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A
Ms
a
n
d
e
l
e
c
t
r
o
n
i
c
l
o
a
d
s
,
t
h
e
r
e
f
o
r
e
,
t
h
e
b
e
h
a
v
i
o
r
o
f
t
h
e
E
P
S
c
o
u
l
d
n
o
t
b
e
p
r
e
d
i
c
t
e
d
c
o
r
r
e
c
t
l
y
[
1
6
]
-
[
1
8
]
.
No
r
m
ally
,
th
e
T
AM
is
r
e
p
r
e
s
en
ted
as
a
co
n
s
tan
t
p
o
we
r
lo
ad
,
o
r
co
n
s
tan
t
im
p
ed
an
ce
[
3
]
,
[
1
9
]
.
Ass
u
m
in
g
co
n
s
tan
t
ac
tiv
e
p
o
wer
m
ay
b
e
ac
ce
p
tab
le
in
s
o
m
e
ca
s
es
b
u
t
ig
n
o
r
in
g
th
e
v
a
r
iatio
n
o
f
r
ea
ctiv
e
p
o
wer
with
v
o
ltag
e
i
n
T
AM
l
ea
d
s
to
s
ig
n
if
ican
t
er
r
o
r
s
.
Neith
er
h
as
th
e
b
eh
a
v
io
r
o
f
th
e
p
o
wer
co
n
s
u
m
ed
b
y
th
e
T
AM
b
ee
n
a
n
aly
ze
d
in
th
e
ev
en
t
o
f
f
r
eq
u
en
cy
d
e
v
iatio
n
s
f
r
o
m
its
n
o
m
in
al
v
al
u
e.
No
r
m
ally
,
in
f
r
e
q
u
en
c
y
s
tab
ilit
y
s
tu
d
ies,
co
n
ce
n
tr
ated
m
o
d
els
o
f
t
h
e
lo
ad
s
ar
e
u
s
ed
,
f
o
r
wh
ich
it
is
n
ec
ess
ar
y
t
o
d
eter
m
in
e
th
e
s
o
-
ca
lled
lo
ad
-
d
am
p
in
g
c
o
n
s
tan
t
[
2
]
.
T
h
e
r
e
ar
e
n
o
co
n
c
r
ete
p
r
o
p
o
s
als
in
th
e
liter
atu
r
e
to
esti
m
ate
th
is
p
ar
am
eter
in
p
r
ed
o
m
in
an
tly
T
AM
lo
ad
s
.
Acc
o
r
d
in
g
to
C
I
GR
E
[
2
0
]
,
th
er
e
ar
e
two
t
y
p
es
o
f
lo
ad
m
o
d
els
d
ep
en
d
in
g
o
n
th
e
way
to
o
b
tain
th
eir
p
ar
am
eter
s
.
On
e
way
is
b
ased
o
n
m
ea
s
u
r
em
e
n
ts
m
ad
e
in
s
itu
an
d
,
a
n
o
th
er
wa
y
is
b
ased
o
n
th
e
k
n
o
wled
g
e
o
f
th
e
co
m
p
o
n
e
n
ts
o
f
th
e
lo
ad
s
an
d
th
e
d
ev
elo
p
m
en
t
o
f
m
o
d
els
esti
m
atin
g
th
e
co
r
r
esp
o
n
d
in
g
p
ar
am
eter
s
.
I
n
th
e
ca
s
e
o
f
th
e
T
AM
,
th
e
m
eth
o
d
b
ased
o
n
m
ea
s
u
r
em
en
ts
is
im
p
r
ac
ticab
le
b
e
ca
u
s
e
it
r
eq
u
ir
es
lab
o
r
ato
r
ies
wh
er
e
a
co
n
s
id
er
a
b
le
n
u
m
b
er
o
f
T
A
Ms
ca
n
b
e
test
ed
,
b
o
th
lo
w
a
n
d
m
e
d
iu
m
v
o
ltag
e
an
d
o
f
d
i
f
f
er
en
t
p
o
wer
an
d
n
u
m
b
er
o
f
p
o
les.
T
h
is
p
ap
er
aim
s
to
p
r
o
p
o
s
e
a
n
ew
m
o
d
el
o
f
th
e
T
AM
th
at
a
llo
ws
its
u
s
e
in
th
e
an
aly
s
is
o
f
E
PS
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
allo
ws
th
e
an
aly
s
is
o
f
th
e
in
f
lu
e
n
ce
o
f
th
e
v
ar
iatio
n
o
f
v
o
ltag
e
an
d
f
r
eq
u
en
cy
d
e
v
iatio
n
,
as
well
as
th
e
ty
p
e
o
f
th
e
m
ec
h
an
ical
lo
ad
d
r
iv
e
n
b
y
th
e
m
o
t
o
r
,
o
n
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
co
n
s
u
m
p
tio
n
o
f
th
e
m
o
to
r
s
.
T
h
e
in
clu
s
io
n
o
f
th
e
co
n
s
id
er
a
tio
n
o
f
th
e
ty
p
e
o
f
m
ec
h
an
ical
lo
ad
d
r
iv
e
n
b
y
th
e
m
o
to
r
in
th
e
co
m
p
o
s
ite
m
o
d
el
is
a
n
o
v
el
a
s
p
ec
t
th
at
ca
n
co
n
t
r
ib
u
te
to
t
h
e
im
p
r
o
v
e
m
en
t
o
f
th
e
E
PS
s
s
im
u
latio
n
s
o
f
twar
e.
Sectio
n
2
d
escr
ib
es
th
e
s
tate
o
f
th
e
ar
t
o
f
d
ev
elo
p
ed
m
o
d
els
o
f
T
AM
s
as
lo
ad
i
n
th
e
E
PS
.
Sectio
n
3
ex
p
lain
s
th
e
m
o
d
el
with
th
e
eq
u
atio
n
s
an
d
th
e
s
eq
u
en
tial
p
r
o
ce
d
u
r
e
f
o
r
its
ap
p
licatio
n
,
wh
ile
th
e
ex
p
lan
atio
n
o
f
th
e
m
o
d
el
is
p
r
esen
ted
in
s
ec
tio
n
4
.
I
n
s
ec
tio
n
5
th
e
c
o
n
clu
s
io
n
s
o
f
th
e
a
r
ticle
ar
e
d
is
cu
s
s
ed
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
St
a
t
e
o
f
t
he
a
rt
o
f
dev
el
o
ped m
o
dels
o
f
T
AM
s
a
s
lo
a
d in t
he
E
P
S.
B
alan
ath
an
et
a
l
.
[
2
1
]
th
e
ap
p
r
o
x
im
ate
eq
u
iv
ale
n
t
cir
cu
it
s
h
o
wn
in
Fig
u
r
e
1
is
p
r
o
p
o
s
ed
.
I
n
th
is
ca
s
e,
th
e
s
tato
r
r
esis
tan
c
e
an
d
m
ag
n
etiza
tio
n
r
ea
ctan
ce
ar
e
n
o
t
co
n
s
id
er
ed
.
Neg
lectin
g
th
e
s
tato
r
r
esis
tan
ce
d
o
es
n
o
t
g
en
er
ate
a
s
ig
n
if
ican
t
er
r
o
r
,
b
u
t
n
o
t
co
n
s
id
er
in
g
th
e
m
ag
n
etiza
tio
n
r
ea
ctan
ce
im
p
lies
s
i
m
p
lify
in
g
th
e
m
ain
co
n
s
u
m
er
o
f
r
ea
ctiv
e
p
o
wer
,
wh
ich
is
u
n
ac
ce
p
tab
le.
W
h
e
r
e
:
P
i
s
t
h
e
ac
t
i
v
e
p
o
w
e
r
,
Q
i
s
t
h
e
r
e
a
ct
i
v
e
p
o
w
e
r
,
I
is
t
h
e
c
u
r
r
e
n
t
,
V
1
i
s
t
h
e
v
o
l
ta
g
e
p
e
r
p
h
a
s
e
,
X
1
is
t
h
e
s
t
at
o
r
l
e
a
k
a
g
e
r
e
a
c
ta
n
c
e
,
X
2
i
s
t
h
e
r
o
t
o
r
l
e
a
k
a
g
e
r
e
ac
t
a
n
c
e,
R
2
i
s
t
h
e
r
o
t
o
r
r
e
s
is
t
a
n
ce
,
E
is
t
h
e
e
l
ec
t
r
o
m
o
t
i
v
e
f
o
r
c
e
i
n
d
u
c
e
d
i
n
t
h
e
r
o
t
o
r
,
a
n
d
s
i
s
t
h
e
s
l
i
p
.
