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[
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I
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[
4
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[
5
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[
6
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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6067
Po
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PQ)
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o
wer
f
lo
w
m
eth
o
d
s
is
u
s
ed
to
an
aly
ze
t
h
e
d
is
tr
ib
u
tio
n
an
d
ef
f
ec
ts
o
f
u
s
in
g
n
o
n
lin
ea
r
l
o
a
d
s
o
n
th
e
R
DS
[
1
1
]
.
T
h
e
FB
S
m
eth
o
d
is
u
s
ed
to
o
b
tain
b
u
s
v
o
ltag
e
v
alu
es,
cu
r
r
en
t
f
o
r
ea
ch
c
h
an
n
el
a
n
d
ch
an
n
el
p
o
wer
lo
s
s
es
at
b
asic
f
r
eq
u
e
n
cies,
wh
ile
th
e
HL
F
m
eth
o
d
is
u
s
ed
to
o
b
tain
v
alu
es
f
o
r
b
u
s
v
o
ltag
e,
cu
r
r
en
t
f
o
r
ea
ch
c
h
an
n
el
an
d
ch
an
n
el
p
o
wer
lo
s
s
es
at
m
u
ltip
les
o
f
th
e
f
r
eq
u
e
n
cy
,
wh
ic
h
is
ca
lled
th
e
h
ar
m
o
n
ic
o
r
d
e
r
[
1
2
]
–
[
1
4
]
.
T
h
e
s
im
p
lifie
d
co
n
tr
o
l
an
d
o
p
er
atio
n
al
p
r
o
ce
s
s
es,
alo
n
g
with
th
e
ef
f
icien
cy
ac
h
ie
v
ed
b
y
cu
s
to
m
er
s
with
th
e
u
s
e
o
f
s
em
ico
n
d
u
cto
r
d
ev
ices
an
d
s
witch
in
g
p
r
o
ce
s
s
es,
n
ec
ess
i
tate
th
at
R
DS
h
av
e
in
tr
icate
r
eq
u
ir
em
e
n
ts
f
o
r
co
n
tr
o
llin
g
th
e
PQ
in
d
ex
,
p
a
r
ticu
lar
ly
ad
d
r
ess
in
g
th
e
ef
f
ec
ts
o
f
p
r
o
p
ag
atin
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
1
5
]
.
T
h
e
elec
tr
icit
y
d
is
tr
ib
u
tio
n
n
etwo
r
k
in
I
n
d
o
n
esia
u
tili
ze
s
a
r
ad
ial
n
et
wo
r
k
co
n
f
ig
u
r
atio
n
.
PT.
PLN
(
Per
s
er
o
)
,
as
th
e
k
e
y
p
lay
er
i
n
d
is
tr
ib
u
tin
g
an
d
o
p
er
atin
g
t
h
e
elec
tr
ic
p
o
we
r
s
y
s
tem
,
en
co
u
n
ter
s
ch
allen
g
es in
m
ain
tain
in
g
s
y
s
tem
p
er
f
o
r
m
an
ce
i
n
ac
co
r
d
an
c
e
with
p
r
ed
ef
i
n
ed
o
p
er
atin
g
s
t
an
d
ar
d
s
[
1
6
]
.
Alth
o
u
g
h
co
n
s
id
er
e
d
an
o
p
tim
izatio
n
m
eth
o
d
with
a
lo
n
g
h
is
to
r
y
,
t
h
e
NR
m
eth
o
d
is
s
till
wid
ely
u
s
e
d
as
an
ev
o
lv
in
g
b
r
ea
k
th
r
o
u
g
h
,
b
o
th
in
ter
m
s
o
f
s
in
g
le
o
p
tim
i
za
tio
n
tech
n
iq
u
es
an
d
i
n
co
m
b
in
atio
n
with
o
th
er
o
p
tim
izatio
n
m
eth
o
d
s
to
en
h
a
n
ce
s
y
s
tem
p
er
f
o
r
m
an
ce
,
in
clu
d
in
g
ad
d
r
ess
in
g
is
s
u
es
r
elate
d
to
th
e
s
p
r
ea
d
in
g
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
1
7
]
.
Fu
n
d
am
e
n
tally
,
NR
alo
n
e
is
u
n
ab
le
to
m
itig
ate
th
e
s
p
r
e
ad
in
g
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
T
h
e
co
n
tr
o
l
o
f
tie
s
witch
es
(
T
S)
an
d
tie
tr
an
s
f
o
r
m
er
s
(
T
T
)
is
cr
u
cial
in
r
eg
u
latin
g
cu
r
r
en
t
f
lo
w
a
n
d
im
p
ed
an
ce
v
al
u
es
o
f
f
ee
d
er
c
o
n
f
ig
u
r
atio
n
co
n
n
ec
tio
n
s
in
th
e
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
(
R
DS)
[
1
8
]
.
