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Har
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3
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th
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[
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[
1
1
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T
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I
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Fro
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p
h
ase
b
an
k
s
o
f
s
in
g
le
-
p
h
ase
tr
an
s
f
o
r
m
e
r
s
ar
e
ex
p
ec
ted
to
b
e
u
s
ed
in
wy
e
–
d
elta
co
n
n
ec
tio
n
(
w
h
en
th
e
th
r
ee
-
p
h
ase
lo
ad
is
g
r
ea
ter
th
a
n
th
e
s
in
g
le
-
p
h
ase
l
o
ad
)
o
r
in
a
n
-
o
p
en
d
elta
co
n
n
ec
tio
n
if
th
is
is
n
o
t
th
e
ca
s
e.
I
n
th
e
ca
s
e
o
f
th
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
er
s
an
d
th
r
ee
-
p
h
ase
b
an
k
s
with
wy
e
co
n
n
ec
tio
n
s
,
th
e
a
n
aly
tical
m
eth
o
d
h
as
b
ee
n
g
en
er
alize
d
to
d
eter
m
in
e
th
e
lo
s
s
es
in
th
e
p
r
esen
ce
o
f
l
o
ad
s
with
h
ar
m
o
n
ic
co
n
ten
t
[
1
4
]
–
[
1
7
]
.
I
n
th
ese
ca
s
es,
th
e
m
eth
o
d
o
l
o
g
y
is
ap
p
lied
b
y
d
eter
m
in
in
g
th
e
f
ac
to
r
s
o
f
c
o
p
p
er
,
e
d
d
y
cu
r
r
en
ts
,
an
d
o
th
er
s
tr
ay
lo
s
s
es.
T
h
is
m
eth
o
d
o
l
o
g
y
y
ield
s
p
r
ec
is
e
v
alu
es
f
o
r
b
an
k
s
with
wy
e
–
wy
e
co
n
n
ec
tio
n
s
.
Ho
wev
er
,
wh
en
th
e
b
an
k
'
s
tr
an
s
f
o
r
m
er
s
d
o
n
o
t
h
av
e
e
q
u
al
ca
p
ac
ity
,
o
r
th
ese
tr
an
s
f
o
r
m
er
s
ar
e
n
o
t
lo
ad
ed
in
th
e
s
a
m
e
way
(
th
r
ee
-
p
h
ase
s
y
s
tem
with
s
in
g
le
-
p
h
ase
l
o
a
d
s
)
,
th
e
an
aly
tical
m
et
h
o
d
o
n
ly
o
f
f
er
s
th
e
to
tal
th
r
ee
-
p
h
ase
lo
s
s
es
o
f
th
e
b
a
n
k
[
1
8
]
,
[
1
9
]
.
I
t is n
o
t a
c
cu
r
ate
to
d
eter
m
in
e
ea
ch
t
r
an
s
f
o
r
m
er
in
d
iv
id
u
ally
.
T
h
is
r
esear
ch
aim
s
to
p
r
o
p
o
s
e
an
ad
ju
s
tm
en
t
to
th
e
a
n
aly
tical
m
o
d
el
o
f
th
e
ANSI
/I
E
E
E
Std
.
C
5
7
.
1
1
0
u
s
es
d
ig
ital
s
im
u
latio
n
to
d
eter
m
in
e
th
e
lo
ad
l
o
s
s
es
in
a
th
r
ee
-
p
h
ase
b
an
k
o
f
th
r
ee
s
in
g
le
-
p
h
ase
tr
an
s
f
o
r
m
e
r
s
with
d
if
f
er
en
t
c
o
n
n
ec
tio
n
s
ch
em
es.
T
o
d
o
th
is
,
we
s
tar
t
b
y
d
escr
ib
in
g
th
e
a
n
aly
tical
m
eth
o
d
p
r
o
v
id
e
d
b
y
th
e
s
tan
d
ar
d
f
o
r
s
in
g
le
-
p
h
ase
d
r
y
co
r
e
o
r
o
il
-
f
illed
tr
an
s
f
o
r
m
er
s
an
d
b
ased
o
n
th
e
p
a
r
a
m
eter
s
o
f
th
e
b
an
k
tr
an
s
f
o
r
m
er
s
an
d
t
h
e
ch
ar
ac
te
r
izatio
n
o
f
th
e
n
o
n
-
lin
ea
r
lo
a
d
,
o
b
tain
th
e
c
u
r
r
e
n
ts
an
d
v
o
l
tag
es
th
at
cir
cu
late
th
r
o
u
g
h
th
e
win
d
in
g
s
o
f
ea
c
h
m
ac
h
in
e
th
at
f
o
r
m
s
t
h
e
th
r
ee
-
p
h
ase
b
an
k
.
