Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
5
,
No
. 2, Oct
o
ber
2
0
1
4
,
pp
. 17
6~
18
4
I
S
SN
: 208
8-8
6
9
4
1
76
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
A Performance Comparison of
DFIG using Power Transfer
Matrix and Direct Po
wer Control Techniques
K
.
V
i
s
w
a
n
a
d
ha
S
Mu
rth
y
,
M
.
K
i
ra
nk
u
m
a
r
,
G
.
R
.
K.
Mu
rt
hy
Department o
f
Electrical and
Electr
onics Engin
e
ering, KL Univer
sity
,
Andhra
Prades
h,
India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 13, 2014
Rev
i
sed
Jun
5, 201
4
Accepte
d J
u
l
2, 2014
This paper
presents a dir
ect pow
er contro
l and
p
o
wer transfer m
a
trix model
for a doubly
-
f
e
d induction gen
e
rator (DFIG)
wind energ
y
s
y
stem (WES).
Control of DFIG wind turbine
s
y
stem is
traditionally
b
a
sed on
eith
er stator-
flux-orien
t
ed or
stator-voltage-o
riente
d vector
control. Th
e perf
ormance of
Direct Power Control (DPC) and Power tr
ansfer Matrix control f
o
r the sam
e
wind speed ar
e studied.
The
Power transfer
matrix Control
gave better
results. Th
e val
i
d
it
y
and per
f
or
m
a
nce of the pr
oposed m
odellin
g and control
approach
es
ar
e
inves
tig
at
ed u
s
ing a
stud
y
s
y
stem
consistin
g of a grid
connected DFI
G
WES. The p
e
rformance of
DFIG with Po
wer Transfer
Matrix and Dir
ect Power Control (DPC) techn
i
ques are obtain
e
d through
sim
u
lation. Th
e
tim
e dom
ain sim
u
lation
of
the stu
d
y
s
y
stem using MATLAB
Simulink is carried out.
The results obt
a
i
ned in th
e
two cas
es
are
c
o
m
p
ared.
Keyword:
D
oub
ly-
f
e
d
I
ndu
ctio
n g
e
n
e
r
a
to
r
(DF
I
G)
D
i
r
ect Pow
e
r co
n
t
ro
l (D
PC)
P
o
w
e
r
T
r
an
sf
er
Ma
tr
ix
Pu
lse
wid
t
h
mo
du
latio
n (PWM)
Wi
n
d
e
n
e
r
g
y
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
G.R.
K. M
u
rt
hy
,
Depa
rtem
ent of Electrical a
n
d
El
ect
ro
ni
cs E
n
gi
nee
r
i
n
g
KL Uni
v
er
sity
Gree
nfi
e
l
d
s,
V
a
dde
swa
r
am
, Gu
nt
u
r
Di
st
ri
ct
, A
n
dh
ra P
r
a
d
e
s
h
52
2
5
0
2
,
I
n
d
i
a
Em
a
il: d
r
g
r
k
m
u
r
t
h
y@k
l
u
n
i
v
e
rsity.in
1.
INTRODUCTION
Gene
ration of
electricity has been la
rgely dom
i
na
t
e
d
by
n
u
cl
ear, hy
d
r
o and f
o
ssi
l
-
f
u
el
ed
t
h
e
r
m
a
l
pl
ant
s
. Ge
ne
ral
l
y
t
h
i
s
t
y
pe of gene
rat
i
o
n i
s
consi
d
ere
d
as con
v
e
n
t
i
onal
p
o
w
er ge
ne
rat
i
o
n
.
The m
a
i
n
dra
w
ba
c
k
of m
o
st
co
nve
nt
i
onal
p
o
we
r
pl
ant
s
i
s
t
h
e a
d
verse i
m
pact
o
n
t
h
e e
n
vi
ro
nm
ent
.
T
h
e g
r
a
d
u
a
l
depl
et
i
o
n o
f
fossi
l
-
fuel (suc
h as
coal, ga
s)
rese
rves is als
o
a
conce
r
n
.
Th
e
so
lu
tion
to
t
h
ese p
r
ob
lem
s
l
i
e
s in
adop
tin
g n
o
n
-
con
v
e
n
t
i
onal
m
e
t
hods
suc
h
as wi
n
d
,
sol
a
r
et
c. i
n
po
wer
gene
rat
i
o
n.
W
i
n
d
i
s
r
e
ga
r
d
ed
as t
h
e
bes
t
sui
t
a
bl
e
rene
wa
ble ene
r
gy
res
o
urce
for production
of power a
nd th
e
b
e
st altern
ativ
e t
o
the
co
nv
en
tio
n
a
l
en
erg
y
resources m
a
inly because
of a
v
ailab
ility of la
rge
wi
nd turbi
n
es
[1].
