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826
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o
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h
t
h
e
p
o
w
er
elec
tr
o
n
ic
s
b
o
r
d
er
s
[
1
]
,
[
2]
.
T
h
e
E
lectr
ical
P
o
w
er
Qu
a
lit
y
is
th
e
s
u
p
p
l
y
o
f
r
eliab
le
p
o
w
er
to
its
cu
s
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esig
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atin
g
o
f
v
o
ltag
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a
n
d
f
r
eq
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en
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y
w
it
h
id
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l
s
in
u
s
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al
v
o
ltag
e
an
d
c
u
r
r
en
t
w
av
e
f
o
r
m
[
3
]
,
it
is
af
f
ec
ted
d
u
e
to
v
ar
io
u
s
r
ea
s
o
n
s
i
n
m
o
d
er
n
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o
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ctr
o
n
ic
w
o
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ld
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ec
au
s
e
o
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th
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s
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ased
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d
p
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q
u
alit
y
d
is
tu
r
b
an
c
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s
[
4
]
,
[
5
]
.
T
h
e
d
ef
in
itio
n
o
f
P
o
w
er
q
u
alit
y
ac
co
r
d
in
g
to
th
e
I
E
E
E
Stan
d
ar
d
“
T
h
e
co
n
ce
p
t o
f
p
o
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er
in
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c
eq
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ip
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ip
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co
m
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le
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it
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th
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p
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m
i
s
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ir
in
g
s
y
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te
m
a
n
d
o
th
er
co
n
n
ec
t
ed
eq
u
ip
m
e
n
t”
[
6
]
.
P
o
w
er
q
u
a
lit
y
p
r
o
b
le
m
i
n
cl
u
d
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p
h
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n
o
m
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s
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c
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as
v
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tag
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ter
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s
a
g
,
a
n
d
h
ar
m
o
n
ics
d
is
to
r
tio
n
[
7
]
,
[
8
]
.
T
h
is
p
ap
er
d
ea
ls
w
it
h
r
ed
u
ctio
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o
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d
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s
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ar
m
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ic
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s
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y
p
e
o
f
p
o
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r
o
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lem
.
Har
m
o
n
ic
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is
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tio
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u
s
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s
o
m
e
u
n
e
x
p
ec
ted
co
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d
itio
n
s
o
n
t
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elec
tr
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s
y
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te
m
.
Har
m
o
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ic
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is
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tio
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ec
r
ea
s
e
t
h
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ac
cu
r
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o
f
th
e
elec
tr
ical
m
e
ter
.
Har
m
o
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ic
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is
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tio
n
m
a
y
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s
o
ca
u
s
e
e
x
ce
s
s
i
v
e
d
is
s
ip
atio
n
o
f
elec
tr
ical
eq
u
ip
m
en
t
s
o
as
to
i
n
cr
ea
s
e
t
h
e
c
o
s
t
o
f
t
h
e
b
ill
[
9
]
,
[
1
0
]
.
Fu
r
t
h
er
m
o
r
e,
h
ar
m
o
n
i
c
d
is
to
r
tio
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ca
u
s
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tr
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e
q
u
ip
m
e
n
t
n
o
t
to
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o
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k
o
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th
e
s
p
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if
ied
p
o
w
er
q
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alit
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t
an
d
ar
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ca
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s
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a
d
ec
r
ea
s
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th
e
li
f
eti
m
e
o
f
th
e
elec
tr
ical
eq
u
ip
m
e
n
t
[
1
1
]
,
[
1
2
]
.
T
h
e
h
ar
m
o
n
ic
s
g
en
er
atio
n
f
r
o
m
r
en
e
w
ab
l
e
en
er
g
y
s
o
u
r
ce
d
ep
en
d
s
o
n
t
h
e
t
y
p
e
o
f
i
n
v
er
ter
s
w
ill
b
e
d
iv
er
g
e
n
t.
