
u
ir
es
an
en
er
g
y
s
to
r
ag
e
s
y
s
tem
n
ee
d
ad
d
itio
n
al
co
n
v
er
ter
s
to
b
e
co
n
n
ec
ted
to
th
e
g
r
id
wh
er
e
e
ac
h
co
n
v
e
r
ter
h
as
its
o
wn
a
d
d
itio
n
al
p
o
wer
lo
s
s
an
d
c
o
s
t
[
9
]
-
[
1
1
]
.
R
en
ewa
b
le
s
o
u
r
ce
s
s
u
ch
as
p
h
o
to
v
o
ltaic
s
o
lar
p
an
els
a
r
e
m
u
ch
m
o
r
e
c
o
h
er
en
t
to
in
teg
r
ate
in
to
th
e
L
VDC
d
is
tr
ib
u
tio
n
n
etwo
r
k
,
wh
ich
o
n
ly
r
eq
u
ir
es
d
ir
ec
t
co
n
n
ec
tio
n
to
th
e
s
y
s
te
m
s
.
T
h
e
n
ee
d
f
o
r
co
n
v
er
t
er
s
i
n
p
o
wer
s
y
s
tem
s
ar
e
r
ed
u
ce
d
b
y
h
elp
o
f
DC
in
s
tall
m
en
ts
wh
er
e
en
er
g
y
s
av
in
g
s
o
f
th
e
s
y
s
tem
is
ab
o
u
t 2
-
3
% [
1
2
]
.
AC
n
etwo
r
k
s
ar
e
f
ac
ed
with
p
r
o
b
lem
s
s
u
ch
as
h
a
r
m
o
n
ic
d
is
to
r
tio
n
ca
u
s
ed
b
y
u
n
wan
ted
o
s
cillatio
n
s
,
s
k
in
ef
f
ec
t
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
[
1
3
]
,
[
1
4
]
.
T
h
e
in
te
g
r
a
tio
n
o
f
elec
tr
ical
tr
a
n
s
p
o
r
tatio
n
v
eh
icles
is
ea
s
ier
th
an
AC
n
etwo
r
k
s
.
Netwo
r
k
i
n
teg
r
atio
n
o
f
tech
n
o
lo
g
ies
s
u
ch
as
u
n
in
ter
r
u
p
ted
p
o
wer
s
u
p
p
ly
(
UPS),
ce
n
tr
al
b
atter
y
s
y
s
tem
(
C
B
S)
,
will
r
e
d
u
ce
lo
s
s
es
in
th
e
D
C
s
y
s
tem
[
1
5
]
.
T
h
e
p
o
wer
ca
lcu
lat
io
n
s
o
f
th
e
DC
n
etwo
r
k
s
ar
e
m
ath
em
atica
lly
s
im
p
le
i
n
co
n
t
r
ast
to
co
n
v
en
tio
n
al
AC
s
y
s
tem
s
.
T
h
e
d
em
an
d
f
o
r
r
e
n
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
ca
n
b
e
in
cr
ea
s
ed
b
y
g
r
o
win
g
th
e
n
u
m
b
er
o
f
DC
n
etwo
r
k
s
,
wh
ich
lead
to
r
e
d
u
c
ed
ca
r
b
o
n
em
is
s
io
n
s
[
1
6
]
.
I
n
a
d
d
itio
n
to
ad
v
an
tag
es,
a
n
u
m
b
e
r
o
f
d
is
ad
v
a
n
tag
e
s
o
f
DC
s
y
s
tem
s
ar
e
n
o
ted
s
u
ch
as
th
e
lack
o
f
s
tan
d
ar
d
izatio
n
s
f
o
r
L
VDC
d
i
s
tr
ib
u
tio
n
n
etwo
r
k
s
,
all
th
e
el
ec
tr
ical
eq
u
ip
m
en
t
h
as
b
ee
n
d
esig
n
ed
f
o
r
th
e
AC
s
y
s
tem
f
o
r
a
ce
n
tu
r
y
.
B
esid
es
in
teg
r
atio
n
o
f
L
VDC
n
etwo
r
k
s
to
th
e
m
ed
iu
m
v
o
lta
g
e
(
M
V)
AC
d
is
tr
ib
u
tio
n
r
eq
u
ir
es
co
n
v
er
ter
s
wh
er
e
h
a
r
m
o
n
ics
an
d
o
th
er
s
ig
n
al
q
u
ality
r
elate
d
is
s
u
es
ar
e
a
v
ail
ab
le.
Alth
o
u
g
h
DC
tr
an
s
m
is
s
io
n
in
HV
tr
an
s
m
is
s
i
o
n
lin
es is
a
g
r
o
win
g
tr
en
d
,
th
er
e
ar
e
s
till
h
esit
atio
n
s
ab
o
u
t
L
VDC d
is
tr
ib
u
tio
n
.
I
n
th
is
s
tu
d
y
,
a
n
o
r
d
in
ar
y
h
o
u
s
e
is
m
o
d
elled
f
o
r
lo
w
v
o
lta
g
e
alter
n
atin
g
cu
r
r
en
t
(
L
VAC)
with
th
e
lev
el
o
f
2
2
0
/3
8
0
V
an
d
v
ar
i
o
u
s
L
VD
C
(
1
1
0
V,
2
5
0
V
an
d
3
2
0
V)
v
o
ltag
es
as
a
p
r
ac
tical
ex
am
p
le.
Dif
f
er
en
t
DC
v
o
ltag
e
lev
els
ar
e
in
v
esti
g
ated
f
o
r
v
a
r
io
u
s
p
er
f
o
r
m
an
c
e
an
d
ap
p
licab
ili
ty
m
etr
ics
b
y
E
T
AP
p
r
o
g
r
am
[
1
7
]
.
A
ty
p
ical
h
o
u
s
e
a
n
d
lo
ad
s
s
u
ch
as
wash
in
g
m
ac
h
i
n
e
,
elec
t
r
ical
o
v
e
n
,
d
r
y
e
r
.
ar
e
em
p
lo
y
ed
to
v
er
if
y
s
y
s
tem
co
m
p
ar
is
o
n
s
.
B
ased
o
n
th
e
d
is
cu
s
s
io
n
m
en
tio
n
ed
ab
o
v
e,
th
e
p
o
wer
lo
s
s
es
in
L
VDC
n
etwo
r
k
s
,
v
o
ltag
e
d
r
o
p
s
u
p
to
en
d
u
s
er
s
,
v
ar
iatio
n
s
o
f
ca
b
le
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
s
,
ef
f
icien
cy
an
d
a
p
p
licab
ilit
y
o
f
p
r
o
p
o
s
ed
L
VDC
s
y
s
tem
is
an
al
y
ze
d
.
2.
DC
SYS
T
E
M
P
RE
F
E
R
E
NC
E
T
O
AC
SY
ST
E
M
Sin
ce
th
e
elec
tr
icity
is
tr
an
s
p
o
r
ted
o
v
er
l
o
n
g
d
is
tan
ce
s
,
it
is
a
v
er
y
ec
o
n
o
m
ical
s
o
lu
tio
n
t
o
u
s
e
less
er
cr
o
ss
-
s
ec
tio
n
al
ca
b
les
as
m
u
c
h
as
p
o
s
s
ib
le.
I
n
cr
ea
s
ed
v
o
lta
g
e
lev
els
in
tr
an
s
m
is
s
io
n
lin
e
s
m
ea
n
s
d
ec
r
ea
s
ed
cu
r
r
en
ts
(
c
o
n
s
tan
t
p
o
wer
)
a
n
d
h
en
ce
s
m
all
cr
o
s
s
-
s
ec
tio
n
al
c
ab
les
with
less
er
cu
r
r
en
t
ca
r
r
y
in
g
ca
p
ac
ity
ca
n
b
e
u
s
ed
in
th
e
n
etwo
r
k
ef
f
icien
tl
y
an
d
ec
o
n
o
m
ically
.