For t
h
e last two
decades, research is bei
ng ca
rrie
d
out specifically on
W
i
nd E
n
ergy Syste
m
s
to
captu
re m
o
re po
we
r at fluct
u
ating
wind s
p
eeds.
With the
im
provem
ent
in the
power e
l
ectronic technology
con
s
t
a
nt
spee
d
const
a
nt
f
r
eq
uency
(C
SC
F
)
generat
o
r
s
we
re repl
ace
d by
vari
abl
e
spee
d co
nst
a
nt
fre
que
ncy
(VSC
F)
gen
e
ra
t
o
rs i
n
WE
S. T
h
e D
o
ubl
y
Fe
d
In
d
u
ct
i
on
Ge
n
e
rat
o
r
(
D
FI
G
)
i
s
cur
r
e
n
t
l
y
t
h
e choi
ce
of
ge
ne
rat
o
r
for m
u
lti-MW
wind
tu
rb
in
es .Th
e
aerod
yn
amic sys
t
e
m
m
u
st b
e
cap
ab
le
of op
erating
ov
er a wid
e
wi
nd
sp
eed
rang
e in
order to
ach
ieve o
p
tim
u
m
a
e
rod
y
n
a
m
i
c
e
fficiency by
tracking the
optim
u
m
tip-spee
d
ratio.T
here
f
o
re
, the ge
nerat
o
r
’
s
roto
r m
u
st be able to
operat
e at a variable rotatio
nal spee
d. T
h
eDFIG syste
m
,
th
er
efor
e op
erates in
b
o
t
h
sub
-
syn
c
hr
ono
us an
d
sup
e
r-
syn
c
hro
nou
s m
o
d
e
s w
ith
a ro
t
o
r
s
p
e
ed
r
a
n
g
e
ar
ound
the sync
hronous spee
d. T
h
e st
ator circ
uit is directly c
onnect
ed to the
g
rid
while the
rotor
winding is connected
via slip-rings
to a
three-pha
se
conver
ter. Forvaria
ble - s
p
ee
d system
s whe
r
e the
s
p
eed ra
nge
re
quirem
e
n
ts a
r
e
sm
al
l
,
(for e
x
a
m
pl
e ±30% o
f
sy
nch
r
o
n
o
u
s
s
p
eed
) t
h
e
DFI
G
o
ffe
rs ade
q
u
a
t
e
perf
orm
a
nc
e and i
s
s
u
f
f
i
c
i
e
nt
fo
r
t
h
e s
p
eed
ran
g
e
re
qui
re
d t
o
e
x
pl
oi
t
t
y
pi
cal
wi
nd
res
o
urces
.
The
do
u
b
l
y
fe
d i
n
d
u
ct
i
o
n
ge
nerat
o
r
(D
FI
G
)
ba
sed
wi
nd t
u
r
b
i
n
e
wi
t
h
va
ri
abl
e
s
p
eed
a
n
d
va
ri
abl
e
pi
t
c
h c
ont
rol
s
c
hem
e
i
s
t
h
e m
o
st
pop
ul
ar
wi
n
d
po
we
r
g
e
nerat
i
o
n sy
st
e
m
i
n
t
h
e
wi
n
d
p
o
we
r i
n
d
u
st
r
y
. Thi
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A Perfo
r
ma
n
c
e Co
mpa
r
ison
of D
F
IG
u
s
i
n
g
Po
wer
Tran
sfer Ma
trix
an
d Direct… (K.Vis
wa
nad
ha
S
Murth
y
)
17
7
machine can be ope
rated either in
gr
id c
o
nnecte
d
m
ode or in standalo
ne m
ode. This
syste
m
has recently
b
eco
m
e
v
e
r
y
po
pu
lar
as
g
e
n
e
r
a
to
r
f
o
r
v
a
r
i
ab
le sp
eed
w
i
nd
tu
rb
in
es. The
m
a
j
o
r
ad
v
a
n
t
ag
e of
th
e doub
ly f
e
d
i
n
d
u
ct
i
o
n
ge
ne
rat
o
r
(
D
FI
G
)
,
whi
c
h ha
s m
a
de i
t
po
pul
ar
, i
s
t
h
at
t
h
e p
o
w
er
el
ect
roni
c e
qui
pm
ent
has t
o
h
a
ndl
e
onl
y
a fract
i
o
n
(2
0-
30
%)
of t
h
e t
o
t
a
l
sy
st
em
powe
r
[
2
]
,
[3
]. Th
at m
ean
s th
e lo
sses in th
e p
o
wer electron
ic
equi
pm
ent
can be re
duce
d
i
n
com
p
ari
s
on t
o
po
wer el
ect
r
o
ni
c eq
ui
pm
ent
t
h
at
has t
o
han
d
l
e
t
h
e t
o
t
a
l
sy
st
em
po
we
r as
f
o
r a
di
rect
-
d
ri
ve
n
sy
nch
r
o
n
o
u
s
g
e
nerat
o
r,
ap
art
fr
om
t
h
e cost
savi
n
g
of
u
s
i
n
g sm
al
l
e
r con
v
e
rt
ers.
