!

Control strategies of the mechanical speed for the wind turbine

N. Cherfia *, D. Kerdoun ** and A. Boumassata **.

LGEC Research Laboratory, Department of Electrical Engineering,

Constantine 1 University, 25000 Constantine, Algeria Phone: +213780102155, e-mail: msn822009@live.fr, kerdjallel@yahoo.fr, boumassata-r10@hotmail.fr

Abstract- A winds turbine role is to convert the kinetic energy of

wind into energy electric. Its components are designed to

maximize the conversion. Different control structures have been

developed according to the characteristic power speed. In our

case, we propose the control strategy of the wind turbine to

maximize power with control of the speed. This control strategy

consists in determining the speed of the turbine which provides

the maximum generated power.

Keywords - Wind, turbine, DFIG, control, PI

I. INTRODUCTION

During the last years, there was a strong penetration of the

renewable resources of energy in the network of power supply. The wind power production played and will continue to play a very important role in this domain for years to come.

Wind turbines have base of the doubly fed induction machine (DFIG) undoubtedly appeared as one of the high technologies for the manufacturers of wind turbines, Demonstrating that it is about an actual cost, Effective and a reliable solution.

The first part is dedicated to the description and modelling of wind turbines based on physical equations responsive operation.

The second part, we present a mathematical model of the (DFIG) will simulate the model in generator mode.

The third is devoted to the study of the technique of indirect control power and compare the simulation results by PI Controller with Anticipation and PI Controller with Phase Advance.

II. MODEL OF THE TURBINE

The model is based on the characteristics of steady state power of the turbine [1]. (1) With (2) : Rotation speed before multiplier. R :rotor radius 35.25 m : air density, 1.225 kg. !" # # $% &'( )!"% * + (3) with :

, -./0# ..12- et 34567 ; 557 ; 38 ;$ 4 ;1 95 ; + 3337: [1].

Fig.1 The power factor for different angles of stalls

Characteristics of in terms of for different values of the pitch angle are shown in figure 1. The maximum value of (;< 38=4= ) is reached of =2 and =10.01. This particular value of is defined as the nominal value >?[1] ,[2].

III. DYNAMIC MODEL OF THE DOUBLY FED

INDUCTION MACHINE A commonly used model for the doubly fed induction

generator (DFIG) is the Park model. The electrical equations of the DFIG in the Park reference frame are given as follows [2], [3]:

@ABC BDEF * FGHIF # JEKELABM BDEL * FGHNF * JEKEF O (4)

@APC PDQF * FGRIF # JQKQLAPM BDQL * FGRNF *JQKQF O (5) The stator and rotor flux are given as: SKBC TBDEF * TDQFKBM TBDEL * TDQL O (6) SKQC TQDQF * TDEFKPM TQDQL * TDEL O (7)

In these equations,UV UW XV and XW are respectively the resistances and the inductances of the stator and the rotor windings,XYis the mutual inductance.

0 5 10 15 20 25-0.1

0

0.1

0.2

0.3

0.4

X: 10.01

Y: 0.4353

report of the tip speed lambda P

ow

er

co

effic

ien

t C

p

B=2

B=10

B=15

B=5

B=20

!

ZV[ ZV\ ZW[] ZW\ ^V[ ^V\ ^W[] ^W\ _V[ _V\ _W[] _W\ are the d and q components of the stator and rotor voltages, currents and flux, whereas `ais the rotor speed in electrical degree.

The electromagnetic torque is expressed as: b cKEF DEL # KEL DEF (8)

Stator and rotor variables are both referred to the stator reference Park frame. With the following orientation, the d component of the stator flux is equal to the total flux whereas the q component of the stator flux is null figure. 2.

Fig.2 Determination of the electrical angles in Park reference frame

KEF KE KEL 3 (9)

By replacing (9) in (6) and (8), the electromagnetic torque can be given as follows: b #c ddH DQLKEF (10)

Assuming that the resistance of the stator winding UV is neglected, and referring to the chosen reference frame, the voltage equations and the flux equations of the stator winding can be simplified in steady state as follows: S eEF 3eEL eE JEKE O (11) SKBC TBDEF * TDQF3 TBDEL * TDQL O (12)

From (12), the equations linking the stator currents to the rotor currents are deduced below:

@DEF GHdH # ddH DQFDEL # ddH DQL O (13)

The active and reactive powers at the stator side are defined as:

SB eBCDEF * eELDELfB eBMDEF * eEFDQL O (14)

Taking into consideration the chosen reference frame, the above power equations can be written as follows: SB eEDELfB eBDEF O (15) Replacing the stator currents by their expressions given in (15), the equations below are obtained:

@ E #eE ddH DQLfE gHGHdH # gHddH DQF O (16) The block diagram of the DFIG model in Park reference frame is depicted in figure 3, assuming a constant stator voltage (vs).

