control for variable speed wind turbine driving a doubly fed induction...

Energy Procedia 18 ( 2012 ) 476 – 485

1876-6102 © 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of The TerraGreen Society.doi: 10.1016/j.egypro.2012.05.059

Control for Variable Speed Wind Turbine Driving a DoublyFed Induction Generator using Fuzzy-PI Control

B.HAMANEa, M. BENGHANEMb, A.M.BOUZIDc, A.BELABBESd,M.BOUHAMIDAe,A.DRAOUf,a*

a,b,c,d,eLDDE laboratory members, University Mohamed Boudiaf USTO 1505Bp El Mnaouer,Oran 31000, Algeria.fDepartment of Electrical Engineering, Hail University, Hail, Saudi Arabia

Abstract

This paper presents a study analysis of a wind energy conversion system (WECS) based on a doubly fed inductiongenerator (DFIG) connected to the electric power grid. The aim of the work is to apply and compare the dynamicperformances of two types of controllers (namely, classical PI and Fuzzy-PI) for the WECS in terms of tracking androbustness with respect to the wind fluctuation as well as the impact on the quality of the energy produced. A vectorcontrol with stator flux orientation of the DFIG is also presented to control the active and reactive powers betweenthe stator and the grid, and further to achieve maximum wind energy capturing. To show the effectiveness of thecontrol method performances analysis of the system are analyzed and compared by simulation in terms of theperformances of the machine.

© 2010 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer]

Keywords:Wind Energy Conversion System;Doubly Fed Induction Generator;Vector Control;PI Control; Fuzzy-PI Control.

1. Introduction

Doubly-fed induction machine is an electrical three-phase asynchronous machine with wound rotoraccessible for control. Since the power handled by the rotor side (slip power) is proportional to the slip,the energy requires a rotor-side power converter which handles only a small fraction of the overall systempower [1]-[2]. This is very attractive for both energy generation and high power drive applications. Fuzzylogic (FL) based techniques have been proposed for wind power generation control [3]. The FL basedcontroller of a given system is capable of embedding, in the control strategy, the qualitative knowledgeand experience of an operator or field engineer about the process, but has been criticized for its

* Corresponding author. Tel.:+213-550-023-222; fax: +213-41-560-328.E-mail address: [email protected] (B.HAMANE) / [email protected] (M.BENGHANEM)[email protected] (A.DRAOU). [email protected] (A.M.BOUZID). [email protected] (A.BELABBES)

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© 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of The TerraGreen Society.

B.HAMANE et al. / Energy Procedia 18 ( 2012 ) 476 – 485 477

limitations, such as the lack of a formal design methodology, the difficulty in predicting stability androbustness of FL controlled systems [4]. The aim of this paper is to present the complete modeling andsimulation analysis and performance comparison of wind turbine driven doubly-fed induction generatorby using both the classical PI and Fuzzy-PI controller. Fuzzy-PI Control strategy was adopted to controlboth the active and reactive power, and achieve the maximum wind energy capturing. The simulationresults show that this strategy has fast dynamic response, good robustness and low dependence on themodel parameters.

Fig.1.Doubly Fed Induction Generator (DFIG)

Nomenclatureqrdrqsds VVVV ,,, Stator and rotor voltage components in the d-q reference frame.

qrdrqsds IIII ,,, Stator and rotor current components in the d-q reference frame.qrdrqsds ,,, Stator and rotor flux components in the d-q reference frame.

rrs ,, Stator frequency, rotor rotating speed and mechanical rotor speed respectively.Pg , Respectively slip and Number of pole pairs.

tss PQP ,, Active reactive stator power and turbine mechanic power respectively.em TT , Mechanical and electromagnetic torques respectively.

pC,,, Wind speed, pitch angle, tip speed ration and the power coefficient respectively.

2. Model of Wind Turbine

A. Model of Turbine

The mechanical power transferred from the wind to the aerodynamic rotor is given in [6]-[13] by:

(1)

Thus, the input torque in the transmission mechanical system is:

(2)

Where t, is the aerodynamic rotor speed.The power coefficient can be expressed in terms of the pitch angle and the tip speed ratio [5]:

(3)

32 ....2

1RCP pt

t

32p

t

tm

.R..C.21

PT

65

432

1 exp..),( CC

CCC

CfCii

p

478 B.HAMANE et al. / Energy Procedia 18 ( 2012 ) 476 – 485

And the power coefficients are given by: C1=0.5, C2=116, C3=0.4, C4=0, C5=5, C6=21.Where i is obtained from:

(4)

Hence the tip speed ratio can be rewritten as in [13]:

(5)

The characteristic of power coefficient versus tip speed is shown in Figure 2. Under certain values ofthe wind power can be controlled by adjusting either tip speed ratio or pitch angle [13]

