I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
w
er
E
ng
ineering
(
I
J
AP
E
)
Vo
l.
4
,
No
.
1
,
A
p
r
il
201
5
,
p
p
.
13
~
22
I
SS
N:
2252
-
8792
13
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
J
APE
Co
m
pa
riso
n b
etw
een Tw
o
-
Lev
el Conv
erte
r and Th
r
ee
-
Lev
el
NPC
Co
nv
erte
r
f
o
r Ev
a
lua
tion the
Q
ua
lity
Pow
er of D
FI
G
Ba
sed Wind Tu
rb
ines
Z
e
rz
o
uri N
o
ra
*
,
L
a
ba
r
H
o
ci
ne
*
,
K
ec
hid
a
Sih
e
m
*
*
*
D
e
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Ba
d
ji
M
o
k
th
a
r
Un
iv
e
rsity
A
n
n
a
b
a
,
A
lg
e
ria
**
A
u
to
m
a
ti
c
Co
n
tro
l
L
a
b
o
ra
to
ry
a
n
d
C
o
m
p
u
ter G
u
e
l
m
a
L
a
ig
,
Un
iv
e
rsit
y
o
f
G
u
e
l
m
a
,
BP
4
0
1
.
G
u
e
lma
2
4
0
0
0
,
A
lg
e
ria
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
u
n
26
,
2
0
1
5
R
ev
i
s
ed
Feb
1
0
,
2
0
1
5
A
cc
ep
ted
Mar
2
3
,
2
0
1
5
T
h
is
p
a
p
e
r
d
e
a
ls
th
e
p
o
w
e
r
c
o
n
tro
l
f
o
r
th
re
e
-
lev
e
l
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rter
NP
C
-
V
S
I
f
e
e
d
s
th
e
ro
to
r
o
f
th
e
d
o
u
b
ly
f
e
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r
‘DFIG
’
b
a
se
d
w
in
d
p
o
w
e
r
g
e
n
e
ra
ti
o
n
sy
st
e
m
.
T
h
is
c
o
n
v
e
rter
a
ll
o
w
s
c
o
n
tro
ll
in
g
th
e
ro
to
r
v
o
lt
a
g
e
in
m
a
g
n
it
u
d
e
a
n
d
p
h
a
s
e
a
n
g
le
w
it
h
a
h
ig
h
f
lex
ib
il
it
y
a
n
d
c
a
n
th
e
re
f
o
re
b
e
u
se
d
f
o
r
a
c
ti
v
e
a
n
d
r
e
a
c
ti
v
e
p
o
w
e
r
c
o
n
tro
l
o
f
DFIG
.
Th
e
c
o
n
tro
l
is
e
sp
e
c
iall
y
d
e
sig
n
e
d
to
re
d
u
c
e
th
e
h
a
rm
o
n
ic
d
ist
o
rti
o
n
o
f
th
e
g
e
n
e
ra
ted
c
u
rre
n
ts
a
n
d
a
c
ti
v
e
p
o
w
e
r
rip
p
le
s
o
f
th
e
c
las
sic
a
l
c
o
n
tro
l.
In
a
d
d
it
io
n
,
it
’s
c
o
n
v
e
n
ien
t
f
o
r
h
ig
h
p
o
w
e
r
d
riv
e
a
n
d
v
a
riab
le
sp
e
e
d
g
e
n
e
ra
to
r
a
p
p
li
c
a
ti
o
n
s
w
it
h
c
o
n
sta
n
t
sw
it
c
h
in
g
f
re
q
u
e
n
c
y
.
T
h
e
d
e
tailed
o
p
e
ra
ti
o
n
p
ri
n
c
ip
le
a
n
d
sim
u
latio
n
re
su
lt
s f
o
r
3
M
W
o
f
DFIG
a
re
a
lso
d
isc
u
ss
e
d
.
K
ey
w
o
r
d
:
Do
u
b
l
y
Fed
I
n
d
u
ctio
n
Ge
n
er
at
o
r
P
W
M
T
ec
h
n
iq
u
e
T
o
tal
Har
m
o
n
ics
W
in
d
T
u
r
b
in
e
Co
p
y
rig
h
t
©
2
0
1
5
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Z
er
zo
u
r
i N
o
r
a,
Dep
ar
te
m
en
t
o
f
E
lectr
ical
E
n
g
in
ee
r
in
g
,
B
ad
j
i M
o
k
th
ar
Un
i
v
er
s
it
y
An
n
ab
a,
Un
i
v
er
s
ité
B
ad
j
i M
o
k
h
tar
-
An
n
ab
a
-
B
.
P
.
1
2
,
A
n
n
ab
a,
2
3
0
0
0
A
l
g
er
ia.
E
m
ail:
n
ze
r
zo
u
r
i@
y
a
h
o
o
.
f
r
1.
I
NT
RO
D
UCT
I
O
N
W
ith
t
h
e
f
a
s
t
i
n
cr
ea
s
i
n
g
o
f
w
i
n
d
en
er
g
y
i
n
s
talled
ca
p
ac
it
y
o
v
er
th
e
last
t
w
o
d
ec
ad
es,
it
is
p
lay
in
g
a
v
ital
r
o
le
in
w
o
r
ld
’
s
en
er
g
y
m
ar
k
ets
at
t
h
e
p
r
esen
t.
I
t
is
ex
p
e
cted
th
at
g
lo
b
al
to
tal
w
in
d
p
o
w
er
g
e
n
er
atio
n
w
i
ll
s
u
p
p
l
y
ar
o
u
n
d
1
2
%
o
f
th
e
t
o
tal
w
o
r
ld
elec
tr
icit
y
g
e
n
er
at
io
n
at
th
e
e
n
d
o
f
2
0
2
0
.
C
u
r
r
en
tl
y
th
e
p
r
e
f
er
r
ed
co
n
f
i
g
u
r
atio
n
f
o
r
w
i
n
d
t
u
r
b
in
e
g
e
n
er
atio
n
is
d
o
u
b
l
y
f
ed
i
n
d
u
ctio
n
g
en
er
ato
r
,
w
h
ic
h
ca
n
b
e
s
ee
n
in
Fi
g
.
1
.
T
h
i
s
ca
n
b
e
d
u
e
to
th
eir
ad
v
an
tag
e
o
u
s
ch
ar
ac
ter
is
t
ics.
I
n
co
m
p
ar
is
o
n
w
it
h
th
e
f
i
x
ed
s
p
e
ed
w
in
d
tu
r
b
in
e,
th
e
y
ca
n
r
ed
u
ce
m
ec
h
an
ica
l
s
tr
es
s
es,
a
n
d
co
m
p
en
s
ate
f
o
r
to
r
q
u
e
an
d
p
o
w
er
p
u
ls
at
io
n
s
,
a
n
d
as
a
r
e
s
u
lt
i
m
p
r
o
v
e
p
o
w
er
q
u
alit
y
.
I
n
ad
d
itio
n
,
v
ar
iab
le
s
p
ee
d
tu
r
b
in
es
ca
n
m
a
x
i
m
ize
th
e
ef
f
icie
n
c
y
o
f
t
h
e
en
er
g
y
c
o
n
v
er
s
io
n
,
as
th
e
y
ca
n
o
p
er
ate
at
o
p
tim
al
r
o
tatio
n
al
v
elo
cit
y
f
o
r
ea
ch
g
i
v
en
win
d
s
p
ee
d
[
1
]
.
T
h
e
DFI
G
w
it
h
a
v
ec
to
r
co
n
tr
o
l
s
tr
ateg
y
d
eliv
er
s
g
o
o
d
p
er
f
o
r
m
an
ce
a
n
d
is
co
m
m
o
n
l
y
u
s
e
d
in
w
i
n
d
tu
r
b
i
n
e
in
d
u
s
tr
y
[
2
]
.
