Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 3
,
Ju
n
e
201
6, p
p
. 1
319
~ 13
31
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.9
306
1
319
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
/
IJECE
Tip Speed Ratio Based MPPT Al
gorithm and Improved Field
Oriented Control for Extracti
ng Optimal Real Power and
Independent Reactive Power
Con
t
rol f
o
r Grid Connect
ed
Doubly Fed Induction Generator
D. V.
N
.
An
an
th
1
, G. V.
N
agesh
Ku
mar
2
1
Department of EEE,
Viswanad
ha
In
stitute
of Technolog
y
and
Manage
ment, Visakhapatn
am,53
1173, India
2
Department of EEE,
GITAM
U
n
iversity
, Visak
h
apatn
a
m, 5300
45, Andhra Prad
esh, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Ja
n
7, 2016
Rev
i
sed
May
1, 201
6
Accepted
May 16, 2016
Doubly
Fed
Ind
u
ction G
e
ner
a
to
r (DFIG) needs
to get adop
ted
to chang
e
in
wind speeds with sudden chang
e
in reacti
ve po
wer or grid terminal voltag
e
as it is requir
e
d f
o
r maintaining s
y
nchron
ism and stability
as per
modern grid
rules.
This pap
e
r proposes a
con
t
rolle
r for DFIG conver
t
ers and
optimal tip
speed ratio bas
e
d maximum p
o
wer point tracking (MPPT) f
o
r turbine to
m
a
intain
equi
lib
rium
in rotor
speed,
gen
e
rator
t
o
rque,
and st
ato
r
and ro
tor
voltag
e
s and als
o
to meet desir
e
d refe
ren
ce r
eal
power during th
e turbul
ences
like sudden ch
ange in reactiv
e
power or
voltag
e
with concurr
e
ntly
chang
i
ng
wind s
p
eed.
The
perform
ance
of
DF
IG is
com
p
ared when th
ere
is
chang
e
in
wind speed only
,
changes in r
eactive pow
er and variation in grid voltag
e
along with v
a
riation in
wind speed.
Keyword:
D
oub
ly f
e
d
indu
ctio
n g
e
n
e
r
a
to
r
Op
tim
al tip
sp
eed
ratio
M
m
ax
i
m
u
m
p
o
w
er
po
in
t
track
ing
Real and reacti
v
e
powe
r c
ontrol
G
r
i
d
sid
e
conver
t
er
W
i
nd
en
e
r
g
y
co
nv
er
s
i
on
s
y
s
t
e
m
Copyright ©
201
6 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. V.
Na
ges
h
Kum
a
r,
Depa
rtem
ent of EEE
,
GIT
A
M
Uni
v
e
r
sity
,
Vi
sak
h
a
p
at
na
m
,
530
04
5,
A
n
dh
ra
Pra
d
es
h,
I
ndi
a.
Em
a
il: d
r
gv
nk1
4@g
m
ai
l.co
m
1.
INTRODUCTION
The wind and
solar electric powe
r ge
nerat
i
o
n sy
st
em
s are
po
p
u
l
a
r
re
newable energy re
sources and
are
get
t
i
ng
si
g
n
i
f
i
cance
d
u
e
t
o
ret
r
eat
i
n
g
of
pri
m
ary
fuel
s a
n
d
beca
use
o
f
eco-
fri
e
ndl
y
na
t
u
re a
n
d i
s
a
v
a
i
l
a
bl
e
fr
om
few ki
l
o
-
w
at
t
po
we
r t
o
m
e
gawat
t
rat
i
n
g. T
h
e e
x
t
r
act
a
b
l
e
m
a
xim
u
m
po
we
r f
r
om
wi
nd
de
pen
d
s m
o
st
l
y
on t
h
e pi
t
c
h angl
e co
nt
r
o
l
of
t
h
e wi
nd t
u
r
b
i
n
e sy
st
em
and o
p
erat
i
n
g rot
o
r at
opt
i
m
al speed f
o
r DF
IG
. Th
e
m
a
xim
u
m
pow
er
poi
nt
t
r
acki
n
g
(M
P
P
T)
o
f
wi
n
d
t
u
r
b
i
n
e
g
e
nerat
o
r
sy
st
em
i
s
for
t
ech
n
o
-ec
o
nom
i
c
benefi
t
s
.
As p
e
r
literature, four
co
n
t
ro
l
techn
i
qu
es are u
s
ed
fo
r ex
tracting
m
a
x
i
m
u
m
real p
o
wer fro
m
wind
.
Th
e
st
rat
e
gi
es are
pert
ur
bat
i
on a
nd
o
b
ser
v
at
i
o
n
(P&
O
) c
ont
r
o
l
,
t
i
p
spee
d r
a
t
i
o
(TSR
) c
o
nt
r
o
l
,
o
p
t
i
m
al
t
o
r
que
cont
rol (OTC
) and Powe
r
signal
fee
dba
c
k
(PSF) control [1]–[8
] with t
h
e
i
r desc
ription i
n
[9],[10]. The
P&O
or hill-clim
b searchi
n
g (HCS
) m
e
thod
ge
nerally requi
res
details on
rotor
spee
d a
n
d va
ri
ation
of wi
nd turbine
p
o
wer for ex
tractin
g
op
ti
m
a
l
p
o
wer. Th
is meth
od
do
es
no
t o
b
lig
e on
ch
aracteristic
curve of wind turbi
n
e or
param
e
t
e
rs o
f
gene
rat
o
r
[1
1]
,
[
1
2
]
.
Ho
we
ver
,
f
o
r
l
a
r
g
e-i
n
er
t
i
a
wi
nd
t
u
rbi
n
e sy
st
em
s t
h
i
s
m
e
t
hod
g
o
es
o
u
t
o
f
step
with
rap
i
d
v
a
riation
i
n
wind
sp
eed
and
p
r
od
u
c
es
o
s
cillatio
n
s
n
e
ar
th
e
p
eak po
in
t
s
of m
a
x
i
m
u
m po
wer
locus
point. In
TSR m
e
thod,
with
variations
in
wind s
p
ee
d, the
wi
nd
turbine rotational
s
p
eed will also
varie
d
to
ach
iev
e
th
e op
ti
m
a
l TSR [13
]
,[14
]. Howev
e
r, an
acc
urate a
n
d cont
inuous wi
nd
tu
rb
in
e
sh
aft speed
and
wind spee
d measurem
ent is require
d
,
wh
ich
in
real tim
e
is v
e
ry d
i
fficu
l
t.
In
OTC
,
t
h
e
cont
r
o
l
o
f
ge
nerat
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
13
1
9
– 13
31
1
320
to
rq
u
e
is don
e
to
m
eet i
t
s o
p
timal v
a
lu
e to
get
m
a
x
i
m
u
m
v
a
lu
e of
co
eff
i
cien
t of
p
o
w
e
r
[1
5
]
,[
16
]. Th
is
meth
od
i
s
sl
owe
r
i
n
per
f
o
r
m
a
nce due
t
o
sl
ow
cal
cul
a
t
i
on
o
f
wi
n
d
s
p
eed a
n
d
ret
r
i
e
v
i
ng
dat
a
pr
oces
ses by
a
n
em
om
et
er.
The
per
f
o
r
m
a
nce of
DF
IG
wi
nd e
n
e
r
gy
c
o
n
v
ersi
on
sy
st
em
i
s
com
p
ared
w
i
t
h
PI,
A
NN a
n
d hy
bri
d
P
I
and
A
NN i
n
[
17]
.
