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m
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USG)
m
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d
co
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d
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s
[
1
]
-
[
5
]
.
T
o
v
alid
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th
is
ap
p
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a
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,
th
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alan
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[
6
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[
1
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R
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[
1
6
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-
[
1
8
]
.
T
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[
1
9
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-
[
2
2
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[
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3
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,
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2
4
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.
I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2088
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8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
15
,
No
.
4
,
Dec
em
b
er
20
24
:
2097
-
2
1
0
4
2098
co
m
p
r
o
m
is
e
b
etwe
en
p
r
ec
is
io
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an
d
s
im
u
latio
n
tim
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T
h
e
o
b
tain
ed
r
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lts
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w
th
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e
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f
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tiv
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h
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y
f
o
r
t
h
e
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eh
a
v
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r
al
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aly
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is
o
f
USG.
2.
USG
ST
A
T
E
M
O
D
E
L
Fo
r
USG,
th
e
s
tato
r
v
o
ltag
e
e
q
u
atio
n
is
ex
p
r
ess
ed
b
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(
1
)
-
(
6
)
[
2
5
]
.
[
]
=
[
]
+
[
]
[
]
(
1
)
W
ith
:
[
]
=
[
]
[
]
(
2
)
[
]
=
[
]
[
]
(
3
)
[
]
=
[
]
[
]
(
4
)
[
]
=
[
+
1
−
1
0
0
1
−
1
−
1
0
+
1
]
(
5
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[
]
=
[
]
[
]
(
6
)
[
]
,
[
]
,
[
]
ar
e
r
esp
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tiv
ely
th
e
v
ec
to
r
o
f
th
e
s
tato
r
f
lu
x
,
s
tato
r
cu
r
r
e
n
ts
,
an
d
lo
ad
v
o
ltag
es,
[
]
,
[
]
ar
e
r
esp
ec
tiv
ely
th
e
m
atr
ix
o
f
th
e
s
tato
r
an
d
lo
ad
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esis
tan
ce
s
.
T
h
e
r
o
to
r
v
o
ltag
e
e
q
u
atio
n
is
ex
p
r
ess
ed
b
y
(
7
)
.
=
−
(
7
)
T
o
estab
lis
h
th
e
s
tate
m
o
d
el
o
f
th
e
USG,
it’s
im
p
o
r
tan
t
t
o
ex
p
r
ess
th
e
m
ac
h
in
e
cu
r
r
en
ts
in
te
r
m
s
o
f
th
e
m
ac
h
in
e
f
lu
x
es.
Fo
r
th
is
,
we
d
ef
in
e
a
v
ec
to
r
o
f
two
in
d
ep
e
n
d
en
t c
u
r
r
e
n
ts
as illu
s
tr
ated
b
y
(
8
)
[
2
5
]
.
[
]
=
[
]
(
8
)
T
h
e
s
tato
r
an
d
r
o
to
r
f
lu
x
es a
r
e
ca
lcu
lated
u
s
in
g
(
9
)
-
(
1
3
)
,
[
]
=
−
[
]
[
]
−
[
]
(
9
)
=
−
[
]
[
]
−
.
(
1
0
)
[
]
=
[
]
[
]
(
1
1
)
w
ith
(
1
2
)
a
n
d
(
1
3
)
.
[
]
=
[
1
−
1
0
0
1
−
1
]
(
1
2
)
[
]
=
[
+
1
0
0
+
1
−
1
−
1
]
(
1
3
)
[
]
is
th
e
m
atr
ix
o
f
th
e
s
tato
r
in
d
u
ctan
ce
s
;
[
]
is
th
e
m
atr
ix
o
f
th
e
s
t
ato
r
-
r
o
to
r
m
u
t
u
al
in
d
u
ctan
ce
s
;
is
th
e
f
ield
cu
r
r
en
t;
an
d
,
ar
e
r
esp
ec
tiv
ely
th
e
in
d
u
ctan
ce
an
d
r
esis
tan
ce
o
f
th
e
r
o
to
r
win
d
in
g
.
T
h
er
ef
o
r
e
,
th
e
s
tato
r
an
d
r
o
t
o
r
cu
r
r
en
ts
ar
e
e
x
p
r
ess
ed
b
y
(
1
4
)
-
(
1
9
)
.