T
h
e
ad
v
an
tag
e
o
f
th
e
ad
ju
s
ted
m
o
d
el
lies
in
th
e
p
o
s
s
ib
ilit
y
o
f
b
ei
n
g
u
s
ed
in
th
r
ee
-
p
h
ase
b
an
k
s
o
f
s
in
g
le
-
p
h
ase
tr
a
n
s
f
o
r
m
e
r
s
with
an
y
co
n
n
ec
tio
n
s
ch
em
e,
also
d
eter
m
in
in
g
th
e
lo
ad
lo
s
s
es
with
g
r
ea
ter
p
r
ec
is
io
n
in
th
ese
ca
s
e
s
in
wh
ich
th
er
e
is
n
o
d
ir
ec
t
co
r
r
esp
o
n
d
en
ce
b
etwe
en
th
e
cu
r
r
en
ts
o
f
th
e
f
ee
d
er
s
an
d
t
h
o
s
e
o
f
th
e
win
d
in
g
s
in
th
r
e
e
-
p
h
ase
d
is
tr
ib
u
tio
n
s
y
s
tem
s
,
u
n
b
alan
ce
d
an
d
with
h
ig
h
co
n
ten
ts
o
f
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
o
f
th
e
cu
r
r
e
n
ts
.
T
h
e
p
r
ac
tical
im
p
o
r
tan
ce
o
f
th
e
s
tu
d
y
o
f
p
o
wer
q
u
ality
,
esp
ec
ially
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
a
n
d
its
in
f
lu
en
ce
o
n
tr
a
n
s
f
o
r
m
atio
n
lo
s
s
es,
lies
in
r
elatin
g
t
h
e
tech
n
ical
i
m
p
r
o
v
e
m
en
ts
th
at
ca
n
b
e
ap
p
l
ied
with
tech
n
ical
im
p
ac
ts
th
a
t
r
esu
lt
in
ec
o
n
o
m
ic
b
en
ef
its
,
b
o
t
h
f
o
r
th
e
c
o
m
p
a
n
y
s
u
p
p
lier
as
well
as
f
o
r
u
s
er
s
an
d
en
v
ir
o
n
m
en
tal
r
esu
lts
lin
k
ed
to
th
e
m
itig
atio
n
o
f
th
e
ef
f
ec
ts
o
f
p
o
llu
tin
g
g
ase
s
r
esu
ltin
g
f
r
o
m
g
en
er
atio
n
.
2.
M
E
T
H
O
D
2
.
1
.
Ana
ly
t
ica
l m
e
t
ho
d f
o
r
e
s
t
im
a
t
ing
lo
a
d lo
s
s
es in e
lect
ric
t
ra
ns
f
o
rm
er
s
T
h
e
lev
el
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
is
d
escr
ib
ed
b
y
th
e
to
tal
h
ar
m
o
n
ic
s
p
ec
tr
u
m
u
s
in
g
ea
ch
co
m
p
o
n
en
t'
s
m
ag
n
itu
d
es
an
d
p
h
ase
an
g
le
[
1
]
.
T
h
e
i
n
d
ic
ato
r
f
r
eq
u
en
tly
u
s
ed
t
o
ev
al
u
ate
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
th
e
v
o
ltag
e
a
n
d
c
u
r
r
en
t
wav
ef
o
r
m
is
th
e
t
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
.
T
h
e
T
HD
r
ep
r
esen
ts
a
m
ea
s
u
r
e
ex
p
r
ess
ed
as
a
p
e
r
c
en
tag
e
o
f
th
e
h
ar
m
o
n
ic
p
o
ll
u
tio
n
lev
el
o
f
a
s
y
s
tem
,
an
d
its
v
alu
e
ca
n
b
e
ca
lcu
lated
b
y
(
1
)
[
2
0
]
,
[
2
1
]
.
=
√
(
1
)
2
−
1
∙
100
(
1
)
w
h
er
e,
is
th
e
m
ea
s
u
r
ed
ac
tu
al
r
m
s
v
o
ltag
e
o
r
cu
r
r
e
n
t,
1
is
t
h
e
ef
f
ec
tiv
e
v
o
ltag
e
o
r
cu
r
r
e
n
t
o
f
th
e
f
u
n
d
am
e
n
tal
h
ar
m
o
n
ic
o
f
t
h
e
s
ig
n
al,
an
d
is
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
f
o
r
v
o
ltag
e
(
)
o
r
f
o
r
cu
r
r
en
t (
)
ex
p
r
ess
ed
in
p
er
ce
n
t
.
I
n
g
e
n
er
al,
th
e
to
tal
lo
s
s
es
(
)
i
n
tr
an
s
f
o
r
m
er
s
ca
n
b
e
in
clu
d
e
d
with
in
t
h
e
lo
a
d
an
d
n
o
-
lo
a
d
lo
s
s
es
o
f
th
e
tr
an
s
f
o
r
m
e
r
[
7
]
,
[
8
]
,
[
1
0
]
,
[
1
2
]
.
=
+
(
2
)
w
h
er
e,
ar
e
th
e
n
o
-
lo
ad
lo
s
s
es,
an
d
ar
e
th
e
lo
ad
lo
s
s
es.
No
-
lo
ad
o
r
co
r
e
lo
s
s
es
ar
e
d
u
e
to
f
lo
w
v
a
r
iatio
n
s
th
at
cir
cu
late
th
r
o
u
g
h
th
e
c
o
r
e
m
ater
ial
o
v
er
tim
e.