Co
n
t
ro
l
o
f
th
e DFIG is m
o
re co
m
p
licated
th
an th
e con
t
ro
l
o
f
a stan
dard ind
u
c
tion
mach
in
e.
In ord
e
r
t
o
co
n
t
ro
l t
h
e
DFIG ro
tor cu
rrent is con
t
ro
lled
b
y
a
p
o
we
r
electr
on
ic conv
er
t
e
r
.
On
e co
mmo
n
w
a
y
of
co
n
t
r
o
lling
the rot
o
r c
u
rre
n
t is by
m
eans of Field oriented (vect
or
) con
t
ro
l. Direct to
rqu
e
con
t
ro
l (DTC
) of in
ductio
n
machines, provides an altern
at
i
v
e t
o
vect
o
r
c
ont
rol
[
5
]
.
B
a
sed o
n
t
h
e p
r
i
n
c
i
pl
es of
DTC
s
t
rat
e
gy
, di
rect
po
we
r
cont
rol
(D
PC
) was de
vel
o
ped
f
o
r
t
h
ree
-
p
h
as
e
p
u
l
s
e wi
dt
h
m
odul
at
i
on (P
WM
)
c
o
nve
rt
e
r
s.
Power tran
sfer
m
a
trix
is a
c
o
n
t
ro
l techn
i
qu
e o
f
DF
IG w
h
i
c
h us
es i
n
st
a
n
t
a
ne
ou
s real
and r
eact
i
v
e
po
we
r i
n
st
ead
of
dq
com
p
o
n
e
nt
s of c
u
r
r
ent
s
i
n
a vect
or c
ont
rol
schem
e
. The m
a
in features
of the propos
ed
m
o
d
e
l co
m
p
ared
to conv
en
ti
o
n
a
l m
o
d
e
ls i
n
th
e
dq
fram
e
of
refe
re
nce a
r
e [
6
]
.
a) Robustne
ss
:
The wa
vef
o
rm
s of powe
r
com
ponent
s
are i
nde
pe
nde
nt
of a refe
re
nce fram
e
;
therefore, t
h
is
approach is
inherently
robust against unacco
unte
d
dynam
i
c
s
suc
h
as
PL
L.
b
)
Sim
p
lici
t
y o
f
realizatio
n
:
Th
e po
wer
co
mp
on
en
ts (state v
a
riab
les o
f
a feed
b
a
ck
con
t
rol
lo
op
)
can
b
e
d
i
rectly ob
t
a
in
ed
fro
m
p
h
ase vo
ltag
e
/curren
t
qu
an
tities, wh
ich sim
p
lif
y th
e Im
p
l
e
m
en
tatio
n of th
e
co
n
t
ro
l
syste
m
.
Fi
gu
re 1.
St
r
u
c
t
ure of
D
F
I
G
wi
n
d
po
we
r ge
nerat
i
n
g
sy
st
e
m
2
.
WIND
T
U
RBINE MODEL
The wi
nd turbine characte
r
istics
m
u
st be a
n
al
y
zed f
o
r ge
t
t
i
ng opt
i
m
u
m
po
wer cu
r
v
e (P
opt
). T
h
e
po
we
r out
put
o
f
W
i
n
d
t
u
rbi
n
e i
s
gi
ve
n by
[
4
]
:
P
0
= C
p
*P
V
= 0.5
S
w
V
3
C
p
(1
)
Whe
r
e ‘
’
is th
e air d
e
n
s
ity; S
w
is wind turbine blade s
w
e
p
t area in
the wi
nd
, V is
win
d
spee
d. C
p
re
presents
the power conversi
on efficiency of t
h
e
wind
turb
in
e. It is
a fu
n
c
tion
o
f
(Tip
-sp
e
ed
Ratio
).
=
ᴨ
=
Whe
r
e ‘R’ is the blade
radi
us;
is
th
e an
gu
lar v
e
l
o
city o
f
th
e ro
tating
b
l
ad
es; N is the ro
tatio
n
a
l speed
in
rev
o
l
u
t
i
o
ns
per
seco
nd
, an
d
V
∞
is th
ewind
sp
eed
withou
t th
e in
terrup
tion
of ro
tor. C
p
can be
calcula
ted by
usi
n
g t
h
e f
o
rm
ul
a:
C
p
=0
.571
6*
(11
6*-
0
.