T
h
er
e
ar
e
m
an
y
r
ea
s
o
n
s
f
o
r
u
s
i
n
g
a
D
FIG
f
o
r
a
v
ar
iab
le
w
i
n
d
s
p
ee
d
,
s
u
c
h
a
s
r
ed
u
ci
n
g
s
tr
ai
n
o
n
m
ec
h
a
n
i
ca
l
p
ar
ts
,
n
o
i
s
e
a
n
d
th
e
p
o
s
s
ib
ilit
y
f
o
r
co
n
tr
o
l
ac
t
i
v
e
a
n
d
r
ea
cti
v
e
p
o
w
er
[
3
]
.
T
h
e
w
i
n
d
s
y
s
te
m
u
s
in
g
a
DFI
G
an
d
th
e
b
ac
k
-
to
-
b
ac
k
P
u
ls
e
W
id
th
Mo
d
u
latio
n
(
P
W
M
)
co
n
v
er
ter
w
h
ich
co
n
n
ec
ts
t
h
e
r
o
to
r
o
f
th
e
g
e
n
er
at
o
r
an
d
th
e
n
et
w
o
r
k
h
as
m
an
y
ad
v
an
tag
e
s
.
On
e
o
f
th
e
m
is
t
h
e
p
o
w
er
co
n
v
er
ter
s
u
s
ed
th
at
ar
e
s
ized
to
p
ass
a
f
r
ac
tio
n
o
f
t
h
e
to
tal
p
o
w
er
o
f
t
h
e
s
y
s
te
m
[
4
]
-
[
5
]
,
th
er
e
b
y
r
ed
u
ci
n
g
lo
s
s
es
i
n
p
o
w
er
elec
tr
o
n
ic
co
m
p
o
n
e
n
t
s
.
T
h
e
p
er
f
o
r
m
a
n
ce
a
n
d
o
u
tp
u
t p
o
w
er
d
o
n
o
t
d
ep
en
d
o
n
l
y
o
n
th
e
DFI
G,
b
u
t a
ls
o
t
h
e
w
a
y
t
h
e
b
ac
k
-
to
-
b
ac
k
co
n
v
er
t
er
is
co
n
tr
o
lled
.
T
h
e
b
ac
k
-
to
-
b
ac
k
co
n
v
er
ter
co
n
s
is
ts
o
f
t
w
o
p
ar
ts
:
t
h
e
m
ac
h
in
e
s
id
e
co
n
v
er
ter
ca
lled
R
o
to
r
Sid
e
C
o
n
v
er
ter
(
R
S
C
)
an
d
th
e
n
e
t
w
o
r
k
s
id
e
co
n
v
er
t
er
ca
lled
Gr
id
Sid
e
C
o
n
v
er
ter
(
GSC
)
.
T
h
e
R
SC
co
n
tr
o
ls
t
h
e
ac
tiv
e
p
o
w
er
an
d
r
ea
ctiv
e
p
o
w
er
p
r
o
d
u
ce
d
b
y
t
h
e
m
ac
h
i
n
e.
T
h
e
GSC
co
n
tr
o
ls
th
e
DC
b
u
s
v
o
ltag
e
a
n
d
p
o
w
er
f
ac
to
r
.
I
n
th
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
4
,
No
.
2
,
A
p
r
il
2
0
1
5
:
13
–
22
14
s
tu
d
y
,
a
tec
h
n
iq
u
e
to
co
n
tr
o
l
th
e
t
w
o
a
n
d
t
h
r
ee
le
v
el
i
n
v
er
ter
is
p
r
esen
ted
a
n
d
t
h
e
w
i
n
d
s
y
s
te
m
d
y
n
a
m
i
c
p
er
f
o
r
m
a
n
ce
i
s
a
n
al
y
ze
d
b
y
s
i
m
u
lati
o
n
s
i
n
Ma
tlab
/
Si
m
u
li
n
k
.
Firstl
y
,
t
h
e
w
i
n
d
tu
r
b
i
n
e
i
s
m
o
d
elled
t
h
en
a
MP
PT
tech
n
iq
u
e
f
o
r
ex
tr
ac
ti
n
g
t
h
e
m
a
x
i
m
u
m
p
o
w
er
is
p
r
esen
ted
.
Su
b
s
eq
u
e
n
tl
y
,
a
m
o
d
el
o
f
th
e
D
FIG
is
d
er
iv
ed
in
d
q
r
ef
er
en
ce
f
r
a
m
e
an
d
p
r
esen
ted
th
e
m
o
d
el
o
f
t
w
o
an
d
t
h
r
ee
lev
el
i
n
v
er
ter
.
Fin
all
y
,
s
i
m
u
latio
n
r
esu
lt
s
an
d
th
e
ir
in
ter
p
r
etatio
n
ar
e
p
r
o
v
id
ed
.
Fig
u
r
e
1
.
W
in
d
tu
r
b
in
e
s
y
s
te
m
w
it
h
d
o
u
b
l
y
f
ed
in
d
u
ctio
n
g
e
n
er
ato
r
2.
M
O
DE
L
O
F
T
H
E
W
I
ND
T
URB
I
NE
A
E
RO
DYN
AM
I
CS
T
h
e
m
ec
h
a
n
ical
p
o
w
er
ex
tr
ac
t
ed
f
r
o
m
a
w
i
n
d
t
u
r
b
in
e,
P
T
,
is
d
ep
en
d
en
t
o
n
t
h
e
p
o
w
er
co
ef
f
icie
n
t,
C
p
,
f
o
r
t
h
e
g
iv
e
n
t
u
r
b
in
e
o
p
er
atio
n
co
n
d
it
io
n
s
an
d
i
s
g
i
v
e
n
b
y
(
)
(
1
)
W
h
er
e
C
p
,
A
,
ρ
an
d
v
ar
e
th
e
p
o
w
er
co
ef
f
ic
ien
t
(
m
ax
i
m
u
m
v
alu
e
B
etz
’
s
li
m
it
0
.
5
9
3
)
,
th
e
ar
ea
s
w
ep
t
b
y
t
h
e
b
lad
es,
th
e
s
p
ec
i
f
ic
d
en
s
it
y
o
f
air
an
d
t
h
e
w
i
n
d
s
p
ee
d
,
r
esp
ec
tiv
el
y
.
T
h
er
ef
o
r
e,
if
t
h
e
air
d
en
s
it
y
,
s
w
ep
t
ar
e
a
an
d
w
i
n
d
s
p
ee
d
ar
e
co
n
s
tan
t,
t
h
e
o
u
tp
u
t
p
o
w
er
o
f
th
e
w
i
n
d
tu
r
b
in
e
w
ill
b
e
a
f
u
n
ctio
n
o
f
C
p
.
Ho
w
ev
er
,
C
p
is
a
f
u
n
ctio
n
o
f
t
h
e
p
itch
a
n
g
el
o
f
t
u
r
b
in
e
r
o
to
r
b
lad
es,
β
,
an
d
th
e
tip
-
s
p
ee
d
r
atio
,
,
w
h
ic
h
is
d
e
f
i
n
ed
as
(
2
)
W
h
er
e
Ω
is
th
e
s
p
ee
d
o
f
tu
r
b
i
n
e
an
d
R
t
h
e
b
lad
e
r
ad
iu
s
.
T
h
e
p
o
w
er
co
ef
f
icie
n
t o
f
t
h
e
t
u
r
b
in
e
is
g
i
v
en
b
y
[
6
]
:
(
)
(
)
(
3
)
A
t
y
p
ical
C
p
c
u
r
v
e
is
s
h
o
w
n
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
P
o
w
er
co
ef
f
icie
n
t
C
p
v
er
s
u
s
t
ip
s
p
ee
d
r
atio
0
5
10
15
20
25
0
0
.
0
5
0
.
1
0
.
1
5
0
.
2
0
.
2
5
0
.
3
0
.
3
5
0
.
4
0
.
4
5
0
.