I
n
s
ev
er
al
s
tu
d
ies
u
tili
zin
g
th
e
I
E
E
E
3
3
-
b
u
s
R
DS
te
s
t
s
y
s
tem
,
m
eth
o
d
s
s
u
ch
as
lo
ad
cu
r
tailm
en
t
[
1
9
]
,
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
[
2
0
]
,
an
t
co
lo
n
y
m
eth
o
d
[
2
1
]
,
g
en
eti
c
alg
o
r
ith
m
[
2
2
]
,
f
ir
e
f
lies
alg
o
r
ith
m
[
2
3
]
,
a
n
d
s
im
u
lated
an
n
ea
lin
g
[
2
4
]
,
wh
ich
ar
e
ar
tific
ial
in
tellig
en
ce
(
AI
)
-
b
ased
m
et
h
o
d
s
,
ar
e
c
o
n
s
id
er
ed
ef
f
ec
tiv
e
in
r
ed
u
cin
g
h
ar
m
o
n
ic
s
p
r
ea
d
in
g
in
d
ices,
d
ec
r
ea
s
in
g
lo
s
s
es,
an
d
im
p
r
o
v
i
n
g
b
u
s
v
o
ltag
e
lev
els
u
s
in
g
N
R
tech
n
iq
u
es.
T
h
e
NR
o
p
tim
izatio
n
tech
n
i
q
u
e
is
also
d
ee
m
e
d
ef
f
ec
tiv
e
in
en
h
a
n
cin
g
p
o
w
er
q
u
ality
(
PQ)
,
as
d
em
o
n
s
tr
ated
in
test
s
o
n
th
e
E
x
ec
u
tiv
e
Un
it
Ser
v
ice
o
r
Un
it
La
ya
n
a
n
P
ela
n
g
g
a
n
(
UL
P)
W
ay
Halim
8
8
-
b
u
s
s
y
s
tem
in
B
an
d
ar
L
am
p
u
n
g
C
ity
,
I
n
d
o
n
esia,
u
s
in
g
th
e
m
u
lti
-
o
b
jectiv
e
PS
O
m
eth
o
d
.
B
o
th
t
est
s
y
s
tem
s
ex
h
ib
it
s
ig
n
if
ican
tly
d
if
f
e
r
en
t
elec
tr
ici
ty
d
em
an
d
v
alu
es
in
th
eir
r
esp
ec
tiv
e
f
ee
d
er
s
[
2
5
]
.
T
h
e
ty
p
e
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
g
r
ea
tly
in
f
lu
en
ce
s
t
h
e
m
a
g
n
it
u
d
e
o
f
h
ar
m
o
n
ic
c
u
r
r
e
n
t
in
je
ctio
n
,
an
d
t
h
is
is
also
h
i
g
h
ly
d
ep
e
n
d
en
t
o
n
th
e
elec
tr
ical
en
er
g
y
m
a
g
n
itu
d
e
in
th
e
f
ee
d
er
[
2
6
]
.
T
h
e
UL
P
Su
n
g
g
u
m
in
asa,
lo
ca
ted
in
th
e
Go
wa
R
eg
en
cy
,
o
v
e
r
s
ee
s
s
ev
er
al
f
ee
d
er
s
.
On
e
o
f
t
h
em
is
th
e
B
ar
o
m
b
o
n
g
-
I
PDN
f
ee
d
e
r
wit
h
a
to
tal
o
f
1
6
5
b
u
s
es.
T
h
e
lo
ad
ty
p
es
in
t
h
is
s
y
s
tem
in
clu
d
e
h
o
u
s
eh
o
ld
s
,
elite
r
esid
en
tial
ar
ea
s
,
an
d
in
d
u
s
tr
ial
zo
n
es,
ea
ch
u
tili
zin
g
d
if
f
er
en
t
h
ar
m
o
n
ic
lo
a
d
ty
p
es.
Ho
u
s
eh
o
ld
s
co
n
s
titu
te
ar
e
m
ajo
r
ity
o
f
t
h
e
lo
a
d
ty
p
es
in
t
h
is
s
y
s
tem
[
2
7
]
.
I
n
a
s
tu
d
y
[
2
8
]
,
it
was
n
o
ted
th
at
p
o
wer
f
lo
w
an
aly
s
is
r
ev
ea
led
s
ev
er
al
f
ee
d
er
s
with
b
u
s
v
o
lta
g
e
lev
els
b
elo
w
0
.
9
5
p
u
.