C
h
o
i
e
t
a
l
.
[
2
2
]
i
t
is
p
r
o
p
o
s
e
d
t
o
i
n
c
o
r
p
o
r
a
t
e
t
h
e
e
q
u
i
v
a
l
e
n
t
c
i
r
c
u
i
t
,
as
a
m
o
d
e
l
,
i
n
p
o
w
e
r
s
y
s
t
e
m
s
t
u
d
ie
s
,
as
i
t
a
p
p
e
a
r
s
i
n
Fi
g
u
r
e
2
,
g
iv
i
n
g
r
i
s
e
t
o
t
h
e
s
o
-
c
a
ll
e
d
"
Z
I
P
m
o
d
e
l
w
i
t
h
T
AM
"
.
Fig
u
r
e
1
.
Ap
p
r
o
x
im
ate
eq
u
i
v
a
len
t c
ir
cu
it o
f
a
T
AM
,
p
r
o
p
o
s
ed
in
th
e
liter
atu
r
e
[
2
1
]
Fig
u
r
e
2
.
Z
I
P m
o
d
el
with
T
A
M
[
2
2
]
W
h
er
e:
I
1
is
th
e
c
u
r
r
en
t
p
er
p
h
ase
in
th
e
s
tato
r
,
Z
is
th
e
i
m
p
ed
an
ce
,
R
1
is
th
e
s
tato
r
r
esis
tan
ce
,
X
m
is
th
e
m
ag
n
etizin
g
r
ea
ctan
ce
,
I
0
is
th
e
c
u
r
r
en
t
p
er
p
h
ase
o
f
m
a
g
n
etiza
tio
n
,
an
d
I
2
is
th
e
c
u
r
r
e
n
t
p
er
p
h
ase
in
th
e
r
o
to
r
.
Ar
ee
[
2
3
]
th
e
eq
u
iv
ale
n
t
cir
cu
it
s
h
o
wn
in
Fig
u
r
e
3
i
s
u
s
ed
to
d
ete
r
m
in
e,
d
u
r
i
n
g
t
h
e
ex
ec
u
tio
n
o
f
th
e
lo
ad
f
lo
w,
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
f
th
e
T
AM
lo
a
d
ac
co
r
d
in
g
to
th
e
v
o
ltag
e
v
alu
es
ca
lcu
lated
in
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
694
A
n
ew a
p
p
r
o
a
c
h
to
th
r
ee
-
p
h
a
s
e
a
s
yn
ch
r
o
n
o
u
s
mo
to
r
mo
d
el
f
o
r
elec
tr
ic
p
o
w
er
…
(
La
u
r
a
C
o
lla
z
o
S
o
la
r
)
2085
s
u
cc
ess
iv
e
iter
atio
n
s
.
T
h
is
cir
cu
it
is
tr
an
s
f
o
r
m
e
d
b
y
ap
p
ly
in
g
T
h
e
v
en
in
'
s
th
eo
r
em
[
2
4
]
an
d
with
th
is
,
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
is
d
eter
m
in
ed
i
n
ea
ch
iter
ati
o
n
.
C
er
tain
in
p
u
t
p
o
wer
is
ass
u
m
ed
(
th
e
wo
r
k
d
o
es
n
o
t
ex
p
lain
h
o
w
to
o
b
tain
th
is
p
o
wer
f
r
o
m
th
e
T
AM
d
ata
a
n
d
i
ts
lo
ad
)
,
an
d
with
it
an
d
th
e
T
AM
p
ar
am
eter
s
o
r
with
ad
d
ed
p
ar
am
eter
s
,
th
e
s
lip
,
an
d
r
ea
ctiv
e
p
o
wer
ar
e
d
et
er
m
in
ed
.
C
o
r
e,
m
ec
h
a
n
ical
an
d
ad
d
itio
n
a
l
lo
s
s
es
ar
e
n
o
t c
o
n
s
id
er
ed
.
W
an
g
et
a
l.
[
1
5
]
a
m
eth
o
d
b
a
s
ed
o
n
a
b
alan
ce
b
etwe
en
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
s
u
p
p
lied
b
y
th
e
n
etwo
r
k
an
d
d
em
an
d
ed
b
y
th
e
T
AM
is
u
s
ed
.
Fro
m
th
e
s
o
lu
tio
n
o
f
th
is
b
alan
ce
,
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
ar
e
d
eter
m
in
ed
in
ea
c
h
iter
atio
n
o
f
th
e
lo
ad
f
lo
w
p
r
o
g
r
am
.
T
h
e
m
eth
o
d
ass
u
m
es
t
h
at
th
e
T
AM
o
u
tp
u
t
p
o
wer
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
th
e
s
q
u
ar
e
o
f
th
e
s
p
ee
d
.
A
r
if
et
a
l
.
[
3
]
an
d
P
er
eir
a
et
a
l.
[
2
5
]
t
h
e
eq
u
iv
alen
t
cir
cu
it sh
o
wn
in
Fig
u
r
e
3
is
also
u
s
ed
.
T
h
is
cir
cu
it d
o
es n
o
t c
o
n
s
id
er
a
p
ar
am
eter
to
r
ep
r
es
en
t th
e
co
n
s
tan
t a
n
d
ad
d
itio
n
al
lo
s
s
es.
T
h
e
SimPo
wer
Sy
s
tem
®
o
f
Ma
tLa
b
®
[
2
6
]
h
as
a
T
AM
m
o
d
el
wh
ich
r
eq
u
ir
es
t
h
e
p
ar
am
eter
s
an
d
th
e
m
ec
h
an
ical
o
u
tp
u
t
p
o
wer
o
f
th
e
T
AM
.
T
h
e
Po
wer
Facto
r
y
®
[
2
7
]
p
r
o
p
o
s
es
two
m
eth
o
d
s
to
r
ep
r
esen
t
th
e
s
tead
y
-
s
tate
m
o
d
el
o
f
t
h
e
T
A
M
in
lo
ad
f
l
o
w
s
tu
d
ies:
-
Sli
p
I
ter
atio
n
(
Sli
p
I
ter
atio
n
AS)
.
I
t
is
b
ased
o
n
th
e
ex
ac
t
eq
u
iv
alen
t
cir
cu
it.
T
h
e
m
o
d
el
eq
u
atio
n
s
ar
e
ev
alu
ated
in
a
s
tead
y
s
tate.
T
h
e
u
s
er
d
e
f
in
es
o
n
ly
t
h
e
E
PS
in
p
u
t.
B
y
p
e
r
f
o
r
m
in
g
th
e
iter
atio
n
s
co
r
r
esp
o
n
d
in
g
t
o
th
e
lo
a
d
f
lo
w
,
th
e
s
lip
an
d
r
ea
ctiv
e
p
o
wer
a
r
e
d
eter
m
in
e
d
.
-
C
o
n
s
tan
t PQ
lo
ad
.
I
t is th
e
class
ical
m
eth
o
d
o
f
r
e
p
r
esen
tin
g
t
h
e
T
AM
.
Usi
n
g
th
e
eq
u
iv
alen
t c
i
r
cu
it d
i
r
ec
tly
as th
e
m
o
d
el
o
f
th
e
T
AM
,
as p
r
o
p
o
s
ed
in
th
e
e
x
is
tin
g
liter
atu
r
e,
h
as th
e
f
o
llo
win
g
d
is
ad
v
an
tag
es:
-
I
t
r
eq
u
ir
es
k
n
o
wled
g
e
o
f
all
th
e
p
ar
am
eter
s
o
f
th
e
cir
c
u
it.
T
h
is
in
f
o
r
m
atio
n
is
n
o
t
p
r
o
v
id
e
d
b
y
alm
o
s
t
an
y
m
an
u
f
ac
tu
r
er
an
d
is
co
m
p
licated
wh
en
wo
r
k
in
g
with
s
ev
er
al
T
AM
s
co
n
n
ec
ted
to
th
e
s
am
e
b
u
s
,
as
is
th
e
ca
s
e
in
alm
o
s
t a
ll in
d
u
s
tr
ies.
-
I
t
d
o
es
n
o
t
co
n
s
id
er
th
e
ef
f
ec
t
o
f
th
e
ty
p
e
o
f
lo
ad
o
r
m
ec
h
a
n
is
m
d
r
iv
en
b
y
th
e
T
AM
.
