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es
[
7
]
a
r
e
o
p
tim
al
f
o
r
t
h
e
i
m
p
le
m
e
n
t
ati
o
n
o
f
t
h
ese
m
u
lt
i
-
p
h
ase
d
r
i
v
es.
T
h
e
ad
v
a
n
ce
m
e
n
t
o
f
t
h
e
m
u
l
ti
-
p
h
as
e
d
o
m
a
in
is
p
r
o
p
e
lle
d
b
y
th
ese
p
a
r
ti
c
u
la
r
i
n
d
u
s
t
r
ia
l
a
p
p
li
ca
t
io
n
s
.
T
h
e
m
u
lt
i
-
p
h
as
e
co
n
c
e
p
t,
in
tu
r
n
,
f
ac
il
ita
tes
a
d
e
cr
ea
s
e
in
th
e
c
o
u
n
t
o
f
s
em
i
c
o
n
d
u
ct
o
r
s
wit
c
h
es
a
n
d
o
t
h
e
r
c
o
m
p
o
n
en
ts
,
p
o
te
n
t
ial
ly
en
h
a
n
ci
n
g
o
v
er
all
r
eli
ab
ilit
y
.
Nev
er
t
h
el
ess
,
i
n
t
h
es
e
ap
p
l
ic
at
io
n
s
,
e
n
s
u
r
in
g
c
o
n
ti
n
u
o
u
s
o
p
e
r
ati
o
n
is
c
r
u
cia
l,
e
v
e
n
in
t
h
e
f
a
ce
o
f
p
o
t
e
n
ti
al
f
ail
u
r
e
s
i
n
t
h
e
in
v
er
t
e
r
,
m
o
to
r
/
g
en
er
a
to
r
,
an
d
co
n
t
r
o
l
s
y
s
te
m
[
8
]
.
T
h
e
h
i
g
h
e
r
n
u
m
b
e
r
o
f
p
h
ases
i
n
m
u
lti
-
p
h
ase
m
o
t
o
r
s
p
r
o
v
i
d
es
a
d
d
it
io
n
al
d
e
g
r
e
es
o
f
f
r
e
e
d
o
m
,
e
n
a
b
l
i
n
g
m
o
r
e
s
o
p
h
is
tic
at
ed
c
o
n
tr
o
l
s
tr
a
te
g
ies
a
n
d
p
o
te
n
ti
all
y
en
h
a
n
ci
n
g
p
e
r
f
o
r
m
a
n
c
e
i
n
v
a
r
i
o
u
s
a
s
p
e
cts
co
m
p
a
r
e
d
t
o
tr
ad
iti
o
n
al
th
r
e
e
-
p
h
as
e
m
o
t
o
r
s
.
I
n
v
ar
io
u
s
ar
ticles,
p
r
o
b
lem
s
co
n
n
ec
ted
with
th
e
f
au
lted
o
p
er
atio
n
o
f
th
e
s
y
s
tem
with
m
ec
h
an
ical
f
au
lts
o
f
th
e
d
r
iv
e
ar
e
p
r
esen
ted
an
d
d
escr
ib
ed
.
T
h
e
m
ain
p
r
o
b
lem
i
n
th
e
s
y
s
tem
is
r
o
to
r
an
d
s
tato
r
f
au
lt
id
en
tific
atio
n
an
d
co
m
p
en
s
atio
n
[
9
]
.
W
h
ile,
i
n
m
u
lti
-
p
h
ase
in
d
u
ctio
n
m
ac
h
i
n
es
an
d
ev
e
n
th
r
ee
-
p
h
ase
in
d
u
ctio
n
m
ac
h
in
e
d
r
iv
e
s
y
s
tem
s
,
s
o
m
e
r
ec
en
t
r
esear
c
h
ef
f
o
r
ts
h
av
e
b
ee
n
f
o
c
u
s
ed
o
n
th
e
f
au
lt
-
to
ler
a
n
t
m
ac
h
in
e
d
esig
n
[
1
0
]
-
[
1
3
]
,
f
a
u
lt
d
etec
tio
n
[
1
4
]
,
[
1
5
]
,
an
d
f
a
u
lt
-
to
ler
an
t c
o
n
tr
o
l sy
s
tem
[
1
6
]
,
[
1
7
]
.
I
n
r
ec
e
n
t y
ea
r
s
,
f
au
lt
-
to
ler
an
t c
o
n
tr
o
l sy
s
tem
s
h
av
e
em
e
r
g
ed
as
a
h
ig
h
l
y
ac
ti
v
e
ar
ea
o
f
r
esear
ch
f
o
r
n
u
m
er
o
u
s
in
v
esti
g
ato
r
s
[
1
8
]
-
[
2
0
]
.
T
h
e
p
r
im
a
r
y
o
b
jectiv
e
o
f
f
a
u
lt
-
to
ler
an
t
co
n
tr
o
l
is
to
g
u
ar
an
tee
th
e
c
o
n
tin
u
o
u
s
f
u
n
c
tio
n
ality
o
f
a
s
y
s
tem
,
ev
en
in
th
e
ev
en
t
o
f
a
f
au
lt.
T
h
r
ee
-
p
h
ase
d
r
iv
es
r
em
ain
p
o
p
u
lar
in
elec
tr
ical
d
r
i
v
e
ap
p
licatio
n
s
d
u
e
t
o
th
eir
p
r
ac
ticality
[
2
1
]
.
Ho
wev
er
,
th
ese
s
y
s
tem
s
f
ac
e
ce
r
tain
l
im
itatio
n
s
,
s
u
ch
as
h
ig
h
to
r
q
u
e
r
ip
p
le
d
u
r
in
g
s
ix
-
s
tep
s
witch
in
g
an
d
r
estricte
d
cu
r
r
en
t
h
an
d
lin
g
ca
p
ac
ity
o
f
p
o
we
r
s
witch
es
[
2
2
]
.
I
n
co
m
p
a
r
is
o
n
,
m
u
lti
-
p
h
ase
d
r
iv
es
o
f
f
er
n
o
tab
le
ad
v
a
n
tag
es,
in
clu
d
in
g
r
ed
u
ce
d
cu
r
r
en
t
p
e
r
p
h
ase
with
o
u
t
r
aisi
n
g
v
o
ltag
e,
m
in
im
ized
DC
h
ar
m
o
n
ics,
an
d
en
h
an
c
ed
o
v
er
all
r
eliab
ilit
y
.
Desp
ite
th
ese
b
en
ef
its
,
o
p
er
atin
g
in
d
u
ctio
n
m
ac
h
in
es
is
m
o
r
e
co
m
p
lex
th
an
DC
m
o
to
r
s
,
lack
in
g
p
r
ec
is
io
n
co
n
tr
o
l
d
u
e
to
c
o
u
p
l
ed
f
lu
x
a
n
d
to
r
q
u
e
co
m
p
o
n
en
t
s
in
th
eir
in
p
u
t
cu
r
r
en
t.
Nev
er
t
h
eless
,
th
e
in
tr
icate
n
o
n
lin
ea
r
d
y
n
a
m
ic
p
er
f
o
r
m
a
n
ce
o
f
in
d
u
ctio
n
m
ac
h
in
es
ca
n
b
e
s
ig
n
if
ican
tly
en
h
an
ce
d
u
s
in
g
th
e
in
d
ir
ec
t
f
ield
-
o
r
ie
n
ted
co
n
tr
o
l
(
I
R
FOC
)
th
eo
r
y
,
en
a
b
lin
g
s
ep
ar
ate
c
o
n
tr
o
l
o
f
to
r
q
u
e
an
d
f
lu
x
.
An
o
th
er
c
r
u
cial
c
o
n
s
id
er
atio
n
f
o
r
m
u
lti
-
p
h
ase
m
ac
h
in
es
is
t
h
e
im
p
ac
t
o
f
DC
-
b
u
s
v
o
lta
g
e
li
m
itatio
n
s
o
n
th
e
m
ax
im
u
m
ac
h
iev
ab
le
o
u
tp
u
t
to
r
q
u
e
u
n
d
er
o
p
tim
al
cu
r
r
en
t
co
n
tr
o
l
with
s
o
m
e
p
h
ases
o
p
en
[
2
3
]
.
W
h
ile
p
r
ev
io
u
s
s
tu
d
ies
h
av
e
an
aly
ze
d
th
e
DC
-
b
u
s
u
tili
za
tio
n
o
f
a
m
u
lti
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
(
VSI
)
u
n
d
er
b
alan
ce
d
co
n
d
itio
n
s
[
2
4
]
,
f
a
u
lt
s
ce
n
ar
io
s
o
f
ten
in
v
o
lv
e
o
p
ti
m
al
cu
r
r
en
t
co
n
tr
o
l.
Ad
d
itio
n
ally
,
ass
u
m
p
tio
n
s
o
f
co
m
p
lete
d
ec
o
u
p
lin
g
b
etwe
en
d
if
f
er
en
t
s
u
b
s
p
ac
es
m
ay
n
o
t
h
o
ld
,
esp
ec
ially
co
n
s
id
er
in
g
th
e
in
f
lu
en
ce
o
f
n
eu
tr
al
co
n
f
ig
u
r
atio
n
o
n
lo
w
-
o
r
d
er
c
u
r
r
en
t/v
o
ltag
e
h
ar
m
o
n
ics
[
2
5
]
.
T
o
ad
d
r
ess
th
ese
co
m
p
lex
ities
,
s
im
p
le
clo
s
ed
-
f
o
r
m
ex
p
r
ess
io
n
s
ar
e
p
r
o
p
o
s
ed
to
esti
m
ate
th
e
m
ax
im
u
m
lin
e
v
o
lt
ag
e
d
eter
m
in
in
g
th
e
m
a
x
im
u
m
ac
h
iev
ab
le
to
r
q
u
e
un
d
er
v
ar
i
o
u
s
p
o
s
t
-
f
au
lt
co
n
tr
o
l
s
tr
ateg
ies
an
d
n
eu
tr
al
co
n
f
ig
u
r
atio
n
s
.
T
h
e
s
am
e
ex
p
r
ess
io
n
s
ar
e
u
tili
ze
d
to
esti
m
ate
th
e
m
in
im
u
m
r
eq
u
ir
e
d
DC
-
lin
k
v
o
ltag
e
m
ag
n
itu
d
e
b
ased
o
n
th
e
ad
o
p
ted
p
o
s
t
-
f
au
lt
s
ce
n
ar
io
f
o
r
t
h
e
m
u
lti
-
p
h
ase
in
d
u
ctio
n
m
ac
h
in
e.