A c
o
m
p
ari
s
on i
s
m
a
de wi
t
h
p
o
w
er t
r
a
n
sfe
r
m
a
t
r
i
x
and
Di
rect
P
o
w
e
r C
o
nt
r
o
l
(D
P
C
). T
h
e
au
tho
r
s fo
und th
at co
m
p
ar
ed
to
D
P
C
,
pow
er
t
r
an
sf
er
matr
ix
is h
a
v
i
n
g
b
e
tter
con
t
r
o
l
o
v
e
r
r
eal
p
o
w
e
r
gene
rat
i
o
n,
fas
t
er co
nt
rol
act
i
o
n
,
st
abl
e
. T
h
e
per
f
o
r
m
a
nce of
DF
IG i
s
st
u
d
i
e
d i
n
[
18]
w
i
t
h
t
h
e o
p
erat
i
on
o
f
rot
o
r
spee
d
ad
j
u
st
i
n
g t
o
s
u
b
-
s
y
nch
r
o
n
ous
a
n
d s
u
per
-
sy
nc
hr
on
o
u
s s
p
ee
d.
Al
so
i
n
depe
n
d
e
nt
c
ont
r
o
l
of
act
i
v
e
an
d reactiv
e po
wer ex
am
in
ed
in th
is
p
a
p
e
r an
d fo
und
that fu
zzy con
t
ro
ller is
b
e
tter
th
an
con
v
e
n
tion
a
l PI
cont
roller.
The fuzzy controller is havi
ng faster c
o
ntrol action a
n
d accurate pe
rform
a
nce due
to faste
r
chan
gi
n
g
di
st
u
r
ba
nces.
A
hy
bri
d
P
I
a
n
d
A
N
N
co
nt
r
o
l
l
e
r
fo
r
DFI
G
i
s
e
x
am
i
n
ed i
n
[1
9]
t
o
rapi
dl
y
c
h
an
gi
n
g
gri
d
voltage conditions. The a
u
thors
found t
h
at, active
and reactive powe
rs are
havi
ng surges a
nd also rotor
and st
at
o
r
para
m
e
t
e
rs got
di
st
ur
be
d
m
u
ch wi
t
h
PI an
d t
h
ei
r
effect
s are l
o
w wi
t
h
A
N
N
.
Ho
we
ver w
h
e
n
usi
n
g
bot
h Pi
an
d A
N
N
,
t
h
e ef
fect
s
sai
d
ab
ove
g
o
t
m
i
nim
i
zed an
d he
nce t
h
e a
u
t
h
o
r
s i
n
[1
9]
co
ncl
u
de t
h
at
hy
bri
d
i
s
b
e
tter con
t
ro
l
wh
en
grid
vo
ltag
e
con
d
ition
s
are h
i
g
h
. In
[2
0
]
, au
t
h
ors co
m
p
ared
th
e perfo
r
m
a
n
ce o
f
DFIG
d
u
r
i
ng
th
r
ee
ph
ase to
gr
oun
d w
h
en
con
t
ro
lled
u
s
i
n
g
PI
an
d fu
zzy
. It is fou
n
d
that w
ith fuzzy, stator and rot
o
r
v
o
ltag
e
, cu
rrent an
d
po
wer
wav
e
fo
rm
s are better an
d h
a
v
e
b
e
tter stab
ility th
an
a conv
entio
n
a
l PI con
t
ro
ller.
Pre
d
i
c
t
i
v
e di
re
ct
powe
r
co
nt
r
o
l
t
echni
que i
s
appl
i
e
d t
o
D
F
IG sy
st
em
i
n
[2
1]
t
o
have
qui
c
k
er a
nd
ro
bus
t
per
f
o
r
m
a
nce t
o
m
a
i
n
t
a
i
n
cons
t
a
nt
DC
l
i
nk v
o
l
t
a
ge wi
t
h
l
e
s
s
er ha
rm
oni
c cur
r
ent
a
nd f
o
r ope
rat
i
o
n d
u
ri
ng s
u
b
sy
nch
r
o
n
o
u
s
and s
upe
r- sy
nc
hr
o
n
o
u
s spee
d
oper
a
t
i
o
n
.
Dr
oo
pi
n
g
cha
r
act
eri
s
t
i
c
s of DF
I
G
i
s
st
udi
ed i
n
[2
2]
and found t
h
at
DFIG
output
powe
r is c
o
ntrolled according t
o
varying
wind spee
d.
In t
h
i
s
pa
per
,
per
f
o
r
m
a
nce o
f
DF
I
G
wa
s c
o
m
p
ared
an
d
an
alyzed
u
n
d
e
r situ
ation
s
like, (i)
with
variation in
wind speed alone
,
(ii)
with react
ive power va
ri
ation a
n
d (iii)
with gri
d
volta
ge variation for
sam
e
variation in wi
nd s
p
eed. In these cases
, v
a
ri
atio
n
in tip
sp
eed
ratio
an
d coefficien
t
o
f
turb
in
e
po
wer, effect o
n
real and reacti
v
e power
flows, volta
ges a
n
d current
from
stator and
ro
t
o
r, rotor s
p
eed
and electrom
a
gnetic
t
o
r
que
are e
x
a
m
i
n
ed. T
h
e
pa
per
was
o
r
ga
ni
zed as
f
o
l
l
o
ws
:
ove
r
v
i
e
w
of
WEC
S
wi
t
h
w
i
nd t
u
r
b
i
n
e
m
odel
i
n
g
an
d p
itch an
g
l
e con
t
ro
ller in
sectio
n
II;
study o
f
m
a
th
e
m
a
t
ical
m
o
d
e
llin
g
o
f
D
F
IG
in sectio
n
III, t
h
e sectio
n
IV deals wit
h
RSC architecture and desi
gn; section V
analyses the perform
a
nce of DFIG
for two ca
ses like
effect
o
f
vari
a
t
i
on o
n
i
)
reac
t
i
v
e po
we
r de
m
a
nd al
o
ng
w
i
t
h
vari
at
i
o
n i
n
wi
nd
spee
d
and i
i
)
gri
d
v
o
l
t
a
ge
vari
at
i
o
n wi
t
h
wi
n
d
s
p
ee
d.
C
oncl
u
si
o
n
was gi
ve
n
i
n
Sect
i
o
n VI f
o
l
l
o
we
d by
ap
pe
ndi
x
a
n
d refe
rences
.
2.
WIND E
N
ERGY
CONVERSION SYSTE
M
(WECS)
In
th
is stud
y, th
e
W
E
CS is desig
n
e
d
u
s
i
n
g
DFIG con
n
ected with
th
e stato
r
co
nn
ected
d
i
rectly to
g
r
id
and t
h
e r
o
t
o
r
v
i
a a back
-t
o
-
ba
ck P
W
M
-
VSC
as sh
ow
n i
n
F
i
gu
re 1
.
Th
e c
ont
rol
of t
h
e s
y
st
em
has bee
n
d
o
n
e
thr
o
u
g
h
the
r
o
tor si
de c
o
n
v
e
r
ter
(RSC) a
n
d
the
gri
d
side
con
v
e
r
ter
(G
S
C
). T
h
e M
P
P
T
alg
o
rithm
h
a
s bee
n
ach
iev
e
d
thro
ug
h con
t
ro
llin
g
th
e turb
i
n
e sh
aft b
l
ad
e an
g
l
e t
o
o
p
tim
al t
i
p
sp
eed, th
e RSC
co
n
t
ro
ls t
h
e
ro
t
o
r t
o
ro
tate and
op
timal sp
eed
. The GSC m
a
in
ta
in
s th
e DC
-
link
vo
ltag
e
at th
e referen
ce valu
e b
y
tran
sferring
activ
e po
wer t
o
th
e grid and
co
n
t
ro
ls t
h
e
e
x
change of
rea
c
tive
power with th
e
g
r
i
d
.