C
o
n
s
id
er
in
g
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
t
y
p
es
r
esu
ltin
g
f
r
o
m
th
e
lo
ad
ch
ar
ac
ter
is
tics
in
th
is
s
y
s
tem
,
th
is
r
e
s
ea
r
ch
attem
p
ts
to
o
p
tim
ize
th
e
NR
m
eth
o
d
in
v
ar
io
u
s
s
ce
n
ar
io
s
.
T
h
is
tech
n
iq
u
e
is
o
p
tim
ized
u
s
in
g
th
e
PS
O
m
eth
o
d
with
th
e
o
b
jectiv
e
o
f
m
in
im
izin
g
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
v
o
ltag
e
(
%THD
v
)
an
d
to
tal
lo
s
s
es
with
in
p
r
ed
ef
in
ed
s
tan
d
ar
d
s
.
T
h
e
o
p
ti
m
izatio
n
r
esu
lts
ar
e
an
ticip
ated
to
m
ak
e
a
s
u
b
s
tan
tial
co
n
tr
ib
u
tio
n
to
th
e
ef
f
ec
ts
o
f
NR
,
co
n
s
id
er
i
n
g
th
e
lo
ad
c
h
ar
ac
ter
is
tics
in
th
e
R
DS.
T
h
e
s
tr
u
ctu
r
e
o
f
th
is
p
a
p
er
is
as
f
o
llo
ws:
s
ec
tio
n
2
is
r
e
s
ea
r
ch
m
eth
o
d
s
is
d
iv
id
ed
in
to
f
o
u
r
p
a
r
ts
n
am
ely
o
b
jectiv
es
an
d
co
n
s
tr
ain
s
,
UL
P
Su
n
g
g
u
m
in
asa
1
6
5
-
b
u
s
,
NR
m
eth
o
d
s
a
n
d
PS
O
m
eth
o
d
.
Simu
latio
n
r
esu
lt
a
n
d
d
is
cu
s
s
io
n
ar
e
s
h
o
wn
in
s
ec
tio
n
3
.
Sectio
n
4
is
co
n
clu
s
io
n
.
2.
M
E
T
H
OD
2
.
1
.
O
bje
ct
iv
es a
nd
c
o
ns
t
ra
ins
E
ac
h
o
p
tim
izatio
n
tech
n
iq
u
e
to
b
e
o
p
tim
ized
h
as
an
o
b
jectiv
e
f
u
n
ctio
n
(
OF)
.
T
h
e
OF
in
th
i
s
r
esear
ch
aim
s
to
m
in
im
ize
%THD
v
an
d
to
tal
lo
s
s
es
.
=
(
)
1
+
(
)
2
(
1
)
=
(
,
,
∗
100%
)
1
+
(
∑
(
1
)
=
1
+
∑
∑
(
ℎ
)
ℎ
ℎ
=
ℎ
0
=
1
)
2
(
2
)
,
an
d
,
ar
e
v
o
ltag
e
b
u
s
in
f
u
n
d
a
m
en
tal
f
r
eq
u
en
cy
an
d
v
o
ltag
e
r
m
s
o
n
b
u
s
i,
ℎ
an
d
ℎ
0
ar
e
th
e
m
ax
an
d
m
in
h
ar
m
o
n
ic
o
r
d
er
s
an
d
(
1
)
an
d
(
ℎ
)
ar
e
th
e
lo
s
s
es o
f
f
u
n
d
am
e
n
tal
an
d
h
a
r
m
o
n
ic
o
r
d
e
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
0
6
6
-
6
0
7
5
6068
B
o
u
n
d
ar
y
c
o
n
d
itio
n
s
n
ee
d
to
b
e
m
et
to
en
h
a
n
ce
th
e
s
elec
tiv
ity
o
f
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
.
−
T
h
e
elec
tr
ical
n
etwo
r
k
to
p
o
l
o
g
y
r
em
ain
s
r
a
d
ial
b
ef
o
r
e
an
d
a
f
ter
NR
.
−
an
d
ar
e
th
e
m
in
im
u
m
an
d
m
ax
im
u
m
v
o
ltag
e
lev
el
b
u
s
n
ee
d
s
to
b
e
k
ep
t
with
in
o
p
er
atio
n
al
lim
its
.
(
0
.
95
)
≤
≤
(
1
.
05
)
(
3
)
−
T
h
e
lim
it
f
o
r
%THD
v
ad
h
er
e
to
t
h
e
s
tan
d
a
r
d
s
o
u
tlin
ed
i
n
I
E
E
E
s
td
9
5
.
an
d
ar
e
to
t
al
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
m
ax
im
u
m
an
d
b
u
s
i.
%
≥
%
(
4
)
2
.
2
.
UL
P
Su
ng
g
um
ina
s
a
165
-
bus
T
h
e
UL
P
Su
n
g
g
u
m
in
asa
o
p
e
r
ates
at
a
v
o
ltag
e
o
f
2
0
k
V.
