Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
5, N
o
. 4
,
A
p
r
il
201
5, p
p
.
58
3
~
59
4
I
S
SN
: 208
8-8
6
9
4
5
83
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
Doubly-Fed Induction Generat
or Drive System Based on
Maximum Power Curve Searching using Fuzzy Logic
Cont
roll
er
Abdelh
ak
Did
a
*,
Djilani Benattous
**
* Department of
Electrical Eng
i
n
eering
,
B
i
skra U
n
iversity
, Biskra, 07000
, Algeria
** Departmen
t
o
f
Electr
i
cal
Engineering
,
El-Oued University
,
El
Oued 39000, Algeria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 18, 2014
Rev
i
sed
Feb 7, 20
15
Accepted
Feb 25, 2015
This paper prop
oses a novel variable speed co
ntrol algor
ithm for a grid
connected dou
bly
-
f
e
d induction gene
rator (DFIG) sy
stem. The main
objec
tive
is
to t
r
ack th
e m
a
xim
u
m
power curve char
ac
teris
t
ic
b
y
us
ing a
n
adaptive fuzzy
logic contro
ller, and
to compare it with the convention
a
l
optimal torque
control method fo
r large
in
ertia wind turbines. Th
e role of the
FLC is to
adap
t th
e tr
ansfer
fu
nction
of th
e h
a
rvested
m
echa
n
ica
l
powe
r
controller accor
d
ing to th
e operating
po
int in
variab
le wind s
p
eed.
Th
e
control s
y
s
t
em has two sub-sy
s
t
ems for the rotor side and th
e grid sid
e
converters (RSC, GSC). Activ
e
and reactiv
e po
wer control of
the back-
t
o-
back
convert
ers
has been
ach
iev
e
d indire
ct
l
y
b
y
controlling
q-ax
is and d-
axis
current components. Th
e main
fu
nction
of
th
e RS
C contro
llers
is to track
the
m
a
xim
u
m
po
wer through contro
lling th
e electro
m
agnetic
torque of the wind
turbine
.
Th
e GSC controls
the
DC-li
nk voltage, and guar
a
ntees
unity
power
factor b
e
tween the GSC and the
grid.
Th
e propos
ed s
y
stem is developed
and
te
ste
d
in MATLAB/SimPo
w
e
r
Sy
ste
m
(SPS) e
n
vironme
n
t.
Keyword:
DFI
G
Fuzzy logic c
o
ntroller
M
a
xi
m
u
m
power
p
o
i
n
t
t
r
ac
ki
n
g
M
a
xi
m
u
m
pow
er c
u
r
v
e
W
i
nd
turb
in
e
Copyright ©
201
5 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
:
Ab
delha
k
Dida
,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Bisk
ra Un
iv
ersity,
Bisk
r
a
, 070
00
,
A
l
g
e
r
i
a.
Em
a
il: ab
d
e
lh
ak
d
i
d
a
@yah
oo
.fr
1.
INTRODUCTION
Do
u
b
l
y
-fe
d
i
n
duct
i
o
n gene
ra
t
o
rs
(
D
F
I
Gs) have bee
n
wi
dely used for la
rge scale
wind gene
ration
sy
st
em
s, and t
h
ei
r c
ont
r
o
l
an
d o
p
e
r
at
i
ons
h
a
ve bee
n
t
h
e
s
u
bject of inte
nse researc
h
during the last fe
w years.
Th
e
r
e
sp
on
se
an
d perf
or
m
a
n
ce of
D
F
I
G
based
w
i
nd
t
u
rb
in
es dur
ing
stead
y state and
tr
an
sien
t con
d
itions
u
n
d
e
r
symmet
r
ical stato
r
v
o
l
tag
e
supp
ly are n
o
w
w
e
ll und
er
sto
o
d
[
1
]-[2
].
W
i
n
d
tu
rb
in
es ar
e con
t
rolled
to
ope
rat
e
o
n
l
y
i
n
a speci
fi
ed
ra
nge
of
w
i
nd
speed
s bou
nd
ed
b
y
cu
t-
i
n
and
c
u
t-out s
p
eeds.
Beyond these l
i
m
i
ts
,
t
h
e t
u
r
b
i
n
e
sh
o
u
l
d
be st
op
pe
d
t
o
p
r
ot
ect
bot
h t
h
e
ge
nerat
o
r
an
d t
u
rbi
n
e. F
i
g.
1 sh
o
w
s t
h
e
t
y
pi
cal
po
wer
cur
v
e
of a
wind turbi
n
e
[3]-[4].
In o
r
der t
o
get
t
h
e opt
i
m
al
operat
i
n
g p
o
i
n
t
of t
h
e wi
nd t
u
rbi
n
e, i
n
cl
u
d
i
n
g a
m
a
xim
u
m
po
we
r poi
nt
track
ing
(M
PPT) algo
rith
m
i
n
th
e system
i
s
essen
tia
l [5
]. Mu
ch
h
a
s
b
e
en
written
on
th
e to
p
i
c
o
f
MPPT
alg
o
r
ith
m
s
,
n
a
mely,
t
i
p
sp
eed
r
a
tio
(TSR)
co
n
t
r
o
l [6
-7
],
o
p
tim
al
to
r
q
u
e
(
O
T)
con
t
ro
l [5
],
ro
bu
st con
t
r
o
l [6
]-
[8],
power si
gnal feedbac
k
(PSF)
c
o
ntrol [9]-[10] and
hill-clim
b sear
ching (HCS) c
ont
rol [11]-[5]. TSR
co
n
t
ro
l regu
lates th
e wind
turb
i
n
e ro
tor speed
to
m
a
in
tai
n
an
op
ti
m
a
l
TSR at wh
ich
m
a
x
i
m
u
m
p
o
w
er i
s
ex
tracted
[7
],
th
is tech
n
i
q
u
e
is li
mited
b
y
th
e d
i
ff
icu
lty to
ob
tain
th
e o
p
tim
al TSR
an
d
t
h
e wi
n
d
sp
eed
m
easurem
ent [6]-[12]. PSF c
ont
rol re
quires
the knowledge of the
wi
nd turbi
n
e’s m
a
xim
u
m
power c
u
rve
(
M
PC)
,
and
track
s th
is curve th
rou
g
h
its co
n
t
r
o
l m
ech
anis
m
s
.