[
]
=
−
(
[
]
−
1
[
]
[
]
)
−
1
(
[
]
−
[
]
)
(
1
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
I
n
ve
s
tig
a
tio
n
s
o
n
t
h
e
b
eh
a
vio
r
a
l a
n
a
lysi
s
o
f u
n
b
a
la
n
ce
d
s
yn
c
h
r
o
n
o
u
s
g
e
n
era
to
r
s
(
Djila
li K
o
u
ch
ih
)
2099
=
−
(
−
[
]
[
]
−
1
[
]
)
−
1
(
−
[
]
[
]
−
1
[
]
)
(
1
5
)
[
]
=
[
]
[
]
[
]
(
1
6
)
[
]
=
[
]
[
]
(
1
7
)
[
]
=
[
]
[
]
(
1
8
)
[
]
=
[
]
(
1
9
)
Fro
m
(
1
)
,
(
8
)
,
(
1
4
)
,
a
n
d
(
1
5
)
,
t
h
e
USG
s
tate
m
o
d
el
will b
e
ex
p
r
ess
ed
b
y
(
2
0
)
a
n
d
(
2
1
)
.
{
[
]
=
−
[
]
[
]
(
[
]
−
1
[
]
[
]
)
−
1
(
[
]
[
]
−
[
]
)
+
[
]
=
+
(
−
[
]
[
]
−
1
[
]
)
−
1
(
−
[
]
[
]
−
1
[
]
[
]
)
=
−
−
(
2
0
)
T
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
is
ex
p
r
ess
ed
b
y
(
2
1
)
.
=
2
[
]
[
]
(
2
1
)
T
m
is
th
e
in
p
u
t
to
r
q
u
e;
J
is
th
e
i
n
er
tia;
is
th
e
v
is
co
s
e
f
r
ictio
n
co
ef
f
icien
t.
T
h
e
n
e
u
tr
al
v
o
ltag
e
v
on
is
ca
lcu
lated
u
s
in
g
(
2
2
)
to
(
2
3
)
[
2
5
]
.
=
∑
(
−
)
=
,
,
3
,
=
,
,
(
2
2
)
W
h
er
e
th
e
s
tato
r
v
o
ltag
es a
r
e
ca
lcu
lated
b
y
(
2
3
)
[
2
5
]
.
=
+
,
=
,
,
(
2
3
)
s
T
is
th
e
s
am
p
lin
g
tim
e.
3.
SI
M
UL
A
T
I
O
N
S
Usi
n
g
MA
T
L
AB
,
th
e
s
tate
m
o
d
el
is
s
im
u
lated
f
o
r
a
s
y
n
ch
r
o
n
o
u
s
g
en
e
r
ato
r
o
f
1
.
5
k
VA,
4
/2
.
3
A,
2
2
0
/3
8
0
V
–
5
0
Hz.
At
t
=
0
,
th
e
f
ield
cu
r
r
en
t
is
estab
lis
h
ed
with
n
o
lo
ad
co
n
d
itio
n
s
(
o
p
e
n
s
tato
r
)
.
Af
ter
th
at,
th
e
b
alan
ce
d
lo
ad
o
f
1
1
0
Ω
is
co
n
n
ec
ted
to
th
e
g
en
er
ato
r
at
t =
0
.
2
5
s
.
An
u
n
b
alan
ce
d
lo
a
d
o
f
r
al
=
2
2
0
Ω
,
r
bl
=
r
cl
=
1
1
0
Ω
is
s
elec
ted
at
t
=
0
.
5
s
.
T
h
e
s
tato
r
,
cu
r
r
en
ts
,
a
n
d
th
eir
f
ast
Fo
u
r
ie
r
tr
a
n
s
f
o
r
m
(
FF
T
)
ar
e
s
h
o
w
n
b
y
Fig
u
r
es
1
(
a)
-
1
(
d
)
(
s
ee
Ap
p
e
n
d
ix
)
,
r
esp
ec
tiv
ely
.
T
h
e
f
ield
c
u
r
r
en
t
an
d
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
ar
e
s
h
o
wn
in
Fig
u
r
es 1
(
e)
-
1
(
f
)
(
s
ee
Ap
p
en
d
i
x
)
,
r
esp
ec
tiv
ely
.
Fig
u
r
es 1
(
g
)
an
d
1
(
h
)
(
s
ee
Ap
p
en
d
ix
)
s
h
o
w
th
e
n
eu
tr
al
v
o
ltag
e
an
d
its
s
p
ec
tr
u
m
an
aly
s
is
,
r
esp
ec
tiv
ely
.