I
t
p
r
o
v
id
es
elec
tr
ic
p
o
wer
to
r
esid
en
ts
,
b
u
s
in
ess
es,
an
d
in
d
u
s
tr
ial
clie
n
ts
in
th
e
n
eig
h
b
o
r
in
g
v
icin
it
y
,
as
illu
s
tr
ated
in
Fig
u
r
e
1
.
I
n
th
is
r
esear
c
h
,
t
h
e
em
p
lo
y
ed
f
ee
d
er
s
wer
e
B
ar
o
m
b
o
n
g
an
d
I
PDN
f
ee
d
er
s
,
co
m
p
r
is
in
g
a
to
tal
o
f
1
6
5
b
u
s
es.
T
h
e
ag
g
r
eg
ate
lo
ad
o
n
its
am
o
u
n
ts
to
1
2
,
3
2
5
MW
an
d
7
.
6
4
MV
AR
.
Har
m
o
n
ic
c
u
r
r
en
ts
will b
e
in
tr
o
d
u
ce
d
t
o
e
ac
h
lo
ad
b
u
s
.
T
h
r
ee
ca
teg
o
r
ies o
f
h
a
r
m
o
n
ic
l
o
ad
s
in
clu
d
e
f
lu
o
r
escen
t la
m
p
s
f
o
r
r
esid
en
tial a
r
ea
s
,
in
v
er
tin
g
d
e
v
i
ce
s
ass
o
ciate
d
with
tem
p
er
atu
r
e
co
n
tr
o
l
eq
u
ip
m
en
t
f
o
r
elite
r
esid
en
tial
ar
ea
s
,
an
d
s
ix
-
p
u
ls
e
v
ar
iab
le
f
r
eq
u
e
n
c
y
d
r
iv
es
(
VFD)
f
o
r
in
d
u
s
tr
ial
ar
ea
s
.
T
h
e
m
a
g
n
itu
d
e
an
d
ty
p
e
o
f
h
ar
m
o
n
ic
lo
ad
in
jectio
n
ar
e
d
etailed
in
T
ab
les
1
an
d
2.
Fig
u
r
e
1
.
UL
P
Su
n
g
g
u
m
i
n
asa
165
-
b
u
s
R
DS
[
2
8
]
T
ab
le
1
.
T
h
e
v
alu
e
o
f
h
a
r
m
o
n
ic
cu
r
r
en
t i
n
jectio
n
f
r
o
m
th
e
h
a
r
m
o
n
ic
lo
a
d
s
[
2
7
]
H
a
r
mo
n
i
c
o
r
d
e
r
Th
e
t
y
p
e
s
o
f
h
a
r
m
o
n
i
c
i
n
j
e
c
t
i
o
n
V
F
D
I
n
v
e
r
t
i
n
g
d
e
v
i
c
e
s
F
l
u
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sc
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n
t
5
th
98∠
140
0
15
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N
etw
o
r
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r
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fig
u
r
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tio
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6069
T
ab
le
2
.
L
o
ca
tio
n
o
f
h
ar
m
o
n
ic
lo
ad
[
2
7
]
Ty
p
e
o
f
h
a
r
m
o
n
i
c
l
o
a
d
Lo
a
d
B
u
s
V
F
D
3
6
,
4
6
,
5
3
,
1
1
7
,
1
2
1
,
1
6
4
I
n
v
e
r
t
i
n
g
d
e
v
i
c
e
s
5
,
1
1
1
5
,
1
8
,
2
0
,
2
3
,
2
5
,
2
7
,
3
0
,
3
4
,
3
8
,
4
1
,
4
4
,
4
8
,
5
9
,
5
8
,
6
4
,
7
1
,
7
3
,
7
8
,
8
2
,
8
5
,
8
8
,
9
1
,
9
4
,
9
6
,
1
0
0
,
1
1
2
,
1
1
9
,
1
2
3
,
1
2
8
,
1
3
0
,
1
3
8
,
1
5
3
F
l
u
o
r
e
sc
e
n
t
3
,
8
,
9
,
1
4
,
1
6
,
2
1
,
2
2
,
2
6
,
2
9
,
3
1
,
3
2
,
3
5
,
4
0
,
4
2
,
4
9
,
5
0
,
5
1
,
5
4
,
5
6
,
5
7
,
6
2
,
6
5
,
6
7
,
6
9
,
7
0
,
7
4
,
7
5
,
7
6
,
7
7
,
7
9
,
8
1
,
8
3
,
8
7
,
9
0
,
9
7
,
9
9
,
1
0
2
,
1
0
4
,
1
0
6
,
1
0
7
,
1
0
8
,
1
0
9
,
1
1
1
,
1
1
4
,
1
1
5
,
1
1
6
,
1
1
8
,
1
2
1
,
1
2
5
,
1
2
7
,
1
3
2
,
1
3
4
,
1
3
6
,
1
3
7
,
1
4
2
,
1
4
3
,
1
4
6
,
1
4
8
,
1
5
1
,
1
5
2
,
1
5
5
,
1
5
7
,
1
5
9
,
1
6
1
,
1
6
2
2
.