A
ccord
in
g to
[
8
]-[9
],
it’
s d
i
f
f
i
cu
lt to
o
b
t
ain
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I
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. 4
,
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r
il 2
015
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3
–
59
4
58
4
with acc
uracy
the MPC i
n
practical applications
. T
h
e
HC
S
t
ech
ni
q
u
e doe
s
n
o
t
req
u
i
r
e
w
i
nd spee
d dat
a
or
t
h
e
turbine c
h
aracteristics [13].
The MPC ca
n be
used as
mechanical power
refe
re
nce
needs to
be
tracke
d
by t
h
e harveste
d
mechanical power
of the
rot
a
ting sha
f
t. The OT con
t
ro
l is d
i
stin
gu
ish
e
d b
y
its fast resp
on
se an
d
its h
i
g
h
efficiency, thus we choose the elect
rom
a
gnet
i
c
t
o
rq
ue as
out
p
u
t
of t
h
e
pr
o
pose
d
M
P
P
T
al
gori
t
h
m
,
and t
h
i
s
can im
pro
v
e t
h
e rapi
di
t
y
of t
h
e con
v
er
ge
nce spee
d. U
nde
r p
o
we
rf
ul
wi
n
d
t
u
r
b
ul
ence, a t
y
pi
cal
pr
op
ort
i
o
nal
-
in
teg
r
al (PI) co
n
t
ro
ller m
a
y
b
e
no
t th
e right ch
o
i
ce, bu
t an
in
tellig
en
t FLC can
d
o
th
e j
o
b
with
its ad
ap
tiv
e
reason
ing
capab
ility. Th
e FLC is n
o
n
lin
ear con
t
ro
ller easy to
i
m
p
l
e
m
en
t, an
d
t
h
e key b
e
h
i
n
d
its
g
ood
per
f
o
r
m
a
nce i
s
by
adju
st
i
ng t
h
e scal
i
ng fact
ors a
nd t
h
e m
e
m
b
ershi
p
fu
nct
i
on sha
p
e w
h
i
c
h are n
o
t
har
d
t
a
sk
fo
r s
o
m
e
one
w
h
o
i
s
a
n
e
xpe
rt
.
Fi
gu
re
1.
P
o
we
r c
u
r
v
e
of
a
var
i
abl
e
spee
d
wi
nd
t
u
rbi
n
e
In t
h
i
s
st
u
d
y
,
a
m
a
xim
u
m
po
wer cu
r
v
e sear
chi
n
g (M
PC
S
)
app
r
oach
base
d o
n
fuzzy
l
o
gi
c i
s
adopt
e
d
as MPPT al
gorithm
,
and c
o
m
p
ared to a
n
other MPPT
a
p
pr
oac
h
wi
t
h
g
o
o
d
per
f
o
rm
ance like the
OT
control
m
e
thod, a
n
d to achieve an int
e
lligent control
of electro
m
a
gnetic torque. S
i
m
u
lation i
nve
stigations have
bee
n
co
ndu
cted
on
a 1
.
5
M
W
DFIG to
v
e
r
i
f
y
t
h
e
resear
ch
ed
study.
2.
VECTO
R
CO
NTROL
OF
THE DF
IG
We c
h
oose
a
d-
q
represen
tatio
n
of
the DFIG, with
th
e
d
-
a
xi
s
ori
e
nt
ed a
l
on
g t
h
e st
at
o
r
-fl
u
x
vect
o
r
p
o
s
ition
.
Sin
c
e th
e stator is con
n
ected
to th
e
g
r
i
d
,
we cou
l
d
mak
e
th
e
fo
llowing
assu
m
p
ti
o
n
s
[14
]
:
a)
The stator
resistance
R
s
can be
ne
glected
(u
sually j
u
stified
in
m
ach
in
es with
a ratin
g o
v
er
1
0kW
).
b)
The stator m
a
gnetizing
curre
nt space
phasor
ms
i
i
s
co
nst
a
nt
i
n
m
a
gni
t
u
de a
n
d
p
h
ase.
c)
Fre
que
ncy
of t
h
e
po
we
r s
u
p
p
l
y
on
t
h
e
st
at
or
i
s
co
nst
a
nt
, i
.
e.
ω
s
=
co
nst
ant
Und
e
r tho
s
e assu
m
p
tio
n
s
, it i
m
p
l
ies th
at:
rq
r
rq
rd
r
ms
s
m
rd
rq
m
sq
s
sq
s
s
ms
m
s
sd
i
L
i
L
i
L
L
i
L
i
L
V
i
L
2
0
(1)
Whe
r
e
r
s
m
L
L
L
/
1
2
and
s
s
V
V
3
,
s
V
is the RMS of the stator-voltage
space phas
or in the stationa
ry
refe
rence
f
r
am
e
t
jw
s
s
s
e
V
V
3
. Th
e stator an
d ro
tor
v
o
ltage can
b
e
written
as [1
4
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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6
9
4
Do
u
b
l
y
-Fe
d
In
duct
i
o
n Ge
ner
a
t
o
r
Dri
ve Syst
em
B
a
se
d
on
Maximum P
o
w
e
r Curve… (A
bdelhak
Dida)
58
5
)
)(
(
)
(
0
2
rd
r
ms
s
m
e
s
rq
r
rq
r
rq
rq
r
e
s
rd
r
rd
r
rd
s
sd
s
sd
s
sq
sq
s
sq
sq
s
sd
sd
s
sd
i
L
i
L
L
dt
di
L
i
R
V
i
L
dt
di
L
i
R
V
V
dt
d
i
R
V
dt
d
i
R
V
(2)
Whe
r
e
ω
s
an
d
ω
e
=p
ω
m
are t
h
e sync
hronous and t
h
e ge
nerator
spee
d respectively.