I
n
th
e
A
C
s
y
s
tem
th
is
co
n
ce
p
t
is
ef
f
ici
en
tly
ap
p
lied
b
y
th
e
aid
o
f
tr
an
s
f
o
r
m
er
s
in
wh
i
ch
v
ar
y
in
g
m
a
g
n
etic
f
ield
s
ar
e
em
p
lo
y
ed
to
v
o
ltag
e
tr
a
n
s
f
o
r
m
ati
o
n
ac
co
r
d
in
g
to
t
h
e
Far
ad
ay
law.
T
h
e
alter
n
atin
g
c
u
r
r
en
t p
r
o
d
u
ce
s
a
v
ar
iab
le
m
a
g
n
etic
f
ield
,
wh
ich
allo
ws tr
an
s
f
o
r
m
er
s
to
o
p
e
r
ate
o
n
alter
n
atin
g
cu
r
r
e
n
t.
No
wad
ay
s
,
it
is
clea
r
l
y
p
r
e
s
en
ted
th
at
t
h
er
e
a
r
e
m
an
y
ad
v
a
n
tag
es
to
s
witch
in
g
t
h
e
p
o
wer
tr
an
s
m
is
s
io
n
lin
es
to
DC
lin
es
o
n
th
e
HV
an
d
MV
s
id
e
in
m
an
y
r
esp
ec
ts
.
Stu
d
ies
h
a
v
e
r
ev
ea
led
th
at
AC
p
o
wer
lo
s
s
es
ar
e
in
cr
ea
s
ed
i
n
co
n
tr
ast
to
DC
p
o
wer
lo
s
s
es
wh
en
lin
e
len
g
th
s
ex
ce
ed
1
0
0
k
m
[
1
8
]
,
[
1
9
]
.
Fu
r
t
h
er
m
o
r
e
,
in
th
r
ee
p
h
ase
tr
an
s
m
is
s
io
n
th
r
ee
p
er
ca
b
le
is
n
ee
d
ed
to
AC
d
is
tr
ib
u
tio
n
n
et
wo
r
k
s
,
wh
ile
o
n
th
e
o
th
er
h
an
d
two
p
er
ca
b
le
is
en
o
u
g
h
f
o
r
DC
d
is
tr
ib
u
tio
n
n
e
two
r
k
s
.
On
th
e
L
V
s
id
e,
th
e
en
er
g
y
ef
f
icien
c
y
ac
h
iev
ed
b
y
th
e
DC
d
is
tr
ib
u
ti
o
n
n
etwo
r
k
,
wh
ich
i
s
f
ed
b
y
an
en
er
g
y
s
to
r
ag
e
s
y
s
tem
,
h
as
b
ee
n
in
cr
e
ased
b
y
1
5
%
-
3
0
%
[
2
0
]
,
[
2
1
]
.
T
h
e
wi
n
d
tu
r
b
i
n
e
an
d
p
h
o
t
o
v
o
ltaic
p
a
n
els
ar
e
co
n
n
ec
ted
t
o
th
e
g
r
i
d
as
s
h
o
wn
in
Fig
u
re
1
in
th
e
co
n
v
e
n
tio
n
al
AC
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
I
n
o
r
d
er
t
o
s
to
r
e
en
er
g
y
in
th
e
b
atter
ie
s
,
i
n
itially
A
C
/D
C
co
n
v
er
s
io
n
is
co
n
d
u
cted
an
d
th
en
it
is
r
ec
o
n
v
er
ted
to
th
e
AC
ag
ain
f
o
r
th
e
b
u
s
b
ar
co
n
n
ec
tio
n
.
I
n
th
e
co
n
v
en
tio
n
al
AC
s
y
s
tem
,
lo
ad
in
g
is
f
u
lf
illed
ac
co
r
d
in
g
t
o
th
e
en
er
g
y
r
eq
u
i
r
em
en
ts
o
f
th
e
eq
u
ip
m
en
t
wh
ic
h
will b
e
en
er
g
ized
,
w
h
er
e
DC
co
n
v
er
s
io
n
is
n
ee
d
ed
a
g
ain
.
T
h
e
en
er
g
y
s
to
r
ed
in
th
e
b
atter
ies
ca
n
b
e
tr
an
s
m
itted
d
ir
ec
tly
to
th
e
b
u
s
b
ar
with
o
u
t
ad
d
itio
n
a
l
co
n
v
er
ter
s
.
Af
ter
war
d
s
,
o
n
ly
DC
/D
C
co
n
v
er
te
r
s
ar
e
em
p
lo
y
ed
f
o
r
DC
b
ased
eq
u
ip
m
en
t
p
o
wer
d
em
an
d
wh
ic
h
ar
e
th
e
m
ajo
r
ity
o
f
d
o
m
esti
c
u
s
e.
I
n
Fig
u
r
e
2
,
a
n
u
m
b
e
r
o
f
o
p
tim
izatio
n
s
ca
n
b
e
m
ad
e
f
o
r
eq
u
ip
m
en
t to
r
ed
u
ce
DC
/A
C
co
n
v
er
s
io
n
.
W
h
en
th
e
n
etwo
r
k
'
s
d
is
tr
ib
u
tio
n
s
tr
u
ctu
r
e
is
m
o
d
elled
as
a
DC
d
is
tr
ib
u
t
io
n
s
y
s
tem
as
in
Fig
u
r
e
2
,
th
e
n
ee
d
f
o
r
co
n
v
e
r
ter
s
is
r
ed
u
ce
d
.
Fo
r
in
s
tan
ce
,
d
ev
ices
s
u
ch
as
w
ash
in
g
m
ac
h
in
es,
d
r
y
er
s
an
d
d
is
h
wash
er
s
ca
n
o
p
er
ate
in
b
o
th
cu
r
r
en
t
ty
p
es
wh
en
u
n
iv
er
s
al
m
o
to
r
s
ar
e
u
s
ed
.
R
ef
r
ig
er
at
o
r
s
ca
n
b
e
p
r
o
d
u
ce
d
with
DC
m
o
to
r
s
.
T
h
e
m
icr
o
w
av
e
in
d
u
ctio
n
h
ea
ter
s
h
av
e
to
co
n
v
er
t
th
e
DC
to
AC
f
o
r
th
e
AC
b
ased
m
ag
n
etic
f
ield
g
en
er
ated
h
ea
t,
h
o
wev
er
,
r
esis
tan
ce
-
b
ased
h
ea
ter
s
ca
n
b
e
o
p
er
ated
in
b
o
th
DC
an
d
AC
.
I
n
s
u
m
m
ar
y
,
we
ca
n
r
ed
u
ce
th
e
n
ee
d
f
o
r
DC
/A
C
co
n
v
er
s
io
n
if
th
e
DC
r
ea
d
y
d
ev
ices
ar
e
em
p
l
o
y
ed
in
th
e
s
y
s
tem
as
m
u
ch
as
p
o
s
s
ib
le.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
co
mp
a
r
a
tive
s
tu
d
y
o
n
A
C
/DC
a
n
a
lysi
s
o
f a
n
o
p
era
tio
n
a
l l
o
w
vo
lta
g
e
d
is
tr
ib
u
tio
n
s
ystem
(
C
ih
a
n
K
a
ta
r
)
195
Fig
u
r
e
1
.
L
VAC d
is
tr
ib
u
tio
n
n
etwo
r
k
s
tr
u
ctu
r
e
Fig
u
r
e
2
.
L
VDC d
is
tr
ib
u
tio
n
s
y
s
tem
s
tr
u
ctu
r
e
3.
I
NT
RO
D
UCING
L
VDC
D
I
ST
R
I
B
U
T
I
O
N
F
O
R
R
E
SI
D
E
NT
AL
AP
P
L
I
CA
T
I
O
N
Alth
o
u
g
h
t
h
er
e
is
n
o
s
tan
d
a
r
d
izatio
n
,
two
b
asic
d
is
tr
ib
u
tio
n
s
tr
u
ctu
r
es
ar
e
in
tr
o
d
u
ce
d
f
o
r
DC
tr
an
s
m
is
s
io
n
lin
es.
