Inter
national
J
our
nal
of
P
o
wer
Electr
onics
and
Dri
v
e
Systems
(IJPEDS)
V
ol.
7,
No.
3,
September
2016,
pp.
677
–
686
ISSN:
2088-8694
677
Backstepping
Contr
ol
of
W
ind
and
Photo
v
oltaic
Hybrid
Renewable
Ener
gy
System
Mar
ouane
El
Azzaoui
*
,
Hassane
Mahmoudi
*
,
and
Karima
Boudaraia
*
*
Electronics
Po
wer
and
Control
T
eam,
Department
of
Electrical
Engineering,
Mohammadia
School
of
Engineers,
Mohammed
V
Uni
v
ersity
,
Rabat,
Morocco.
Article
Inf
o
Article
history:
Recei
v
ed
Jun
14,
2016
Re
vised
Aug
19,
2016
Accepted
Aug
30,
2016
K
eyw
ord:
Doubly
fed
induction
generator
W
ind
turbine
Backstepping
control
L
yapuno
v
approach
PV
system
ABSTRA
CT
This
paper
deals
with
the
interconnected
grid
h
ybrid
rene
w
able
ener
gy
system
(HRES).
The
w
ind
ener
gy
con
v
ersion
system
(WECS),
is
b
uilt
around
a
wind
turbine
coupled
to
a
doubly
fed
induction
generator
(DFIG).
The
stator
of
DFIG
is
directly
related
to
the
grid
and
the
rotor
is
connected
to
the
grid
through
back-to-back
po
wer
con
v
erters.
The
proposed
algorithm
combines
the
nonlinear
Backstepping
approach
and
the
field
orientation
applied
to
control
the
DFIG.
In
a
first
step,
this
technique
is
applied
to
the
side
con
v
erter
rotor
(RSC),
to
control
the
electromagnetic
torque
and
reacti
v
e
po
wer
,
and
secondly
,
it
is
applied
to
the
grid
side
con
v
erter
(GSC)
to
control
the
po
wer
e
xchanged
with
the
grid
and
re
gulate
the
DC
b
us
v
oltage.
The
PV
ener
gy
system
is
composed
by
the
PV
array
and
the
DC-DC
boost
con
v
erter
which
controlled
by
the
MPPT
method
to
e
xtract
the
optimal
po
we
r
.
Simulations
results
present
the
performances
in
terms
of
set
point
tracking,
stability
,
and
rob
ustness
with
respect
to
the
v
ariation
in
wind
speed
and
irradiation.
Copyright
c
2016
Insitute
of
Advanced
Engineeering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Marouane
El
Azzaoui
Electronics
Po
wer
and
Control
T
eam,
Department
of
Electric
al
Engineering,
Mohammadia
School
of
Engineers,
Mo-
hammed
V
Uni
v
ersity
,
Rabat,
Morocco.
E-mail:
marouane.elazzaoui@research.emi.ac.ma
1.
INTR
ODUCTION
Hybrid
systems
rene
w
able
ener
gies
(HRES)
are
became
popular
in
the
typologies
of
rene
w
able
ener
gy
.
A
HRES
is
composed
of
tw
o
or
more
rene
w
able
ener
gy
sources
with
appropriate
ener
gy
con
v
ersion
technology
con-
nected
together
to
feed
po
wer
to
the
local
load
or
grid
[1].
W
e
are
intereste
d
in
this
paper
to
combine
wind
and
PV
because
the
y
are
the
most
promising
technologies
for
s
upplying
load
in
remote
and
rural
re
gions.
The
most
used
generator
in
wind
turbine
is
the
DFIG
due
to
its
adv
antages
in
v
ariable
wind
speed
such
as
the
lo
w
sizing
of
the
back-to-back
con
v
erter
,
and
its
stability
on
the
h
ypo
and
h
yper
synchronous
modes
[2].
This
paper
presents
a
theoretical
frame
w
ork
for
a
Backstepping
control
strate
gy
of
the
doubly
fed
induction
generator
and
related
po
wer
equipments.
This
technique
is
a
relati
v
ely
ne
w
control
method
for
nonlinear
systems.
It
allo
ws
sequentially
and
systematically
,
to
determine
the
system’
s
control
la
w
,
by
the
choice
of
a
L
yapuno
v
function.
Its
principle
is
to
set
up
in
a
constructi
v
e
manner
the
control
la
w
of
the
non
l
inear
system
by
considering
some
state
v
ariables
as
virtual
dri
v
es
and
de
v
elop
intermediate
control
la
ws
[3].
The
DC-DC
boost
con
v
erter
is
controlled
by
MPPT
strate
gy
to
follo
ws
the
maximum
po
wer
point.
This
paper
is
or
g
anized
as
follo
ws:
in
Section
2,
a
brief
description
of
the
system
studied
is
presented.
In
section
3,
the
modeling
of
the
turbine,
the
DFIG,
and
the
photo
v
oltaic
system
is
presented
respecti
v
ely
.
