 Open Access
 Total Downloads : 590
 Authors : Laakam Makhlouf, Lassaad Sbita
 Paper ID : IJERTV3IS031458
 Volume & Issue : Volume 03, Issue 03 (March 2014)
 Published (First Online): 23042014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
RST Control of a Doublyfed Induction Generator for Wind Energy Conversion
Makhlouf Laakam
Research unit of Systems Photovoltaic, Wind and Geothermal.
National Engineering School of Gabes (ENIG).
Gabes,Tunisia.
LassaÃ¢d Sbita
Research unit of Systems Photovoltaic, Wind and Geothermal.
National Engineering School of Gabes (ENIG).
Gabes,Tunisia.
AbstractThe purpose of thispaper is to studya differentcontrol strategyofactive and reactive powera doubly fed induction generator (DFIG)used for energy generation. The DFIG model we used is obtained by the application of the Park transformation. To control the power exchanged between the DFIG and the grid, a vector control strategy using integral proportional (PI) controller and polynomial RST controller based on poleplacement theory is presented.The simulation calculations were achieved by using MATLABÂ®SIMULINKÂ® package. The results obtained from different operating points, illustrate the efficient control performances of the system
KeywordsDFIG; Wind Turbine; Variable Speed; Power control; PI controller; RST controller.

INTRODUCTION
Today, wind energy has become a viable solution for the generation of electrical energy. Although the majority of installed wind turbines have a fixed speed, the number of wind turbines which have a variable speed is increasing [1]. The doublefed asynchronous generator with a vectorial control is a machine that has excellent performance and is commonly used in wind turbine industry. There are many reasons for the use of a doublefed induction generator for a variable speed wind turbine; for instance, the reduction of efforts on the mechanical parts, the reduction of noise and the ability to control the active and reactive power. The wind system which uses DGIF and a "backtoback" converter that connects the rotor generator to the grid has many advantages. An advantage of this structure is that the used power converters are designed to flow a fraction of the total power of the system [23]. The performances of this system depend not only on the DFIG, but also on how the "backtoback" converter is controlled. While the rotor side converter controls the active and reactive power produced by the generator, the grid side converter allows us to control the DC bus voltage and the power factor of the grid side. In order to control the stator exchanged active and reactive power between the DFIG and the grid, a vectorcontrol
strategy is used to control PI and RST controllers independently. The aim of these controllers is to obtain high dynamic performances. The proposed control system is simulated using MATLABÂ®SIMULINKÂ® package. The obtained results are presented and discussed.

MODELLING OF THE STUDIED SYSTEM

The studied system
The scheme of the device studied is given in the Fig.1.The system studied is made up of a wind turbine and a DFIG directly connected through the stator to the grid and supplied through the rotor by AC/DC and DC/AC Converter.
Fig. 1. Wind system conversion

The double fed induction generator model
The electrical equations of DFIG in dq reference can be written as follows [45]:
v R i
ds s ds
d
dt ds s qs
d
frequency are constant (stable network). In our study, the frequency and the voltage are constant. It can be concluded from equation (11), that there is a strong coupling between fluxes and currents. Indeed, the electromagnetic torque is the
cross product between the flux and stator currents, which makes the control of DFIG particularly difficult. To make
v R i
DFIG control easier, we approximate its model to that of a
qs s qs
dt qs s ds
d
DC machine which has the advantage of having a natural decoupling between the fluxes and the currents. For this, we
v R i ( )
dr r dr dt dr s qr
apply the vector control. We choose a twophase dq reference
linked to the rotating field. The stator flux is oriented
along d axis. Thus, we can write: s
v R i
d
(
)
qr r qr
dt qr s dr
ds s
(1)
qs 0
(6)
ds Lsids Midr s
(7)
qs Lsiqs Miqr 0
= .
With:
=
(8)
The expression of electromagnetic torque becomes:
ds Lsids Midr
= .
L i