B
ey
o
n
d
cu
r
r
e
n
t
lim
its
,
v
o
ltag
e
co
n
s
tr
ain
ts
ar
e
cr
itical
in
d
ef
in
in
g
m
ac
h
in
e
p
e
r
f
o
r
m
an
ce
,
p
ar
ticu
lar
ly
co
n
ce
r
n
in
g
th
e
m
a
x
im
u
m
ac
h
iev
ab
le
s
p
ee
d
an
d
p
o
wer
.
Desp
ite
th
is
,
d
is
cu
s
s
io
n
s
o
n
v
o
ltag
e
co
n
s
tr
ain
ts
in
m
u
lti
-
p
h
ase
m
ac
h
in
es
d
u
r
in
g
o
p
en
-
p
h
ase
f
au
lt
(
OPF
)
r
em
ain
lim
ited
.
Un
lik
e
cu
r
r
en
t
lim
its
,
v
o
ltag
e
co
n
s
tr
ain
ts
in
in
d
u
ctio
n
m
ac
h
in
es
ar
e
in
f
lu
en
ce
d
b
y
s
p
ec
if
ic
m
ac
h
in
e
p
ar
am
eter
s
,
n
ec
ess
itatin
g
an
ac
cu
r
ate
m
eth
o
d
f
o
r
p
ar
am
eter
esti
m
atio
n
to
d
eter
m
in
e
p
o
s
t
-
f
a
u
lt
v
o
ltag
e
lim
i
ts
ef
f
ec
tiv
ely
.
T
h
is
s
tu
d
y
ai
m
s
t
o
an
aly
ze
th
e
p
er
f
o
r
m
an
ce
o
f
m
u
lti
-
p
h
ase
in
d
u
ctio
n
m
ac
h
in
e
d
r
iv
e
s
y
s
tem
s
,
with
a
f
o
cu
s
o
n
estab
lis
h
in
g
th
e
b
est
ap
p
r
o
ac
h
f
o
r
in
co
r
p
o
r
atin
g
f
au
lt
-
to
ler
an
t
f
ea
tu
r
es
in
m
u
lti
-
p
h
ase
d
r
iv
es.
T
h
e
u
n
iq
u
e
co
n
tr
ib
u
tio
n
o
f
th
is
r
esear
ch
is
in
id
en
tify
in
g
p
o
s
t
-
f
a
u
lt
c
u
r
r
e
n
t
an
d
v
o
ltag
e
co
n
s
tr
ain
ts
f
o
r
s
y
m
m
etr
ical
s
ix
-
p
h
ase
in
d
u
ctio
n
m
ac
h
in
es
(
S6
-
I
M
an
d
D3
-
I
M)
with
co
n
f
ig
u
r
atio
n
s
o
f
s
in
g
le
an
d
d
u
al
is
o
lated
n
eu
tr
als
u
n
d
er
1
OPF.
Ad
d
itio
n
ally
,
th
e
im
p
ac
t
o
f
s
lip
f
r
eq
u
en
cy
(
ω
slip
)
an
d
s
y
n
c
h
r
o
n
o
u
s
f
r
eq
u
e
n
cy
(
ω
s
)
is
ass
e
s
s
ed
.
R
e
s
u
lts
r
ev
ea
l
th
at,
f
o
r
th
e
S6
-
I
M
co
n
s
id
er
ed
h
er
e,
th
e
cu
r
r
e
n
t
co
n
s
tr
ain
t
is
g
en
er
ally
r
ea
c
h
ed
b
e
f
o
r
e
th
e
v
o
l
tag
e
co
n
s
tr
ain
t
in
m
o
s
t
f
au
lt
ca
s
es,
in
d
icatin
g
th
at
cu
r
r
en
t lim
its
p
r
im
ar
ily
r
estrict
p
o
s
t
-
f
au
lt o
p
e
r
atio
n
.
C
o
n
v
er
s
ely
,
in
th
e
D3
-
I
M,
v
o
ltag
e
c
o
n
s
tr
ain
ts
ar
e
u
s
u
ally
en
co
u
n
ter
e
d
f
ir
s
t.
Un
d
er
s
tan
d
i
n
g
th
ese
lim
its
aid
s
en
g
in
ee
r
s
in
d
ev
elo
p
in
g
r
o
b
u
s
t
co
n
tr
o
l
s
y
s
tem
s
,
p
r
ev
en
tin
g
m
ac
h
in
e
f
ailu
r
es,
a
n
d
p
r
o
lo
n
g
i
n
g
m
ac
h
i
n
e
life
wh
ile
en
s
u
r
in
g
s
af
e
an
d
e
f
f
icien
t o
p
er
atio
n
.
2.
SI
X
-
P
H
AS
E
I
NDU
CT
I
O
N
M
ACH
I
N
E
S D
RIV
E
SY
ST
E
M
Ov
er
tim
e,
n
u
m
e
r
o
u
s
f
a
u
lt
-
to
l
er
an
t
co
n
tr
o
l
s
tr
ateg
ies
h
a
v
e
e
m
er
g
ed
f
o
r
m
u
lti
-
p
h
ase
m
ac
h
in
es
[
2
6
]
,
in
clu
d
in
g
th
o
s
e
with
s
ix
p
h
ase
s
[
2
7
]
-
[
3
0
]
.
Ad
d
itio
n
ally
,
v
a
r
i
o
u
s
co
n
tr
o
ller
s
h
a
v
e
b
ee
n
d
ev
elo
p
ed
s
p
ec
i
f
ically
f
o
r
h
a
n
d
lin
g
o
p
en
-
p
h
ase
f
a
u
lts
(
OPF),
s
u
ch
as scalar
V/F [
3
1
]
,
[
3
2
]
d
ir
ec
t to
r
q
u
e
c
o
n
tr
o
l (
D
T
C
)
[
3
3
]
,
[
3
4
]
an
d
m
o
d
el
-
b
ased
p
r
ed
ictiv
e
co
n
tr
o
l
(
MPC
)
[
3
5
]
.
Desp
ite
th
e
d
iv
er
s
ity
o
f
ap
p
r
o
ac
h
es,
th
e
m
ajo
r
ity
o
f
th
ese
m
eth
o
d
s
r
ely
o
n
f
ield
-
o
r
ien
ted
c
o
n
tr
o
l
(
FOC
)
[
3
6
]
,
[
3
7
]
wh
er
e
m
ac
h
in
e
p
h
ase
v
a
r
iab
les
u
n
d
e
r
g
o
tr
an
s
f
o
r
m
atio
n
in
to
eith
er
a
s
tatio
n
ar
y
o
r
r
o
tatin
g
r
ef
er
e
n
ce
f
r
am
e.
T
h
is
tr
an
s
f
o
r
m
atio
n
,
f
ac
ilit
ated
b
y
a
s
u
ita
b
le
m
atr
ix
,
is
th
en
r
eg
u
lated
u
s
in
g
c
o
n
tr
o
ller
s
lik
e
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI)
,
p
r
o
p
o
r
tio
n
al
-
r
eso
n
an
t
(
PR
)
,
o
r
p
r
e
d
ictiv
e
co
n
tr
o
ller
s
.
T
h
er
e
ar
e
two
m
ain
a
p
p
r
o
a
ch
e
s
to
FOC
:
d
ir
ec
t
r
o
to
r
FOC
an
d
in
d
ir
ec
t
r
o
t
o
r
FOC
.
T
h
ese
tw
o
ap
p
r
o
ac
h
es
d
if
f
er
in
h
o
w
th
ey
d
eter
m
i
n
e
th
e
r
o
t
o
r
an
g
le.
So
,
th
is
p
ap
er
will
u
s
e
in
d
ir
ec
t
r
o
to
r
FOC
(
I
R
FOC
)
as
th
e
co
n
tr
o
llin
g
m
ec
h
an
is
m
f
o
r
th
e
s
ix
-
p
h
ase
m
ac
h
in
es.
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.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
162
-
174
164
2
.
1
.
Six
-
ph
a
s
e
m
a
chines
win
din
g
s
T
h
e
s
i
x
-
p
h
ase
d
r
i
v
e
co
n
s
is
ts
o
f
a
s
i
x
-
p
h
ase
in
d
u
c
ti
o
n
m
o
to
r
e
q
u
i
p
p
e
d
w
it
h
two
i
n
d
e
p
e
n
d
e
n
t
t
h
r
ee
-
p
h
ase
win
d
i
n
g
s
ets
(
a
1
b
1
c
1
a
n
d
a
2
b
2
c
2
)
,
e
ac
h
p
o
w
er
e
d
s
e
p
a
r
at
el
y
b
y
t
wo
i
n
s
u
lat
e
d
-
g
a
te
b
i
p
o
la
r
tr
an
s
is
to
r
(
I
GB
T
)
-
b
ase
d
two
-
l
ev
el
v
o
l
ta
g
e
s
o
u
r
c
e
co
n
v
er
t
er
s
(
VSC
1
a
n
d
VSC
2
)
.
W
i
n
d
i
n
g
s
1
an
d
2
a
r
e
c
o
n
n
ec
te
d
in
a
s
t
ar
c
o
n
f
ig
u
r
at
io
n
,
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
(
a
)
,
wit
h
t
h
e
n
e
u
t
r
a
ls
,
n
1
an
d
n
2
,
eit
h
er
k
ep
t
is
o
lat
ed
f
o
r
a
tw
o
-
n
e
u
tr
al
(
2
N
)
s
et
u
p
o
r
j
o
i
n
e
d
in
a
s
i
n
g
le
-
n
e
u
t
r
a
l
(
1
N
)
c
o
n
f
i
g
u
r
ati
o
n
.
T
y
p
i
ca
l
ly
,
t
h
e
t
h
r
ee
-
p
h
ase
w
in
d
i
n
g
s
1
an
d
2
ar
e
v
ie
we
d
as
s
p
ati
all
y
d
is
p
la
ce
d
b
y
a
n
an
g
l
e,
d
e
n
o
te
d
as
,
ill
u
s
t
r
ate
d
in
Fi
g
u
r
e
1
(
b
)
f
o
r
t
h
e
S6
-
I
M
a
n
d
Fi
g
u
r
e
1
(
c
)
f
o
r
t
h
e
D
3
-
I
M
.