5
V
i
t
e
s
s
e
d
e
V
e
n
t
(
m
/
s
)
c
o
e
f
f
i
c
i
e
n
t
C
p
1
b
e
t
a
=
0
2
b
e
t
a
=
2
3
b
e
t
a
=
4
4
b
e
t
a
=
6
5
b
e
t
a
=
8
6
b
e
t
a
=
1
0
7
b
e
t
a
=
1
2
8
b
e
t
a
=
1
4
9
b
e
t
a
=
1
6
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
C
o
mp
a
r
is
o
n
b
etw
ee
n
Tw
o
-
Lev
el
C
o
n
ve
r
ter a
n
d
Th
r
ee
-
Leve
l NPC
C
o
n
ve
r
ter fo
r
…
(
Zer
z
o
u
r
i No
r
a
)
15
T
h
e
p
ar
am
eter
s
o
f
w
in
d
t
u
r
b
i
n
e
f
o
r
t
h
is
ca
lc
u
latio
n
ar
e
s
h
o
w
n
in
T
ab
le
I
V.
T
h
e
s
am
e
p
ar
am
eter
s
ar
e
also
ad
o
p
ted
in
s
i
m
u
latio
n
o
f
s
ec
ti
o
n
V.
A
s
i
t
ca
n
b
e
s
ee
n
,
t
h
er
e
is
a
v
a
lu
e
o
f
λ
f
o
r
w
h
ich
C
p
v
alu
e
is
m
a
x
i
m
ized
(
C
pmax
)
b
y
a
g
i
v
en
p
itc
h
an
g
le
β
v
alu
e,
an
d
t
h
e
C
pmax
v
alu
e
is
r
ed
u
ce
d
w
it
h
t
h
e
β
v
al
u
e
in
cr
ea
s
ed
.
T
o
ex
tr
ac
t
th
e
m
a
x
i
m
u
m
w
i
n
d
en
er
g
y
,
p
itch
a
n
g
le
i
s
u
s
u
all
y
ar
o
u
n
d
z
er
o
w
h
en
t
h
e
w
i
n
d
s
s
p
ee
d
b
elo
w
t
h
e
r
ated
v
al
u
e
[
7
]
.
W
ith
co
n
s
tan
t
b
lad
e
p
itch
an
g
le,
t
h
e
m
a
x
i
m
u
m
v
al
u
e
o
f
t
h
e
p
o
w
er
co
ef
f
icie
n
t
C
pmax
w
o
u
ld
b
e
o
b
tain
ed
at
a
p
ar
ticu
lar
v
al
u
e
o
f
,
d
ef
in
ed
as
opt.
Fo
r
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
tr
ac
k
i
n
g
(
MP
PT
)
,
s
h
o
u
ld
b
e
m
ai
n
tai
n
ed
at
th
is
o
p
ti
m
al
v
a
lu
e.
T
h
e
Ma
x
i
m
u
m
o
u
tp
u
t p
o
w
er
o
f
th
e
w
i
n
d
tu
r
b
in
es
P
t
m
a
x
ca
n
b
e
ex
p
r
es
s
ed
b
y
[
7
]
,
[
8
]
:
(
4
)
3.
DF
I
G
M
O
DE
L
L
I
N
G
AND
P
O
WE
R
CO
NT
RO
L
3
.
1
.
Do
ub
ly
F
ed
I
nd
uct
io
n M
a
ch
ine Eq
ua
t
io
ns
T
h
e
DFI
G
is
a
w
o
u
n
d
r
o
to
r
i
n
d
u
ctio
n
g
e
n
er
ato
r
in
w
h
ic
h
t
h
e
r
o
to
r
cir
cu
it
is
co
n
n
ec
ted
to
th
e
g
r
id
th
r
o
u
g
h
t
w
o
b
ac
k
-
to
b
ac
k
co
n
v
er
ter
s
a
n
d
a
d
c
-
lin
k
ca
p
ac
it
o
r
[
9
]
.
T
h
e
ab
ilit
y
to
s
u
b
tr
ac
t
an
d
s
u
p
p
l
y
p
o
w
er
f
r
o
m
t
h
e
r
o
to
r
m
a
k
e
s
it
p
o
s
s
i
b
le
to
o
p
er
ate
th
e
DFI
G
a
t
s
u
b
s
y
n
c
h
r
o
n
o
u
s
o
r
s
u
p
er
s
y
n
c
h
r
o
n
o
u
s
s
p
ee
d
w
h
ile
k
ee
p
in
g
co
n
s
ta
n
t
t
h
e
v
o
lta
g
e
an
d
f
r
eq
u
e
n
c
y
o
n
t
h
e
s
tato
r
.
T
h
e
d
−
q
m
o
d
el
i
n
an
ar
b
itra
r
y
r
ef
er
e
n
ce
f
r
a
m
e
i
s
ex
p
r
ess
ed
as f
o
llo
w
s
[
1
0
]
,
[
1
1
]
:
{
(
)
(
)
(
5
)
T
h
e
f
lu
x
eq
u
atio
n
s
ar
e:
{
(
6
)
W
h
er
e
ω
s
: s
y
n
ch
r
o
n
o
u
s
a
n
g
u
lar
f
r
eq
u
en
c
y
ω
r
: r
o
to
r
an
g
u
lar
f
r
eq
u
e
n
c
y
Rs
,
Rr
: e
q
u
iv
a
len
t r
es
is
ta
n
ce
s
o
f
s
tato
r
an
d
r
o
to
r
w
in
d
i
n
g
s
,
r
esp
ec
tiv
el
y
Ls
,
Lr
,
M
:
s
el
f
an
d
m
u
t
u
al
i
n
d
u
ctan
ce
s
o
f
s
tato
r
an
d
r
o
to
r
w
i
n
d
in
g
s
,
r
esp
ec
ti
v
el
y
T
h
e
m
o
tio
n
eq
u
atio
n
s
ar
e
g
i
v
e
n
as
f
o
llo
w
s
:
(
7
)
(
)
(
8
)
(
9
)
W
h
er
e
g
:
s
lip
an
g
u
lar
f
r
eq
u
en
c
y
s
: sli
p
C
m
:
m
ec
h
a
n
ical
to
r
q
u
e
p
r
o
v
id
ed
to
th
e
w
i
n
d
tu
r
b
in
e
C
e
: e
lectr
o
m
ag
n
etic
to
r
q
u
e
J
:
m
o
m
e
n
t o
f
i
n
er
tia
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
4
,
No
.
2
,
A
p
r
il
2
0
1
5
:
13
–
22
16
3.
2
.
Ro
t
o
r
s
ide C
o
nv
er
t
er
I
n
t
h
e
r
o
to
r
s
id
e
co
n
v
er
ter
,
r
ea
ctiv
e
p
o
w
er
a
n
d
t
h
e
r
e
f
er
en
ce
d
to
r
q
u
e
d
eter
m
i
n
e
t
h
e
c
u
r
r
en
t
r
ef
er
en
ce
s
,
w
h
ic
h
d
eter
m
i
n
e
t
h
e
v
o
lta
g
es to
b
e
ap
p
lied
to
th
e
r
o
to
r
s
id
e.
A
w
in
d
-
t
u
r
b
in
e
g
en
er
ato
r
m
u
s
t
b
e
f
u
ll
y
co
n
tr
o
llab
le
s
o
t
h
at
i
t
ca
n
o
p
er
ate
at
a
s
h
a
f
t
s
p
ee
d
th
at
i
s
i
n
d
ep
en
d
en
t
o
f
w
i
n
d
co
n
d
itio
n
s
to
g
a
in
th
e
s
tato
r
v
o
lta
g
e
w
h
ic
h
is
th
e
s
a
m
e
to
g
r
id
v
o
lta
g
e,
in
c
lu
d
i
n
g
t
h
e
s
a
m
e
a
m
p
lit
u
d
e,
f
r
eq
u
en
c
y
a
n
d
p
h
ase.
I
n
th
i
s
s
ec
t
io
n
,
t
h
e
co
n
tr
o
l
m
o
d
el
o
f
r
o
to
r
s
id
e
co
n
v
er
ter
is
an
al
y
ze
d
.