4
2
1
λ
1
1
0.08
0
.
035
1
Max
i
m
u
m
p
o
w
er fro
m
th
e win
d
turb
i
n
e is:
P
ma
x
=K
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
76 –
18
4
17
8
Whe
r
e
0
.
5
S
w
*C
p
3. DI
RECT P
O
WER
C
O
N
T
ROL
O
F
DF
IG
Fi
gu
re
2.
Eq
ui
val
e
nt
ci
rc
ui
t
o
f
D
F
I
G
i
n
t
h
e
sy
nch
r
o
n
o
u
s
d-
q refe
rence
f
r
a
m
e
Fi
gu
re
3.
St
at
o
r
a
n
d
r
o
t
o
r fl
ux
vect
o
r
s i
n
syn
c
hr
ono
us d
-
q
f
r
a
m
e
The e
qui
val
e
nt
ci
rcui
t
of a
D
F
IG i
n
t
h
e sy
n
c
hr
o
n
o
u
s
d
–
q
fra
m
e
, ro
tatin
g
at th
e sp
eed
of
ω
1
, i
s
sh
ow
n
in
Figu
re 2
.
Th
e
d
-a
xi
so
f t
h
e sy
nch
r
o
n
o
u
s
fram
e
i
s
fi
xed t
o
t
h
e st
at
or
fl
u
x
, as s
h
ow
n i
n
Fi
gu
re
3.
W
i
t
h
refe
rence
t
o
Fi
gu
re
2,
t
h
e st
at
or
v
o
l
t
a
ge
vect
or
i
n
t
h
e sy
nc
h
r
o
n
ous
d
–
q
re
fe
rence
f
r
am
e i
s
gi
ve
n as:
V
s
s
= R
s
I
s
s
+ (d
Ψ
s
s
/d
t) +
j
Ψ
s
s
(
5
)
Un
de
r bal
a
nce
d
ac vol
t
a
ge sup
p
l
y
, t
h
e am
pl
i
t
ude an
d rot
a
t
i
ng spee
d o
f
t
h
e st
at
or fl
ux
are co
nst
a
nt
.
Th
er
efo
r
e, in
t
h
e sy
n
c
hr
ono
us
d
–
q
fram
e, th
e stato
r
flux
m
a
in
tain
s a con
s
tan
t
v
a
lue [5
].
Thu
s
;
Ψ
s
s
=
Ψ
sd
(d
Ψ
s
s
/dt) =
0
(6)
C
onsi
d
eri
n
g
E
quat
i
o
n
(
5
) a
n
d
negl
ect
i
n
g t
h
e v
o
l
t
a
ge
dr
o
p
acro
ss t
h
e
st
a
t
orre
si
st
ance,
Eq
uat
i
o
n
(
6
)
can
b
e
sim
p
lified
as:
V
s
s
=
j
Ψ
s
s
=
j
Ψ
sd
(
7
)
The st
at
o
r
c
u
r
r
e
nt
i
n
t
h
e sy
nc
hr
o
n
o
u
s
d-
q
f
r
a
m
e
i
s
gi
ve
n as
:
r
s
s
r
m
s
s
s
m
r
s
s
r
m
s
s
r
s
s
L
L
L
L
L
L
L
L
L
I
2
(
8
)
Thu
s
th
e stato
r
activ
e an
d reactiv
e
powe
r i
n
puts
can be
calculated as:
rd
m
sd
r
sd
rq
sd
s
s
r
s
rq
rd
m
s
sd
sd
s
r
s
s
r
m
s
s
s
sd
s
s
L
L
j
k
jQ
P
L
L
j
L
L
j
jQ
P
L
L
L
L
j
jQ
P
1
1
1
2
/
3
2
/
3
(
9
)
Sp
littin
g
Equ
a
tio
n
(9
) i
n
to
real an
d im
ag
in
ary p
a
rts yield
s
:
sd
m
r
rd
sd
s
rq
sd
s
L
L
k
Q
k
P
1
1
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A Perfo
r
ma
n
c
e Co
mpa
r
ison
of D
F
IG
u
s
i
n
g
Po
wer
Tran
sfer Ma
trix
an
d Direct… (K.Vis
wa
nad
ha
S
Murth
y
)
17
9
As the
stator flux is c
o
nstant
, accordi
n
g to
Eq
uation (10), the active a
n
d reacti
v
e power c
h
a
nge
s
ove
r a
co
nst
a
nt
pe
ri
o
d
are
gi
v
e
n
by
:
rd
sd
s
rq
sd
s
K
Q
K
P
1
1
(
1
1
)
Equation
(10)
indicates that t
h
e stat
or reacti
v
e a
nd active
powe
r cha
n
ges
are
determ
ined by t
h
e c
h
anges of
t
h
e r
o
t
o
r
fl
u
x
c
o
m
pone
nt
s
on
t
h
e d
-
q a
x
i
s
, i
.
e
.