Fi
gu
re
1.
Si
n
g
l
e
l
i
n
e di
a
g
ram
of
g
r
i
d
c
o
nnect
ed
DFI
G
2.
1.
The wind turbine mo
delling
Th
e
wind
turbin
e is th
e
p
r
i
m
e
m
o
v
e
r
wh
i
c
h
facilitates in
co
nv
erting
kin
e
tic en
erg
y
o
f
wind
i
n
to
mechanical energy which
fu
rther c
o
nve
rted into electric
a
l energy.
From
basic theory of wi
nd energy
conve
r
sion, t
h
e
output m
echanical
p
o
we
r
fr
o
m
turbi
n
e is
gi
ven
by
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Tip
S
p
e
ed
Ra
ti
o
Ba
sed
MPPT Algo
rith
m and I
m
p
r
o
v
ed
Fiel
d
O
r
ien
t
ed
Con
t
ro
l f
o
r
.... (
D
.
V. N. An
an
t
h
)
1
321
=
Cp
(
λ
,
β
)
(
1
)
Whe
r
e
is th
e m
ech
an
ical po
wer
ou
tpu
t
fro
m
win
d
tu
rb
i
n
e, C
p
is
coe
f
ficient of
wind
powe
r as
a
fu
nct
i
o
n o
f
pi
t
c
h an
gl
e (
β
) and
tip
sp
eed
ratio
(
ρ
i
s
speci
fi
c
den
s
i
t
y
of ai
r,
r i
s
ra
di
us
of
w
i
nd t
u
r
b
i
n
e
bl
ade
,
i
s
wi
nd
spee
d.
Cp
(
λ
,
β
)
=
0
.
517
6 (
-
0.
4
β
- 5)
+ 0.006
8
λ
(
2
)
Th
e tip sp
ed
ratio
is a relation b
e
tween
t
u
rb
i
n
e sp
eed
(
ra
di
us
of
t
u
r
b
i
n
e
b
l
ades a
n
d
wi
nd
spee
d
and
t
i
p
s
p
ee
d r
a
t
i
o
at
pa
rt
i
c
ul
ar a
ngl
e
‘i
’ i
s
g
i
ven t
h
e
rel
a
t
i
on as
sh
o
w
n
bel
o
w
λ
=
and
=
–
(3
)
t
h
e o
u
t
p
ut
po
w
e
r at
nom
i
n
al
wi
n
d
s
p
ee
d i
s
gi
ve
n
by
t
h
e
be
l
o
w e
q
uat
i
o
n
=
(4
)
Wh
ere Psh
is th
e tu
rb
i
n
e sh
aft p
o
wer an
d
C
p
m
a
x
is
m
a
xim
u
m
m
echanical power c
o
efficient. The m
a
xim
u
m
po
we
r f
r
o
m
wi
nd
t
u
rbi
n
e ca
n
be e
x
t
r
act
ed
by
usi
n
g
t
h
e e
q
ua
t
i
o
n
=
πρ
(5
)
2.
2.
Pitch angle
contr
o
ller
The wi
nd t
u
rbine bla
d
e angle
s
are controlled by us
ing servo m
echanism
to m
a
ximize tu
rbi
n
e output
mechanical power duri
ng
st
e
a
dy
st
at
e an
d t
o
pr
ot
ect
t
h
e t
u
rbi
n
e
du
ri
n
g
hi
gh
wi
nd
s
p
eed
s.
Thi
s
co
nt
r
o
l
m
echani
s
m
i
s
kn
ow
n as
pi
t
c
h a
ngl
e c
ont
ro
ller.
W
h
en
wind
speed
is at cu
t-in sp
eed, th
e
b
l
ad
e
p
itch
ang
l
e is set to pro
d
u
ce
op
ti
m
a
l
p
o
wer, at
ra
ted wind
sp
eed
;
it is set to
p
r
od
uce rated ou
tpu
t
po
wer
fr
om
generat
o
r
.
At
hi
g
h
er wi
nd s
p
ee
ds, t
h
i
s
angl
e i
n
crea
ses and m
a
kes t
h
e t
u
rbi
n
e t
o
prot
ect
f
r
om
ove
r-
spee
di
n
g
. T
h
e
pi
t
c
h a
ngl
e
co
n
t
rol
l
e
r ci
rc
ui
t
i
s
as s
h
o
w
n i
n
Fi
gu
re
2a.
Fi
gu
re
2a.
Pi
t
c
h a
ngl
e c
o
nt
r
o
l
l
e
r desi
gn
f
o
r
wi
n
d
t
u
r
b
i
n
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
13
1
9
– 13
31
1
322
Fig
u
re
2b
. MPPT algo
rith
m
fo
r wi
n
d
tu
rb
ine to
d
e
v
e
l
o
p
o
p
ti
m
a
l ro
tor sp
eed
estim
at
io
n
In this sy
stem
refe
rence
gene
rator s
p
ee
d is
1.
2p
u an
d act
u
a
l
speed o
f
t
h
e
gene
rat
o
r i
s
Wr
. I
n
the sim
i
lar wa
y
,
the
diffe
re
n
ce in
refe
rence
(P
*=
1) a
n
d
ac
t
u
al
p
o
we
r
o
u
t
put
s
f
r
om
tu
rb
i
n
e
(PT) is co
n
t
ro
lled
by
PI c
ont
rol
l
er. B
o
t
h
t
h
e
o
u
t
p
ut
s fr
om
PI cont
r
o
l
l
e
r a
r
e
desi
g
n
ed t
o
g
e
t
refere
nce
pi
t
c
h an
gl
e co
nt
rol
l
e
r
(
β
re
f)
. T
h
e cl
ose
d
l
o
op c
o
n
t
rol
o
f
pi
t
c
h
angl
e i
s
obt
ai
ned a
s
sh
o
w
n
i
n
Fi
g
u
re
2a.
The
opt
i
m
al
spee
d
esti
m
a
t
i
o
n
(
s
pd
_r
ef or
W
R
) i
s
show
n in Figu
r
e
2b
. U
s
i
n
g
Tip
Sp
eed
Ratio
(
T
SR),
w
i
nd
sp
eed
,
C
o
eff
i
cien
t
of
Power (CP) and m
echanical
po
we
r out
put
f
r
om
t
u
rbi
n
e ar
e used as m
a
in i
n
p
u
t
s
t
o
ge
nerat
e
re
fere
nc
e rot
o
r
sp
eed
.
Th
e co
ntro
l sch
e
m
e
is
u
s
efu
l
to
ex
tract
m
a
x
i
m
u
m mechanical
power,
there
b
y m
o
re
m
echanical torque
(Tm
)
by
usi
n
g
t
h
e o
p
t
i
m
al
ti
p spee
d rat
i
o
ba
s
e
d M
P
P
T
al
g
o
r
i
t
h
m
.
Fi
gu
re
3.
Eq
ui
val
e
nt
ci
rc
ui
t
o
f
D
F
I
G
i
n
r
o
t
a
t
i
ng
refe
re
nce
f
r
am
e at
speed
ω
2.
3.
