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v
ar
iab
le
-
s
p
ee
d
w
i
n
d
tu
r
b
in
e
is
co
n
s
id
er
ed
w
it
h
D
FIG
an
d
a
m
u
ltil
e
v
el
ca
s
ca
d
ed
H
-
B
r
id
g
e
I
n
v
er
ter
C
HB
I
.
Mu
ltil
e
v
el
in
v
er
ter
s
ar
e
AC
-
DC
-
AC
co
n
v
er
ter
s
,
w
ell
s
u
ite
d
f
o
r
m
ed
i
u
m
an
d
h
ig
h
-
p
o
w
er
ap
p
licatio
n
s
[
5
]
d
u
e
to
th
eir
ab
ilit
y
to
m
ee
t
t
h
e
in
cr
ea
s
in
g
d
e
m
a
n
d
o
f
p
o
w
er
r
atin
g
s
an
d
p
o
w
er
q
u
alit
y
a
s
s
o
ciate
d
w
it
h
r
ed
u
ce
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
l
o
w
er
elec
tr
o
m
a
g
n
etic
i
n
ter
f
er
en
ce
,
an
d
h
ig
h
er
ef
f
icien
c
ies
w
h
en
co
m
p
ar
ed
w
it
h
t
h
e
co
n
v
e
n
tio
n
al
t
w
o
o
r
th
r
ee
lev
el
to
p
o
lo
g
y
[
6
]
.
T
h
e
in
cr
ea
s
i
n
g
n
u
m
b
e
r
o
f
v
o
ltag
e
lev
el
s
lead
to
t
h
e
p
r
o
d
u
ctio
n
o
f
h
i
g
h
-
p
o
w
er
q
u
al
it
y
w
a
v
e
f
o
r
m
s
[
7
]
,
ca
u
s
i
n
g
t
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
T
HD
to
b
e
lo
w
er
.
Mu
ltil
e
v
el
co
n
v
er
ter
s
ar
e
a
g
o
o
d
tr
ad
eo
f
f
s
o
lu
t
io
n
b
et
w
ee
n
p
er
f
o
r
m
an
ce
an
d
co
s
t
in
w
i
n
d
h
i
g
h
-
p
o
w
er
s
y
s
te
m
s
[
8
].
T
h
e
m
o
s
t
t
y
p
i
c
a
l
c
o
n
n
e
c
t
i
o
n
d
i
a
g
r
a
m
o
f
t
h
i
s
D
F
I
G
i
s
t
o
c
o
n
n
e
c
t
s
t
a
t
o
r
d
i
r
e
c
t
l
y
t
o
t
h
e
g
r
i
d
,
w
h
i
l
e
t
h
e
r
o
t
o
r
i
s
s
u
p
p
l
i
e
d
t
h
r
o
u
g
h
a
c
o
n
t
r
o
l
l
e
d
p
o
w
e
r
c
o
n
v
e
r
t
e
r
.
T
h
i
s
s
o
l
u
t
i
o
n
i
s
m
o
r
e
a
t
t
r
a
c
t
i
v
e
f
o
r
a
l
l
a
p
p
l
i
c
a
t
i
o
n
s
w
h
e
r
e
s
p
e
e
d
v
a
r
i
a
t
i
o
n
s
a
r
e
l
i
m
i
t
e
d
a
r
o
u
n
d
t
h
e
s
y
n
c
h
r
o
n
o
u
s
s
p
e
e
d
b
e
c
a
u
s
e
t
h
i
s
a
r
e
a
o
p
e
r
a
t
i
n
g
p
r
e
s
e
n
t
s
l
o
w
s
l
i
p
,
an
d
t
h
er
ef
o
r
e
th
e
co
n
v
er
ter
as
s
o
ciate
d
w
ith
th
e
r
o
to
r
h
as
to
b
e
tr
ea
ted
o
n
l
y
f
o
r
a
f
r
ac
tio
n
o
f
2
0
to
3
0
%
o
f
t
h
e
n
o
m
i
n
al
co
n
v
er
s
io
n
s
y
s
te
m
p
o
w
er
;
t
h
is
m
ea
n
s
th
a
t
t
h
e
lo
s
s
es
in
t
h
e
c
o
n
v
er
ter
ar
e
r
ed
u
ce
d
(
p
o
w
er
s
u
p
p
lied
to
th
e
r
o
to
r
is
lo
w
)
a
n
d
th
e
co
s
t
th
er
eo
f
is
r
ed
u
ce
d
.