Mo
s
t
T
AM
s
d
r
iv
e
p
u
m
p
s
,
co
m
p
r
ess
o
r
s
,
o
r
ce
n
tr
i
f
u
g
al
f
an
s
,
w
h
ich
ar
e
v
ar
iab
le
to
r
q
u
e
m
ec
h
an
is
m
s
wh
o
s
e
s
lip
v
ar
ies with
th
e
v
o
ltag
e.
T
h
is
asp
ec
t
is
n
o
t
co
n
s
id
er
ed
in
m
o
s
t
o
f
th
e
m
eth
o
d
s
p
r
o
p
o
s
ed
in
th
e
liter
atu
r
e
c
o
n
s
u
lted
,
n
o
r
in
th
e
SimPo
wer
Sy
s
tem
® o
r
Dig
Sil
en
t Po
wer
Facto
r
y
® so
f
twar
e.
-
T
h
ey
d
o
n
o
t c
o
n
s
id
er
th
e
ef
f
ec
t o
f
f
r
e
q
u
en
c
y
v
ar
iatio
n
d
ir
ec
tl
y
.
-
T
h
e
m
o
d
els
r
eq
u
ir
e
d
f
o
r
p
o
wer
f
lo
w
s
tu
d
ies
u
s
u
ally
d
ir
ec
tly
r
ef
lect
th
e
f
u
n
ctio
n
al
r
el
atio
n
s
h
ip
o
f
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
c
o
n
s
u
m
ed
,
with
th
e
v
o
ltag
e
an
d
f
r
eq
u
en
cy
d
ev
iatio
n
ar
o
u
n
d
i
ts
n
o
m
in
al
v
alu
e.
T
h
e
co
n
s
id
er
atio
n
o
f
th
e
v
ar
iat
io
n
o
f
th
e
f
r
eq
u
en
cy
a
n
d
th
e
v
o
ltag
e
in
th
e
o
p
er
atio
n
o
f
th
e
T
AM
is
an
asp
ec
t
th
at
g
ain
s
r
elev
an
ce
in
th
ese
tim
es
d
u
e
to
th
e
in
cr
ea
s
i
n
g
u
s
e
o
f
v
ar
iab
le
s
p
ee
d
d
r
iv
e
s
an
d
o
f
d
is
tr
ib
u
ted
g
en
er
atio
n
s
o
u
r
ce
s
th
a
t
u
s
e
n
o
n
-
lin
ea
r
elem
en
ts
[
2
8
]
.
T
h
e
ty
p
e
o
f
m
ec
h
an
ical
l
o
ad
th
at
t
h
e
m
o
to
r
s
d
r
i
v
e
is
a
n
im
p
o
r
tan
t
asp
ec
t
th
at
m
u
s
t
b
e
ass
es
s
ed
as
it
d
eter
m
in
es
th
eir
o
p
er
atin
g
c
h
ar
ac
ter
is
tics
an
d
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
d
em
an
d
f
r
o
m
th
e
E
PS
.
Ab
o
u
t
5
5
%
o
f
elec
tr
ic
m
o
to
r
s
d
r
iv
e
p
u
m
p
s
an
d
f
a
n
s
an
d
3
7
%
d
r
i
v
e
co
m
p
r
ess
o
r
s
an
d
c
o
n
v
e
y
o
r
s
[
2
9
]
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
s
p
ee
d
an
d
m
ec
h
an
ical
to
r
q
u
e
o
f
p
u
m
p
s
an
d
f
an
s
is
q
u
ad
r
atic,
an
d
th
at
o
f
co
m
p
r
es
s
o
r
s
an
d
co
n
v
e
y
o
r
s
is
co
n
s
tan
t.
I
n
o
th
er
ty
p
es
o
f
m
ec
h
a
n
ical
lo
ad
d
r
iv
e
n
b
y
th
e
m
o
to
r
s
u
ch
as m
ix
er
s
o
r
e
x
tr
u
d
er
s
,
th
e
r
elatio
n
s
h
ip
b
etwe
en
s
p
ee
d
an
d
to
r
q
u
e
is
lin
ea
r
[
4
]
.
Fig
u
r
e
3
.
T
h
e
eq
u
iv
alen
t c
ir
cu
it is
p
r
o
p
o
s
ed
in
t
h
e
b
ib
lio
g
r
ap
h
y
[
2
3
]
I
n
s
u
m
m
a
r
y
,
in
E
PS
s
tu
d
ies,
T
AM
is
r
ep
r
esen
ted
as
a
p
u
r
ely
elec
tr
ical
lo
ad
o
f
co
n
s
tan
t
p
o
wer
o
r
co
n
s
tan
t
im
p
ed
an
ce
o
r
,
at
b
est,
ex
p
r
ess
ed
b
y
c
o
n
s
tan
t
s
lip
[
1
7
]
,
[
3
0
]
,
[
3
1
]
.
I
n
T
AM
,
th
e
b
eh
av
io
r
o
f
ac
tiv
e
an
d
r
ea
ct
iv
e
p
o
wer
co
n
s
u
m
p
tio
n
to
v
o
ltag
e
a
n
d
f
r
eq
u
e
n
cy
d
ep
en
d
s
o
n
th
e
ty
p
e
o
f
m
ec
h
an
i
ca
l
lo
ad
th
at
d
r
iv
es
an
d
th
e
lo
a
d
f
ac
to
r
.
I
n
th
is
wo
r
k
,
th
ese
f
ac
to
r
s
ar
e
co
n
s
id
er
e
d
.
2
.
2
.
P
r
o
po
s
ed
m
o
del
Static
lo
ad
m
o
d
els
h
av
e
lo
n
g
b
ee
n
a
p
p
lied
to
r
ep
r
esen
t
s
tatic
lo
ad
co
m
p
o
n
e
n
ts
,
s
u
ch
as
r
e
s
is
tiv
e
an
d
lig
h
tin
g
lo
a
d
s
,
an
d
to
esti
m
ate
d
y
n
a
m
ic
lo
ad
co
m
p
o
n
e
n
ts
in
E
PS
s
[
3
2
]
.
T
h
ese
m
o
d
els
ar
e
m
ain
ly
u
s
ed
in
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
0
8
3
–
2
0
9
4
2086
an
aly
s
is
o
f
th
e
eq
u
ilib
r
iu
m
c
o
n
d
itio
n
o
f
E
PS
[
3
3
]
.
Static
lo
ad
m
o
d
els
ca
n
b
e
e
x
p
r
ess
ed
as
a
p
o
ly
n
o
m
ial
o
r
ex
p
o
n
e
n
tial m
o
d
el.
T
h
e
m
o
s
t u
s
ed
is
th
e
p
o
ly
n
o
m
ial
m
o
d
el
d
ef
in
ed
as
[
2
]
:
=
0
⋅
[
1
⋅
(
)
2
+
2
⋅
(
)
+
3
]
(
1
)
=
1
⋅
2
+
2
⋅
+
3
(
2
)
=
0
⋅
[
1
⋅
(
)
2
+
2
⋅
(
)
+
3
]
(
3
)
=
1
⋅
2
+
2
⋅
+
3
(
4
)
W
h
er
e:
(
p
1
,
p
2
,
p
3
)
ar
e
th
e
c
o
e
f
f
icien
ts
o
f
t
h
e
Z
I
P
m
o
d
el
f
o
r
th
e
ac
tiv
e
p
o
wer
,
P
pu
is
th
e
a
ct
iv
e
p
o
wer
in
p
.
u
,
P
0
is
th
e
a
ctiv
e
p
o
wer
at
th
e
b
ase
v
o
ltag
e
,
(
q
1
,
q
2
,
q
3
)
ar
e
th
e
c
o
e
f
f
icien
ts
o
f
th
e
Z
I
P
m
o
d
el
f
o
r
th
e
r
ea
ctiv
e
p
o
wer
,
V
is
th
e
v
o
ltag
e,
V
base
is
th
e
b
ase
v
o
ltag
e,
V
pu
is
th
e
v
o
ltag
e
in
p
.
u
,
Q
0
is
t
h
e
r
ea
ctiv
e
p
o
wer
at
th
e
b
ase
v
o
lt
ag
e
,
an
d
Q
pu
is
th
e
r
ea
ctiv
e
p
o
wer
in
p
.
u
.