Ma
them
a
t
i
c
al
mod
e
l
i
n
g of
DFIG
Th
e equ
i
v
a
len
t
circu
it o
f
DFIG in
ro
tating
refe
re
nce fram
e
at an arbitr
ary refere
nce speed of
ω
is
sh
own
in Fi
g
u
re 3
.
Th
e stator
d
i
rect an
d qu
ad
rat
u
re ax
is
(dq
)
vo
ltag
e
s
of
DFIG can
b
e
written
as
=
-
+
(6
)
=
+
+
(7
)
The
rot
o
r dire
c
t
and qua
d
rat
u
re axis a
r
e
deri
ves as
=
+
(8
)
=
+
+
(9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Tip
S
p
e
ed
Ra
ti
o
Ba
sed
MPPT Algo
rith
m and I
m
p
r
o
v
ed
Fiel
d
O
r
ien
t
ed
Con
t
ro
l f
o
r
.... (
D
.
V. N. An
an
t
h
)
1
323
The
differe
n
ce
between stator s
p
eed
and rotor s
p
ee
d
is
kn
own
as slip
sp
eed
. For
m
o
to
rin
g
action
,
t
h
is
d
i
fference is less th
an
zero and
fo
r
g
e
n
e
rating
,
th
e
slip
sp
eed is
n
e
gativ
e. Th
e stat
o
r
and
rot
o
r
fl
u
x
l
i
n
ka
ges i
n
a
x
i
s
f
r
a
m
e are gi
ven
b
e
l
o
w
=
+
(1
0)
=
(1
1)
=
+
(1
2)
=
+
(1
3)
=
+
(1
4)
The stator
real
powe
r in term
s
of
two
ax
is
v
o
ltag
e
and
cu
rren
t is
=
(
+
) (1
5)
Th
e
ro
t
o
r real
p
o
wer in term
s
of two
ax
is
v
o
ltag
e
and
cu
rren
t is
=
(
+
) (1
6)
The stator
reac
tive powe
r i
n
t
e
rm
s of
two
axis vo
ltag
e
an
d
cu
rren
t is
=
(
) (1
7)
The
rot
o
r react
ive power in te
rm
s of
two a
x
i
s
voltage a
n
d c
u
rrent is
=
(
) (1
8)
Th
e qu
adrature
and
d
i
rect
ax
is
ro
to
r curren
t
i
n
term
s o
f
stato
r
p
a
ram
e
ters can
b
e
written
as
=
=
(1
9)
=
+
(2
0)
The
o
u
t
p
ut
el
ect
rom
a
gnet
i
c
t
o
r
q
ue i
s
gi
ve
n
by
t
h
e e
q
uat
i
o
n
=
(
) (2
1)
Th
e m
ech
an
ical to
rq
u
e
ou
tpu
t
fro
m
th
e tu
rb
ine in
term
s of mechanical
power a
n
d rotor s
p
eed is
=
(2
2)
3.
ROTOR SIDE CONTROLLER
(RSC) AND GRID
SI
DE
CONT
ROLLER (GSC)
AR
CHITE
C
T
URE A
N
D
D
E
SIGN
The c
ont
r
o
l
ci
rcui
t
f
o
r
gri
d
s
i
de co
nt
r
o
l
l
e
r (GSC
) i
s
sh
o
w
n i
n
Fi
gu
re 4a
. The
rot
o
r si
d
e
con
v
e
r
t
e
r
(R
SC
) i
n
Fi
g
u
r
e 4
b
i
s
used
t
o
cont
rol
t
h
e s
p
e
e
d
of
rot
o
r
an
d
al
so
hel
p
s i
n
m
a
i
n
t
a
i
n
i
ng
de
si
red
gri
d
vol
t
a
ge as
dem
a
nded.
Th
e GSC
a
nd R
S
C
have
fo
u
r
co
nt
r
o
l
l
o
o
p
s eac
h, l
a
t
e
r
has o
n
e
spee
d co
nt
r
o
l
l
o
o
p
,
ot
he
r i
s
r
eact
i
v
e
po
we
r and l
a
st
t
w
o are di
rect
and
qua
dr
at
ure
axi
s
curre
nt
cont
rol
l
o
ops
. The spee
d an
d r
eact
i
v
e po
wer
cont
ro
l
l
o
o
p
s are cal
l
e
d o
u
t
e
r co
nt
rol
l
oop an
d di
r
e
c
t
and qua
d
r
at
u
r
e axi
s
cont
r
o
l
l
o
o
p
s are cal
l
e
d
i
nner co
nt
r
o
l
l
o
o
p
s.
The
di
f
f
ere
n
ce
bet
w
een
re
fer
e
nce s
p
ee
d
of
gene
rat
o
r a
n
d
act
ual
spee
d
o
f
ge
nerat
o
r
i
s
s
a
i
d
t
o
be
r
o
t
o
r
spee
d
err
o
r
.
Spe
e
d e
r
ro
r i
s
m
i
nim
i
zed an
d m
a
i
n
t
a
i
n
ed nea
r
l
y
at
zero
val
u
e
by
usi
ng s
p
ee
d co
nt
r
o
l
l
e
r l
o
op
whi
c
h i
s
a
PI con
t
ro
ller.
Th
e ou
t
p
u
t
from sp
eed
con
t
ro
ller is m
u
lt
ip
lie
d wi
t
h
st
at
o
r
fl
u
x
(Fs
)
a
nd
r
a
t
i
o
of st
at
o
r
a
nd
rot
o
r
(Ls an
d L
r) in
ducta
nces to
g
e
t refere
nce q
u
a
drat
ure c
u
r
r
e
n
t (I
qr
) f
o
r
rot
o
r
.
The e
r
r
o
r i
n
re
fere
nce an
d actual
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
13
1
9
– 13
31
1
324
react
i
v
e p
o
we
r
gi
ve refe
re
nce
di
rect
axis current (Iqr). The
diffe
re
nce be
t
w
een the
s
e reference a
nd act
ual two
axi
s
c
u
r
r
ent
s
i
s
co
nt
r
o
l
l
e
d
by
t
une
d
PI
co
nt
r
o
l
l
e
r t
o
get
res
p
ect
i
v
e di
rect
a
n
d
qua
d
r
at
ure
a
x
i
s
vol
t
a
ges
.
Fi
gu
re
4a.
G
r
i
d
si
de c
o
nt
rol
l
e
r
f
o
r
DF
IG
Fig
u
r
e
4b
.
Ro
to
r sid
e
con
t
ro
ller
for
D
F
IG
For
gi
ve
n
wi
n
d
speed
, re
fere
n
ce or c
ont
r
o
l
p
o
we
r f
r
om
t
u
rb
i
n
e i
s
est
i
m
a
t
e
d usi
ng l
o
o
k
u
p
t
a
bl
e. Fr
om
equat
i
o
n (
1
5),
st
at
or real
p
o
w
e
r (Pst
ator) is calculated and the error in
powers is differe
n
ce betwee
n these two
p
o
wers (d
P) wh
ich
is to
b
e
main
tain
ed
n
ear
zero
b
y
PI co
ntro
ller. Th
e
o
u
t
p
u
t
fro
m
PI co
n
t
ro
ller is
m
u
ltip
lied
wi
t
h
real
p
o
w
e
r
c
onst
a
nt
(
K
p
)
gi
ves act
ual
cont
rol
l
a
bl
e
p
o
w
er
aft
e
r
di
st
u
r
ba
nce.
