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Energy Procedia 18 (2012) 476 - 485

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

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

a b c deLDDE laboratory members, University Mohamed BoudiafUSTO 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 induction generator (DFIG) connected to the electric power grid. The aim of the work is to apply and compare the dynamic performances of two types of controllers (namely, classical PI and Fuzzy-PI) for the WECS in terms of tracking and robustness with respect to the wind fluctuation as well as the impact on the quality of the energy produced. A vector control with stator flux orientation of the DFIG is also presented to control the active and reactive powers between the stator and the grid, and further to achieve maximum wind energy capturing. To show the effectiveness of the control method performances analysis of the system are analyzed and compared by simulation in terms of the performances of the machine.

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

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 rotor accessible 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 system power [1]-[2]. This is very attractive for both energy generation and high power drive applications. Fuzzy logic (FL) based techniques have been proposed for wind power generation control [3]. The FL based controller of a given system is capable of embedding, in the control strategy, the qualitative knowledge and 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: hamane.bekhada@yahoo.com (B.HAMANE) / mbenghanem69@yahoo.fr (M.BENGHANEM) adraou@yahoo.com (A.DRAOU). allalbouzid@live.fr (A.M.BOUZID). abdallah.belabbes@gmail.com (A.BELABBES)

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

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

Nomenclature

Vds, Vqs, Vdr, Vqr Stator and rotor voltage components in the d-q reference frame.

Ids, Iqs, Idr, Iqr Stator and rotor current components in the d-q reference frame.

(pds, ç>qs,(pdr, (pqr Stator and rotor flux components in the d-q reference frame.

cos,ar, fi r Stator frequency, rotor rotating speed and mechanical rotor speed respectively.

g, P Respectively slip and Number of pole pairs.

Ps, Qs, Pt Active reactive stator power and turbine mechanic power respectively.

Tm, Te Mechanical and electromagnetic torques respectively.

v,/M, Cp 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 2 3 P , = —.Cp .p .R .V 3

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

1 2 3 pt -.cp.P.r2.V3

cot G>t

Where cot, is the aerodynamic rotor speed.

The power coefficient can be expressed in terms of the pitch angle ß and the tip speed ratio X [5]:

CP = f (A,J3) = Ci--C3.ß -C4

+ C 6X

And the power coefficients are given by: C/=0.5, C=116, Cj=0.4, C4=0, Cj=5, Cô=21. Where A,i is obtained from:

ki A + 0.08 p p + 1 Hence the tip speed ratioA, can be rewritten as in [13]: co t.R cor .G .R

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

Fig. 2. Example of Cp ( X) curve B. Model ofDFIG

In 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]:

Vds = RsIds H---(Os(pqs

Vqs = RsIqs + -+ (OsCpds

Vdr = RrIdr H---{(Os — (Or)(pqr

Vqr = RrIqr h---1- {cas - (Or)q>dr

(pds = LsIds + LmIdr (pqs = LsIqs + LmIqr (pdr = LrIdr + LmIds (pqr = LrIqr + LmIqs

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

Te = — — P-((pdslqr— (pqslds)

J-+ filr = Te~Tm

3. Control of Active and Reactive Power of DFIG

Figure 4 represents the control of the active and reactive power of DFIG:

Fig. 4. Control power between the stator and the network

To 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 with d-axis, we shall have (pds = (ps and<pqs = 0 .

Te =--P-(ÇdsIqr)

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

I Vds = 0

[ Vqs = Vs = (Os(pds (pds = (ps = LsIds + LmIdr I (pqs = 0 — LsIqs 4" LmIqr

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

Ps = VdsIds + VqsIqs = —Vs-Iqr

Lm (ps

Qs = Vqs Ids — VdsIqs = —Vs-Idr + Vs-

L s L s

Vdr = RrIdr +

Vqr — RrIqr "I"

-Idr — gGk

- Iqr + gGk

Idr + g-

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

Za f t'f 'ft a I V > v/ i hfij

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 to achieve 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 tuning parameters with explicit action on the dynamical response. The second objective takes into account the non-linearity and cross-coupling terms. Finally, the last objective is to give parametric insensibility properties to the closed-loop against over-heating and ageing. And for that, we will synthesize two controllers namely, PI and Fuzzy-PI.

A. PI controller design

The power block diagram is equivalent on each axis to a first order transfer function as shown in Figure 6[12],

Fig. 6. Equivalent PI control scheme

To keep the property of symmetry of the open-loop, the controllers' gains are voluntarily chosen symmetric:

{Kpp = Kpq (13)

Kip = Kiq

And the values of A and B are obtained from:

A = LsRr+ p(LrLs — Lm )

B = LmV

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

Fig.7. The PI controller structure

The transfer function of the open loop including the regulator is:

Ki L m Vs

p + - -2—

G(p) = _—._(LrLs~Lm )__(15)

p LsRr

- p + -"

K p ( L rL s — L m )

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

Ki LsRr

Kp (LrLs Lm )

The transfer function of the open loop becomes:

L m V i

( L rL S - L m )

G ( p ) = -

The transfer function of the closed loop is expressed by:

1 Which 1 L

sL r — L m

H ( P ) =-----> *r =--(18)

1+ P Tr K p L m V s

For a response time t r(5%) = 10_3s the Kvand Kt expressions were given by equation (18).

