Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol.
6, No. 4, Decem
ber
2015, pp. 808~
818
I
S
SN
: 208
8-8
6
9
4
8
08
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
Low Voltage Ride-through
Capability Enhancement
of Doubly Fed Induction
Gen
e
rato
r based
Wind Turbines Under Voltage Dips
Y
o
u
n
e
s
s
Bo
ukh
ris
,
Ab
ou
ba
kr El Ma
k
r
in
i,
H
a
ss
an
El Moussaoui, H
a
ss
ane El
Markh
i
The Sign
als, S
y
s
t
ems and Components
Laborator
y, Sidi Mohame
d
Ben Abdellah
University
, FST F
ez, Morocco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 18, 2015
Rev
i
sed
No
v
19
, 20
15
Accepted Nov 30, 2015
Based on
the advantag
es of do
ubly
fe
d
indu
ction gener
a
tor
(DFIG)-based
wind turbine (
W
T). This p
a
per proposes
a new control str
a
teg
y
to improve
the rid
e
-through
capab
ility
of D
F
IG-based WTs in the
even
t of
a grid f
a
ult.
The proposed method is performed b
y
us
ing th
e DFIG converters control an
d
the addition of the damping resistances c
onnect
ed
to the DC circui
t, to follow
the requir
e
ments defined b
y
the grid
codes. The proposed ride-through
solution lim
its
t
h
e peak
valu
es of the DC
lin
k voltag
e
,
the r
o
tor inrush
current, electro
m
agnetic
to
rque and DFIG transient
response at the
times
of
occurren
ce and
clearing the fau
lt. Th
e proposed solution is si
mulated an
d
com
p
ared wit
h
t
h
e crowb
a
r s
o
lut
i
on
using MATLAB/Simu
link en
vironment.
Keyword:
Dam
p
ing resistances
DFI
G
Gri
d
fau
lt
LVRT
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
:
Y
oun
ess B
o
ukh
r
i
s,
The
Si
g
n
al
s, S
y
st
em
s and C
o
m
ponent
s La
b
o
rat
o
ry
,
Si
di
M
o
ham
e
d B
e
n
A
bdel
l
a
h
Uni
v
ersi
t
y
,
Faculty of Scie
nces a
n
d Tec
h
ni
ques Fez,
B.P.
2
202
,
M
o
rocco
.
Em
ail: youness
.boukhris
@
us
m
b
a.ac.
m
a
1.
INTRODUCTION
W
i
n
d
e
n
er
gy
i
s
gai
n
i
n
g i
n
c
r
e
a
si
ng
i
m
port
a
n
ce t
h
r
o
ug
h
out
t
h
e
wo
rl
d
.
T
h
i
s
fast
de
vel
o
pm
ent
o
f
wi
n
d
ener
gy
t
echn
o
l
ogy
has l
a
r
g
e i
m
pli
cat
i
ons fo
r
a num
ber of p
e
opl
e an
d i
n
st
i
t
ut
i
ons
. As
WTs becom
e
l
a
rger a
n
d
l
e
vel
of
penet
r
at
i
on bec
o
m
e
s
hi
g
h
er i
n
el
ect
r
i
cal
powe
r
sy
st
em
s, gri
d
ope
r
a
t
o
rs
have m
odi
fi
ed t
h
e
gri
d
code
s.
According to t
h
ese
new grid codes,
WTs
m
u
st re
m
a
in
connected to t
h
e gri
d
a
n
d
supp
ly reactiv
e
po
wer to
g
u
a
ran
t
ee th
e g
r
i
d
vo
ltag
e
du
ri
n
g
th
e
g
r
id
fau
lts. Th
is ab
ility
o
f
W
T
s is called
th
e fau
lt rid
e
th
ro
ugh
(FRT)
cap
ab
ility [1
],
an
d
m
o
re sp
ecifically fo
r vo
l
t
ag
e d
i
p
s
, low v
o
ltage rid
e
th
rou
g
h
(LVR
T) capab
ility [2
],[3
].
Nowad
a
ys,
DFIG is th
e m
o
st u
s
ed
gen
e
rator for
WTs du
e t
o
th
e adv
a
n
t
ages of
v
a
riab
le-sp
e
ed
ab
ility, h
i
gh
er
en
erg
y
cap
ture, i
m
p
r
ov
ed
p
o
wer
q
u
a
lity an
d
u
s
i
n
g
co
nv
erte
rs rated
fo
r
p
a
rtial-scale co
nv
erters [4
]. On
t
h
e
o
t
h
e
r h
a
nd
,
b
e
cau
se th
e
stator of th
e
DFIG
is d
i
rectly co
nn
ected
t
o
th
e
g
r
i
d
, it is v
e
ry sen
s
itiv
e to
t
h
e g
r
i
d
di
st
ur
ba
nces,
p
a
rt
i
c
ul
arl
y
v
o
l
t
a
ge di
ps [
5
]
-
[
1
2
]
.
The t
r
an
si
ent
s
v
o
l
t
a
ges
o
n
r
o
t
o
r si
de
d
u
r
i
n
g g
r
i
d
faul
t
s
, are
hi
g
h
er t
h
an t
h
e st
at
or si
de
,
and t
h
us t
h
e
rot
o
r si
de converter (RSC
)
and i
n
term
ediate DC circui
t are
p
a
rticu
l
arly suscep
tib
le to b
e
d
e
stru
cted
du
e
to
vo
ltag
e
transien
ts.