The
di
ffe
rence
i
n
s
q
u
a
re
of
refe
rence
v
o
l
t
a
ge ac
ros
s
ca
pa
ci
t
o
r
dc l
i
n
k
(
V
dc
*
)
a
n
d
sq
u
a
re of
a
c
t
u
al
d
c
l
i
nk v
o
l
t
a
ge (V
dc)
i
s
c
ont
r
o
l
l
e
d
u
s
ing
PI con
t
ro
ller to
g
e
t referen
ce co
n
t
ro
ll
ab
le real
powe
r. T
h
e error in
the refe
rence and act
ual controllable
po
we
r i
s
di
vi
d
e
d by
usi
n
g 2/
3Vs
d
t
o
get
di
rect
axi
s
(
d
-a
x
i
s) refe
re
nce c
u
r
r
ent
near
gri
d
t
e
rm
i
n
al
(Ig
dre
f
)
.
Diffe
re
nce in Igdref and act
ual d-a
x
is
gri
d
c
u
rrent is
co
nt
r
o
l
l
e
d by
P
I
c
o
nt
rol
l
e
r t
o
get
d-
axi
s
vol
t
a
ge
.
Sim
ilarly
from
stator
RM
S
vo
ltage (
V
s)
o
r
re
fere
n
ce
reactive powe
r, actual
st
at
or
v
o
l
t
a
ge
or
react
i
v
e
po
we
r i
s
su
bt
r
act
ed by
P
I
c
ont
rol
l
e
r a
n
d
m
u
lt
i
p
l
i
e
d w
ith appropriate
reactive power
co
nstan
t
(Kq) to
g
e
t
actual refe
rence reactive power c
o
m
p
ensa
ting pa
ram
e
te
r
.
From
equation
(17), actua
l reactive power is
cal
cul
a
t
e
d an
d
t
h
e di
ffe
re
nce
i
n
t
h
i
s
and ac
t
u
al
com
p
ensat
i
ng react
i
v
e
p
o
w
er a
nd
whe
n
di
vi
de
d
by
2/
3
V
sq
,
we get qu
ad
rature axis (
q
-
a
xi
s) refe
rence c
u
rre
nt (I
qre
f).
Whe
n
the diffe
r
ence in Iq
re
f and stator actua
l q-axis
cur
r
ent
(
I
q
)
i
s
cont
rol
l
e
d
by
PI c
o
nt
rol
l
e
r
,
r
e
fere
nce
q-
ax
is vo
ltag
e
is ob
tain
ed
. To
im
p
r
ov
e tran
sien
t resp
on
se
and t
o
c
o
nt
rol
st
eady
st
at
e erro
r, dec
o
upl
e
d
q-a
x
i
s
v
o
l
t
a
ge
has t
o
be a
d
d
e
d as sh
o
w
n i
n
Fi
g
u
re
4a. F
i
nal
l
y
bot
h d
an
d
q a
x
i
s
v
o
l
t
a
ge
par
a
m
e
t
e
rs so o
b
t
a
i
n
ed a
r
e c
o
n
v
e
rt
ed t
o
t
h
ree
a
x
i
s
abc
pa
ram
e
t
e
rs by
usi
n
g i
nve
rse
Par
k
’s t
r
a
n
s
f
o
r
m
a
t
i
on an
d re
f
e
rence
v
o
l
t
a
ge
i
s
gi
ve
n t
o
scalar PW
M contro
ller to
g
e
t
pu
lses fo
r grid
sid
e
cont
roller.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Tip
S
p
e
ed
Ra
ti
o
Ba
sed
MPPT Algo
rith
m and I
m
p
r
o
v
ed
Fiel
d
O
r
ien
t
ed
Con
t
ro
l f
o
r
.... (
D
.
V. N. An
an
t
h
)
1
325
The
ge
neral
fo
rm
of s
p
eed
re
gul
at
i
o
n i
s
gi
v
e
n
by
= J
+ B
+
(2
3a)
=
(Js+B)
+
(
23b
)
Whe
r
e
to
rq
u
e
, J is m
o
m
e
n
t
o
f
i
n
ertia and
B is frictio
n
co
efficien
t,
is
co
nsid
ered
t
o
be d
i
sturb
a
n
ce.
Mu
ltip
lyin
g
b
o
th
sid
e
s with
,
we
g
e
t th
e equatio
n
as
= (Js +
B)
+
(2
4)
C
o
n
s
id
e
r
in
g
const
a
nt
a
n
d c
h
a
nge
i
n
spe
e
d
e
r
r
o
r
i
s
is con
t
ro
l variab
le, th
e abo
v
e eq
u
a
t
i
on
becom
e
s.
= (
s +
)
+
(2
5)
As p
r
od
u
c
t of to
rq
u
e
and
sp
eed
is po
wer, we
w
ill b
e
g
e
tting
stator
referen
ce
p
o
wer an
d d
i
sturb
a
n
c
e
po
we
r as s
h
ow
n
bel
o
w.
= (
s +
)
(2
6)
Whe
r
e,
J*
B*
Fin
a
lly d
i
rect ax
is referen
ce
vo
ltag
e
can
b
e
writte
n
b
y
u
s
ing
eq
u
a
tion
(2
6)
and
fro
m
Fig
.
5
b
is
=
(
+
) +
(
+
)
(2
7)
=
(
+
) (2
8)
The r
o
t
a
t
i
n
g di
rect
an
d q
u
a
d
r
a
t
u
re re
fe
rence
vol
t
a
ge
s
of rot
o
r a
r
e converte
d into
stationa
ry abc fram
e
param
e
t
e
rs by
usi
n
g i
n
ver
s
e
par
k
s t
r
a
n
s
f
o
r
m
a
t
i
on. Sl
i
p
f
r
e
que
ncy
i
s
u
s
e
d
t
o
gen
e
rat
e
s
i
nus
oi
dal
a
nd
cosi
ne
param
e
t
e
rs
fo
r i
nve
rse par
k
s
t
r
ans
f
orm
a
t
i
on.
4.
R
E
SU
LT
ANA
LY
SIS: CASE STUD
IES
The
dy
nam
i
c
per
f
o
r
m
a
nce o
f
t
h
e D
F
I
G
sy
st
em
i
s
i
nvest
i
g
at
ed
un
de
r t
w
o
di
f
f
ere
n
t
c
a
ses an
d t
h
e
rat
i
ng s
p
eci
fi
c
a
t
i
ons f
o
r
DFI
G
an
d wi
n
d
t
u
rbi
n
e par
a
m
e
t
e
rs i
s
gi
ve
n i
n
appe
n
d
i
x
. T
h
e
wi
n
d
spee
d ch
ange i
n
these two cas
e
s
in m
e
ters per seconds as
8,
15, 20
an
d
10
at
15,
25 a
n
d 3
5
seco
n
d
s. T
h
e
react
i
v
e p
o
we
r an
d
vol
t
a
ge
val
u
e c
h
an
ge i
n
i
ndi
vi
dual
t
w
o
cases
wi
t
h
c
h
a
n
ge i
n
t
i
m
e i
s
from
-0
.6
p
u
at
12
se
con
d
s
t
o
0
p
u
c
h
an
ge
at
20 seco
nd
s. It
was fu
rt
he
r chan
ge
d fr
om
0p
u t
o
+0
.6
p
u
m
a
gni
t
ude at
3
0
seco
nd
s. D
u
e t
o
addi
t
i
on
o
f
l
a
rge
furnace
or induction m
o
tor or
non linea
r type loa
d
, leading reacti
v
e pow
er greater t
h
a
n
0pu is
re
quire
d, while
for light loa
d
laggi
ng reacti
v
e power is re
quire
d
(<0pu
).