Fo
r
v
alu
es
less
th
a
n
8
%
o
f
T
H
Dv
,
th
e
n
o
-
lo
ad
lo
s
s
es
in
th
e
t
r
an
s
f
o
r
m
er
ar
e
co
n
s
id
er
ed
c
o
n
s
tan
t
[
7
]
,
[
8
]
,
[
1
0
]
,
[
1
2
]
.
L
o
a
d
lo
s
s
es,
r
esu
ltin
g
f
r
o
m
h
ar
m
o
n
ics,
ca
n
b
e
d
iv
id
ed
in
to
J
o
u
le
e
f
f
ec
t
l
o
s
s
es,
also
ca
lled
o
h
m
ic
o
r
co
p
p
er
lo
s
s
es,
p
r
esen
t
in
th
e
co
p
p
er
o
f
th
e
tr
an
s
f
o
r
m
e
r
win
d
in
g
s
[
8
]
,
[
9
]
,
[
1
1
]
,
[
1
2
]
,
an
d
in
to
ad
d
itio
n
al
lo
s
s
es
d
u
e
to
ed
d
y
cu
r
r
en
ts
.
T
h
ese
lo
s
s
es
wil
l
in
cr
ea
s
e
in
a
q
u
ad
r
atic
p
r
o
p
o
r
tio
n
with
th
e
lo
ad
cu
r
r
en
t
an
d
as
th
e
s
q
u
ar
e
o
f
t
h
e
f
r
e
q
u
en
c
y
[
9
]
.
O
n
th
e
o
th
e
r
h
an
d
,
th
e
l
o
ad
lo
s
s
es
ca
n
b
e
o
b
tain
e
d
p
r
ac
tically
f
r
o
m
th
e
m
ac
h
in
e'
s
s
h
o
r
t
-
cir
cu
it test.
T
h
is
ca
n
b
e
ex
p
r
ess
ed
in
th
e
f
o
llo
win
g
wa
y
:
[
7
]
,
[
8
]
,
[
1
0
]
,
[
1
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
S
imu
la
tio
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f lo
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s
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a
th
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p
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f tra
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r
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(
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co
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)
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=
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w
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in
th
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in
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itio
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d
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u
r
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ar
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ay
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Ad
d
itio
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d
y
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r
r
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n
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lo
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also
ca
lled
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u
e
t
o
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tr
ay
f
lu
x
in
t
h
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co
r
e,
c
o
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e
clam
p
,
tan
k
wall,
an
d
o
th
e
r
s
tr
u
ctu
r
al
p
a
r
ts
o
f
t
h
e
tr
an
s
f
o
r
m
er
.
T
h
e
o
th
e
r
ad
d
itio
n
al
lo
s
s
es
in
clu
d
e
“E
d
d
y
C
u
r
r
en
t”
lo
s
s
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th
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win
d
in
g
co
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s
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d
lo
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es
d
u
e
t
o
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f
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en
ts
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ar
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is
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B
y
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atu
r
e,
th
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e
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ac
tical
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r
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ate
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d
itio
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d
y
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r
r
en
t
lo
s
s
es
f
r
o
m
th
e
o
th
er
f
u
r
th
er
lo
s
s
es.
Fo
r
th
is
r
ea
s
o
n
,
th
e
to
tal
a
d
d
it
io
n
al
lo
s
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es
(
)
,
m
ad
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u
p
o
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th
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s
u
m
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f
with
,
a
r
e
ca
lcu
lated
f
r
o
m
th
e
d
if
f
er
e
n
ce
b
etwe
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th
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lo
ad
lo
s
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a
n
d
th
e
co
p
p
e
r
J
o
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le
ef
f
ec
t lo
s
s
es,
u
s
in
g
th
e
ex
p
r
ess
io
n
(
4
)
.
=
+
=
−
(
4
)
w
h
er
e,
ar
e
th
e
co
p
p
er
lo
s
s
es in
th
e
tr
an
s
f
o
r
m
er
.
T
h
e
co
p
p
er
lo
s
s
es wil
l b
e
ca
lcu
lated
b
y
e
x
p
r
ess
io
n
(
5
)
.
=
2
(
5
)
w
h
er
e,
is
th
e
ef
f
ec
tiv
e
v
alu
e
o
f
th
e
tr
an
s
f
o
r
m
er
lo
ad
c
u
r
r
en
t,
an
d
is
th
e
d
ir
ec
t
cu
r
r
en
t
r
es
is
tan
ce
o
f
th
e
win
d
in
g
.
Fro
m
th
e
t
h
eo
r
y
o
f
an
al
y
s
is
o
f
n
o
n
-
s
in
u
s
o
id
al
p
er
io
d
ic
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ig
n
als,
it
is
k
n
o
wn
th
at,
in
th
e
p
r
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ce
o
f
h
ar
m
o
n
ics,
th
e
ef
f
ec
tiv
e
v
alu
e
o
f
th
e
s
ig
n
al
is
d
eter
m
in
ed
b
y
ex
p
r
ess
io
n
(
6
)
.
=
√
∑
ℎ
2
∞
ℎ
=
1
(
6
)
T
h
en
th
e
elec
tr
ical
lo
s
s
es a
r
e
d
eter
m
in
ed
ac
c
o
r
d
in
g
to
[
1
0
]
u
s
in
g
ex
p
r
ess
io
n
(
7
)
.
