RST Control of a Doubly-fed Induction Generator for Wind Energy Conversion

DOI : 10.17577/IJERTV3IS031458

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RST Control of a Doubly-fed Induction Generator for Wind Energy Conversion

Makhlouf Laakam

Research unit of Systems Photovoltaic, Wind and Geothermal.

National Engineering School of Gabes (ENIG).


Lassaâd Sbita

Research unit of Systems Photovoltaic, Wind and Geothermal.

National Engineering School of Gabes (ENIG).


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 pole-placement theory is presented.The simulation calculations were achieved by using MATLAB®-SIMULINK® 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.


    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 double-fed 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 double-fed 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 "back-to-back" 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 [2-3]. The performances of this system depend not only on the DFIG, but also on how the "back-to-back" 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 vector-control

    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 MATLAB®-SIMULINK® package. The obtained results are presented and discussed.


  1. 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

  2. The double fed induction generator model

    The electrical equations of DFIG in dq reference can be written as follows [4-5]:

    v R i

    ds s ds


    dt ds s qs


    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


    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 two-phase dq reference

    linked to the rotating field. The stator flux is oriented

    along d axis. Thus, we can write: s

    v R i




    qr r qr

    dt qr s dr

    ds s


    qs 0


    ds Lsids Midr s


    qs Lsiqs Miqr 0

    = .




    The expression of electromagnetic torque becomes:

    ds Lsids Midr

    = .

    L i

    • Mi



    qs s qs qr

    dr Lridr Mids

    qr Lriqr Miqs



    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


    = : 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 )



    Wherep: number of pole pairs of the DFIG.



    The active and reactive powers of the stator and rotorcan be


    written as follows [4-5]:

    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


    = .

    Qr vqr .idr vdr .iqr

    = . .

  3. Vector control of DFIG

= .


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

= .


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


The six coefficients c1, c2, c3, c4, c5 and c6 are modified for

maximumCp equal to 0.498 for = 0°. With A which depends on and :

Q = Q + Q = Vs s + g 1 V M i


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


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


electrical power.

With: Performance of the DFIG and two power converters.

  1. Turbine modelling

    By applying the theory of movement quantity and Bernoulli theorem, we can determine the incidental power (theoretical power) generated by wind [2-3]:

    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

  2. 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



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 [3-4]:

DFIG is used as a reference for a proportional-integral 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




(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]:


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


Cmax , =




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]:


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.


    The block-diagram of a system with its RST controller is presented in fig. 5


    Fig.3. Power-Speed characteristics of the wind turbine

    1. 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 transfer-function



      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


      + pL (L M )andB = MV

      E s r

      s r Ls s


      Where p is the Laplace operator.

      The transfer-function of the regulated system is calculated as:

      Fig.4. Block diagram of the RST controller.

      = 1 +


      BT BS

      Y = Yref + AS + BR AS + BR


      We suppose:



      By applying the Bezout equation, we put:

      D = AS + BR = CF


      We can make the compensation of the zero introduced by the Proportional Integral controller with the pole of the open-loop 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 +



      In our case:

      deg(D) = 2m + 1 deg(S) = deg(A) + 1 deg(R) = deg(A).





      is response time.


      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


      (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

      = = =


      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


      As T=R (0), we conclude that h =




      pc =





        The simulation presented is that of the DFIG which is directly connected to the network through the stator, and is controlled


        pf =



        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 )


        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


        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


        lim p = 0



        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]:


        P(W )




        d3 a1 0 0 0 S2


        d2 = 0 a1 0 0 S1



        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:


        lim = 1


        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


        P(W )




        synthesis of a R ST controller

        Consigne Sortie

        0 1 2 3 4 5 6 7 8 9 10

        tem ps ( s)


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 stator-flux oriented control technique has been used to control stators active and reactive power, using integral-proportional (PI) controller and polynomial RST based on pole-placement 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.


  1. T. Ackermann and Soder, L. « An Overview of Wind Energy-Status 2002 ». Renewable and Sustainable Energy Reviews 6(1-2), 67-127 (2002).

    Fig.7. Active stator power response with its reference (RST controller)

    synthesis of a PI controller


  2. 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: 846-852.



    Q(V A R)





    Consigne Sortie

    0 1 2 3 4 5 6 7 8 9 10

    tem ps ( s)

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

  4. M. Dhaoui, "Optimisation du fonctionnement de lactionneur à induction par logique floue, les réseaux de neurones et les algorithmes génétiques", Doctorat Thesis ENIG, University of Gabes, Tunisia 2011.

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

  6. M. Dhaoui and L. Sbita, "A New Method for Losses Minimization in IFOC Induction Motor Drives", International Journal of Systems Control, Vol.1-2010/Iss.2, pp: 93-99.

  7. B. Beltran, Maximisation de la puissance produite par une génératrice asynchrone Double alimentation dune éolienne par mode glissant dordre supérieur, JCGE08 Lyon 17,18 Décembre 2008.

  8. P. De Larminat, "Automatique Commande des systèmes linéaires", Seconde Edition 1997 Hermes.

    Fig.8. Reactive stator power response with its reference (PI controller)

    synthesis of a R ST controller

  9. Laakam Makhlouf , Dhaoui Mehdi and Sbita Lassaad Power Maximization of a Doubly Fed Induction Generator (DFIG)International conference (STA), 2011 pp 1-14.

  10. Y.Mokhtari,Y.Madi,Dj.RekiouaConversion Wind Power Using





    Q(V A R)










    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,July-2013, pp 2373-2378.

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

  12. F. Poitiers , T. Bouaouiche, M. MachmoumAdvanced control of a doubly-fed 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.

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