I
n
P
h
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to
v
o
ltaic
d
ep
e
n
d
s
o
n
t
h
e
t
y
p
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o
f
co
n
tr
o
l
s
tr
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a
n
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th
e
s
ize
o
f
P
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te
m
s
a
n
d
also
o
n
t
h
e
g
r
id
v
o
lta
g
e
h
ar
m
o
n
ic
s
[
1
3
]
.
I
n
w
i
n
d
en
er
g
y
,
th
e
co
n
v
er
ter
i
s
u
s
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to
co
n
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er
t
v
ar
iab
le
v
o
ltag
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f
r
o
m
t
h
e
in
d
u
ctio
n
g
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er
ato
r
to
D
C
v
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j
u
s
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s
s
u
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f
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r
elec
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o
p
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s
i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
o
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p
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g
I
SS
N:
2088
-
8708
Ha
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Mo
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[
1
4
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P
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5
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T
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h
ar
m
o
n
ic
v
o
ltag
e
s
in
in
s
tall
atio
n
s
w
h
er
e
t
h
e
s
u
p
p
l
y
v
o
lta
g
e
is
d
is
tu
r
b
ed
[
1
6
]
.
Var
io
u
s
m
e
th
o
d
s
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
d
esig
n
i
n
g
th
e
p
as
s
iv
e
f
ilter
s
[
1
7
]
-
[
2
0
]
.
T
h
e
g
o
al
is
to
m
i
n
i
m
ize
th
e
h
ar
m
o
n
ic
i
m
p
ed
an
ce
at
s
p
ec
i
f
ic
f
r
eq
u
e
n
cie
s
an
d
to
m
ax
i
m
ize
th
e
f
u
n
d
a
m
en
tal
f
r
eq
u
e
n
c
y
i
m
p
ed
an
ce
o
f
t
h
e
f
ilter
f
o
r
m
in
i
m
izin
g
lo
s
s
es.
H
o
w
e
v
er
,
r
e
-
ca
lcu
la
tio
n
s
ar
e
r
e
q
u
ir
ed
f
o
r
ea
ch
lo
ad
ch
an
g
e
[
1
6
]
.
I
n
th
i
s
r
esear
ch
,
t
h
e
n
u
clea
r
r
esear
ch
r
ea
cto
r
is
th
e
ca
s
e
s
tu
d
y
to
r
ed
u
ce
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
T
h
e
au
th
o
r
s
d
esig
n
o
f
s
i
n
g
le
-
t
u
n
ed
p
as
s
i
v
e
f
ilter
f
o
r
s
u
p
p
r
ess
in
g
t
h
e
h
ar
m
o
n
ic
c
u
r
r
e
n
ts
.
T
w
o
t
y
p
es
o
f
h
ar
m
o
n
ics p
r
o
d
u
ce
d
b
y
th
e
g
r
i
d
an
d
b
y
r
e
n
e
w
ab
le
e
n
er
g
y
s
o
u
r
ce
s
ar
e
m
o
d
eled
u
s
in
g
E
T
AP
.
T
h
e
li
m
itatio
n
o
f
h
ar
m
o
n
ics
p
o
llu
tio
n
p
r
esen
t
a
t
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
li
n
g
(
P
C
C
)
h
ad
b
ee
n
co
n
tr
o
l
b
y
I
E
E
E
Std
.
5
1
9
to
i
m
p
r
o
v
e
th
e
p
o
w
er
q
u
alit
y
,
wh
ich
w
id
el
y
ac
ce
p
ted
in
n
u
cle
ar
r
esear
ch
r
ea
cto
r
.
2.
P
ASSI
V
E
H
ARM
O
NICS
F
I
L
T
E
RS
Fo
r
m
iti
g
ati
n
g
t
h
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
p
ass
i
v
e
f
ilter
i
n
g
i
s
th
e
s
i
m
p
les
t
co
n
v
en
t
io
n
al
s
o
l
u
tio
n
[
2
1
]
.
P
ass
iv
e
ele
m
en
t
s
lik
e
r
esi
s
ta
n
ce
,
in
d
u
cta
n
ce
an
d
ca
p
ac
ita
n
ce
ar
e
u
s
ed
b
y
t
h
e
p
ass
i
v
e
f
ilter
s
to
co
n
tr
o
l
th
e
ha
r
m
o
n
ics.