Fig. 2. Example of Cp ( ) curve

B. Model of DFIGIn the rotating field reference frame, the model of the DFIG is shown in Figure 3:

Fig.3. PARK’s Model of the DFIG

The stator and rotor voltage equations and flux components are given below [14]:

(6)

1

035.0

.08.0

113

i

R.G.R. rt

qsqrrqr

dsmdrrdr

qrmqssqs

drmdssds

drrsqr

qrrqr

qrrsdr

drrdr

dssqs

qssqs

qssds

dssds

LmIIL

ILIL

ILIL

ILIL

dt

dIRV

dt

dIRV

dt

dIRV

dt

dIRV

)(

)(


The equations of the electromagnetic and mechanical torques are [14]:

(7)

3. Control of Active and Reactive Power of DFIGFigure 4 represents the control of the active and reactive power of DFIG:

Fig. 4. Control power between the stator and the networkTo achieve a stator active and reactive power vector control as illustrate on figure 4, we choose a d-

q reference frame synchronized with the stator flux [8]-[10]. By setting the stator flux vector aligned withd-axis, we shall have sds and 0qs .

)(L

LPT qrds

s

me I

23

(8)

Note that this torque represents a disturbance for the wind turbine and takes a negative value. Theelectromagnetic torque and the active power will only depend on the q-axis rotor current. Neglecting theper phase stator resistance Rs (that's the case for medium and high power machines used in wind energyconversion systems) [9], the stator voltages and fluxes can be rewritten as follows:

(9)

(10)

The stator active and reactive power and voltages are given by:

(11)

(12)

dsssqs

ds

VV

V 0

qrmqssqs

drmdsssds

ILIL

ILIL

0

s

smdr

s

mrsqr

s

mrqrrqr

qrs

mrsdr

s

mrdrrdr

LLg

LLLLL

LLL

LLL

VIgI

dt

d

LIRV

IgIdt

dIRV

22

22

s

ssdrs

msqsdsdsqss

qrs

msqsqsdsdss

LVI

L

LVIVIVQ

IL

LVIVIVP

merr

dsqsqrdss

m

TTfJ

L

Le

dtd

IIPT )(23


In steady state, the second derivative terms in (12) are nil. The third terms constitutes cross-couplingterms. The block-diagram representing the internal model of the system is presented in Figure 5. Theinput blocks relating to represent the simplified rotor converter model. Knowing equations (11)and (12), it is then possible to synthesize the regulators.

Fig .5. Block diagram of the power system

4. Controllers Synthesis

This section deals with the synthesis of PI and Fuzzy-PI controllers. Both controllers are designed toachieve the following control objectives [12]:

Performing active and reactive power reference tracking;Efficient disturbance rejection ;Parametric robustness.

The first objective induces fast dynamics of the transient response but it may lead to few tuningparameters with explicit action on the dynamical response. The second objective takes into account thenon-linearity and cross-coupling terms. Finally, the last objective is to give parametric insensibilityproperties to the closed-loop against over-heating and ageing. And for that, we will synthesize twocontrollers namely, PI and Fuzzy-PI.

A. PI controller designThe power block diagram is equivalent on each axis to a first order transfer function as shown in Figure6[12].

Fig. 6. Equivalent PI control scheme


To keep the property of symmetry of the open-loop, the controllers’ gains are voluntarily chosensymmetric:

(13)

And the values of A and B are obtained from:

(14)

It is a simple and fast controller to implement. Figure 7 shows a closed loop system corrected by a PIController.

Fig.7. The PI controller structureThe transfer function of the open loop including the regulator is:

)LLL(

RLp

)LLL(

VL

.

K

pK

Kp

)p(G

2msr

rs

2msr

sm

p

p

i

(15)

To cancel the pole we added a zero at the same location as the pole, equation (15) gives a pole value.

(16)

The transfer function of the open loop becomes:

(17)

The transfer function of the closed loop is expressed by:

(18)

For a response time (5%) = 10 the and expressions were given by equation (18).

(19)

sm

rsiqipi

sm

mrspqppp

VL

RLKKK

VL

LLLKKK

3

3

10

110

1 2

VLB

LLLpRLA

m

msrrs )(2

iqip

pqpp

KK

KK

pLLL

VLK

pG msr

smp

)()(

2

)( 2msr

rs

p

i

LLL

RL

K

K

sm

mrs

pr

r VL

LLL

KWhich

ppH

21

1

1)(


B. Fuzzy-PI controller designAccording to the operational features of DFIG and control requirements, a Fuzzy-PI control strategy ispresented in this paper, system structure shown in Figure 8. It consists of a Fuzzy-PI Controller [7]. Themethod used in this synthesis is the Gain Scheduling which is a technique that acts on the parameters ofPI Controller ( , ) to be varied during the control system .This makes the PI controller adapted tononlinear systems. The Fuzzy Controller adjusts the parameters of the PI and it generates new parametersso that it fits all operating conditions, based on the error and its derivative. And the majority of thedeveloped controllers use the simple diagram suggested by Mamdani [15].