T
h
e
s
tato
r
f
lu
x
o
r
ien
tatio
n
r
e
f
er
s
to
t
h
e
d
-
ax
i
s
s
y
n
c
h
r
o
n
o
u
s
r
o
tatin
g
d
q
co
o
r
d
in
ate
s
y
s
te
m
o
r
ien
ted
in
t
h
e
d
ir
ec
tio
n
o
f
th
e
d
o
u
b
l
y
-
f
ed
m
o
t
o
r
s
ta
to
r
f
l
u
x
,
s
h
o
w
n
in
F
ig
u
r
e
3
.
Fig
u
r
e
3
.
Stato
r
f
ield
o
r
ien
ted
co
n
tr
o
l o
f
DFI
G
W
e
ca
n
o
b
tain
th
e
f
o
llo
w
in
g
r
elatio
n
s
h
ip
:
{
(
1
0
)
T
o
k
ee
p
th
e
s
tato
r
f
l
u
x
ϕ
s
co
n
s
tan
t,
t
h
e
v
o
lta
g
e
eq
u
atio
n
s
ca
n
b
e
ex
p
r
ess
ed
as:
{
(
1
1
)
W
h
er
e
V
s
is
th
e
s
p
ac
e
v
ec
to
r
am
p
lit
u
d
e
o
f
s
tato
r
v
o
lta
g
e.
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
s
o
f
s
tato
r
ca
n
b
e
d
er
iv
ed
as:
{
(
)
(
)
(
1
2
)
Fro
m
ab
o
v
e
p
o
w
er
eq
u
atio
n
s
,
it
is
clea
r
to
d
escr
ib
e
th
e
p
o
w
er
f
lo
w
i
n
th
e
D
FIG
f
o
r
s
u
b
-
s
y
n
c
h
r
o
n
o
u
s
an
d
s
u
p
er
s
y
n
c
h
r
o
n
o
u
s
o
p
er
atio
n
.
A
b
o
v
e
s
y
n
c
h
r
o
n
o
u
s
s
p
ee
d
,
th
e
f
o
u
r
q
u
ad
r
a
n
t c
o
n
v
er
ter
o
p
er
ates a
s
a
g
e
n
er
ato
r
o
f
ac
tiv
e
p
o
w
er
d
eli
v
er
in
g
p
o
wer
to
th
e
g
r
id
.
Un
d
er
t
h
e
c
o
n
d
itio
n
o
f
s
u
b
s
y
n
ch
r
o
n
o
u
s
;
th
e
f
o
u
r
-
q
u
ad
r
an
t
co
n
v
er
ter
cir
cu
late
s
ac
ti
v
e
p
o
w
er
f
r
o
m
th
e
g
r
id
in
to
t
h
e
r
o
to
r
cir
cu
it.
Usi
n
g
eq
u
at
io
n
s
(
1
0
)
to
(
6
)
,
th
e
r
o
to
r
cu
r
r
en
ts
ca
n
b
e
d
er
iv
ed
in
th
e
f
o
llo
w
i
n
g
f
o
r
m
.
{
(
1
3
)
Fin
all
y
,
t
h
e
r
o
to
r
r
ef
er
en
ce
v
o
l
tag
es a
r
e
ca
lcu
lated
u
s
i
n
g
{
(
1
4
)
I
t
is
clea
r
f
r
o
m
th
e
s
ta
to
r
p
o
w
er
e
x
p
r
ess
io
n
s
(
1
0
)
,
th
at
s
t
ato
r
ac
tiv
e
p
o
w
er
is
co
n
tr
o
ll
ed
b
y
I
dr
,
w
h
ile
I
qr
co
n
tr
o
ls
s
tato
r
r
ea
cti
v
e
p
o
w
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
C
o
mp
a
r
is
o
n
b
etw
ee
n
Tw
o
-
Lev
el
C
o
n
ve
r
ter a
n
d
Th
r
ee
-
Leve
l NPC
C
o
n
ve
r
ter fo
r
…
(
Zer
z
o
u
r
i No
r
a
)
17
T
h
e
R
S
C
co
n
tr
o
l
s
tr
ate
g
y
is
il
lu
s
tr
ated
in
Fi
g
u
r
e
4
.
Fo
r
t
h
e
s
tato
r
to
o
p
er
ate
at
u
n
it
y
p
o
w
er
f
ac
to
r
,
t
h
e
f
lo
w
o
f
r
ea
ctiv
e
p
o
w
er
f
r
o
m
t
h
e
s
tato
r
s
id
e
to
g
r
id
is
s
et
to
ze
r
o
,
th
u
s
I
rq
*
ca
n
b
e
d
eter
m
in
ed
f
r
o
m
(
1
0
)
,
s
o
I
d
r
*
ca
n
b
e
ca
lcu
lated
f
r
o
m
(
1
2
)
.
No
w
t
h
e
ac
tu
al
r
o
to
r
cu
r
r
en
ts
I
dr
an
d
I
qr
a
r
e
co
m
p
ar
ed
w
it
h
t
h
e
r
e
f
er
en
ce
r
o
to
r
cu
r
r
en
t
s
I
dr
*
a
n
d
I
qr
*
b
ef
o
r
e
b
ein
g
p
r
o
ce
s
s
ed
u
s
in
g
i
n
n
er
P
I
cu
r
r
en
t
co
n
tr
o
ller
s
,
i
n
a
s
i
m
i
lar
m
a
n
n
er
to
th
e
o
n
e
s
u
s
ed
f
o
r
GSC
,
t
h
en
ad
d
ed
w
it
h
c
r
o
s
s
-
ter
m
s
,
to
f
in
al
l
y
g
en
er
ate
t
h
e
co
n
tr
o
l sig
n
als
f
o
r
th
e
R
SC
[
1
0
]
.
Fig
u
r
e
3
.
Vec
to
r
co
n
tr
o
l o
f
DFI
G
w
it
h
g
r
id
a
n
d
r
o
to
r
s
id
e
co
n
v
er
ter
s
.
4.
M
O
DE
L
L
I
N
G
P
WM
I
NVE
RT
E
R
4
.
1
.
T
w
o
-
lev
el
inv
er
t
er
s
A
p
o
w
er
cir
cu
it
o
f
t
h
r
ee
-
p
h
as
e
v
o
ltag
e
-
s
o
u
r
ce
b
ac
k
-
to
b
ac
k
P
W
M
co
n
v
er
ter
s
i
n
cl
u
d
in
g
t
w
o
lel
v
e
p
o
w
er
s
e
m
ico
n
d
u
cto
r
s
w
itc
h
es
is
s
h
o
w
n
in
Fi
g
u
r
e
5
,
w
h
er
e
th
e
t
w
o
co
n
v
er
ter
s
ar
e
lin
k
ed
th
r
o
u
g
h
a
DC
ca
p
ac
ito
r
.
As
ca
n
b
e
s
ee
n
i
n
Fi
g
u
r
e5
,
th
e
D
C
/
A
C
in
v
er
ter
h
a
s
a
n
i
n
p
u
t
v
o
ltag
e
(
Vd
c)
an
d
p
r
o
d
u
ce
s
t
h
r
ee
o
u
tp
u
t
v
o
ltag
e(
v
a’
(
t)
;
v
b
’
(
t)
;
v
c
’
(
t)
)
,
w
h
ic
h
is
t
h
e
i
n
p
u
t
v
o
lta
g
e
o
f
t
h
e
in
v
er
ter
,
w
h
er
ea
s
th
e
th
r
ee
p
h
ase
v
o
lta
g
e
s
(
v
a(
t)
; v
b
(
t)
; v
c(
t)
)
d
esig
n
ate
t
h
e
in
p
u
t te
r
m
in
al
o
f
th
e
co
n
v
e
r
ter
Fig
u
r
e
5
.
C
ir
cu
it c
o
n
f
i
g
u
r
at
io
n
o
f
t
w
o
-
lev
el
b
ac
k
-
to
-
b
ac
k
P
W
M
co
n
v
er
ter
s
.