T
h
e
f
ir
s
t
o
n
e
is
th
e
u
n
i
p
o
lar
a
n
d
th
e
s
ec
o
n
d
o
n
e
is
th
e
b
ip
o
lar
s
y
s
tem
.
I
n
u
n
ip
o
lar
s
y
s
tem
s
,
en
er
g
y
is
ca
r
r
ied
o
v
er
a
s
in
g
l
e
ca
b
le
p
air
with
th
e
p
o
ten
tia
l
d
if
f
er
en
ce
o
f
+2
V
DC
[
2
2
]
,
[
2
3
]
.
T
h
e
u
n
ip
o
l
ar
d
is
tr
ib
u
tio
n
s
tr
u
ctu
r
e
is
g
i
v
en
i
n
Fig
u
r
e
3.
Fig
u
r
e
3
.
L
VDC Un
ip
o
lar
d
is
tr
ib
u
tio
n
s
tr
u
ctu
r
e
I
n
b
i
p
o
lar
s
y
s
tem
s
,
e
n
er
g
y
is
tr
an
s
f
er
r
ed
to
th
e
p
o
s
itiv
e
an
d
n
eg
ati
v
e
en
d
with
a
n
e
u
tr
al
r
ef
er
e
n
ce
.
B
y
th
is
way
,
th
e
v
o
ltag
e
lev
e
l
is
r
ed
u
ce
d
an
d
two
d
i
f
f
er
en
t
v
o
ltag
e
le
v
els
as
+
V
DC
an
d
–
V
DC
(2
V
DC
)
ar
e
g
iv
en
in
th
e
s
y
s
tem
[
2
4
]
.
T
h
e
b
ip
o
lar
d
is
tr
ib
u
tio
n
s
tr
u
ctu
r
e
is
g
iv
en
in
Fig
u
r
e
4
.
I
n
ad
d
iti
o
n
,
b
ip
o
la
r
s
y
s
tem
s
ar
e
ab
le
to
o
v
er
c
o
m
e
p
o
wer
o
u
tag
es
s
in
ce
th
e
s
y
s
tem
is
d
esig
n
ed
to
b
e
en
er
g
ized
o
n
a
s
in
g
le
s
id
e
o
f
t
h
e
b
ip
o
lar
s
y
s
tem
wh
ich
will p
r
e
v
en
t sy
s
tem
f
ailu
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
1
9
3
–
206
196
Fig
u
r
e
4
.
B
ip
o
lar
d
is
tr
ib
u
tio
n
s
tr
u
ctu
r
e
3
.
1
.
F
e
a
s
ibi
lity
a
nd
ef
f
iciency
o
f
v
o
lt
a
g
e
lev
el
o
n L
VDC
dis
t
ributio
n sy
s
t
em
Dete
r
m
in
in
g
th
e
v
o
ltag
e
lev
el
in
th
e
p
lan
n
ed
L
VDC
n
etwo
r
k
is
th
e
m
o
s
t
im
p
o
r
tan
t
p
a
r
am
et
er
f
o
r
th
e
n
etwo
r
k
an
al
y
s
is
.
T
h
e
p
r
o
p
o
s
ed
v
o
ltag
e
lev
el
s
h
o
u
l
d
p
r
o
v
id
e
an
o
p
tim
al
s
o
lu
tio
n
f
o
r
b
o
th
ec
o
n
o
m
ic
an
d
s
af
ety
is
s
u
es
s
in
ce
v
o
ltag
e
d
r
o
p
s
an
d
cu
r
r
en
t d
em
an
d
b
y
th
e
lo
ad
s
ar
e
d
eter
m
in
ed
b
y
v
o
ltag
e
lev
el.
Acc
o
r
d
in
g
to
th
e
ca
lcu
late
d
cu
r
r
en
t
v
alu
e,
th
e
ca
b
le
cr
o
s
s
s
ec
tio
n
al
ar
ea
s
ar
e
o
p
tim
ize
d
an
d
h
e
n
ce
v
o
lt
ag
e
d
r
o
p
o
f
th
e
s
y
s
tem
is
ca
lcu
lated
[
2
5
]
.
I
n
a
d
d
itio
n
,
s
izes
o
f
cir
cu
it
p
r
o
tectio
n
elem
en
ts
ar
e
ch
a
n
g
ed
b
y
th
e
cu
r
r
en
t
r
atin
g
s
o
f
th
e
s
y
s
tem
.
Fu
r
th
er
m
o
r
e,
th
e
s
h
o
r
t
-
cir
cu
it
cu
r
r
e
n
ts
th
at
m
ay
o
cc
u
r
in
th
e
in
s
tallatio
n
ar
e
d
ir
ec
tly
d
ep
en
d
e
n
t
o
n
th
e
ca
b
le
le
n
g
th
a
n
d
v
o
ltag
e
lev
el.
I
n
ca
s
e
o
f
an
y
co
n
tact
with
e
lectr
icity
,
wh
ich
en
d
a
n
g
er
s
h
u
m
an
life
is
ch
a
r
ac
ter
ized
b
y
th
e
r
ated
v
o
ltag
e
lev
el
ac
co
r
d
in
g
to
s
af
ety
is
s
u
es.
T
h
e
ef
f
ec
ts
o
f
d
if
f
e
r
en
t
v
o
ltag
e
lev
els
f
o
r
t
h
e
h
u
m
an
b
o
d
y
ar
e
s
h
o
wn
in
T
ab
le
1
.
AC
ca
u
s
es
m
u
s
cle
co
n
tr
ac
tio
n
s
d
u
e
to
o
s
cillatio
n
s
o
f
AC
s
ig
n
als
an
d
wh
ich
s
h
o
u
ld
b
e
p
r
ev
en
ted
.
T
h
er
ef
o
r
e,
th
e
th
r
esh
o
ld
o
f
h
a
za
r
d
o
u
s
v
o
ltag
e
lev
el
o
f
AC
is
lo
wer
th
an
DC
.
As
s
h
o
wn
in
T
ab
le
1
,
wh
ile
th
e
m
u
s
cle
co
n
tr
o
l
is
lo
s
t
at
1
5
m
i
lliam
p
er
e
(
mA
)
lev
els
in
th
e
AC
,
m
u
s
cle
co
n
tr
o
l
is
lo
s
t
at
lev
el
o
f
7
5
m
A
in
th
e
DC
[
2
6
]
.
T
ab
le
1
.
Ph
y
s
ical
ef
f
ec
ts
o
f
el
ec
tr
icity
in
v
ar
io
u
s
cu
r
r
en
ts
P
h
y
s
i
c
a
l
e
f
f
e
c
t
s
o
f
e
l
e
c
t
r
i
c
i
t
y
DC
A
C
(
5
0
-
6
0
h
z
)
S
e
n
sa
t
i
o
n
a
n
d
p
e
r
c
e
p
t
i
o
n
1
mA
0
.
4
-
0
.
5
mA
S
l
i
g
h
t
s
h
o
c
k
5
mA
1
-
1
.
5
mA
P
a
i
n
f
u
l
sh
o
c
k
,
m
u
sc
l
e
c
o
n
t
r
o
l
ma
i
n
t
a
i
n
e
d
55
mA
10
mA
P
a
i
n
w
i
t
h
l
o
ss m
u
sc
l
e
c
o
n
t
r
o
l
75
mA
15
mA
S
e
v
e
r
e
p
a
i
n
d
i
f
f
i
c
u
l
t
y
b
r
e
a
t
h
i
n
g
90
mA
25
mA
H
e
a
r
t
h
f
i
b
r
i
l
l
a
t
i
o
n
5
0
0
mA
1
0
0
mA
I
n
co
n
tact
with
elec
tr
icity
,
th
e
cu
r
r
e
n
t
th
r
o
u
g
h
th
e
b
o
d
y
is
lar
g
ely
d
ep
e
n
d
en
t
o
n
b
o
d
y
r
esis
tan
ce
.
B
o
d
y
r
esis
tan
ce
ca
n
b
e
d
iv
id
e
d
in
to
two
m
ai
n
g
r
o
u
p
s
,
wh
ic
h
ar
e
s
k
in
r
esis
tan
ce
a
n
d
i
n
ter
n
al
b
o
d
y
r
esis
tan
ce
.