Also, the vo
ltag
e
sag
at th
e stator termin
als
d
u
e
to
th
e grid fau
lts cau
ses th
e ro
t
o
r
o
v
e
r-cu
r
ren
t
s, DC-link
ov
er vo
ltag
e
an
d
to
rqu
e
o
s
cillatio
n
s
th
at
co
ul
d
l
ead t
o
dest
r
u
c
t
i
on
of t
h
e p
o
w
er c
o
nve
rter and
m
echanical
parts. So, w
ith
ou
t a
p
r
op
er
co
n
t
ro
l strategy, th
e
DFIG is
una
bl
e to stay connected to
th
e
grid
du
ri
n
g
t
h
e
g
r
i
d
fau
lts [5
]. Lik
e
wise, th
e DFIG system is n
o
t
cont
rol
l
e
d
du
ri
ng t
h
e cri
t
i
cal
t
i
m
e
of gri
d
fa
ul
t
s
and t
h
e sy
st
em
cannot
su
pp
o
r
t
t
h
e gri
d
. Pre
v
i
o
us ap
pr
o
aches
of resea
r
c
h
es h
a
ve bee
n
pres
e
n
t
e
d t
o
ad
dres
s
DFI
G
FR
T i
ssues. T
h
e m
o
st com
m
on FR
T sol
u
t
i
on i
s
t
o
sho
r
t
circu
it th
e ro
t
o
r wi
nd
ing
s
with
th
e crowb
a
r circu
it [6
]-[7]. Wh
en
th
e ro
tor ov
er-curren
t
is d
e
tected
, The
crowb
a
r circu
i
t sh
ort circu
its th
e ro
tor wi
nd
ing
s
wh
en
the rot
o
r
overc
u
rre
nt is detecte
d
,
whic
h isolat
es the
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Lo
w Vo
ltag
e
Rid
e
-th
r
ou
gh
C
a
p
a
b
ility Enh
ancemen
t
o
f
Doub
ly Fed
Ind
u
c
ti
o
n
.... (Youn
ess Bou
k
h
r
is)
80
9
R
S
C
fr
om
t
h
e
rot
o
r
t
o
p
r
ot
ect
t
h
e c
o
nve
rt
er,
whi
l
e
t
h
e
DF
I
G
ope
rat
i
o
n i
s
chan
ge
d t
o
a
s
qui
rrel
ca
ge i
n
duct
i
o
n
gene
rat
o
r (SC
I
G)
o
p
er
at
i
o
n
,
whi
c
h
a
b
s
o
r
b
s react
i
v
e po
we
r
fr
om
t
h
e gri
d
. In
[
8
]
,
t
h
e
a
u
t
h
ors
p
r
op
ose
d
t
h
e us
e
o
f
an en
erg
y
st
o
r
ag
e system
(ESS) th
at is con
n
ected
t
o
th
e
DC-link
o
f
DFIG. Th
is ESS can
regu
late th
e DC-
lin
k
v
o
ltag
e
du
ri
n
g
grid
faults. Alth
oug
h
RSC can
still o
p
erate in
t
h
e g
r
i
d
fau
lt, i
t
n
eed
s to
b
e
sized
accordingly to account fa
ult whic
h increase
s
com
p
lexity a
nd c
o
st of
the
syste
m
. In [9], a FRT scheme is
p
r
op
o
s
ed
u
s
ing an
ad
d
ition
a
l Series Grid-Si
d
e Conv
erte
r
(SGSC
)
. Th
e SGSC is conn
ected
to
th
e
DC-l
in
k
and
t
o
t
h
e
ope
n t
e
r
m
i
n
al
s of
DF
I
G
st
at
o
r
wi
ndi
ngs
t
h
at
re
g
u
l
a
tes th
e stato
r
fl
u
x
to
b
e
co
m
p
atib
le with
th
e
v
o
ltag
e
at th
e g
r
i
d
con
n
ection
po
in
t
o
f
DFIG du
ri
n
g
grid
fau
lt
wh
ich
im
p
r
o
v
es LVRT. Th
i
s
so
lu
tion
also n
eeds
ad
d
ition
a
l h
a
rdware
wh
ich
add
s
to
th
e co
mp
lex
ity an
d
cost o
f
th
e system
. In
[1
0
]
th
e au
tho
r
s
p
r
op
osed
an
efficien
t con
t
ro
l sch
e
m
e
to
i
m
p
r
o
v
e
th
e LVRT cap
ab
ilit
y o
f
th
e DFIG
u
n
d
e
r b
a
lan
c
ed v
o
ltag
e
d
i
p
s
,
b
y
u
s
ing
a passi
ve resi
st
i
v
e ha
rd
wa
re c
a
l
l
e
d st
at
or
da
m
p
i
ng resi
st
o
r
(SDR
) l
o
cat
e
d
i
n
seri
es
wi
t
h
t
h
e st
at
o
r
wi
ndi
ngs
.
The SDR
m
e
t
hod ca
n en
hanc
e t
h
e DFI
G
v
o
l
t
a
ge di
p be
ha
vi
o
u
r by
re
d
u
c
i
ng t
h
e pea
k
r
o
t
o
r faul
t
cu
rre
nt
and
min
i
mizin
g
tran
sien
t
o
s
cillati
o
n
s
of electrical to
rqu
e
a
n
d
DFIG tran
sien
t respon
se,
bu
t co
nn
ecting
resi
stan
ces
wi
t
h
st
at
or cre
a
t
e
s a l
a
rge di
ssi
pat
i
on a
nd
m
a
y
di
sconne
ct
generat
o
r.
I
n
[1
1]
, st
at
or
fl
u
x
i
s
regul
at
ed by
i
m
p
r
ov
ing
ro
tor curren
t
con
t
ro
l. During
grid
fau
lt, a
larg
e EMF (
E
lectrom
o
t
i
v
e
f
o
rce)
induced i
n
the
rot
o
r
ci
rcui
t
w
h
i
c
h i
s
t
h
e re
sul
t
of
DC
a
nd
ne
ga
t
i
v
e seq
u
e
n
ce
com
pone
nt
s i
n
duce
d
i
n
t
h
e
s
t
at
or fl
ux
l
i
n
k
a
ge
of
DFI
G
.
A m
odi
fi
ed R
S
C
co
nt
r
o
l
w
h
i
c
h c
ont
r
o
l
s
t
h
e r
o
t
o
r cu
rre
nt
can
be us
ed t
o
op
p
o
se t
h
e DC
a
nd
ne
g
a
t
i
v
e-
sequ
en
ce co
mp
on
en
ts o
f
th
e stato
r
flux
lin
k
a
g
e
. Th
e ad
van
t
ag
e of th
is so
lu
tion
is th
at it d
o
e
s n
o
t
n
e
ed
any
ad
d
ition
a
l co
st
. Bu
t th
e effici
en
cy o
f
th
is meth
od
d
e
p
e
n
d
s
o
n
th
e sev
e
rity o
f
th
e fau
lt and
pre-fau
lt cond
itio
n
o
f
th
e
WT. Con
s
eq
u
e
n
tly, it is on
ly su
itab
l
e
for sm
all d
i
p
s
.