In
the
section
4,
the
control
strate
gy
of
the
h
ybrid
wind/PV
system
is
depicted,
in
which
we
propose
a
backstepping
control
for
the
RSC
and
GSC
respecti
v
ely
.
Then
the
MPPT
PV
subsystem
is
sho
wn
and
the
DC-b
us
v
oltage
is
e
xposed.
The
control
performances
are
illustrated
through
numerical
simulations
in
section
6.
J
ournal
Homepage:
http://iaesjournal.com/online/inde
x.php/IJPEDS
Evaluation Warning : The document was created with Spire.PDF for Python.
678
ISSN:
2088-8694
2.
PRESENT
A
TION
OF
THE
STUDIED
SYSTEM
The
basic
configuration
of
the
whole
system
is
presented
in
figure
(1).
The
studied
system
is
formed
by
three
bladed
rotors
with
a
corresponding
mechanical
gearbox,
a
DFIG,
tw
o
po
wer
con
v
erters
(RSC
and
GSC),
a
DC
b
us
v
oltage,
a
PV
generator
,
a
DC-DC
boost
con
v
erter
and
a
grid
filter
.
The
coupling
of
the
tw
o
subsystems
(wind
and
PV)
is
made
via
a
DC-b
us.
GSC
w
orks
as
a
rectifier
and
RSC
w
orks
as
an
in
v
erter
when
the
machine
is
dri
v
en
belo
w
synchronous
speed.
In
this
case
the
rotor
of
the
DFIG
recei
v
es
the
po
wer
from
the
grid.
When
the
machine
is
dri
v
en
abo
v
e
the
synchronous
speed,
GSC
w
orks
as
an
in
v
erter
and
RSC
w
orks
as
a
rectifier
,
in
this
case
the
rotor
of
the
DFIG
generates
the
po
wer
to
the
grid.
RSC
GSC
Blade
DFIG
Grid
Gearbox
P
f
P
r
P
s
i
s
i
r
i
g
i
f
Ω
P
g
P
V
Boost
Converter
P
pv
Figure
1.
W
ind
ener
gy
con
v
ersion
system
3.
MODELING
OF
THE
HYBRID
WIND/PV
SYSTEM
COMPONENTS
3.1.
T
urbine
modeling
The
e
xpression
of
aerodynamic
po
wer
of
the
turbine
is
gi
v
en
by:
P
t
=
1
2
::
:R
2
:C
p
(
;
)
:v
3
(1)
is
the
air
density
,
R
is
the
blade
radius,
is
the
speed
ratio,
is
the
pitch
angle
,
v
is
the
wind
speed,
and
C
p
is
the
po
wer
coef
ficient
The
e
xpression
of
the
torque
is
obtained
by
di
viding
the
po
wer
by
the
torque
speed.
T
t
=
1
2
t
::
:R
2
:C
p
(
;
)
:v
3
(2)
Po
wer
coef
ficient
is
gi
v
en
as
function
of
pitch
angle
and
speed
ratio,
i
ts
e
xpression
in
this
w
ork
is
e
xpressed
by
the
the
follo
wing
equation
[4]:
C
p
(
;
)
=
A:
sin
:
(
+
0
:
1)
14
:
34
0
:
3
:
(
2)
B
(3)
with:
[
A
=
0
:
35
0
:
0167
:
(
2)
and
B
=
0
:
00184
:
(
3)(
2)
.
The
speed
ratio
is
gi
v
en
by:
=
R
t
v
(4)
Speeds
and
torques
of
the
turbine
and
the
generator
are
related
respecti
v
ely
by:
T
t
=
GT
g
(5)
IJPEDS
V
ol.
7,
No.
3,
September
2016:
677
–
686
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
679
=
G
t
(6)
The
dynamics
of
the
mechanical
speed
of
the
DFIG
is
obtained
by
applying
the
fundamental
equation
of
dynamics:
J
d
dt
=
T
g
f
T
em
(7)
Where:
T
em
is
the
electromagnetic
torque,
J
is
the
total
inertia,
and
f
is
the
friction
coef
ficient.
Figure
(2)
sho
ws
the
block
diagram
of
the
turbine
obtained
by
the
abo
v
e
equations.
C
p
λ
λ
=
R
Ω
t
Ω
t
v
1
G
1
G
1
J
s
+
f
v
T
t
T
g
T
e
m
Ω
1
2Ω
t
.ρ.π.R
2
.C
p
(
λ,
β
)
.v
3
Figure
2.
Block
diagram
of
the
turbine
C
p
λ
λ
=
R
Ω
t
Ω
t
v
1
G
1
G
1
J
s
+
f
v
T
t
T
g
Ω
1
2Ω
t
.ρ.π.R
2
.C
p
(
λ,
β
)
.v
3
T
∗
em
1
2
G
3
λ
3
opt
C
pmax
ρπ
R
5
Ω
2
−
f
Ω
Figure
3.