T
h
at
is
w
h
y
w
e
f
i
n
d
th
is
m
ac
h
i
n
e
i
n
h
i
g
h
p
o
w
er
v
ar
iab
le
s
p
ee
d
an
d
co
n
s
ta
n
t
f
r
e
q
u
en
c
y
f
o
r
p
r
o
d
u
ctio
n
s
y
s
te
m
s
.
A
s
ec
o
n
d
r
ea
s
o
n
is
t
h
e
p
o
s
s
ib
ilit
y
o
f
co
n
tr
o
llin
g
t
h
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
in
t
h
e
s
tato
r
v
i
a
th
e
co
n
tr
o
l o
f
th
e
p
o
w
er
co
n
v
er
ter
[
9
]
.
Fu
r
t
h
er
v
ar
iab
le
s
p
ee
d
w
in
d
t
u
r
b
in
e
is
m
o
d
eled
to
f
i
n
d
a
r
elatio
n
s
h
ip
b
et
w
ee
n
t
h
e
elec
tr
o
m
a
g
n
eti
c
to
r
q
u
e
an
d
th
e
m
ec
h
a
n
ical
win
d
s
p
ee
d
.
A
f
ter
d
escr
ib
in
g
m
ec
h
a
n
ical
a
n
d
elec
tr
ical
m
o
d
e
l
o
f
th
e
DFI
G
in
s
ec
tio
n
3
,
a
v
ec
to
r
co
n
tr
o
l
m
e
th
o
d
b
ased
o
n
s
tato
r
f
lu
x
o
r
ie
n
tatio
n
SF
O
C
is
co
n
s
id
er
ed
:
d
ir
ec
t
v
ec
to
r
co
n
tr
o
l
b
ased
o
n
P
I
co
n
tr
o
ller
s
.
T
h
e
s
i
n
u
s
p
u
l
s
e
w
a
v
e
m
o
d
u
l
a
t
i
o
n
(
S
P
W
M
)
c
o
n
t
r
o
l
s
t
r
a
t
e
g
y
f
o
r
m
u
l
t
i
l
e
v
e
l
i
n
v
e
r
t
e
r
s
i
s
g
i
v
e
n
i
n
s
e
c
t
i
o
n
4
.
Fi
n
a
l
l
y
,
s
i
m
u
l
a
t
i
o
n
a
n
d
r
e
s
u
l
t
s
a
r
e
p
r
e
s
e
n
t
e
d
;
p
e
r
f
o
r
m
a
n
c
e
s
o
f
t
h
e
s
y
s
t
e
m
a
r
e
t
h
e
n
e
v
a
l
u
a
t
e
d
.
2.
WI
ND
T
URB
I
N
E
M
O
DE
L
Me
ch
an
ical
p
o
w
er
av
a
ilab
le
o
n
th
e
s
h
a
f
t o
f
a
w
i
n
d
tu
r
b
i
n
e
is
ex
p
r
ess
ed
b
y
[
1
0
]
:
=
1
2
3
=
1
2
2
3
(
1
)
w
h
er
e:
ρ
:
air
d
en
s
it
y
(
1
.
2
5
Kg
/
m
3
)
;
R
:
B
lad
e
len
g
th
i
n
m
eter
s
;
V
v
:
w
in
d
v
elo
cit
y
i
n
m
/s
.
T
h
e
ae
r
o
d
y
n
a
m
ic
p
o
w
er
ex
tr
ac
ted
f
r
o
m
w
in
d
t
u
r
b
in
e
ca
n
b
e
ca
lcu
lated
as
:
=
=
1
2
3
=
1
2
2
3
.
(
,
)
(
2
)
=
Ω
.
(3
)
w
h
er
e:
C
p
:
P
o
w
er
co
ef
f
icie
n
t;
β
:
P
itch
an
g
le
(
d
eg
)
;
λ
:
T
ip
s
p
ee
d
r
atio
;
Ω
Turb
:
T
u
r
b
in
e
s
p
ee
d
(
r
d
/s
)
.
