Conversion Wind Power Using Doubly Fed Induction Machine

Conversion Wind Power Using Doubly Fed Induction Machine

Vol. 2 Issue 7, July – 2013

Y. Mokhtari, Y. Madi, Pr. Dj. Rekioua

1,2,3 Laboratory of Industrial Technology and Information, Electrical engineering Department, A.Mira University, Bejaïa, Algeria,

Abstract

In this paper we study different ways of control of the powers active and reactive of a DFIG (Doubly Fed Induction Machine) used in the production of the energy, especially in wind turbine.

The model used for the DFIG is a diphase one obtained by the application of the Park transformation. In order to control stator active and reactive power exchanged between the DFIG and the grid; we present a synthesized control law based on a vector control strategy using classical integralproportional (PI) controller and polynomial RST controller based on pole-placement theory. Simulation calculations were achieved using MATLAB®-SIMULINK® package. The obtained results are presented for the two controllers.

Index Terms DFIG, Wind Energy, Power control, RST controllers, PI controllers.

NOMENCLATURE

vds , vqs , vdr , vqr : Two-phase statoric and rotoric voltages.

ids , iqs , idr , iqr : Two-phase statoric and rotoric currents.

Ls , L : Total cyclic statoric and rotoric inductances.

r

dfig : Torque of the machine

is the air density, R is the blade length V the wind speed.

mec : Shaft speed.

: Tip-speed ratio.

1. INTRODUCTION

   Different ways are used in order to produce the electrical energy (Gas, hydraulicect). But, there are several reasons for using variable-speed operation of wind turbine, among those are possibilities to reduce stresses of the mechanical structure, acoustic noise reduction and the possibility to control active and reactive power [6].

   In order to produce the energy and to meet the power needs, the DFIG (Doubly Fed Induction Generator) is the alternative given in this paper, because of its wide range of variation in all four quadrants.

   The control of electrical power exchanged between the stator of the DFIG and the power network is treated by controlling independently with PI regulators and RST controllers under conditions of unity stator side

   s

   s

   power factor ( Pref P and Qref 0 ).

   Rs , Rr : Per phase statoric and rotoric resistances.

   ds , qs , dr , qr : Two-phase statoric and rotoric fluxes.

   Vs : statoric tension.

   g : Generator Slip.

   M : Magnetizing inductance.

   s : statoric flux.

   s , : statoric and rotoric angular frequency.

   : Mechanical speed.

   The aim of these regulators is to obtain high dynamic performances

   The proposed control system is then simulated using MATLAB®-SIMULINK® package. The obtained results are presented and discussed.

2. MODELING OF THE STUDIED SYSTEM

   1. The studied system

      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 static frequency

      em , r

      : Electromagnetic and resistant Torque.

      converter (Figure 1).

      J , f : Inertia and viscous friction.

      p : Number of pole pairs.

      Ps , Qs : Active and reactive statoric power.

      C p : Power ratio.

      turbine: Turbine torque.

      turbine: Turbine speed.

      G : Gear ratio.

      Figure 1. Wind system conversion

   2. The double fed induction generator model

      The electrical equation is written in d_q reference frame is as follows:

      tip-speed ratio. It is assumed that the wind tVuorbl.i2nIessuise 7, July – 2013

      operated at high Cp values most of the time [3].

      d

      vds Rs .ids dt ds s .qs

      v R .i d .

      qs

      s qs

      dt qs

      d

      s ds

      .(1)

      v

      dr

      Rr .idr

      • dr

        dt

        d

        (s

        ).qr

        vqr Rr .iqr

        qr (s ).dr

        dt

        The stator flux can be expressed as:

        ds Ls .ids M .idr

        Figure 2. relationship between the power coefficient and the tip-speed ratio

        qs

        Ls .iqs

      • M .iqr

        .(2)

        The action of the speed corrector must achieve two

        The rotor flux can expressed as

        dr Lr .idr M .ids

        tasks:

        – It must control mechanical speed

        mec with its

        s

        s

        qr

        qr

        qr

        qr

        qs

        qs

        L .i

        M .i

        .(3)

        reference mec _ ref [4].

        The electromagnetic torqueis defined as:

        qs

        qs

        It must attenuate the action of the wind torque which

        em

        p. .i

        ds

        qs

        .ids

        .(4)

        constitutes an input disturbance [4]. The simplified representation in the form of diagram blocks is given in

        em

        J. d

        r dt

        f .