T
h
e
P
W
M
tech
n
iq
u
e
is
o
b
tain
ed
b
y
co
m
p
ar
is
o
n
o
f
a
t
r
ian
g
u
lar
ca
r
r
ier
w
a
v
e
f
o
r
m
w
it
h
th
e
r
ef
er
e
n
ce
s
in
u
s
o
id
al
w
a
v
e
f
o
r
m
at
t
h
e
f
u
n
d
a
m
e
n
tal
f
r
eq
u
e
n
c
y
o
f
t
h
e
o
u
tp
u
t v
o
lta
g
e.
T
h
en
,
t
h
e
s
w
itc
h
i
n
g
p
u
ls
e
s
(
S
1
’
; S
4
’
)
f
o
r
p
h
ase
A
ar
e
illu
s
tr
ated
in
T
ab
le
1
T
ab
le
1
.
Sw
itch
in
g
s
tate
s
o
f
T
w
o
-
L
ev
el
O
n
e
-
P
h
ase
I
n
v
er
ter
S
w
i
t
c
h
i
n
g
st
a
t
e
s
O
u
t
p
u
t
v
o
l
t
a
g
e
(
v
ao
)
S
1
’
S
4
’
1
0
Vd
c
/
2
0
1
-
Vd
c
/
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
4
,
No
.
2
,
A
p
r
il
2
0
1
5
:
13
–
22
18
4
.
2
.
I
nv
er
t
er
M
o
del
T
h
e
o
u
tp
u
t
v
o
ltag
e
s
(
v
ab
’
(
t
)
,
v
bc
’
(
t)
,
v
ca
’
(
t
)
)
ar
e
m
ad
e
u
p
b
y
u
s
i
n
g
s
w
i
tch
in
g
f
u
n
ct
io
n
s
.
W
h
er
e
ca
n
b
e
f
o
r
m
u
lated
as f
o
llo
w
i
n
g
s
:
{
(
)
(
)
(
)
(
)
(
)
(
)
(
1
5
)
W
h
er
e
Sa’
(
t)
,
Sb
’
(
t)
,
an
d
Sc
’
(
t)
ar
e
s
w
itch
in
g
f
u
n
ctio
n
s
f
o
r
ea
ch
le
g
o
f
a
t
w
o
-
le
v
el
DC
/AC
i
n
v
er
ter
.
T
h
e
f
u
n
ctio
n
m
o
d
el
f
o
r
a
DC
/
AC
i
n
v
er
ter
ca
n
b
e
ex
p
r
es
s
ed
as:
{
(
)
(
)
(
)
(
)
(
)
(
)
(
1
6
)
4
.
3
.
T
hree
L
ev
el
I
nv
er
t
er
T
h
e
cir
cu
it
co
n
f
i
g
u
r
atio
n
o
f
t
h
r
ee
-
le
v
el
b
ac
k
-
to
b
ac
k
P
W
M
co
n
v
er
ter
s
co
n
s
i
s
ts
o
f
t
w
o
n
e
u
tr
al
-
p
o
i
n
t
cla
m
p
ed
co
n
v
er
ter
s
,
li
n
k
ed
th
r
o
u
g
h
D
C
ca
p
ac
ito
r
s
,
w
h
ic
h
is
s
h
o
w
n
i
n
Fig
u
r
e5
.
E
ac
h
i
n
v
er
ter
u
s
e
s
t
w
el
v
e
s
w
itc
h
es
a
n
d
s
ix
ad
d
itio
n
al
d
io
d
es.
Fig
u
r
e
5
.
C
ir
cu
it c
o
n
f
i
g
u
r
at
io
n
o
f
t
h
r
ee
-
le
v
el
b
ac
k
-
to
-
b
ac
k
P
W
M
co
n
v
er
ter
s
.
T
o
g
en
er
ate
th
e
s
w
i
tch
i
n
g
p
u
l
s
es
f
o
r
th
e
i
n
v
er
ter
s
,
t
w
o
ca
r
r
ier
w
av
e
f
o
r
m
s
ar
e
s
i
m
u
lta
n
eo
u
s
l
y
co
m
p
ar
ed
w
it
h
a
s
in
u
s
o
id
al
w
a
v
e
f
o
r
m
at
t
h
e
f
u
n
d
a
m
en
ta
l
f
r
eq
u
e
n
c
y
.
I
n
t
h
e
ca
s
e
o
f
p
h
ase
A
,
f
o
r
i
n
s
ta
n
ce
s
,
t
h
e
s
w
i
tch
in
g
p
u
ls
es (
Sa1
; Sa2
; Sa3
; Sa4
)
ar
e
d
escr
ib
ed
in
T
a
b
le
2
.
T
ab
le
2
.
Sw
itch
in
g
s
tate
s
o
f
T
h
r
ee
-
L
e
v
el
O
n
e
-
P
h
a
s
e
I
n
v
er
te
r
S
w
i
t
c
h
i
n
g
st
a
t
e
s
O
u
t
p
u
t
v
o
l
t
a
g
e
(
v
ao
)
S
a
1
’
S
a
2
’
S
a
3
’
S
a
4
’
S
a
’
1
1
0
0
+
+
Vd
c
/
2
0
1
1
0
0
0
0
0
1
1
-
-
Vd
c
/
2
4
.
4
.
I
nv
er
t
er
M
o
del
T
h
e
o
u
tp
u
t
v
o
lta
g
es
(
v
a
’
(
t
)
,
v
b
’
(
t
)
,
v
c
’
(
t)
)
ar
e
m
ad
e
u
p
b
y
u
s
in
g
s
w
i
tch
i
n
g
f
u
n
ctio
n
s
.
W
h
er
e
ca
n
b
e
f
o
r
m
u
lated
as f
o
llo
w
i
n
g
s
:
{
(
)
(
)
(
)
(
)
(
)
(
)
(
1
7
)
W
h
er
e
Sa’
(
t)
,
Sb
’
(
t)
,
an
d
Sc’
(
t)
ar
e
s
w
itc
h
i
n
g
f
u
n
ct
io
n
s
f
o
r
ea
ch
leg
o
f
a
th
r
ee
-
le
v
el
D
C
/
AC
in
v
er
ter
.
T
h
e
f
u
n
ctio
n
m
o
d
el
f
o
r
a
DC
/
AC
i
n
v
er
ter
ca
n
b
e
ex
p
r
es
s
ed
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
C
o
mp
a
r
is
o
n
b
etw
ee
n
Tw
o
-
Lev
el
C
o
n
ve
r
ter a
n
d
Th
r
ee
-
Leve
l NPC
C
o
n
ve
r
ter fo
r
…
(
Zer
z
o
u
r
i No
r
a
)
19
{
(
)
(
)
(
)
(
)
(
)
(
)
(
1
8
)
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
Si
m
u
latio
n
r
esu
lts
w
er
e
p
er
f
o
r
m
ed
u
s
i
n
g
s
o
f
t
w
ar
e
Ma
tla
b
/
Si
m
u
lin
k
.
T
o
v
alid
ate
th
e
co
n
tr
o
ls
p
r
o
p
o
s
ed
in
th
is
p
ap
er
,
w
e
p
r
esen
t
t
w
o
o
p
er
atin
g
p
o
in
t
s
i
n
h
y
p
o
-
o
r
h
y
p
er
-
s
y
n
c
h
r
o
n
o
u
s
f
as
h
io
n
.
Fo
r
th
ese
s
i
m
u
lat
io
n
s
,
w
e
co
n
s
id
er
th
at
th
e
w
in
d
s
y
s
te
m
is
s
tead
y
an
d
w
o
r
k
i
n
g
in
t
h
e
zo
n
e
o
f
o
p
ti
m
a
l
f
u
n
ctio
n
in
g
(
zo
n
e
2
)
,
th
at
is
to
s
a
y
th
a
t
it
p
r
o
d
u
c
es
m
a
x
i
m
u
m
p
o
w
er
v
er
s
u
s
s
p
ee
d
o
f
th
e
w
in
d
.
T
h
e
r
ef
er
e
n
c
e
v
o
ltag
e
o
f
t
h
e
D
C
lin
k
is
s
et
at
1
2
0
0
V.