3
.
NR
m
et
ho
d a
nd
s
t
ud
y
ca
s
e
T
h
e
T
S
co
n
n
ec
t
lo
a
d
b
u
s
es
in
t
o
g
r
o
u
p
s
to
id
en
tif
y
th
e
m
o
s
t o
p
tim
al
co
m
b
in
ati
o
n
[
2
9
]
.
T
h
er
e
ar
e
f
iv
e
clu
s
ter
s
d
eter
m
in
ed
b
ased
o
n
T
S
an
d
SS
will
u
n
d
er
g
o
r
e
co
n
f
ig
u
r
atio
n
.
T
h
e
co
m
b
i
n
atio
n
o
f
T
S
an
d
SS
s
witch
es
i
s
em
p
lo
y
ed
to
estab
lis
h
th
e
s
ea
r
ch
s
p
ac
e
in
t
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
[
3
0
]
.
T
h
e
SS
will
b
e
d
is
co
n
n
ec
ted
,
allo
win
g
a
n
ew
cir
cu
it
to
b
e
co
n
n
ec
ted
th
r
o
u
g
h
th
e
T
S
clo
s
u
r
e
p
r
o
ce
s
s
b
ased
o
n
th
e
s
ea
r
ch
r
esu
lts
f
r
o
m
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
[
3
1
]
,
[
3
2
]
.
C
lu
s
ter
d
at
a
is
p
r
esen
ted
in
T
ab
le
3
.
Tab
le 3
.
Clu
ste
r
d
a
ta fo
r
NR i
n
U
LP
S
u
n
g
g
u
m
i
n
a
sa
C
l
u
st
e
r
f
o
r
N
R
TS
SS
1
44
-
67
41
-
4
2
,
4
2
-
4
3
,
4
3
-
4
4
,
6
2
-
6
3
,
6
3
-
6
4
,
6
4
-
6
5
,
6
5
-
66
2
23
-
76
20
-
2
1
,
2
1
-
2
2
,
2
2
-
2
3
,
7
0
-
7
4
,
7
4
-
7
5
,
7
5
-
76
3
30
-
1
6
5
26
-
2
7
,
2
7
-
2
8
,
2
8
-
2
9
,
2
9
-
3
0
,
1
6
0
-
1
6
1
,
1
6
1
-
1
6
2
,
1
6
2
-
1
6
3
,
1
6
3
-
1
6
4
,
1
6
4
-
1
6
5
4
1
2
0
-
135
1
1
6
-
1
1
7
,
1
1
7
-
1
1
8
,
1
1
8
-
1
2
0
,
1
3
3
-
1
3
4
,
1
3
4
-
135
5
1
0
8
-
151
1
0
4
-
1
0
6
,
1
0
6
-
1
0
7
,
1
0
7
-
1
0
8
,
1
4
9
-
1
5
0
,
1
5
0
-
151
Sev
er
al
s
im
u
lated
ca
s
e
s
tu
d
ies
h
av
e
b
ee
n
c
o
n
d
u
cted
to
ass
ess
th
e
ef
f
ec
tiv
en
ess
o
f
NR
o
p
tim
izatio
n
tech
n
iq
u
es o
p
tim
ized
u
s
in
g
P
SO.
T
h
e
ca
s
e
s
tu
d
ies in
clu
d
e:
−
C
ase
1
.
Activ
atio
n
o
f
1
T
S f
r
o
m
clu
s
ter
1
.
−
C
ase
2
.
Activ
atio
n
o
f
2
T
S f
r
o
m
clu
s
ter
1
an
d
2
.
−
C
ase
3
.
Activ
atio
n
o
f
3
T
S f
r
o
m
clu
s
ter
1
,
2
an
d
3
.
−
C
ase
4
.
Activ
atio
n
o
f
4
T
S f
r
o
m
clu
s
ter
1
,
2
,
3
a
n
d
4
.
−
C
ase
5
.
Activ
atio
n
o
f
5
T
S f
r
o
m
clu
s
ter
1
,
2
,
3
,
4
an
d
5
.
2
.
4
.
P
SO
m
et
ho
d
I
n
PS
O,
ea
ch
p
ar
ticle
n
av
ig
atin
g
th
e
-
d
im
en
s
io
n
al
p
r
o
b
l
em
h
y
p
er
s
p
ac
e
r
e
p
r
esen
ts
a
p
o
ten
tial
s
o
lu
tio
n
f
o
r
a
s
p
ec
if
ic
p
r
o
b
le
m
.