T
h
e
m
ai
n
t
y
p
es
o
f
s
ix
-
p
h
ase
m
ac
h
i
n
es
a
r
e
d
e
f
i
n
e
d
b
y
v
a
lu
es:
=
6
0
º
f
o
r
S
6
-
I
M
a
n
d
=
0
º
f
o
r
D3
-
I
M.
(
a)
(
b
)
(
c)
Fig
u
r
e
1
.
Six
-
p
h
ase
m
ac
h
in
e
win
d
in
g
s
:
(
a)
s
in
g
le
a
n
d
two
n
eu
tr
als co
n
n
ec
tio
n
,
(
b
)
S6
-
IM
,
an
d
(
c)
D3
-
I
M
t
h
at
s
p
atially
d
is
p
lace
d
b
y
a
n
ar
b
itra
r
y
an
g
le,
γ
b
e
twee
n
th
r
ee
-
p
h
ase
win
d
in
g
s
2
.
2
.
T
he
lim
it
s
o
f
curr
ent
Fo
r
a
h
ea
lth
y
d
r
iv
e,
th
e
cu
r
r
en
t
lim
it
is
estab
lis
h
ed
b
ased
o
n
t
h
e
r
ated
p
h
ase
cu
r
r
e
n
t,
wh
ich
is
o
b
s
er
v
ed
wh
en
th
e
m
ac
h
in
e
o
p
er
ates
at
its
r
ated
s
y
n
ch
r
o
n
o
u
s
f
r
eq
u
en
cy
(
ω
s
)
an
d
r
ated
s
lip
f
r
e
q
u
en
cy
(
ω
slip
)
.
Un
d
e
r
n
o
r
m
al
co
n
d
itio
n
s
,
th
e
m
ac
h
i
n
e’
s
o
p
er
atio
n
is
co
n
tr
o
lled
b
y
m
an
a
g
in
g
th
e
α
-
β
cu
r
r
en
t
co
m
p
o
n
en
ts
wh
ile
en
s
u
r
in
g
th
at
t
h
e
x
-
y
a
n
d
ze
r
o
-
s
eq
u
en
ce
co
m
p
o
n
en
ts
r
em
ain
at
ze
r
o
.
T
o
ev
al
u
ate
m
a
ch
in
e
p
er
f
o
r
m
a
n
ce
f
o
llo
win
g
a
f
a
u
lt,
th
e
d
er
atin
g
f
ac
to
r
,
d
e
n
o
ted
as
a
,
is
ap
p
lie
d
.
T
h
is
f
ac
to
r
r
ep
r
esen
ts
t
h
e
p
er
-
u
n
it
v
alu
e
o
f
th
e
m
o
d
u
lu
s
o
f
th
e
p
o
s
t
-
f
au
lt
α
-
β
cu
r
r
en
t
p
h
aso
r
,
with
a
co
n
s
tr
ain
t
th
at
th
e
m
a
x
im
u
m
p
h
ase
cu
r
r
en
t
p
o
s
t
-
f
au
lt
d
o
es
n
o
t su
r
p
ass
th
e
r
ated
p
h
ase
cu
r
r
en
t [
3
4
]
,
f
o
r
m
u
lated
as
(
1
)
.
=
|
|
−
|
|
(
1
)
T
h
e
d
er
atin
g
f
ac
t
o
r
,
d
en
o
ted
a
s
a
,
is
u
s
ed
t
o
ev
al
u
ate
th
e
p
o
s
t
-
f
au
lt
to
r
q
u
e
ca
p
ac
ity
o
f
a
m
ac
h
in
e
with
a
s
p
ec
if
ic
f
au
lt
wh
ile
en
s
u
r
in
g
it
r
em
ai
n
s
with
in
th
e
s
tan
d
ar
d
cu
r
r
en
t
li
m
it.
A
lar
g
er
d
er
atin
g
f
ac
to
r
in
d
icate
s
th
at
a
h
ig
h
er
m
ax
im
u
m
to
r
q
u
e
ca
n
b
e
attain
ed
wh
ile
s
till
r
esp
ec
tin
g
th
e
cu
r
r
en
t lim
it r
estrictio
n
.
2
.
3
.
T
he
lim
it
s
o
f
v
o
lt
a
g
e
R
ec
en
t
s
tu
d
ies,
s
u
ch
as
ar
ticle
[
3
8
]
,
h
av
e
e
x
am
in
ed
th
e
f
a
u
lt
-
to
ler
an
t
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
o
f
th
r
ee
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
d
r
iv
es
with
r
esp
ec
t
to
cu
r
r
en
t
an
d
v
o
ltag
e
co
n
s
tr
ain
ts
.
Fo
r
f
au
lt
-
t
o
ler
an
t
m
u
lti
-
p
h
ase
m
ac
h
in
es,
r
esear
ch
h
as
ex
p
lo
r
ed
DC
-
lin
k
v
o
ltag
e
lim
itatio
n
s
u
n
d
er
ce
r
tain
o
p
en
-
p
h
ase
co
n
d
itio
n
s
to
ac
h
ie
v
e
o
p
tim
al
cu
r
r
e
n
t
in
th
e
r
e
m
ain
i
n
g
o
p
e
r
atio
n
al
p
h
ases
[
2
4
]
.
Fu
r
th
er
m
o
r
e
,
th
e
m
a
x
im
u
m
u
tili
z
atio
n
o
f
th
e
DC
-
b
u
s
v
o
ltag
e
with
in
th
e
lin
ea
r
m
o
d
u
latio
n
r
a
n
g
e
f
o
r
n
o
r
m
al
o
p
er
ati
o
n
is
d
ef
in
ed
wh
en
th
e
p
ea
k
li
n
e
v
o
ltag
e
m
atc
h
es
th
e
DC
-
b
u
s
v
o
ltag
e.
I
n
a
s
tar
-
co
n
n
ec
ted
s
ix
-
p
h
ase
m
ac
h
in
e,
th
e
v
o
ltag
e
lim
it
ca
n
v
ar
y
d
e
p
en
d
in
g
o
n
wh
eth
er
th
e
n
eu
tr
als ar
e
co
n
n
ec
ted
in
a
1
N
o
r
2
N
co
n
f
i
g
u
r
atio
n
.
3.
M
AT
H
E
M
AT
I
CA
L
M
O
D
E
L
L
I
NG
O
F
SI
X
-
P
H
AS
E
I
N
DUCT
I
O
N
M
ACH
I
NE
S
3
.
1
.
Vec
t
o
r
s
pa
ce
deco
m
po
s
it
io
n
m
o
del
Usi
n
g
th
e
v
ec
to
r
s
p
ac
e
d
ec
o
m
p
o
s
itio
n
(
VSD)
m
eth
o
d
a
n
d
th
e
g
en
er
alize
d
C
lar
k
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
,
th
e
p
h
ase
cu
r
r
e
n
ts
ca
n
b
e
b
r
o
k
en
d
o
wn
in
t
o
α
,
β
,
x
,
y
,
0
+
,
an
d
0
-
co
m
p
o
n
en
ts
,
as r
ep
r
esen
ted
b
y
(
2
)
.
[
0
+
0
−
]
=
[
6
]
∙
[
1
1
1
2
2
2
]
(
2
)
I
n
th
is
p
ap
er
,
th
e
co
m
m
o
n
l
y
u
tili
ze
d
s
ix
-
p
h
ase
d
ec
o
u
p
lin
g
tr
an
s
f
o
r
m
atio
n
m
atr
ices
f
o
r
S6
-
I
M
an
d
D
3
-
I
M
m
ac
h
in
es a
r
e
em
p
l
o
y
ed
,
as p
r
o
v
id
ed
i
n
(
3
)
[
3
9
]
,
wh
e
r
e
=
ar
b
itra
r
y
a
n
g
le
an
d
=
2
3
⁄
.
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
P
o
s
t
-
fa
u
lt v
o
lta
g
e
limit a
s
s
ess
men
t fo
r
s
ix
-
p
h
a
s
e
in
d
u
ctio
n
ma
ch
in
es:
…
(
N
o
o
r
a
d
z
ia
n
ie
Mu
h
a
mma
d
Zin
)
165
[
6
]
=
1
√
3
∙
[
1
c
os
(
)
c
os
(
2
)
c
os
(
)
c
os
(
+
)
c
os
(
2
+
)
0
s
in
(
)
s
in
(
2
)
s
in
(
)
s
in
(
+
)
s
in
(
2
+
)
1
c
os
(
2
)
c
os
(
)
−
c
os
(
)
−
c
os
(
+
)
−
c
os
(
2
+
)
0
s
in
(
2
)
s
in
(
)
s
in
(
)
s
in
(
+
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s
in
(
2
+
)
1
√
2
⁄
1
√
2
⁄
1
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2
⁄
1
√
2
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1
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2
⁄
1
√
2
⁄
1
√
2
⁄
1
√
2
⁄
1
√
2
⁄
−
1
√
2
⁄
−
1
√
2
⁄
−
1
√
2
⁄
]
(
3
)
Ap
p
ly
in
g
th
e
estab
lis
h
ed
VSD
f
r
am
ewo
r
k
,
th
e
v
o
ltag
e
eq
u
ati
o
n
s
in
th
e
α
-
β
s
u
b
s
p
ac
e
ca
n
b
e
ex
p
r
ess
ed
as
f
u
n
ctio
n
s
o
f
m
ac
h
in
e
p
ar
a
m
eter
s
,
alo
n
g
with
s
tato
r
an
d
r
o
to
r
f
lu
x
,
a
n
d
s
tato
r
,
an
d
r
o
t
o
r
cu
r
r
en
ts
.
I
n
(
4
)
-
(
7
)
,
th
e
p
ar
am
eter
s
R
r
,
R
s
,
L
r
,
L
s
,
an
d
L
m
r
ep
r
esen
t
t
h
e
r
o
t
o
r
r
es
is
tan
ce
,
s
tato
r
r
esis
tan
ce
,
r
o
to
r
in
d
u
ctan
ce
,
s
tato
r
in
d
u
ctan
ce
,
an
d
m
ag
n
etizin
g
in
d
u
cta
n
ce
r
esp
ec
tiv
ely
,
wit
h
th
e
s
y
m
b
o
l
^
in
d
icatin
g
t
h
eo
r
etica
l
v
alu
es
o
f
v
o
ltag
es
an
d
f
lu
x
.