Du
r
in
g
t
h
e
elec
tr
ical
s
h
o
ck
,
c
u
r
r
en
t
p
ass
es
th
r
o
u
g
h
t
h
e
s
k
i
n
an
d
co
n
tin
u
es
th
r
o
u
g
h
th
e
i
n
ter
n
al
o
r
g
an
s
an
d
th
en
co
m
e
s
b
ac
k
o
u
t
o
f
th
e
s
k
in
an
d
co
m
p
letes
its
p
ath
.
T
o
tal
r
esis
tan
ce
i
s
d
eter
m
in
ed
b
y
p
ath
o
f
cu
r
r
en
t
s
in
ce
it c
o
n
tain
s
s
k
in
r
esis
tan
ce
an
d
in
ter
n
al
r
esis
tan
ce
to
g
et
h
er
.
T
h
e
s
k
in
r
esis
tan
ce
is
d
eter
m
i
n
ed
b
y
v
ar
io
u
s
f
ac
to
r
s
.
W
h
ile
th
e
r
es
is
tan
ce
o
f
a
d
r
y
s
k
in
is
at
1
0
0
k
Ω
lev
els,
a
m
o
is
t
s
k
in
is
ab
o
u
t
1
k
Ω
[
2
7
]
.
I
n
ad
d
itio
n
to
th
e
s
k
in
r
esis
tan
ce
,
th
e
av
er
ag
e
in
ter
n
al
r
esis
tan
ce
wh
ich
is
r
elate
d
to
in
te
r
n
al
o
r
g
an
s
is
ab
o
u
t 3
0
0
-
5
0
0
k
Ω
.
Du
r
in
g
th
e
elec
tr
ical
c
o
n
t
ac
t
h
i
g
h
er
s
k
in
r
esis
tan
ce
is
b
r
o
k
e
n
d
o
wn
d
u
e
to
th
e
ac
ce
le
r
ated
v
o
ltag
e
s
tr
ess
an
d
ex
ce
s
s
iv
e
cu
r
r
en
ts
o
b
s
er
v
ed
t
h
r
o
u
g
h
o
u
t
th
e
b
o
d
y
.
W
ith
th
e
in
cr
ea
s
ed
v
o
ltag
e
lev
els,
b
r
ea
k
d
o
wn
o
f
th
e
r
elate
d
r
es
is
tan
ce
s
co
u
ld
b
e
m
u
ch
ea
s
ier
.
T
h
is
p
h
en
o
m
e
n
o
n
r
ed
u
ce
s
th
e
e
f
f
e
ct
o
f
s
k
in
r
esis
tan
ce
an
d
h
en
ce
to
tal
r
esis
tan
ce
.
B
ased
o
n
th
e
av
e
r
ag
e
v
alu
e
s
,
b
o
d
y
r
esis
tan
ce
s
v
ar
y
d
ep
en
d
in
g
o
n
t
h
e
v
o
ltag
e
lev
el
an
d
th
e
f
au
lt
cu
r
r
en
t
v
alu
e
r
esu
ltin
g
f
r
o
m
h
a
n
d
-
to
-
f
o
o
t
m
ea
s
u
r
e
m
en
ts
,
wh
ich
ar
e
s
h
o
wn
i
n
T
ab
le
2
.
T
ab
le
2
.
Haz
ar
d
o
u
s
h
a
nd
-
to
-
f
o
o
t c
u
r
r
e
n
ts
an
d
r
elate
d
r
esis
tan
ce
s
f
o
r
AC
an
d
DC
v
o
ltag
es
C
u
r
r
e
n
t
so
u
r
c
e
V
o
l
t
a
g
e
(
V
)
H
a
n
d
t
o
f
o
o
t
c
u
r
r
e
n
t
(
mA
)
To
t
a
l
b
o
d
y
r
e
si
s
t
a
n
t
(
o
h
m)
1
1
0
8
2
.
1
1
3
4
0
DC
2
5
0
2
6
3
.
2
9
5
0
3
2
0
3
8
1
.
0
8
4
0
AC
2
2
0
2
2
0
.
0
1
0
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
co
mp
a
r
a
tive
s
tu
d
y
o
n
A
C
/DC
a
n
a
lysi
s
o
f a
n
o
p
era
tio
n
a
l l
o
w
vo
lta
g
e
d
is
tr
ib
u
tio
n
s
ystem
(
C
ih
a
n
K
a
ta
r
)
197
As
s
h
o
wn
in
T
ab
le
1
,
th
e
m
u
s
cle
co
n
tr
o
l
is
lo
s
t
at
8
0
-
9
0
m
A
in
DC
v
o
ltag
e
[
2
8
]
.
T
h
is
v
alu
e
g
iv
es
u
s
th
e
m
ax
im
u
m
p
o
s
s
ib
le
v
o
ltag
e
v
alu
e
wh
ich
is
n
o
ted
as
a
s
a
f
ety
th
r
esh
o
ld
.
T
h
e
er
r
o
r
cu
r
r
e
n
ts
ca
lcu
lated
with
th
e
b
o
d
y
r
esis
tan
ce
ar
e
at
th
e
m
o
s
t
r
eliab
le
lev
el
f
o
r
1
1
0
V
DC
as
s
h
o
wn
in
T
ab
le
2
.
S
in
ce
th
e
alter
n
atin
g
cu
r
r
en
t
ex
ce
ed
s
3
0
m
A
lev
els,
an
o
p
er
atio
n
al
s
af
ety
is
s
u
e
i
s
em
er
g
ed
an
d
s
o
m
e
m
ea
s
u
r
e
s
s
h
o
u
ld
b
e
tak
en
.
Fo
r
th
is
p
u
r
p
o
s
e,
th
e
r
esid
u
al
cu
r
r
e
n
t
r
ela
y
s
,
wh
ich
ar
e
m
a
n
u
f
ac
tu
r
e
d
to
co
m
p
ar
e
p
h
ase
cu
r
r
en
t
an
d
n
eu
t
r
al
c
u
r
r
en
t
f
o
r
d
etec
tin
g
p
o
s
s
ib
le
leak
ag
e
cu
r
r
e
n
ts
ar
e
u
s
ed
[
2
9
]
.
I
n
a
DC
s
y
s
tem
n
ee
d
f
o
r
r
esid
u
al
cu
r
r
e
n
t
r
elay
s
is
d
ec
r
ea
s
ed
in
wh
ich
DC
s
y
s
tem
is
s
aid
to
b
e
m
u
c
h
m
o
r
e
ec
o
n
o
m
ical.
Alth
o
u
g
h
t
h
e
1
1
0
V
DC
s
y
s
tem
is
th
e
m
o
s
t
n
o
n
-
h
az
ar
d
o
u
s
d
is
tr
ib
u
ti
o
n
in
th
e
p
r
o
p
o
s
ed
s
ce
n
ar
io
s
,
d
if
f
e
r
e
n
t
DC
lev
els
(
2
5
0
V
DC
an
d
3
2
0
V
DC
)
ar
e
in
v
esti
g
ated
f
o
r
p
r
o
p
er
co
m
p
a
r
is
o
n
.
3
.
2
.
A
pra
c
t
ica
l r
esid
ent
ia
l buil
d
ing
m
o
del
E
T
AP
p
o
wer
f
lo
w
an
al
y
s
is
is
co
n
d
u
cte
d
f
o
r
ty
p
ical
h
o
u
s
e
m
o
d
els
an
d
ca
lcu
latio
n
s
ar
e
i
n
v
esti
g
ated
.
AC
an
aly
s
is
o
f
3
8
0
/
2
2
0
V
h
o
u
s
e
d
is
tr
ib
u
tio
n
m
o
d
el,
wh
er
e
s
in
g
le
lin
e
d
iag
r
am
(
SLD)
i
s
g
iv
en
in
Fig
u
r
e
5
.
T
h
e
3
3
k
V
MV
n
etwo
r
k
is
co
n
v
er
ted
to
a
L
V
o
f
0
.