Fig.3 Block diagram of the DFIG model

IV. REGULATION WITH BUCKLE OF POWER

to improve the control system the DFIG, we will introduce an additional loop control of active and reactive power in the block diagram of the control loop without power so that each axis controller contains two PI control, one to control the power and the other rotor current (figure 4) [4]

APC

APM hB

iB jkP * lmP # mnomB

#TETE

#TETE

pPmP # mnomB

pPmP # mnomB qBomBpB

pP mnmB rB

jkP * lmP # mnomB

sPM

sPC

0

d,q frame

Stator axis

tn tB

tP uvvwBx uvvwPx

uvvwPy uvvwC

uvvwM qvvwB

rvvwB uvvwBy

!

Fig.4 Schema block indirect regulation with loop power

V. SYNTHESIS OF THE REGULATOR PI FOR

THE CONTROL OF THE POWER

It is a simple and easy to implement controller. Figure 5 shows a closed loop system corrects by a PI controller. In our

case, the transfer function is in the form z{ * z|{ as shown in Figure 5

Fig.5 diagram of the control system by PI

The transfer function of the open loop (FTBO) with

regulators is written as follows [2 ,6 ,7]:

}~ -"

RRR- (17)

Applying the method of compensation pole transfer

function 1, we obtain the following equality: " RdR (18)

After compensation, the following are obtained FBO: }~ dR (19)

This gives us the transfer function following closed loop: }~ - (20) With: dR and 5 # ddHdR% : is the response time of the system that we fix the order of

10ms.In this case, the gains of the PI controllers are expressed in terms of machine parameters and response time as follows:

@ dR R O (21) We used the method of compensation poles for its speed; it

is clear that n 'not the only valid method for the synthesis of PI controller.

VI. MODEL OF THE MULTIPLIER

MECHANICAL PART

The mechanical party of the turbine includes three directional blades pitch and of length R. They are fixed to a drive shaft in a rotation speed], a multiplier Connected of gain G. This multiplier causes the electric generator. We can model all the three blades as one and the same mechanical system characterized by the sum of all the mechanical characteristics. Due to the aerodynamic blade design, we believe that the coefficient of friction with respect to the air is very small and can be neglected. Also, the speed of the turbine being very low, Friction losses will be negligible compared to the friction losses on the side of the generator. On the basis of these hypotheses, is then obtained a mechanical model consisting of two masses as shown in figure 6, the validity, relative to the complete model of the turbine, has already been verified [1], [5].

5kP * lmP

l * sl P

DFIG

JQTQ PI

JQTJETE EL PI

JQTQ

# TETE

# TETE

PI

PI

ELJETE E fE

DQF

DQL QLQb

QFQb

DQLQb

DQFQb

EQb

fEQb

!

"

Fig.6 Mechanical model of the wind turbine

With: : Moment of inertia of the turbine to the equivalent

inertia of the three blades of the turbine. : the moment of inertia of the DFIG. : The coefficient due to viscous friction of DFIG. : mechanical torque on the shaft of the DFIG. : the rotational speed of the DFIG. : the electromagnetic torque of the DFIG. By considering that the multiplier is ideal, That is to say,

the mechanical losses are negligible, it is then modelled by the following two equations: (22) =G. (23)

From Figure 6, we can write the fundamental equation of dynamics of the mechanical system of the mechanical shaft DFIG by: * % FF * # b (24) The total inertia J : * % (25)

VII. CONTROL STRATEGIES OF THE TURBINE

The control strategy is to adjust the torque appearing on the tree turbine speed so as to fix a reference. To achieve this, we will use a speed control [2] ,[3].

According to equation (24) and (25): FF # # b (26)

The electromagnetic torque is: bQb Qb # b (27) Qb Q>bQb (28)

The reference speed of the turbine corresponds to the

optimum value corresponding to the speed ratio]{ (fixed on the blade angle to 2).

Q>bQb ! (29)

The couple thus determined by the controller is used as a reference torque of the turbine model as can be seen in figure 7.

Fig.7 Block diagram of the controller with mechanical speed

VIII. CORRECTION OF THE SPEED OF THE TURBINE

Different technologies can be considered markers for control of the speed; in our case we describe two types of regulations:

A. PI Controller with Anticipation

We consider a correction proportional integral (PI): bQb * E % Qb # b (30) j : proportional gain and : integral gain, correction parameters are determined. It is necessary to increase the parameter to reduce the action of wind torque. The natural frequency and damping coefficient are given by: J> and -- (31)

Can impose a time response and damping factor given was:

. J> and # # (32)

qA j

j

jB * n n

kPsqA l o B qA j

n

PI G l qAk

P

Control device with control of the speed

mechanical

Turbine Multiplier

Tree

n

G

b

f

!