Hence
DFIG
will bec
o
m
e
better ge
nerat
o
r source i
f
it can s
u
pply a
n
y de
sire
d re
a
c
tive power
effectively. T
h
e
change
in
grid
term
inal voltage ta
kes
place
whe
n
su
dd
en
ly switch
i
ng
o
n
or
o
f
f l
a
rg
e lo
ad
s
o
r
du
e to sm
all fau
lts n
ear
PCC.
The cha
n
ges in tip- spee
d ration and power coef
ficient Cp bot
h reactive powe
r and
wind spe
e
d
v
a
riation
in
Fig
u
re
5
a
(i
) and v
a
riation
with g
r
i
d
term
in
al
vol
t
a
ge
an
d
wi
nd
spee
d
b
o
t
h
i
s
sh
ow
n i
n
Fi
gu
re
5a
(ii).
Wh
en
wind
sp
eed is at 8m/s, tip
sp
eed
ratio
(TSR)
i
s
hi
g
h
near 4.
8 d
e
grees
an
d
sl
ow
ly d
ecr
eases
to
2.6o
at 15s
when s
p
eed increa
ses
to 15m
/
s, furt
her i
n
crease
d
t
o
1
.
9
o
at
25
s
whe
n
s
p
ee
d o
f
wi
n
d
i
s
20m
/s an
d
decrease
d
to 3.9o when wind spee
d
dec
r
ease
d
to 10m
/s
at
3
5
s
. In
th
e
similar way, Cp
is also
ch
ang
i
ng fro
m
3.
25 t
o
1
.
7
at
15s
, a
nd
fu
rt
he
r dec
r
ease
d
t
o
1.
25 at
2
5
s, a
n
d t
h
e
n
i
n
c
r
ease
d
t
o
2.
55
at
3
5
seco
nds
wi
t
h
wi
n
d
spee
d va
ri
at
i
o
n f
r
om
8 t
o
1
5
an
d t
h
en t
o
20
, an
d
1
0
m
/
s. The
va
ri
at
i
on i
n
TSR
a
n
d C
p
wi
t
h
c
h
a
nge i
n
react
i
v
e p
o
we
r
i
s
i
ndepe
nde
n
t
and has
no e
ffect
as sh
o
w
n
in
Fig
u
re 5
a
(ii). Howev
e
r,
with
ch
ang
e
in g
r
i
d
terminal voltage, a
very sm
all cha
nge
i
n
TS
R
and
C
p
can
be
obse
r
ved
.
It
i
s
due to the
fact that the T
S
R and
C
p
depe
n
d
s
on
pa
ram
e
t
e
rs as descri
bed
by
e
quat
i
o
ns
1
t
o
5
an
d i
s
i
nde
pe
n
d
ent
o
n
vol
t
a
g
e
an
d
react
i
v
e
po
we
r.
The
refe
rence
m
echani
cal
t
u
r
b
i
n
e t
o
r
que
an
d ge
ne
rat
o
r t
o
rq
ue
wi
t
h
m
a
gni
t
ude
s o
v
e
r
l
a
ppi
ng
a
n
d
variatio
n
of
rot
o
r
spee
d
fo
r tw
o cases c
o
m
p
ariso
n
is s
h
own
in
Figu
r
e
5b
.
W
i
t
h
in
cr
ease i
n
w
i
nd
sp
eed, t
o
rqu
e
is in
creasi
n
g an
d v
i
ce-v
ersa.
Till ti
me u
p
t
o
15
secon
d
s
,
wi
n
d
sp
eed
is at lo
w v
a
lu
e
of 8m/s,
so
torq
u
e
is
at
-
0.2pu a
nd i
n
creased to
-0.5pu at 15s wit
h
increase i
n
w
i
nd
sp
eed
t
o
15m/s. Th
e to
rque f
u
r
t
h
e
r
in
cr
eased
to
-
0.
9p
u w
h
e
n
wi
nd s
p
ee
d i
s
20
m
/
s and decre
a
sed t
o
-
0
.
2
8pu when s
p
ee
d decrease
d
to
10m
/
s. there are s
m
all
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
13
1
9
– 13
31
1
326
surges in t
o
rque wave
form
because
of s
u
dde
n
cha
n
ge in wi
nd s
p
ee
d.
W
i
t
h
the cha
n
ge in wi
nd s
p
ee
d,
rot
o
r
sp
eed
is also
varyin
g bu
t is main
tain
ed n
e
ar
ly
at
co
nstan
t
valu
e
of
1
.
3p
u RPM.
The c
h
a
nge
s i
n
t
o
r
que
h
a
s e
ffect
wi
t
h
c
h
a
nge
i
n
react
i
v
e
p
o
we
r a
s
i
n
F
i
g.
5b
(i
) a
n
d
f
u
rt
her
m
o
re
sur
g
es bee
n
o
b
ser
v
e
d
whe
n
gri
d
v
o
l
t
a
ge d
i
st
urba
nce occ
u
r
r
ed
as
i
n
Fi
gu
re 5b
(i
i
)
i
s
t
a
ki
n
g
pl
ace
. Whe
n
reactiv
e po
wer is lag
g
i
n
g
at -0
.6
pu
, th
er
e is a s
m
all surge in torque at 20
seco
nds
. Ge
ner
a
t
o
r spee
d i
s
al
so l
o
w
at 1
.
2
7pu
at -0
.6
pu
reactive powe
r, while
at
0pu r
eactiv
e
po
wer, it is 1.32p
u
sp
ee
d. B
u
t rotor speed i
n
creased
t
o
1.
4p
u s
p
eed
at
l
o
w t
e
rm
i
n
al
gri
d
vol
t
a
ge
o
f
0.
8
p
u
.
When
,
react
i
v
e po
we
r cha
nges t
o
0
p
u
fr
om
-0.6
p
u
,
rot
o
r
spee
d i
n
crease
from
1.3
p
u
t
o
1.2
7
pu a
n
d gr
i
d
t
e
rm
i
n
al
vol
t
a
ge cha
nges t
o
1
pu
fr
om
0.8
pu
bet
w
ee
n 2
0
t
o
30
seconds.
Speed furt
her increased t
o
1.35pu with
leading reactive
power of
+0.
6pu and
decreased
when gri
d
vol
t
a
ge i
n
c
r
eas
e from
1pu t
o
1.
2p
u. T
h
ere
f
o
r
e rot
o
r s
p
eed i
n
crease
s
i
f
rea
c
t
i
v
e po
wer c
h
ange
s fr
om
l
a
g
g
i
n
g (-
ve) t
o
l
eadi
n
g
(+ve
) an
d rot
o
r spee
d decrea
ses wi
t
h
i
n
cre
a
se i
n
gri
d
t
e
r
m
i
n
al
vol
t
a
ge bey
o
nd
1p
u va
l
u
e i
n
rm
s. Th
e su
rg
es in
torq
u
e
will b
e
ob
serv
ed
very h
i
gh
wh
en
termin
al g
r
id vo
ltag
e
ch
ang
e
s is du
e to th
e
fact o
f
change i
n
m
echanical
powe
r
is not that faster
in com
p
arison
with electric
a
l powe
r c
h
ange.
a (i)
a (ii)
Fi
gu
re
5a.