4
kV
with
a
5
0
0
k
VA
tr
an
s
f
o
r
m
er
an
d
th
en
co
n
v
er
ted
to
DC
with
a
r
ec
tifie
r
.
T
h
e
d
is
tan
ce
b
etwe
en
th
e
tr
an
s
f
o
r
m
er
an
d
t
h
e
b
u
ild
in
g
is
co
n
s
id
er
ed
as
2
0
0
m
.
I
n
a
d
d
itio
n
to
r
eg
u
lar
l
o
ad
s
,
lig
h
t
-
em
itti
n
g
d
io
d
e
(
L
E
D)
lu
m
in
air
es
o
f
1
1
u
n
its
,
ea
c
h
h
as
2
5
W
p
o
wer
a
n
d
1
5
0
0
lu
m
en
ar
e
u
s
ed
f
o
r
lig
h
tin
g
.
T
h
e
lu
m
in
ai
r
es
ar
e
en
er
g
ize
d
b
y
two
lin
es,
wh
er
e
th
e
f
ir
s
t
lin
e
h
as
f
iv
e
ar
m
atu
r
es
an
d
th
e
s
ec
o
n
d
lin
e
h
a
s
s
ix
ar
m
at
u
r
e
c
o
n
n
ec
tio
n
s
.
T
o
tal
illu
m
in
atio
n
p
o
wer
f
o
r
b
o
th
lin
es is
3
3
0
W.
Fig
u
r
e
5
.
E
T
AP SL
D
o
f
3
8
0
/2
2
0
V
AC
d
is
tr
ib
u
tio
n
Sm
all
p
o
wer
d
is
tr
ib
u
tio
n
h
as
b
ee
n
n
o
ted
f
o
r
th
e
u
s
e
o
f
g
en
er
al
s
o
ck
et
an
d
k
itch
en
eq
u
ip
m
en
t.
W
ith
s
m
a
ll
p
o
wer
d
is
tr
ib
u
tio
n
,
elec
tr
o
n
ic
d
ev
ices
s
u
ch
as
co
m
p
u
t
er
s
,
telev
is
io
n
s
an
d
telep
h
o
n
e
s
ca
n
b
e
en
er
g
ized
.
T
h
e
s
m
all
p
o
wer
d
is
tr
ib
u
tio
n
m
o
d
el
ass
u
m
es
an
av
er
ag
e
p
o
wer
co
n
s
u
m
p
tio
n
o
f
1
5
0
-
3
0
0
watts
p
er
s
o
ck
et.
T
wo
lin
es
ar
e
g
iv
en
f
o
r
g
en
e
r
al
u
s
e,
wh
er
e
o
n
e
o
f
th
em
is
in
ten
d
ed
to
b
e
u
s
ed
f
o
r
th
e
k
itch
en
eq
u
ip
m
e
n
t.
B
esid
es
a
to
tal
o
f
1
.
5
k
W
p
o
wer
co
n
s
u
m
p
tio
n
is
esti
m
ated
f
o
r
two
-
lin
e
co
m
m
o
n
s
o
ck
et
s
an
d
co
n
s
eq
u
en
tly
to
tal
p
o
wer
co
n
s
u
m
p
tio
n
is
p
r
ed
icted
as 1
.
5
6
k
W
f
o
r
k
itch
en
eq
u
ip
m
e
n
t.
T
h
e
r
e
m
ain
in
g
eq
u
ip
m
en
t
d
em
an
d
s
h
i
g
h
-
p
o
wer
an
d
ea
c
h
o
f
th
is
e
q
u
ip
m
en
t
is
en
er
g
ized
with
s
ep
ar
ate
lin
es.
B
r
ief
ly
b
o
th
m
o
d
els
(
AC
an
d
DC
)
co
n
tain
m
u
ltip
le
co
n
n
ec
tio
n
s
f
o
r
s
m
all
p
o
wer
co
n
s
u
m
p
tio
n
,
lig
h
tin
g
co
n
s
u
m
p
tio
n
an
d
h
ig
h
-
p
o
wer
co
n
s
u
m
p
tio
n
s
as
well.
T
h
e
m
ain
p
r
o
b
lem
is
th
e
co
m
p
ati
b
ilit
y
o
f
th
e
eq
u
ip
m
en
t
to
th
e
DC
co
n
n
ec
tio
n
(
DC
r
ea
d
y
o
r
n
o
t)
.
SLD
an
aly
s
is
o
f
1
1
0
V
DC
d
is
tr
ib
u
tio
n
m
o
d
el
is
g
iv
en
in
Fig
u
r
e
6
.
SLD
an
aly
s
is
o
f
2
5
0
V
DC
d
is
tr
ib
u
tio
n
m
o
d
el
an
d
3
2
0
V
DC
d
is
tr
ib
u
tio
n
m
o
d
el
ar
e
g
iv
en
in
Fig
u
r
e
7
an
d
Fig
u
r
e
8
r
esp
ec
tiv
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
1
9
3
–
206
198
Fig
u
r
e
6
.
E
T
AP SL
D
o
f
1
1
0
V
DC
d
is
tr
ib
u
tio
n
Fig
u
r
e
7
.
E
T
AP SL
D
o
f
2
5
0
V
DC
d
is
tr
ib
u
tio
n
All
ca
b
les
an
d
eq
u
ip
m
en
t
m
u
s
t
b
e
p
r
o
tecte
d
f
r
o
m
s
h
o
r
t
-
cir
cu
it
an
d
o
v
e
r
cu
r
r
e
n
t
f
au
lts
.
I
n
o
r
d
er
t
o
p
r
o
tect
th
e
lig
h
tin
g
cir
c
u
its
in
DC
n
etwo
r
k
s
,
m
in
iatu
r
e
cir
c
u
it
b
r
ea
k
er
s
with
1
0
A
o
v
e
r
l
o
ad
p
r
o
tectio
n
a
n
d
4
.
5
k
A
s
h
o
r
t
cir
c
u
it
p
r
o
tectio
n
ar
e
u
s
ed
.
Min
iatu
r
e
cir
cu
it
b
r
e
a
k
er
with
1
6
A
o
v
er
lo
a
d
an
d
4
.
5
k
A
s
h
o
r
t
cir
cu
it
cu
r
r
en
t
ar
e
u
s
ed
f
o
r
p
r
o
tectio
n
o
f
2
5
0
V
DC
an
d
3
2
0
V
DC
n
e
two
r
k
s
.
T
h
e
ty
p
ical
p
r
o
tectio
n
v
alu
es
f
o
r
th
e
1
1
0
V
DC
n
etwo
r
k
ar
e
s
i
m
ilar
to
2
5
0
V
DC
an
d
3
2
0
V
DC
n
etwo
r
k
s
in
th
e
E
T
AP
m
o
d
el,
h
o
wev
er
o
n
ly
two
f
ee
d
e
r
lin
es
with
ap
p
r
o
x
im
ately
2
k
W
p
o
wer
r
atin
g
s
ar
e
p
r
o
tecte
d
b
y
m
in
iatu
r
e
cir
c
u
it
b
r
ea
k
er
s
with
th
e
o
v
er
lo
a
d
ca
p
ac
ity
o
f
2
0
A
in
t
h
e
1
1
0
V
DC
n
etwo
r
k
wh
en
co
m
p
a
r
ed
to
o
th
er
n
etwo
r
k
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
co
mp
a
r
a
tive
s
tu
d
y
o
n
A
C
/DC
a
n
a
lysi
s
o
f a
n
o
p
era
tio
n
a
l l
o
w
vo
lta
g
e
d
is
tr
ib
u
tio
n
s
ystem
(
C
ih
a
n
K
a
ta
r
)
199
Fig
u
r
e
8
.