,
∆
Ψ
rd
and
,
∆
Ψrq,
resp
ectiv
ely.
4. A
C
TIVE A
N
D
RE
ACTI
V
E
PO
WER
CO
NTR
O
L
The active a
n
d reactive
power c
o
nt
rol ca
lculates the re
qui
red
rot
o
r
voltage that wil
l
reduce the
act
i
v
e an
d
reac
t
i
v
e p
o
we
r e
r
r
o
rs
t
o
ze
r
o
du
r
i
ng a
co
nst
a
nt
sam
p
l
i
ng t
i
m
e
peri
od
o
f
Ts
.
A P
W
M
m
odu
l
a
t
o
r i
s
t
h
en
use
d
t
o
ge
nerat
e
t
h
e a
ppl
i
e
d r
o
t
o
r
vol
t
a
ge
fo
r t
h
e
t
i
m
e
peri
od
o
f
Ts
.
W
i
t
h
in
th
e time p
e
rio
d
of Ts, th
e ro
t
o
r
v
o
ltag
e
requ
ired
to
eli
m
in
at
e th
e p
o
w
er erro
rs in
d-q
refe
rence
frame are calc
u
lated as
[7]-[9]:
rd
s
sd
s
s
rq
rq
s
sd
s
s
rd
k
P
T
V
k
Q
T
V
1
1
1
1
(
1
2
)
Ho
we
ver
,
i
t
s
a
ccuracy
c
o
ul
d
be af
f
ected by
the va
riation of Lm
(Mutua
l i
n
ductance
). An
altern
ativ
e meth
od
base
d on
Eq
uat
i
on (
1
1
)
gi
ves:
sd
s
rq
sd
m
r
sd
s
rd
k
P
L
L
k
Q
1
1
(
1
3
)
From
t
h
e
E
qua
t
i
on (1
2)
an
d (
1
3
)
we get
:
sd
m
r
sd
s
s
sd
s
s
sd
s
s
sd
s
s
L
L
k
Q
k
P
T
k
P
k
Q
T
1
1
rq
1
1
rd
1
V
1
V
(
1
4
)
Th
e first term
s
o
n
th
e ri
g
h
t
han
d
si
d
e
redu
ce p
o
wer erro
rs wh
ile th
e seco
nd
term
s co
mp
ensate the
rot
o
r
slip that c
a
uses t
h
e
diffe
r
e
nt r
o
ta
ting s
p
eeds
of the
stator and
rot
o
r flux.
Fi
gu
re
4.
Sc
he
m
a
t
i
c
di
agram
of
t
h
e
DPC
f
o
r
a D
F
I
G
sy
st
e
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
76 –
18
4
18
0
5. PRI
N
CIPL
ES
OF PO
WER TRANSFERMATRI
X
The sc
hem
a
t
i
c
di
ag
ram
of a
DFI
G
wi
n
d
t
u
r
b
i
n
e
ge
nerat
o
r
i
s
re
prese
n
t
e
d
i
n
Fi
gu
re
1.
T
h
e
po
we
r
Con
v
erte
r incl
ude
s Rot
o
r
-
sid
e
-co
n
v
erter
(R
SC) to
c
ontr
o
l
spee
d
o
f
the
gene
rato
r a
n
d
Gri
d
-si
d
e c
o
n
v
e
rter
(GSC
) to
inj
e
ct reactiv
e p
o
wer to
th
e system
. Th
e in
st
antaneous
real and reactive
po
w
e
r com
pon
ent
s
of t
h
e
gri
d
si
de
co
n
v
e
r
t
e
r,
p
g
(t
)an
d
q
g
(t)in t
h
e sy
nc
h
r
o
n
ous
d
-
q
f
r
a
m
e of
refe
ren
c
e are
[6]
:
gq
gd
sd
sq
sq
sd
g
g
i
i
v
v
v
v
t
q
t
p
2
3
)
(
)
(
(
1
5
)
6.