W
e
h
av
e
v
ar
y
t
h
e
s
tato
r
r
ea
ctiv
e
p
o
w
er
Qs
p
la
y
in
g
o
n
its
r
ef
er
en
ce
v
alu
e.
T
h
e
p
ar
am
eter
s
o
f
th
e
D
FIG
ar
e
g
i
v
en
i
n
T
ab
le
I
I
I
.
5
.
1
.
Wind
po
w
er
s
y
s
t
e
m
o
pera
t
io
n
m
o
de
hy
po
s
y
nchro
no
u
s
.
Fo
r
th
i
s
m
o
d
e,
a
w
i
n
d
v
elo
cit
y
eq
u
a
l
to
8
m
s
-
1
is
ap
p
lied
o
n
w
in
d
tu
r
b
i
n
e
b
lad
es,
w
h
ic
h
c
o
r
r
esp
o
n
d
s
to
a
s
p
ee
d
o
f
DFI
G
in
MP
PT
co
n
tr
o
l
ap
p
r
o
x
i
m
atel
y
1
3
8
0
tr
/
m
i
n
,
a
s
h
i
f
t
3
0
%
h
y
p
o
s
y
n
ch
r
o
n
o
u
s
m
o
d
e,
a
s
s
h
o
w
n
in
F
ig
u
r
e
7
.
Fig
u
r
e
8
s
h
o
w
s
th
e
te
m
p
o
r
al
ev
o
lu
tio
n
o
f
th
e
v
ar
io
u
s
p
o
w
er
s
u
p
p
l
y
Qs,
P
s
an
d
P
r
,
Qr
.
A
t
ti
m
e
t
=
2
s
,
th
e
w
i
n
d
s
y
s
te
m
o
p
er
ates a
s
a
u
n
it
y
p
o
w
er
f
ac
to
r
an
d
r
ea
cti
v
e
p
o
w
er
Qs_
r
e
f
i
m
p
o
s
ed
ze
r
o
.
Fro
m
ti
m
e
t =
2
s
to
t
=
3
,
5
s
,
w
e
s
e
t
th
e
s
tato
r
r
ea
ctiv
e
p
o
w
er
r
e
f
er
en
ce
eq
u
al
to
-
1
MV
ar
co
r
r
esp
o
n
d
in
g
to
ch
an
g
es
in
th
e
r
ef
er
en
ce
d
ir
ec
t
cu
r
r
en
t
r
o
to
r
an
d
also
o
n
th
e
r
o
to
r
r
ea
ctiv
e
p
o
w
er
Qr
.
Fro
m
ti
m
e
t
=
3
.
5
s
w
e
s
et
th
e
s
tato
r
r
ef
er
en
ce
r
ea
ctiv
e
p
o
w
er
eq
u
a
l to
1
MV
ar
,
ag
ain
,
d
if
f
er
e
n
t r
ea
ctiv
e
p
o
w
er
s
ar
e
p
r
o
p
er
ly
r
e
g
u
la
ted
.
Fig
u
r
e
7
.
Gen
er
ato
r
s
p
ee
d
Fig
u
r
e
8
.
P
s
,
Qs,
P
r
,
Qr
,
ir
d
,
ir
q
an
d
iar
(
h
y
p
o
s
y
n
ch
r
o
n
o
u
s
)
0
0
.
5
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
0
200
400
600
800
1000
1200
1400
T
i
m
e
(
s
)
G
e
n
e
r
a
t
o
r
s
p
e
e
d
N
r
(
t
r
/
m
i
n
)
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
-3
-2
-1
0
1
2
3
T
i
m
e
(
s
)
Q
s(
M
V
A
R
)
P
s(
M
W
)
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
-
0
.
8
-
0
.
6
-
0
.
4
-
0
.
2
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
T
i
m
e
(
s
)
P
r
(
M
W
)
Q
r
(
M
V
a
r
)
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
-
2
0
0
0
-
1
5
0
0
-
1
0
0
0
-
5
0
0
0
500
1000
1500
2000
2500
3000
T
i
m
e
(
s
)
I
q
r
(
A
)
I
d
r
(
A
)
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
-
2
5
0
0
-
2
0
0
0
-
1
5
0
0
-
1
0
0
0
-
5
0
0
0
500
1000
1500
2000
2500
T
i
m
e
(
s
)
R
o
t
o
r
p
h
a
s
e
c
u
r
e
n
t
I
a
r
(
A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
4
,
No
.
2
,
A
p
r
il
2
0
1
5
:
13
–
22
20
5
.
2
.
Wind
po
w
er
s
y
s
t
e
m
o
pera
t
io
n
m
o
de
hy
per
s
y
nchro
no
u
s
Fo
r
th
is
m
o
d
e,
a
w
i
n
d
s
p
ee
d
eq
u
al
to
1
1
m
/
s
co
r
r
esp
o
n
d
s
to
th
e
n
o
m
in
al
o
p
er
atio
n
o
f
t
h
e
tu
r
b
in
e
i
s
ap
p
lied
o
n
w
i
n
d
tu
r
b
in
e
b
lad
e
s
,
w
h
ic
h
co
r
r
esp
o
n
d
s
to
a
s
p
e
ed
o
f
DFI
G
in
MP
PT
c
o
n
tr
o
l
ap
p
r
o
x
im
a
tel
y
1
9
5
0
tr
/
m
i
n
,
a
s
h
i
f
t
o
f
-
3
0
%
h
y
p
er
s
y
n
ch
r
o
n
o
u
s
m
o
d
e,
as
s
h
o
w
n
i
n
Fi
g
u
r
e
9
an
d
Fig
u
r
e
1
0
.
T
h
e
s
a
m
e
s
tato
r
r
ea
ctiv
e
p
o
w
er
v
ar
iatio
n
s
h
a
v
e
b
ee
n
ap
p
lied
to
th
is
m
o
d
e
as
th
e
p
r
ev
io
u
s
.
W
e
also
n
o
te
th
at
th
e
d
q
ax
is
r
o
to
r
cu
r
r
en
ts
ar
e
p
er
f
e
ctl
y
d
ec
o
u
p
l
ed
th
r
o
u
g
h
th
e
d
ec
o
u
p
lin
g
s
tr
ateg
y
b
y
en
s
u
r
i
n
g
n
atu
r
al
P
W
M.
W
e
also
o
b
s
er
v
e
th
e
r
o
to
r
p
h
ase
cu
r
r
en
t
f
o
llo
w
s
p
er
f
ec
tl
y
t
h
e
r
ef
er
e
n
ce
o
b
tain
ed
b
y
th
e
o
r
ien
ta
tio
n
o
f
t
h
e
s
tato
r
f
l
u
x
.
B
o
th
m
o
d
e
s
ar
e
v
alid
ated
an
d
in
d
ep
en
d
en
t c
o
n
tr
o
l o
f
d
i
f
f
er
e
n
t p
o
w
er
s
o
f
th
e
w
i
n
d
s
y
s
te
m
.
Fig
u
r
e
9
.
Gen
er
ato
r
s
p
ee
d
Fig
u
r
e
1
0
.
P
s
,
Qs,
Pr,
Qr
,
ir
d
,
i
r
q
an
d
iar
(
h
y
p
er
s
y
n
c
h
r
o
n
o
u
s
)
Fig
u
r
e
1
1
an
d
Fig
u
r
e
1
2
s
h
o
w
t
h
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
o
f
o
u
tp
u
t
p
h
a
s
e
s
tato
r
cu
r
r
en
t
o
b
tain
ed
u
s
i
n
g
Fas
t
Fo
u
r
ier
T
r
an
s
f
o
r
m
(
FF
T
)
tec
h
n
iq
u
e
f
o
r
P
W
M
f
o
r
2
-
lev
el
an
d
3
-
lev
el
i
n
v
er
ter
r
esp
ec
tiv
el
y
.
I
t
ca
n
b
e
clea
r
o
b
s
er
v
ed
th
at
all
t
h
e
lo
w
er
o
r
d
er
h
ar
m
o
n
ic
s
ar
e
r
ed
u
ce
d
f
o
r
3
-
lev
e
l
i
n
v
er
ter
(
T
HD
=
3
.