Mi
(2)
(9)
qs s qs qr
dr Lridr Mids
qr Lriqr Miqs
With
(3)
In the field of wind energy production, medium and high power machines are mainly used. Thus, we neglect the stator resistance. If we consider the stator flux constant, we can write:
vds 0
vqs Vs s .s
(10)
= : Cyclical inductance of a stator phase.
= : Cyclical inductance of a rotor phase.
[ ls ] , [lr ] : Inductances of a stator and rotor phase.Ms, , : Mutual inductances and Maximum mutual inductance between stator and rotor phases respectively.
The expression of theelectromagnetic torque of theDFIGismore:
Vs is the line voltage. According to equation (16), we can see that by controlling the magnitude quadrature rotor current (iqr), we can control the electromagnetic torque of the DFIG.
= .
By applying vector control of DFIG we can write the expressions of power as follows:
Tem p.( ds .iqs qs .ids )
(4)
=
Wherep: number of pole pairs of the DFIG.
=
=
The active and reactive powers of the stator and rotorcan be
(11)
written as follows [45]:
P v .i v .i
= +
=
s ds ds
qs qs
Qs vqs .ids vds .iqs
The active and reactive power can be written as:
Pr vdr .idr vqr .iqr
(5)
= .
Qr vqr .idr vdr .iqr
= . .


Vector control of DFIG
= .
(12)
The control strategies of the DFIG are based on two different approaches [2]:

Flux control in a closed loop, where the frequency and the voltage are considered variable (unstable network).

Flux control in an open loop where the voltage and the
= .
(19)
Total powers involved in the wind turbine are represented by equations (13) and (14):
C , = c . c2 c . c . e
p 1 A 3 4
c 5
A + c6.
Pt = Ps + Pr
= g 1 V M i
s Ls qr
(13)
The six coefficients c1, c2, c3, c4, c5 and c6 are modified for
maximumCp equal to 0.498 for = 0Â°. With A which depends on and :
Q = Q + Q = Vs s + g 1 V M i
(14)
t s r Ls s Ls dr
The principle of vector control power is used. It is necessary to follow the DFIG an instruction of power, with the best electrical dynamics and taking into account the limittion of
1 1 0.035
=
A + 0.08. 1 + 3
(21)
the frequency commutation of power switches. In order to obtain a power factor equal to one on the stator side, the reactive power on the stator is maintained zero(Qs = 0). The reference active power to be imposed on the DFIG is defined by equation (15) [2]:
Figure 1 shows the curves of the power coefficient depending on with different values of . A maximum power coefficient of 0.498 is obtained with a speed ratio which is 8 (opt ). By setting and respectively to their
optimal values, the wind system provides an optimal
Ps_ref = Pmec _opt
(15)
electrical power.
With: Performance of the DFIG and two power converters.

Turbine modelling
By applying the theory of movement quantity and Bernoulli theorem, we can determine the incidental power (theoretical power) generated by wind [23]:
Pt 1 ..S.V 3
2 (16)
S : the area swept by the blades of the turbine [ m2 ] : air density ( = 1.225 kg/m3 at atmospheric pressure). v : wind speed [m/ s ]
Due to various losses in wind energy system, the power extracted from the turbine rotor is less than the incidental power. The extracted power is expressed by [3]:
1 2 3
Fig. 2. Power coefficient for the wind turbine model

EXTRACTION OF MAXIMUM POWER To capture the maximum power of the incidental wind energy, it is necessary to adjust the rotation speed of the wind
Pt .C p .. .R .V
2
(17)
turbine to the wind speed. The optimal mechanical speed of the turbine corresponds to opt and = 0o. The speed of the
Cp (, ) : is called the power coefficient, which expresses
the aerodynamic efficiency of the turbine. The power coefficient depends on angle orientation of the blades and the ratio , which represents the relationship between the blades speed at their tips and wind speed. The ratio can be expressed by the following equation [34]:
DFIG is used as a reference for a proportionalintegral controller type (PI.). This type of regulator determines the control instruction which is the electromagnetic torque that should be applied to rotate the generator at its optimum speed.
Thus, the torque determined by the controller is used as a
reference torque of the turbine model (Figure 3). The variation of the system of the blades angle orientation
t . R
=
v
(18)
(variation of the incidence angle) allows changing the ratio
between the lift and the drag. In order to extract the
The maximum power coefficient Cp was determined by Albert Betz (1920) as [5]:
16
maximum power and keep it constant, we should adjust the angle of the blades to the wind speed. The "Pitch Control" is a technique that adjusts mechanically the blade pitch angle to shift the curve of the power
p
Cmax , =
0.593
27
(19)
coefficient of the turbine [7]. However, this technique is quite expensive and is usually
The power factor is intrinsic to the design of the wind turbine and depends on the blades and their profiles. We can model the power coefficient with a single equation that depends on the speed ratio and the blade pitch angle [6]:
(20)
used for high and medium wind turbinespower. In our model, the "Stall Control" technique, which is a passive approach that allows a natural aerodynamic stall (decrease of the lift when the wind speed becomes more important). The
Regulation of the rotation speed of the turbine by blade pitch angle occurs when the generator speed exceeds 30% of its ratedspeed. In the opposite case, will be zero.