Block
diagram
of
wind
turbine
MPPT
3.2.
W
ind
turbine
Maximum
po
wer
extraction
In
this
section,
a
MPPT
technique
without
sensing
the
wind
speed
is
presented.
The
strate
gy
proposed
assumes
that
the
wind
speed
v
aries
a
little
in
permanent
re
gime.
Under
this
consideration
the
mechanical
equation
is
described
by
[5]:
J
d
m
dt
=
0
=
T
mec
=
T
f
a
T
em
f
(8)
Electromagnetic
torque
e
xpression
becomes:
T
em
=
1
2
G
t
C
pmax
S
v
3
f
(9)
in
this
w
ork
the
pitch
angle
is
maintained
constant.
Equation
(4)
allo
ws
to
estimate
the
wind
speed
as
follo
ws:
v
=
R
t
opt
(10)
Substituting
Equation
(10)
in
(9)
The
electromagnetic
torque
reference
becomes:
T
em
=
1
2
G
3
3
opt
C
pmax
R
5
2
f
(11)
The
block
diagram
of
the
MPPT
without
sensing
the
wind
speed
is
sho
wn
in
figure
(3).
3.3.
DFIG
modeling
Stator
and
rotor
v
oltages
of
the
DFIG
in
d-q
frame
reference
is
written
as
follo
ws
[6]:
8
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
:
V
sd
=
R
s
I
sd
+
d'
sd
dt
!
s
'
sq
V
sq
=
R
s
I
sq
+
d'
sq
dt
+
!
s
'
sd
V
r
d
=
R
r
I
r
d
+
d'
r
d
dt
!
r
'
r
q
V
r
q
=
R
r
I
r
q
+
d'
r
q
dt
+
!
r
'
r
d
(12)
Bac
kstepping
Contr
ol
of
wind
and
photo
voltaic
hybrid
Rene
wable
Ener
gy
System
Evaluation Warning : The document was created with Spire.PDF for Python.
680
ISSN:
2088-8694
Stator
and
rotor
flux
are
e
xpressed
by:
8
>
>
>
<
>
>
>
:
'
sd
=
L
s
I
sd
+
L
m
I
r
d
'
sq
=
L
s
I
sq
+
L
m
I
r
q
'
r
d
=
L
r
I
r
d
+
L
m
I
sd
'
r
q
=
L
r
I
r
q
+
L
m
I
sq
(13)
Stator
,
rotor
,
and
mechanical
speed
are
link
ed
by
the
follo
wing
equation:
!
r
=
!
s
p
(14)
Stator
and
rotor
e
xpressions
of
the
acti
v
e
and
reacti
v
e
po
wers
are
gi
v
en
by:
8
>
>
>
<
>
>
>
:
P
s
=
V
sd
I
sd
+
V
sq
I
sq
Q
s
=
V
sq
I
sd
+
V
sd
I
sq
P
r
=
V
r
d
I
r
d
+
V
r
q
I
r
q
P
r
=
V
r
q
I
r
d
+
V
r
d
I
r
q
(15)
The
electromagnetic
torque
is
gi
v
en
by:
T
em
=
pL
m
L
s
(
'
sq
I
r
d
'
sd
I
r
q
)
(16)
W
e
consider
the
assumption
that
the
stator
resistance
is
ne
glected.
This
assumption
is
v
erified
for
the
medium
and
high
po
wer
machines
used
in
wind
turbines
[7].
Under
stator
field
orientation
control,
stator
v
oltage
becomes:
(
V
ds
=
0
V
q
s
=
V
s
=
!
s
'
sd
(17)
The
e
xpressions
of
the
acti
v
e
and
reacti
v
e
po
wer
equations
become:
8
>
>
<
>
>
:
P
s
=
V
s
L
m
L
s
I
r
q
Q
s
=
V
s
Lm
Ls
I
r
d
+
V
2
s
!
s
Ls
(18)
The
electromagnetic
torque
becomes:
T
em
=
pLmV
s
!
s
L
s
I
r
q
(19)
Hence,
rotor
currents
as
function
of
the
rotor
v
oltages
is
gi
v
en
by:
8
>
>
<
>
>
:
dI
r
d
dt
=
1
Lr
(
V
r
d
R
r
I
r
d
+
Lr
!
r
I
r
q
)
dI
r
q
dt
=
1
Lr
(
V
r
d
R
r
I
r
q
Lr
!
r
I
r
d
g
L
m
V
s
L
s
)
(20)
3.4.
Photo
v
oltaic
system
modeling
The
phenomenenon
named
photo
v
oltaic
ef
fect
consists
mainly
transforming
the
solar
light
in
electric
ener
gy
by
means
of
the
semi
conductor
de
vices
named
photo
v
oltaic
cells.
Figure
(4)
sho
ws
the
equi
v
alent
circuit
diagram
of
a
single
solar
cell.