C
o
m
m
o
n
t
y
p
e
s
o
f
p
ass
iv
e
f
ilter
s
an
d
th
e
ir
co
n
f
i
g
u
r
atio
n
s
ar
e
d
ep
icted
in
Fi
g
u
r
e
1
.
Fig
u
r
e
1
.
P
ass
iv
e
p
o
w
er
f
ilter
s
T
h
e
s
h
u
n
t
co
n
n
ec
t
io
n
o
f
p
ass
i
v
e
f
ilter
s
w
i
th
th
e
p
o
w
er
s
y
s
te
m
p
r
o
v
id
es
lea
s
t
i
m
p
ed
a
n
ce
p
ath
to
t
h
e
h
ar
m
o
n
ic
c
u
r
r
en
t
at
t
u
n
i
n
g
f
r
eq
u
en
c
y
.
A
s
co
m
p
ar
ed
to
t
h
e
s
h
u
n
t
f
ilter
s
er
ies
f
ilter
is
d
esig
n
ed
to
ca
r
r
y
f
u
ll
lo
ad
cu
r
r
en
t
t
h
er
ef
o
r
e
t
h
e
y
n
ee
d
o
v
er
cu
r
r
en
t
p
r
o
tectio
n
d
ev
ices.
W
h
er
ea
s
s
h
u
n
t
p
ass
iv
e
f
ilter
ca
r
r
ies
a
f
r
ac
tio
n
o
f
s
er
ie
s
f
ilter
c
u
r
r
en
t.
T
h
e
s
er
ies
f
i
lter
is
r
ela
tiv
el
y
m
o
r
e
ex
p
en
s
i
v
e
h
en
ce
s
h
u
n
t
p
ass
i
v
e
f
ilter
i
s
co
m
m
o
n
l
y
u
s
ed
as
h
ar
m
o
n
ic
f
ilter
.
F
u
r
th
er
m
o
r
e
i
t
also
p
r
o
v
id
es
r
ea
cti
v
e
p
o
w
er
at
s
y
s
te
m
o
p
er
atin
g
f
r
eq
u
e
n
c
y
.
T
h
e
m
o
s
t u
s
e
o
f
p
ass
i
v
e
f
ilter
is
a
Si
n
g
le
T
u
n
ed
Fil
ter
(
ST
F).
T
h
e
m
o
s
t c
o
m
m
o
n
l
y
u
s
ed
p
ass
iv
e
f
ilte
r
is
th
e
s
i
n
g
le
-
t
u
n
ed
f
il
ter
.
T
h
is
f
ilter
is
s
i
m
p
le
a
n
d
least
ex
p
en
s
iv
e
a
s
co
m
p
ar
ed
w
it
h
o
th
er
m
ea
n
s
f
o
r
m
iti
g
ati
n
g
th
e
h
ar
m
o
n
ic
p
r
o
b
le
m
s
[
2
2
]
,
[
2
3
]
.
T
h
e
L
C
S
T
F
(
Sin
g
le
Ser
ies
Fi
lter
)
is
m
o
s
t
co
m
m
o
n
a
n
d
in
ex
p
e
n
s
i
v
e
t
y
p
e
o
f
p
as
s
iv
e
f
i
lter
.
T
h
is
f
ilter
i
s
co
n
n
ec
ted
i
n
s
h
u
n
t
w
i
th
th
e
m
ain
d
is
tr
ib
u
tio
n
s
y
s
te
m
an
d
i
s
tu
n
ed
to
p
r
esen
t
lo
w
i
m
p
ed
an
ce
to
a
p
ar
ticu
lar
h
ar
m
o
n
i
c
f
r
eq
u
en
c
y
.
T
h
er
ef
o
r
e;
h
ar
m
o
n
ic
c
u
r
r
en
t
s
ar
e
d
iv
er
ted
f
r
o
m
th
e
least
i
m
p
ed
a
n
ce
p
ath
th
r
o
u
g
h
t
h
e
f
ilter
.