Fig.8. The Fuzzy-PI Controller structureThe PI Controller parameters used are taken normalized in the interval [0, 1], using the following lineartransformations [11]:

(20)

The inputs of fuzzy controller are: error (e) and derivative (de/dt) of error, the outputs are: the normalizedvalue of the proportional action ( ) and the normalized value of the integral action ( ).The inputssignals have 3 membership functions, while the proportional gain has 4 and the integral gain has2.The 3 membership functions of the active and reactive power controllers of the inputs are designed asshown in Figure 9. (a). The membership functions for the proportional gain and the integral gain ofthe active and reactive power controller are designed as in Figure 9. (b).

(a) (b)Fig.9. (a) The error and its variation membership functions ;( b) The and membership functionsWhich: Negative Big noted NB; Zero noted ZE; Positive Big noted PB; Positive Medium noted MP;Positive Small noted PS.

)/()(

)/()(

minmaxmin'

minmaxmin'

iiiip

ppppp

KKKKK

KKKKK


The fuzzy rules of the active and reactive power controllers, as shown:Table 1.The Fuzzy Controller for rule base Table 2.The Fuzzy Controller rule base

Once the values and are obtained the new parameters of the PI Controller are calculated by theequation [11]:

(21)

5. Simulation Results

To analyze the system and compare efficiently the two proposed controllers, a set of simulation testshave been performed for 0.1sec, using Matlab –Simulink environment. The 2 regulators are tested andcompared by two different criteria’s; namely reference tracking, and robustness by varying the parametersof the system. DFIG and the turbine parameters used in the simulation are listed in table 3and 4,respectively.

A. Reference trackingThe machine is first tested as in ideal conditions mode and driven to 1500 rpm. Different step inputs

for an active and a reactive power were applied and we observed the response obtained with both classicalPI and the Fuzzy-PI controller. Results are presented in figure 10.

(a) (b)Fig.10. Dynamic Responses to the active and reactive power step change

(a) Using PI Controller; (b) Using Fuzzy-PI Controller

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

2

4

6

8

10

12x 105

Time (sec)

Theactivepower(W)

Ps-mes

Ps-ref

0 0.02 0.04 0.06 0.08 0.10

1

2

3

4

5x 105

Time (sec)

Thereactivepower(VAr)

Qs-mes

Qs-ref

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

2

4

6

8

10

12x 10

5

Time (sec)

Theactivepower(W) Ps-mes

Ps-ref

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5x 105

Time (sec)

Thereactivepower(VAr)

Qs-mes

Qs-ref

eU NB ZE PB

NB PB PB PBde/dt ZE ZE PB ZE

PB PB PB PB

eU NB ZE PB

NB ZE ZE ZEde/dt ZE PB PS PB

PB ZE PM ZE

min'

maxmax

min'

minmax

)(

).(

iiiii

ppppp

KKKKK

KKKKK


B. Robustness

In order to test the robustness of the two controllers, the value of mutual inductance Lm is decreasedby 10% of its nominal value. Figure 11 (a) and 11 (b); show the effect of parameters variation on theactive and reactive power response for the two controllers.

(a) (b)Fig.11. Active and reactive power behaviour with Lm variation

(a) Using PI Controller; (b) Using Fuzzy-PI ControllerThis test shows clearly that in the case of the classical PI regulator, the time response is strongly

altered whereas in the case of the proposed Fuzzy-PI controller it is almost unaltered.

C. Comparison of the behavior of the two controllers

Fig.12. Comparative response of the active power using the PI Controller and Fuzzy-PI Controller respectivelyThus we can conclude from these results that the Fuzzy-PI Controller is more powerful than the

classical one.

6. Conclusion

In this paper, a decoupling control method of active and reactive powers for DFIG has been developed.Moreover, an appropriate model and vector control strategy have been established. Further, two types of

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

2

4

6

8

10

12x 105

Time (sec)

Theactivepower(W)

Ps-mesPs-ref

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

2

4

6

8

10

12x 10

5

Time (sec)

Theactivepower(W)

Ps-mes

Ps-ref

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1

0

1

2

3

4

5x 10

5

Time (sec)

Thereactivepower(VAr) Qs-mes

Qs-ref

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5x 10

5

Time (sec)

Thareactivepower(VAr) Qs-mes

Qs-ref

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350

1

2

3

4

5

6x 105

Time (sec)

Theactivepower(W)

Ps-mes (PI)Ps-mes (Fuzzy-PI)


controllers using respectively a classical PI and Fuzzy-PI are synthesized to perform powers referencetracking and efficient disturbance rejection. The results have shown that with the Fuzzy-PI controller, thesettling time is reduced considerably, peak overshoot of values are limited and oscillations are dampedout faster compared to the conventional PI Controller. The transient response provided by the Fuzzy-PIController has been superior to the classical PI controller.