T
h
e
p
ar
am
eter
s
(
p
1
,
p
2
,
p
3
)
an
d
(
q
1
,
q
2
,
q
3
)
m
u
s
t
m
ee
t
th
e
co
n
d
itio
n
s
:
1
+
2
+
3
=
1
(
5
)
1
+
2
+
3
=
1
(
6
)
As
ca
n
b
e
s
ee
n
,
th
ese
eq
u
atio
n
s
h
av
e
th
r
ee
c
o
m
p
o
n
en
ts
:
th
e
f
ir
s
t,
p
r
o
p
o
r
tio
n
al
to
th
e
s
q
u
ar
e
o
f
t
h
e
v
o
ltag
e,
c
o
r
r
esp
o
n
d
s
to
a
co
n
s
tan
t
im
p
ed
an
ce
lo
ad
,
t
h
e
s
ec
o
n
d
,
p
r
o
p
o
r
tio
n
al
to
t
h
e
v
o
ltag
e,
co
r
r
esp
o
n
d
s
to
a
co
n
s
tan
t c
u
r
r
en
t lo
ad
,
a
n
d
th
e
th
ir
d
,
as a
co
n
s
tan
t te
r
m
,
co
r
r
e
s
p
o
n
d
s
to
a
co
n
s
tan
t p
o
wer
lo
ad
.
B
ec
au
s
e
o
f
th
is
,
th
is
r
ep
r
esen
tatio
n
o
f
th
e
lo
ad
is
ca
lled
th
e
Z
I
P m
o
d
el
(
Z
I
m
p
ed
an
ce
,
I
C
u
r
r
en
t,
P Po
wer
)
.
T
h
e
eq
u
atio
n
s
o
f
th
e
p
o
ly
n
o
m
i
al
m
o
d
el
to
tak
e
in
to
ac
co
u
n
t a
ls
o
th
e
f
r
eq
u
e
n
cy
v
ar
iatio
n
ar
e
[
3
]
:
=
0
⋅
[
1
⋅
(
)
2
+
2
⋅
(
)
+
3
]
⋅
(
1
+
⋅
)
(
7
)
=
(
1
⋅
2
+
2
⋅
+
3
)
⋅
(
1
+
⋅
)
(
8
)
=
0
⋅
[
1
⋅
(
)
2
+
2
⋅
(
)
+
3
]
⋅
(
1
+
⋅
)
(
9
)
=
(
1
⋅
2
+
2
⋅
+
3
)
⋅
(
1
+
⋅
)
(
1
0
)
W
h
er
e:
K
pf
i
s
th
e
c
o
ef
f
icien
t o
f
v
ar
iatio
n
o
f
th
e
ac
tiv
e
p
o
wer
,
K
qf
is
th
e
c
o
ef
f
icien
t o
f
v
ar
iatio
n
o
f
th
e
r
ea
ctiv
e
p
o
wer
,
an
d
Δf
is
th
e
d
ev
iatio
n
o
f
t
h
e
f
r
e
q
u
en
c
y
f
r
o
m
th
e
n
o
m
in
al
.
T
h
e
m
o
d
el
ca
n
b
e
r
ep
r
esen
ted
s
ch
em
atica
lly
as sh
o
wn
in
Fig
u
r
e
4.
Fig
u
r
e
4
.
Sch
em
atic
o
f
th
e
p
o
l
y
n
o
m
ial
m
o
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el
o
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wh
er
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en
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PS
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2
.
2
.
1
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E
s
t
im
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a
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ly
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ial
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ta
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m
ate
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e
p
ar
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ete
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s
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f
Fig
u
r
e
4
(
i.e
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,
p
1
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p
2
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p
3
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q
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q
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Kp
f
,
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d
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.
I
n
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is
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v
esti
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th
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iv
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t c
i
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it sh
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Fig
u
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
A
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ew a
p
p
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p
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2087
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s
ed
ap
p
ly
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g
th
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f
o
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g
m
eth
o
d
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l
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y
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ith
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d
atash
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o
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ated
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eth
o
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ex
p
lain
ed
in
[
3
4
]
.
-
C
o
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s
id
er
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g
th
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ch
ar
ac
ter
is
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th
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d
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iv
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ec
h
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m
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eth
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e
is
v
ar
ied
in
a
s
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itab
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r
an
g
e
at
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n
o
m
in
al
f
r
eq
u
en
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.
Fo
r
ea
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alu
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th
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cir
cu
it
is
s
o
lv
ed
,
an
d
t
h
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ctiv
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d
r
ea
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u
t
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o
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eter
m
i
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ed
.
At
th
e
s
am
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e,
th
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m
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th
at
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elat
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e
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it is
o
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tain
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d
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-
T
h
e
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in
(
2
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(
4
)
ar
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ep
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2
b
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t v
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g
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eq
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en
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y
d
ev
iatio
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th
e
n
o
m
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al
v
o
ltag
e.
-
T
h
e
p
ar
am
eter
s
in
(
7
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an
d
(
9
)
ar
e
o
b
tain
ed
u
s
in
g
a
c
u
r
v
e
f
itti
n
g
m
eth
o
d
.
Fig
u
r
e
5
.
E
x
ac
t e
q
u
i
v
alen
t c
ir
cu
it o
f
th
e
T
AM
[
2
7
]
wh
er
e
f
is
th
e
f
r
e
q
u
en
c
y
o
f
th
e
E
PS
.
2
.
2
.
2
.
Co
ns
idera
t
io
n o
f
t
he
i
nfluence
o
f
m
ec
ha
nica
l lo
a
d
driv
en
by
t
he
T
A
M
Nex
t,
how
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
co
n
s
id
er
s
th
e
in
f
l
u
en
ce
o
f
th
e
ty
p
e
o
f
m
ec
h
an
ical
lo
ad
t
h
at
d
r
iv
es
th
e
T
AM
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n
th
e
b
e
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av
io
r
o
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h
e
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wer
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em
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a
n
d
th
e
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o
ltag
e
an
d
f
r
eq
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en
cy
o
f
th
e
E
PS
is
ex
p
lain
ed
.
T
h
e
two
ty
p
es o
f
m
ec
h
an
ical
lo
ad
th
at
ca
n
d
r
iv
e
A
T
Ms a
r
e:
−
C
o
n
s
tan
t to
r
q
u
e
lo
a
d
s
.
=
(
1
1
)
−
Var
iab
le
to
r
q
u
e
lo
ad
s
.
=
0
+
1
⋅
+
2
⋅
2
(
1
2
)
wh
er
e:
T
mec
is
th
e
m
ec
h
an
ical
to
r
q
u
e,
T
c
is
th
e
t
o
r
q
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e
at
th
e
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ter
s
ec
tio
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p
o
in
t
o
f
t
h
e
ch
a
r
ac
ter
is
tic
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r
v
e
o
f
th
e
m
o
to
r
an
d
th
e
lo
a
d
,
(
T
o
,
T
1
,
T
2
)
ar
e
t
h
e
v
ar
ia
b
le
to
r
q
u
e
m
o
d
el
co
e
f
f
icien
ts
,
an
d
n
is
th
e
s
p
ee
d
o
f
th
e
r
o
to
r
s
h
af
t
.
T
h
e
eq
u
atio
n
o
f
elec
tr
o
m
ag
n
etic
to
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q
u
e
p
r
o
d
u
ce
d
b
y
th
e
T
AM
,
d
ep
e
n
d
in
g
o
n
t
h
e
p
ar
am
eter
s
o
f
t
h
e
eq
u
iv
alen
t c
ir
cu
it,
is
[
2
4
]
:
=
3
⋅
1
2
⋅
2
⋅
[
(
1
+
2
)
2
+
(
1
+
2
)
2
]
(
1
3
)
wh
er
e
T
em
is
th
e
elec
tr
o
m
ag
n
e
tic
to
r
q
u
e
an
d
ω
s
is
th
e
a
n
g
u
la
r
s
y
n
ch
r
o
n
ic
v
elo
city
.
I
n
th
e
s
tead
y
-
s
tate
o
p
er
atin
g
z
o
n
e
o
f
th
e
T
AM
,
th
e
f
o
llo
win
g
is
f
u
lf
illed
:
2
>
>
1
(
1
4
)
2
>
>
1
+
2
(
1
5
)
C
o
n
s
id
er
in
g
(
1
4
)
an
d
(
1
5
)
,
(
1
3
)
ca
n
b
e
wr
itten
as:
=
3
⋅
1
2
⋅
2
⋅
(
1
6
)
C
o
n
s
id
er
in
g
th
at
3
,
ω
s
,
an
d
R
2
ar
e
co
n
s
tan
ts
,
(
1
6
)
ca
n
b
e
wr
itten
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
0
8
3
–
2
0
9
4
2088
=
1
⋅
1
2
⋅
(
1
7
)
T
h
e
co
n
s
tan
t K
1
ca
n
b
e
e
x
p
r
e
s
s
ed
as:
1
=
1
2
⋅
(
1
8
)
W
h
er
e
K
1
is
th
e
c
o
n
s
tan
t
u
s
ed
f
o
r
t
h
e
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
m
o
d
el
as
a
f
u
n
ctio
n
o
f
v
ar
iab
le
v
o
ltag
e
a
n
d
co
n
s
tan
t f
r
eq
u
en
cy
,
T
mecn
is
th
e
n
o
m
in
al
m
ec
h
an
ical
to
r
q
u
e
a
n
d
V
1n
is
th
e
n
o
m
i
n
al
v
o
ltag
e
p
er
p
h
ase.