LVRT is a
p
a
rt o
f
th
e
grid
co
d
e
wh
ich
i
n
th
e ev
en
t
o
f
g
r
id
vo
ltag
e
sag
,
th
e
W
T
s are
requ
ired
t
o
rem
a
i
n
con
n
ec
t
e
d t
o
t
h
e
gri
d
fo
r a
speci
fi
c
a
m
ount
o
f
t
i
m
e
bef
o
re
bei
n
g
al
l
o
we
d t
o
di
sc
o
nnect
,
t
h
i
s
s
p
e
c
i
f
i
c
am
ount
of t
i
m
e can be
di
f
f
er
ent
fr
om
one g
r
i
d
co
de t
o
a
n
ot
he
r m
o
reove
r t
h
e se
veri
t
y
of t
h
e
fa
ul
t
m
i
ght
be
di
ffe
re
nt
as we
l
l
.
Fi
gure
1
dep
i
ct
s requi
r
e
m
e
nt
s o
f
t
h
e
WE
C
S
du
ri
n
g
v
o
l
t
a
ge di
ps i
n
di
f
f
ere
n
t
co
unt
ri
es as an
exam
ple [12].
Fi
gu
re
1.
R
e
q
u
i
rem
e
nt
s of t
h
e
W
E
C
S
d
u
r
i
n
g
vol
t
a
ge
di
ps i
n
di
ffe
re
nt
co
u
n
t
r
i
e
s [
1
2]
Fu
rt
h
e
rm
o
r
e, so
m
e
u
tilit
ies req
u
i
re th
at t
h
e
W
T
s h
e
l
p
sup
port grid
vo
ltag
e
d
u
ring
faults. LVRT
depe
n
d
s
on t
h
e
m
a
gni
t
u
de o
f
vol
t
a
ge
d
r
o
p
at
t
h
e P
o
i
n
t
o
f
C
o
m
m
on C
o
u
p
l
i
ng
(PC
C
)
d
u
ri
ng t
h
e fa
ul
t
an
d t
h
e
t
i
m
e
t
a
ken by
t
h
e
gri
d
sy
st
em
t
o
rec
o
ver t
o
t
h
e norm
al state [13].
In
o
r
de
r t
o
o
v
erc
o
m
e
t
h
e afo
r
em
ent
i
one
d
pr
obl
em
s, t
h
i
s
pa
pe
r
pr
o
pos
es a c
o
nt
r
o
l
st
rat
e
gy
t
o
i
m
p
r
ov
e th
e FRT cap
ab
ility o
f
th
e DFIG d
u
r
i
n
g
g
r
i
d
fau
lts in
clu
d
i
ng
g
r
i
d
vo
ltag
e
sag
con
d
itions. Th
e
pr
o
pose
d
s
o
l
u
t
i
on i
n
v
o
l
v
es t
h
e use o
f
dam
p
ing
resi
st
ances
as wel
l
as by
p
a
ss swi
t
c
hi
ng
devi
ces c
o
upl
e
d
wi
t
h
DC circu
it.
Thi
s
pa
per
has
been
or
ga
ni
zed as f
o
l
l
o
ws:
I
n
Sect
i
o
n 2,
D
F
IG
WT sy
st
e
m
m
odel
l
i
ng and c
ont
rol
i
s
descri
bed
.
I
n
Sect
i
on
3, t
h
e
pr
op
ose
d
FR
T cont
rol
st
rat
e
gy
i
s
di
scuss
e
d an
d i
n
Sect
i
on
4, t
h
e si
m
u
l
a
t
i
o
n
resu
lts
with
the p
r
op
osed solu
tio
n
and
with
th
e cr
ow
ba
r
sol
u
t
i
on a
r
e
sho
w
n a
n
d
co
m
p
ared. Fi
nal
l
y
, t
h
e
concl
u
sions a
r
e summ
arized in Section
5.
2.
MODELLING AND
CONTRO
L OF
DFIG SYSTEM
Ty
pi
cal
confi
g
urat
i
o
n o
f
t
h
e WT usi
ng
DFI
G
i
s
sho
w
n i
n
Fi
gu
re 2
.
The
gene
rat
o
r i
s
co
nnect
e
d
t
o
t
h
e
t
u
r
b
i
n
e
vi
a s
h
a
f
t
s
an
d a
gea
r
bo
x.
The
D
F
I
G
i
s
fe
d
fr
om
bot
h st
at
o
r
si
d
e
w
h
i
c
h i
s
di
r
ect
l
y
connect
e
d
t
o
t
h
e
gri
d
, and rotor side that is connected
t
o
a back-to-bac
k
c
o
nve
r
ter and from
th
ere to
th
e grid
.
In
t
h
is way,
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6
,
No
.
4
,
D
ecem
b
er
2
015
:
80
8 – 818
81
0
vari
a
b
l
e
s
p
eed
ope
rat
i
o
n beco
m
e
s
pos
si
ble a
s
m
echanical and electrical ro
tor fre
quencies
are dec
o
uple
d
.
T
h
e
diffe
re
nce bet
w
een
fre
quenc
i
es is co
m
p
ensated by a
power electronic
converte
r
which
in
j
ects th
e ro
tor
cu
rren
t with
variab
le frequ
ency. The aerody
n
am
ic
powe
r
c
ont
rol of th
is ty
pe of
WT is no
rm
ally
perfo
rm
ed
by
pi
t
c
h
co
nt
r
o
l
.
A wel
l
-
k
n
o
w
n
m
e
t
hod f
o
r
DF
IG
p
o
w
er
con
v
e
r
t
e
r
pr
ot
ect
i
on i
s
usi
n
g
C
r
o
w
bar ci
rc
ui
t
.
Th
e
ove
ral
l
pr
ot
ect
i
on sc
hem
e
i
s
that
d
u
ri
ng a
v
o
l
t
a
ge sag t
h
e
g
a
t
e
of R
S
C
i
s
t
u
r
n
e
d
o
ff a
nd t
h
e r
o
t
o
r i
s
co
n
n
ect
ed
to
th
e C
r
owb
a
r circu
it,
DFIG
starts to
act as
a con
v
e
n
tion
a
l
in
du
ctio
n gen
e
rato
r.