Fo
r
d
esig
n
in
g
t
h
e
s
i
n
g
le
t
u
n
ed
f
il
ter
it is
ess
e
n
tia
l to
s
elec
t
t
h
e
ap
p
r
o
p
r
iate
ca
p
ac
ito
r
v
alu
e
th
at
en
ab
le
s
g
o
o
d
p
o
w
er
f
ac
to
r
at
s
y
s
te
m
f
r
eq
u
e
n
c
y
.
P
laci
n
g
t
h
ese
f
ilter
s
i
n
clo
s
e
p
r
o
x
i
m
it
y
to
th
e
d
is
tu
r
b
i
n
g
d
ev
ice
s
is
a
m
o
r
e
ex
p
en
s
iv
e
s
o
l
u
tio
n
,
b
u
t
it
is
a
s
o
lu
tio
n
th
a
t
p
r
o
v
id
es r
ed
u
ce
d
lo
s
s
es in
t
h
e
p
o
w
er
n
et
w
o
r
k
[
2
4
]
,
[
2
5
]
.
3.
E
T
AP
S
I
M
UL
AT
I
O
N
AND
M
I
T
I
G
A
T
I
O
N
O
F
H
ARM
O
NICS
3
.
1
.
B
rief
i
ntr
o
du
ct
io
n o
f
E
T
AP
s
o
f
t
w
a
re
E
T
A
P
is
a
co
m
p
r
eh
e
n
s
i
v
e
an
al
y
s
is
to
o
l
f
o
r
p
o
w
er
s
y
s
te
m
d
esi
g
n
a
n
d
test
i
n
g
d
ev
elo
p
ed
b
y
OT
I
c
o
m
p
an
y
.
E
T
A
P
is
en
ter
p
r
is
e
s
o
f
t
w
ar
e
w
it
h
f
u
ll
y
g
r
ap
h
ical
i
n
ter
f
ac
e.
I
t
ca
n
s
w
itc
h
m
u
ltip
le
f
u
n
ctio
n
al
in
ter
f
ac
e
s
i
n
th
e
s
a
m
e
p
r
o
g
r
am
an
d
t
h
e
o
p
er
atio
n
is
v
er
y
c
o
n
v
e
n
ien
t.
T
h
e
E
T
A
P
h
ar
m
o
n
ic
an
a
l
y
s
is
m
o
d
u
l
e
ca
n
s
i
m
u
late
v
ar
io
u
s
p
o
w
er
co
m
p
o
n
e
n
t
s
a
n
d
d
ev
ice
s
ac
c
u
r
atel
y
.
T
h
e
m
o
d
u
le
h
a
s
t
w
o
an
al
y
s
i
s
m
et
h
o
d
s
:
h
ar
m
o
n
ic
w
a
v
e
p
o
w
er
f
lo
w
a
n
d
h
ar
m
o
n
ic
f
r
eq
u
en
c
y
s
ca
n
.
I
n
o
r
d
er
to
ex
p
lo
r
e
t
h
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
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&
C
o
m
p
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n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il
201
9
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8
2
6
-
8
3
4
828
d
if
f
u
s
io
n
ch
ar
ac
ter
i
s
tics
i
n
th
e
n
u
clea
r
r
esear
ch
r
ea
cto
r
,
th
is
p
ap
er
c
o
n
d
u
cts
t
h
e
an
al
y
s
i
s
an
d
ca
lcu
latio
n
u
s
i
n
g
th
e
h
ar
m
o
n
ic
a
n
al
y
s
i
s
to
o
l
in
E
T
A
P
.
T
h
is
to
o
l,
w
h
ich
co
m
p
lies
w
it
h
I
E
E
E
5
1
9
s
ta
n
d
ar
d
s
,
e
m
b
ed
d
ed
th
e
p
o
w
er
f
lo
w
al
g
o
r
ith
m
o
f
Ne
wto
n
-
R
ap
h
s
o
n
an
d
Gau
s
s
-
Seid
el
an
d
ca
n
c
u
s
to
m
ize
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
m
o
d
el,
is
ab
le
to
ev
alu
ate
t
h
e
d
is
to
r
tio
n
r
ate
an
d
s
y
s
te
m
r
eso
n
a
n
ce
q
u
ick
l
y
.