We defi
ne i
n
Eq
uat
i
on (
3
) t
h
e
'
rd
V
and
'
rq
V
as th
e o
u
t
pu
ts of th
e PI cu
rren
t con
t
ro
llers. Vo
ltag
e
s
rd
V
and
rd
V
will b
e
u
s
ed
to con
t
ro
l th
e
ro
t
o
r
vo
ltag
e
s t
h
ro
ugh
the RSC.
dt
di
L
i
R
V
dt
di
L
i
R
V
rq
r
rq
r
rq
rd
r
rd
r
rd
'
'
(3)
We
rewrite the
stator acti
v
e a
n
d reactive
power
, a
n
d the el
ectrom
a
gnetic torque
equations as:
s
s
s
rd
s
m
s
s
rq
ms
s
m
em
L
V
i
L
L
V
Q
i
i
L
L
p
T
1
2
2
(4)
Fro
m
Equ
a
tio
n (4), it can
b
e
seen
t
h
at th
e electro
m
a
g
n
e
tic to
rq
ue d
e
p
e
nds on
ly on
th
e
q
-
ax
is ro
t
o
r
current. T
h
e stator reactive
p
o
we
r o
n
l
y
dep
e
nd
s on t
h
e
d-
axi
s
rot
o
r cu
rrent. The
r
efore
,
th
e indirect vector
cont
rol
of stator active a
n
d re
active powe
r
has bee
n
ac
hi
ev
ed in
the stato
r
-flu
x
refe
re
nce
fram
e
and
p
r
e
s
ented
in
Figu
re 2. PI con
t
ro
l is typ
i
cally u
s
ed
for
th
e ro
tor curren
t
s loo
p
s
and
can
satisfy th
e con
t
ro
l
requ
ire
m
en
t
un
de
r
no
rm
al
operat
i
o
n c
o
ndi
t
i
ons
.
Fi
gu
re
2.
Vect
or
co
nt
r
o
l
o
f
t
h
e DF
IG
3.
VECTO
R
CO
NTROL
OF
GSC
Th
e con
t
ro
l obj
ectiv
e
o
f
th
e
GSC is t
o
m
a
i
n
tain
con
s
tan
t
DC-link
v
o
ltage reg
a
rd
less
o
f
th
e ch
ang
i
ng
rot
o
r
p
o
we
r.
V
ect
or c
ont
rol
h
a
s bee
n
a
ppl
i
e
d t
o
e
n
a
b
le d
e
co
up
led con
t
rol o
f
t
h
e active
and reactive
powe
rs
f
l
ow
ing
b
e
t
w
een
th
e gr
id
and
th
e G
S
C
th
ro
ugh
th
e choke [
1
5
]
. Th
e
vo
ltag
e
eq
u
a
tion
s
in th
e
d
-
q
fram
e
rot
a
t
i
n
g at
gri
d
v
o
l
t
a
ge
pul
sat
i
on
are
gi
ven
as
f
o
l
l
o
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
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,
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. 4
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–
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4
58
6
gq
gd
g
s
gq
gq
g
fq
gd
gq
g
s
gd
gd
g
fd
V
i
L
dt
di
L
i
R
V
V
i
L
dt
di
L
i
R
V
(5)
The rotatin
g re
fere
nce fram
e
is
aligne
d
with
t
h
e
g
r
i
d
v
o
ltag
e
, so we ob
tain
:
g
g
gd
V
V
V
3
and
0
gq
V
(6)
The a
n
gl
e p
o
si
t
i
on
of
t
h
e
gri
d
v
o
l
t
a
ge i
s
c
o
m
put
e
d
as:
s
s
s
s
V
V
dt
1
tan
(7)
Thus
we ca
n
write the active a
n
d reac
tiv
e power equ
a
tion
s
o
f
th
e
GSC as:
gq
g
g
gd
g
g
i
V
Q
i
V
P
(8)
It can
be clearly seen t
h
at ac
tive an
d
reactiv
e
po
wers are propo
rtion
a
l t
o
i
gd
an
d
i
gq
re
spectively.
There
f
ore
we can achie
ve the decoupled c
ont
ro
l of th
e activ
e an
d
reactiv
e po
wers thro
ugh
i
gd
and
i
gq
. W
e
assum
e
the ba
ck-t
o-back converter is los
s
less and
ne
gl
ect the losses i
n
t
h
e inductor re
sistance (c
hoke),
we
al
so ass
u
m
e
t
h
at
harm
oni
cs
d
u
e t
o
t
h
e
swi
t
c
hi
n
g
ca
n
be
ne
gl
ect
ed, t
h
e
n
b
a
sed
o
n
t
h
e
DC
-l
i
n
k
m
odel
we
ha
ve:
dc
r
dc
g
dc
dc
dc
c
i
i
d
t
dV
C
i
(9)
gd
GSC
dc
g
dc
GSC
g
gd
g
dc
g
dc
g
i
m
i
V
m
V
i
V
i
V
P
2
2
(10)
Whe
r
e
m
GSC
i
s
t
h
e m
odul
at
i
o
n i
n
dex
o
f
t
h
e
GSC
.
We c
ons
i
d
er
i
r-dc
as dist
ance, a
n
d appl
y Laplace transform
to
Eq
u
a
tion
(9
) th
en we can ob
tain
th
e
V
dc
as
f
unct
i
o
n
of
i
gd
:
)
(
.
2
s
i
s
C
m
V
gd
dc
GSC
dc
(11)
Whe
r
e s
is the
Laplace
ope
rat
o
r.
A PI co
nt
r
o
l
l
e
r has bee
n
use
d
t
o
gua
ra
nt
ee cons
t
a
nt
DC
-l
i
nk v
o
l
t
a
ge an
d ge
nerat
e
refe
rence
d
-a
xi
s
current c
o
m
p
onent
gd
i
to
th
e i
n
n
e
r con
t
ro
l loo
p
.
We set
0
gq
i
because we wa
nt
the gri
d
-si
d
e
reactive
po
we
r t
o
be ze
ro
.
W
e
de
fi
ne
'
d
GSC
V
and
'
q
GSC
V
as t
h
e out
put
s
of t
h
e i
n
n
e
r PI cu
rre
nt
c
ont
rol
l
e
rs
, t
h
en
from
vol
t
a
ge
E
quat
i
on
(
5
)
,
t
h
e
re
fe
rence
co
n
v
ert
e
r
vol
t
a
ges
are:
gd
g
s
fq
fq
gd
gq
g
s
fd
fd
i
L
V
V
V
i
L
V
V
'
'
)
(
(12)
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I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Do
u
b
l
y
-Fe
d
In
duct
i
o
n Ge
ner
a
t
o
r
Dri
ve Syst
em
B
a
se
d
on
Maximum P
o
w
e
r Curve… (A
bdelhak
Dida)
58
7
The
overall c
o
ntrol structure
of th
e GSC
is p
r
esen
ted
in
Fig
u
re 3
.