No
w
i
n
d
t
u
r
b
in
e
co
u
ld
co
n
v
er
t
m
o
r
e
t
h
an
5
9
%
o
f
t
h
e
k
i
n
et
ic
en
er
g
y
o
f
t
h
e
w
i
n
d
i
n
to
m
e
ch
an
ical
en
er
g
y
t
u
r
n
in
g
a
r
o
to
r
[
1
1
]
.
T
h
is
is
k
n
o
w
n
as
th
e
B
etz
li
m
it
,
an
d
it
is
th
e
t
h
eo
r
etica
l
m
ax
i
m
u
m
co
ef
f
icie
n
t
o
f
p
o
w
er
f
o
r
a
n
y
w
i
n
d
t
u
r
b
in
e:
C
p
ma
x
=
1
6
/2
7
≈
0
.
5
9
3
.
T
h
e
m
u
ltip
lier
i
s
m
at
h
e
m
a
ticall
y
m
o
d
eled
b
y
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
:
{
=
Ω
=
Ω
=
2
+
=
Ω
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
0
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
4
5
9
2
-
4603
4594
w
h
er
e:
Ω
turb
,
Ω
m
:
T
u
r
b
in
e
s
p
ee
d
r
esp
e
ctiv
el
y
b
e
f
o
r
e
an
d
af
ter
th
e
m
u
ltip
lier
;
T
turb
:
ae
r
o
d
y
n
a
m
ic
to
r
q
u
e;
T
m
:
to
r
q
u
e
af
ter
th
e
m
u
ltip
lier
;
G:
Gea
r
r
atio
;
J
g
:
Gen
er
ato
r
in
er
tia
;
J
T
: T
o
tal
in
er
tia;
J
Turb
: T
u
r
b
in
e
i
n
er
tia
.
T
h
e
f
u
n
d
a
m
e
n
tal
eq
u
at
io
n
o
f
d
y
n
a
m
ics
to
d
eter
m
i
n
e
t
h
e
e
v
o
lu
t
io
n
o
f
t
h
e
m
ec
h
a
n
ical
s
p
ee
d
f
r
o
m
th
e
to
tal
m
ec
h
a
n
ical
to
r
q
u
e
ap
p
lied
to
th
e
r
o
to
r
:
Ω
=
=
−
−
Ω
(5
)
w
h
er
e:
T
em
:
E
lectr
o
m
a
g
n
et
ic
to
r
q
u
e
;
C
f
:
Vis
co
u
s
f
r
ictio
n
co
e
f
f
ic
ien
t
.
2
.
1
.
M
o
delin
g
o
f
t
he
DF
I
G
,
P
a
rk’
s
m
o
de
l
T
h
e
d
-
q
ax
is
r
ep
r
esen
ta
tio
n
o
f
DFI
G
i
s
u
s
ed
f
o
r
m
o
d
eli
n
g
,
co
n
s
id
er
in
g
f
lu
x
as
v
ar
iab
le
b
ased
o
n
P
ar
k
'
s
m
o
d
el.
A
ll
r
o
to
r
q
u
an
t
ities
ar
e
r
ef
er
r
ed
to
s
tato
r
s
id
e.
T
h
e
DFI
G
m
o
d
el
r
ep
r
esen
ted
b
y
v
o
lta
g
e
(
6
)
.