Fi
gu
re
2.
The
s
c
hem
a
t
i
c
di
agram
of t
h
e
gri
d
con
n
ect
ed
D
F
I
G
base
d wi
n
d
t
u
r
b
i
n
e
sy
st
em
2.
1.
DFIG
m
o
del
The e
quations
of the electrical
m
odel of
DFIG in
sync
hronous re
fe
re
nce fram
e (dq-fram
e) are
exprese
d
as
[14]:
(1
)
(2
)
(3
)
(4
)
(5
)
(6
)
(7
)
(8
)
Whe
r
e
,
are the
voltage
and curre
n
t;
,
are
the re
sistance
and inductanc
e
;
is th
e m
a
g
n
e
tic
flu
x
;
is the
ge
nerat
o
r m
u
tual inductance;
Subs
cripts
,
,
, a
n
d
refer t
o
the
stator,
r
o
tor
,
d
-
axis a
n
d q
-
axis com
p
one
n
ts res
p
ectivel
y;
;
;
rep
r
es
ents the
diffe
renc
e
bet
w
ee
n sy
nch
r
o
n
ous
spe
e
d
a
n
d
r
o
t
o
r s
p
ee
d;
and
are stator a
n
d rotor
leakage inductance
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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PED
S
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208
8-8
6
9
4
Lo
w Vo
ltag
e
Rid
e
-th
r
ou
gh
C
a
p
a
b
ility Enh
ancemen
t
o
f
Doub
ly Fed
Ind
u
c
ti
o
n
.... (Youn
ess Bou
k
h
r
is)
81
1
Act
i
v
e p
o
w
e
r f
l
ows t
h
ro
u
gh
r
o
t
o
r an
d st
at
or
of t
h
e
gene
rat
o
r an
d com
b
i
n
at
i
on o
f
b
o
t
h
c
o
nst
r
uct
s
t
h
e
to
tal activ
e power. To
tal activ
e an
d reactiv
e po
wers
e
q
uat
i
ons
o
f
DF
IG
ar
e expres
sed as
[15]:
(9
)
(1
0)
2.
2.
Co
ntr
o
l of DF
IG
The power electronic part of the DFIG consists
of t
w
o v
o
l
t
a
ge-so
u
r
ce con
v
e
r
t
e
rs (R
S
C
and GSC
)
and a ca
pacitor in
betwee
n t
h
at is called DC
-link. T
h
e
o
v
e
rall co
n
t
ro
l
o
b
jectiv
es of
v
a
ri
ab
le speed
op
eratio
n
of
WTs are
di
vi
de
d i
n
t
o
el
ec
t
r
i
cal
powe
r
t
r
ansfe
r
co
nt
r
o
l
and
gen
e
rat
o
r
spee
d co
nt
r
o
l
.
The ge
ne
rat
o
r
spee
d
co
n
t
ro
ller is asso
ciated
with RSC an
d
its g
o
a
l is to
co
ntro
l th
e activ
e an
d
reactiv
e
p
o
wer of th
e
DFIG
i
nde
pen
d
e
n
t
l
y
. Th
ou
g
h
t
h
e
G
S
C
kee
p
s t
h
e
DC
-l
i
n
k v
o
l
t
a
g
e
con
s
t
a
nt
rega
rdl
e
ss
of t
h
e
d
i
rect
i
on
of t
h
e
rot
o
r
po
we
r fl
ow
an
d
gene
rat
e
s a
n
i
nde
pen
d
e
n
t
re
act
i
v
e p
o
we
r
w
h
i
c
h i
s
i
n
ject
ed
i
n
t
o
t
h
e
gri
d
.
The stator voltage vector is sel
ect
ed t
o
be al
i
gned t
o
t
h
e d
-
axi
s
o
f
t
h
e d-
q sy
nch
r
on
o
u
s
fram
e
, as
resu
lt:
(
)
By co
n
s
id
ering
th
e
GSC to
b
e
reactiv
e
n
e
u
t
ral (
and t
h
e
converte
rs are
prim
arily used to
su
pp
ly th
e activ
e power
fro
m
th
e ro
to
r t
o
g
r
id
[1
6
]
. So
,
from eq
u
a
tion
(9
) th
e relatio
n
b
e
tween
activ
e
po
wer
and the c
u
rre
nt
s connected
GSC to
t
h
e grid can be deduce
d
as:
(1
1)
In steady-state
and
by ne
gle
c
ting stator
re
sistance
:
,
an
d
fr
om
equat
i
o
ns
(7
)
and (8):
,
. T
h
e
equations
between stator currents
a
n
d
rot
o
r
cur
r
ent
s
can
be
de
duce
d
a
s
:
(1
2)
(1
3)
C
onsi
d
eri
ng t
h
e assum
p
t
i
ons as abo
v
e an
d f
r
o
m
equat
i
ons (
9
) a
nd (
1
0)
, t
h
e exp
r
essi
o
n
s
of t
h
e act
i
v
e
and reactive
power:
(1
4)
(1
5)
In order to ac
hieve indepe
ndent co
ntrol of the stator active power
, and reactive power
by
mean
s of ro
tor cu
rren
t reg
u
l
atio
n
(Fast con
t
ro
l cu
rr
ent
)
, t
h
e instanta
neous three
-
phase
rotor curre
nts
are
sam
p
l
e
d and t
r
ansf
o
r
m
e
d t
o
d-
q c
o
m
pone
nt
s
and
in
th
e
stato
r
-vo
ltag
e
o
r
ie
nted
refe
re
nce fram
e. The
refe
rence
val
u
es f
o
r
and
(
and
) can be
determ
ined directly from
, a
n
d
co
mman
d
s
respectively.
Th
e activ
e power set po
i
n
t of th
e
conv
erter is g
e
n
e
rated
by th
e ro
to
r sp
eed
co
n
t
ro
ller.
Th
e
reactive
po
we
r set
poi
n
t
i
s
base
d
on
t
e
rm
i
n
al
vol
t
a
ge
or
p
o
w
e
r
fact
o
r
c
ont
r
o
l
l
e
r.