POWER CONTROL WITH RST CONTROLLER
The blockdiagram of a system with its RST controller is presented in fig. 5
+
Fig.3. PowerSpeed characteristics of the wind turbine

POWER CONTROL WITH PI CONTROLLER We can represent the system to control as follow:
Fig. 5. Block diagram of the RST controller.
The system with the transferfunction
B
A
has Yref as reference and is disturbed by the variable , R, S
and T are polynomials which constitutes the controller. In our case, we have:
1 +
+
Y A = L R
2
+ pL (L M )andB = MV
E s r
s r Ls s
(27)
Where p is the Laplace operator.
The transferfunction of the regulated system is calculated as:
Fig.4. Block diagram of the RST controller.
= 1 +
(22)
BT BS
Y = Yref + AS + BR AS + BR
(28)
We suppose:
=
(23)
By applying the Bezout equation, we put:
D = AS + BR = CF
(29)
We can make the compensation of the zero introduced by the Proportional Integral controller with the pole of the openloop system:
Where C is the polynomial command and F is the polynomial filtering. In order to have a high accuracy adjustment, we chose a strictly proper regulator. So if A is a polynomial of mdegree (deg(A) = m) we must have:
=
The transfer function of the closed loop becomes:
1
=
1 +
(24)
(25)
In our case:
deg(D) = 2m + 1 deg(S) = deg(A) + 1 deg(R) = deg(A).
(30)
With
1
=
is response time.
(26)
A = a1p + a0 B = b0
R = r1 p + r0
the term BT
AS +BR
only dependent on C. We then consider T=hF
S = s2p2 + s1 p + s0
D = d3p3 + d2p2 + d1 p + d0
(31)
(where h is real) and we can write:
To find the coefficients of polynomials R and S, the robust
BT BT B. h. F B. h
= = =
(38)
pole placement method is adopted with Tc as horizon control and Tf as filtering horizon [9][11][12]. We have:
AS + BR D
C. F C
R(0)
As T=R (0), we conclude that h =
1
F(0)
And
pc =
T
c
(32)

RESULTS AND INTERPRETATION
The simulation presented is that of the DFIG which is directly connected to the network through the stator, and is controlled
1
pf =
Tf
(33)
by its rotor through an AC/DC and DC/AC converter.To control the power exchanged between the stator and the
Where pc is the pole of C and pf is the double pole of F. The pole pc must accelerate the system and is generally chosen three to five times greater than the pole paof A.
In our case [12]:
network, one uses the vector control with direct stator flux. We make the variation of the active and reactive references power (Fig.6 to Fig.9).
The results of simulations, are obtained with reactive power Qs_ref = 0 and application of the echelon of active power Ps_ref = 2.5KW at time 1s.
Tf 1
T = = =
Ls (Lr
M2 )
Ls
Fig.6 and fig.7 show respectively active power response
obtained respectively when use PI controller and in the case
c 3 3pa
5Ls Rr
(34)
of RST controller.
Fig.8 and Fig.9 show respectively reactive stator
Perturbations are generally considered as piecewise constant. To obtain good disturbance rejections, the final value
powerresponse obtained respectively when use PI controller and in the case of RST controller.
theorem indicates that the term
+
must tend towards zero: .
Consigne Sortie
synthesis of a PI controller
S
lim p = 0
(35)
500
p0 D p 0
The Bezout equation results to four equations with four unknown terms where the coefficients of D are related to the coefficients of polynomials R and S by the Sylvester Matrix [23] [24] [25]:
500
P(W )
1000
1500
2000
d3 a1 0 0 0 S2
2500
d2 = 0 a1 0 0 S1
(36)
3000
0 1 2 3 4 5 6 7 8 9 10
d1 0 a0 b0 0 r1
d0 0 0 0 b0 r0
tem ps ( s)
Fig.6. Active stator power response with its reference (PI controller)
To determine the coefficients of T, we consider that in a steady state Y must be equal to Yref so:
BT
lim = 1
(37)
p0 AS + BR
As we know that S (0)=0, we conclude that T=R (0). In order to separate regulation and reference tracking, we try to make
0
P(W )
500
1000
1500
synthesis of a R ST controller
Consigne Sortie
0 1 2 3 4 5 6 7 8 9 10
tem ps ( s)