Fo
r
ea
ch
o
f
th
e
two
v
ec
to
r
s
,
is
th
e
p
o
s
itio
n
v
ec
to
r
,
an
d
is
th
e
v
elo
city
v
ec
to
r
.
Ad
d
itio
n
ally
,
ea
ch
p
ar
t
icle
ca
n
r
e
m
em
b
er
its
p
er
s
o
n
al
b
est
ex
p
er
ien
c
e
ev
er
en
c
o
u
n
ter
ed
,
r
ep
r
esen
ted
b
y
th
e
p
er
s
o
n
al
b
est
p
o
s
itio
n
v
ec
to
r
.
T
h
e
p
o
s
itio
n
attain
ed
b
y
th
e
b
est
p
ar
ticle
in
t
h
e
co
m
m
u
n
ity
is
d
e
n
o
ted
as
.
Ma
th
em
atica
lly
,
in
th
e
(
+
1
)
iter
atio
n
o
f
th
e
s
ea
r
ch
p
r
o
c
ess
,
th
e
th
d
im
en
s
io
n
o
f
p
ar
ticle
's
v
elo
city
,
,
(
+
1
)
,
an
d
p
o
s
itio
n
,
(
+
1
)
ar
e
u
p
d
ated
as f
o
llo
w
[
3
3
]
,
[
3
4
]
.
(
+
1
)
=
(
)
+
1
1
(
(
)
−
(
)
)
+
2
2
(
(
)
−
(
)
)
(
5
)
(
+
1
)
=
(
)
+
(
+
1
)
(
6
)
is
s
p
ee
d
o
f
p
a
r
ticle,
1
an
d
2
ar
e
ac
ce
ler
atio
n
c
o
ef
f
icien
t,
1
an
d
2
ar
e
p
o
s
itio
n
o
f
r
an
d
o
m
p
ar
ticle,
is
p
o
s
itio
n
o
f
p
ar
ticle,
is
iter
atio
n
,
is
p
o
s
itio
n
o
f
lo
ca
l
b
est
an
d
is
p
o
s
itio
n
o
f
g
lo
b
al
b
est
[
3
5
]
,
[
3
6
]
.
T
h
e
v
alu
e
o
f
1
=
2
=
2
,
iter
atio
n
=
1
0
0
a
n
d
p
o
p
u
latio
n
=
1
0
0
is
u
s
ed
in
PS
O
p
ar
am
eter
s
.
C
o
n
s
id
er
in
g
th
e
h
ar
m
o
n
ic
in
jectio
n
v
alu
es
p
r
o
v
id
ed
b
y
th
e
t
y
p
e
o
f
n
o
n
lin
ea
r
lo
ad
b
ased
o
n
th
e
lo
ad
ca
teg
o
r
ies
at
UL
P
Su
n
g
g
u
m
in
asa,
a
n
ew
n
etwo
r
k
to
p
o
lo
g
y
is
p
r
o
p
o
s
ed
b
y
ac
tiv
atin
g
a
co
m
b
in
atio
n
o
f
th
e
ex
is
tin
g
T
S
an
d
SS
f
u
n
ctio
n
s
u
s
in
g
th
e
PS
O
m
eth
o
d
.
T
h
is
m
eth
o
d
s
ee
k
s
th
e
o
b
jectiv
e
f
u
n
ctio
n
with
th
e
s
p
ec
if
ied
co
n
s
tr
ain
ts
.
3.
RE
SU
L
T
S
W
h
en
n
o
n
lin
ea
r
lo
ad
s
in
ject
h
ar
m
o
n
ic
cu
r
r
en
ts
in
to
a
n
e
lectr
ical
s
y
s
tem
,
th
e
lev
el
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
g
en
er
ate
d
is
co
n
tin
g
en
t
u
p
o
n
th
e
am
o
u
n
t
o
f
elec
tr
ical
p
o
wer
co
n
s
u
m
e
d
b
y
t
h
e
lo
ad
b
u
s
.
As
th
e
p
o
wer
c
o
n
s
u
m
p
tio
n
i
n
cr
ea
s
es,
th
e
s
ev
er
ity
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
also
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izatio
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Halim
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ess
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s
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o
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e
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s
o
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ly
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p
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.
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%.
T
h
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d
is
cr
ep
a
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d
u
e
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b
s
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tial
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l
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ad
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an
d
th
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ty
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es
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f
h
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r
m
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ic
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s
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ch
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s
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in
th
e
test
o
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jects.
T
h
e
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n
g
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m
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ic
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ich
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if
f
er
s
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ar
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ly
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r
o
m
th
o
s
e
in
th
e
o
th
er
s
y
s
tem
s
s
tu
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ied
.