Here
I
ph
is
the
photo
current
source
with
a
re
v
erse
connected
diode.
R
s
and
R
sh
are
series
and
shunt
resistances
respecti
v
ely
.
IJPEDS
V
ol.
7,
No.
3,
September
2016:
677
–
686
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
681
I
ph
R
sh
R
s
D
I
pv
V
pv
Figure
4.
Electric
model
of
a
photo
v
oltaic
cell
The
output
current
from
the
photo
v
oltaic
array
is:
I
pv
=
I
ph
I
d
(21)
The
direct
current
diode
is
writing
as
follo
ws:
I
d
=
I
s
exp
q
V
d
K
T
1
(22)
Where
I
s
is
the
re
v
erse
saturation
current
of
the
diode,
q
is
the
electron
char
ge,
V
d
is
the
v
oltage
across
the
diode,
K
is
Boltzmann
constant
1
:
38
10
19
J
=K
and
T
is
the
junction
temperature
in
K
elvin
(k).
Substituting
(22)
in
(21)
gi
v
es:
I
pv
=
I
ph
I
s
exp
q
V
d
K
T
1
(23)
The
v
oltage
across
diode
writes
as:
V
d
=
V
pv
I
pv
R
s
N
(24)
Substituting
(24)
in
(23)
gi
v
es:
I
pv
=
I
ph
I
s
exp
q
(
V
pv
I
pv
R
s
)
N
K
T
1
(25)
Where,
V
pv
is
the
PV
cell
v
oltage
and
N
is
the
diode
ideality
f
actor
.
4.
HYBRID
WIND/PV
SYSTEM
CONTR
OL
STRA
TEGY
Each
of
the
tw
o
ener
gy
sources
(W
ind
and
PV)
is
controlled
so
as
to
deli
v
er
ener
gy
at
optimum
ef
ficienc
y
.
The
adapti
v
e
Backst
epping
control
is
emplo
yed
t
o
achie
v
e
maximum
po
wer
tra
cking
for
a
DFIG
dri
v
en
by
a
wind
turbine
and
PV
to
deli
v
er
this
MPPT
to
re
gulate
the
output
v
oltage.
4.1.
Backstepping
contr
ol
of
RSC
The
basic
idea
of
the
Backstepping
design
is
the
use
of
the
so-called
virtual
control
to
systematically
decom-
pose
a
comple
x
nonlinear
control
design
problem
into
simpler
,
smaller
ones.
Roughl
y
speaking,
Ba
ckstepping
design
is
di
vided
into
v
arious
design
steps
[8,
9].
In
each
step
we
essentially
deal
with
an
easier
,
single-input-single-output
design
problem,
and
each
step
pro
vides
a
reference
for
the
ne
xt
design
step.
The
o
v
erall
stability
and
performance
are
achie
v
ed
by
a
L
yapuno
v
function
for
the
whole
system.
The
synthesis
of
this
control
can
be
achie
v
ed
in
tw
o
steps
[10].
4.1.1.
Step
1:
calculation
of
the
r
otor
curr
ents
Let’
s
define
e
1
the
error
between
the
actual
reference
toques,
and
e
2
the
error
between
the
stator
reacti
v
e
po
wer
and
its
reference.
(
e
1
=
T
em
T
em
e
2
=
Q
s
Q
s
(26)
Bac
kstepping
Contr
ol
of
wind
and
photo
voltaic
hybrid
Rene
wable
Ener
gy
System
Evaluation Warning : The document was created with Spire.PDF for Python.
682
ISSN:
2088-8694
The
deri
v
ati
v
e
of
errors
are
calculated
as:
8
>
>
<
>
>
:
_
e
1
=
_
T
em
+
pLmV
s
!
s
L
s
_
I
r
q
_
e
2
=
_
Q
s
+
L
m
V
s
L
s
_
I
r
d
(27)
The
first
L
yapuno
v
function
is
defined
as:
V
1
=
1
2
e
2
1
+
1
2
e
2
2
(28)
Its
deri
v
ati
v
e
is:
_
V
1
=
e
1
_
e
1
+
e
2
_
e
2
(29)
Substituting
(27)
into
(29),
we
get:
_
V
1
=
e
1
_
T
em
+
pL
m
V
s
L
r
L
s
!
s
V
r
q
R
r
I
r
q
!
r
I
r
d
g
L
m
V
s
L
s
+
e
2
_
Q
s
+
L
m
V
s
L
r
L
s
(
V
r
d
R
r
I
r
d
+
!
r
I
r
q
)
(30)
T
o
track
references
v
alues
of
the
torque
and
reacti
v
e
po
wer
,
references
rotor
currents
are
calculated
as
follo
ws:
8
<
:
I
r
q
=
A
1
[
k
1
e
1
+
T
em
+
A
2
(
V
r
q
L
r
!
r
I
r
d
g
L
m
V
s
L
s
)]
I
r
d
=
B
1
[
k
2
e
2
+
Q
s
+
B
2
(
V
r
d
+
L
r
!
r
I
r
q
)]
(31)
W
ith
:
A
1
=
L
r
L
s
!
s
pL
m
V
s
R
r
A
2
=
L
r
pL
m
V
s
!
s
L
s
B
1
=
L
r
L
s
L
m
V
s
R
r
B
2
=
L
r
L
s
L
m
V
s
where
k
1
and
k
2
are
positi
v
e
constants.