In t
h
e
gri
d
si
de
cont
r
o
l
,
gene
r
a
l
l
y
DC
-l
i
nk v
o
l
t
a
ge
is co
m
p
ared
with the refere
nce
D
C
l
i
n
k
vol
t
a
ge
an
d
er
r
o
r
i
s
fe
d t
o
P
I
c
ont
rol
l
e
r t
o
m
a
in
tain
con
s
tan
t
DC-link
v
o
ltage.
C
o
n
s
id
e
r
in
g
b
o
t
h
th
e
co
n
t
r
o
l s
t
r
a
t
e
g
i
e
s
o
n
th
e
s
t
a
t
o
r
a
n
d t
h
e
rot
o
r
sides,
the sc
hem
a
tic of the
vector
cont
rol
st
ruct
ur
e i
s
de
pi
ct
ed i
n
Fi
g
u
re
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
80
8 – 818
81
2
Fi
gu
re
3.
R
o
t
o
r
si
de a
n
d
gri
d
s
i
de co
nt
r
o
l
l
e
rs
3.
THE PROPOSED L
VRT
CONTROL ST
RATEGY
In
th
is section
,
th
e co
n
t
ro
l strateg
y
is p
r
op
osed
to
im
p
r
o
v
e
th
e LVRT capab
ility o
f
th
e DFIG during
t
h
e g
r
i
d
faul
t
s
.
The sc
hem
a
t
i
c di
ag
ram
of t
h
e
dam
p
i
ng re
si
st
ances an
d t
h
e
by
pass
swi
t
chi
n
g
devi
ces
i
n
t
h
e
D
F
IG
syste
m
is show
n in
Figu
r
e
4.
Fi
gu
re 4.
Si
m
u
l
a
t
i
on
co
n
f
i
g
ur
at
i
on of
D
F
I
G
sy
st
em
unde
r g
r
i
d
faul
t
3.
1.
An
al
ysi
s
of
D
F
IG
be
ha
vi
o
u
r
duri
n
g gri
d
vol
ta
ge di
ps
In
ord
e
r to
faci
litate th
e an
alysis o
f
DFIG, the Park
m
o
d
e
l in
th
e
statio
n
a
ry co
ord
i
n
a
te syste
m
is u
s
ed
as [17]:
(1
6)
(1
7)
(1
8)
(1
9)
Whe
r
e
is the
rotor electrical
spee
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Lo
w Vo
ltag
e
Rid
e
-th
r
ou
gh
C
a
p
a
b
ility Enh
ancemen
t
o
f
Doub
ly Fed
Ind
u
c
ti
o
n
.... (Youn
ess Bou
k
h
r
is)
81
3
From
(1
6
)
-
(
1
9
)
t
h
e rot
o
r v
o
l
t
a
ge
ca
n be obt
ai
ned
as:
(2
0)
Whe
r
e:
Th
e stator flux
ind
u
c
ed
in
t
h
e po
ten
tial of th
e ro
t
o
r si
d
e
as ex
pressed
in
(20),
wh
en
v
o
ltag
e
d
i
ps
occu
r i
n
t
h
e p
o
we
r g
r
i
d
, t
h
e
st
at
or v
o
l
t
a
ge
fol
l
o
ws t
h
e c
h
an
ge
of
gri
d
vol
t
a
ge
, b
u
t
fl
ux ca
n
not
be
chan
ge,
lead
in
g to
th
e
ap
p
e
aren
ces
o
f
th
e tran
sien
t
DC co
m
p
on
ent o
f
th
e stato
r
flu
x
,
po
sitiv
e an
d
n
e
g
a
tiv
e seq
u
e
n
c
e
com
pone
nt
s.
Ig
n
o
ri
n
g
t
h
e
v
o
l
t
a
ge d
r
op
on
t
h
e st
at
or re
si
st
ance, t
h
e
rel
a
t
i
ons
hi
p
bet
w
een t
h
e c
o
m
ponent
s
of t
h
e
st
at
or
fl
u
x
a
n
d
t
h
e st
at
or
v
o
l
t
a
ge c
o
m
pone
nt
s
u
nde
r t
h
e fa
ul
t
,
are
ex
pre
ssed
as:
(2
1)
Whe
r
e:
is th
e stato
r
flux
d
u
ring
th
e fau
lt;
is th
e tran
sient DC stato
r
fl
ux
du
ri
n
g
t
h
e fau
lt;
and
are resp
ectiv
ely th
e p
o
s
itiv
e an
d
n
e
g
a
t
i
v
e
sequ
ence of th
e stato
r
flux
du
ri
n
g
t
h
e fau
lt;
for th
e
in
stan
tan
e
ou
s stato
r
vo
ltag
e
before th
e fau
lt;
and
are resp
ectiv
ely th
e p
o
s
itiv
e an
d
n
e
g
a
tiv
e seq
u
en
ce
o
f
th
e stator
vo
ltag
e
d
i
ring
t
h
e
fau
lt;
i
s
t
h
e st
at
or
fl
u
x
t
i
m
e
const
a
nt
o
f
t
h
e t
r
a
n
si
e
n
t
DC
c
o
m
pone
n
t
;
is
stator a
n
gular s
p
ead.
Due to the rot
a
tion of the
roto
r windings
, each seque
n
ce
of st
ator flux com
ponent will
induce a
corres
ponding electrical pot
ential in
the
rot
o
r
winding. In t
h
e roto
r refe
rence
fra
m
e, each se
quence
com
pone
nt
ca
n
be e
x
pres
sed
a
s
:
(2
2)
(2
3)
(2
4)
Whe
r
e:
is th
e
slip
; ,
,
and
are p
o
s
itiv
e seq
u
e
n
ce,
n
e
g
a
t
i
v
e
seq
u
e
n
ce an
d
th
e
DC
com
pone
nt
s o
f
t
h
e st
at
o
r
t
r
a
n
si
ent
s
i
n
duce
d
i
n
t
h
e
rot
o
r
si
d
e
. The
val
u
e
of
t
h
e sl
i
p
ge
nera
l
l
y
bet
w
een
-0
.
3
a
n
d
0
.