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h
ile
th
is
s
tu
d
y
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ig
h
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h
ts
th
e
NR
m
eth
o
d
'
s
ca
p
ab
ilit
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ed
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lo
s
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d
im
p
r
o
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g
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e
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it
also
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o
s
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s
in
h
an
d
lin
g
d
iv
er
s
e
lo
a
d
ty
p
es a
n
d
p
o
wer
v
ar
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s
.
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n
s
u
m
m
a
r
y
,
th
e
s
tu
d
y
aim
ed
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ev
alu
ate
th
e
ef
f
ec
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ess
o
f
th
e
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m
eth
o
d
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o
p
tim
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e
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P
Su
n
g
g
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m
i
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1
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s
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y
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te
m
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T
h
e
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in
d
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g
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u
n
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e
r
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co
r
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t
h
e
im
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r
tan
ce
o
f
co
n
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id
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g
lo
ad
ch
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r
ac
ter
is
tics
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d
h
ar
m
o
n
ic
lo
a
d
ty
p
es
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o
p
tim
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n
p
r
o
ce
s
s
es.
W
h
ile
th
e
NR
m
et
h
o
d
s
h
o
wed
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o
ten
tial,
its
v
ar
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r
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ee
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I
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t J E
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esear
ch
s
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o
u
ld
e
x
p
lo
r
e
m
o
r
e
ad
ap
tiv
e
tech
n
i
q
u
es
th
at
c
an
ac
co
m
m
o
d
ate
th
e
d
iv
er
s
e
lo
ad
p
r
o
f
iles
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d
h
ar
m
o
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ic
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tu
r
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ce
s
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co
m
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lex
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y
s
tem
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lik
e
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P
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n
g
g
u
m
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asa.
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an
s
wer
ed
q
u
esti
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n
s
r
em
ain
r
eg
a
r
d
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ir
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u
ch
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n
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4.
CO
NCLU
SI
O
N
I
n
th
is
s
tu
d
y
,
we
in
v
esti
g
ated
th
e
im
p
ac
t
o
f
n
o
n
lin
ea
r
lo
ad
s
,
s
u
ch
as
VFDs
,
in
v
er
tin
g
d
ev
ices,
an
d
f
lu
o
r
escen
t
lam
p
s
,
o
n
th
e
1
6
5
-
b
u
s
UL
P
Su
n
g
g
u
m
in
asa
s
y
s
tem
,
s
p
ec
if
ically
f
o
c
u
s
in
g
o
n
th
e
r
esu
ltin
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
an
d
th
ei
r
ef
f
ec
t
o
n
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
e
NR
o
p
tim
izatio
n
tech
n
iq
u
e,
u
tili
zin
g
th
e
PS
O
m
eth
o
d
,
was
e
m
p
lo
y
ed
to
m
in
im
ize
%THD
v
an
d
to
t
al
lo
s
s
es
with
in
p
r
ed
e
f
in
ed
li
m
its
.
Ou
r
f
i
n
d
in
g
s
in
d
icate
th
at
C
ase
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,
wh
ich
i
n
v
o
lv
e
d
th
e
ac
tiv
atio
n
o
f
all
tie
s
witch
es,
d
em
o
n
s
tr
ated
t
h
e
h
ig
h
est
lev
el
o
f
ef
f
ec
tiv
en
ess
am
o
n
g
all
s
im
u
lated
ca
s
e
s
tu
d
ies.
T
h
is
was
ev
id
en
ce
d
b
y
a
s
ig
n
if
ica
n
t
r
e
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c
tio
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to
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e
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ag
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v
b
y
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.
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8
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.
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9
2
%).
Ad
d
itio
n
ally
,
th
e
a
v
er
ag
e
b
u
s
v
o
ltag
e
lev
el
in
c
r
ea
s
ed
b
y
0
.
0
0
2
5
4
p
u
(
0
.
2
6
3
5
%).
T
h
ese
r
esu
lts
h
ig
h
lig
h
t
th
e
p
o
ten
tial
o
f
th
e
NR
o
p
tim
izati
o
n
tech
n
i
q
u
e
in
en
h
a
n
cin
g
s
y
s
tem
p
er
f
o
r
m
an
ce
,
alb
eit
with
v
ar
y
in
g
d
eg
r
ee
s
o
f
ef
f
ec
tiv
en
ess
co
m
p
ar
e
d
to
p
r
e
v
io
u
s
r
esear
ch
o
n
o
th
er
s
y
s
te
m
s
.
T
h
e
r
elativ
ely
lo
wer
ef
f
ec
tiv
en
ess
o
b
s
er
v
ed
in
o
u
r
s
tu
d
y
u
n
d
er
s
co
r
es
th
e
cr
itical
im
p
ac
t
o
f
lo
ad
ch
ar
ac
ter
is
tics
an
d
th
e
ty
p
es
o
f
n
o
n
lin
ea
r
lo
ad
s
o
n
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
.