The
deri
v
ati
v
e
of
the
L
yapuno
v
function
is
ne
g
ati
v
e:
_
V
1
=
k
1
e
2
1
k
2
e
2
2
<
0
(32)
4.1.2.
Step
2:
calculation
of
the
r
otor
v
oltages
In
this
step,
the
rotor
currents
errors,
are
defined
by:
(
e
3
=
I
r
q
I
r
q
e
4
=
I
r
d
I
r
d
(33)
Their
deri
v
ati
v
es
are:
8
>
>
<
>
>
:
_
e
3
=
_
I
r
q
1
L
r
V
r
q
+
C
1
_
e
4
=
_
I
r
d
1
L
r
V
r
d
+
C
2
(34)
with:
C
1
=
1
l
r
R
r
I
r
q
+
L
r
!
r
I
r
d
+
g
L
m
V
s
L
s
C
2
=
1
l
r
(
R
r
I
r
d
L
r
!
r
I
r
q
)
Final
L
yapuno
v
function
is
defined
by
the
follo
wing
equation:
V
2
=
1
2
(
e
2
1
+
e
2
2
+
e
2
3
+
e
2
4
)
(35)
its
deri
v
ati
v
e
is:
_
V
2
=
e
1
_
e
1
+
e
2
_
e
2
+
e
3
_
e
3
+
e
4
_
e
4
(36)
IJPEDS
V
ol.
7,
No.
3,
September
2016:
677
–
686
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
683
PWM
RSC
I
r
d
I
r
q
C
a
l
cu
l
a
t
i
o
n
C
a
l
cu
l
a
t
i
o
n
C
a
l
cu
l
a
t
i
o
n
C
a
l
cu
l
a
t
i
o
n
e
1
e
2
T
∗
em
T
em
Q
∗
s
Q
s
I
∗
r
d
I
∗
r
d
I
∗
r
q
I
∗
r
q
e
3
e
4
V
∗
r
d
V
∗
r
d
V
∗
r
q
V
∗
r
q
Figure
5.
Block
diagram
of
backstepping
control
of
the
RSC
By
Substituting
all
errors
e
xpressions,
we
get
the
ne
xt
e
xpression
of
the
lyapuno
v
function:
_
V
2
=
k
1
e
2
1
k
2
e
2
2
k
3
e
2
3
k
4
e
2
4
+
e
3
(
k
3
e
3
+
_
I
r
q
1
L
r
V
r
q
+
C
1
)
+
e
4
(
k
4
e
4
+
_
I
r
d
1
L
r
V
r
d
+
C
2
)
(37)
Therefore,
the
rotor
v
oltages
are
gi
v
en
by:
(
V
r
q
=
L
r
(
k
3
e
3
+
_
I
r
q
+
C
1
)
V
r
d
=
L
r
(
k
4
e
4
+
_
I
r
d
+
C
2
)
(38)
Where
k
3
and
k
4
are
positi
v
e
constants.
So,
the
lyapuno
v
function
is
ne
g
ati
v
e
as
sho
wn
in
the
ne
xt
equation:
_
V
2
=
k
1
e
2
1
k
1
e
2
2
k
3
e
2
3
k
4
e
2
4
<
0
(39)
Block
diagram
of
the
RSC
control
is
presented
in
figure
(5).
4.2.
Backstepping
Contr
ol
of
Grid
side
con
v
erter
The
currents
crossing
the
RL
filter
,
are
e
xpressed
in
d-q
frame
reference
by:
8
>
>
<
>
>
:
dI
f
d
dt
=
V
f
d
L
f
R
f
Lf
I
f
d
+
!
s
I
f
q
dI
f
q
dt
=
V
f
q
L
f
R
f
Lf
I
f
q
!
s
I
f
d
+
V
sq
L
f
(40)
Considering
the
stator
field
orientation
(
V
sd
=
0
).