3
[1
8
]
, and
fro
m
th
e eq
u
a
tion
(2
2)-(2
4): the p
o
s
itiv
e seque
n
ce co
m
p
on
en
t is p
r
op
ortion
a
l to
th
e slip
(s), th
e
negative se
que
n
ce com
pone
nt is proportional to (2-s)
a
n
d the DC co
m
pone
nt is proportional to the speed.
Su
per
p
osi
t
i
on
of t
h
ese c
o
m
pone
nt
s c
oul
d c
a
use t
h
e
r
o
t
o
r
wi
n
d
i
n
gs t
o
i
n
duce
a l
a
r
g
e E
M
F, an
d
due
t
o
t
h
e
li
mited
cap
acity o
f
th
e RSC
,
th
e latter cann
o
t p
r
o
v
i
d
e
enoug
h
vo
ltag
e
to
reg
u
l
ate th
e EM
F du
ri
n
g
fau
lt,
wh
ich
will lead
to th
e ro
to
r ov
ercurren
t.
Fro
m
th
ese eq
u
a
tion
s
we can
size a contro
ller fo
r t
h
e ro
tor curren
t
with
in
serting
d
a
m
p
in
g
resistances c
oupled
with t
h
e
DC circ
uit.
3.
2.
Met
h
o
d
ol
og
y
of
da
mpi
n
g re
si
stanc
e
s
acti
v
a
ti
on
The DF
I
G
ope
rat
i
on i
s
di
vi
de
d i
n
t
o
t
h
ree
op
erat
i
ng p
h
ase
s
:
pre-
faul
t
,
d
u
r
i
ng fa
ul
t
and
p
o
st
-
f
aul
t
.
I
n
no
rm
al
condi
t
i
ons
, t
h
e
dam
p
i
n
g
resi
st
a
n
ces
pr
ot
ect
i
o
n
i
s
i
n
act
i
v
e. T
h
e L
V
R
T
pr
ot
ect
i
o
n
st
eps f
o
r
vol
t
a
ge
di
ps
are gi
ve
n
i
n
Fi
gu
re 5
a
n
d des
c
ri
be
d bel
o
w:
The g
r
i
d
i
s
m
oni
t
o
re
d fo
r v
o
l
t
a
ge sag
occ
u
r
r
ence
s. O
n
c
e
a gri
d
v
o
l
t
a
ge di
p i
s
det
e
ct
ed, t
h
e dam
p
i
n
g
resistances (DR) are activated. In
th
is step
, DFIG is d
e
mag
n
e
tized
and
th
e d
a
m
p
in
g o
f
th
e tran
sien
t
respon
se is imp
r
ov
ed.
Oth
e
rwise th
e m
o
n
ito
ri
n
g
con
tinu
e
s.
The dam
p
ing resistances re
main activated and the
vo
ltag
e
of DC circu
it (Vd
c
) is
m
o
n
ito
red
.
If
Vdc
decrease
s
bel
o
w a ce
rt
ai
n t
h
r
e
sh
ol
d
DR
a
r
e
di
sabl
e
d
.
Ot
he
r
w
i
s
e, t
h
e
pr
oce
ss co
nt
i
n
ues.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
80
8 – 818
81
4
Th
e grid
is
m
o
n
ito
red
fo
r clearan
ce
o
f
th
e prev
i
o
u
s
ly d
e
tected
fau
lt.
After the fault has been cleared, DR
are a
g
ain activated.
On
ce th
e
g
r
i
d
fau
lt is elimin
ated
, th
e pro
c
ess return
s
to t
h
e first step where the
gri
d
is
m
onitored a
g
ai
n.
The RSC
swit
ches t
o
norm
al operation m
ode to res
u
m
e
real and reacti
v
e powe
r
c
o
ntrol with rate
d
grid
vol
t
a
ge
.
Fig
u
r
e
5
.
Flow ch
ar
t of
p
r
op
osed
LV
RT
str
a
teg
y
4.
SIMULATION AND RESULTS
The sy
st
em
under st
udy
,
gi
ve
n i
n
Fi
gu
re
4,
con
s
i
s
t
s
of a
9
M
W
wi
nd
far
m
(si
x
1.
5M
W
DF
IG
base
d
W
T
)
exp
o
r
ting p
o
w
e
r
t
o
a 120
kV
g
r
id
t
h
roug
h
a
(
30k
m
,
2
5
k
V
)
f
e
ed
er
an
d
tr
an
sf
or
m
e
r
s
(
25k
V
/
1
20kV
)
an
d
(5
7
5
V/
25
k
V
).
In t
h
i
s
st
u
d
y
,
t
h
e si
m
u
l
a
t
i
ons were c
o
nd
uct
e
d u
s
i
n
g M
A
T
L
AB
/
S
IM
U
L
I
N
K s
o
ft
wa
re, c
o
here
nt
m
odel
of t
h
e si
x
gene
rat
o
rs i
s
use
d
. Si
m
u
l
a
t
i
on
pa
ram
e
t
e
rs of
t
h
e
DF
IG
sy
st
em
are p
r
ese
n
t
e
d i
n
Ta
bl
e
1
.
Tabl
e 1. Si
m
u
lat
i
on param
e
t
r
es
o
f
DFI
G
sy
st
em
Para
m
e
ters
Valu
es
Rated power
9 M
W
Power coef
f
i
cient
0.9
Rated voltage
575 V
Rated fr
equency
(F)
50 Hz
Stator resistance
(
R
s
)
0.
0070
6
pu
Rotor resistance (
R
r
)
0.
005 pu
Stator leakage ind
u
ctance (L
ls
) 3.
07
pu
Rotor leakage inductance (
L
l
r
)
3.
056
pu
Stator
and r
o
tor
m
u
tual inductance (
L
m
)
2.
9
pu
Nu
m
b
er
of pole pair
s (
p
)
6
In
t
h
is section
th
e DFIG ri
d
e
-th
r
o
ugh
cap
ab
i
lity is
si
m
u
late
d
fo
r a three
ph
ases
v
o
ltag
e
dip
,
in
wh
ich
t
h
e gri
d
v
o
l
t
a
g
e
i
n
t
h
ree p
h
as
e dr
ops t
o
1
5
%
of i
t
s
n
o
m
i
nal
val
u
e
(8
5
%
vol
t
a
ge
di
p
)
at
t
=
0.9s an
d
l
a
st
s for
30
0m
s. I
n
t
h
i
s
pa
per
,
t
w
o
di
st
i
n
ct
cases a
r
e i
n
ves
tigated and c
o
m
p
are
d
.