T
h
e
s
lip
is
r
elate
d
to
s
p
ee
d
th
r
o
u
g
h
:
=
⋅
(
1
−
)
(
1
9
)
I
n
th
e
ca
s
e
o
f
c
o
n
s
tan
t
to
r
q
u
e
lo
ad
,
(
1
1
)
is
u
s
ed
,
eq
u
atin
g
t
h
e
m
ec
h
a
n
ical
to
r
q
u
e
with
th
a
t
o
f
th
e
l
o
ad
.
I
f
th
e
v
o
ltag
e
d
ec
r
ea
s
es,
th
e
s
lip
m
u
s
t
in
cr
ea
s
e
s
o
th
at
th
e
to
r
q
u
e
r
em
ain
s
c
o
n
s
tan
t
an
d
v
ice
v
er
s
a.
T
h
is
m
a
k
es
it
p
o
s
s
ib
le
to
ass
u
m
e
th
at
th
e
p
r
o
d
u
ct
(
s
⸳
V1
2
)
r
em
ain
s
c
o
n
s
tan
t (
s
ee
(
1
7
)
)
an
d
t
h
en
:
=
1
2
⋅
(
2
0
)
W
h
er
e
K
v
is
th
e
c
o
n
s
tan
t
u
s
e
d
f
o
r
t
h
e
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
m
o
d
el
as
a
f
u
n
ctio
n
o
f
v
ar
iab
le
v
o
ltag
e
a
n
d
co
n
s
tan
t f
r
eq
u
en
cy
.
T
h
e
alg
o
r
ith
m
to
b
e
p
r
o
g
r
a
m
m
ed
is
b
ased
o
n
ass
u
m
in
g
a
lo
ad
to
r
q
u
e
v
alu
e
f
o
r
wh
ich
th
e
co
r
r
esp
o
n
d
in
g
Kv
is
ca
lcu
late
d
an
d
th
en
v
ar
y
i
n
g
th
e
v
o
ltag
e
f
r
o
m
8
0
%
to
1
2
0
%
o
f
t
h
e
n
o
m
in
al
o
n
e.
Fo
r
ea
c
h
v
o
ltag
e
v
al
u
e,
ca
lcu
late
th
e
a
ctiv
e
p
o
wer
an
d
th
e
r
ea
ctiv
e
i
n
p
u
t
p
o
wer
.
T
h
is
m
ak
es
it
p
o
s
s
ib
le
to
o
b
tain
t
h
e
ch
ar
ac
ter
is
tics
o
f
th
ese
two
v
a
r
iab
les as a
f
u
n
ctio
n
o
f
th
e
v
o
l
tag
e.
I
n
th
e
ca
s
e
o
f
v
ar
iab
le
to
r
q
u
e,
it
s
h
o
u
ld
b
e
n
o
ted
th
at
v
a
r
y
in
g
th
e
s
lip
also
ch
an
g
es
th
e
to
r
q
u
e
as
th
e
s
p
ee
d
n
=
n
s
(
1
-
s
)
v
a
r
ies.
wh
er
e
n
s
is
th
e
s
y
n
ch
r
o
n
ic
s
p
e
ed
.
Fo
r
th
e
v
ar
ia
b
le
to
r
q
u
e
,
it is
s
atis
f
ied
th
at:
=
0
+
1
⋅
+
2
⋅
2
(
2
1
)
=
0
+
1
⋅
⋅
(
1
−
)
+
2
⋅
2
⋅
(
1
−
2
⋅
+
2
)
(
2
2
)
=
(
0
+
1
⋅
+
2
⋅
2
)
−
(
1
⋅
+
2
⋅
2
⋅
2
)
⋅
+
2
⋅
2
⋅
2
(
2
3
)
Su
b
s
titu
tin
g
(
1
6
)
in
(
1
8
)
it is
o
b
tain
ed
th
at:
1
=
3
⋅
2
(
2
4
)
E
q
u
at
io
n
(
1
7
)
an
d
(
2
3
)
an
d
m
ak
in
g
s
o
m
e
tr
a
n
s
f
o
r
m
atio
n
s
ar
e
o
b
tain
ed
:
0
=
(
0
+
1
⋅
+
2
⋅
2
)
−
(
1
⋅
+
2
⋅
2
⋅
2
+
1
⋅
1
2
)
⋅
+
2
⋅
2
⋅
2
(
2
5
)
0
=
(
0
+
1
⋅
+
2
⋅
2
)
(
2
6
)
1
=
(
1
⋅
+
2
⋅
2
⋅
2
+
1
⋅
1
2
)
(
2
7
)
2
=
2
⋅
2
(
2
8
)
W
h
er
e
A
0
, A
1
, A
2
ar
e
v
ar
iab
le
lo
ad
an
d
co
n
s
tan
t f
r
e
q
u
en
c
y
m
o
d
el
co
ef
f
icien
ts
.
T
h
e
eq
u
atio
n
th
at
g
iv
es th
e
s
lip
v
alu
e
f
o
r
ea
c
h
v
o
ltag
e
v
alu
e
is
:
0
=
0
−
1
⋅
+
2
⋅
2
(
2
9
)
T
h
is
eq
u
atio
n
h
as two
s
o
lu
tio
n
s
,
o
n
e
o
f
th
e
m
is
with
in
th
e
r
an
g
e
o
f
p
o
s
s
ib
le
s
lip
v
alu
es (
0
<s <
1
)
an
d
th
e
o
th
er
s
o
lu
tio
n
e
x
ce
ed
s
th
i
s
v
alu
e
b
y
m
o
r
e
t
h
an
1
0
tim
e
s
an
d
is
th
er
ef
o
r
e
n
o
t
co
n
s
id
e
r
ed
.
W
ith
th
e
s
lip
v
alu
e
g
iv
en
b
y
th
ese
eq
u
atio
n
s
,
th
e
eq
u
iv
alen
t
cir
cu
it
is
s
o
l
v
ed
f
o
r
ea
c
h
o
f
th
e
v
o
ltag
e
v
a
lu
es
an
d
th
e
v
alu
es
o
f
ac
tiv
e
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
ar
e
ca
lcu
lated
,
as it w
as d
o
n
e
in
th
e
co
n
s
tan
t to
r
q
u
e
lo
ad
.
I
n
th
e
ca
s
e
o
f
f
r
eq
u
en
cy
v
ar
iat
io
n
,
in
(
8
)
a
n
d
(
1
0
)
th
e
v
o
ltag
e
is
m
ad
e
in
p
er
u
n
it e
q
u
al
to
1
an
d
is
o
b
tain
ed
:
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
694
A
n
ew a
p
p
r
o
a
c
h
to
th
r
ee
-
p
h
a
s
e
a
s
yn
ch
r
o
n
o
u
s
mo
to
r
mo
d
el
f
o
r
elec
tr
ic
p
o
w
er
…
(
La
u
r
a
C
o
lla
z
o
S
o
la
r
)
2089
=
(
1
+
⋅
)
(
3
0
)
=
(
1
+
⋅
)
(
3
1
)
Fre
q
u
en
cy
v
ar
iatio
n
im
p
lies
a
n
ew
v
alu
e
o
f
s
y
n
ch
r
o
n
o
u
s
s
p
e
ed
an
d
r
e
q
u
ir
es
a
n
ew
wa
y
o
f
d
eter
m
in
in
g
to
r
q
u
e
f
r
o
m
:
=
3
⋅
1
2
⋅
2
⋅
−
(
3
2
)
=
3
2
⋅
(
1
)
2
⋅
(
−
)
(
3
3
)
T
h
e
ter
m
V1
/ω
s
e
x
p
r
ess
ed
p
er
u
n
it
c
o
in
cid
es
with
th
e
m
ag
n
etic
f
lu
x
p
er
u
n
it
(
V/f
=k
)
b
ec
au
s
e
it
is
p
r
o
p
o
r
tio
n
al
to
it.
T
h
e
f
o
llo
win
g
ter
m
is
th
en
d
ef
in
e
d
as “
E
q
u
iv
alen
t Flu
x
”.