E
T
AP SL
D
o
f
3
2
0
V
DC
d
is
tr
ib
u
tio
n
T
h
e
r
eq
u
ir
ed
to
tal
c
u
r
r
e
n
t
ca
n
b
e
d
r
awn
f
r
o
m
th
e
m
ai
n
b
o
ar
d
to
th
e
s
ec
o
n
d
ar
y
b
o
ar
d
b
y
a
c
ab
le
with
5
0
m
m
2
cr
o
s
s
s
ec
tio
n
al
ar
ea
,
wh
ich
is
s
u
itab
le
f
o
r
v
o
ltag
e
d
r
o
p
a
n
d
cu
r
r
en
t
ca
r
r
y
in
g
ca
p
ac
ity
.
Af
ter
ca
b
le
o
p
tim
izatio
n
,
it
is
n
ec
ess
ar
y
to
d
eter
m
in
e
th
e
p
ar
am
ete
r
s
o
f
th
e
cir
cu
it
p
r
o
tectio
n
elem
en
ts
to
p
r
o
tect
th
e
n
etwo
r
k
f
r
o
m
o
v
e
r
lo
ad
an
d
s
h
o
r
t
cir
cu
it
f
au
lt
c
u
r
r
e
n
ts
.
I
n
ad
d
itio
n
,
t
h
er
m
al
p
r
o
tec
tio
n
an
d
m
ag
n
etic
p
r
o
tectio
n
ar
e
r
eq
u
ir
e
d
to
p
r
e
v
en
t
o
v
er
lo
ad
an
d
s
h
o
r
t
cir
cu
its
r
esp
ec
tiv
ely
.
Fo
r
th
is
r
ea
s
o
n
,
c
o
m
p
ac
t
cir
cu
it
b
r
ea
k
er
s
,
wh
ich
co
n
tain
b
o
th
m
en
tio
n
ed
p
r
o
tectio
n
s
ar
e
ch
o
s
en
as c
ir
cu
it p
r
o
tectiv
e
elem
e
n
ts
.
Fo
r
th
e
5
0
m
m
2
ca
b
le
p
r
o
tecti
o
n
in
1
1
0
V
DC
s
y
s
tem
,
co
m
p
ac
t
s
witch
es
with
8
0
A
o
v
er
c
u
r
r
en
t
a
n
d
10
k
A
s
h
o
r
t
cir
c
u
it
ch
ar
ac
ter
i
s
tics
ar
e
in
s
talled
to
th
e
m
ain
d
is
tr
ib
u
tio
n
b
o
ar
d
o
u
t
p
u
t
an
d
th
e
last
d
is
tr
ib
u
tio
n
b
o
ar
d
in
p
u
t
Fig
u
r
e
6
.
I
n
th
e
2
5
0
V
DC
s
y
s
tem
f
o
r
th
e
1
6
m
m
2
ca
b
le
p
r
o
tectio
n
,
c
o
m
p
ac
t
s
witch
es
wi
th
5
0
A
o
v
er
cu
r
r
en
t
an
d
1
0
k
A
s
h
o
r
t
c
ir
cu
it
ch
ar
a
cter
is
tics
ar
e
in
s
talled
to
th
e
m
ain
d
is
tr
ib
u
tio
n
b
o
ar
d
o
u
tp
u
t
a
n
d
th
e
last
d
is
tr
ib
u
tio
n
b
o
ar
d
in
p
u
t
F
ig
u
r
e
7
.
Fin
ally
,
f
o
r
th
e
1
0
m
m
2
ca
b
le
p
r
o
tectio
n
in
3
2
0
V
DC
s
y
s
tem
,
co
m
p
ac
t
s
witch
es
w
ith
3
2
A
o
v
er
cu
r
r
e
n
t
an
d
1
0
k
A
s
h
o
r
t
cir
cu
it
ch
ar
ac
ter
is
tics
ar
e
in
s
talled
to
th
e
m
ain
d
is
tr
ib
u
tio
n
b
o
ar
d
o
u
tp
u
t a
n
d
t
h
e
last
d
is
tr
ib
u
tio
n
b
o
ar
d
in
p
u
t
Fig
u
r
e
8
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
o
r
d
er
to
in
v
esti
g
ate
th
e
p
r
o
p
o
s
ed
h
o
u
s
e
d
is
tr
ib
u
tio
n
m
o
d
el,
v
ar
io
u
s
an
aly
s
es
h
av
e
b
ee
n
co
n
d
u
cte
d
.
Po
wer
an
al
y
s
is
,
cu
r
r
en
t
ca
r
r
y
in
g
ca
p
ac
ity
a
n
aly
s
is
,
v
o
ltag
e
d
r
o
p
an
aly
s
is
an
d
h
ar
m
o
n
ic
an
aly
s
is
ar
e
co
n
d
u
cted
wh
ich
ar
e
ac
ce
p
ted
as
k
e
y
p
ar
am
eter
s
f
o
r
d
is
tr
ib
u
tio
n
s
y
s
tem
p
lan
n
in
g
.
A
n
aly
s
es
ar
e
g
iv
en
in
d
etail
f
o
r
AC
an
d
DC
co
m
p
ar
i
s
o
n
.
4
.
1
.
M
o
del
p
a
ra
m
et
er
s
T
h
e
L
VDC
SLD
o
f
an
o
r
d
in
ar
y
h
o
u
s
e
is
m
o
d
elled
in
t
h
e
E
T
AP
p
r
o
g
r
am
.
T
h
e
r
esp
o
n
s
es
o
f
th
e
n
etwo
r
k
t
o
d
i
f
f
er
en
t
v
o
ltag
e
le
v
els
ar
e
an
al
y
ze
d
a
n
d
co
r
r
esp
o
n
d
in
g
r
esu
lts
f
o
r
1
1
0
V
DC
,
2
5
0
V
DC
an
d
3
2
0
V
DC
n
etwo
r
k
s
ar
e
i
n
ter
p
r
eted
r
esp
e
ctiv
ely
.
T
h
e
p
ar
am
eter
s
r
e
q
u
ir
ed
f
o
r
E
T
AP
s
im
u
latio
n
ar
e
c
alcu
lated
an
d
g
iv
en
as f
o
llo
ws.
4
.
1
.
1
.
AC
s
o
urce
pa
ra
m
e
t
er
s
:
T
h
e
p
ar
am
eter
s
u
s
ed
in
AC
n
etwo
r
k
s
ar
e
g
iv
en
as
f
o
llo
ws,
r
esp
ec
tiv
ely
.
S
K
=
MV
A
wh
ic
h
d
en
o
tes
AC
s
o
u
r
ce
s
h
o
r
t
-
cir
cu
it
p
o
we
r
,
V
AC
=3
3
k
V,
C
is
th
e
v
o
lta
g
e
co
ef
f
icien
t,
wh
ich
ca
n
b
e
co
n
s
id
er
ed
1
,
1
f
o
r
m
ed
iu
m
v
o
ltag
e
s
y
s
tem
.
Z
=
1
.
1
9
7
9
Ω
,
X
=
1
.
1
9
1
9
Ω
(
X
=
Z
x
0
,
9
9
5
)
,
R
=
0
.
1
1
9
1
9
Ω
(
R
=
Z
x
0
,
1
)
wh
ich
Z
,
X
,
an
d
R
d
en
o
te
im
p
ed
an
c
e
r
ea
ctan
ce
an
d
r
esis
tan
ce
r
esp
ec
t
iv
ely
.
B
y
ap
p
r
o
x
im
atio
n
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el,
t
h
e
r
atio
o
f
X/R
is
g
iv
en
as 1
0
.
T
h
e
im
p
ed
an
ce
is
ca
lcu
lated
b
y
th
e
e
x
p
r
ess
io
n
:
2
AC
CV
Zq
Sk
=
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
1
9
3
–
206
200
4
.
1
.
2
.
T
ra
ns
f
o
rm
er
pa
ra
m
et
er
s
:
I
n
th
e
n
etwo
r
k
3
3
k
V/0
.
4
k
V,
5
0
0
k
VA
tr
a
n
s
f
o
r
m
er
with
th
e
tr
an
s
f
o
r
m
er
im
p
ed
a
n
ce
o
f
4
%
is
u
s
ed
.
T
h
e
r
atio
o
f
X/R
is
s
elec
ted
as
1
.