3
.
2
.
E
T
AP
s
i
m
ula
t
io
n o
f
elec
t
rica
l sy
s
t
e
m
f
o
r
nu
clea
r
re
s
ea
rc
h r
ea
ct
o
r
I
n
th
i
s
p
ap
er
,
th
e
m
icr
o
g
r
id
o
f
n
u
clea
r
r
esear
ch
r
ea
cto
r
is
s
i
m
u
latio
n
b
y
E
T
A
P
1
2
.
6
.
A
f
ee
d
er
w
it
h
s
h
o
r
t
-
c
ir
cu
it
p
o
w
er
Ss
c=
6
5
MV
Asc
co
n
n
ec
ted
to
th
e
1
1
k
V
b
u
s
,
b
u
s
2
(
P
C
C
)
co
n
n
ec
ted
to
th
e
1
1
k
V
b
u
s
v
i
a
5
0
0
k
VA
(
1
1
/0
.
4
k
V)
tr
an
s
f
o
r
m
er
.
T
h
er
e
ar
e
f
o
u
r
lu
m
p
ed
lo
ad
s
(
t
w
o
s
tat
ic
lo
ad
s
an
d
th
e
o
th
er
t
w
o
ar
e
m
o
to
r
lo
ad
s
)
,
1
0
0
KVA
ea
c
h
.
I
n
ad
d
itio
n
,
th
e
R
e
n
e
w
ab
le
e
n
er
g
y
s
o
u
r
ce
co
n
tain
s
p
h
o
to
v
o
ltaic
p
an
els
(
1
5
0
KVA
)
an
d
w
in
d
t
u
r
b
in
es
(
4
0
0
KV
A
)
ar
e
co
n
n
ec
ted
to
b
u
s
3
.
L
u
m
p
ed
lo
ad
5
is
an
ex
ter
n
al
lo
ad
.
T
h
e
cir
cu
it
d
iag
r
a
m
is
s
h
o
w
n
in
F
i
g
u
r
e
2
,
an
d
t
h
e
r
elev
an
t
ele
m
en
t
p
ar
a
m
eter
s
ar
e
s
h
o
w
n
in
th
e
d
iag
r
a
m
.
T
h
er
e
ar
e
t
w
o
s
t
u
d
y
ca
s
es o
f
s
o
u
r
ce
o
f
h
ar
m
o
n
ic
a
n
d
ef
f
ec
ted
o
n
P
C
C
.
Fig
u
r
e
2
.
C
ir
cu
it
m
o
d
el
in
E
T
A
P
1
2
.
6
C
ase
1
: H
ar
m
o
n
ic
f
r
o
m
Gr
id
:
T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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o
n
M
o
d
e
rn
Po
we
r S
y
ste
ms
(
M
PS
),
pp
.
1
-
4
,
Ju
n
.
2
0
1
7
.
[1
5
]
M
.
Hu
a
n
g
,
X
.
W
a
n
g
,
P
.
C.
L
o
h
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.
Blaa
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jerg
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si
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r
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ted
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tab
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it
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d
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o
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stn
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ss
,
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IEE
E
Ap
p
li
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d
P
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we
r
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e
c
tro
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o
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re
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p
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2
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1
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.
[1
6
]
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.
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.
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a
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,
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t
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ter
De
sig
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r
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4
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7
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ter
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se
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if
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g
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n
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o
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m
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r,
"
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,
p
p
.
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e
p
.
2
0
1
6
.
[1
8
]
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A
.
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n
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.
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.
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u
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il
i,
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.
A
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a
r,
"
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rm
o
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it
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ti
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o
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strial
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o
w
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y
ste
m
Us
in
g
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ss
iv
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il
ters
,
"
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e
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ra
n
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ive
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o
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rn
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n
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&
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y
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l.