        .(5)

        Figure 3. We can use different technologies of correctors by in our work we opt for RST regulator to control our model.

   3. Wind Turbine Modeling

   The power capacity produced by a wind turbine is dependent on the power ratio Cp . It is given by:

   P 1 .C ..S.V 3

   t 2 p 1

   .(6)

   The turbine torque is the ratio of the output power to the shaft speed turbine, where

   turbine

   Pt

   turbine

   .(7)

   The turbine is normally coupled to the generator shaft through a gear box whose gear ratio G is chosen so as to maintain the generator shaft speed within a desired speed range. Neglecting the transmission losses, the torque and shaft speed of the wind turbine, referred to the generator side of the gearbox, are given by:

   Figure 3. The block diagram of control speed

   A.Turbine control with RST regulators

   The block-diagram of a system with its RST controller is presented on Figure 10.

   G

   G

   dfig turbine

   .(8)

   B( p)

   and mec

   G.turbine

   .(9)

   The system with the transfer-function has E p

   Where

   A( p)

   dfig is the torque of the machine and mec is its shaft

   As reference and is disturbed by the variable p . R ,

   speed.

   The wind turbine can be characterized by its C

   S and T are polynomials which constitutes the controller. In our case, we have:

   p

   (curve shown in Figure 2.). where the is the tip- speed ratio, that is the ratio between the linear speed of the tip of the blade with respect to the wind speed. It is

   A( p) f p.J

   B( p) 1

   Where p is the Laplace operator.

   .(10)

   shown that the power coefficient

   Cp varies with the

   The transfer-function of the regulated system is:

   s2

   a 0

   0 0 d3

   Vol. 2 Issue 7, July – 2013

   Y B.T E B.S P

   .(11)

   s 1

   A.S B.R

   A.S B.R

   1 inv 0 a1 0

   0 d2

   .(20)

   By applying the Bezout equation, we take:

   r

   0 a b

   0 . d

   D A.S B.R C.F

   1

   0 0 1

   .(12)

   r

   0 0

   0 b0 d

   Where C is the command polynomial and F is the filtering polynomial. In order to have good adjustment

   0

   0

   accuracy, we choose a strictly proper regulator. So if A

   is a polynomial of n degree

   In order to determine the coefficients of T, we consider

   that in seady state Y must be equal to E

   degA n 1

   so:

   lim

   B.T 1

   .(21)

   We must have:

   degD 2.n 1 3 degS degA 1 2

   .(13)

   .(14)

   p0 A.S B.R

   As we know that S(0)=0, we conclude that T=R(0). In order to separate regulation and reference tracking, we

   degR degA 1

   .(15)

   try to make the term

   B.T

   A.S B.R

   only dependent on C.

   In our case:

   A a1 p a

   We then consider T=h.F (where h is real) and we can write:

   B b0

   D d

   0

   p3 d

   p 2 d

   p d

   .(16)

   B.T

   A.S B.R

   B.T

   D

   B.h.F C.F

   B.h C

   .(22)

   3 2 1 0

   R0

   1 0

   1 0

   R r p r

   S s2 p s1 p s0

   S s2 p s1 p s0

   2

   12

   12

   To find the coefficients of polynomials R and S, the robust pole placement method is adopted with Tc as

   As T R0, we conclude that h

   F 0

   S( p) 0.3601p2 0.3313p

   R( p) 0.2349 p 0.0204

   T ( p) 0.1312 p2 0.1034 p 0.0204

   .(23)

   .(24)

   .(25)

   control horizon and T f

   We have:

   as filtering horizon [2],[5].

   11

   1

   pc

   Tc

   and p f

   1

   T

   10

   .(17)

   9

   Where F.

   f

   pc is the pole of C and p f

   8

   Wind (m/s)

   Wind (m/s)

   the double pole of 7

   6

   5

   The pole

   pc must accelerate the system and is

   4

   0 2 4 6 8 10 12 14 16 18 20

   t (s)

   generally chosen three to five times greater than the

   pole of A pa . p f is generally chosen three times

   4

   x 10

   0

   Figure 4. Wind profile

   smaller than

   pc . In our case:

   M 2

   -0.5

   -1

   L . L

   1 1 s r L

   -1.5

   Tc

   T f

3. Pa

s

5.Ls .Rr

.(18)

P (Kw)

P (Kw)

-2

-2.5

Perturbations are generally considered as piecewise -3

constant. Pp can then be modeled by a step input.