Kp = Kpp = Kpq =

1 LsLr — Lm

10 LmVs (19)

1 LsRr

Ki = Kip = Kiq —-—--

10 3 LmVs

B. Fuzzy-Pl controller design

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

Fig.8. The Fuzzy-PI Controller structure

The PI Controller parameters used are taken normalized in the interval [0, 1], using the following linear transformations [11]:

K p — ( Kp — Kp min) /( Kp max — Kp min) Kp — (Ki — Ki min) /( Ki max — Ki min)

The inputs of fuzzy controller are: error (e) and derivative (de/dt) of error, the outputs are: the normalized value of the proportional action (Kp) and the normalized value of the integral action (K/).The inputs signals have 3 membership functions, while the proportional gain Kp has 4 and the integral gain K[ has 2.The 3 membership functions of the active and reactive power controllers of the inputs are designed as shown in Figure 9. (a). The membership functions for the proportional gain Kp and the integral gain K[ of the 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 Kp and K[ membership functions

Which: Negative Big noted NB; Zero noted ZE; Positive Big noted PB; Positive Medium noted MP;

Positive Small noted PS.

The fuzzy rules of the active and reactive power controllers, as shown:

Table 1.The Fuzzy Controller for Kp rule base Table 2.The Fuzzy Controller K[ rule base

U NB ZE PB

NB ZE ZE ZE

de/dt ZE PB PS PB

PB ZE PM ZE

U NB ZE PB

de/dt NB PB PB PB

ZE ZE PB ZE

PB PB PB PB

Once the values Kp andK[ are obtained the new parameters of the PI Controller are calculated by the equation [11]:

Kp — (Kp max — Kp min). K p + Ki

Ki — (Ki max — Ki max)K' + Ki 5. Simulation Results

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

A. Reference tracking

The 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 classical PI and the Fuzzy-PI controller. Results are presented in figure 10.

_ 10 g

• Ps-mes ' Ps-ref

.c T 2

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 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Time (sec)

Time (sec)

I 3 ■

* 1 .c

- Qs-mes !4 CD 5 3 o 6 e > 2 ct (Q e . 1 .C T - Qs-mes

• Qs-ref Qs-ref

0.04 0.06

Time (sec)

0.1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Time (sec)

Fig.10. Dynamic Responses to the active and reactive power step change (a) Using PI Controller; (b) Using Fuzzy-PI Controller

B. Robustness

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

_ 10 s

is 8 Î

=■ 6

(Q V É 2

o 1 ta 1 tu

jï 0 h-

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Time (sec)

s—-. ---V

Qs-ref / \ ;

/ \ ]

1 \ 1 1

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Time (sec)

_ 10 S

É 2 0

- Ps-mes

- Ps-ref

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Time (sec)

■ Qs-mes " Qs-ref

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Time (sec)

Fig.11. Active and reactive power behaviour with Lm variation

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

■ Ps-mes (PI)

■ Ps-mes (Fuzzy-PI)

0.01 0.015 0.02 Time (sec)

Fig.12. Comparative response of the active power using the PI Controller and Fuzzy-PI Controller respectively

Thus 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

-0.005

controllers using respectively a classical PI and Fuzzy-PI are synthesized to perform powers reference tracking and efficient disturbance rejection. The results have shown that with the Fuzzy-PI controller, the settling time is reduced considerably, peak overshoot of values are limited and oscillations are damped out faster compared to the conventional PI Controller. The transient response provided by the Fuzzy-PI Controller 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 oflECON 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, International Symposium 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 power generator, ", 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 energy conversion systems,"/EEE 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 Power System," 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 thesis electrical engineering department, university Mohamed Boudiaf USTO 2006.

Appendix

Table 3.Parameters of DFIG

Table 4.Parameters of Turbine

Symbol Value Symbol Value

Rated Power Pm 1.5 MW Radius of the wind R 35.25 m

Stator resistance Rs 0.012 Q Gain multiplier G 90

Rotor resistance Rr 0.021 a Air density p 1.225 kg/m3

Pole Pairs P 2

Stator inductance Ls Rotor inductance Lr 0.0137 H 0.0136 H Table 5.Parameters of Feed

Mutual inductance Lm The friction coefficient f The moment of inertia J Slip g The angular speed tas 0.0135 H 0.0024 N.m.s1 1000 kg.m2 0.03 157 rad/sec Symbol Value

Stator rated voltage Vs Rated frequency stator f Rotor rated voltage f Rated frequency stator Vr 398/690 V 50 Hz 225 / 389 V 14 Hz