Fi
gu
re
3.
Vect
or
co
nt
r
o
l
o
f
t
h
e GSC
4.
WIN
D
T
URB
INE MO
DELING A
N
D
C
O
NTROL
4.
1.
Wind Tu
r
b
ine Model
The turbi
n
e is
the prim
e
m
o
v
e
r of
WECS that enab
l
e
s
t
h
e con
v
e
r
si
o
n
o
f
ki
net
i
c
ene
r
gy
of wi
n
d
E
w
in
to
m
ech
an
ical p
o
wer
P
m
a
nd eve
n
tually int
o
electrical ene
r
gy
[16].
i
e
C
C
AV
C
t
E
P
i
p
p
w
p
w
m
5
.
12
3
5
4
.
0
116
22
.
0
)
,
(
)
,
(
2
1
(13)
Whe
r
e
V
w
is the wind
sp
eed at th
e cen
ter
of th
e ro
tor (m
/s),
ρ
is th
e air
d
e
nsity (Kg
/
m
3
),
A=
π
R
2
is t
h
e
frontal a
r
ea
of the
wind t
u
rbine
(m
2
) and
R
is the r
o
t
o
r
ra
d
i
us (m
).
C
p
is t
h
e e
fficiency c
o
efficient
whic
h i
n
t
u
r
n
de
pe
nds
u
p
o
n
t
h
e
t
u
rbine characte
r
istics (
β
- bl
ade pi
t
c
h
an
gl
e,
a
nd
λ
- TSR) t
h
at is resp
o
n
sible f
o
r th
e
l
o
sses i
n
t
h
e
en
ergy
c
o
nve
rsi
o
n
pr
ocess
,
a
n
d
λ
i
=f(
λ
,
β
)
i
s
gi
v
e
n
by
:
1
035
.
0
08
.
0
1
1
3
i
w
t
V
R
(14)
3.
2.
T
w
o-
mas
s
Dri
v
e T
r
ai
n
e
M
o
del
The p
o
w
er t
r
a
n
sm
i
ssi
on fr
o
m
t
u
rbi
n
e a
x
i
s
t
o
ge
nerat
o
r a
x
i
s
i
s
d
one
by
a com
pone
nt
cal
l
e
d dri
v
e-
t
r
ai
n. T
h
ree
di
f
f
ere
n
t
d
r
i
v
e-t
r
a
i
n m
odel
s
(o
ne
, t
w
o
,
an
d t
h
re
e-m
a
ss
m
odel
s
) us
ual
l
y
use
d
t
o
m
odel
t
h
e d
r
i
v
e-
train [17]. The
so-called two-mass
m
odel is
sim
p
le and
sufficient with re
asonable
accuracy, for the tra
n
sient
stab
ility an
aly
s
is esp
ecially
th
e in
ter
actio
n w
ith
th
e g
r
i
d
[
1
8
]-[1
9
]
, th
e tw
o
-
m
a
ss d
r
iv
e-
tr
ai
n
str
u
ct
u
r
e is
sho
w
n i
n
Fi
gu
r
e
4.
Fi
gu
re
4.
Tw
o
-
m
a
ss dri
v
e t
r
ai
n m
odel
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
. 4
,
Ap
r
il 2
015
:
58
3
–
59
4
58
8
The aerody
na
mic
torque
T
t
causes the turbine s
p
eed
ω
m
, whi
c
h gi
ve
s t
h
e dy
nam
i
c equat
i
o
ns as
fo
llows [2
0
]
:
lss
t
t
t
T
T
dt
d
J
(15)
Here, th
e low-sp
eed sh
aft torqu
e
T
lss
acts
as a brak
i
n
g to
rqu
e
, it is ob
tain
ed
b
y
Eq
u
a
tion
(16
)
:
m
t
t
t
m
t
hss
g
g
m
damp
g
m
stiff
lss
and
T
N
N
D
N
K
T
)
(
)
(
(1
6)
Th
e g
e
n
e
rator in
ertia
J
g
is driv
en
t
h
ro
ugh
t
h
e
h
i
gh
-sp
e
ed
sh
aft, th
e
h
i
gh-sp
eed
sh
aft torqu
e
T
hss
is
bra
k
e
d
by
ge
ne
rat
o
r
el
ect
rom
a
gnet
i
c
t
o
r
que
T
em
, i
t
s
dy
nam
i
c sy
st
em
i
s
desc
ri
be
d
by
:
m
em
hss
m
g
b
T
T
dt
d
J
(17)
Whe
r
e:
T
t
and
T
g
: aerod
yna
m
i
c to
rq
u
e
of tu
rb
in
e ro
tor an
d
g
e
n
e
rator electro
m
a
g
n
etic to
rq
u
e
respectively,
J
t
and
J
g
: : turb
i
n
e
ro
tor an
d g
e
n
e
rato
r m
o
m
e
n
t
o
f
in
ertia resp
ectiv
ely,
ω
t
and
ω
m
: t
u
rb
in
e ro
tor an
d g
e
n
e
rato
r m
ech
an
ical sp
eed
resp
ect
iv
ely,
5.
M
A
X
I
M
U
M POWER
CUR
V
E
SEARCHING
A
L
GOR
I
THM
The m
a
xim
u
m
po
we
r c
u
r
v
e se
archi
n
g
(M
PC
S) m
e
t
hod
i
s
o
n
e
of
n
u
m
e
rou
s
sol
u
t
i
o
n
s
f
o
r
m
a
xim
i
zi
ng
th
e o
u
t
p
u
t
p
o
wer in
wind
tu
rb
in
e system
,
it is
b
a
sed
on
th
e MPC ch
aracteristic wh
ich
d
e
p
e
nd
s o
f
t
h
e
structural cha
r
acteristics of t
h
e wi
nd t
u
rbine whic
h s
o
m
e
how
sim
ilar to
th
e OT con
t
ro
l, an
o
t
h
e
r sim
ila
rity i
s
th
e ou
tpu
t
electro
m
ag
n
e
tic torqu
e
o
f
re
fere
nce which e
n
force the ra
pi
dne
ss of
th
e
pr
opo
sed
algor
ith
m
.