MO
DEL O
F
DF
IG
USI
N
G IN
STA
N
T
ANEO
U
S
PO
WER
CO
MP
ONENT
S
The c
h
a
nge
in
real power a
nd reactive
p
o
we
r ca
n
be e
x
p
r
es
sed as
[
1
2]
-[
14
]
:
rd
sd
sq
s
s
sl
s
rd
sq
sd
s
sl
s
s
u
g
g
q
g
p
dt
dq
u
g
g
q
p
g
dt
dp
5
4
1
5
4
1
(
1
6
)
Whe
r
e,
r
s
sd
m
r
s
s
s
r
s
rq
rd
rq
s
s
rq
rd
rd
L
L
v
L
g
L
L
r
L
L
r
g
v
g
v
g
u
L
v
v
g
v
g
u
'
2
'
1
2
3
'
2
3
2
2
3
;
2
3
r
s
sq
r
r
sd
r
r
s
sq
r
r
sd
r
r
s
sq
m
L
L
v
L
v
r
g
L
L
v
L
v
r
g
L
L
v
L
g
'
5
'
4
'
3
2
3
2
3
2
3
(
1
7
)
The electrom
e
chanical
dyna
mi
c
m
o
d
e
l o
f
th
e m
ach
in
e is:
m
e
r
T
T
J
P
dt
d
(
1
8
)
Whe
r
e
P,J
and
Tm
are th
e
num
b
e
r o
f
po
le pairs, in
ertia of
th
er
otor, and
mechanical to
rque
of t
h
e m
a
chine,
respect
i
v
el
y
.
T
h
eel
ect
ri
c
t
o
rq
ue
i
s
gi
ve
n by
[1
0]
, [1
1]
:
sd
sq
sq
sd
e
i
i
P
T
2
3
(
1
9
)
m
s
s
r
T
J
P
q
g
p
g
d
t
d
7
6
(
2
0
)
Whe
r
e,
2
2
7
2
2
6
s
sq
sq
sd
sd
s
sq
sd
sd
sq
v
v
v
J
P
g
v
v
v
J
P
g
(
2
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A Perfo
r
ma
n
c
e Co
mpa
r
ison
of D
F
IG
u
s
i
n
g
Po
wer
Tran
sfer Ma
trix
an
d Direct… (K.Vis
wa
nad
ha
S
Murth
y
)
18
1
Fi
gu
re
6.
Sc
he
m
a
t
i
c
di
agram
of
t
h
e st
udy
sy
st
em
of
po
we
r
t
r
ans
f
er m
a
t
r
i
x
6. RES
U
LTS AN
D CO
MP
ARI
SIO
N
The
follo
win
g
param
e
ters are
use
d
to
ve
rify
t
h
e real
power, Reactive
powe
r
an
d d
c
lin
k vo
ltag
e
s:
Para
m
e
ters
Values
Units
Rated power
(
P
)
1.
5
M
W
Rated voltage(
V
)
0.
575
KV
Rated fr
equency
(
F)
60
Hz
Rated wind speed(
V
w
) 12
m
/
s
Stator resistance
(R
s
)
1.
4
m
Ω
Rotor resistance(R
r
)
0.
99
m
Ω
Stator leakage ind
u
ctance(L
S
) 89.
98
H
Rotor leakage inductance(L
R
) 82.
08
H
M
a
gnetizationindu
ctance(
L
m
) 1.
526
m
H
Stator
/r
otor
tur
n
s ratio
1
-
Poles 6
-
Tu
rb
in
e ro
to
r d
i
a
m
eter
7
0
M
L
u
m
p
ed iner
tia constant
5.
05
S
Figure 7.
Tra
p
ezoidal pattern
for wind
s
p
ee
d
Fi
gu
re
8(a
)
.
R
eal
po
we
r f
r
o
m
po
we
r t
r
a
n
sfe
r
m
a
t
r
i
x
co
nt
r
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
76 –
18
4
18
2
Fi
gu
re
8(
b
)
. R
e
act
i
v
e p
o
we
r
fr
om
powe
r
t
r
a
n
sfer
m
a
t
r
i
x
con
t
rol
Fi
gu
re
9(a
)
.
R
eal
po
we
r f
r
o
m
DPC
Figu
re
9(
b
)
. Re
active p
o
we
r
fr
om
DPC
Figu
re
1
0
(a
).
Vdc
f
r
om
Po
w
e
r tra
n
sfe
r
m
a
trix
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A Perfo
r
ma
n
c
e Co
mpa
r
ison
of D
F
IG
u
s
i
n
g
Po
wer
Tran
sfer Ma
trix
an
d Direct… (K.Vis
wa
nad
ha
S
Murth
y
)
18
3
Fig
u
r
e
10
(b
).