=
∑
ℎ
2
∞
ℎ
=
1
(
7
)
Fo
r
its
p
ar
t,
th
e
lo
s
s
es
d
u
e
t
o
p
a
r
asit
ic
cu
r
r
en
ts
o
f
th
e
tr
an
s
f
o
r
m
er
ca
n
b
e
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eter
m
in
e
d
ac
co
r
d
in
g
to
[
1
2
]
th
r
o
u
g
h
th
e
e
x
p
r
ess
io
n
(
8
)
.
=
∙
∑
(
ℎ
)
2
ℎ
2
∞
ℎ
=
1
(
8
)
w
h
er
e,
ar
e
th
e
n
o
m
in
al
ed
d
y
cu
r
r
en
t
lo
s
s
es
o
f
th
e
tr
an
s
f
o
r
m
er
,
an
d
is
th
e
ef
f
ec
tiv
e
v
alu
e
o
f
th
e
n
o
m
in
al
cu
r
r
en
t
o
f
th
e
tr
a
n
s
f
o
r
m
er
.
Acc
o
r
d
in
g
to
th
e
ANSI
/I
E
E
E
C
5
7
.
1
1
0
s
tan
d
ar
d
,
it
is
estab
li
s
h
ed
th
at
th
e
n
o
m
in
al
v
alu
e
o
f
th
e
o
th
er
s
tr
ay
lo
s
s
es
(
p
OSLn
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is
6
7
%
o
f
th
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to
tal
lo
s
s
es
(
p
TAL
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f
o
r
o
il
tr
an
s
f
o
r
m
er
s
a
n
d
3
3
%
f
o
r
d
r
y
tr
an
s
f
o
r
m
er
s
[
1
2
]
.
C
o
n
s
id
er
in
g
th
is
cr
iter
io
n
,
it is
p
r
o
p
o
s
ed
th
at
th
e
o
th
er
a
d
d
itio
n
al
lo
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s
es will b
e
d
eter
m
in
ed
ac
co
r
d
in
g
to
(
9
)
.
=
∙
∑
(
ℎ
)
2
ℎ
0
.
8
∞
ℎ
=
1
(
9
)
2
.
2
.
H
a
rmo
nic lo
s
s
f
a
ct
o
rs (
F
HL
)
T
h
e
h
ar
m
o
n
ic
lo
s
s
f
ac
to
r
is
estab
lis
h
ed
as
a
p
r
o
p
o
r
tio
n
ality
f
ac
to
r
ap
p
lied
to
th
e
lo
s
s
es
in
co
n
d
itio
n
s
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
I
t
r
ep
r
esen
ts
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
lo
s
s
es
in
th
e
tr
an
s
f
o
r
m
er
with
h
ar
m
o
n
ics
an
d
th
ese
lo
s
s
es
in
n
o
m
in
al
c
o
n
d
itio
n
s
,
o
r
th
at
wo
u
ld
b
e
h
ad
with
p
u
r
ely
s
in
u
s
o
id
al
s
ig
n
als
[
1
2
]
.
T
h
ey
ar
e
r
ep
r
esen
ted
ac
co
r
d
in
g
to
(
1
0
)
.
=
(
1
0
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w
h
er
e,
ar
e
th
e
lo
s
s
es in
th
e
p
r
esen
ce
o
f
h
ar
m
o
n
ics,
an
d
ar
e
th
e
n
o
m
in
al
l
o
s
s
es.
I
n
th
is
way
,
th
e
c
o
p
p
e
r
lo
s
s
es c
an
b
e
d
eter
m
in
ed
u
s
in
g
(
1
1
)
.
=
=
√
∑
ℎ
2
∞
ℎ
=
1
2
=
√
∑
ℎ
2
∞
ℎ
=
1
2
(
1
1
)
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.
1
4
,
No
.
5
,
Octo
b
e
r
2
0
2
4
:
4
8
2
7
-
4
8
3
7
4830
E
x
p
r
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n
(
1
2
)
is
u
s
ed
to
ca
lc
u
late
ed
d
y
c
u
r
r
e
n
t lo
s
s
es.
=
=
∙
∑
(
ℎ
)
2
ℎ
2
∞
ℎ
=
1
=
∑
(
ℎ
)
2
ℎ
2
∞
ℎ
=
1
=
−
(
1
2
)
Fo
r
th
e
o
th
e
r
s
tr
ay
lo
s
s
es,
ex
p
r
ess
io
n
(
1
3
)
is
u
s
ed
.
=
=
∙
∑
(
ℎ
)
2
ℎ
0
.
8
∞
ℎ
=
1
=
∑
(
ℎ
)
2
ℎ
0
.
8
∞
ℎ
=
1
(
1
3
)
I
n
th
e
ca
s
e
o
f
th
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
er
s
an
d
th
r
ee
-
p
h
ase
b
a
n
k
s
with
wy
e
co
n
n
ec
tio
n
s
,
th
e
an
aly
tical
m
eth
o
d
h
as
b
ee
n
g
en
e
r
alize
d
to
d
eter
m
in
e
th
e
lo
s
s
es
in
th
e
p
r
esen
ce
o
f
lo
ad
s
with
h
ar
m
o
n
ic
co
n
ten
t
[
5
]
,
[
9
]
.