Simu
latio
n
r
esu
lts
s
h
o
w
th
at
d
is
to
r
tio
n
is
p
r
o
d
u
ce
d
th
r
o
u
g
h
th
e
tem
p
o
r
ar
y
v
o
ltag
es
an
d
cu
r
r
en
ts
as
illu
s
tr
ated
b
y
Fig
u
r
es
1
(
a)
an
d
1
(
c)
,
r
esp
ec
tiv
ely
.
As
m
en
tio
n
ed
in
Fig
u
r
es
1
(
b
)
an
d
1
(
d
)
,
th
e
s
p
ec
tr
u
m
an
aly
s
is
s
h
o
ws
th
at
s
o
m
e
h
ar
m
o
n
ics
o
f
im
p
air
ed
o
r
d
e
r
s
(
1
5
0
Hz,
2
5
0
Hz,
…)
ar
e
g
en
er
ated
o
v
er
th
e
s
tato
r
v
o
ltag
es
an
d
cu
r
r
en
ts
.
Du
e
to
t
h
e
m
ag
n
etic
in
ter
ac
tio
n
b
etwe
en
s
tato
r
a
n
d
r
o
t
o
r
cir
cu
its
,
th
e
f
ield
cu
r
r
en
t
is
af
f
ec
ted
as
illu
s
tr
ated
b
y
Fig
u
r
e
1
(
e)
.
Fig
u
r
e
1
(
f
)
s
h
o
ws th
at
a
p
u
ls
atin
g
to
r
q
u
e
is
cr
ea
ted
c
au
s
in
g
u
n
d
esira
b
le
ef
f
ec
ts
s
u
ch
as
v
ib
r
atio
n
,
n
o
is
e
,
an
d
h
ea
tin
g
o
f
th
e
u
n
b
alan
ce
d
g
en
er
at
o
r
s
.
R
eg
ar
d
in
g
th
e
n
eu
tr
al
v
o
lta
g
e,
it
is
ab
o
u
t
6
5
V
as
s
h
o
wn
in
Fig
u
r
e
1
(
g
)
.
Fig
u
r
e
1
(
h
)
s
h
o
ws
th
at
s
p
ec
if
ic
h
ar
m
o
n
ics
o
f
im
p
air
e
d
o
r
d
er
s
ar
e
o
b
s
er
v
ed
th
r
o
u
g
h
th
e
s
p
ec
tr
u
m
an
al
y
s
is
o
f
th
e
n
eu
tr
al
v
o
ltag
e.
4.
E
XP
E
R
I
M
E
N
T
S
An
ex
p
er
im
e
n
tal
test
h
as b
ee
n
co
n
d
u
cted
o
n
a
th
r
ee
-
p
h
ase
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
o
f
1
.
5
k
VA,
4
/ 2
.
3
A,
2
2
0
/3
8
0
V
–
5
0
Hz.
T
h
e
r
o
to
r
cu
r
r
e
n
t
is
estab
lis
h
ed
with
o
p
en
s
tato
r
.
Af
ter
th
at,
a
b
ala
n
ce
d
lo
ad
o
f
1
1
0
Ω
is
co
n
n
ec
ted
to
th
e
g
en
er
at
o
r
.
Asy
m
m
etr
ical
lo
ad
o
f
r
al
=
2
2
0
Ω
,
r
bl
=
r
cl
=
1
1
0
Ω
is
co
n
s
id
er
ed
.
T
h
e
n
e
u
tr
al
v
o
ltag
e
an
d
its
s
p
ec
tr
u
m
an
al
y
s
is
ar
e
illu
s
tr
ated
in
Fig
u
r
es
2
(
a)
an
d
2
(
b
)
r
esp
ec
tiv
ely
.
Fig
u
r
es
2
(
c)
an
d
2
(
d
)
illu
s
tr
ate
th
e
s
p
ec
tr
u
m
an
aly
s
i
s
o
f
th
e
s
tato
r
v
o
lta
g
es a
n
d
cu
r
r
en
ts
r
esp
ec
tiv
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
15
,
No
.
4
,
Dec
em
b
er
20
24
:
2097
-
2
1
0
4
2100
Fo
r
an
u
n
b
ala
n
ce
d
l
o
ad
,
th
e
n
eu
tr
al
v
o
ltag
e
r
ea
ch
es
a
b
o
u
t
5
5
V
as
illu
s
tr
ated
b
y
Fi
g
u
r
e
2
(
a)
.