=
1
(
3
4
)
Su
b
s
titu
tin
g
(
3
4
)
in
(
3
3
)
it is
o
b
tain
ed
th
at:
=
⋅
2
⋅
(
−
)
(
3
5
)
W
h
er
e
K
ω
is
t
h
e
c
o
n
s
tan
t
u
s
e
d
f
o
r
t
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
m
o
d
el
as
a
f
u
n
ctio
n
o
f
v
ar
iab
le
v
o
ltag
e
a
n
d
f
r
eq
u
e
n
cy
,
ɸ
eq
is
th
e
e
q
u
iv
alen
t f
lu
x
an
d
ω
r
is
th
e
a
n
g
u
lar
s
h
a
f
t sp
ee
d
.
T
h
e
c
o
n
s
tan
t K
ω
is
c
alcu
lated
as
:
=
2
⋅
(
−
)
(
3
6
)
W
h
er
e
ɸ
eqn
is
th
e
n
o
m
in
al
eq
u
iv
alen
t
f
lu
x
,
ω
rn
is
th
e
n
o
m
i
n
al
an
g
u
lar
s
h
af
t
s
p
ee
d
an
d
ω
sn
is
th
e
n
o
m
in
a
l
an
g
u
lar
s
y
n
ch
r
o
n
ic
v
elo
city
.
I
n
th
e
ca
s
e
o
f
c
o
n
s
tan
t to
r
q
u
e
l
o
ad
,
f
r
eq
u
e
n
cy
v
al
u
es a
r
e
ex
p
r
ess
ed
as:
=
+
(
3
7
)
W
h
er
e
fn
is
th
e
n
o
m
in
al
f
r
e
q
u
en
cy
.
T
h
is
f
r
eq
u
e
n
cy
is
s
u
b
s
titu
ted
in
:
=
2
⋅
⋅
(
3
8
)
W
h
er
e
p
is
th
e
n
u
m
b
er
o
f
p
o
les o
f
th
e
m
o
t
o
r
.
T
h
is
eq
u
atio
n
an
d
(
3
4
)
with
t
h
e
n
o
m
in
al
p
a
r
am
eter
s
ar
e
r
e
p
lace
d
in
(
3
6
)
.
T
h
e
r
ea
ctan
ce
v
alu
es
ar
e
ch
an
g
ed
ac
co
r
d
in
g
to
th
e
f
r
e
q
u
en
c
y
.
W
ith
th
ese
v
alu
es a
n
d
th
e
o
th
er
T
AM
p
ar
am
eter
s
,
th
e
eq
u
iv
alen
t c
ir
cu
it is
s
o
lv
ed
,
an
d
th
e
ac
tiv
e
p
o
wer
a
n
d
th
e
r
ea
ctiv
e
p
o
wer
a
r
e
ca
lcu
lated
.
I
f
th
e
lo
a
d
is
o
f
v
ar
iab
le
to
r
q
u
e,
(
2
3
)
is
(
3
5
)
an
d
th
e
s
p
ee
d
in
r
p
m
(
n
)
is
r
ep
lace
d
b
y
th
e
s
p
ee
d
in
r
ad
/s
(
ω
s
)
ap
p
ly
in
g
(
3
9
)
.
=
⋅
(
30
)
(
3
9
)
0
=
(
0
+
1
⋅
(
30
)
⋅
+
2
⋅
(
30
)
2
⋅
2
)
−
(
⋅
2
⋅
+
1
⋅
(
30
)
⋅
+
2
⋅
2
⋅
(
30
)
2
⋅
2
)
⋅
+
(
2
⋅
(
30
)
2
⋅
2
)
⋅
2
(
4
0
)
0
=
(
0
+
1
⋅
(
30
)
⋅
+
2
⋅
(
30
)
2
⋅
2
)
(
4
1
)
1
=
(
⋅
2
⋅
+
1
⋅
(
30
)
⋅
+
2
⋅
2
⋅
(
30
)
2
⋅
2
)
(
4
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
0
8
3
–
2
0
9
4
2090
2
=
(
2
⋅
(
30
)
2
⋅
2
)
(
4
3
)
W
h
er
e
(
B
0
, B
1
, B
2
)
ar
e
th
e
v
ar
iab
le
lo
ad
an
d
f
r
e
q
u
en
c
y
m
o
d
el
co
ef
f
icien
ts
.
I
n
(
4
0
)
is
th
en
lik
e:
0
−
1
⋅
+
2
⋅
2
=
0
(
4
4
)
So
lv
in
g
th
is
s
ec
o
n
d
-
d
eg
r
ee
e
q
u
atio
n
,
two
s
o
lu
tio
n
s
ar
e
o
b
tain
ed
,
th
e
s
m
allest
(
0
<
s
<1
)
is
v
alid
b
ec
au
s
e
i
t
co
r
r
esp
o
n
d
s
to
th
e
n
o
r
m
al
v
al
u
es
o
f
s
lip
in
th
e
T
AM
.
T
h
e
r
est
o
f
th
e
p
r
o
ce
d
u
r
e
is
th
e
s
a
m
e
as
f
o
r
a
co
n
s
tan
t
to
r
q
u
e
lo
a
d
.
3.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
NS
−
Ap
p
licatio
n
o
f
t
h
e
m
eth
o
d
to
a
ca
s
e
s
tu
d
y
T
o
illu
s
tr
ate
th
e
m
et
h
o
d
,
th
e
T
AM
o
f
th
e
f
ee
d
i
n
g
p
u
m
p
o
f
a
th
er
m
al
p
o
wer
p
lan
t
o
f
2
5
0
0
k
W
;
6
0
0
0
V;
2
p
o
les an
d
6
0
Hz
is
s
elec
ted
,
wh
o
s
e
d
ata
is
p
r
o
v
id
ed
b
y
th
e
m
an
u
f
ac
t
u
r
er
,
a
n
d
p
a
r
am
et
er
s
ca
lcu
lated
f
r
o
m
th
ese
d
ata,
ap
p
ea
r
in
[
3
4
]
.
T
o
d
eter
m
in
e
th
e
ch
ar
ac
ter
is
tics
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
as
a
f
u
n
ctio
n
o
f
v
o
ltag
e
f
o
r
b
o
th
co
n
s
tan
t
an
d
v
ar
iab
le
to
r
q
u
e,
a
n
o
p
er
atin
g
p
o
in
t
at
a
n
o
m
in
al
v
o
ltag
e
c
o
r
r
esp
o
n
d
in
g
to
7
5
%
o
f
th
e
n
o
m
in
al
lo
a
d
was
ass
u
m
ed
in
b
o
th
ca
s
es,
at
wh
ich
th
e
ac
tiv
e
p
o
wer
co
n
s
u
m
e
d
is
P=1
8
1
7
k
W
an
d
th
e
r
ea
ctiv
e
Q=
1
1
3
4
k
VAr
.
Fo
r
th
is
,
a
MA
T
L
AB
[
2
6
]
p
r
o
g
r
am
was
u
s
ed
with
t
h
e
alg
o
r
i
th
m
d
escr
ib
ed
in
a
p
r
ev
io
u
s
s
ec
tio
n
.
Fig
u
r
e
6
(
a)
s
h
o
ws
th
e
ch
a
r
ac
t
er
is
tic
o
f
ac
tiv
e
p
o
wer
as
a
f
u
n
ctio
n
o
f
v
o
ltag
e
an
d
in
Fig
u
r
e
6
(
b
)
th
e
ch
ar
ac
ter
is
tic
o
f
r
ea
ctiv
e
p
o
w
er
as
a
f
u
n
ctio
n
o
f
v
o
ltag
e
at
n
o
m
in
al
f
r
eq
u
en
cy
.
I
n
b
o
th
c
ases
f
o
r
a
c
o
n
s
tan
t
to
r
q
u
e
lo
ad
an
d
a
v
ar
iab
le
to
r
q
u
e
lo
a
d
.
T
h
e
ch
ar
ac
ter
is
ti
cs
v
ar
y
v
er
y
litt
le
with
th
e
ty
p
e
o
f
lo
a
d
.
I
t
is
o
n
ly
n
o
ticea
b
le
in
th
e
ac
tiv
e
p
o
wer
ch
ar
ac
ter
is
tic,
f
o
r
v
o
ltag
e
v
al
u
es
ar
e
f
ar
f
r
o
m
th
e
n
o
m
in
al
o
n
e.
