Copyright © 2014 IJECCE, All right reserved

**Control of a Doubly-Fed Induction Generator **

**Makhlouf Laakam, Lassaâd Sbita **

**Abstract****– In this paper, a grid connected wind power **
**generation scheme using a doubly fed induction generator **
**(DFIG) is studied. The aims of this paper are: The modelling **
**and simulation of the operating in two quadrants **
**(torque-speed) of a DFIG, the analysis employs a stator flux vector **
**control algorithm to control rotor current using the PI **
**regulator. The simulation calculations were achieved using **
**MATLAB®-SIMULINK® package. The obtained results are **
**presented, illustrating the good control performances of the **
**system. **

**Keywords ****–****DFIG, Vector Control, PI Controller, Variable **
**Speed. **

**I.**

**I**

**NTRODUCTION**

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 [1-3]. 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. The aim of PI vector-controller is to obtain high dynamic performances. The proposed control system is simulated using MATLAB®-SIMULINK® package. The obtained results are presented and discussed.

**II.**

**M**

**ODELLING OF**

**T**

**HE**

**S**

**TUDIED**

**S**

**YSTEM**

*A.*

*The Studied System *

Fig.1. Wind system conversion

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.

*B.*

*The Double Fed Induction Generator Model *

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

( )

*ds* *s ds* *ds* *s* *qs*
*qs* *s qs* *qs* *s* *ds*
*dr* *r dr* *dr* *s* *qr*
*qr* *r qr* *qr* *s* *dr*

*d*

*v* *R i*

*dt*
*d*

*v* *R i*

*dt*
*d*

*v* *R i*

*dt*
*d*

*v* *R i*

*dt*

(1)

With:

*L i _{s}*

*Mi*

*ds* *ds* *dr*

*L i* *Mi*

*qs* *s qs* *qr*

_{} _{}

###

###

(2)*L i _{r}*

*Mi*

*dr* *dr* *ds*

*L i* *Mi*

*qr* *r qr* *qs*

_{} _{}

###

###

(3)With

Ls = ls − Ms : Cyclical inductance of a stator phase. = − : Cyclical inductance of a rotor phase. [ ls ], [lr ] : Inductances of a stator and rotor phase. M , M : Mutual inductances and Maximum mutual inductance between stator and rotor phases respectively.

The expression of the electromagnetic torque of the DFIG is more:

###

*T*

_{em}*p*.( .

*i*

_{qs}*.*

_{qs}*i*)

###

*ds* *ds*

(4)

Where p: number of pole pairs of the DFIG. The active and reactive powers of the stator and rotor can be written as follows [4-5]:

. .

. .

. .

. .

*P _{s}*

*v*

*i*

*v*

_{qs qs}i*ds ds*

*Q _{s}*

*v*

_{qs}i*v*

*i*

_{qs}*ds*

*ds*

*P*

_{r}*v*

*i*

*v*

_{qr qr}i*dr dr*

*Q _{r}*

*v*

_{qr}i*v*

*i*

_{qr}*dr*

*dr*

_{} _{}

_{} _{}

(5)

*C.*

*Vector Control of DFIG *

The control strategies of the DFIG are based on two different approaches [2]:

electromagnetic torque is the cross product between the flux and stator currents, which makes the control of DFIG particularly difficult. To make DFIG control easier, we approximate its model to that of a DC machine which has the advantage of having a natural decoupling between the fluxes and the currents. For this, we apply the vector control. We choose a two-phase dq reference linked to the rotating field. The stator flux Ψs is oriented along d axis. Thus, we can write:

0

*s*
*ds*
*qs*

_{}

###

###

###

(6)0

*L i _{s}*

*Mi*

_{s}*ds* *ds* *dr*

*L i* *Mi*

*qs* *s qs* *qr*

_{} _{} _{}

###

###

###

(7)� =� − .�

� =− � (8) The expression of electromagnetic torque becomes: � =− �.� (9)

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:

.

0

*v _{ds}*

*v _{qs}*

*V*

_{s}

_{s}

_{s}

_{} _{}

###

(10) Vs is the line voltage.