V
d
c
fr
o
m
D
P
C
The res
u
l
t
s
are
obt
ai
ne
d at
a wi
n
d
spee
d o
f
12 m
/
sec. The t
r
apez
oi
dal
wa
ve f
o
rm
show
n
i
n
Fi
gu
re 7
sh
ows th
e p
a
tt
ern of
step
ch
an
g
e
in th
e reactiv
e refere
nce whi
c
h i
s
appl
i
e
d t
o
bot
h t
h
e cont
rol
t
echni
q
u
e
s.Th
e
trapez
oidal pat
t
ern wass
elected to
exam
i
n
e t
h
e sy
st
em
behavi
or f
o
l
l
o
wi
ng
vari
at
i
o
n i
n
t
h
e wi
n
d
spee
d wi
t
h
b
o
t
h
n
e
g
a
tiv
e an
d
p
o
sitiv
e slo
p
e
s. Th
e
selected
wind
sp
eed
p
a
ttern sp
ans an
inp
u
t
m
ech
an
ical wind
po
we
rf
rom
0.
7
t
o
1
p.
u.
(
7
0
t
o
1
0
0
%
of t
h
e t
u
r
b
i
n
e
-
ge
ne
rat
o
r
rat
e
d
p
o
we
r)
.
Fi
gu
res 8
(
a) a
nd
8(
b) s
h
o
w
t
h
e R
eal
and R
eact
i
v
e po
we
r t
r
acki
n
g o
f
DFI
G
agai
nst
di
st
ur
ba
nces
prese
n
t in the give
n wind speed patte
rn. Because of coupling
of all powe
rs interli
nke
d to each ot
he
r, the
co
up
ling
effect
is ob
tain
ed
at t
=
0
.
3
sec.
Fi
gu
re
9(a
)
s
h
ows
t
h
e R
eal
po
we
r t
r
ac
ki
n
g
of
DF
I
G
a
g
ai
nst
di
st
ur
bance
s
i
n
t
h
e
gi
v
e
n
wi
n
d
s
p
ee
d
pat
t
e
rn
. He
re t
h
e di
p i
n
t
h
e
wave
fo
rm
shows t
h
e st
art
of
real
p
o
we
r
gene
rat
i
o
n at
t
=
0.
2 sec. Fi
gu
re 9
(
b
)
indicates the
re
active powe
r
ab
sorp
tio
n fo
r 0.
4
sec.
Fig
u
r
e
s
10
(
a
)
an
d 10
(b)
sh
ow
th
e d
c
lin
k
v
o
ltag
e
s
o
f
P
o
w
e
r
tr
a
n
sf
er
ma
tr
ix
co
n
t
ro
l an
d DP
C.
Th
e
ch
ang
e
in
wind
sp
eed
lead
s t
o
th
e fluctu
ation
s
of th
e d
c
link
vo
ltag
e
.
Du
e to
th
e co
up
ling
of all p
o
wers v
dc
of
po
we
r t
r
a
n
s
f
er
m
a
t
r
i
x
have
s
o
m
e
vari
at
i
ons
.
Whe
r
e as
in
D
P
C t
h
er
e is
no
cou
p
ling
of
t
h
e
po
w
e
r
s
and th
e
d
c
l
i
nk vol
t
a
g
e
i
s
con
s
t
a
nt
.
C
h
a
nge
i
n
wi
n
d
sp
eed doe
s not
a
f
fect
dc
l
i
n
k
v
o
l
t
age
7. CO
N
C
L
U
S
I
ON
Upon
ex
am
in
i
n
g th
e
resu
lts o
f
bo
th
Power tran
sfe
r
m
a
t
r
i
x
an
d
DPC
t
echni
ques
f
o
r t
h
e sam
e
di
st
ur
ba
nces t
h
e R
eal
po
we
r
gene
rat
i
o
n i
s
b
e
t
t
e
r i
n
p
o
w
er
tran
sfer m
a
trix
con
t
ro
l
t
h
an
with DPC. Als
o
the
gene
rat
i
o
n o
f
po
we
r st
art
s
i
n
DPC
wi
t
h
a d
e
l
a
y
of 0.
2 sec
.
Hence
p
o
we
r
t
r
ansfe
r
m
a
t
r
ix m
e
t
hod i
s
gi
vi
n
g
b
e
tter resu
lts t
h
an th
e
DPC
meth
od
.
REFERE
NC
ES
[1]
Wind techno
log
y
2011024/29. G
l
obal wind
ener
g
y
council (onlin
e). Availab
l
e
at
www.
gwec.
net
[2]
LH Hansen, L Helle, F Balaabjerg, E
Ritchie, S
munk-ni
elsen, H binder.
Conseptual Survey of Generators An
d
Powe
r Ele
c
tronic
s
For Wind Turbine
s
.
R
i
so natio
nal
laborator
y
.
[3]
L Morel, H God
froid.