W
ith
in
th
e
I
R
FO
C
s
tr
ateg
y
,
r
o
to
r
q
u
an
titi
e
s
ca
n
n
o
t
b
e
d
ir
ec
tly
m
ea
s
u
r
ed
an
d
th
er
ef
o
r
e
m
u
s
t
b
e
esti
m
ated
u
s
in
g
th
e
m
ac
h
in
e
p
ar
am
eter
s
,
n
ec
ess
itatin
g
th
eir
r
em
o
v
al
f
r
o
m
th
e
v
o
lt
ag
e
eq
u
atio
n
s
.
B
y
lev
er
ag
in
g
(
8
)
a
n
d
(
9
)
,
th
e
α
-
β
v
o
ltag
es
f
o
r
th
e
in
d
u
ctio
n
m
a
ch
in
e
ar
e
d
e
f
in
ed
in
ter
m
s
o
f
m
ac
h
in
e
p
ar
am
eter
s
,
s
tato
r
cu
r
r
en
ts
,
an
d
o
p
e
r
atin
g
co
n
d
itio
n
s
.
̂
=
∙
+
̂
;
̂
=
∙
+
∙
(
4
)
̂
=
∙
+
̂
;
̂
=
∙
+
∙
(
5
)
0
=
∙
+
̂
+
̂
;
̂
=
∙
+
∙
(
6
)
0
=
∙
+
̂
−
̂
;
̂
=
∙
+
∙
(
7
)
̂
=
(
+
2
∙
∙
(
1
+
2
∙
2
2
⁄
)
)
∙
−
(
∙
∙
+
2
∙
(
1
+
2
∙
2
2
⁄
)
)
∙
;
=
1
−
2
⁄
(
8
)
̂
=
(
∙
∙
+
2
∙
(
1
+
2
∙
2
2
⁄
)
)
∙
+
(
+
2
∙
∙
(
1
+
2
∙
2
2
⁄
)
)
∙
;
=
−
(
9
)
T
h
e
v
o
ltag
es
in
th
e
x
-
y
an
d
0
-
s
u
b
s
p
ac
es
ca
n
b
e
ca
lcu
lated
u
s
in
g
cu
r
r
en
ts
an
d
m
ac
h
in
e
p
ar
a
m
eter
s
.
I
n
co
n
tr
ast
to
th
e
α
-
β
s
u
b
s
p
ac
e,
th
e
eq
u
atio
n
s
f
o
r
th
e
x
-
y
an
d
0
-
v
o
ltag
es
ar
e
m
u
ch
s
im
p
ler
,
as
th
ey
d
o
n
o
t
in
v
o
lv
e
an
y
r
o
t
o
r
co
m
p
o
n
en
ts
,
as sh
o
wn
in
(
1
0
)
-
(
1
2
)
:
̂
=
∙
+
∙
(
1
0
)
̂
=
∙
+
∙
(
1
1
)
̂
0
_
=
∙
0
−
+
0
−
∙
0
−
(
1
2
)
T
h
e
m
ac
h
in
e
p
ar
am
eter
s
L
ls0
-
an
d
L
lsxy
ar
e
th
e
s
tato
r
leak
a
g
e
in
d
u
ctan
ce
f
o
r
0
-
an
d
x
-
y.
3
.
2
.
P
ro
ce
s
s
o
f
pa
ra
m
e
t
er
estim
a
t
io
n
Fig
u
r
e
2
p
r
esen
ts
th
e
co
m
p
r
eh
en
s
iv
e
m
eth
o
d
f
o
r
esti
m
atin
g
m
ac
h
in
e
p
a
r
am
eter
s
.
T
h
e
p
ar
am
eter
esti
m
atio
n
ap
p
r
o
ac
h
b
eg
in
s
w
ith
th
e
x
-
y
s
u
b
s
p
ac
es,
p
r
o
ce
ed
s
with
th
e
0
-
s
u
b
s
p
ac
e
esti
m
atio
n
f
o
r
a
s
ix
-
p
h
ase
in
d
u
ctio
n
m
ac
h
in
e
in
a
1
N
co
n
f
ig
u
r
atio
n
,
an
d
c
o
n
clu
d
es
with
th
e
α
-
β
s
u
b
s
p
ac
es.
Acc
o
r
d
i
n
g
to
(
1
0
)
-
(
1
2
)
,
t
h
e
p
ar
am
eter
s
L
ls0
-
,
L
lsxy
,
an
d
ω
s
r
ep
r
esen
t th
e
s
tato
r
leak
a
g
e
in
d
u
ctan
ce
f
o
r
th
e
0
-
s
u
b
s
p
ac
e,
x
-
y
s
u
b
s
p
ac
e,
an
d
th
e
s
y
n
ch
r
o
n
o
u
s
f
r
eq
u
en
cy
,
r
esp
ec
tiv
ely
.
Du
r
in
g
p
o
s
t
-
f
au
lt
o
p
er
a
tio
n
,
x
-
y
an
d
0
-
cu
r
r
e
n
ts
ca
n
b
e
ex
p
r
ess
ed
in
ter
m
s
o
f
α
-
β
cu
r
r
en
ts
,
u
s
in
g
c
o
ef
f
ici
en
ts
K1
-
K8
as o
u
tlin
ed
i
n
(
1
3
)
-
(
1
5
)
:
̂
=
∙
+
∙
(
1
3
)
̂
=
∙
+
∙
(
1
4
)
̂
0
−
=
∙
+
∙
(
1
5
)
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.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
162
-
174
166
B
ased
o
n
α
-
β
cu
r
r
e
n
ts
f
o
r
th
e
in
d
u
ctio
n
m
o
to
r
,
it will
b
e
s
im
p
lifie
d
th
e
x
-
y
a
n
d
0
-
v
o
ltag
e
a
s
in
(
1
6
)
-
(
2
1
)
.
=
∙
1
+
∙
∙
2
(
1
6
)
=
∙
2
−
∙
∙
1
(
1
7
)
=
∙
3
+
∙
∙
4
(
1
8
)
=
∙
4
−
∙
∙
3
(
1
9
)
=
∙
7
+
∙
0
∙
8
(
2
0
)
=
∙
8
−
∙
0
∙
7
(
2
1
)
T
h
e
m
ac
h
in
e
is
in
itially
o
p
er
ated
in
p
s
eu
d
o
-
o
p
tim
al
p
o
wer
f
ac
to
r
m
o
d
e
at
1
4
0
0
r
p
m
,
u
s
in
g
r
ated
co
n
tr
o
l
v
o
ltag
e,
ω
slip
,
a
n
d
ω
s
.
T
h
e
lo
ad
is
in
cr
ea
s
ed
g
r
ad
u
ally
u
n
til
th
e
p
h
ase
cu
r
r
e
n
t
r
ea
ch
es
its
r
ated
th
r
esh
o
ld
wh
ile
m
ain
tain
in
g
th
e
f
lu
x
cu
r
r
en
t
at
1
.
3
A.
Me
asu
r
em
en
ts
f
o
r
co
n
tr
o
l
c
u
r
r
e
n
ts
,
v
o
ltag
es
,
an
d
s
y
n
ch
r
o
n
o
u
s
f
r
eq
u
e
n
cy
a
r
e
g
ath
er
ed
o
v
er
o
n
e
f
u
n
d
am
e
n
tal
cy
cle,
an
d
th
e
n
ex
p
o
r
ted
to
ex
ce
l
f
o
r
p
a
r
am
e
ter
o
p
tim
izatio
n
.
I
n
E
x
ce
l,
So
lv
er
is
em
p
l
o
y
ed
to
f
in
e
-
tu
n
e
m
ac
h
in
e
p
ar
am
eter
s
(
R
s
,
L
ls0
,
an
d
L
lsxy
)
b
y
r
ed
u
cin
g
d
is
cr
ep
a
n
cies
b
etwe
en
o
b
s
er
v
ed
a
n
d
th
eo
r
et
ical
v
o
ltag
es
in
th
e
0
-
an
d
x
-
y
s
u
b
s
p
ac
es.
Su
b
s
eq
u
en
tly
,
p
ar
am
eter
s
in
th
e
α
-
β
p
lan
e
(
L
m
,
R
r
,
L
lr
αβ
,
an
d
L
ls
αβ
)
ar
e
d
eter
m
in
ed
,
ass
u
m
in
g
th
at
th
e
s
tato
r
r
esis
tan
ce
(
R
s
)
is
c
o
n
s
is
ten
t
with
th
at
d
er
iv
ed
f
r
o
m
th
e
x
-
y
s
u
b
s
p
ac
e.
I
n
itial
esti
m
ate
s
ar
e
u
s
ed
t
o
co
m
p
u
te
th
eo
r
etica
l
α
-
β
v
o
ltag
es,
an
d
f
u
r
th
er
o
p
tim
izatio
n
is
c
o
n
d
u
cted
u
s
in
g
e
x
ce
l
s
o
lv
er
.
Un
lik
e
in
th
e
x
-
y
s
u
b
s
p
ac
e,
α
-
β
p
a
r
am
eter
s
ar
e
s
en
s
itiv
e
t
o
th
e
m
ac
h
in
e'
s
o
p
er
atin
g
c
o
n
d
itio
n
s
,
p
ar
ticu
lar
ly
s
y
n
ch
r
o
n
o
u
s
a
n
d
s
lip
f
r
eq
u
en
cies.
W
h
en
ω
s
a
n
d
ω
slip
ar
e
h
ig
h
,
th
e
m
ag
n
etizin
g
b
r
an
c
h
b
ec
o
m
es
d
o
m
in
an
t,
wh
ile
at
lo
wer
ω
s
an
d
ω
slip
v
al
u
es,
th
e
r
o
to
r
b
r
a
n
ch
ex
e
r
ts
a
m
o
r
e
s
ig
n
if
ican
t
in
f
lu
en
ce
.
T
o
a
d
d
r
ess
th
ese
v
ar
iatio
n
s
,
o
p
tim
iza
tio
n
is
p
er
f
o
r
m
ed
u
n
d
e
r
two
d
is
tin
ct
co
n
d
itio
n
s
:
Hig
h
ω
s
an
d
ω
slip
(
1
4
0
0
r
p
m
with
r
ated
i
q
=
3
.
3
A)
a
n
d
L
o
w
ω
s
an
d
ω
slip
(
3
5
0
r
p
m
at
n
o
lo
ad
,
i
q
=
0
.