According to equation (5), 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:

=� � =− �.�

=� � =� � − �

=� � +� �

=� � − � �

(11)

The active and reactive power can be written as: =− �.�

=�.� −�. �

=� �.�

=� �.�

(12)

Total powers involved in the wind turbine are represented by equations (13) and (14):

Pt= Ps+ Pr = g−1 Vs M

Lsiqr (13) Qt= Qs+ Qr=

Vsψs

Ls + g−1 Vs M

Lsidr (14) 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

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) [6], [9], [11]: Ps_ref =ηPmec _opt (15) With: η Performance of the DFIG and two power converters.

**III.**

**R**

**ESULTS AND**

**I**

**NTERPRETATION**

We present the simulation of the DFIG connected directly to the network through the stator, and controlled by its rotor through an AC/DC and DC/AC converter. To control the power exchanged between the stator and the network, one uses the vector control with direct stator flux.

The results of simulations, are obtained with reactive power Qs_ref = 0.

Figure 2 and figure 3 show respectively the rotor current and voltage waveforms. The frequency of these voltage and current, vary according to the slip g. For g = 0, the rotor voltage and current are continuous. Figure 4 and figure 5 show respectively the rotor flux and the stator flux in the dq reference. Figure 6and figure 7 show respectively current and voltage waveforms of the stator. The sizes (stator current and voltage) are independent of the variation of the wind and depend only on the active and reactive reference powers. Figure 8 shows the electromagnetic torque. Figure 9 shows the speed of the double fed induction generator.

The Figure 10 shows rotor reactive power. For g=0, the reactive power is null. The network power varies according of the speed. The machine works as asynchronous compensator.

Figure 11 and figure 12 showrespectively reactive and active stator power, note that the machine supplies a network with the stator active power.

Figure 13and figure 14 show respectively voltage and current waveforms of the stator the dq reference.

Figure 15 gives rotor active power. It varies according to the wind speed. For g>0, DFIG absorbs a rotor active power. For g<0, The DFIG supplies network with a rotor active power. For g=0, the rotor active power remained constant corresponding to the rotor joules losses.