Fig
u
r
e
2
(
b
)
s
h
o
ws
th
e
FF
T
o
f
th
e
n
e
u
tr
al
v
o
ltag
e
w
h
er
e
s
p
ec
if
ic
h
ar
m
o
n
ics
o
f
im
p
air
ed
o
r
d
er
s
ar
e
g
e
n
er
ated
.
T
h
ese
h
ar
m
o
n
ics
ar
e
s
im
ilar
to
th
e
h
ar
m
o
n
ics
o
f
th
e
s
tato
r
v
o
ltag
es
an
d
cu
r
r
e
n
ts
as
illu
s
tr
a
ted
b
y
Fig
u
r
es
2
(
c)
an
d
2
(
d
)
,
r
esp
ec
tiv
ely
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
2
.
USG
ex
p
e
r
im
en
tal
r
esu
lts
:
(
a)
n
eu
tr
al
v
o
ltag
e,
(
b
)
FF
T
o
f
n
eu
tr
al
v
o
ltag
e,
(
c)
FF
T
o
f
s
tato
r
v
o
ltag
es,
an
d
(
d
)
FF
T
o
f
s
tato
r
c
u
r
r
e
n
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
I
n
ve
s
tig
a
tio
n
s
o
n
t
h
e
b
eh
a
vio
r
a
l a
n
a
lysi
s
o
f u
n
b
a
la
n
ce
d
s
yn
c
h
r
o
n
o
u
s
g
e
n
era
to
r
s
(
Djila
li K
o
u
ch
ih
)
2101
5.
CO
NCLU
SI
O
NS
A
n
ew
m
eth
o
d
o
lo
g
y
h
as
b
ee
n
in
v
esti
g
ated
f
o
r
th
e
b
eh
av
i
o
r
al
an
aly
s
is
o
f
th
e
U
SG.
T
o
tes
t
t
h
e
v
alid
ity
o
f
th
is
m
eth
o
d
o
lo
g
y
,
u
n
b
alan
c
ed
lo
ad
h
as b
ee
n
co
n
s
id
er
ed
.
S
ev
er
e
ef
f
ec
ts
ar
e
m
e
n
tio
n
ed
li
k
e
v
ib
r
atio
n
,
n
o
is
e,
an
d
e
x
ce
s
s
iv
e
h
ea
tin
g
o
f
th
e
U
SG.
Fo
r
th
is
r
ea
s
o
n
,
it’s m
an
d
ato
r
y
t
o
a
v
o
id
all
asy
m
m
etr
ies
b
ef
o
r
e
t
h
ey
lead
t
o
a
p
r
o
g
r
ess
iv
e
d
estru
ctio
n
o
f
th
e
g
en
er
at
o
r
s
.
T
h
e
FF
T
o
f
th
e
n
eu
tr
al
v
o
ltag
e,
s
tato
r
v
o
ltag
e
s
,
an
d
c
u
r
r
e
n
ts
h
av
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
t
h
e
d
etec
tio
n
o
f
s
tato
r
asy
m
m
etr
ies.
T
h
is
wo
r
k
m
ay
b
e
ex
ten
d
ed
to
s
ev
er
al
f
au
lts
lik
e
o
p
en
-
p
h
ase
an
d
s
h
o
r
t
-
cir
cu
its
.
AP
P
E
NDI
X
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
.
USG
s
im
u
latio
n
r
esu
lts
: (
a)
s
tato
r
v
o
ltag
es,
(
b
)
FF
T
o
f
s
tato
r
v
o
ltag
es,
(
c)
s
tato
r
c
u
r
r
en
ts
,
an
d
(
d
)
FF
T
o
f
s
tato
r
cu
r
r
en
ts
0
.4
5
0
.4
6
0
.4
7
0
.4
8
0
.4
9
0
.5
0
.5
1
0
.5
2
0
.5
3
0
.5
4
0
.5
5
-
6
0
0
-
4
0
0
-
2
0
0
0
200
400
600
T
i
m
e
(
s
)
S
t
a
t
o
r
V
o
l
t
a
g
e
s
(
V
)
v
a
n
v
b
n
v
c
n
A
s
y
m
m
e
t
r
i
c
a
l
l
o
a
d
c
o
n
d
i
t
i
o
n
s
0
50
100
150
200
250
300
350
400
450
500
10
-2
10
-1
10
0
10
1
10
2
10
3
F
r
e
q
u
e
n
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jk
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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I
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15
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4
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Dec
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20
24
:
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Re
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n
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l
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se
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o
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c
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n
b
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c
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t
a
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ted
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m
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m
sb
o
u
c
h
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r
it
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m
a
il
.
c
o
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.