CONCLUSION


The work presented in this research is devoted to the study of the performance of a doubly fed induction generator used in the conversion wind system. The statorflux oriented control technique has been used to control stators active and reactive power, using integralproportional (PI) controller and polynomial RST based on poleplacement theory. To evaluate performances of PI controller and RST controller, we have applied the same conditions. The simulations presented above show the performance of each control and we have concluded that PI controller gives the best time responses and in two cases that the power follow their reference perfectly.
REFERENCES

T. Ackermann and Soder, L. Â« An Overview of Wind EnergyStatus 2002 Â». Renewable and Sustainable Energy Reviews 6(12), 67127 (2002).
Fig.7. Active stator power response with its reference (RST controller)
synthesis of a PI controller
1500

D. Seyoum and C. Grantham, "Terminal voltage control of a wind turbine driven isolated induction generator using stator oriented field control", IEEE transactions on industrial Applications, September 2003, pp: 846852.
1000
500
Q(V A R)
0
500
1000
1500
Consigne Sortie
0 1 2 3 4 5 6 7 8 9 10
tem ps ( s)

N. Aouani, F. Bacha, R. Dhifaoui Â« Control Strategy of a Variable Speed Wind Energy Conversion System Based on a Doubly Feed Induction Generator Â», IREACO, Vol.2, no.2, March 2009.

M. Dhaoui, "Optimisation du fonctionnement de lactionneur Ã induction par logique floue, les rÃ©seaux de neurones et les algorithmes gÃ©nÃ©tiques", Doctorat Thesis ENIG, University of Gabes, Tunisia 2011.

K.B. Mohanty, Â«Study of Wind Turbine Driven DFIG Using AC/DC/AC ConverterÂ», PhD thesis, National Institute of Technology Rourkela, 2008.

M. Dhaoui and L. Sbita, "A New Method for Losses Minimization in IFOC Induction Motor Drives", International Journal of Systems Control, Vol.12010/Iss.2, pp: 9399.

B. Beltran, Maximisation de la puissance produite par une gÃ©nÃ©ratrice asynchrone Double alimentation dune Ã©olienne par mode glissant dordre supÃ©rieur, JCGE08 Lyon 17,18 DÃ©cembre 2008.

P. De Larminat, "Automatique Commande des systÃ¨mes linÃ©aires", Seconde Edition 1997 Hermes.
Fig.8. Reactive stator power response with its reference (PI controller)
synthesis of a R ST controller

Laakam Makhlouf , Dhaoui Mehdi and Sbita Lassaad Power Maximization of a Doubly Fed Induction Generator (DFIG)International conference (STA), 2011 pp 114.

Y.Mokhtari,Y.Madi,Dj.RekiouaConversion Wind Power Using
1
0.8
0.6
0.4
Q(V A R)
0.2
0
0.2
0.4
0.6
0.8
1
Consigne
Sortie
0 1 2 3 4 5 6 7 8 9 10
tem ps ( s)
Doubly Fed Induction MachineInternational Journal of Engineering &Technology (IJERT),Vol.2 Issue 7,July2013, pp 23732378.

M.Machmoum,Member IEEE,F.Poitiers, C.Darengosse and A.QuericDynamic Performances of a Doublyfed Induction Machine for a variable speed Wind Energy Generation,IEEE 2002, pp 2431 2436.

F. Poitiers , T. Bouaouiche, M. MachmoumAdvanced control of a doublyfed induction generator for wind energy conversionElectric Power Systems Research (2009) ,pp 10851096.
Fig.9. Reactive stator power response with its reference (RST controller)
We can observe in two cases that the power follow their reference perfectly and the performances are different.