T
h
is
s
u
g
g
ests
th
at
wh
ile
th
e
N
R
m
et
h
o
d
is
b
en
ef
icial,
it
m
ay
r
eq
u
ir
e
in
teg
r
atio
n
with
o
th
er
o
p
tim
izatio
n
tech
n
iq
u
es
to
ad
d
r
ess
th
e
u
n
iq
u
e
ch
allen
g
es
p
o
s
ed
b
y
d
if
f
e
r
en
t
p
o
wer
s
y
s
tem
s
ef
f
ec
tiv
ely
.
T
h
e
co
n
tr
i
b
u
tes
o
f
r
esear
ch
t
o
th
e
f
ield
b
y
p
r
o
v
id
in
g
a
n
u
an
ce
d
u
n
d
er
s
tan
d
in
g
o
f
h
o
w
d
if
f
er
en
t
t
y
p
es
o
f
n
o
n
lin
ea
r
lo
ad
s
af
f
ec
t
t
h
e
p
er
f
o
r
m
an
ce
o
f
p
o
wer
s
y
s
tem
s
a
n
d
th
e
e
f
f
ec
tiv
en
ess
o
f
o
p
tim
izatio
n
tech
n
iq
u
es
lik
e
th
e
NR
m
eth
o
d
.
T
h
ese
f
i
n
d
in
g
s
em
p
h
asize
th
e
n
ee
d
f
o
r
tailo
r
ed
o
p
tim
izatio
n
s
tr
ateg
ies
th
at
co
n
s
id
er
th
e
s
p
ec
if
ic
lo
ad
p
r
o
f
iles
an
d
h
ar
m
o
n
ic
ch
a
r
ac
ter
is
tics
o
f
ea
ch
s
y
s
tem
.
Fu
tu
r
e
r
esear
ch
s
h
o
u
ld
f
o
c
u
s
o
n
co
m
b
in
in
g
v
ar
i
o
u
s
o
p
tim
izatio
n
tech
n
iq
u
es
to
f
u
r
t
h
er
en
h
a
n
ce
s
y
s
tem
p
er
f
o
r
m
an
c
e,
p
a
r
ticu
lar
ly
in
r
ed
u
cin
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
.
A
d
d
itio
n
ally
,
in
v
esti
g
atin
g
th
e
im
p
ac
t
o
f
s
tr
ateg
ic
p
lace
m
en
t
o
f
ch
ar
g
in
g
s
tatio
n
s
f
o
r
elec
tr
ic
v
eh
icles
co
u
ld
o
f
f
er
n
ew
in
s
ig
h
ts
in
to
m
an
ag
in
g
h
ar
m
o
n
ic
l
o
ad
s
an
d
im
p
r
o
v
in
g
o
v
er
all
s
y
s
tem
s
tab
ilit
y
an
d
ef
f
icien
cy
.
B
y
ad
d
r
ess
in
g
th
ese
ar
ea
s
,
we
ca
n
d
ev
elo
p
m
o
r
e
r
o
b
u
s
t
an
d
ad
ap
tiv
e
o
p
tim
izatio
n
ap
p
r
o
ac
h
es
th
at
ca
te
r
to
th
e
ev
o
lv
in
g
d
em
an
d
s
o
f
m
o
d
er
n
p
o
wer
s
y
s
tem
s
,
u
ltima
tely
c
o
n
tr
i
b
u
tin
g
to
im
p
r
o
v
ed
r
eliab
ilit
y
an
d
p
e
r
f
o
r
m
an
ce
f
o
r
th
e
co
m
m
u
n
ity
.
ACK
NO
WL
E
DG
E
M
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NT
S
Fin
an
cial
s
u
p
p
o
r
t
f
o
r
th
is
s
tu
d
y
is
p
r
o
v
id
e
d
b
y
t
h
e
Ad
v
an
ce
d
I
n
d
o
n
esia
I
I
I
I
n
n
o
v
atio
n
R
esear
ch
Pro
g
r
am
(
R
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3
-
B
R
I
N)
-
L
PDP I
n
d
o
n
esia.
RE
F
E
R
E
NC
E
S
[
1
]
H
.
A
z
a
d
i
,
B
.
A
k
b
a
r
i
,
a
n
d
M
.
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.
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e
p
a
s
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a
n
,
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o
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u
a
l
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h
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me
n
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s u
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t
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,
”
2
0
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S
m
a
r
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ri
d
C
o
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2
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M
.
J.
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.
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o
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h
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d
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I
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2
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8
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I
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Vo
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14
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6
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Dec
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24
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6
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6
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6074
B
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c
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.
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I
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