I
n
th
ese
ca
s
es,
th
e
m
eth
o
d
o
l
o
g
y
is
ap
p
lied
b
y
s
elec
tin
g
t
h
e
f
ac
to
r
s
o
f
co
p
p
er
l
o
s
s
es
d
u
e
to
p
a
r
asit
ic
an
d
ad
d
itio
n
al
cu
r
r
en
ts
as a
n
av
er
a
g
e
o
f
th
e
m
p
er
p
h
ase
o
f
th
e
b
a
n
k
[
6
]
,
[
9
]
.
=
Ø
+
Ø
+
Ø
3
(
1
4
)
w
h
er
e,
Ø
,
Ø
,
Ø
ar
e
th
e
lo
s
s
es
d
u
e
to
h
ar
m
o
n
ics
f
o
r
p
h
ases
A,
B
an
d
C
r
esp
ec
tiv
ely
.
Fin
ally
,
th
e
th
r
ee
-
p
h
ase
l
o
s
s
es
o
f
th
e
tr
an
s
f
o
r
m
er
o
r
b
an
k
ar
e
d
eter
m
i
n
ed
b
y
m
u
ltip
ly
in
g
th
e
r
esp
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tiv
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f
ac
to
r
s
b
y
th
e
n
o
m
in
al
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r
ee
-
p
h
ase
lo
s
s
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2
.
3
.
M
o
del f
o
r
dig
it
a
l sim
ula
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n o
f
t
he
t
hree
-
ph
a
s
e
ba
nk
o
f
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ing
le
-
ph
a
s
e
t
ra
ns
f
o
rm
er
s
T
h
e
b
asic
m
o
d
el
t
o
d
eter
m
i
n
e
th
e
lo
ad
lo
s
s
es
in
th
e
tr
an
s
f
o
r
m
er
th
r
o
u
g
h
s
im
u
latio
n
is
b
a
s
ed
o
n
th
e
s
ch
em
e
in
Fig
u
r
e
1
.
T
h
e
s
y
s
tem
is
b
ased
o
n
th
e
m
o
d
el
o
f
a
tr
an
s
f
o
r
m
er
a
n
d
its
p
ar
am
eter
s
,
wh
ich
co
r
r
esp
o
n
d
to
th
e
d
ata
o
f
its
eq
u
iv
alen
t
cir
cu
it,
wh
ich
ar
e
o
b
tain
ed
f
r
o
m
lab
o
r
ato
r
y
test
s
.
T
h
e
t
r
an
s
f
o
r
m
er
s
u
p
p
lies
p
o
wer
to
a
n
o
n
-
lin
ea
r
lo
a
d
,
wh
ich
is
d
esig
n
ed
b
ased
o
n
th
e
v
alu
es
o
f
th
e
in
d
iv
id
u
al
h
ar
m
o
n
ics o
f
th
e
cu
r
r
e
n
t.
Fig
u
r
e
1
.
Mo
d
el
f
o
r
s
im
u
latio
n
an
d
a
d
ju
s
tm
en
t o
f
lo
s
s
ca
lcu
latio
n
T
h
e
s
im
u
latio
n
allo
ws
o
b
tain
i
n
g
th
e
d
is
cr
ete
v
alu
es
o
f
th
e
v
o
ltag
es
an
d
cu
r
r
en
ts
at
two
p
o
in
ts
in
th
e
s
y
s
tem
,
s
p
ec
if
ically
,
th
e
v
o
ltag
es
an
d
cu
r
r
en
ts
in
th
e
tr
an
s
f
o
r
m
er
win
d
i
n
g
s
(
v
w
an
d
i
w
)
a
n
d
th
e
v
o
ltag
es
an
d
cu
r
r
en
ts
in
th
e
lin
e
(
v
L
an
d
i
L
)
.
T
h
e
d
ig
ital
p
r
o
ce
s
s
in
g
o
f
th
e
s
ig
n
als
will
allo
w
o
b
tai
n
in
g
t
h
e
h
a
r
m
o
n
ic
s
p
ec
tr
u
m
o
f
t
h
e
cu
r
r
en
ts
in
t
h
e
tr
an
s
f
o
r
m
er
win
d
in
g
s
,
th
e
T
HD
v
alu
e,
ca
lcu
latin
g
th
e
el
ec
tr
ical
lo
s
s
es,
an
d
d
eter
m
in
in
g
t
h
e
ac
tiv
e,
r
ea
cti
v
e,
d
is
to
r
tio
n
,
a
n
d
ap
p
ar
en
t
p
o
wer
s
f
o
r
ea
ch
o
f
th
e
win
d
in
g
s
o
f
th
e
tr
a
n
s
f
o
r
m
e
r
.
Fin
ally
,
th
e
n
o
m
i
n
al
d
ata
o
f
t
h
e
m
ac
h
in
e
a
n
d
th
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
o
f
t
h
e
cu
r
r
en
ts
in
th
e
win
d
in
g
s
ar
e
u
s
ed
to
d
eter
m
in
e
th
e
lo
ad
l
o
s
s
es u
s
in
g
th
e
an
al
y
tical
m
eth
o
d
o
f
A
NSI
/I
E
E
E
Std
.