Ti
p
spee
d rat
i
o
an
d
C
o
ef
fi
ci
ent
of
po
we
r C
p
f
o
r
(
i
) react
i
v
e
p
o
w
er c
h
an
ge
&
wi
nd
sp
eed
va
ri
at
i
on,
(ii) bo
th grid vo
ltag
e
& wi
nd
sp
eed
ch
ang
e
s
b
(i)
b
(ii)
Figure
5b. Re
ference
and act
ual ge
ne
rator t
o
rque a
n
d ro
tor s
p
eed va
riation with tim
e
for (i
) reacti
v
e
powe
r
chan
ge & wi
n
d
spee
d vari
at
i
o
n, (i
i
)
bot
h gri
d
v
o
l
t
a
ge
&
wi
n
d
s
p
ee
d
c
h
an
ge
s
From
Figure
5c (i), there is a
n
in
creas
e in current from
0.
18
p
u
t
o
0.
5
pu
at
15 seco
n
d
s
wi
t
h
i
n
crea
se
in win
d
sp
eed
from
8 to 1
5
m
/s and fu
rthe
r increase
d
to
0.9pu am
ps when s
p
ee
d increased to
20m
/s and
decrease
d
t
o
0
.
3p
u am
ps whe
n
spee
d o
f
wi
n
d
i
s
10m
/
s
. Wh
en react
i
v
e p
o
w
er (
Q
) c
h
a
n
g
e
from
0pu t
o
-
0
.
6
p
u
,
current inc
r
eas
ed from
0.1
5pu 0.5pu am
ps and
decrease
d
to 0.5pu
am
ps
whe
n
Q cha
nges from
-0.6pu to 0pu
and
i
n
c
r
eased
t
o
1p
u
am
ps wh
en
s
p
ee
d of wi
nd
i
s
20m
/
s
and react
i
v
e po
w
e
r
i
s
0.
6p
u.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Tip
S
p
e
ed
Ra
ti
o
Ba
sed
MPPT Algo
rith
m and I
m
p
r
o
v
ed
Fiel
d
O
r
ien
t
ed
Con
t
ro
l f
o
r
.... (
D
.
V. N. An
an
t
h
)
1
327
c
(i)
c
(ii)
Fi
gu
re
5c.
St
at
or
v
o
l
t
a
ge a
n
d
cur
r
ent
t
h
ree
p
h
ase
wa
ve
fo
rm
with
tim
e fo
r (i) reactiv
e power ch
ang
e
&
win
d
sp
eed
v
a
riation,
(ii) bo
th
grid
v
o
ltag
e
& wi
nd
sp
eed
ch
ang
e
s
W
i
t
h
su
d
d
en
d
ecrease i
n
g
r
i
d
t
e
r
m
i
n
al
vol
t
a
ge fr
om
1pu t
o
0.8
p
u
v
o
l
t
s
at
12 sec
o
n
d
s
,
sl
owl
y
st
at
o
r
current dec
r
ea
sed
e
x
ponentia
lly
w
h
en
w
i
nd sp
eed
is
v
e
r
y
lo
w
of
0.1pu
a
m
p
s
at 8
m
/s
an
d th
is cu
rr
en
t w
a
s
im
pro
v
ed
t
o
1
p
u
whe
n
wi
n
d
s
p
eed
i
n
c
r
ease
d
t
o
15m
/
s
. B
u
t
whe
n
t
e
rm
i
n
al
vol
t
a
ge
c
h
an
ge
d t
o
1
p
u
fr
om
0.
8p
u
at
20s
, c
u
r
r
ent
agai
n
reac
hed
t
o
n
o
r
m
a
l
value
of
0.
5
pu
a
m
ps as in case
1 a
n
d the c
u
rrent increased to a
g
ain
1p
u
whe
n
wi
n
d
s
p
eed
reac
he
s 2
0
m
/
s. when
t
h
e g
r
i
d
t
e
rm
i
n
al
v
o
l
t
a
ge i
n
c
r
eased t
o
1.
2p
u f
r
om
1p
u, t
h
e st
at
or
current a
g
ai
n
decreased to 0.8pu am
ps
an
d
w
h
en
wi
nd
s
p
ee
d
fi
nal
l
y
reac
h
e
s 1
0
m
/
s wi
t
h
vol
t
a
ge
at
1.
2p
u, t
h
e
cur
r
ent
i
s
0.
2p
u Am
ps as i
n
Fi
gu
re 5c (i
i
)
.
Hence
wi
t
h
i
n
crease i
n
vol
t
a
ge at
const
a
nt
wi
n
d
spee
d, c
u
r
r
ent
d
ecreases an
d
with
i
n
crease in
wind
sp
eed
at sam
e
v
o
ltag
e
cu
rren
t
will in
crease and
v
i
ce-v
ersa. In
t
h
e si
m
i
lar
way as do
es i
n
stato
r
vo
ltage an
d
curren
t
,
ro
t
o
r
v
o
ltage
an
d
curren
t
will also
v
a
ry, bu
t
ro
t
o
r cu
rren
t
is b
i
-
d
i
rection
a
l un
lik
e stator cu
rren
t do
es.
In
t
h
ese
t
w
o c
a
ses,
rot
o
r
v
o
l
t
a
ge i
s
nea
r
l
y
c
onst
a
nt
at
0.
3
2
p
u
,
but
cu
rre
nt
i
s
va
ry
i
n
g
wi
t
h
bot
h
wi
n
d
spee
d a
n
d
reac
t
i
v
e p
o
we
r c
h
a
nge
i
n
Fi
g
u
re
5d
(i
)
an
d
f
o
r
vol
t
a
ge
a
n
d
wi
nd
s
p
eed
va
ri
a
t
i
on as
i
n
Fi
g
u
r
e
5d
(
ii)
.
W
h
en
r
e
activ
e p
o
w
e
r
at
-
0
.6pu
, ro
tor
cu
rr
en
t is 0.8pu is ev
en
low
at 8
m
/s w
i
n
d
speed
and
in
cr
eased
to
1pu am
ps whe
n
wind s
p
eed
reaches 15m
/
s a
s
in Fig. 5d
(i
). Whe
n
reactive
power
reach
es
1pu, rotor current is
0.
5p
u am
ps at
wi
n
d
s
p
eed
o
f
15m
/
s
and
fo
r l
eadi
n
g re
act
i
v
e
p
o
we
r
of +
0
.
6
pu
, t
h
e
r
o
t
o
r
cu
rre
nt
i
s
agai
n
1
p
u
at
wi
n
d
spee
d o
f
20m
/
s
and 0.
5p
u am
ps at
1
0
m
/
s wi
nd s
p
e
e
d.
W
i
t
h
i
n
c
r
e
a
se i
n
wi
nd s
p
eed o
r
at
l
eadi
ng
or
lagging reactive
powe
r, rot
o
r current
is
als
o
increasing like
stator c
u
rrent.
In t
h
e sam
e
scenari
o
,
rot
o
r c
u
rrent
is d
ecreasing
with
in
crease i
n
g
r
i
d
term
in
al v
o
ltag
e
an
d
vi
ce-
versa
b
u
t
wi
t
h
out
a
n
y
a
p
p
r
eci
abl
e
c
h
a
nge
i
n
rot
o
r
v
o
l
t
a
ge.