T
h
e
s
tato
r
an
d
r
o
to
r
s
id
e
f
lu
x
l
in
k
a
g
e
eq
u
at
io
n
s
ar
e
g
iv
e
n
as
[1
2
-
14
]:
{
=
+
Ф
−
Ф
=
+
Ф
+
Ф
=
+
Ф
−
(
−
)
Ф
=
+
Ф
+
(
−
)
Ф
(6
)
T
h
e
s
tato
r
an
d
r
o
to
r
f
lu
x
ca
n
b
e
ex
p
r
ess
ed
as
:
{
Ф
=
+
Ф
=
+
Ф
=
+
Ф
=
+
(7
)
E
lectr
o
m
a
g
n
etic
to
r
q
u
e
is
al
s
o
ex
p
r
ess
ed
in
ter
m
s
o
f
c
u
r
r
en
t
s
an
d
f
l
u
x
:
=
(
Ф
−
Ф
)
(8
)
w
h
er
e:
R
s
,
R
r
,
ar
e
r
e
s
p
ec
tiv
el
y
th
e
s
t
ato
r
an
d
r
o
to
r
r
esis
ta
n
ce
s
;
L
s
,
L
r
:
in
d
u
cta
n
ce
s
o
f
t
h
e
s
tato
r
a
n
d
r
o
to
r
w
in
d
i
n
g
s
;
L
m
is
t
h
e
m
u
t
u
al
i
n
d
u
c
tan
ce
;
V
d
s
,
V
q
s
,
V
d
r
et
V
q
r
:
Dir
ec
t
an
d
q
u
ad
r
ate
co
m
p
o
n
en
ts
o
f
t
h
e
s
p
ac
e
p
h
a
s
o
r
s
o
f
th
e
s
tato
r
an
d
r
o
to
r
v
o
lta
g
es
;
I
d
s
,
I
q
s
,
I
d
r
,
I
q
r
:
Dir
ec
t
a
n
d
q
u
ad
r
ate
co
m
p
o
n
en
ts
o
f
t
h
e
s
p
ac
e
p
h
aso
r
s
o
f
th
e
s
tato
r
an
d
r
o
to
r
cu
r
r
en
t
s
;
φ
d
s
,
φ
qs
,
φ
dr
et
φ
qr
:
Dir
ec
t
a
n
d
q
u
ad
r
ate
co
m
p
o
n
e
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I
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I
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N:
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1
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I
SS
N
:
2088
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8708
I
n
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2
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r
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2
.
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r
m
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g
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3:
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u
r
e
3
.
C
lo
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lo
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co
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o
l
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
C
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n
tr
o
l o
f th
e
p
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q
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a
lity f
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p
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w
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b
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mu
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l in
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(
Ha
ch
emi
Ha
ch
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)
4597
3.
CASCAD
E
D
H
-
B
RID
G
E
I
N
VE
R
T
E
R
CH
B
I
T
H
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RY
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m
u
lt
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el
to
p
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lo
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s
ed
f
o
r
g
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id
co
n
n
ec
tio
n
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
[
2
0
,
21
]
.
Mu
ltil
e
v
e
l
co
n
v
er
ter
s
tr
u
ct
u
r
es
h
av
e
th
r
e
e
m
aj
o
r
class
i
f
icatio
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s
;
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e
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tr
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t
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la
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f
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d
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d
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-
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s
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C
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g
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r
e
4
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ar
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w
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t
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th
e
m
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lt
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l
C
HB
I
h
as
m
a
n
y
d
is
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ct
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v
a
n
ta
g
es:
S
w
itc
h
d
ev
ices r
eq
u
ir
ed
ar
e
less
u
n
d
er
th
e
s
a
m
e
s
w
itc
h
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g
f
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en
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d
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e
l n
u
m
b
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.
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h
e
h
ar
m
o
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ic
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te
n
t i
s
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e
o
u
tp
u
t
v
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f
o
r
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g
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en
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w
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h
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n
g
f
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eq
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e
n
c
y
.
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lar
ized
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cu
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la
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t
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n
d
p
ac
k
ag
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s
e
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ce
ll
h
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t
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s
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m
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tr
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e,
an
d
th
er
e
ar
e
n
o
ex
tr
a
cla
m
p
in
g
d
io
d
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th
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ca
s
e
o
f
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cla
m
p
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to
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th
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o
f
t
h
e
ca
p
ac
ito
r
clam
p
ed
to
p
o
lo
g
y
[
22
].
.
Vd
c
S
1
S
2
S
3
S
4
Vo
u
t
+
-
Fig
u
r
e
4
.
Sin
g
le
p
h
ase
H
-
b
r
id
g
e
in
v
er
ter
3
.
1
.
T
heo
ry
o
f
ca
s
ca
ded H
-
B
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e
m
u
lt
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el
inv
er
t
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h
e
ca
s
ca
d
ed
H
b
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id
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e
m
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l
til
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ter
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t
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o
f
in
d
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b
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h
ich
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n
d
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s
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p
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a
c
h
H
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r
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d
g
e
c
e
l
l
c
o
n
t
a
i
n
s
f
o
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s
w
i
t
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s
.
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t
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s
t
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I
G
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s
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,
2
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2088
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8708
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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lec
&
C
o
m
p
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I
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N:
2088
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8708
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Evaluation Warning : The document was created with Spire.PDF for Python.