The
po
wers
pro
vided
by
GSC
are
gi
v
en
by:
(
P
f
=
V
sq
I
f
q
Q
f
=
V
sq
I
f
d
(41)
The
control
of
po
wers
is
obtained
by
controlling
the
currents,
this
is
wh
y
errors
e
1
and
e
2
are
the
dif
ference
between
the
desired
and
actual
d-q
currents:
(
e
1
=
(
I
f
d
)
d
I
f
d
e
2
=
(
I
f
q
)
d
I
f
q
(42)
Their
deri
v
ati
v
es
are:
8
>
>
<
>
>
:
_
e
1
=
(
_
I
f
d
)
d
+
V
f
d
L
f
+
R
f
Lf
I
f
d
!
s
I
f
q
_
e
2
=
(
_
I
f
q
)
d
+
V
f
q
L
f
+
R
f
Lf
I
f
q
+
!
s
I
f
d
V
sq
L
f
(43)
The
lyapuno
v
function
is
chosen
as:
V
=
1
2
(
e
2
1
+
e
2
2
)
(44)
Bac
kstepping
Contr
ol
of
wind
and
photo
voltaic
hybrid
Rene
wable
Ener
gy
System
Evaluation Warning : The document was created with Spire.PDF for Python.
684
ISSN:
2088-8694
Its
deri
v
ati
v
e
is:
_
V
=
e
1
_
e
1
+
e
2
_
e
2
(45)
Replacing
the
terms
of
errors,
we
get:
_
V
=
e
1
(
_
I
f
d
)
d
+
V
f
d
L
f
+
R
f
Lf
I
f
d
!
s
I
f
q
+
e
2
(
_
I
f
q
)
d
+
V
f
q
L
f
+
R
f
Lf
I
f
q
+
!
s
I
f
d
V
sq
L
f
(46)
Finnaly
,
the
control
v
oltages
is
gi
v
en
by:
8
>
>
<
>
>
:
V
f
d
=
L
f
(
_
I
f
d
)
d
+
R
f
Lf
I
f
d
!
s
I
f
q
+
k
1
e
1
V
f
q
=
L
f
(
_
I
f
q
)
d
+
R
f
Lf
I
f
q
+
!
s
I
f
d
V
sq
L
f
+
k
2
e
2
(47)
Where
k
1
and
k
2
are
positi
v
e
constants.
Block
diagram
of
the
RSC
control
is
presented
in
figure
(6).
PWM
GSC
I
f
d
(
I
f
q
)
d
(
I
f
d
)
d
I
f
q
C
a
l
cu
l
a
t
i
o
n
C
a
l
cu
l
a
t
i
o
n
V
f
d
V
f
q
V
f
d
V
f
q
e
1
e
2
Figure
6.
Backstepping
control
of
the
GSC
I
pv
I
L
L
pv
C
pv
V
pv
K
V
dc
I
pv
D
C
Figure
7.
Circuit
Diagram
of
boost
con
v
erter
4.3.
Contr
ol
of
PV
subsystem
In
a
DC-DC
Boost
con
v
erter
,
the
a
v
erage
output
v
oltage
V
out
is
greater
than
the
input
v
oltage
V
in
[11].
Boost
Con
v
erter
mainly
consists
of
one
inductor
and
tw
o
switches
(usually
a
transistor
switch
and
a
diode)
as
sho
wn
in
figure
(7).
The
output
v
oltage
of
boost
con
v
erter
is
gi
v
en
by:
V
out
=
V
in
1
D
(48)
While
D
is
the
duty
c
ycle.
The
commonly
used
control
technique
of
the
PV
subsystem
is
the
MPPT
method
that
acting
on
the
duty
c
ycle
automatically
of
the
boos
t
con
v
erter
to
bring
the
PV
at
its
optimum
operating
v
alue
whate
v
er
the
weather
instability
or
sudden
v
ariations
in
loads
that
can
occur
at
an
y
ti
me
as
presented
in
the
figure.9.
The
classical
MPPT
technique
is
the
P&O
algorithm
which
consists
of
creating
a
perturbation
by
decreasing
or
increasing
the
duty
c
ycle
of
the
boost
con
v
erter
and
then
observing
the
direction
of
po
wer
change
in
the
PV
output.
If
the
PV
po
wer
increases,
the
direction
of
perturbation
is
maintained.
Otherwise,
it
is
re
v
ersed
to
resume
con
v
er
g
e
nce
to
w
ards
the
ne
w
maximum
po
wer
point.The
flo
w
chart
of
the
P&O
algorithm
is
sho
wn
in
Figure
(8).
4.4.
DC
b
us
v
oltage
contr
ol
By
ne
glecting
the
con
v
erter
losses,
In
subsynchronous
mode
the
flo
w
of
po
wers
is
written
as
[12]:
P
f
=
P
c
+
P
r
P
pv
(49)
Where
P
c
=
V
dc
i
c
is
the
po
wer
in
the
DC
b
us.
By
adjusting
the
po
wer
P
f
,
it
is
possible
to
control
the
po
wer
P
c
in
the
capacitor
and
therefore
to
re
gulate
the
DC
b
us
v
oltage
(Figure
10).
IJPEDS
V
ol.
7,
No.