-3.5

-4

To obtain good disturbance rejections, the final value

0 2 4 6 8 10 12 14 16 18 20

t (s)

theorem indicate that the term

towards zero:

B.S

A.S B.R

must tend

Figure 5. Power profile delivered

lim

S.B Pp

p. . 0

.(19)

1. POWER CONTROL

   p0 D p

   To obtain a good stability in steady-state, we must have D(0)=0 and respect relation (19). The Bezout equation leads 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:

   The power control approach presented in this paper is based on a synthesized control law based on a vector control strategy using classical integralproportional (PI) and polynomial RST controllers. The energy exchanged between DFIG and the grid is obtained by

   controlling independently the active and reactive powers.

   R g.s . Lr

   M 2

   .iqr

   Vol. 2 Issue 7, July – 2013

   1

   The connection of the DFIG to the grid must be done

   in three steps. In first order we have to do the

   Ls

   M 2

   M .V

   .(30)

   regulation of of the stator voltages with the grid

   R g.s . Lr

   .idr g.s . s

   2

   voltages as reference. Then, the stator connection to

   Ls

   s .Ls

   the grid can be done. Finally, once the connection is achieved, the transit power and the DFIG can be given.

   The stator flux vector is orienting according to the d

   From the equation (29) we can write:

   Ls

   iqr V .M .Ps

   axis in the Parks reference frame. Where: s

   .(31)

   qs

   0 , ds s

   .(26)

   i

   dr

   Ls V .M

   s

   .Qs s

   M

   and

   vds 0 ,

   vqs Vs

   .(27)

   The terms, which constitute cross-coupling terms can be neglected because of their small influence [2], and

   M

   M

   If the voltage drops due to the stator resistance

   Rs , we

   by replacing the equations (31) in (28). We obtain:

   can write:

   R .L

   1. s

   2. dQs

   2 L

   2 L

   R .

   r s

   M 2 di M 2

   vdr M .V

   s

   .Qs (Lr

   ).(

   Ls M .Vs

   ).

   dt M

   .(32)

   v R .i

   • (L

   ). dr g. .(L

   ).i

   R .L

   2 L

   M .

   r

   r

   L

   L

   dr

   1. dr

      Ls dt

   2. r qr

   s

   (28)

   vqr (

   r s

   M .V

   ).Ps (Lr

   M ).( s

   L M .V

   ). dPs

   dt

   g. . s

   s L

   M 2 di

   M 2 M .V

   s s s s

   v R .i (L ). qr g. .(L

   L

   L

   ).i g. . s

   Knowing relation (32), it is possible to synthesize the

   r

   r

   qr

   1. qr

      Ls dt

   2. r dr

   s

   s .L

   regulators and establish the global block- diagram of

   s

   s

   s

   s

   We can notice that the two equations of rotorique voltage are coupled. The decoupling is obtained by compensation in order to assure the control of Ps and Qs, independently of each other. So we get a first order system, and its control is simplified and realized by a PI controller [1][6].

   The stator active Ps and reactive power Qs can be written according to the rotor current:

   the controlled system (Figure 8.) [7].

   s

   s

   L

   L

   P V . M .i

   s qr

   s

   .(29)

   s

   s

   L

   L

   s

   s

   Q V . s Vs .M .i

   s L dr

   The system after compensation becomes:

   Figure 6. Scheme of the system with feed-back loop

   The global scheme of the control through PI controller can be given as follows:

   Figure 8. Power control with PI controller

   B.Power Control with PI regulators

   We can represent the system to control as follow:

   Figure 9. Scheme of the PI and system form with feed-back loop

   The gain PI is in the form:

   C ( p)

   K

   i (1

   p

   K

   p . p)

   K

   .(33)

   We suppose:

   i

   T A

   B

   .(34)

   We can compensate the zero introduced by PI with the pole in open loop of the system.

   Figure 7. Global scheme of control through PI

   K p A A

   regulators

   K K .

   p i

   p i

   K B B

   i

   .(35)

   Where :

   In closed loop we obtain:

   Ki B. Simulation calculations.

   Vol. 2 Issue 7, July – 2013

   H ( p)

   Where:

   .K

   p

   K

   1 i .K p

   H ( p)

   1

   1 1 . p Ki .K

   .(36)

   We make the same conditions in two cases. We take reactive power Qs*=0 and we applied the echelon of active power Ps*=-15 kW at time t=0.5s. Figure 11 and Figure 12 represent active power response obtained

   respectively when we use PI controller and in the case

   1

   Ki .K

   Ki

   1

   .K

   .(37)

   of RST controller.