Reference[1] J.Soltani, A. Farrokh Payam, “A Robust Adaptive Sliding-Mode Controller for Slip Power Recovery Induction Machine

Drives,” IEEE Trans. Power Electronics and Motion Control Conference, vol.3, pp. 3-8, 2006.[2] Sergei Peresada, Andrea Tilli, Alberto Tonielli, “Indirect Stator Flux-Oriented Output Feedback Control of a Doubly Fed

Induction Machine,” IEEE Trans .Control Systems Technology, vol.11, pp.875-888, Nov 2003.[3] Gilbert0 C, D. Sousa and, B. K. Bose, “Fuzzy logic applications to power electronics and drives - an overview,”

Proceedings of IECON 1995, Nov 1995, pp.57-62.[4] J. G. Slootweg, H. Polin der and, W. L. Kling, “Initialization of wind turbine models in power systems dynamic

simulations,” IEEE Trans .Power Tech Conference, Porto Portugal, Vol. 3, 6 pp, Sep 2001.[5] H. M. Soloumah and N. C. Kar, “Fuzzy logic based vector control of a doubly-fed induction generator for wind power

application,” IEEE Trans .Wind Engineering, vol. 30, no. 3, pp. 201-224, 2006.[6] Siegfried Heier, ‘Grid Integration of Wind Energy Conversion Systems,’ John Wiley & Sons Ltd, ISBN 0-471-97143-X,

1998.[7] Yao Xing-jia, Liu Zhong-liang, Cui Guo-sheng “Decoupling Control of Doubly-Fed Induction Generator based on

Fuzzy-PI Controller,” IEEE Trans.Mechanical and Electrical Technology (ICMET 2010) , pp 226-230 ,2010.[8] T.D. Mai, B.L. Mai, D.T. Pham, and H.P. Nguyen: “Control of doubly-fed induction generators using Dspace R&D

controller board – an application of rapid control coordinated with Matlab/Simulink ,“ October 2007, InternationalSymposium on Electrical & Electronics Engineering, Track. 3, pp 302-307.

[9] L. Zhang, C. Watthansarn and W. Shehered: “A matrix converter excited doubly-fed induction machine as a wind powergenerator, “, IEEE Trans.Power Electronics and Variable Speed Drives, vol. 2, pp 532 - 537, 06 août 2002.

[10] F. Poitiers M. Machmoum R. Le Daeufi and M.E. aim, “Control of a doubly-fed induction generator for wind energyconversion systems,”IEEE Trans .Renewable Energy, Vol. 3, N°. 3, pp.373-378, December 2001.

[11] T.J.Porcyk and E.H.Mamdani, “A linguistic self-organizing process controller, ”Automatica, vol.15, pp.15-30, 1979.[12] M. Machmoum, F. Poitiers, C. Darengosse and A. Queric, “Dynamic Performances of a Doubly-fed Induction Machine

for a Variable-speed Wind Energy Generation,” IEEE Trans. Power System Technology, vol. 4, pp. 2431-2436, Dec.2002.

[13] Md. Rabiul Islam1, Youguang Guo, Jian Guo Zhu, “Steady State Characteristic Simulation of DFIG for Wind PowerSystem,” IEEE Trans. Electrical and Computer Engineering (ICECE), pp. 151-154, 2011.

[14] T. Luu, A. Nasiri, “Power Smoothing of Doubly Fed Induction Generator for Wind Turbine Using Ultra capacitors,“IEEE Trans.IECON 2010 - 36th Annual Conference., pp. 3293-3298, 2010

[15] A.Hazzab, " Commande des systèmes par logique floue, Réseau de neurones et Algorithmes géniques", Doctoral thesiselectrical engineering department, university Mohamed Boudiaf USTO 2006.

AppendixTable 3.Parameters of DFIG

Symbol ValueRated Power PmStator resistance Rs

1.5 MW0.012

Rotor resistance Rr 0.021Pole Pairs PStator inductance LsRotor inductance LrMutual inductance LmThe friction coefficient fThe moment of inertia JSlip gThe angular speed s

20.0137 H0.0136 H0.0135 H0.0024 N.m.s-1

1000 kg.m2

0.03157 rad/sec

Table 4.Parameters of Turbine

Symbol ValueRadius of the wind RGain multiplier G

35.25 m90

Air density 1.225 kg/m3

Table 5.Parameters of Feed

Symbol ValueStator rated voltage VsRated frequency stator fs

398 / 690 V50 Hz

Rotor rated voltage frRated frequency stator Vr

225 / 389 V14 Hz

control for variable speed wind turbine driving a doubly fed induction...

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