I
t
is
also
an
al
y
ze
d
h
o
w
th
e
c
o
n
s
u
m
p
tio
n
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
v
a
r
ies
as
a
f
u
n
ct
io
n
o
f
th
e
v
o
ltag
e
w
h
e
n
th
e
m
ec
h
an
ical
lo
ad
o
f
th
e
T
AM
also
v
ar
ie
s
,
b
o
th
f
o
r
c
o
n
s
tan
t
an
d
v
a
r
iab
le
to
r
q
u
e
lo
ad
at
n
o
m
in
al
f
r
eq
u
e
n
cy
.
Fig
u
r
e
s
7
(
a)
-
(
b
)
s
h
o
ws
th
e
c
h
ar
ac
ter
is
tics
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
as
a
f
u
n
ctio
n
o
f
v
o
ltag
e.
I
n
th
is
ca
s
e,
th
e
to
r
q
u
e
lo
ad
s
with
co
n
s
tan
t
an
d
v
ar
i
ab
le
ch
ar
ac
ter
is
tics
h
av
e
th
e
s
am
e
b
eh
av
i
o
r
.
Fig
u
r
e
6
.
T
h
ese
f
ig
u
r
es a
r
e;
(
a
)
c
h
ar
ac
ter
is
tic
o
f
ac
tiv
e
p
o
we
r
as a
f
u
n
ctio
n
o
f
th
e
v
o
ltag
e
,
(
b
)
c
h
ar
ac
ter
is
tic
o
f
r
ea
ctiv
e
p
o
wer
as a
f
u
n
ctio
n
o
f
th
e
v
o
ltag
e
Fig
u
r
e
7
.
C
h
ar
ac
ter
is
tics
o
f
; (
a
)
ac
tiv
e
p
o
wer
an
d
(
b
)
r
ea
ctiv
e
p
o
wer
as a
f
u
n
ctio
n
o
f
v
o
ltag
e
at
d
if
f
er
en
t l
o
ad
f
ac
to
r
s
f
o
r
c
o
n
s
tan
t
an
d
v
ar
iab
le
to
r
q
u
e
lo
a
d
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
694
A
n
ew a
p
p
r
o
a
c
h
to
th
r
ee
-
p
h
a
s
e
a
s
yn
ch
r
o
n
o
u
s
mo
to
r
mo
d
el
f
o
r
elec
tr
ic
p
o
w
er
…
(
La
u
r
a
C
o
lla
z
o
S
o
la
r
)
2091
I
t
is
o
b
s
er
v
ed
th
at
th
e
h
ig
h
e
r
t
h
e
lo
ad
,
th
e
g
r
ea
ter
th
e
v
ar
iati
o
n
o
f
th
e
ac
tiv
e
p
o
we
r
with
th
e
v
o
ltag
e
an
d
th
e
lo
wer
th
e
r
ea
ctiv
e
p
o
wer
.
I
t
ca
n
also
b
e
n
o
ted
th
at,
in
b
o
th
ca
s
es,
th
e
lo
wer
th
e
lo
ad
,
th
e
lin
ea
r
ity
o
f
th
e
ch
ar
ac
ter
is
tic
in
c
r
ea
s
es.
Usi
n
g
th
e
B
asic
Fit
tin
g
o
p
tio
n
o
f
MA
T
L
AB
[
2
6
]
,
th
e
p
ar
am
eter
s
co
r
r
esp
o
n
d
in
g
to
th
e
v
o
ltag
e
f
o
r
th
e
m
o
d
el
a
r
e
g
iv
en
b
y
(
2
)
an
d
(
4
)
we
r
e
d
eter
m
in
ed
a
n
d
ap
p
ea
r
in
T
a
b
le
1
f
o
r
t
h
e
ca
s
e
o
f
v
ar
iab
le
to
r
q
u
e
.
T
o
d
ete
r
m
in
e
th
e
c
h
ar
ac
ter
is
tics
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
as
a
f
u
n
cti
o
n
o
f
t
h
e
f
r
eq
u
e
n
cy
d
ev
iatio
n
f
o
r
b
o
th
c
o
n
s
tan
t
to
r
q
u
e
a
n
d
v
ar
iab
le
to
r
q
u
e,
an
o
p
er
atin
g
p
o
in
t
at
a
n
o
m
in
al
v
o
ltag
e
co
r
r
esp
o
n
d
in
g
to
7
5
%
o
f
th
e
n
o
m
in
al
lo
a
d
was
ass
u
m
ed
in
b
o
th
ca
s
es,
at
w
h
ich
th
e
p
o
wer
co
n
s
u
m
ed
is
P
=
1
8
1
7
k
W
an
d
Q
=
1
1
3
4
k
VAr
.
T
ab
le
1
.
Mo
d
el
p
ar
am
ete
r
s
f
o
r
v
ar
iab
le
to
r
q
u
e
lo
a
d
,
at
d
i
f
f
er
en
t lo
ad
f
ac
to
r
s
,
an
d
n
o
m
in
al
f
r
eq
u
en
c
y
P
a
r
a
me
t
e
r
s
1
0
0
%
7
5
%
5
0
%
2
5
%
p1
-
0
.
4
4
-
0
.
2
8
-
0
.
1
3
0
.
0
0
4
6
p2
1
.
2
0
.
7
4
0
.
3
9
0
.
1
3
p3
0
.
2
8
0
.
5
3
0
.
7
4
0
.
8
7
q1
1
.
3
1
.
3
1
.
2
1
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1
q2
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2
.
1
-
1
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7
-
1
-
0
.
3
1
q3
1
.
7
1
.
3
0
.
7
8
0
.
2
1
Fig
u
r
es
8
(
a)
-
(
b
)
s
h
o
ws
th
e
ac
tiv
e
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
ch
ar
ac
ter
is
tic
s
as
a
f
u
n
ctio
n
o
f
th
e
f
r
eq
u
e
n
cy
d
ev
iatio
n
i
n
b
o
th
ca
s
es,
f
o
r
a
co
n
s
tan
t
to
r
q
u
e
lo
ad
an
d
a
v
ar
iab
le
to
r
q
u
e
lo
a
d
.
As
ca
n
b
e
s
ee
n
in
F
ig
u
r
e
8
th
e
ac
tiv
e
p
o
wer
ch
a
r
ac
ter
is
tics
as
a
f
u
n
ctio
n
o
f
th
e
f
r
eq
u
e
n
cy
d
e
v
iatio
n
f
r
o
m
th
e
n
o
m
in
al,
a
r
e
lin
ea
r
with
a
m
u
ch
g
r
ea
ter
s
lo
p
e
in
th
e
ca
s
e
o
f
v
ar
iab
le
to
r
q
u
e
l
o
ad
s
.
Ho
wev
er
,
th
e
v
a
r
iatio
n
i
n
r
ea
ctiv
e
p
o
wer
is
p
r
ac
tically
n
eg
lig
i
b
le.
T
h
is
b
eh
av
io
r
ex
p
lain
s
th
e
ad
v
a
n
ta
g
e
o
f
u
s
in
g
v
ar
iab
le
s
p
ee
d
d
r
iv
es
in
th
is
ty
p
e
o
f
m
ec
h
an
ical
lo
a
d
d
r
iv
en
b
y
th
e
m
o
to
r
f
o
r
s
av
i
n
g
elec
tr
ical
en
er
g
y
[
8
]
,
[
3
5
]
.
Nex
t,
th
e
v
a
r
iatio
n
o
f
th
e
ac
tiv
e
an
d
r
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o
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n
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m
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aly
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as
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n
ctio
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t
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e
f
r
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en
c
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m
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al
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wh
en
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f
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f
th
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T
AM
also
v
ar
ies.
Fig
u
r
es
9
(
a)
-
(
b
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s
h
o
ws
th
e
v
ar
iatio
n
f
o
r
c
o
n
s
tan
t
to
r
q
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e
lo
a
d
s
an
d
Fig
u
r
e
1
0
(
a)
-
(
b
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s
h
o
ws
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o
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v
ar
ia
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le
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e
lo
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.
I
n
b
o
th
c
ases
,
th
e
ac
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p
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r
ep
r
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Fig
u
r
es 9
(
a)
,
a
n
d
1
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a
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th
en
t
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e
r
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ctiv
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o
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in
Fig
u
r
es 9
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b
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,
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n
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b
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.
Fig
u
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e
8
.
C
h
ar
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ter
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tic
o
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a
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ac
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o
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a
n
d
(
b
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e
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tiv
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p
o
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f
u
n
ctio
n
o
f
f
r
e
q
u
en
cy
v
ar
iatio
n
Fig
u
r
e
9
.