C
5
7
.
1
1
0
[
1
2
]
.
Fro
m
th
e
en
er
g
y
d
iag
n
o
s
is
in
elec
tr
ical
s
er
v
ice,
it
is
p
o
s
s
ib
le
to
m
ea
s
u
r
e
th
e
av
er
ag
e
v
al
u
es
o
f
th
e
in
d
iv
id
u
al
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
f
th
e
lin
e
cu
r
r
en
ts
u
s
in
g
a
r
ec
o
r
d
in
g
in
s
tr
u
m
e
n
t
(
th
r
ee
-
p
h
ase
n
etwo
r
k
an
aly
ze
r
)
.
W
ith
th
ese
m
ea
s
u
r
em
en
ts
,
it
is
p
o
s
s
ib
le
to
b
u
ild
th
e
n
o
n
lin
ea
r
lo
ad
m
o
d
e
l
ac
co
r
d
in
g
t
o
its
d
ev
elo
p
m
e
n
t in
th
e
Fo
u
r
ier
s
er
ies
.
(
)
=
∑
[
ℎ
(
ℎ
+
ℎ
)
]
∞
ℎ
=
1
(
1
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
S
imu
la
tio
n
o
f lo
s
s
es in
a
th
r
e
e
-
p
h
a
s
e
b
a
n
k
o
f tra
n
s
fo
r
mers
i
n
th
e
p
r
esen
ce
o
f
…
(
F
r
a
n
k
G
r
a
u
-
Mer
co
n
ch
in
i
)
4831
w
h
er
e,
ℎ
is
th
e
am
p
litu
d
e
o
f
th
e
h
-
o
r
d
er
h
a
r
m
o
n
ic
o
f
th
e
s
ig
n
al,
an
d
ℎ
is
th
e
p
h
ase
s
h
if
t
o
f
th
e
h
-
o
r
d
er
h
ar
m
o
n
ic
o
f
th
e
s
ig
n
al.
Fro
m
th
e
am
p
litu
d
e
an
d
p
h
ase
s
p
ec
tr
u
m
o
f
th
e
lin
e
cu
r
r
en
t
s
,
it
is
p
o
s
s
ib
le
to
r
ec
o
n
s
tr
u
ct
th
e
c
u
r
r
en
t
s
ig
n
al
as
a
s
u
m
o
f
cu
r
r
en
t
s
o
u
r
ce
s
o
f
am
p
litu
d
e
ℎ
with
a
p
h
ase
s
h
if
t
an
g
le
ℎ
as
r
ep
r
esen
ted
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
No
n
lin
ea
r
lo
a
d
m
o
d
el
b
ased
o
n
th
e
in
d
iv
id
u
al
h
ar
m
o
n
ics o
f
th
e
cu
r
r
e
n
ts
Fo
r
th
e
tr
an
s
f
o
r
m
er
s
im
u
latio
n
,
th
e
th
r
ee
-
win
d
i
n
g
lin
ea
r
tr
an
s
f
o
r
m
er
,
wh
o
s
e
d
ata
co
m
es
f
r
o
m
th
e
Stein
m
etz
m
o
d
el
[
7
]
.
O
b
tain
e
d
f
r
o
m
th
e
n
o
m
in
al
v
al
u
es
o
f
th
e
tr
an
s
f
o
r
m
er
a
n
d
p
a
r
am
ete
r
s
o
f
its
eq
u
iv
alen
t
cir
cu
it
d
eter
m
in
ed
f
r
o
m
th
e
te
s
ts
,
will
b
e
u
s
ed
,
Fig
u
r
e
3
.
T
h
is
m
o
d
el
elem
en
t
aim
s
to
o
b
ta
in
th
e
v
o
ltag
es
a
n
d
cu
r
r
en
ts
in
th
e
m
ac
h
in
e
win
d
in
g
s
.
Fig
u
r
e
3
.
E
x
ac
t e
q
u
i
v
alen
t c
ir
cu
it r
ef
er
r
e
d
to
th
e
h
ig
h
v
o
ltag
e
s
id
e
2
.
4
.
P
r
a
ct
ica
l i
m
plem
ent
a
t
io
n in a
ca
s
e
s
t
ud
y
T
h
e
in
d
u
s
tr
ial
elec
tr
ical
s
er
v
ice
o
f
t
h
e
s
o
y
b
ea
n
p
r
o
ce
s
s
in
g
p
lan
t,
b
elo
n
g
i
n
g
to
th
e
C
er
ea
ls
B
ase
B
u
s
in
ess
Un
it
o
f
San
tiag
o
d
e
C
u
b
a,
is
p
ar
t
o
f
a
th
r
ee
-
p
h
ase
b
an
k
o
f
th
r
ee
s
in
g
le
-
p
h
ase
tr
an
s
f
o
r
m
er
s
,
with
a
Y/∆
co
n
n
ec
tio
n
with
a
ce
n
tr
al
tap
g
r
o
u
n
d
ed
b
y
th
e
s
ec
o
n
d
a
r
y
.