In t
h
e
first
case
(Figure
6), the
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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S
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:
208
8-8
6
9
4
Lo
w Vo
ltag
e
Rid
e
-th
r
ou
gh
C
a
p
a
b
ility Enh
ancemen
t
o
f
Doub
ly Fed
Ind
u
c
ti
o
n
.... (Youn
ess Bou
k
h
r
is)
81
5
pr
o
pose
d
LVR
T
ap
pr
oac
h
i
s
appl
i
e
d
,
a
n
d t
h
e seco
n
d
case
(
F
i
g
u
r
e
7)
d
e
m
onst
r
at
es t
h
e
D
F
IG
wi
t
h
t
h
e
c
r
o
w
b
a
r
circuit protecti
o
n.
Figu
re 6. Simu
latio
n
resu
lts
o
f
DFIG system
with
the propos
ed LVRT
st
rategy
under 85% t
h
ree
phase
s
v
o
ltag
e
d
i
p
,
(a) Gri
d
vo
ltag
e
,
(b
) Ro
tor cu
rren
t,
(c)
Electromag
n
e
tic to
rque and
(d)
DC lin
k vo
ltag
e
Fi
gu
re
7.
Si
m
u
l
a
t
i
on res
u
l
t
s
o
f
D
F
I
G
sy
st
em
wi
t
h
t
h
e c
o
n
v
e
n
t
i
onal
c
r
ow
ba
r
pr
ot
ect
i
on,
(a
) G
r
i
d
v
o
l
t
a
ge,
(b
)
Rotor
cu
rre
nt, (c) Electrom
a
gnetic
tor
q
ue
a
n
d (d
) DC
lin
k v
o
ltage
Fig
u
re 6
and
Fig
u
re 7
illu
strate
grid
v
o
ltag
e
, ro
t
o
r curren
t
, electro
m
a
gn
etic to
rq
u
e
an
d
DC-li
n
k
vol
t
a
ge
wave
f
o
rm
s, wi
t
h
t
h
e
p
r
o
p
o
sed
L
V
R
T
ap
pr
oac
h
(Fig
ure
6
)
an
d
with
the crowb
a
r circu
it p
r
otectio
n
(Figu
r
e 7). By ap
p
l
ying
th
e pro
p
o
s
ed
LVRT
so
lu
tion
,
th
e si
m
u
la
tio
n
s
sh
ow
p
o
s
itiv
e results, th
u
s
th
e electrical
val
u
es
i
.
e.
rot
o
r c
u
r
r
ent
,
el
ect
rom
a
gnet
i
c
t
o
r
que
an
d
DC
-l
i
n
k
v
o
l
t
a
ge
ha
v
e
passe
d t
o
re
aso
n
abl
e
val
u
e
s
an
d
m
u
ch
b
e
tter th
an
tho
s
e ob
tain
ed
u
s
ing
th
e
crowb
a
r ci
rc
uit protection. T
h
is im
provem
e
n
t of the elect
rical
v
a
lu
es abo
v
e
-men
tio
n
e
d wil
l
allo
w: (i) Th
e
WT to
re
main connecte
d
to t
h
e gr
id for a long
er ti
m
e
s,
respon
d
i
n
g
to
th
e requ
irem
en
ts of th
e
g
r
id
co
d
e
w
ith
ou
t m
u
ch
trou
b
l
e
an
d
with
ou
t
mak
i
ng
d
a
m
a
g
e
s to
th
e
eq
u
i
p
m
en
t o
f
th
e
W
T
, (ii) Avo
i
d
m
ech
an
ical stress d
u
e
to
t
h
e i
m
p
o
r
tan
t
oscillatio
n
s
d
u
rin
g
fau
lt. So
wi
th
th
e
p
r
op
o
s
ed
LVR
T
so
l
u
tio
n th
e
o
s
cillatio
n
s
and
th
e im
p
act
o
n
th
e fu
n
c
ti
o
n
i
n
g
of th
e DFIG in
cl
u
d
i
n
g
con
v
e
rters
and ca
paci
t
y
are si
gni
fi
cant
l
y
reduce
d
.
On
t
h
e ot
her
han
d
, wi
t
h
t
h
e
us
e of cr
ow
ba
r ci
rcui
t
pr
ot
ect
i
on i
t
i
s
obs
er
ved t
h
at
du
ri
n
g
t
h
e
faul
t
t
h
e rot
o
r c
u
r
r
e
nt
an
d DC
l
i
n
k v
o
l
t
a
ge al
m
o
st
zero
due t
o
t
h
e i
s
ol
at
i
on
o
f
t
h
e
con
v
e
r
ters
(c
o
n
side
red
as im
po
rtant
pa
rt in
the
o
v
er
all
o
p
eratio
n of t
h
e
WT) fro
m
th
e ro
t
o
r
wh
ich loses th
e
co
n
t
ro
l of DFIG, th
is imp
act will resu
lts freq
u
e
n
t
b
r
eakd
own
s
of th
e
W
T
, cu
rren
t an
d
accid
e
n
t
al
d
i
sconn
ectio
n
s
o
f
th
e
W
T
fro
m
th
e g
r
id
, p
o
o
r
q
u
a
lity o
f
serv
ice, grid
cod
e
no
t resp
ected
, very h
i
gh
m
a
i
n
t
e
nance cost
and t
h
e c
o
st
of t
h
e
W
T
s
di
sco
n
n
ect
i
on
i
s
very
penal
i
z
i
ng f
o
r b
o
t
h
t
h
e pro
d
u
cers a
n
d t
h
e
(a)
(b
)
(c)
(d
)
(c)
(d
)
(a)
(b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
80
8 – 818
81
6
gri
d
ope
r
ators.
So it is clear that
t
h
e pe
rf
orm
a
nce
of t
h
e p
r
op
ose
d
LVR
T
approac
h
is m
o
re efficient c
o
m
p
are
d
to
th
e cro
w
b
a
r
circu
it pro
t
ecti
o
n.