8
8
%)
w
h
e
n
co
m
p
ar
ed
to
2
-
lev
el
i
n
v
er
ter
(
T
HD
=
4
.
0
9
%).
(
a)
(
b
)
0
0
.
5
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
0
200
400
600
800
1000
1200
1400
1600
1800
2000
T
i
m
e
(
s
)
G
e
n
e
r
a
t
o
r
s
p
e
e
d
N
r
(
t
r
/
m
i
n
)
0
0
.
5
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
-
1
0
-5
0
5
10
15
T
i
m
e
(
s
)
Q
s(
M
V
A
R
)
P
s(
M
W
)
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
-1
-
0
.
5
0
0
.
5
1
T
i
m
e
(
s
)
Q
r
(
M
V
A
R
)
P
r
(
M
W
)
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
-
2
0
0
0
-
1
0
0
0
0
1000
2000
3000
4000
T
i
m
e
(
s
)
I
q
r
(
A
)
I
d
r
(
A
)
1
1
.
5
2
2
.
5
3
3
.
5
4
4
.
5
5
-
4
0
0
0
-
3
0
0
0
-
2
0
0
0
-
1
0
0
0
0
1000
2000
3000
4000
T
i
m
e
(
s
)
R
o
t
o
r
p
h
a
s
e
c
u
r
e
n
t
I
a
r
(
A
)
1
.
6
1
.
6
5
1
.
7
1
.
7
5
1
.
8
1
.
8
5
1
.
9
1
.
9
5
2
-
8
0
0
-
6
0
0
-
4
0
0
-
2
0
0
0
200
400
600
800
T
i
m
e
(
s
)
R
o
t
o
r
p
h
a
s
e
v
o
l
t
a
g
e
V
a
r
(
V
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
2
-
1
.
5
-1
-
0
.
5
0
0
.
5
1
1
.
5
x
1
0
4
T
i
m
e
(
s
)
S
t
a
t
o
r
p
h
a
s
e
c
u
r
r
e
n
t
I
a
s
(
A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
C
o
mp
a
r
is
o
n
b
etw
ee
n
Tw
o
-
Lev
el
C
o
n
ve
r
ter a
n
d
Th
r
ee
-
Leve
l NPC
C
o
n
ve
r
ter fo
r
…
(
Zer
z
o
u
r
i No
r
a
)
21
(c
)
Fig
u
r
e
1
1
. (
a)
R
o
to
r
p
h
ase
v
o
l
tag
e,
(
b
)
Stato
r
p
h
ase
cu
r
r
en
t,
(
c)
Sp
ec
tr
u
m
h
ar
m
o
n
ic
s
u
s
in
g
2
-
lev
el
(
a)
(
b
)
(
c)
Fig
u
r
e
1
2
. (
a)
R
o
to
r
p
h
ase
v
o
l
tag
e,
(
b
)
Stato
r
p
h
ase
cu
r
r
en
t,
(
c)
Sp
ec
tr
u
m
h
ar
m
o
n
ic
s
u
s
in
g
3
-
lev
el
T
ab
le
3
.
3
M
W
W
T
G
I
n
d
u
ctio
n
Ma
ch
i
n
e
P
ar
a
m
eter
s
p
a
r
a
me
t
r
e
v
a
l
u
e
R
o
t
o
r
r
e
si
st
o
r
p
e
r
p
h
a
se
2
,
9
7
m
Ω
R
o
t
o
r
r
e
si
st
o
r
p
e
r
p
h
a
se
3
,
8
2
m
Ω
I
n
d
u
c
t
a
n
c
e
o
f
t
h
e
st
a
t
o
r
w
i
n
d
i
n
g
I
n
d
u
c
t
a
n
c
e
o
f
t
h
e
r
e
t
o
r
w
i
n
d
i
n
g
M
u
t
u
a
l
I
n
d
u
c
t
a
n
c
e
N
u
mb
e
r
o
f
p
o
l
e
p
a
i
r
s
I
n
e
r
t
i
a
R
a
t
e
d
p
o
w
e
r
R
a
t
e
d
v
o
l
t
a
g
e
1
2
1
mH
5
7
,
3
mH
1
2
,
1
2
mH
2
1
1
4
k
g
.
m
2
3MW
6
9
0
V
T
ab
le
4
.
T
h
e
p
ar
am
eter
s
o
f
w
i
n
d
tu
r
b
in
e
p
a
r
a
me
t
r
e
v
a
l
u
e
N
o
mb
e
r
o
f
b
l
a
d
e
3
R
e
t
e
d
s
p
e
e
d
I
n
e
r
t
i
a
G
e
a
r
b
o
x
r
a
t
i
o
R
o
t
o
r
D
i
a
me
t
e
r
1
1
m
/
s
1
1
4
k
g
.
m
2
1
0
0
45m
1
.
6
1
.
6
5
1
.
7
1
.
7
5
1
.
8
1
.
8
5
1
.
9
1
.
9
5
2
-
8
0
0
-
6
0
0
-
4
0
0
-
2
0
0
0
200
400
600
800
T
i
m
e
(
s
)
R
o
t
o
r
p
h
a
s
e
v
o
l
t
a
g
e
V
a
r
(
V
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
2
-
1
.
5
-1
-
0
.
5
0
0
.
5
1
1
.
5
x
1
0
4
T
i
m
e
(
s
)
S
t
a
t
o
r
p
h
a
s
e
c
u
r
r
e
n
t
I
a
s
(
A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
4
,
No
.
2
,
A
p
r
il
2
0
1
5
:
13
–
22
22
6.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
p
r
esen
ts
s
i
m
u
latio
n
r
es
u
lts
o
f
Field
o
r
ien
tatio
n
m
et
h
o
d
co
n
tr
o
l
f
o
r
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
co
n
tr
o
l
o
f
a
DFI
G,
u
s
i
n
g
t
h
e
m
o
d
u
latio
n
s
tr
ateg
y
o
f
th
e
P
W
M
in
v
er
ter
f
o
r
t
w
o
a
n
d
th
r
ee
lev
el.
W
ith
r
esu
lt
s
o
b
tain
ed
f
r
o
m
s
i
m
u
la
tio
n
,
it
is
c
lear
t
h
at
f
o
r
th
e
s
a
m
e
o
p
er
atio
n
co
n
d
itio
n
,
t
h
e
DFI
G
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
co
n
tr
o
l
w
it
h
f
ield
o
r
ien
ted
co
n
tr
o
l
u
s
in
g
in
th
e
th
r
ee
lev
e
l
h
ad
b
etter
p
e
r
f
o
r
m
an
ce
t
h
a
n
th
e
P
W
M
tech
n
iq
u
e
t
w
o
le
v
el
a
n
d
th
at
is
clea
r
in
th
e
s
p
ec
tr
u
m
o
f
p
h
a
s
e
s
tato
r
cu
r
r
en
t
h
ar
m
o
n
i
cs
w
h
ich
th
e
u
s
e
o
f
th
e
th
r
ee
le
v
el,
it is
r
ed
u
ce
d
o
f
h
ar
m
o
n
ics
m
o
r
e
t
h
an
t
w
o
le
v
el
i
n
v
er
ter
.
RE
F
E
R
E
NC
E
S
[
1
]
A
.
B
a
b
a
ie
L
a
ji
m
i,
S
.
As
g
h
a
r
G
h
o
lam
ian
,
M
.
S
h
a
h
a
b
i
.
M
o
d
e
li
n
g
a
n
d
Co
n
tro
l
o
f
a
DFI
G
-
B
a
se
d
W
in
d
T
u
rb
in
e
d
u
ri
n
g
a
G
rid
V
o
lt
a
g
e
Dro
p
.
ET
A
S
R
-
En
g
in
e
e
rin
g
,
T
e
c
h
n
o
lo
g
y
&
A
p
p
li
e
d
S
c
ien
c
e
Re
se
a
rc
h
V
o
l
.