-10 -5 0 5 10 15

*I(*

*A*

*)*

Copyright © 2014 IJECCE, All right reserved Fig.3. The rotor votage

Fig.4. The rotor flux in the dq reference

Fig.5. The stator flux in the dq reference

Fig.6. The stator current

Fig.7. The stator votage

Fig.8. The electromagnetic torque

0 0.5 1 1.5 2 2.5 3

-250 -200 -150 -100 -50 0 50 100 150 200 250

*tem ps ( s)*

*T*

*en*

*si*

*on*

*(V*

*)*

Vra Vrb Vrc

0 0.5 1 1.5 2 2.5 3

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

*tem ps ( s)*

*flu*

*x *

*(W*

*b)*

_{r}d
_{r}q

0 0.5 1 1.5 2 2.5 3

-0.5 0 0.5 1 1.5 2 2.5 3

*tem ps ( s)*

* (*

*W*

*b)*

_{s}d

sq

0 0.5 1 1.5 2 2.5 3

-10 -8 -6 -4 -2 0 2 4 6 8

*tem ps ( s)*

*I(*

*A*

*)*

Isa Isb Isc

0 0.5 1 1.5 2 2.5 3

-250 -200 -150 -100 -50 0 50 100 150 200 250

*tem ps ( s)*

*T*

*en*

*si*

*on*

*(V*

*)*

Vsa Vsb Vsc

0 0.5 1 1.5 2 2.5 3

-15 -10 -5 0 5 10 15 20

*tem ps ( s)*

*C*

*ou*

*pl*

*e *

*(N*

*m*

*)*

Fig.9. Speed of the generator

Fig.10. The rotor reactive power

Fig.11. The stator reactive power

Fig.12. The stator active power

Fig.13. The stator voltage in the dq reference

Fig.14. The stator current in the dq reference

0 0.5 1 1.5 2 2.5 3

-20 0 20 40 60 80 100 120 140 160

*tem ps ( s)*

* (*

*rd*

*/s*

*)*

_{r}ef

0 0.5 1 1.5 2 2.5 3

-200 0 200 400 600 800 1000 1200 1400

*tem ps ( s)*

*Q*

*r(*

*V*

*A*

*R*

*)*

Qr

0 0.5 1 1.5 2 2.5 3

-2000 -1500 -1000 -500 0 500 1000

*tem ps ( s)*

*Q*

*s(*

*V*

*A*

*R*

*)*

Qs

0 0.5 1 1.5 2 2.5 3

-1400 -1200 -1000 -800 -600 -400 -200 0

*tem ps ( s)*

*P*

*s(*

*W*

*)*

Ps

0 0.5 1 1.5 2 2.5 3

-300 -200 -100 0 100 200 300

*tem ps ( s)*

*T*

*en*

*si*

*on*

*(V*

*)*

Vsd Vsq

0 0.5 1 1.5 2 2.5 3

-10 -8 -6 -4 -2 0 2 4 6 8 10

*tem ps ( s)*

*I(*

*A*

*)*

Copyright © 2014 IJECCE, All right reserved Fig.5. The rotor active power

**IV.**

**C**

**ONCLUSION**

The work presented in this paper is devoted to the analysis, modelling and simulation of a doubly fed induction. Stable operation of the DFIG was achieved by means of stator-flux oriented control technique. The operational principal of the proposed generator model and the validity of the control system were illustrated by the steady-state and transient responses of the power control associated to the DFIG. The machine supplies network with an active power in all operating phases.

The simulations presented above show the performance of each control and we have concluded that PI controller gives the best time responses and the speed of the generator follows its reference perfectly.

**R**

**EFERENCES**

[1] 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.

[2] 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.

[3] M. Dhaoui, "Optimisation du fonctionnement de l’actionneur à induction par logique floue, les réseaux de neurones et les algorithmes génétiques", Doctorat Thesis ENIG, University of Gabes, Tunisia 2011.

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

[5] 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. [6] B. Beltran, “ Maximisation de la puissance produite par une

génératrice asynchrone Double alimentation d’une éolienne par

mode glissant d’ordre supérieur”, JCGE’08 Lyon 17,18

Décembre 2008.

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

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

[9] B. Beltran, “ Maximisation de la puissance produite par une

génératrice asynchrone Double alimentation d’une éolienne par mode glissant d’ordre supérieur”, JCGE’08 Lyon 17,18

Décembre 2008.

[10] P. De Larminat, "Automatique – Commande des systèmes linéaires", Seconde Edition 1997 Hermes.

[11] Laakam Makhlouf, Dhaoui Mehdi and Sbita Lassaad “Power Maximization of a Doubly Fed Induction Generator

(DFIG)”International conference (STA), 2011 pp 1-14. [12] Y.Mokhtari, Y.Madi, Dj.Rekioua”Conversion Wind Power

Using Doubly Fed Induction Machine”International Journal of

Engineering &Technology (IJERT), Vol.2 Issue 7, July-2013, pp 2373-2378.

[13] M.Machmoum, Member IEEE,F.Poitiers, C.Darengosse and

A.Queric” Dynamic Performances of a Doubly-fed Induction Machine for a variable –speed Wind Energy Generation”,IEEE 2002, pp 2431-2436.

[14] F. Poitiers, T. Bouaouiche, M. Machmoum”Advanced control of a doubly-fed induction generator for wind energy conversion” Electric Power Systems Research (2009), pp 1085–1096.

**A**

**UTHOR**

**’**

**S**

**P**

**ROFILE**

**Makhlouf Laakam**

obtained the master degree of automatic and industrial computer sciences in May 2003 from the National School of Engineering in Sfax ENIS, Tunisia.Currently, he works as a Technologue Teacher, at the Higher institute of Technological Studies of Djerba, Tunisia. His fields of interest include power electronics, machine drives, automatic control and Fuzzy logic.

**Lassaâd Sbita**

obtained the doctorate thesis in July 1997 in Electrical engineering from ESSTT of Tunis, Tunisia. He works as a Professor at the electrical-automatic genius department of the National Engineering School of Gabes, Tunisia. His fields of interest include power electronics, machine drives, automatic control, modelling, observation and identification.

0 0.5 1 1.5 2 2.5 3

-1400 -1200 -1000 -800 -600 -400 -200 0 200 400

*tem ps ( s)*

*P*

*r(*

*W*

*)*