T
h
e
ca
p
ac
ity
o
f
tr
an
s
f
o
r
m
e
r
1
is
7
5
k
VA,
a
n
d
tr
an
s
f
o
r
m
er
s
2
an
d
3
h
av
e
a
to
tal
o
f
1
0
0
k
VA.
T
h
e
s
tu
d
y
was
d
ev
elo
p
ed
in
co
n
ju
n
ctio
n
with
th
e
Of
f
ice
f
o
r
th
e
R
eg
u
latio
n
an
d
R
atio
n
al
U
s
e
o
f
E
n
er
g
y
(
ONURE)
in
San
tiag
o
d
e
C
u
b
a
as
p
a
r
t
o
f
a
n
e
n
er
g
y
d
iag
n
o
s
is
f
o
r
th
is
en
tity
.
T
h
e
m
ea
s
u
r
em
e
n
ts
wer
e
ca
r
r
ied
o
u
t u
s
in
g
a
C
h
au
v
in
Ar
n
au
x
C
.
A
n
etwo
r
k
an
al
y
ze
r
8
3
3
3
4
B
.
Fig
u
r
e
4
s
h
o
ws
th
e
tr
an
s
f
o
r
m
er
b
an
k
an
d
lo
ad
co
n
f
ig
u
r
atio
n
p
ar
am
eter
s
u
s
in
g
a
g
r
a
p
h
ical
u
s
er
in
ter
f
ac
e
d
esig
n
e
d
in
MA
T
L
AB
.
T
h
e
lo
ad
is
co
n
f
i
g
u
r
e
d
f
r
o
m
th
e
h
ar
m
o
n
ic
am
p
litu
d
e
d
is
to
r
tio
n
s
p
ec
tr
u
m
v
alu
es
f
o
r
th
e
lin
e
c
u
r
r
en
ts
m
ea
s
u
r
ed
in
th
e
g
en
e
r
al
d
is
tr
ib
u
tio
n
b
o
ar
d
o
f
th
e
s
er
v
ice.
T
h
e
m
ea
s
u
r
em
en
ts
s
h
o
wed
h
ig
h
h
a
r
m
o
n
ic
c
o
n
ta
m
in
atio
n
,
with
a
h
ig
h
c
o
n
ten
t
o
f
h
ar
m
o
n
ics
in
th
e
lin
e
cu
r
r
en
ts
,
m
ain
ly
in
o
d
d
h
ar
m
o
n
ics,
h
i
g
h
lig
h
tin
g
th
e
h
a
r
m
o
n
ics
o
f
o
r
d
e
r
5
th
,
7
th
,
1
1
t
h
,
an
d
1
3
th
.
Fo
r
th
e
s
im
u
latio
n
o
f
th
e
t
r
an
s
f
o
r
m
er
u
s
in
g
MA
T
L
AB
,
th
e
eq
u
iv
alen
t
cir
cu
it
p
ar
a
m
eter
s
f
o
r
tr
an
s
f
o
r
m
er
s
with
s
tan
d
a
r
d
ized
ca
p
ac
ities
o
f
1
0
0
k
VA
an
d
7
5
k
VA,
r
esp
ec
tiv
ely
.
T
h
e
Simu
lin
k
m
o
d
el
o
f
th
e
t
h
r
ee
-
p
h
ase
b
an
k
a
n
d
th
e
v
o
lt
ag
e
an
d
c
u
r
r
e
n
t
s
ig
n
als
o
b
tai
n
ed
in
th
e
win
d
in
g
s
o
f
ea
ch
t
r
an
s
f
o
r
m
e
r
th
r
o
u
g
h
d
i
g
ital
s
im
u
latio
n
ar
e
p
r
esen
ted
in
Fig
u
r
e
5
.
T
h
e
m
o
d
el
cr
ea
ted
f
o
r
th
e
d
ig
ital
s
im
u
latio
n
o
f
th
e
tr
an
s
f
o
r
m
er
b
a
n
k
,
with
wy
e
–
d
elta
co
n
n
ec
tio
n
a
n
d
n
o
n
-
lin
ea
r
lo
a
d
s
o
n
ea
ch
f
ee
d
er
,
s
h
o
wn
in
Fig
u
r
e
5
(
a)
,
allo
ws
th
e
cu
r
r
e
n
ts
an
d
v
o
ltag
es
in
ea
ch
win
d
in
g
o
f
th
e
tr
an
s
f
o
r
m
er
s
th
at
m
ak
e
u
p
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h
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Evaluation Warning : The document was created with Spire.PDF for Python.
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b
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t
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e
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b
tain
ed
,
Fig
u
r
e
5
(
b
)
.
W
ith
th
ese
r
esu
lts
,
it
is
p
o
s
s
ib
le
to
d
eter
m
i
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e
all
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e
o
p
er
atin
g
p
ar
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m
eter
s
o
f
th
e
m
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es.
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p
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f
th
ese
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ig
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als
p
r
o
v
id
es
th
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
o
f
t
h
e
cu
r
r
en
ts
f
o
r
u
s
in
g
th
e
ANSI
/I
E
E
E
Std
.
C
5
7
.
1
1
0
an
al
y
tical
m
o
d
el.