5
.
4
.
1
.
3
.
Ca
ble pa
ra
m
et
er
s
:
I
n
th
e
L
VDC
an
d
L
VAC
n
etwo
r
k
s
,
ca
b
les
with
th
e
cr
o
s
s
-
lin
k
ed
p
o
ly
eth
y
le
n
e
(
XL
PE)
i
n
s
u
latio
n
an
d
p
o
ly
v
in
y
l
ch
lo
r
id
e
(
PVC
)
jack
ets
ar
e
u
s
ed
.
DC
r
esis
tan
ce
s
(
p
er
len
g
th
)
o
f
ca
b
les
ar
e
g
i
v
en
as
7
5
5
5
.
6
µ
Ω
/m
,
4
7
0
0
.
6
µ
Ω
/m
,
3
1
4
0
.
5
µ
Ω
/
m
an
d
3
9
4
.
6
µ
Ω
/m
f
o
r
t
h
e
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
s
o
f
2
.
5
mm
2
,
4
mm
2
,
6
mm
2
an
d
50
mm
2
r
esp
ec
tiv
ely
.
T
h
e
s
h
o
r
t c
ir
cu
it (
1
s
ec
o
n
d
)
cu
r
r
en
t (
5
0
mm
2
ca
b
le)
is
7
,
0
5
k
A.
Af
t
er
th
e
eq
u
ip
m
en
t a
n
d
p
ar
am
eter
s
ar
e
d
eter
m
in
ed
,
t
h
e
v
o
ltag
e
d
r
o
p
a
n
d
th
e
c
u
r
r
en
t
ca
r
r
y
in
g
ca
p
ac
ity
o
f
t
h
e
ca
b
les
s
h
o
u
ld
b
e
d
eter
m
in
ed
f
o
r
th
e
ca
b
le
o
p
tim
izatio
n
an
d
p
o
wer
a
n
aly
s
is
.
4
.
2
.
Curre
nt
ca
rr
y
ing
ca
pa
c
it
y
T
h
e
cu
r
r
e
n
t d
r
awn
co
n
d
u
cto
r
is
p
r
o
n
e
to
fa
ce
with
in
cr
ea
s
ed
tem
p
er
atu
r
e
d
u
e
to
its
r
esis
tan
ce
.
As th
e
ca
b
le
h
ea
ts
u
p
,
its
ef
f
icien
c
y
d
ec
r
ea
s
es.
Fu
r
th
er
m
o
r
e,
i
f
th
e
tem
p
er
atu
r
e
ex
ce
e
d
s
th
e
p
er
m
is
s
ib
le
th
r
esh
o
ld
,
it
m
ay
er
o
d
e
th
e
in
s
u
latio
n
m
at
er
ial
an
d
m
ay
ca
u
s
e
f
ir
e.
T
h
e
r
m
al
lim
its
d
eter
m
in
e
th
e
m
ax
im
u
m
cu
r
r
en
t
lim
it
th
at
ca
b
les
ca
n
ca
r
r
y
.
N
o
m
in
al
cu
r
r
en
t
ca
r
r
y
i
n
g
ca
p
ac
ities
o
f
h
alo
g
en
-
f
r
ee
an
d
XL
PE
in
s
u
lated
ca
b
les
ar
e
g
iv
en
in
T
a
b
le
3
.
So
m
e
r
ep
ea
ti
n
g
ca
b
les wh
ich
h
av
e
th
e
s
am
e
p
r
o
p
e
r
ties
ar
e
n
o
t
g
iv
en
in
T
ab
le
3
.
T
ab
le
3
.
No
m
i
n
al
cu
r
r
e
n
t c
ar
r
yi
n
g
ca
p
ac
ities
o
f
h
alo
g
e
n
-
f
r
e
e
an
d
XL
PE
in
s
u
lated
ca
b
les
C
u
r
r
en
t
ca
r
r
y
in
g
ca
p
ac
ities
ar
e
af
f
ec
ted
b
y
th
e
in
s
tallatio
n
m
eth
o
d
o
f
ca
b
les.
T
h
e
co
r
r
ec
t
io
n
f
ac
to
r
m
u
s
t
b
e
ap
p
lied
to
th
e
c
u
r
r
en
t
ca
r
r
y
in
g
ca
p
a
city
in
ac
co
r
d
a
n
ce
with
th
e
in
s
tallatio
n
ty
p
e.
T
ab
le
3
s
h
o
ws
th
e
m
ax
im
u
m
p
er
m
is
s
ib
le
cu
r
r
en
t
ca
r
r
y
i
n
g
ca
p
ac
ities
o
f
th
e
in
s
t
allatio
n
ca
b
les
ac
co
r
d
in
g
to
th
e
in
s
tallatio
n
ty
p
e.
W
h
ile
th
e
cu
r
r
en
t
ca
r
r
y
in
g
ca
p
ac
ity
o
f
2
,
5
m
m
2
ca
b
le
is
3
0
A,
th
is
ca
p
ac
ity
d
ec
r
ea
s
es
to
2
8
.
8
A
wh
en
it
is
in
s
talled
in
s
id
e
th
e
b
u
ild
in
g
.
Ma
x
im
u
m
cu
r
r
e
n
t
ca
r
r
y
in
g
c
ap
ac
ity
is
ca
lcu
lated
b
y
u
s
i
n
g
co
r
r
ec
tio
n
f
ac
t
o
r
,
wh
er
e
all
cu
r
r
en
t
v
alu
es
ar
e
ca
lcu
lated
ac
co
r
d
in
g
to
I
E
C
6
0
3
6
4
s
tan
d
ar
d
[
3
0
]
.
Fo
r
i
n
s
tan
ce
,
wh
en
th
e
m
ax
im
u
m
p
o
wer
o
f
th
e
eq
u
ip
m
en
t
is
ass
u
m
ed
as
2
k
W
,
t
h
e
to
tal
cu
r
r
en
t
d
em
a
n
d
is
ap
p
r
o
x
im
ately
1
8
A,
w
h
ich
is
v
er
if
ied
b
y
th
e
(
2
)
.
F
o
r
2
,
m
m
2
ca
b
le,
th
e
m
ax
im
u
m
cu
r
r
e
n
t
allo
wed
is
2
8
A.
Al
l
th
e
eq
u
i
p
m
en
t
ca
n
b
e
en
er
g
ize
d
with
2
,
5
m
m
2
ca
b
le
in
th
e
1
1
0
V
DC
n
etwo
r
k
.
(
)
(
)
(
)
W
D
C
D
C
P
V
I
=
(
2
)
4
.
3
.
Vo
l
t
a
g
e
d
ro
o
p
I
n
th
e
p
r
ev
io
u
s
s
ec
tio
n
,
t
h
e
in
s
tallatio
n
is
ex
am
in
ed
f
o
r
c
u
r
r
en
t
ca
r
r
y
in
g
ca
p
ac
ities
with
r
e
g
ar
d
to
t
h
e
co
r
r
ec
tio
n
f
ac
to
r
s
.
Du
e
to
th
e
r
esis
tan
ce
o
f
th
e
ca
b
le,
v
o
lta
g
e
d
r
o
p
o
cc
u
r
s
f
r
o
m
th
e
s
ec
o
n
d
ar
y
o
u
tp
u
t
o
f
t
h
e
tr
an
s
f
o
r
m
er
s
to
th
e
e
n
d
u
s
er
.
I
f
th
e
v
o
ltag
e
d
r
o
p
is
ab
o
v
e
th
e
lim
its
,
it
m
ay
d
am
a
g
e
o
r
in
t
er
r
u
p
t
t
h
e
o
p
er
atio
n
o
f
elec
tr
o
n
ic
e
q
u
ip
m
e
n
t.
Acc
o
r
d
in
g
to
r
eg
u
latio
n
s
,
0
.
4
k
V
v
o
ltag
e
at
th
e
s
ec
o
n
d
ar
y
o
f
t
h
e
tr
an
s
f
o
r
m
er
s
h
o
u
l
d
h
av
e
a
m
ax
im
u
m
d
r
o
p
o
f
1
0
%
th
r
o
u
g
h
o
u
t
th
e
lin
e.