A
f
ter
the estim
a
tion of MPC c
h
a
r
acteristic, and the
harves
t
e
d
m
ech
an
ical p
o
wer i
n
th
e ro
tating
sh
aft with
consideri
ng all
the electrical
and m
echanica
l
losses (
∑
lo
sses) in
th
e
wind
tu
rb
in
e. A
fu
zzy lo
g
i
c co
ntro
ller
w
ith
its ad
ap
tiv
e r
e
ason
ing
i
s
app
lied
to un
sur
e
t
h
e conver
g
en
ce
o
f
th
e p
r
op
osed
m
e
t
h
od
t
h
ro
ugh
var
i
ab
le
o
u
t
p
u
t
step
-size sign
al un
til th
e erro
r b
e
co
mes zero
.
If th
e
o
p
e
rating
p
o
i
n
t
is to
t
h
e left
of th
e p
e
ak
po
int after
ch
ang
i
ng
i
n
the wind
sp
eed
(p
o
i
n
t
A), th
e co
n
t
ro
ller m
u
st m
o
v
e
it to
th
e righ
t to
b
e
cl
o
s
er to
th
e
p
e
ak
u
n
til it
get
s
t
o
t
h
e
zer
o e
r
r
o
r
(
p
oi
nt
B
)
, a
n
d
vi
ce
v
e
rsa i
f
i
t
i
s
on
t
h
e
ot
her
si
de
as sh
o
w
n
i
n
Fi
gu
re
5.
A
d
di
t
i
onal
l
y
,
choosi
ng a
n
a
p
propriate step-size (or s
cal
i
n
g
fact
or
s) i
n
t
h
e
out
put
i
s
not
a
n
easy task
, t
h
o
ugh
larg
er step
-size
mean
s a
faster resp
on
se and
m
o
re o
s
cillatio
n
s
aroun
d th
e
p
eak po
i
n
t, and
h
e
n
c
e, less efficien
cy, a sm
aller
step-size m
a
y threat t
h
e c
o
nve
r
ge
nce
of the
s
y
ste
m
.
Fi
gu
re
5.
Wo
r
k
i
n
g m
echani
s
m
of M
P
C
S
approach
Fi
gu
re 6.
FLC
st
ruct
u
r
e
of the
m
echanical power
Fu
zzy log
i
c con
t
ro
l h
a
s t
h
e cap
a
b
ility to
con
t
ro
l no
n
lin
ear, un
certain
and ad
ap
ti
v
e
system
s, wh
ich
gi
ves
st
r
o
n
g
r
o
b
u
st
per
f
o
rm
ance fo
r para
m
e
t
e
r
vari
at
i
o
n
[
2
1]
-[
2
2
]
.
T
h
e gene
ral
st
r
u
ct
ure of
a fuzz
y
l
i
k
e-P
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Do
u
b
l
y
-Fe
d
In
duct
i
o
n Ge
ner
a
t
o
r
Dri
ve Syst
em
B
a
se
d
on
Maximum P
o
w
e
r Curve… (A
bdelhak
Dida)
58
9
cont
rol
l
e
r i
s
sh
ow
n i
n
Fi
g
u
r
e
6
whe
r
e t
h
e
i
n
put
si
gnal
s
are
t
h
e er
ro
r a
n
d
i
t
s
cha
nge
(
E
and
Δ
E)
and
t
h
e
out
pu
t
si
gnal
i
s
t
h
e c
o
m
m
a
nd cha
n
ge
(
Δ
U
).
T
h
e
fuz
z
y
M
e
m
b
ershi
p
fu
nctio
ns
(M
Fs) a
r
e
defi
ned
as f
o
llo
ws:
Z
=zero,
PS
=Po
s
itiv
e Sm
all,
PM
=Po
s
itiv
e Med
i
u
m
,
PB
=Po
s
itiv
e Big
,
NS
=Neg
ativ
e s
m
all,
NM
=
Negat
i
v
e
M
e
di
um
,
NB
= Nega
t
i
v
e B
i
g.
FLC ru
les tab
l
e co
nsists o
f
series "
if-an
d-th
en
" f
u
zzy
l
o
gi
c con
d
i
t
i
on
sent
e
n
ces. T
h
e
desi
gn
of t
h
es
e
ru
les is
b
a
sed
o
n
a qu
alitativ
e k
nowledg
e,
d
e
du
ced
fro
m
ex
ten
s
i
v
e sim
u
latio
n
tests u
s
i
n
g
a conv
en
tion
a
l PI
cont
roller
o
f
th
e sy
stem
for
di
ffe
rent
values
of
K
p
and
K
i
, an
d with d
i
fferen
t
op
eratin
g con
d
ition
s
[23
]
.
In
t
h
is stud
y, t
h
e m
easu
r
ed ro
tatio
n
a
l sp
eed and
st
ator power
will b
e
u
s
ed
as i
n
pu
ts to th
e MPPT
syste
m
, th
e erro
r in
estim
a
t
ed
m
echanical powe
r
and its change (
EP
m
a
nd
∆
EP
m
) are u
s
ed
as in
pu
ts to
th
e
FLC
,
a
n
d
t
h
e
out
put
i
s
t
h
e
chan
ge
o
n
el
e
c
t
r
om
agnet
i
c
t
o
r
q
ue
of
re
fer
e
nce
(
∆
T
em
*
).
MFs and the
surface
created
by the
fuzzy c
ont
rol
l
er are
s
h
o
w
n
i
n
Fi
g
u
re
7.
T
r
i
a
n
gul
ar
sy
m
m
e
t
r
i
cal
m
e
mbers
h
i
p
f
unct
i
ons
are
su
itab
l
e for th
e in
pu
t an
d ou
t
p
u
t
, wh
ich g
i
ve m
o
re sen
s
itivity esp
ecially a
s
v
a
riab
les appro
a
ch
t
o
zero
.
Tab
l
e
1
gi
ves
t
h
e c
o
rres
p
on
di
n
g
ru
l
e
of
t
h
i
s
Fuzz
y
-
M
P
C
S
c
o
n
t
ro
ller.