5
A)
,
a
k
in
to
lo
ck
ed
-
r
o
to
r
an
d
n
o
-
l
o
ad
t
ests
.
Fin
ally
,
m
ac
h
in
e
p
ar
am
eter
s
f
r
o
m
all
s
u
b
s
p
ac
es
ar
e
u
tili
ze
d
to
ca
lcu
late
th
eo
r
etica
l v
o
ltag
es
.
3
.
3
.
F
a
ult
-
t
o
lera
nt
s
t
ra
t
eg
y
ba
s
e
d o
n m
a
x
i
m
um
t
o
rque
(
M
T
)
Ma
in
tain
in
g
th
e
n
o
m
in
al
cu
r
r
en
t
lim
it
is
e
s
s
en
tial
f
o
r
th
e
in
v
er
ter
,
wh
ich
is
g
en
er
ally
s
et
to
o
p
er
ate
with
a
ca
p
p
ed
c
u
r
r
e
n
t v
al
u
e
to
p
r
o
tect
th
e
d
r
iv
e,
ev
e
n
in
f
au
lt
co
n
d
itio
n
s
.
W
h
en
ap
p
ly
i
n
g
t
h
e
m
ax
im
u
m
to
r
q
u
e
(
MT
)
s
tr
ateg
y
d
u
r
in
g
p
o
s
t
-
f
a
u
lt,
th
e
o
b
jecti
v
e
is
to
m
in
im
ize
th
e
p
ea
k
p
h
ase
cu
r
r
en
t
in
th
e
r
e
m
ain
in
g
f
u
n
ctio
n
al
p
h
ases
.
Sev
er
al
m
eth
o
d
s
ar
e
a
v
ailab
le
to
o
p
tim
ize
p
o
s
t
-
f
a
u
lt
cu
r
r
e
n
ts
;
h
er
e,
we
a
d
o
p
t
th
e
a
p
p
r
o
ac
h
o
u
tlin
ed
i
n
[
1
6
]
,
wh
ich
r
elies
o
n
d
ec
o
u
p
l
ed
v
ar
iab
les.
T
h
e
co
ef
f
icien
t
'
K'
is
u
s
ed
to
d
e
f
in
e
th
e
r
elatio
n
s
h
ip
b
etwe
en
n
o
n
-
en
er
g
y
-
co
n
v
er
tin
g
cu
r
r
en
ts
an
d
th
e
α
-
β
r
ef
er
en
ce
s
.
Fo
r
a
s
ix
-
p
h
ase
m
ac
h
in
e,
o
p
tim
izatio
n
is
r
eq
u
ir
ed
o
n
ly
f
o
r
th
e
x
-
y
cu
r
r
e
n
ts
an
d
th
e
ze
r
o
-
s
eq
u
en
ce
cu
r
r
e
n
t,
0
-
as
s
h
o
wn
in
(
2
2
)
-
(
2
5
)
,
with
ze
r
o
-
s
eq
u
e
n
ce
0+
s
et
to
ze
r
o
,
lead
in
g
to
K5
an
d
K6
b
ein
g
eq
u
al
to
0
.
∗
=
1
∙
∗
+
2
∙
∗
(
2
2
)
∗
=
3
∙
∗
+
4
∙
∗
(
2
3
)
∗
0
+
=
5
∙
∗
+
6
∙
∗
(
2
4
)
∗
0
−
=
7
∙
∗
+
8
∙
∗
(
2
5
)
A
n
o
n
-
lin
ea
r
o
p
tim
izatio
n
tech
n
iq
u
e,
s
p
ec
if
ically
th
e
g
e
n
er
alize
d
r
ed
u
ce
d
g
r
ad
ien
t
(
GR
G)
m
eth
o
d
av
ailab
le
in
th
e
“So
lv
e
r
”
to
o
l
in
MS
Of
f
ice
E
x
ce
l,
is
ap
p
lied
to
o
p
tim
ize
p
o
s
t
-
f
au
lt
c
u
r
r
en
ts
.
Fo
r
m
ax
im
u
m
to
r
q
u
e
(
MT
)
m
o
d
es,
th
e
o
p
tim
izatio
n
o
b
jectiv
es
ar
e
d
r
awn
f
r
o
m
(
26
)
an
d
s
er
v
e
as
th
e
co
s
t
f
u
n
ctio
n
,
,
with
th
e
g
o
al
o
f
m
ax
im
izin
g
to
r
q
u
e.
T
h
is
in
v
o
lv
es
m
a
x
im
izin
g
th
e
α
-
β
p
h
aso
r
a
m
p
litu
d
e
wh
i
le
ad
h
er
in
g
to
th
e
co
n
s
tr
ain
ts
lis
ted
in
(
2
7
).
=
|
|
(
2
6
)
=
0
{
ℎ
}
0
+
=
0
;
m
in
the
m
a
x
p
h
a
s
e
cu
rre
nt
ϵ
{
h
e
a
l
t
h
y
p
h
a
s
e
s
}
(2
7
)
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
P
o
s
t
-
fa
u
lt v
o
lta
g
e
limit a
s
s
ess
men
t fo
r
s
ix
-
p
h
a
s
e
in
d
u
ctio
n
ma
ch
in
es:
…
(
N
o
o
r
a
d
z
ia
n
ie
Mu
h
a
mma
d
Zin
)
167
T
ab
le
s
1
an
d
2
illu
s
tr
ate
th
e
c
o
n
n
ec
tio
n
b
etwe
en
α
-
β
,
x
-
y
,
0
-
,
an
d
0+
cu
r
r
en
ts
ac
r
o
s
s
all
f
au
lt
s
ce
n
ar
io
s
an
d
n
eu
tr
al
c
o
n
f
ig
u
r
atio
n
s
f
o
r
th
e
S6
-
I
M
an
d
D
3
-
I
M,
r
esp
ec
tiv
e
ly
.
T
h
e
im
p
lem
e
n
tatio
n
o
f
co
ef
f
icien
ts
K1
-
K8
in
th
e
eq
u
atio
n
s
ig
n
if
ies th
e
in
f
lu
en
ce
o
f
ze
r
o
s
eq
u
e
n
ce
cu
r
r
en
t
an
d
x
-
y
c
o
m
p
o
n
en
ts
o
n
p
o
s
t
-
f
a
u
lt e
x
ec
u
tio
n
.
Fig
u
r
e
2
.
Par
am
eter
esti
m
atio
n
f
lo
wch
ar
t
T
ab
le
1
.
Po
s
t
-
f
au
lt st
r
ateg
y
b
a
s
ed
o
n
x
-
y
,
0
-
,
a
n
d
0
+
cu
r
r
en
t
co
m
p
o
n
en
ts
r
ec
o
n
f
ig
u
r
atio
n
o
v
er
1
OPF s
ce
n
ar
io
d
u
r
in
g
2
N
an
d
1
N
f
o
r
S6
-
IM
C
a
se
C
o
e
f
f
i
c
i
e
n
t
s,
K
K1
K2
K3
K4
K5
K6
K7
K8
H
e
a
l
t
h
y
0
0
0
0
0
0
0
0
1
F
a
u
l
t
y
p
h
a
se
(
1
N
)
1
O
P
F
-
0
.
6
4
8
0
0
-
0
.
3
6
8
0
0
-
0
.
4
9
7
0
0
.
7
7
1
F
a
u
l
t
y
p
h
a
se
(
2
N
)
1
O
P
F
-
1
0
0
-
0
.
3
3
3
0
0
0
0
0
.
5
0
0
T
ab
le
2
.
Po
s
t
-
f
au
lt st
r
ateg
y
b
a
s
ed
o
n
x
-
y
,
0
-
,
an
d
0
+
c
u
r
r
e
n
t
co
m
p
o
n
en
ts
r
ec
o
n
f
ig
u
r
atio
n
o
v
er
1
OPF s
ce
n
ar
io
d
u
r
in
g
2
N
an
d
1
N
f
o
r
D3
-
IM
C
a
se
C
o
e
f
f
i
c
i
e
n
t
s,
K
K1
K2
K3
K4
K5
K6
K7
K8
H
e
a
l
t
h
y
0
0
0
0
0
0
0
0
1
F
a
u
l
t
y
p
h
a
se
(
1
N
)
1
O
P
F
-
0
.
6
6
7
0
.
5
7
7
1
.
7
3
2
0
0
0
-
0
.
4
7
1
-
0
.
8
1
7
0
.
5
0
0
F
a
u
l
t
y
p
h
a
se
(
2
N
)
1
O
P
F
-
1
0
0
-
0
.
3
3
3
0
0
0
0
0
.
5
0
0
4.
P
O
ST
-
F
AUL
T
P
E
RF
O
R
M
ANCE
F
O
R
SI
X
-
P
H
AS
E
I
M
UND
E
R
DIFF
E
RE
N
T
O
P
E
RAT
I
NG
P
O
I
NT
It
is
im
p
o
r
tan
t
to
k
ee
p
in
m
in
d
th
at
b
ased
o
n
o
p
er
atin
g
p
o
in
ts
th
e
m
ax
im
u
m
lin
e
-
to
-
lin
e
v
o
ltag
e
ca
n
v
ar
y
,
p
ar
tic
u
lar
ly
ω
s
an
d
ω
sl
ip
.
Un
d
er
s
tan
d
in
g
h
o
w
lin
e
-
to
-
lin
e
v
o
ltag
e
v
a
r
ies
with
t
h
ese
p
ar
am
eter
s
is
im
p
o
r
tan
t.
T
h
e
ω
s
is
d
ef
in
e
d
a
s
s
h
o
wn
in
(
2
8
).
=
2
(2
8
)
W
h
en
o
p
er
atin
g
u
p
to
th
e
b
ase
s
p
ee
d
,
th
e
f
r
e
q
u
en
c
y
(
f
)
m
atc
h
es th
e
r
ated
f
r
eq
u
en
c
y
wh
en
t
h
e
m
ax
im
u
m
v
al
u
e
o
f
ω
s
is
r
ea
ch
ed
.
Fo
r
a
5
0
Hz
in
d
u
ctio
n
m
ac
h
in
e,
t
h
e
p
ea
k
ω
s
eq
u
als
3
1
4
r
ad
/s
.
C
o
n
v
e
r
s
ely
,
ω
slip
d
ep
e
n
d
s
o
n
f
ac
to
r
s
s
u
ch
as th
e
r
o
t
o
r
tim
e
c
o
n
s
tan
t,
i
qs
an
d
i
ds
as d
etailed
in
(
2
9
).