3,
September
2016:
677
–
686
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
685
Start
measure
V
(k)
I
(k)
and
P
(k)
=
V
(k)
x
I
(k)
P
(k-1)
P
(k)
>
V
(k-1)
V
(k)
>
V
(k-1
)
V
(k)
>
D
(k)
=
D
(
k-1)
Δ
D
+
D
(k)
=
D
(k-1)
Δ
D
D
(k)
=
D
(k-1)
Δ
D
D
(k)
=
D
(
k-1
)
Δ
D
+
-
-
Y
e
s
N
o
Y
e
s
N
o
N
o
Y
e
s
Figure
8.
Flo
w
chart
of
Perturb
and
observ
e
algorithm
P
V
Boost
converter
Load
MPPT
control
Duty cycle
I
V
Figure
9.
MPPT
control
of
PV
P
I
V
∗
dc
V
dc
I
c
P
c
P
r
P
f
V
sq
I
∗
f
q
P
pv
Figure
10.
Control
loop
of
the
DC
b
us
v
oltage
5.
SIMULA
TIONS
RESUL
TS
Simulations
are
made
using
Matlab/Simulink.
In
the
follo
wing,
we
present
the
results
for
v
ariable
speed
which
is
illustrated
in
figure
(11a)
representing
subsynchronous
and
h
ypersynchronous
modes,
with
irradiance
1000
W
=m
2
and
temperature
298
K
.
0
0.2
0.4
0.6
0.8
1
700
750
800
850
900
950
1000
1050
1100
Time (s)
Irradiance (W/m
2
)
(a)
Irradiance
v
ariation
0
0.2
0.4
0.6
0.8
1
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Time (s)
DC bus voltage (V)
V
dc
*
V
dc
(b)
DC
b
us
v
oltage
0
0.
2
0.
4
0.
6
0.
8
1
−1
0
1
2
3
4
5
6
7
8
9
x 10
5
Tim
e
(
s)
Po
wers (W
)
Ps
Pf
Pg
Pr
Pp
v
(c)
HRES
po
wers
Figure
12.
Simulation
results
for
HRES
for
constant
wind
speed
(12.5
m/s)
and
v
ariable
irradiance
Figure
(11b)
sho
ws
that
the
reference
DC
b
us
v
oltage
of
h
ybrid
system.
This
justifies
the
ef
ficienc
y
and
the
reliability
of
the
DC
b
us
control
loop
in
tracking
the
predicted
references.
Figure
(11c)
sho
ws
that
25%
of
the
po
wer
injected
to
the
grid
passes
by
the
po
wer
con
v
erter
.
As
well
the
grid
po
wer
P
g
is
equal
to
the
sum
of
the
stator
po
wer
P
s
,
the
rotor
po
wer
P
r
,
and
the
PV
po
wer
P
pv
.
Figure
(12)
sho
ws
the
simulation
results
for
a
constant
wind
speed
and
v
ariable
irradiance.
As
sho
wn
by
figure
(12b),
the
DC
b
us
v
oltage
is
well
re
gulated.
Figure
(12c)
illustrates
the
v
ariations
of
the
PV
,
wind
and
h
ybrid
po
wers
during
the
seek
of
the
ne
w
maximum
po
wer
point.
F
or
a
constant
wind
speed
and
v
ariable
irradiance
the
system
produces
the
maximum
po
wer
(
P
s
+
P
r
+
P
pv
=
P
g
).
The
po
wer
supplied
to
the
grid
is
the
sum
of
wind
and
photo
v
oltaic
sources.
6.
CONCLUSION
This
paper
e
xamines
a
wind/PV
h
ybrid
ener
gy
system.
The
first
subsystem
consists
of
a
wind
system
based
DFIG,
and
the
second
consists
of
a
photo
v
oltaic
generator
PV
.
Bac
kstepping
Contr
ol
of
wind
and
photo
voltaic
hybrid
Rene
wable
Ener
gy
System
Evaluation Warning : The document was created with Spire.PDF for Python.
686
ISSN:
2088-8694
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
50
100
150
200
Time (s)
mechanical speed (rad/s)
(a)
Rotor
speed
0
0.2
0.4
0.6
0.8
1
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Time (s)
DC bus voltage (V)
V
dc
*
V
dc
(b)
DC
b
us
v
oltage
0
0.
2
0.
4
0.
6
0.
8
1
−2
−1
0
1
2
3
4
5
6
7
8
9
x 10
5
Tim
e
(
s)
Po
wers (W
)
Ps
Pf
Pg
Pr
Pp
v
(c)
HRES
po
wers
Figure
11.
Simulation
results
for
HRES
for
v
ariable
wind
speed
and
constant
irradiance
The
wind
ener
gy
system
comprises
tw
o
con
v
erters
connected
by
a
DC
b
us
v
oltage
allo
wi
ng
the
e
xchange
of
po
wer
flo
wing
between
the
grid
and
the
machine.
W
e
used
the
non
linear
backstepping
technique
to
control
the
RSC
and
GSC
con
v
erters.
The
DC
b
us
collects
the
ener
gy
generated
by
the
tw
o
subsystems.