T
h
e
v
o
ltag
e
d
r
o
p
f
r
o
m
th
e
last
p
a
n
el
to
t
h
e
lig
h
tin
g
an
d
s
o
ck
et
lo
ad
is
d
eter
m
in
e
d
as
3
%.
Ad
d
itio
n
all
y
,
v
o
ltag
e
d
r
o
p
is
d
eter
m
in
ed
as 1
.
5
% f
o
r
th
e
m
o
to
r
cir
c
u
its
.
T
h
e
p
er
ce
n
tag
e
o
f
v
o
ltag
e
d
r
o
p
is
ca
lcu
lated
as
in
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
s
.
I
n
(
3
)
d
if
f
er
e
n
ce
s
b
etwe
en
in
p
u
t
an
d
o
u
tp
u
t
v
o
ltag
es a
r
e
ca
lcu
lated
an
d
in
(
4
)
p
er
ce
n
tag
e
o
f
th
e
v
o
ltag
e
d
r
o
p
is
ca
l
cu
lated
.
21
D
C
D
C
D
C
U
U
U
=
−
(
3
)
%
1
0
0
DC
DC
U
U
U
=
(
4
)
T
h
e
p
o
ten
tial d
i
f
f
er
en
ce
in
th
e
n
etwo
r
k
ca
n
b
e
c
o
m
p
u
te
d
b
y
ca
b
le
r
esis
tan
ce
.
ID
kV
C
o
n
d
.
/
C
a
b
l
e
S
i
z
e
(
mm
²)
Le
n
g
t
h
(
m)
P
h
a
se
B
a
se
A
mp
.
I
n
st
a
l
l
a
t
i
o
n
A
l
l
o
w
a
b
l
e
A
mp
.
(
I
EC
6
0
3
6
4
)
µ
O
h
ms
(
2
5
°
C
)
/
U
n
i
t
Le
n
g
t
h
(
m)
C
a
b
l
e
0
1
1
4
/
C
50
2
0
0
A
C
-
3P
2
0
9
Emb
e
d
d
e
d
D
i
r
e
c
t
2
0
0
3
9
4
,
6
C
a
b
l
e
0
2
1
3/
C
50
30
DC
1
7
5
A
/
G
C
o
n
d
u
i
t
1
6
8
3
9
4
.
6
C
a
b
l
e
0
3
1
3
/
C
2
.
5
15
DC
30
B
u
i
l
d
i
n
g
V
o
i
d
s
2
8
.
8
7
5
5
5
.
6
C
a
b
l
e
0
5
1
3
/
C
4
.
0
35
DC
40
B
u
i
l
d
i
n
g
V
o
i
d
s
3
8
.
4
4
7
0
0
.
6
C
a
b
l
e
0
8
1
3
/
C
6
.
0
20
DC
51
B
u
i
l
d
i
n
g
V
o
i
d
s
49
3
1
4
0
.
5
C
a
b
l
e
1
3
1
3
/
C
10
38
DC
69
B
u
i
l
d
i
n
g
V
o
i
d
s
6
6
.
2
1
8
6
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
co
mp
a
r
a
tive
s
tu
d
y
o
n
A
C
/DC
a
n
a
lysi
s
o
f a
n
o
p
era
tio
n
a
l l
o
w
vo
lta
g
e
d
is
tr
ib
u
tio
n
s
ystem
(
C
ih
a
n
K
a
ta
r
)
201
D
C
c
a
b
le
U
I
R
=
(
5
)
C
ab
le
r
esis
tan
ce
f
o
r
b
o
t
h
u
n
ip
o
lar
an
d
b
i
p
o
lar
s
y
s
tem
s
ar
e
g
iv
en
i
n
(
6
)
wh
er
e
ρ
d
en
o
tes
r
esis
tiv
ity
,
l
is
th
e
len
g
th
an
d
S r
ep
r
esen
ts
th
e
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
o
f
th
e
ca
b
le.
Vo
ltag
e
d
r
o
p
o
f
th
e
DC
s
y
s
tem
is
g
iv
en
in
(
7
)
.
2
c
a
b
le
l
R
S
=
(
6
)
()
2
%
2
0
0
w
DC
Pl
U
US
=
(
7
)
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8
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I
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Sep
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206
202
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4
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a
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(
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C
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(
mm
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C
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(A)
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g
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t
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11
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T
h
e
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r
s
with
1
2
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n
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2
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p
u
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ar
e
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ar
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ize
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r
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p
er
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t
o
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d
e
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ice
r
atin
g
(X
C
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d
m
ax
im
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m
h
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r
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o
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ic
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er
(
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Har
m
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ic
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aly
s
is
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s
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n
d
u
cted
an
d
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
v
alu
es
ar
e
co
m
p
u
te
d
.
T
HD
is
an
ef
f
icien
t
alg
o
r
ith
m
f
o
r
a
n
aly
zin
g
h
ar
m
o
n
ic
im
p
a
ct
o
f
th
e
r
ec
tifie
r
o
f
th
e
co
n
v
e
r
s
io
n
s
y
s
tem
.
T
H
D
is
co
m
p
u
ted
b
y
u
s
in
g
th
e
f
o
llo
win
g
e
q
u
atio
n
s
[
3
4
]
.
I
n
itially
,
ar
ith
m
etic
s
u
m
m
atio
n
o
f
m
ag
n
itu
d
es o
f
a
ll c
o
m
p
o
n
e
n
ts
ar
e
co
m
p
u
ted
i
n
(
8
)
.
1
k
A
SU
M
V
i
=
=
(
8
)
T
h
en
r
o
o
t
m
ea
n
s
q
u
ar
e
(
R
MS)
o
f
f
u
n
d
am
e
n
tal
p
lu
s
all
h
ar
m
o
n
ics
is
ca
lcu
lated
i
n
(
9
)
.
Fin
ally
,
T
HD
is
co
m
p
u
ted
ac
co
r
d
in
g
to
(
1
0
)
.
2
1
k
R
M
S
V
i
=
=
(
9
)
2
2
2
2
3
4
1
....
v
o
ltag
e
V
V
V
T
H
D
V
+
+
+
=
(
1
0
)
I
n
(
8
)
V
i
r
ep
r
esen
ts
am
p
litu
d
e
o
f
th
e
V
TH
h
ar
m
o
n
ic
a
n
d
V
1
i
s
th
e
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
t
(
5
0
Hz
in
th
e
p
r
o
p
o
s
ed
m
o
d
el)
.
T
a
b
le
7
s
h
o
ws
th
e
T
HD
o
f
B
u
s
two
f
o
r
2
4
p
u
ls
e
an
d
1
2
p
u
ls
e
r
ec
tifie
r
s
.
T
HD
lim
it
s
h
o
u
ld
b
e
m
ax
im
u
m
f
iv
e
p
e
r
c
en
t f
o
r
I
E
E
E
5
1
9
[
3
5
]
s
y
s
te
m
s
,
wh
ich
h
av
e
r
ated
v
o
ltag
e
less
th
an
1
k
V.
E
f
f
ec
ts
o
f
th
e
T
HD
o
n
th
e
AC
n
etwo
r
k
ar
e
g
iv
en
in
Fig
u
r
e
9
an
d
Fig
u
r
e
1
0
,
wh
ich
r
ev
ea
l sig
n
al
d
is
to
r
tio
n
s
ca
u
s
ed
b
y
h
ar
m
o
n
ics.
T
ab
le
7
.
T
DH
f
o
r
2
4
p
u
ls
e
an
d
1
2
p
u
ls
e
r
ec
tifie
r
s
B
u
s
I
D
B
u
s
k
V
R
M
S
A
S
U
M
TH
D
B
u
s
2
-
2
4
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u
l
s
e
0
.
4
9
9
,
7
7
1
0
2
,
6
5
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,
4
6
B
u
s
2
-
1
2
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u
l
s
e
0
,
4
9
9
,
7
8
1
0
2
,
0
5
1
,
9
3
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