   : is the response time.

   1. Power Control with RST regulators

      The block-diagram of a system with its RST controller is presented on Figure 10.

      Figure 10. Block diagram of the RST controller

      Figure 11. Ps response with its reference (PI controller)

      The system with the transfer-function

      B( p)

      A( p)

      has Ep

      As reference and is disturbed by the variable Pp. R , S and T are polynomials which constitutes the controller. In our case, we have:

      M 2

      A( p) Ls .Rs p.Ls . Lr

      L

      .(38)

      B( p) M .Vs

      s

      Figure 12. Ps response with its reference (RST controller)

      We apply a power providing from the wind turbine.

      By following the steps above we will have:

      S( p) 7.9904.103 p2 1.5513.107 p

      R( p) 1.5872.105 p 3.9618.107

      .(39)

      .(40)

      Figure 13. shows random wind turbine speed.

      T ( p) R(0) r0

      3.9618.107

      .(41)

      Simulation and results

      The simulation of the global studied system is presented using MATLAB/SIMULINK software Parameters identification are obtained from an experimental bench.

      1. Parameters identification.

   The experimental bench is made up of DFIG (15KW, p=1, N=1500 rpm).mechanically coupled to a DC machine.

   We made different tests;

   No load test at synchronous, locked rotor test, transformer test and test for define the friction coefficient and moment of inertia.

   After calculating the parameters, we obtain the results below:

   Rs = 0.272 , Ls = 36.4 mH , Rr = 0.269

   Lr = 36.9 mH , M = 34.9 mH , f =0.073 N.m.s/rad

   J = 2.555 kg.m2

   Figure 13. Wind turbine speed

   Figure 14. and Figure 15 show respectively the active and reactive stator powers when we use PI controller.

   Figure 14. Active power response with its reference (PI controller)

   Figure 15. Reactive power response

   In Figure 16. and Figure 17. we represent the active and reactive stator powers when we use RST controller.

   Figure 16. Active power response with its reference (RST controller)

   Figure 17. Reactive power response

   We can observe in the two cases that the powers follow their reference perfectly and the performances are different.

   applied parameters variations which showVoeld. 2 Istshuee 7, July – 2013

   efficiency and the robustness of the RST controller. The simulations presented above show the performance of each control and we have concluded that:

   • PI gives the best time responses.

   • RST is less sensitive to speed variation.

   • RST show a great strength towards the different variations of parameters.

   REFERENCES

   1. C. Belfedal, S.Moreau, G.Champenois, T.Allaoui, M.Denai, Comparison of PI and Direct Power Control with SVM of Doubly Fed Induction Generator, Journal of Electrical & Electronics Engineering, N°2, Vol 8, 2008,pp 633-641.

   2. F. Poitiers, M. Machmoum, R. Le Doeuff and M.E. Zaim, Control of a doubly-fed induction generator for wind energy conversion systems, International Journal of Renewable Energy Engeneering,Vol.3 N°3 December 2001, pp 373-378.

   3. The Australasian Universities Power Engineering Conference (AUPEC), Curtin University of Technology,

      Perth, 23,26, Sept, 2001

   4. E.Muljadi, C.P. Butterfield Pitch-controlled variable- speed wind turbine generation, IEEE trans on Industry Applications , Vol 37 N°1,pp 240-246; January/February 2001.

   5. S. Yuvarajan, Lingling Fan, A doubly-fed induction generator-based wind generation system with quasi-sine rotor injection, Journal of Power Sources, Volume 184, Issue 1, 15 September 2008, Pages 325-330.

   6. K.Ghedamsi, D.Aouzellag, E.M.Berkouk « Control of wind generator associated to a flywheel energy storage system », ScienceDirect Renewable Energy 33 (2008) 21452156

   7. M.Machmoum, Member IEEE, F.Poitiers, C.Darengosse and A.Queric « Dynamic Performances of Doubly-fed Induction Machine for a Variable-speed Wind Energy Generation », IEEE 2002, 2431-2436.

2. CONCLUSION

This paper is devoted to the study of the performance of a double fed induction generator supplying a conversion wind system, using the turbine win speed control using RST controllers. Vector control strategy has been used to control statoric active and reactive power exchanged between the DFIG and the grid. To evaluate performances of PI controller and RST controller,

Firstly , we have applied the same conditions (active Power step reference -15 KW) and then we have