1
,
No
.
5
,
2
0
1
1
,
121
-
1
2
5
.
[
2
]
M
A
.
M
o
ss
a
.
F
ield
Orie
n
tati
o
n
C
o
n
tr
o
l
o
f
a
W
in
d
Driv
e
n
DFI
G
Co
n
n
e
c
ted
to
th
e
G
rid
.
W
S
E
A
S
T
R
A
NS
A
C
T
ION
S
o
n
P
OW
ER
S
YST
EM
S
,
Iss
u
e
4
,
V
o
l
u
m
e
7
,
Oc
to
b
e
r
2
0
1
2
.
[
3
]
A
.
Bo
u
m
a
ss
a
ta,
D.Ke
rd
o
u
n
,
N.C
h
e
rf
ia,
N.Be
n
n
e
c
ib
.
P
e
rf
o
rm
a
n
c
e
o
f
w
in
d
e
n
e
rg
y
c
o
n
v
e
rsio
n
s
y
ste
m
s
u
sin
g
a
c
y
c
lo
c
o
n
v
e
rte
r
to
c
o
n
tro
l
a
d
o
u
b
l
y
f
e
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r.
En
e
rg
y
P
ro
c
e
d
ia
4
2
(2
0
1
3
)
1
4
3
–
1
5
2
[M
e
d
it
e
rra
n
e
a
n
G
re
e
n
En
e
rg
y
F
o
ru
m
M
G
EF
1
3
]
.
[
4
]
S
a
i
S
in
d
h
u
ra
K,
G
.
S
rin
iv
a
s Ra
o
.
Co
n
tr
o
l
a
n
d
M
o
d
e
li
n
g
o
f
Do
u
b
ly
F
e
d
In
d
u
c
ti
o
n
M
a
c
h
in
e
f
o
r
W
in
d
T
u
rb
in
e
s
.
In
t.
J
o
u
r
n
a
l
o
f
En
g
in
e
e
ri
n
g
Re
se
a
rc
h
a
n
d
A
p
p
li
c
a
ti
o
n
s,
Vo
l.
3
,
Iss
u
e
6
,
N
o
v
-
De
c
2
0
1
3
,
p
p
.
5
3
2
-
5
3
8
.
[
5
]
S
rin
a
th
V
a
n
u
k
u
ru
,
S
a
tee
sh
S
u
k
h
a
v
a
si
.
Ac
ti
v
e
&
R
e
a
c
ti
v
e
P
o
w
e
r
Co
n
tr
o
l
Of
A
Do
u
b
ly
F
e
d
In
d
u
c
ti
o
n
G
e
n
e
ra
to
r
Driv
e
n
B
y
A
W
in
d
T
u
rb
in
e
.
In
t
e
rn
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
P
o
w
e
r
S
y
s
tem
Op
e
ra
ti
o
n
a
n
d
En
e
rg
y
M
a
n
a
g
e
m
e
n
t,
IS
S
N
(P
RINT
):
2
2
3
1
–
4
4
0
7
,
V
o
l
u
m
e
-
1
,
Iss
u
e
-
2
,
2
0
1
1
.
[
6
]
Zh
e
n
S
u
n
,
Ho
n
g
y
u
W
a
n
g
,
Yin
g
L
i
.
M
o
d
e
ll
in
g
a
n
d
S
im
u
la
ti
o
n
o
f
Do
u
b
ly
-
Fe
d
In
d
u
c
ti
o
n
W
in
d
Po
w
e
r
S
y
ste
m
Ba
se
d
o
n
M
a
tl
a
b
/S
imu
li
n
k
.
S
u
sta
in
a
b
le
P
o
w
e
r
G
e
n
e
ra
ti
o
n
a
n
d
s
u
p
p
ly
(S
u
p
e
rg
e
n
2
0
1
2
),
In
tr
n
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
,
8
-
9
se
p
t.
2
0
1
2
,
p
a
g
e
(s).
1
-
5.
[
7
]
H.
L
i.
,
Z.
C
h
e
n
.
O
p
ti
ma
l
P
o
we
r
Co
n
tro
l
S
tra
teg
y
o
f
M
a
x
imizi
n
g
W
in
d
E
n
e
rg
y
T
ra
c
k
in
g
a
n
d
Co
n
v
e
rs
io
n
fo
r
VS
C
F
Do
u
b
ly
Fed
In
d
u
c
ti
o
n
Ge
n
e
ra
to
r
S
y
ste
m
.
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
M
o
ti
o
n
C
o
n
t
ro
l
C
o
n
f
e
re
n
c
e
,
2
0
0
6
.
I
P
EM
C
2
0
0
6
.
CES
/IE
EE
5
th
I
n
tern
a
ti
o
n
a
l
,
V
o
l
u
m
e
3
,
P
u
b
li
c
a
ti
o
n
Ye
a
r:
2
0
0
6
,
P
a
g
e
(s):
1
-
6
,
IEE
E
CON
F
ERE
NCE
P
UBL
ICAT
ION
S
.
[
8
]
J.
T
ian
.
Rea
c
ti
v
e
P
o
we
r
Ca
p
a
b
il
it
y
o
f
th
e
W
in
d
T
u
r
b
in
e
wit
h
Do
u
b
ly
Fed
In
d
u
c
ti
o
n
Ge
n
e
ra
to
r
.
In
d
u
stria
l
El
e
c
tro
n
ics
so
c
iety
IECON
2
0
1
3
,
3
9
th
A
n
n
u
a
l
Co
n
f
e
re
n
c
e
o
f
th
e
IEE
E,
P
u
b
li
c
a
ti
o
n
Ye
a
r:
2
0
1
3
,
P
a
g
e
(s):
5
3
1
2
–
5
3
1
7
.
[
9
]
Do
n
g
k
y
o
u
n
g
Ch
w
a
,
Ky
o
-
Be
u
m
L
e
e
.
V
a
riab
le
S
tru
c
t
u
re
Co
n
tro
l
o
f
th
e
A
c
ti
v
e
a
n
d
Re
a
c
ti
v
e
P
o
w
e
rs
f
o
r
a
DFIG
in
W
in
d
T
u
rb
in
e
s.
IE
EE
T
RAN
S
A
C
T
ION
S
ON
IND
UST
R
Y
A
P
P
L
ICAT
ION
S
,
V
OL
.
4
6
,
NO
.
6
,
NO
V
EM
BER/
DECE
M
BER
2
0
1
0
.
[
1
0
]
M
o
h
a
m
m
a
d
S
leim
a
n
,
Ba
c
h
ir
Ke
d
jar,
A
b
d
e
lh
a
m
id
Ha
m
a
d
i,
Ka
m
a
l
A
l
-
Ha
d
d
a
d
,
Ha
d
i
Y.
Ka
n
a
a
n
.
M
o
d
e
li
n
g
,
Co
n
tro
l
a
n
d
S
im
u
la
t
io
n
o
f
DFIG
fo
r
M
a
x
imu
m
Po
we
r
P
o
in
t
T
ra
c
k
in
g
.
Co
n
tr
o
l
C
o
n
f
e
re
n
c
e
(A
S
CC),
2
0
1
3
9
t
h
A
sia
n
,
P
u
b
l
ica
ti
o
n
Ye
a
r:
2
0
1
3
,
P
a
g
e
(s):
1
–
6,
IEE
E
CON
F
ER
ENCE
P
U
BL
IC
AT
ION
S
.
[1
1
]
Z
e
rz
o
u
ri
No
ra
,
L
a
b
a
r
Ho
c
in
e
.
A
c
ti
v
e
a
n
d
Re
a
c
ti
v
e
P
o
we
r
Co
n
tro
l
o
f
a
Do
u
b
ly
F
e
d
In
d
u
c
ti
o
n
G
e
n
e
ra
to
r.
In
tern
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
S
y
ste
m
(IJP
E
DS).
Vo
l.
5
,
N
o
.
2
,
Oc
to
b
e
r
2
0
1
4
,
p
p
.
2
4
4
~
2
5
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.