Th
e FLC is efficien
t to
track
t
h
e m
a
x
i
m
u
m
p
o
wer po
in
t, esp
ecially in
case o
f
frequ
e
n
tly ch
ang
i
ng
wind
con
d
ition
s
[24
]
. Th
e ov
erall b
l
o
c
k
d
i
agram o
f
th
e
M
PPT co
nt
r
o
l
i
s
show
n i
n
Fi
gu
re 8
.
B
y
est
i
m
a
ti
ng
all the electrical
and m
echanic
al losses in the wind
tu
rb
in
e,
th
e fo
llo
wing
relatio
ns
are ob
tain
ed
:
m
s
r
s
m
P
P
g
losses
P
P
P
*
1
.
0
)
1
(
(18)
1111
.
1
*
)
1
(
s
m
P
g
P
(1
9)
For
defi
ni
ng
t
h
e M
P
C
a
n
d a
ccor
d
i
n
g t
o
t
h
e Eq
uat
i
o
n
(1
3
)
a
n
d
(
1
4
)
,
i
f
t
h
e
rot
o
r i
s
r
u
n
n
i
n
g at
t
h
e
o
p
tim
al TSR (
λ
opt
), it will also
run
at
C
pmax
.
Th
us, t
h
e M
P
C
ex
pres
si
o
n
i
s
obt
ai
ne
d:
3
3
3
max
5
_
2
1
m
opt
m
opt
p
MPC
m
K
C
R
P
(20)
This MPC
rela
tion is
use
d
as
refe
rence
to t
h
e m
echanical powe
r l
o
op.
(a)
(b
)
(c)
(d
)
Fi
gu
re
7.
M
e
m
b
ers
h
i
p
f
u
nct
i
o
ns
of
F
u
zzy
-M
PC
S co
nt
r
o
l
l
e
r
(a,
b
) I
n
p
u
t
m
e
m
b
ership fu
nct
i
ons
o
f
EP
m
and
Δ
EP
m
resp
ect
iv
ely (c)
Ou
tput
m
e
m
b
ersh
ip fu
n
c
tion
s
of
Δ
T
em-ref
(d) Surface c
r
e
a
ted by t
h
e
fuz
z
y cont
roller
-1
-0
.5
0
0.5
1
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
EPm
D
e
gr
ee of me
mb
er
s
h
ip
NG
NM
NP
Z
E
PP
PM
PG
-1
-0.
5
0
0.5
1
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
d
EP
m
D
e
g
r
ee
of
me
mb
er
s
h
i
p
NG
NM
NP
Z
E
PP
P
M
PG
-1
-0.
5
0
0.5
1
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
dT
em
-ref
D
e
gr
e
e
of
me
mb
er
s
h
i
p
N
G
NM
NP
ZE
PP
PM
P
G
-1
-0.
5
0
0.
5
1
-1
0
1
-0.5
0
0.
5
EP
m
dE
P
m
dTem
-
r
e
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
58
3
–
59
4
59
0
Fi
gu
re 8.
B
l
oc
k di
ag
ram
of M
P
C
S
-M
PPT
cont
rol
sy
st
em
Tabl
e 1.
Rule
table of Fuzzy-MPCS controller
EP
m
(
pu)
Δ
EP
m
(
pu)
NB NM
NS
Z
PS
PM
PB
NB NB
NB
NB
NB
NM
NS
Z
NM
NB
NB
NB
NM
NS
Z
PS
NS NB
NB
NM
NS
Z
PS
PM
Z NB
NM
NS
Z
PS
PM
PB
PS NM
NS
Z
PS
PM
PB
PB
PM
NS
Z
PS
PM
PB
PB
PB
PB
Z
PS
PM
PB PB
PB PB
In
or
de
r t
o
b
e
ho
nest
,
we
hav
e
t
o
com
p
are t
h
e M
P
C
S
al
g
o
r
i
t
h
m
wi
t
h
a goo
d se
ns
orl
e
ss
M
PPT m
e
t
hod
,
th
e OT co
n
t
ro
l
seem
s su
itab
l
e with
its sup
e
rio
r
ity in te
rm
of efficiency a
n
d s
p
eed
of
r
e
sp
on
se, H
o
w
e
v
e
r,
th
e
efficiency is lower c
o
m
p
ared
to th
at
o
f
TSR
cont
rol
m
e
t
hod
, beca
use i
t
does not use t
h
e
wind s
p
eed
directly,
meaning that wind cha
n
ges
are not re
flected insta
n
tane
ously and signifi
cantly on the
refe
rence si
gnal [25].
C
onsi
d
eri
ng t
h
at
P
m
=T
hss
ω
m
i
n
t
h
e hi
gh
spee
d sha
f
t
a
nd
wi
t
h
c
onsi
d
eri
ng E
q
uat
i
on
(2
0
)
,
T
hss
can be
rearrange
d
as follows:
2
2
3
max
5
_
2
1
m
opt
m
opt
p
opt
hss
K
C
R
T
(21)
The
OT i
s
a
t
o
r
q
ue co
nt
r
o
l
base
d m
e
t
hod,
w
h
ere t
h
e a
n
a
l
y
t
i
cal
expressi
on
o
f
t
h
e
o
p
t
i
m
u
m
t
o
rq
ue
cur
v
e,
rep
r
ese
n
t
e
d
by
Eq
uat
i
on
(2
1
)
, i
s
gi
v
e
n as a re
fere
nce torque
for t
h
e controller
t
h
at is connecte
d
to the
wind
turb
in
e
[5
]. Th
e
o
v
e
rall d
i
agram
o
f
the OT con
t
ro
l is rep
r
esen
ted in
Fi
g
u
re
9
.
Acco
rd
ing
t
o
th
e
wi
nd
t
u
r
b
i
n
e
param
e
t
e
rs m
e
nt
i
oned
i
n
t
h
e
ap
pe
ndi
x, t
h
e
1.
5M
W
wind turbine c
h
aracteristics a
r
e s
h
own in Fi
gure
1
0
, th
is yield
to
K
opt
= 0.
43
6
Fi
gu
re
9.
B
l
oc
k
di
ag
ram
of O
T
co
nt
r
o
l
M
P
P
T
m
e
t
hod
Figu
re 1
0
. Po
w
e
r
c
o
ef
fici
ent c
u
rve
versus
TSR and
pi
t
c
h a
ngl
e
0
5
10
15
20
0
5
10
15
20
0
0.