The
DC-DC
boost
con
v
erter
is
inte
grated
with
a
PV
generator
and
used
to
t
ransfer
the
produced
po
wer
to
the
grid
through
GSC.
A
MPPT
strate
gy
is
used
to
e
xtract
the
maximum
po
wer
of
the
PV
by
adjusting
the
duty
c
ycle
of
the
boost
con
v
erter
.
Simulation
results
using
Matlab/Simulink
present
the
rob
ustness
ag
ainst
wind
speed
and
irradiance
v
ariations.
REFERENCES
[1]
G.Notton
,
M.
Louche,
”Autonomous
h
ybrid
photo
v
oltaic
po
wer
plant
using
a
back-up
generator:
a
case
study
,
”
Mediterranean
Island.
Rene
w
Ener
gy
,pp.
371–91,
1996.
[2]
S.
Khojet
El
Khil,
I.
Slama-Belkhodja,
M.
Piet
rzak-Da
vid
and
B.
De
F
ornel,
”Po
wer
distrib
ution
la
w
in
a
Doubly
Fed
Induction
Machine,
”
Mathematics
and
Computers
in
Simulation
,
v
olume
71,
pages
360–368,
2006.
[3]
A.
Elmansouri,
J.
El
mhamdi
and
A.
Boualouch,
”Control
by
Back
Stepping
of
the
DFIG
Used
in
the
W
ind
T
urbine,
”
International
Journal
of
Emer
ging
T
echnology
and
Adv
anced
Engineering
,V
olume
5,
Issue
2,
February
2015.
[4]
S.
El
Aimani,
B.
Franc
¸
ois,
F
.
Mi
nn
e
et
B.
Robyns,
”Comparison
analysis
of
control
structures
for
v
ariable
wind
speed
turbine,
”
Proceedings
of
CESA
,
Lille,
France,
Juillet
2003.
[5]
M.
El
Azzaoui,
H.
Mahmoudi,
”Modeling
and
control
of
a
doubly
fed
induct
ion
generator
base
wind
turbine
system
optimizition
of
the
po
wer
,
”
Journal
of
Theoretical
and
Applied
Information
T
echnology
,
V
ol
80,
No
2,
pp
304-314
October
2015.
[6]
O.E.
Elbashir
,
W
.
Zezhong,
L.
Qihui,
”Analysis
of
DFIG
W
ind
T
urbine
During
Steady-State
and
T
ransient
Oper
-
ation,
”
TELK
OMNIKA
Indonesian
Journal
of
Electrical
Engineering
,
V
ol.12,
No.6,
June
2014,
pp.
4148-4156.
[7]
L.
Zhang,
C.
W
atthansarn
and
W
.
Shehered,
“
A
matrix
con
v
erter
e
xcited
doubly-fed
induction
machine
as
a
wind
po
wer
generator
,
”
IEEE
T
rans.Po
wer
Electronics
and
V
ariable
Speed
Dri
v
es
,
v
ol.
2
,pp
532–537,
august
2002.
[8]
M.R
Jo
v
ano
vic,
B.
Bamieh,
”Architecture
Induced
by
Distrib
uted
Backstepping
Design,
”
IEEE
T
ransactions
on
Automatic
Control
,
V
ol.52,
Issue.
1,
pp.
108-113,
January
2007.
[9]
M.
Moutchou,
A.
Abbou,
H.
Mahmoudi,
”MRAS-based
sensorless
speed
backstepping
control
for
induction
ma-
chine,
using
a
flux
sliding
mode
observ
eer
,
”
T
urkish
Journal
of
Electrical
Engineering
and
Computer
Sciences
,
23:
187-200,
2015.
[10]
M.
El
Azzaoui,
H.
Mahmoudi
and
C.
Ed-dahmani,
”Backstepping
control
of
a
Doubly
Fed
Induction
Generator
inte
grated
to
wind
po
wer
system,
”
2016
International
Conference
on
Electrical
and
Information
T
echnologies
(ICEIT),
T
angiers,
2016,
pp.
306-311.
[11]
S.D.
Stallon,
K.V
K
umar
,
S.S
K
umar
,
”High
Ef
ficient
Module
of
Boost
Con
v
erter
in
PV
Module,
”
International
Journal
of
Electrical
and
Computer
Engineering
(IJECE)
,
V
ol.2,
No.6,
December
2012,
pp.
758-781.
[12]
Jerbi
L.,
Krichen
L.
and
Ouali
A,
”A
fuzzy
logic
supervisor
for
acti
v
e
and
reacti
v
e
po
wer
control
of
a
v
ariable
speed
wind
ener
gy
con
v
ersion
system
associated
to
a
flywheel
storage
system,
”
Electric
Po
wer
Systems
Research
,
V
ol.
79,
No
6,
pp.
919–925,
2009.
IJPEDS
V
ol.
7,
No.
3,
September
2016:
677
–
686
Evaluation Warning : The document was created with Spire.PDF for Python.