W
i
t
h
s
u
dde
n c
h
an
ges
i
n
v
o
l
t
a
ge at
1
2
,
2
0
a
n
d
30
sec
o
n
d
s
,
t
h
ere
are
fe
w s
p
i
k
es
i
n
r
o
t
o
r
c
u
r
r
ent
due
t
o
su
d
d
en
r
e
versal
o
f
c
u
r
r
e
nt
m
a
gni
t
ude
and
an
g
l
e
with
resp
ect t
o
term
in
al vo
ltag
e
s
resp
ectiv
ely.
d
(
i
)
d
(
i
i
)
Figure
5d. R
o
tor voltage a
n
d
current t
h
ree
phase
wa
ve
fo
rm
with
tim
e fo
r (i) reactiv
e power ch
ang
e
&
win
d
sp
eed
v
a
riation,
(ii) bo
th
grid
v
o
ltag
e
& wi
nd
sp
eed
ch
ang
e
s
The stator real
and reactive
powe
r fl
ow
for all th
ree ca
s
e
s is shown i
n
Figure
5d. T
h
e re
fere
nce
po
we
r w
h
i
c
h i
s
t
h
e m
echani
cal
po
wer
out
pu
t
from
t
u
rbi
n
e
and act
ual generator
real power c
h
ange is
shown
i
n
Fi
g
u
re
5e
.
W
i
t
h
c
h
an
ge i
n
wi
n
d
sp
eed
,
wi
t
h
very
l
o
w
wi
n
d
s
p
ee
d o
f
8m
/
s
, out
put
st
at
or
real
p
o
w
er i
s
0
.
1
p
u
watts till 1
5
seco
nd
s. Wh
en
wind
speed
reach
e
s 15m/s
, stato
r
real p
o
wer increased
to
0.5pu
and
fu
rt
h
e
r
in
cr
eased
to
0
.
8
p
u
f
o
r
2
0
m
/s
w
i
nd
sp
eed at 2
5
s
and
d
ecreased
to 0.2pu p
o
w
e
r
at 35
s f
o
r
1
0
m
/s sp
eed
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
13
1
9
– 13
31
1
328
sho
w
n i
n
Fi
g
u
r
e
6g (i
)
.
D
u
ri
n
g
t
h
e cha
nge i
n
wi
n
d
spee
d, real
power
alone
is
changing and reactive
powe
r
is
constant at reference
of
0pu. There
a
r
e fe
w
surges in t
h
e reactive powe
r due
t
o
ch
ang
e
in
vo
ltag
e
ang
l
e with
respect
t
o
gri
d
and
al
so
m
a
i
n
ly
due
t
o
c
h
a
n
g
e
i
n
st
at
o
r
a
n
d
rot
o
r c
u
rre
nt
fl
ows
an
d
r
o
t
o
r
vol
t
a
ge
cha
n
ge
.
W
i
t
h
t
h
e chan
ge i
n
react
i
v
e p
o
we
r
dem
a
nd from
gri
d
f
r
om
0p
u t
o
-0
.6
p
u
an
d +0.
6
pu at
1
2
an
d 3
0
seco
nds a
r
e
sho
w
n i
n
Fi
g
u
r
e 5
d
(i
).
W
i
t
h
cha
nge
i
n
rea
c
t
i
v
e p
o
we
r
fr
om
0pu
t
o
-0
.6
pu
, re
act
i
v
e
po
wer
fr
om
gene
rat
o
r
i
s
chan
gi
n
g
wi
t
h
a sm
al
l
tim
e l
a
g o
f
0.
8s an
d
r
eal
po
wer m
a
int
a
i
n
ed
nea
r
l
y
con
s
t
a
nt
val
u
e
of
0.
1
pu at
8m
/s wi
n
d
sp
eed
.
Similarl
y with
reactiv
e po
wer ch
an
g
i
n
g
to 0pu
an
d
+0
.6
pu
, th
e reactiv
e power is ch
ang
i
ng
with
in
1
seco
nd
an
d
rea
l
po
we
r i
s
al
m
o
st
c
onst
a
nt
wi
t
h
sm
al
l
surg
es
in real
stator powe
r duri
ng
t
h
is tran
sien
t. In
case
wi
t
h
bot
h
vol
t
a
ge a
n
d
wi
nd
spee
d ch
an
gi
n
g
,
wi
t
h
t
h
e g
r
i
d
vol
t
a
ge
va
ri
a
t
i
on f
r
o
m
1 t
o
0.
8p
u at
1
2
t
h
s
econ
d
,
real
p
o
we
r w
h
i
c
h i
s
at
0.
1p
u
chan
ge
d t
o
0.
0
5
p
u
a
nd
react
i
v
e p
o
w
er
whi
c
h i
s
at
0p
u r
e
a
c
hed
1
pu at
t
h
i
s
12t
h
secon
d
in
stan
t
an
d slowly d
e
cayin
g
to
r
each
to
r
e
f
e
r
e
n
ce
0pu
v
a
lu
e as sh
ow
n in
Figu
r
e
5d
(
ii). Th
is ch
an
g
e
i
n
reactive
powe
r is to m
a
ke vol
t
age of
stator
t
o
g
e
t
adju
sted
to
g
r
i
d
v
o
ltag
e
with
ou
t
losing
syn
c
hron
ism
.
e
(
i
)
e
(
i
i
)
Figure
5e. Stator real a
n
d rea
c
tive powe
r
wa
veform
w
ith ti
me for (i) react
ive power cha
n
ge & wi
nd s
p
e
e
d
v
a
riation
,
(ii) bo
th
grid
vo
ltage
& wind
sp
eed
ch
ang
e
s
The
refe
rence
m
echani
cal
powe
r
out
put
a
n
d
ge
ne
rat
o
r
a
c
t
u
al
p
o
we
r i
s
m
a
t
c
hi
ng
wi
t
h
re
fer
e
n
c
e
powe
r a
nd t
h
e
mis
m
atch is because
of l
o
oses in t
u
rb
ine
,
gea
r
wheels a
n
d ge
ne
rator a
n
d this m
i
s
m
a
t
ch is
in
ev
itab
l
e.
W
i
t
h
in
crease in
wind
spee
d,
re
fere
nce power is increasing and
vice ve
rsa
.
W
ith the c
h
a
nge i
n
v
o
ltag
e
at
g
r
i
d
, stato
r
term
i
n
al real
power is m
a
in
tain
ed at
const
a
nt
v
a
l
u
e but
w
ith
su
rg
es at in
stan
t o
f
transient
but
reactive powe
r
is ad
j
u
sting till sta
t
or voltage reache
s
the grid
volta
ge
for m
a
intaining
syn
c
hr
on
ism
a
s
sh
own
in
Figu
r
e
5
d
(
ii)
an
d 5
e
(
ii)
. A
t
th
e in
stan
t o
f
20
s an
d
30
s, th
ere is su
rg
e in
real an
d
react
i
v
e
po
wer
s
b
u
t
we
re m
a
int
a
i
n
i
n
g c
onst
a
nt
st
at
or
o
u
t
p
ut
real
po
we
rs
of
0.
5 a
n
d 0
.
8
p
u
wat
t
s
a
nd
0
p
u
v
a
r
as
in
Figu
r
e
5d
(
ii)
.
f
(i
)
f
(ii)
Figure 5f. gene
rator
re
fere
nce and
actual
real
powe
r wave
form
with tim
e
for (i
) reacti
v
e
powe
r c
h
a
nge
&
wi
n
d
s
p
ee
d
var
i
at
i
on,
(i
i
)
bot
h
g
r
i
d
v
o
l
t
a
ge &
wi
n
d
s
p
ee
d c
h
ange
s
Evaluation Warning : The document was created with Spire.PDF for Python.