Fig
u
r
e
4
.
Gr
a
p
h
ical
u
s
er
in
ter
f
ac
e
f
o
r
th
e
co
n
f
i
g
u
r
atio
n
o
f
t
h
e
n
o
n
-
lin
ea
r
lo
ad
an
d
t
h
e
tr
an
s
f
o
r
m
er
b
an
k
with
th
e
d
ata
o
f
t
h
e
s
o
y
b
ea
n
p
r
o
ce
s
s
in
g
p
lan
t ser
v
ice
(
a)
(
b
)
Fig
u
r
e
5
.
Simu
lin
k
m
o
d
el
im
p
lem
en
tatio
n
o
f
t
h
e
th
r
ee
-
p
h
ase
b
an
k
o
f
th
r
ee
s
in
g
le
-
p
h
ase
tr
an
s
f
o
r
m
er
s
with
Y/Δ
co
n
n
ec
tio
n
.
(
a)
m
o
d
el
f
o
r
th
e
d
ig
ital simu
latio
n
o
f
th
e
t
h
r
ee
-
p
h
ase
b
an
k
a
n
d
(
b
)
e
x
am
p
le
o
f
th
e
v
o
ltag
es
an
d
cu
r
r
en
ts
in
ea
ch
win
d
in
g
o
f
tr
an
s
f
o
r
m
er
1
o
f
t
h
e
b
an
k
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&
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4833
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Fro
m
th
e
s
im
u
latio
n
,
it
is
p
o
s
s
ib
le
to
d
eter
m
in
e
th
e
lo
ad
lo
s
s
es
o
f
ea
ch
tr
an
s
f
o
r
m
er
,
an
d
f
r
o
m
th
em
,
th
e
to
tal
ad
d
itio
n
al
lo
s
s
es
ca
n
b
e
ca
lcu
late
d
.
T
h
ese
o
p
er
at
io
n
s
ar
e
ca
r
r
ie
d
o
u
t
b
y
ap
p
l
y
in
g
th
e
e
x
p
r
ess
io
n
s
(5
)
-
(
8
)
t
h
r
o
u
g
h
wh
ich
it
is
p
o
s
s
ib
le
to
ca
lcu
late
th
e
t
o
tal
a
d
d
itio
n
al
lo
s
s
es
(
)
b
ec
au
s
e
o
f
th
e
d
i
f
f
er
en
ce
b
etwe
en
th
e
l
o
ad
l
o
s
s
es
an
d
t
h
e
co
p
p
er
l
o
s
s
es
o
r
elec
tr
ical
l
o
s
s
es
in
ea
ch
win
d
in
g
.
E
x
p
r
es
s
io
n
(
1
6
)
is
u
s
ed
to
d
eter
m
in
e
th
e
elec
tr
ical
lo
s
s
e
s
.
B
ased
o
n
th
e
d
is
cr
ete
v
alu
es
o
f
th
e
cu
r
r
en
ts
in
ea
c
h
tr
a
n
s
f
o
r
m
er
win
d
in
g
o
b
tain
ed
in
th
e
s
im
u
latio
n
,
it i
s
p
o
s
s
ib
le
to
r
ef
o
r
m
u
late
th
is
ex
p
r
ess
io
n
,
Fig
u
r
e
s
6
(
a)
an
d
6
(
b
)
.
(
a)
(
b
)
Fig
u
r
e
6
.
E
x
am
p
le
o
f
s
im
u
latio
n
r
esu
lts
f
o
r
tr
a
n
s
f
o
r
m
e
r
1
o
f
th
e
th
r
ee
-
p
h
ase
b
an
k
with
n
o
n
-
lin
ea
r
lo
ad
.
(
a)
v
o
ltag
es a
n
d
cu
r
r
en
ts
in
ea
ch
win
d
in
g
o
f
tr
a
n
s
f
o
r
m
er
1
o
f
th
e
b
an
k
an
d
(
b
)
h
ar
m
o
n
ic
s
p
ec
tr
u
m
o
f
am
p
litu
d
e
(
% o
f
th
e
f
u
n
d
am
e
n
tal
h
ar
m
o
n
ic)
an
d
p
h
ase
o
f
th
e
cu
r
r
en
ts
o
f
th
e
win
d
i
n
g
s
o
f
tr
an
s
f
o
r
m
er
1
=
∑
(
)
2
=
1
(
1
6
)
w
h
er
e,
is
th
e
n
u
m
b
er
o
f
d
ata
elem
en
ts
,
is
th
e
in
s
tan
tan
eo
u
s
cu
r
r
en
t in
ea
c
h
o
f
th
e
win
d
in
g
s
,
an
d
is
th
e
r
esis
tan
ce
o
f
th
e
win
d
in
g
s
d
eter
m
in
ed
in
t
h
e
tr
an
s
f
o
r
m
er
m
o
d
el.
B
ased
o
n
th
e
d
iag
n
o
s
es
ca
r
r
ied
o
u
t
an
d
u
s
in
g
th
e
m
o
d
el
a
d
ju
s
ted
f
o
r
th
e
d
ig
ital
s
im
u
latio
n
o
f
th
e
th
r
ee
-
p
h
ase
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RE
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