#

B. PI Controller with Phase Advance

We consider a correction proportional integral (PI): bQb ;E-;E- Qb # b (33)

j,] et] are the parameters to determine the corrector and s is the Laplace variable. It is necessary to increase the parameter to reduce the action of wind torque. The natural frequency and damping coefficient are given by:

J> ;- and --;;- (34)

IX. SIMULATION RESULTS:

The simulation is done by imposing active and reactive

power reference (a a), While the machine is entailed in variable speed Qb ?, fQb 3 with: : Performance DFIG; ?: The optimal mechanical power the simulation results are given by the following figures.

Fig.8 Mechanical speed with anticipation control

Fig.9 Electrical active power produced with anticipation control

Fig.10 Electrical reactive power produced with anticipation control

Fig.11 Mechanical speed with phase advance control

Fig.12 Electrical active power produced with phase advance control

0 1 2 3 40

1000

2000

3000

4000

5000

time [s]

Me

ch

an

ica

l sp

ee

d (

tr/m

in)

anticipation

0 1 2 3 4-16

-14

-12

-10

-8

-6

-4

-2

0

2x 10

5

time [s]

active p

ow

er [W

]

anticipation

Pmes

Pref

0 1 2 3 4-1

-0.5

0

0.5

1x 10

5

time [s]

re

active

po

we

r [V

AR

]

anticipation

Qmes

Qref

0 1 2 3 40

500

1000

1500

2000

2500

time [s]

Mechanic

al speed (tr/m

in)

phase advance

0 1 2 3 4-10

-8

-6

-4

-2

0

2x 10

5

time [s]

activ

e p

ow

er [W

]

phase advance

Pmes

Pref

!

$

Fig.13 Electrical reactive power produced with phase

advance control

X. CONCLUSION

In our work, we have established the model of the machine using its power equations in the dq axis system related to synchronization. We have also developed the method of vector control power of the machine to know the order.

The two methods of maximizing power were almost granny gives results (speed mechanical, power active and reactive) the only difference and the transient time in the case of PI with big anticipation and compared PI phase advance. APPENDIX

NOMINAL POWER =1.5(MW)

STATOR PER PHASE RESISTANCE =0.012 ()

ROTOR PER PHASE RESISTANCE=0.021 ()

STATOR LEAKAGE INDUCTANCE= 2.0372.10-004 (H)

ROTOR LEAKAGE INDUCTANCE= 1.7507.10-004 (H)

MAGNETIZING INDUCTANCE= 0.0135 (H)

NUMBER OF POLES PAIRS=2

MOMENT OF INERTIA= 1000 (KG.M2)

FRICTION COEFFICIENT =0.0024

RFERENCES [1] Z. Lubosny, Wind Turbine Operation in Electric Power Systems, Berlin, Germany: Springer, 2003. [2] S.El Aimani, Modlisation De Diffrentes Technologies Doliennes Intgres Dans Un Rseau De Moyenne Tension. [3].F.Poitiers, Etude Et Commande De Gnratrices Asynchrones Pour Lutilisation De Lnergie Eolienne,2003. [4] A. Mehdary, tude dune chaine de conversion dnergie olienne

base dune aroturbine ,6mes Journes des doctorants, Laboratoire des sciences de linformation et des systmes LSIS, universit de St Jrme, Marseille,2009 [5] J. Usaola, P. Ledesma, J. M. Rodriguez, J. L. Fernadez, D. Beato, R. Iturbe,J. R. Wihelmi, Transient stability studies in grids with great wind power penetration. Modeling issues and operation requirements, Proceedings of the IEEE PES Transmission and Distribution Conference and Exposition, September 7-12, 2003, Dallas (USA). [6].Moriarty P.J. Butterfield S.B. Wind Turbine Modeling Overview for Control Engineers, In Proc .American Control Conf., St.louis, MO, 2009. [7] Multon B. Obin G. Gergaud O. Ben Ahmed H. Le Gnie Electrique dans le vent : tat de lart et recherches dans le domaine de la gnration olienne, JCGE03, Saint-Nazaire, 2003.

0 1 2 3 4-1

0

1

2

3

4x 10

4

time [s]

re

ac

tiv

e p

ow

er

[VA

R]

phase advance

Qmes

Qref