1
0.
2
0.
3
0.
4
0.
5
P
i
t
c
h an
gle
[
r
ad]
T
i
p s
p
e
ed
r
a
t
i
o
E
f
f
i
ci
e
n
cy co
e
f
f
i
c
i
e
n
t
C
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Do
u
b
l
y
-Fe
d
In
duct
i
o
n Ge
ner
a
t
o
r
Dri
ve Syst
em
B
a
se
d
on
Maximum P
o
w
e
r Curve… (A
bdelhak
Dida)
59
1
6.
SIM
U
LATI
O
N
RESULTS
AN
D DIS
C
US
SION
In
vest
i
g
at
i
o
n
has be
en
per
f
o
rm
ed o
n
a 1.
5M
W
DF
IG s
y
st
em
i
n
corp
o
r
at
i
ng t
h
e p
r
o
pos
ed F
u
zzy
-
M
P
C
S
cont
r
o
l
l
er. The pa
ram
e
t
e
rs of t
h
e D
F
IG a
r
e i
n
spi
r
ed fr
om
[14]
-[
26]
. T
h
e sim
u
l
a
t
i
on o
b
ject
i
v
e
i
s
t
o
ap
p
l
y a
r
a
ndom w
i
n
d
sp
eed
p
r
o
f
ile to
em
u
l
ate n
o
r
m
al w
i
n
d
t
u
rbu
l
en
ce;
th
e pro
p
o
s
ed
MPCS str
a
tegy h
a
s to
gi
ve t
h
e o
p
t
i
m
al
el
ect
ro
m
a
gn
et
i
c
t
o
rque t
o
t
h
e sy
st
em
, and t
o
co
nt
en
d t
h
e OT co
nt
r
o
l
m
e
t
hod i
n
t
e
rm
s of
efficiency and
spee
d of res
ponse. T
h
e
w
i
nd
sp
eed
pr
of
ile is ch
o
s
en
in
or
d
e
r to cove
r the
whole va
riable
speed
ope
rat
i
n
g m
o
d
e
o
f
t
h
e
D
F
I
G
sy
st
em
whi
c
h i
s
bet
w
een
t
h
e
1.
2 a
n
d
0
.
7
[
p
u]
. T
h
e c
ont
rol
sy
st
em
i
s
per
f
o
rm
ed
in the
per-unit
(pu) syst
em
according to the rate
d c
h
ara
c
teristics
of t
h
e wind turbine
(see a
ppe
ndix), the
si
m
u
latio
n
results are d
e
no
ted
in
Figure
1
1
.
(a)
(b
)
(c)
(d
)
(e)
(
f)
Fig
u
r
e
11
.
D
yna
m
i
c r
e
sp
on
ses of
th
e fu
zzy-MPCS algo
r
ithm
in
th
e
v
a
r
i
able sp
eed
m
o
d
e
(a)
Win
d
spee
d
p
r
o
f
ile (
b
) R
o
t
a
tional s
p
eed
(
c
)
Mecha
n
ical
powe
r (d) Ou
t
put electrical
powe
r
(e)
Stator
cu
rre
nts (
f
)
Rot
o
r c
u
rre
nts
Th
e
Figu
r
e
11 show
s the
d
y
n
a
m
i
c r
e
sp
on
se of
th
e
w
i
nd
t
u
rb
in
e, th
e Figu
r
e
11
(
a
)
show
s a r
a
nd
o
m
wi
n
d
spee
d p
r
ofi
l
e
co
vere
d alm
o
st
t
h
e whol
e vari
abl
e
spee
d o
p
erat
i
n
g ra
n
g
e of
wi
n
d
spe
e
d, b
o
u
n
d
e
d
b
y
cut
-
in
and
t
h
e r
a
ted
w
i
nd
sp
eeds. Th
e
Figu
r
e
11(
b)
sh
ow
s t
h
e
ro
tatio
n
a
l sp
eed resp
on
se and
i
t
s th
eoretical op
ti
m
a
l
val
u
e, i
t
i
s
cha
ngi
ng acc
or
di
n
g
t
o
t
h
e
wi
n
d
s
p
eed
val
u
e
,
and com
p
ared
wi
th the OT
c
ont
rol,
the Fig
u
re 12
(
d
)
sho
w
s a g
o
od
and st
a
b
l
e
resp
ons
e fo
r b
o
t
h
t
echni
que
s. The
Fi
gure
11
(c) s
h
o
w
s t
h
e o
u
t
p
ut
m
echani
cal
po
w
e
r
and i
t
s
t
h
eo
ret
i
cal
opt
im
u
m
refe
rence acc
o
r
di
ng t
o
t
h
e a
v
ai
l
a
bl
e ki
net
i
c po
wer o
f
t
h
e wi
nd
, t
h
e o
u
t
p
ut
mechanical power trac
k its re
fere
nce
pr
ecise
ly thanks
of the FLC. The Fi
gu
re
11
(d
) sh
ows t
h
e to
tal electrical
out
put
po
wer
of t
h
e
DF
IG
, t
h
e act
i
v
e p
o
w
e
r
i
s
t
h
e ha
rv
est
e
d power from the availa
ble
mechanical power i
n
th
e h
i
gh
sp
eed sh
aft, it’s a little b
it lesser than
th
e m
ech
anical p
o
w
er
b
e
cau
s
e
o
f
the co
l
l
ectiv
e lo
sses
o
f
t
h
e
syste
m
. Th
e Fig
u
r
e
11(
e)
an
d th
e Figu
r
e
1
1
(f
)
sh
ow
th
e
st
a
t
or an
d t
h
e
r
o
t
o
r c
u
r
r
ent
s
res
p
ect
i
v
el
y
obt
ai
ned
by
t
h
e F
u
zzy
-M
P
C
S co
nt
r
o
l
m
e
t
h
o
d
, t
h
ey
are
cha
ngi
ng a
c
c
o
r
d
i
n
g t
o
t
h
e
out
put
p
o
we
r
m
a
gni
t
ude
, t
h
e
rot
o
r
currents
fre
que
ncy is changing accordi
ng t
o
the rotational speed, on contrary
the stator c
u
rrents
fre
que
ncy is
main
tain
ed
th
e grid
frequ
en
cy
.