Fi
gu
re
8.
Ge
ne
rat
o
r
s
p
eed
u
n
d
er
8
5
% t
h
ree
pha
ses
vol
t
a
ge
di
p
wi
t
h
t
h
e
pr
op
ose
d
L
V
R
T
app
r
oach
Fig
u
r
e
8
dep
i
ct
s th
e gen
e
r
a
tor r
e
spon
se
w
ith
8
5
% thr
ee ph
ases vo
ltag
e
d
i
p w
ith
th
e pr
opo
sed
LV
R
T
ap
pro
ach.
A
s
sh
own
in Figu
re 8
,
th
e
operati
n
g spee
d
be
fore the fault is
1.
20
5
p
u
an
d t
h
e
m
a
xim
u
m
gen
e
rat
o
r
spee
d d
u
r
i
n
g t
h
e f
a
ul
t
i
s
1.
24
4p
u.
Th
us
, t
h
e
gene
rat
o
r s
lip
s du
ring
and
after th
e
fau
lt is with
in
t
h
e allowab
l
e
ran
g
e a
n
d t
h
e
back
-t
o
-
bac
k
c
o
n
v
e
r
t
e
r i
s
a
b
l
e
t
o
ha
ndl
e t
h
e
sl
i
p
po
wer
.
F
u
rt
herm
ore,
g
r
owt
h
of
t
h
e
ge
nerat
o
r
sp
eed
d
u
ring
t
h
e
fau
lt is
relativ
ely lo
w. Th
erefor
e, t
h
e system
d
o
e
s no
t face ang
l
e-sp
eed i
n
stab
ility.
Fi
gu
re
9.
Eval
uat
i
o
n
o
f
DF
I
G
st
at
o
r
cu
rrent, (a) with th
e
pr
opo
sed LV
RT app
r
o
a
ch
(b)
w
ith
th
e conv
en
tio
n
a
l
cr
owb
a
r
pr
o
t
ectio
n
Fig
u
r
e
9
d
e
p
i
cts th
r
ee ph
ases stato
r
cu
rr
en
t w
ith
th
e pr
oposed
LV
RT
(
F
i
g
ur
e 9
a
)
and
th
e cro
w
b
a
r
circuit protection (Figure
9b).
Figure
9a shows that the stator currents
take acceptable va
lues during and after
clearin
g
t
h
e fau
lt, in
th
e
op
po
site Figu
re
9b
sh
ows th
at t
h
e stator curre
nts alm
o
st zero during the
fault and
tak
e
v
e
ry h
i
gh
v
a
lu
es after clearing
th
e
fau
lt
(up
to
5
.
9
tim
e
s
th
e no
m
i
n
a
l
v
a
lu
e), so
it is clear th
at after
LVRT
com
p
ensation the stator
cu
rr
en
ts
a
r
e b
a
lan
c
ed
.
5.
CO
NCL
USI
O
N
Th
is
p
a
p
e
r
p
r
esen
ts a LVRT
strateg
y
to
m
a
i
n
ta
in
th
e pro
d
u
c
tio
n of
D
F
IG
-b
ased
W
T
s
an
d pr
event
d
e
terioration
of th
e con
v
e
rters wh
en th
e
pow
er
gr
id
is exper
i
en
cing
a
f
a
ult.
The st
rat
e
gy
pre
s
ent
e
d i
s
b
a
sed
on
the us
e of t
h
e
dam
p
ing
resis
t
ances a
n
d swi
t
ching de
vices
connecte
d
to
the DC ci
rcuit
.
The res
u
lts
of the
sim
u
lation of t
h
e system
show that
t
h
e
pr
o
pos
ed
st
rat
e
gy
reg
u
l
a
t
e
s t
h
e
DC
v
o
l
t
a
ge
an
d si
gni
fi
ca
nt
l
y
red
u
ces
the peak val
u
e
s
of t
h
e rot
o
r,
stator
cu
rren
t,
an
d th
e electromag
n
e
tic to
rque
, it also m
i
nimizes the oscil
l
ations
o
f
th
e
electromag
n
e
tic torqu
e
and
th
e in
t
e
rm
ed
iate circu
it vo
ltag
e
du
rin
g
t
h
e
fau
lt an
d im
p
r
o
v
e
s t
h
e FR
T
cap
ab
ility o
f
th
e DFIG. As resu
lt th
e
W
T
eq
u
i
p
m
en
ts
will b
e
well p
r
o
t
ected
an
d
th
e i
m
p
o
r
tan
t
co
st o
f
replacem
ent of suc
h
e
q
uipm
ent will
be a
v
oided, also
t
h
e WT operating ti
m
e
is
m
a
xi
mized.
The
r
efore,
the
p
r
op
o
s
ed
so
l
u
tio
n is m
o
re efficien
t th
an
th
e crowbar so
l
u
tion
.
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BIOGRAP
HI
ES
OF AUTH
ORS
Y
o
u
n
e
s
s
Bouk
hris
was born in
Taouna
te, Moro
cco in 1988. He
receiv
e
d his en
gineer degr
ee
in Electronic Sy
stems and Te
lecomunication in 2012, from
Sidi Mohamed
Ben Abellah
University
, Facu
lty
of Science
and Techno
log
y
Fez, Morocco. I
n
2013, he jo
ined the Signals,
S
y
stems and Co
mponents Labor
ator
y
at Sidi M
ohamed Ben Ab
dell
ah University
,
to pursue
his Ph.D. His f
i
elds of in
ter
e
st in
clude r
e
ne
wab
l
e
energ
y
,
pow
er
e
l
ec
tronics
and s
m
art grids
.
Abou
bakr
El
M
a
kr
ini
was born in Morrocco in 1978. He receiv
e
d the
Engineer degr
ee in
electrical
engin
e
ering from Hassan II Universi
ty
,
Casablan
ca in
2002. He is curr
ently
a PhD
student at Sidi Mohamed Ben
Abdellah
Universit
y
.H
is m
a
i
n
resear
ch in
te
rests includ
e
ele
c
tri
cal
grid
, p
o
wer s
y
s
t
em
s
an
d renew
a
ble
en
e
r
g
y
s
y
s
t
em
s
.
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