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,
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3
5
5
-
3
6
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A
p
r
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2
0
1
2
.
[1
9
]
H.
Hu
,
Z.
He
,
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.
G
a
o
,
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e
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ter
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e
sig
n
f
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r
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in
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h
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d
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r
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ics
,
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ra
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p
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4
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b
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2
0
1
5
.
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0
]
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M
.
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o
o
m
ro
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.
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.
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lm
e
li
a
n
,
"
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ti
m
a
l
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sig
n
o
f
a
S
in
g
le
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n
e
d
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ss
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ter
to
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te
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rm
o
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in
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o
w
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r
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re
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,
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o
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rn
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n
g
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n
d
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p
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l.
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0
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n
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1
9
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p
p
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9
0
0
9
-
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0
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4
,
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t.
2
0
1
5
.
[2
1
]
J.
C.
Da
s,
"
P
a
ss
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e
F
il
ters
-
P
o
ten
ti
a
li
ti
e
s
a
n
d
L
i
m
it
a
ti
o
n
s,"
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r
a
n
sa
c
ti
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s
o
n
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d
u
stry
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p
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s,
v
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l.
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p
p
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2
3
2
-
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4
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,
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e
b
.
2
0
0
4
.
[2
2
]
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S
.
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h
o
,
H.
Ch
a
,
"
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S
in
g
le
-
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u
n
e
d
P
a
ss
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r
m
o
n
ic
F
il
ter
De
sig
n
Us
in
g
T
ra
n
s
f
e
r
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u
n
c
ti
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n
A
p
p
ro
a
c
h
f
o
r
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d
u
strial
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ro
c
e
ss
A
p
p
li
c
a
ti
o
n
,
"
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ter
n
a
t
io
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a
l
J
o
u
rn
a
l
o
f
M
e
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h
a
tr
o
n
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a
n
d
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u
to
m
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ti
o
n
,
v
o
l.
1
,
n
o
.
2
,
p
p
.
90
-
9
6
,
Ja
n
.
2
0
1
1
.
[2
3
]
D.
Bu
la,
M
.
P
a
sk
o
,
"
H
y
b
rid
P
o
w
e
r
F
il
ter
w
it
h
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in
g
le
T
u
n
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d
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ss
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F
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ter
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y
n
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m
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l
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ro
p
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rti
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s,"
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ter
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ti
o
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l
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c
h
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si
n
u
s
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l
C
u
rr
e
n
t
s a
n
d
Co
m
p
e
n
sa
ti
o
n
,
pp
.
80
-
8
3
,
J
u
n
.
2
0
1
0
.
[2
4
]
Y.
Y.
Ho
n
g
,
C.
S
.
C
h
iu
,
S
.
W
.
H
u
a
n
g
,
"
M
u
lt
i
-
S
c
e
n
a
rio
P
a
ss
iv
e
F
i
lt
e
r
P
lan
n
i
n
g
in
F
a
c
to
ry
Distrib
u
t
io
n
S
y
ste
m
b
y
Us
in
g
M
a
rk
o
v
M
o
d
e
l
a
n
d
P
r
o
b
a
b
il
isti
c
S
u
g
e
n
o
F
u
z
z
y
Re
a
so
n
in
g
,
"
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p
li
e
d
S
o
ft
C
o
m
p
u
ti
n
g
,
v
o
l.
4
1
,
p
p
.
3
5
2
-
3
6
1
,
A
p
r.
2
0
1
6
.
[2
5
]
F
.
S
.
D
o
s
Re
is,
e
t
a
l
.
,
"
Ha
rm
o
n
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M
it
ig
a
ti
o
n
i
n
W
in
d
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rb
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n
e
E
n
e
rg
y
Co
n
v
e
rsio
n
S
y
ste
m
s,
"
3
7
t
h
IEE
E
Po
we
r
El
e
c
tro
n
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S
p
e
c
ia
li
sts C
o
n
fer
e
n
c
e
,
p
p
.
1
-
7
,
J
u
n
.
2
0
0
6
.
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