0
5
10
15
7
8
9
10
11
12
Ti
m
e
[
s
]
W
i
nd s
peed [
m
/
s
]
0
5
10
15
0
0.5
1
1.5
T
i
m
e
[s
]
Rot
a
t
i
o
nal
s
p
eed [
pu]
T
h
eori
t
i
c
al
O
p
ti
m
a
l
S
peed
Meas
u
r
ed S
peed
0
5
10
15
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
T
i
m
e
[s
]
M
e
c
han
i
c
a
l
pow
er [
p
u
]
Pm
P
m
-ref
0
5
10
15
-0.
2
0
0.2
0.4
0.6
0.8
1
1.2
T
i
m
e
[s
]
O
u
t
put
el
e
c
t
r
i
c
a
l
po
wer [
pu]
Ps
+
P
r
Qs
+
Q
r
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
. 4
,
Ap
r
il 2
015
:
58
3
–
59
4
59
2
(a)
(b
)
(c)
(d
)
Fig
u
r
e
12
. D
yna
m
i
c
r
e
sp
on
se co
m
p
ar
iso
n
b
e
t
w
een OT a
n
d
MPCS control
techniques
(a) C
o
ef
ficient
of
p
o
w
e
r
(
b
)
T
S
R (c
) Electr
o
m
a
gnetic tor
q
u
e
o
f
re
fere
nce
(
d
)
Rotation
a
l s
p
eed
The
po
wer c
o
e
fficient res
p
on
se is prese
n
ted
in Fig
u
re
1
2
(a), in
term
o
f
sp
ee
d and e
fficiency, the two
m
e
thods seem
fast and e
fficie
n
t, but the Fuz
z
y-MPCS m
e
thod is a little bit superi
or. T
h
e Figure 12(b)
shows
th
e TSR ch
aracteristics, it reach
e
s t
h
e
o
p
timal v
a
lu
e
and
k
e
ep
s it in bo
th
MPPT m
e
th
o
d
s.
Tabl
e 2.
Rule
table of Fuzzy-MPCS controller
T
echnique
Pr
incipal
Co
m
p
lexity
Conver
g
ence speed
W
i
nd speed
m
e
asure
m
ent
Per
f
orm
a
nce
Med
i
an
Cp
OT
Contr
o
l
OT
character
istics
Sim
p
le Fast
No
Very
good
0.
490
M
P
CS Contr
o
l
M
P
C character
istics
Sim
p
le Fast
No
Very
good
0.
495
Tabl
e
3.
Det
a
i
l
e
d
param
e
t
e
rs of
DF
I
G
a
n
d
t
h
e wi
n
d
t
u
r
b
i
n
e
sy
st
em
[14]
-
[
2
6
]
par
a
m
e
tr
e sym
bole
value
Rated wind speed
V
w
12 m
/
s
Rated appar
e
nt power
S
out
1,
5/0.
9 M
V
A
Rated active powe
r
P
out
1,
5 M
W
Rated voltage (line to line)
V
s
575 V
Rated DC-
link voltage
V
dc
1200 V
Rated Gr
id fr
equency
f
60 Hz
Nu
m
b
er
of pole pair
s
p
3
Stator/rotor turns ratio
m
1/3
Stator resistance
R
s
0.
023 pu
Ro
to
r resistan
ce
R
r
0.
016 pu
Stator leakage ind
u
ctance
L
s
0.
18 pu
Rotor leakage inductance
L
r
0.
16 pu
M
a
gnetizing induc
tance
L
m
2.
9 pu
DC-link capacitan
ce
C
dc
0.
01 F
Choke (
r
e
sistance/
inductance)
R
g
/
L
g
0.
003 / 0.
3 pu
Filter (resistance/
c
a
pacitor)
R
f
/ C
f
0.
53
Ω
/ 1333
m
F
Networ
k
V
L
/l
L
/Z
L
25KV / 30Km
/
(
3
.45+11.
87)
Ω
T
r
ansform
e
r (
power
,
voltage)
(
w
inding1/windi
ng
2)
P
t
, V
1
/V
2
(R
1
/L
1
)
/ (R
2
/L
2
)
1.
75 KW
/
(
25/0.
575)
KV
(
0
.
025/30,
0.
02
5)
p
u
/(
0.
025/3
0
,
0.
025
)
pu
Generator lu
m
p
ed
inertia constant =
J
g
/2
H
g
0.
685 s
Turbine lu
m
p
ed inertia constant =
J
t
/2
H
t
3 s
Equivalent torsional stiffness coeffici
ent
K
s
ti
ff
1.
11 pu
E
quivalent dam
p
in
g coefficient
D
dam
p
1.
5 pu
Generator f
r
iction
coef
f
i
cient
b
0.
01 pu
Gear
box r
a
tio
N
g
91
Rotor dia
m
eter
2R
72 m
Air
density
ρ
1.
225 kg/m
3
0
5
10
15
0.4
8
0.4
9
0.
5
0.5
1
0.5
2
T
i
m
e
[s
]
C
o
e
ffi
c
i
e
n
t o
f
p
o
w
e
r
(
C
p
)
T
h
eor
i
t
i
c
a
l
Cpm
a
x
OT
C
o
n
t
r
o
l
MP
C
S
Con
t
r
o
l
0
5
10
15
8
9
10
11
12
13
T
i
m
e
[s
]
TS
R
T
h
eo
ri
ti
c
a
l
opti
m
al
T
S
R
OT C
o
n
t
r
o
l
MP
CS
Con
t
r
o
l
0
5
10
15
0
0.2
0.4
0.6
0.8
1
T
i
m
e
[s
]
E
-
M
t
o
r
q
ue of
r
e
f
e
r
enc
e [
p
u]
OT
C
o
n
t
r
o
l
MP
CS
Con
t
r
o
l
0
5
10
15
0.
7
0.
8
0.
9
1
1.
1
1.
2
1.
3
Tim
e
[
s
]
Rot
a
t
i
on
al
s
p
ee
d [
p
u]
T
h
e
o
r
i
t
i
c
a
l O
p
t
i
m
a
l S
p
e
e
d
OT C
o
n
t
rol
M
P
CS
Con
t
r
o
l
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