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.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
162
-
174
168
=
1
.
;
=
(2
9
)
T
h
e
m
ax
im
u
m
s
lip
f
r
eq
u
en
cy
ca
n
b
e
d
ete
r
m
in
ed
as
a
f
u
n
c
tio
n
o
f
i
qs
,
i
ds
u
p
t
o
th
e
r
ated
co
n
d
itio
n
,
an
d
th
e
d
er
atin
g
f
ac
t
o
r
,
a
as sp
ec
if
ied
in
(
30
)
an
d
(
3
1
).
|
′
|
≤
|
|
√
′
2
+
′
2
≤
|
|
;
=
|
|
(
3
0
)
√
2
+
(
.
.
)
2
≤
∴
≤
√
2
−
2
2
.
2
=
√
2
|
|
−
2
2
.
2
=
√
2
(
2
+
2
)
−
2
2
.
2
=
√
(
)
2
−
(
1
−
2
2
)
(
3
1
)
Yet,
th
e
m
ax
im
u
m
s
lip
f
r
eq
u
e
n
cy
,
,
is
o
n
ly
v
alid
u
n
d
e
r
th
e
c
o
n
d
itio
n
s
p
ec
if
ie
d
in
(
3
2
).
∙
>
(3
2
)
5.
RE
SU
L
T
AND
DI
SCUS
SI
O
NS
T
h
e
p
er
f
o
r
m
an
ce
o
f
an
elec
tr
ical
m
ac
h
in
e
is
in
f
lu
en
ce
d
n
o
t
ju
s
t
b
y
cu
r
r
en
t
lim
its
b
u
t
b
y
v
o
ltag
e
co
n
s
tr
ain
ts
also
.
T
h
ese
v
o
ltag
e
lim
its
ar
e
co
n
n
ec
ted
to
th
e
in
v
er
ter
’
s
ab
ilit
y
to
p
r
o
v
id
e
th
e
r
eq
u
ir
ed
v
o
ltag
es to
th
e
m
ac
h
in
e,
wh
ich
ar
e
p
r
im
a
r
ily
d
eter
m
in
ed
b
y
th
e
d
esig
n
o
f
th
e
in
v
er
ter
,
th
e
win
d
in
g
c
o
n
f
ig
u
r
atio
n
o
f
th
e
m
ac
h
in
e,
a
n
d
th
e
DC
-
lin
k
v
o
ltag
e.
On
ce
t
h
e
p
o
s
t
-
f
au
lt
c
u
r
r
en
ts
ar
e
d
eter
m
in
e
d
,
th
e
v
o
ltag
e
n
ec
ess
ar
y
to
p
r
o
d
u
ce
th
ese
cu
r
r
en
ts
is
af
f
ec
ted
b
y
b
o
th
th
e
d
e
r
atin
g
f
ac
to
r
an
d
th
e
m
ac
h
in
e'
s
p
ar
am
et
er
s
,
as
s
h
o
wn
ea
r
lier
in
T
ab
les
1
an
d
2
.
T
a
b
le
3
,
o
n
th
e
o
th
er
h
an
d
,
s
u
m
m
ar
izes
th
e
m
ac
h
in
e
p
ar
am
ete
r
s
u
s
ed
f
o
r
t
h
e
S6
-
I
M
an
d
D3
-
I
M
m
o
d
els.
W
ith
th
e
g
iv
en
v
o
ltag
e
eq
u
atio
n
s
an
d
m
ac
h
i
n
e
p
ar
am
eter
s
,
th
e
v
o
ltag
es
f
o
r
th
e
m
ac
h
in
e
’
s
d
ec
o
u
p
le
d
s
u
b
s
p
ac
es
ca
n
b
e
c
o
m
p
u
ted
b
ased
o
n
th
e
p
o
s
t
-
f
au
lt
cu
r
r
en
ts
an
d
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
e
p
o
s
t
-
f
au
lt
p
h
ase
v
o
ltag
es
ca
n
b
e
d
er
iv
e
d
b
y
ap
p
ly
in
g
th
e
in
v
er
s
e
C
lar
k
e
tr
an
s
f
o
r
m
atio
n
to
th
e
co
m
p
o
n
en
ts
v
α
-
β,
x
-
y,
0+
0
-
.
T
h
e
p
o
s
t
-
f
au
lt
lin
e
-
to
-
lin
e
v
o
ltag
es
ar
e
ca
lcu
lated
b
y
f
in
d
in
g
th
e
d
if
f
er
en
ce
s
b
etwe
en
th
ese
p
h
ase
v
o
ltag
es,
en
ab
lin
g
th
e
d
eter
m
in
atio
n
o
f
th
e
m
a
x
i
m
u
m
lin
e
-
to
-
lin
e
v
o
ltag
e
u
n
d
e
r
d
if
f
er
e
n
t
f
au
lt
o
p
e
r
atin
g
s
ce
n
ar
io
s
.
T
h
er
ef
o
r
e,
th
e
r
esu
lts
will b
e
p
r
esen
ted
in
two
s
ec
tio
n
s
,
b
ased
o
n
th
e
v
o
ltag
e
lim
it r
elativ
e
to
ω
s
an
d
ω
slip
a
p
p
r
o
ac
h
.
T
ab
le
3
.
Ma
ch
i
n
e
p
ar
am
ete
r
s
f
o
r
S6
-
I
M
a
n
d
D3
-
IM
M
a
c
h
i
n
e
p
a
r
a
m
e
t
e
r
s
C
o
n
v
e
r
t
e
r
p
a
r
a
m
e
t
e
r
s
=
12
.
532
=
5
.
776
=
78
=
420
=
6
=
3
.
634
0
=
6
_
=
29
.
04
/
=
280
=
50
5
.
1
.
Vo
lt
a
g
e
lim
it
s
in re
la
t
io
n
t
o
s
y
nchro
no
us
f
re
q
uency
,
ω
s
Un
d
er
h
ea
lth
y
o
p
e
r
atin
g
co
n
d
itio
n
s
,
b
o
th
m
ac
h
in
e
ty
p
es
o
p
er
ate
at
1
p
er
u
n
it
(
p
.
u
.
)
,
in
d
i
ca
tin
g
th
at
n
o
n
e
o
f
th
e
p
h
ases
ar
e
ex
p
er
i
en
cin
g
f
au
lts
.
T
h
e
lin
e
-
to
-
lin
e
v
o
ltag
es
ar
e
n
o
r
m
alize
d
ag
ai
n
s
t
th
e
m
ax
im
u
m
h
ea
lth
y
lin
e
-
to
-
lin
e
v
o
ltag
e
f
o
r
ea
ch
s
ix
-
p
h
ase
m
a
ch
in
e
ty
p
e.
As a
r
esu
lt,
th
e
v
o
ltag
e
lim
its
d
if
f
er
ac
co
r
d
in
g
t
o
th
e
n
eu
tr
al
c
o
n
f
ig
u
r
atio
n
:
S6
-
IM
-
1
N
h
as
a
lim
it
o
f
1
p
.
u
.
,
w
h
ile
S6
-
IM
-
2
N
is
lim
ited
to
0
.
8
6
6
p
.
u
.
;
b
o
th
D3
-
IM
-
1
N
an
d
D3
-
IM
-
2
N
h
av
e
a
v
o
ltag
e
lim
it
o
f
1
p
.
u
.
I
t
r
em
ain
s
u
n
clea
r
wh
eth
e
r
th
e
v
o
l
tag
e
lim
it
will
b
e
r
ea
ch
e
d
p
r
io
r
to
t
h
e
c
u
r
r
en
t
lim
it,
as
th
e
latter
c
o
u
ld
b
ec
o
m
e
a
lim
i
tin
g
f
ac
to
r
d
u
r
in
g
p
o
s
t
-
f
au
lt
o
p
er
atio
n
s
.
T
o
f
u
lly
u
n
d
er
s
tan
d
th
e
p
o
s
t
-
f
au
lt
ca
p
a
b
ilit
ies
o
f
th
e
S6
-
I
M
an
d
D3
-
I
M,
it
is
cr
u
cial
t
o
co
n
s
id
er
b
o
th
th
e
cu
r
r
e
n
t
an
d
v
o
ltag
e
lim
its
.
C
o
n
s
eq
u
en
tly
,
t
h
is
s
tu
d
y
ex
p
l
o
r
es
th
e
p
o
s
t
-
f
au
lt
v
o
ltag
e
lim
its
f
o
r
ea
ch
in
d
u
c
tio
n
m
ac
h
in
e
ty
p
e.
Fig
u
r
e
s
3
(
a)
-
3
(
c
)
illu
s
tr
ates
th
e
v
o
ltag
e
lim
its
in
ter
m
s
o
f
lin
e
-
to
-
lin
e
v
o
ltag
es
at
d
if
f
er
en
t v
alu
es
o
f
s
f
o
r
th
e
S6
-
I
M
m
ac
h
in
e
,
wh
ile
Fig
u
r
e
s
4
(a
)
-
4
(
c)
d
o
es
th
e
s
am
e
f
o
r
th
e
D3
-
I
M
m
ac
h
in
e,
b
o
th
ass
u
m
in
g
r
ated
cu
r
r
en
t
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
P
o
s
t
-
fa
u
lt v
o
lta
g
e
limit a
s
s
ess
men
t fo
r
s
ix
-
p
h
a
s
e
in
d
u
ctio
n
ma
ch
in
es:
…
(
N
o
o
r
a
d
z
ia
n
ie
Mu
h
a
mma
d
Zin
)
169
an
d
ω
slip
.
T
h
e
v
er
tical
d
ash
ed
l
in
e
in
th
e
g
r
ap
h
s
m
ar
k
s
th
e
r
at
ed
s
p
ee
d
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d
th
e
h
o
r
izo
n
tal
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ash
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e
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icate
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th
e
v
o
ltag
e
lim
it.
All r
esu
lts
ar
e
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ased
o
n
t
h
e
p
o
s
t
-
f
a
u
lt st
r
ateg
y
d
escr
ib
e
d
in
T
ab
les 1
an
d
2
.