C
h
ar
ac
ter
is
tics
o
f
; (
a
)
ac
tiv
e
p
o
wer
an
d
(
b
)
r
ea
ctiv
e
p
o
wer
as a
f
u
n
ctio
n
o
f
f
r
eq
u
e
n
cy
v
ar
iatio
n
at
d
if
f
er
en
t lo
a
d
f
ac
to
r
s
f
o
r
c
o
n
s
tan
t to
r
q
u
e
lo
ad
Evaluation Warning : The document was created with Spire.PDF for Python.
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SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
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lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
0
8
3
–
2
0
9
4
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Fig
u
r
e
1
0
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C
h
ar
ac
ter
is
tics
o
f
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a)
ac
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p
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wer
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d
(
b
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r
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ctiv
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p
o
wer
as a
f
u
n
ctio
n
o
f
f
r
eq
u
en
cy
v
ar
iati
o
n
at
d
if
f
er
en
t lo
a
d
f
ac
to
r
s
f
o
r
v
ar
ia
b
le
to
r
q
u
e
lo
ad
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h
e
ac
tiv
e
p
o
wer
ch
ar
ac
te
r
is
tic
as
a
f
u
n
ctio
n
o
f
th
e
f
r
eq
u
en
cy
d
ev
iatio
n
ab
o
u
t
th
e
n
o
m
in
al
is
p
r
ac
tically
in
d
e
p
en
d
e
n
t
o
f
th
e
lo
ad
f
ac
to
r
,
th
at
is
,
it
ca
n
b
e
ass
u
m
ed
th
at
it
o
n
ly
d
ep
e
n
d
s
o
n
th
e
ty
p
e
o
f
lo
a
d
.
R
eg
ar
d
in
g
th
e
r
ea
ctiv
e
p
o
wer
ch
ar
ac
ter
is
tic,
it
ca
n
s
till
b
e
ass
u
m
ed
th
at
th
e
v
ar
iatio
n
o
f
th
e
r
ea
ctiv
e
p
o
wer
with
th
e
f
r
eq
u
e
n
cy
d
e
v
iatio
n
i
s
p
r
ac
tically
n
eg
lig
ib
le.
T
ab
le
2
s
h
o
ws
th
e
p
ar
am
eter
s
r
elat
ed
to
th
e
f
r
e
q
u
en
c
y
v
ar
iatio
n
o
f
th
e
m
o
d
el
o
f
(
1
5
)
.
T
ab
le
2
.
Mo
d
el
p
ar
am
ete
r
s
co
r
r
esp
o
n
d
i
n
g
to
f
r
eq
u
en
cy
d
ev
i
atio
n
,
at
d
if
f
e
r
en
t lo
a
d
f
ac
to
r
s
,
an
d
n
o
m
in
al
v
o
ltag
e
P
a
r
a
me
t
e
r
s
1
0
0
%
7
5
%
5
0
%
2
5
%
K
p
f
(
c
o
n
s
t
a
n
t
l
o
a
d
)
0
.
8
1
0
.
8
8
0
.
9
2
0
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9
3
K
p
f
(
v
a
t
i
a
b
l
e
l
o
a
d
)
2
.
5
2
.
6
2
.
8
2
.
8
4.
CO
NCLU
SI
O
N
Acc
o
r
d
in
g
to
th
e
r
esu
lts
,
th
e
f
o
llo
win
g
co
n
clu
s
io
n
s
ca
n
b
e
r
ea
ch
ed
:
T
h
e
r
ep
r
esen
tatio
n
o
f
th
e
T
AM
th
r
o
u
g
h
a
q
u
ad
r
atic
p
o
l
y
n
o
m
ial
is
v
er
y
s
u
itab
le
f
o
r
its
ap
p
l
icatio
n
in
th
e
an
aly
s
is
o
f
E
PS
p
er
f
o
r
m
an
ce
.
T
h
e
m
o
s
t
co
n
v
e
n
ien
t
p
r
o
ce
d
u
r
e
to
d
eter
m
in
e
th
e
m
o
d
el
p
ar
am
et
er
s
is
,
b
ased
o
n
t
h
e
in
f
o
r
m
ati
o
n
p
r
o
v
id
e
d
b
y
th
e
m
an
u
f
ac
tu
r
er
,
to
ca
lcu
late
th
e
p
ar
am
eter
s
o
f
th
e
e
x
ac
t
eq
u
iv
alen
t
cir
cu
it
an
d
,
th
r
o
u
g
h
it,
to
d
eter
m
in
e
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
c
h
ar
ac
ter
is
tics
as
a
f
u
n
ctio
n
o
f
th
e
v
o
ltag
e
an
d
th
e
f
r
eq
u
e
n
c
y
d
ev
i
atio
n
ar
o
u
n
d
n
o
m
in
al
o
n
e
.
W
ith
th
ese
ch
ar
ac
ter
is
tics
,
an
d
ap
p
ly
in
g
s
o
m
e
cu
r
v
e
f
itti
n
g
m
eth
o
d
,
d
eter
m
in
e
th
e
p
ar
am
eter
s
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el.
T
h
e
m
o
d
el
p
ar
am
eter
s
d
ep
en
d
,
in
g
e
n
er
al,
o
n
th
e
ty
p
e
(
co
n
s
tan
t
to
r
q
u
e
o
r
v
a
r
iab
le
to
r
q
u
e)
an
d
m
ag
n
itu
d
e
o
f
th
e
m
ec
h
an
ical
lo
a
d
d
r
iv
en
b
y
th
e
T
AM
.
T
h
e
ch
ar
ac
te
r
is
tics
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
as
a
f
u
n
ctio
n
o
f
th
e
v
o
ltag
e
d
o
n
o
t
d
e
p
en
d
o
n
th
e
ty
p
e
o
f
lo
a
d
,
b
u
t
o
n
its
m
ag
n
itu
d
e,
wh
ile
th
e
ch
ar
ac
ter
is
tics
as
a
f
u
n
ctio
n
o
f
th
e
f
r
e
q
u
en
c
y
d
e
v
iatio
n
d
ep
en
d
o
n
th
e
t
y
p
e
o
f
lo
ad
b
u
t
n
o
t
o
n
its
m
ag
n
itu
d
e.
Activ
e
p
o
wer
v
ar
ies
m
u
c
h
m
o
r
e
with
f
r
e
q
u
en
c
y
in
th
e
ca
s
e
o
f
a
T
AM
th
at
d
r
iv
e
s
a
v
ar
iab
le
to
r
q
u
e
m
ec
h
an
is
m
th
an
if
th
e
m
ec
h
a
n
is
m
is
co
n
s
tan
t
to
r
q
u
e.
T
h
e
r
ea
ctiv
e
p
o
wer
co
n
s
u
m
ed
b
y
t
h
e
T
AM
v
ar
ies
v
er
y
litt
le
as a
f
u
n
ctio
n
o
f
t
h
e
f
r
e
q
u
en
cy
d
e
v
iatio
n
.
B
ec
au
s
e
o
f
th
i
s
,
it is
p
r
o
p
o
s
ed
to
d
is
r
eg
ar
d
it
.
RE
F
E
R
E
NC
E
S
[1
]
J.
J.
G
ra
in
g
e
r
a
n
d
W
.
D.
S
tev
e
n
so
n
,
“
P
o
we
r
s
y
ste
m
a
n
a
ly
sis,”
Ne
w Yo
rk
:
M
c
G
ra
w Hil
l,
1
9
9
4
.
[2
]
P
.
S
.
Ku
n
d
u
r
,
“
P
o
we
r
S
y
ste
m
S
ta
b
il
it
y
a
n
d
Co
n
tro
l,
T
h
ir
d
Ed
it
io
n
.
M
c
G
ra
w Hil
l,
”
In
c
.
,
1
9
9
3
.
[3
]
A.
Arif,
Z.
Wan
g
,
J
.
Wa
n
g
,
B.
M
a
t
h
e
r,
H.
Ba
sh
u
a
l
d
o
a
n
d
D.
Zh
a
o
,
“
Lo
a
d
M
o
d
e
li
n
g
-
A
Re
v
iew
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
m
a
rt Grid
,
v
o
l.
9
,
n
o
.
6
,
p
p
.
5
9
8
6
-
5
9
9
9
,
2
0
1
8
,
d
o
i
:
1
0
.
1
1
0
9
/T
S
G
.
2
0
1
7
.
2
7
0
0
4
3
6
.
[4
]
M
.
J.
S
.
Zu
b
e
ri,
A.
Ti
j
d
in
k
,
a
n
d
M
.
K.
P
a
tel,
“
Tec
h
n
o
-
e
c
o
n
o
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