Df
im Con
verter Opt
i
misat
i
on And
Fi
eld O
r
iented
Control
Without
Positio
ning Sensor
. I
E
E
proc.elctr.power
appl. 1998; 145(
4): 360-368.
[4]
SN Bhadra, D Kast
ha, S Ban
a
rjee.
W
i
nd Electrical
Systems
.
Oxford Unive
r
sity
pre
ss
[5]
Dawei Zhi,
Lie
Xu.
Direct
Pow
e
r Control of D
F
IG with Const
ant Swtch
i
ng Fr
equency and Im
proved Transient
Performance”IEEE Transacti
ons
on En
ergy Con
v
ersion
. 2007; 22
(1).
[6]
Es
m
aeil Re
zae
i,
Ahm
a
dreza T
a
bes
h
, M
oham
m
a
d Ebrahim
i
. D
ynam
i
c M
odel an
d Control of DF
IG W
i
nd Energ
y
S
y
ste
m
s Ba
se
d on Powe
r Tra
n
sfer Ma
trix.
I
E
EE T
r
ansactions on Power Delivery
. 2
012; 27(3).
[7]
P Kra
u
se
,
O Was
y
n
c
z
u
k,
S Sudhoff,
IPE
Socie
t
y
.
Ana
l
ysis of Electric Ma
chiner
y and Drive Sys
t
ems
.
Pi
sc
at
a
w
ay
,
NJ: IEEE. 2002
.
[8]
Abdelmalek Bo
ulahia.
Ment
ouri university
of Constantine,
Alg
e
ria;
Khalil
NABTI; Hocine
BENALLA,
Algeria
Direct Power C
ontrol for
Threelevel
NPC Based
PWM AC/DC/
AC Converter
in
Doubly
Fed
Ind
u
ction Gen
e
rator
s
Based Wind
Tur
b
ine In
tern
ation
a
l Journal of
Electrical and
Comp
uter Engineering
(IJECE).
2012; 2(3):
425-436
.
[9]
NRN Idris,
AHM Yatim.
Direct Torque Control of Indu
ction
Machin
es with
Constant Switch
ing Frequen
c
y
and
Reduced Torque Ripp
le
.
IEEE Trans. I
nd. Electron.
, 2004; 51(4)
:
758–767.
[10]
J Kang,
S Sul. New Direct To
r
q
u
e
Control of Ind
u
ction Motor
for
Mini
mum Torque Ripple
and C
onstant Switch
i
n
g
Frequency
.
IEEE Trans. Ind. Ap
pl.
, 1999; 35(5):
1076–1082.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
76 –
18
4
18
4
[11]
T Noguchi, H Tomiki, S Kondo, I Takah
a
shi.
Direct Po
wer C
ontrol Of Pwm
Converter With
out Power-Source
Voltage Sensors.
IEEE Trans.Ind
. App
l
.
, 1998
; 34
(3): 473–479.
[12]
G Escobar, AM
Stankovi
c, JM C
a
rrasco
,
E Galvan, R Ortega. Analy
s
is
and Design Of Direct Power Control (Dpc)
For A Three Ph
ase S
y
nchronou
srectif
ier Via O
u
tput Regul
atio
n Subspaces.
IEEE T
r
ans. Power Electron.
, 200
3;
18(3): 823–830.
[13]
M Ma
linowski,
MP Ka
z
m
ie
rkowski,
S Ha
nse
n
,
F Bl
aabjerg,
GD Marques.
VIRT
UAL-FLUX-
BASED DIREC
T
POWER CONT
ROL OF THREE-
PHASEPWM RECTIFIERS.
I
EEE Trans. Ind.
Appl.
, 2001
; 37(
4): 1019–1027.
[14]
KP Gokhale, D
W
Karra
ker, SJ
Heikkila.
Contr
o
ller for A
Wou
ndrotor Slip Rin
g
Induction Ma
chine.
U
.
S.
Pa
te
nt 6
448 735 B1. 200
2.
[15]
L Xu,
P Cartwright.
Direct
ac
ti
ve and re
ac
tive
power
control o
f
DFIGfor wind
energ
y
gen
e
ration.
IEEE Trans.
Ener
gy Con
ver
s
.
, 2006; 21(3): 75
0–758.
[16]
Wang Zezhong, Liu Qihui
.
Anal
y
s
is
of DF
IG W
i
nd Turbine during S
t
ea
d
y
s
t
a
t
e and Tr
ans
i
ent Opera
t
i
o
n
.
TELKOMNIKA Indonesian Journ
a
l
of Electrical
Engineering
. 20
14; 12(6): 4148-
4156.
Evaluation Warning : The document was created with Spire.PDF for Python.