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
Vo
ltag
e
lim
it u
n
d
e
r
d
if
f
er
en
t
ω
s
at
r
ated
ω
slip
a
n
d
r
ated
cu
r
r
e
n
t f
o
r
S6
-
I
M:
(
a)
h
ea
lth
y
co
n
d
itio
n
,
1
OPF u
n
d
er
(
b
)
1
N,
an
d
(
c)
2
N
c
o
n
f
ig
u
r
atio
n
s
(a
)
(b
)
(c
)
Fig
u
r
e
4
.
Vo
ltag
e
lim
it u
n
d
e
r
d
if
f
er
en
t
ω
s
at
r
ated
ω
slip
a
n
d
r
ated
cu
r
r
e
n
t f
o
r
D3
-
I
M:
(
a)
h
ea
lth
y
co
n
d
itio
n
,
1
OPF u
n
d
er
(
b
)
1
N,
an
d
(
c)
2
N
c
o
n
f
ig
u
r
atio
n
s
Fig
u
r
e
3
(
a
)
illu
s
tr
ates
th
e
r
esu
l
ts
f
o
r
h
ea
lth
y
o
p
er
atio
n
u
n
d
er
d
if
f
er
en
t
ω
s
at
r
ate
d
ω
slip
an
d
r
a
ted
cu
r
r
e
n
t
o
f
th
e
S6
-
I
M,
wh
ile
Fig
u
r
es
3
(
b
)
a
n
d
3
(
c)
illu
s
tr
ate
th
e
lin
e
-
to
-
lin
e
v
o
ltag
es
f
o
r
1
OPF
with
o
n
e
n
e
u
tr
al
(
1
N)
an
d
two
n
e
u
tr
als
(
2
N)
,
r
esp
ec
tiv
ely
.
As
s
h
o
wn
in
Fig
u
r
e
3
,
it
i
s
clea
r
th
at
in
1
OPF
s
ce
n
ar
io
s
,
wh
eth
er
u
n
d
er
1
N
o
r
2
N
c
o
n
f
ig
u
r
atio
n
s
,
th
e
cu
r
r
en
t lim
it is
r
ea
ch
ed
b
e
f
o
r
e
th
e
v
o
ltag
e
lim
it.
Sp
ec
ial
atten
tio
n
s
h
o
u
ld
b
e
g
iv
e
n
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
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w
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lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
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1
,
Ma
r
c
h
20
2
5
:
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-
174
170
th
e
1
OPF
with
1
N,
wh
er
e
th
e
m
ax
im
u
m
lin
e
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lin
e
v
o
ltag
e
s
alm
o
s
t
h
it
th
e
v
o
ltag
e
lim
it,
p
o
ten
tially
d
u
e
to
th
e
im
p
ac
t o
f
th
e
0
-
s
u
b
s
p
ac
e
.
Fig
u
r
e
4
(
a)
d
is
p
lay
s
th
e
r
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lt
s
f
o
r
a
h
ea
lth
y
-
o
p
er
ated
D3
-
I
M,
wh
ile
Fig
u
r
es
4
(
b
)
an
d
4
(
c
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illu
s
tr
ate
th
e
lin
e
-
to
-
lin
e
v
o
ltag
es
u
n
d
er
1
OPF
with
1
N
an
d
2
N
co
n
f
ig
u
r
atio
n
s
,
r
esp
ec
tiv
ely
.
T
h
e
r
esu
lts
s
h
o
wn
in
Fig
u
r
es
4
d
em
o
n
s
tr
ate
t
h
at
th
e
v
o
ltag
e
lim
it
o
f
D3
-
I
M
is
r
ea
ch
ed
b
e
f
o
r
e
t
h
e
c
u
r
r
en
t
lim
it.
T
h
is
in
d
icate
s
th
at
th
e
D3
-
I
M
is
p
r
im
ar
ily
d
eter
m
in
e
d
b
y
v
o
ltag
e
lim
itatio
n
s
at
d
if
f
er
e
n
t
ω
s
wh
en
o
p
e
r
atin
g
at
r
ated
ω
sli
p
an
d
r
ated
c
u
r
r
en
t.
I
n
s
u
m
m
ar
y
,
t
h
e
S6
-
I
M
g
en
e
r
a
lly
o
p
er
ates
with
in
th
e
cu
r
r
en
t
lim
it
d
u
r
in
g
m
o
s
t
f
a
u
lt
s
ce
n
ar
i
o
s
.
On
th
e
o
th
er
h
a
n
d
,
th
e
D3
-
I
M
is
en
ti
r
ely
co
n
tr
o
lled
b
y
th
e
lim
itatio
n
o
f
v
o
ltag
e
ac
r
o
s
s
all
f
au
lt
s
ce
n
ar
io
s
.
On
e
ca
n
ag
r
ee
th
at
D3
-
I
M
is
less
ag
g
r
e
s
s
iv
e
to
th
e
m
ac
h
in
e
win
d
in
g
s
f
o
r
n
o
t w
o
r
k
in
g
at
th
e
cu
r
r
en
t
lim
its
; d
esp
ite
th
is
,
D3
-
I
M
s
ee
m
s
to
b
e
n
o
t a
b
le
to
wo
r
k
at
h
ig
h
e
r
s
p
ee
d
s
.
T
h
e
S
6
-
I
M,
h
o
wev
er
,
ca
n
m
ain
tain
h
ig
h
er
s
p
ee
d
s
u
n
d
er
OPF
co
n
d
itio
n
s
,
m
ak
in
g
it
ad
v
an
tag
eo
u
s
in
v
ar
i
o
u
s
s
itu
atio
n
s
.
C
o
m
p
ar
ativ
ely
,
th
e
S6
-
I
M
is
co
n
s
id
er
ed
to
h
a
v
e
th
e
b
est
f
au
lt
-
to
ler
an
t
ca
p
ab
ili
ty
b
ased
o
n
its
v
o
ltag
e
lim
it
ac
r
o
s
s
d
if
f
er
en
t
ω
s
at
r
ated
ω
sli
p
an
d
cu
r
r
e
n
t.
T
h
is
in
d
icate
s
th
at
th
e
p
o
s
t
-
f
au
lt
b
e
h
av
io
r
o
f
th
e
S6
-
I
M
is
lar
g
ely
g
o
v
er
n
ed
b
y
th
e
c
u
r
r
en
t lim
it.
5
.
2
.
Vo
lt
a
g
e
lim
it
s
in re
la
t
io
n
t
o
s
lip
f
re
qu
e
ncy
,
ω
slip
Fro
m
th
e
α
-
β
v
o
ltag
e
eq
u
atio
n
s
d
is
cu
s
s
ed
in
s
ec
tio
n
3
,
it
is
ev
id
en
t
th
at
v
o
ltag
e
d
ep
en
d
s
o
n
cu
r
r
e
n
t,
o
p
er
atin
g
co
n
d
itio
n
s
,
an
d
m
ac
h
in
e
p
ar
am
eter
s
wh
ich
ar
e
p
r
i
m
ar
ily
in
f
lu
en
ce
d
b
y
ω
slip
an
d
ω
s
at
r
ated
cu
r
r
en
t.
T
o
co
m
p
r
eh
en
s
iv
ely
an
aly
ze
th
e
p
o
s
t
-
f
a
u
lt
p
er
f
o
r
m
an
ce
o
f
e
ac
h
in
d
u
ctio
n
m
ac
h
in
e,
it
is
es
s
en
tial
to
ev
alu
ate
th
e
v
o
ltag
e
lim
its
ac
r
o
s
s
v
ar
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
.
T
ab
le
s
4
an
d
5
p
r
o
v
id
e
th
e
m
ax
im
u
m
s
lip
f
r
eq
u
en
cies
f
o
r
th
e
S6
-
I
M
an
d
D3
-
I
M,
r
esp
ec
tiv
ely
,
co
n
s
id
er
in
g
2
N
an
d
1
N
co
n
f
ig
u
r
atio
n
s
u
n
d
er
1
OPF s
ce
n
ar
io
.
T
ab
le
4
.
Ma
x
im
u
m
s
lip
f
r
e
q
u
e
n
cy
,
ω
slip
o
f
S6
-
I
M
b
ased
o
n
n
eu
tr
al
co
n
n
ec
tio
n
s
f
o
r
1
OPF s
ce
n
ar
io
C
a
se
Ma
x
ω
s
l
i
p
(
r
a
d
/
s)
H
e
a
l
t
h
y
2
9
.
4
F
a
u
l
t
y
p
h
a
se
(
1
N
)
1
O
P
F
2
1
.
4
3
F
a
u
l
t
y
p
h
a
se
(
2
N
)
1
O
P
F
1
0
.
7
3
T
ab
le
5
.
Ma
x
im
u
m
s
lip
f
r
e
q
u
e
n
cy
,
ω
slip
o
f
D3
-
I
M
b
ased
o
n
n
eu
tr
al
co
n
n
ec
tio
n
s
f
o
r
1
OPF s
ce
n
ar
io
C
a
se
Ma
x
ω
s
l
i
p
(
r
a
d
/
s)
H
e
a
l
t
h
y
2
9
.
0
4
1
4
.
5
2
1
4
.
5
2
F
a
u
l
t
y
p
h
a
se
(
1
N
)
1
O
P
F
F
a
u
l
t
y
p
h
a
se
(
2
N
)
1
O
P
F
I
n
p
o
s
t
-
f
au
lt
co
n
tr
o
l,
th
e
f
lu
x
cu
r
r
en
t
,
i
ds
is
m
ain
tain
ed
at
its
r
ated
v
alu
e
o
f
1
.
3
A
f
o
r
b
o
th
S6
-
I
M
an
d
D3
-
I
M
m
ac
h
i
n
es.
T
h
e
s
y
n
ch
r
o
n
o
u
s
f
r
eq
u
e
n
cy
,
ω
s
is
s
et
to
3
1
4
r
ad
/s
as
d
ef
in
e
d
in
(
2
8
)
,
with
i
qs
r
ef
lectin
g
th
e
to
r
q
u
e
as
d
escr
ib
e
d
in
(
2
9
)
.
T
h
e
s
lip
f
r
eq
u
e
n
cy
lim
it,
ω
slip
r
ep
r
esen
ts
th
e
cu
r
r
en
t
c
o
n
s
tr
ai
n
t
f
o
r
th
e
p
o
s
t
-
f
au
lt
m
ac
h
in
e,
en
s
u
r
i
n
g
th
e
m
a
x
im
u
m
p
h
ase
cu
r
r
en
t
d
o
es
n
o
t
ex
ce
ed
th
e
r
ated
p
h
ase
cu
r
r
en
t.
C
o
n
s
eq
u
en
tly
,
th
e
m
ax
im
u
m
s
lip
f
r
e
q
u
en
c
y
,
ω
slip
max
ca
lcu
lated
u
s
in
g
(
3
1
)
,
d
ete
r
m
in
es
th
e
cu
r
r
e
n
t
lim
it
f
o
r
1
OPF
co
n
d
itio
n
s
.
On
th
e
o
th
er
h
an
d
,
t
h
e
v
o
ltag
e
li
m
it
is
in
f
lu
en
ce
d
b
y
th
e
n
eu
tr
al
co
n
f
ig
u
r
atio
n
s
.
No
tab
ly
,
in
s
ce
n
ar
io
s
an
aly
zin
g
v
o
ltag
e
ag
ai
n
s
t
ω
slip
,
m
e
d
iu
m
lin
e
-
to
-
lin
e
v
o
ltag
es
o
f
te
n
s
u
r
p
ass
lar
g
e
lin
e
-
to
-
lin
e
v
o
ltag
e
s
.
T
h
is
p
h
en
o
m
en
o
n
is
m
ain
ly
attr
ib
u
ted
to
th
e
im
p
ac
t
o
f
th
e
x
-
y
a
n
d
0
-
co
m
p
o
n
e
n
ts
,
lead
in
g
to
u
n
ev
en
ω
slip
ef
f
ec
ts
o
n
lin
e
-
to
-
lin
e
v
o
ltag
es.
Fig
u
r
es
5
an
d
6
illu
s
tr
ate
th
ese
v
o
ltag
e
co
n
s
tr
ain
ts
as
lin
e
-
to
-
lin
e
v
o
ltag
es
ac
r
o
s
s
d
if
f
er
en
t
ω
slip
s
ce
n
ar
io
s
at
r
ated
ω
s
an
d
cu
r
r
e
n
t
f
o
r
S6
-
I
M
an
d
D3
-
I
M,
r
esp
ec
tiv
ely
.
I
n
th
ese
f
ig
u
r
es,
th
e
v
er
tical
d
ash
ed
lin
e
in
d
icate
s
th
e
r
ated
v
alu
es
f
o
r
v
ar
io
u
s
f
au
lt
c
o
n
d
itio
n
s
,
with
th
e
d
er
atin
g
f
ac
to
r
,
a
r
ep
r
esen
tin
g
th
e
c
u
r
r
e
n
t
lim
it,
wh
ile
th
e
h
o
r
izo
n
tal
d
ash
ed
li
n
e
d
en
o
tes th
e
v
o
ltag
e
lim
it.
Fig
u
r
e
5
(
a)
illu
s
tr
ates
th
e
o
u
t
co
m
es
o
f
h
ea
lth
y
o
p
er
atio
n
f
o
r
S6
-
I
M,
wh
er
ea
s
Fig
u
r
es
5
(
b
)
an
d
5
(
c)
d
is
p
lay
th
e
lin
e
-
to
-
lin
e
v
o
ltag
e
s
u
n
d
er
1
OPF
s
ce
n
ar
io
with
1
N
an
d
2
N
co
n
f
ig
u
r
atio
n
s
,
r
esp
ec
tiv
ely
.
Un
d
er
r
ated
ω
s
,
it
is
o
b
s
er
v
ed
th
at,
th
e
cu
r
r
en
t
lim
it
o
f
m
ax
im
u
m
lin
e
v
o
ltag
es
is
r
ea
ch
ed
b
ef
o
r
e
th
e
v
o
lt
ag
e
lim
it.
No
tab
ly
,
f
o
r
1
OPF
u
n
d
e
r
1
N
f
o
r
S6
-
I
M,
th
e
m
ax
im
u
m
lin
e
-
to
-
lin
e
v
o
ltag
es
n
ea
r
ly
r
ea
c
h
th
e
v
o
ltag
e
lim
it
d
u
e
to
th
e
in
f
lu
en
ce
o
f
t
h
e
0
-
s
u
b
s
p
ac
e
s
am
e
as
r
esu
lts
in
s
ec
tio
n
5
.
1
.
Fig
u
r
e
6
(
a)
illu
s
tr
ate
s
th
e
r
esu
lts
f
o
r
a
h
ea
lth
y
-
o
p
er
ated
D3
-
I
M
,
wh
ile
Fig
u
r
es
6
(
b
)
an
d
6
(
c)
d
ep
ict
th
e
lin
e
-
to
-
lin
e
v
o
ltag
es
u
n
d
er
1
O
PF
with
1
N
an
d
2
N
co
n
f
ig
u
r
atio
n
s
,
r
esp
ec
tiv
ely
.
Up
o
n
an
aly
s
is
o
f
th
e
r
esu
lts
f
o
r
t
h
e
D3
-
I
M,
it
is
o
b
s
er
v
e
d
t
h
at
u
n
d
er
f
au
lt
s
ce
n
a
r
io
s
with
2
N,
th
e
m
ax
im
u
m
lin
e
-
to
-
lin
e
v
o
ltag
es
r
ea
ch
t
h
e
cu
r
r
en
t lim
it f
ir
s
t.
C
o
n
v
er
s
ely
,
f
o
r
f
a
u
lt scen
ar
io
s
wh
er
e
D3
-
I
M
is
co
n
f
i
g
u
r
ed
with
1
N
,
th
e
m
ax
im
u
m
lin
e
-
to
-
lin
e
v
o
ltag
es
h
it
th
e
v
o
ltag
e
lim
it
b
ef
o
r
e
r
ea
ch
in
g
th
e
cu
r
r
en
t
lim
it.
I
n
c
o
n
clu
s
io
n
,
D
3
-
I
M
with
2
N
is
p
r
im
ar
ily
in
f
l
u
en
ce
d
b
y
th
e
lim
itatio
n
o
f
c
u
r
r
en
t,
wh
ile
with
1
N,
v
o
ltag
e
b
ec
o
m
es th
e
lim
itin
g
f
ac
to
r
.
I
n
s
u
m
m
ar
y
,
S6
-
I
M
p
r
e
d
o
m
i
n
an
tly
o
p
e
r
ates
with
in
th
e
cu
r
r
en
t
lim
it
d
u
r
in
g
m
o
s
t
f
au
lt
s
ce
n
ar
io
s
.
C
o
n
v
er
s
ely
,
D3
-
I
M
is
co
n
s
is
t
en
tly
co
n
tr
o
lled
b
y
th
e
d
em
o
n
s
tr
ates
s
u
p
er
io
r
f
au
lt
-
to
ler
a
n
t
ca
p
ab
ilit
y
b
ased
o
n
its
v
o
ltag
e
lim
it
u
n
d
er
d
if
f
er
en
t
ω
slip
at
r
ated
ω
s
an
d
cu
r
r
en
t.
Ov
er
all,
v
o
ltag
e
lim
itatio
n
h
elp
s
to
co
n
tr
o
l
th
e
d
am
ag
e
d
u
e
to
o
v
er
c
u
r
r
en
t
[
3
9
]
.
B
y
u
s
in
g
t
h
is
co
n
tr
o
l
m
eth
o
d
in
s
tead
o
f
th
e
cu
r
r
en
t
c
o
n
tr
o
l,
s
y
n
ch
r
o
n
izatio
n
in
s
tab
ilit
y
ca
n
b
e
av
o
id
e
d
.
T
h
is
in
s
tab
ilit
y
is
ty
p
ically
ca
u
s
ed
b
y
th
e
lim
itatio
n
s
o
n
h
o
w
l
o
n
g
th
e
c
u
r
r
en
t
ca
n
r
em
ain
at
a
s
atu
r
ated
lev
el.
I
n
co
n
tr
ast,
v
o
ltag
e
c
o
n
tr
o
l d
o
es n
o
t
im
p
o
s
e
s
u
ch
c
o
n
s
tr
ain
ts
in
v
ar
io
u
s
s
itu
atio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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8
6
9
4
P
o
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t
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fa
u
lt v
o
lta
g
e
limit a
s
s
ess
men
t fo
r
s
ix
-
p
h
a
s
e
in
d
u
ctio
n
ma
ch
in
es:
…
(
N
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r
a
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ia
n
ie
Mu
h
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d
Zin
)
171
So
,
it
ca
n
b
e
s
aid
th
at
S6
-
I
M
is
th
e
b
est
f
au
lt
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to
ler
a
n
t
ca
p
ab
ilit
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ased
o
n
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o
s
t
-
f
au
lt
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e
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m
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f
o
r
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ap
p
r
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h
es wh
ich
ar
e
b
y
u
s
in
g
r
ated
ω
slip
as e
x
p
lain
ed
in
s
e
ctio
n
5
.
1
an
d
r
ated
ω
s
.
(
a)
(
b
)
(
c)
Fig
u
r
e
5
.
S6
-
I
M
v
o
ltag
e
lim
it u
n
d
er
d
if
f
er
e
n
t
ω
slip
at
r
ated
c
u
r
r
en
t a
n
d
ω
s
d
u
r
in
g
(
a)
h
ea
lth
y
co
n
d
itio
n
,
1
OPF u
n
d
er
(
b
)
1
N,
an
d
(
c)
2
N
c
o
n
f
ig
u
r
atio
n
s
(
a)
(
b
)
(
c)
Fig
u
r
e
6
.
D3
-
I
M
v
o
ltag
e
lim
it
u
n
d
er
d
if
f
er
e
n
t
ω
slip
at
r
ated
c
u
r
r
en
t a
n
d
ω
s
d
u
r
in
g
(
a)
h
ea
lth
y
co
n
d
itio
n
,
1
OPF u
n
d
er
(
b
)
1
N
,
an
d
(
c)
2
N
c
o
n
f
ig
u
r
atio
n
s
6.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
i
n
v
esti
g
ated
h
o
w
p
o
s
t
-
f
au
lt
co
n
d
itio
n
s
af
f
ec
t
th
e
m
ax
im
u
m
lin
e
-
to
-
lin
e
v
o
ltag
e
in
S6
-
I
M
an
d
D3
-
I
M
at
v
ar
io
u
s
s
y
n
ch
r
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n
o
u
s
a
n
d
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lip
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r
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o
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e
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atin
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o
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ts
.
A
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lated
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er
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er
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s
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elp
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g
to
Evaluation Warning : The document was created with Spire.PDF for Python.