vector control of a dfig based wind turbine

7/26/2019 Vector Control of a DFIG Based Wind Turbine

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ISTANBUL UNIVERSITY –

JOURNAL OF ELECTRICAL & ELECTRONICS ENGINEERING

YEAR

VOLUME

NUMBER

: 2009

: 9

: 2

(1057-1066)

Received Date: 05.02.2009 Accepted Date: 05.11.2009

VECTOR CONTROL

OF A DFIG BASED WIND TURBINE

1Md. ARIFUJJAMAN, 2M.T. IQBAL, 2John E. QUAICOE

1,2 Faculty of Engineering and Applied ScienceMemorial university of Newfoundland

St. John’s, NL, Canada A1B3X5

1Email: [email protected]

ABSTRACT

Variable speed wind turbines (WT) based on the Doubly-Fed Induction Generator (DFIG) iscommercially offered and is frequently used in grid connected mode. The variable speed operation in such wind turbines is achieved by means of a four-quadrant ac-dc-ac power converter among therotor winding and the grid while the stator is directly connected to the grid. Below rated wind speed,tracking the maximum power/torque curve realized by speed/current control mode while pitch

control ensures the rated power for above rated wind speed. In this research, a maximum powercontrol strategy is incorporated with the DFIG whereby the produced power serves as the dynamic

active power reference for the DFIG. Stator flux oriented vector control is applied to decouple thecontrol of active and reactive power generated by the DFIG based WT. Details of the control strategyand system simulation results in Simulink are presented in the paper to show the effectiveness of the proposed control strategy.

Keywords: Variable speed wind turbine; Doubly fed induction generator; Pitch control; Vectorcontrol; Maximum power control .

1. NOMENCLATURE

,ds qsV V : d- and q- axis stator voltages

respectively

,dr qr

V V : d- and q- axis rotor voltages

respectively.

,ds qs I I : d- and q- axis stator currents

respectively.

,dr qr

I I : d- and q- axis rotor currents

respectively.

,ds qs

ϕ ϕ : d- and q- axis stator flux linkages

respectively.

,dr qr

ϕ ϕ : d- and q-axis rotor flux linkages

respectively.

, s r

R R : Stator and rotor resistances

respectively.

, s r L L : Stator and rotor inductances

respectively.

m L : Mutual inductance of stator and

rotor.

, ,m s r

ω ω ω : Mechanical, synchronous and rotor

speeds respectively.

, ,m s s

P P Q : Mechanical, stator active and rotor

reactive powers respectively.



1058Vector Control Of A Dfig Based Wind Turbine

Md. ARIFUJJAMAN M.T. IQBAL J.E. QUAICOE

,m e

T T : Mechanical and electrical torques

respectively.

2. INTRODUCTION

A Doubly-Fed Induction Generator can realize

the variable speed operation and thus maximizethe output power from the wind turbine [1]. Therotor windings of the DFIG are fed to the gridvia a four-quadrant ac-dc-ac power converter.This arrangement has several advantagesincluding rotor speed variation from subsynchronous to super synchronous speed basedon the wind speed, independent control of active

and reactive power and reduced flicker.

Fig. 1 A typical Grid connected WT based onDFIG

Typically the rotor converter adapts the slip power (usually 25% of the generator rating),

which results in reduced cost of the convertersystem. A typical grid connected WT based onDFIG is presented in Fig. 1.

Two converters namely, Rotor side converter(RSC) and Grid side converter (GSC) are anintegral part of such configuration. Scalar orvector control of the DFIG allows optimum

performance of the system. The vector control

scheme (VCS) is favored when a fast dynamicresponse and accurate control is required [2].Applying VCS allows decouple control of active

and reactive power produced by the DFIG. TheRSC can realize the decouple control of activeand reactive power by adopting the stator flux or

voltage control strategy while the GSC canrealize the control of the DC link and network power factor by using the grid voltage orientedvector control strategy.

Based on the control of DFIG and WT, severalcontrol strategies have been proposed in the

literature [3-5]. The strategies are based on thefact that below rated wind speed (BRWS), theWT will trace the maximum power/torque curveand above rated wind speed (ARWS), the output power is limited to its rated power. To trace themaximum power/torque curve, speed/current

control mode is favored, while pitch regulationensures the rated power for ARWS of the WT.The scope of the present work is limited to thedevelopment of a control strategy for operationBRWS. The proposed maximum powerextraction control strategy for the DFIG basedgrid connected wind turbine employs the produced power as a dynamic active reference

power for the DFIG in BRWS mode. A fourthorder DFIG model is developed and stator fluxorientation vector control scheme is adopted todecouple the control of active and reactive power production by the DFIG. The q- axis

component of the rotor current is controlled toachieve the control of active power production

by the DFIG while d- axis component of therotor current is controlled to achieve the control

of reactive power production. The control of thegrid side converter is not of primary concern forthis study as the focus of the work is thetracking of the maximum power of the windturbine and the control of the active and reactive power produced by the stator of the DFIG.

This paper is organized as follows. The secondsection gives a short overview of the DFIG

based WT. In the third section, thecharacteristics of the wind turbine are depicted.The dynamic model of the DFIG and controlleranalysis is presented in the fourth and fifthsections respectively, and the sixth section

contains the simulation results. Finally, thefindings of the investigations are highlighted inthe conclusions.

3. WIND TURBINE

CHARACTERISTIC

A wind turbine can be characterized by the non-dimensional curve of power coefficient C p as a

function of Tip-Speed Ratio (TSR) λ, where, λ isgiven in terms of rotor speed, ωm (rad/s), wind

speed, V (m/s), and rotor radius, R (m) as

m R

V

ω λ = (1)

Wind turbine power coefficient, C p is dependent

upon λ. If pitch angle, β is incorporated, C p





becomes a function of λ and β , i.e.

( ), pC f λ β = . The power coefficient as a

function of λ and β can be expressed as [6]

( )21

116, 0.5176 0.4 5

0.0068

i

p

i

C e λ

λ β β λ

λ

−⎛ ⎞

= − −⎜ ⎟

⎝ ⎠+

(2)

here,3

1 1 0.035

0.08 1i

λ λ β β = −

+ +

Fig. 2 Power coefficient as a function of tip-speed ratio and pitch angle.

The ( ), p

C f λ β = curves for some β values

are shown in Fig. 2. It can be seen that as

β increases, C p decreases, thus reducing the

power produced by the WT.

The mechanical output power of the windturbine can be expressed as

( ) ( )33

10.5 ,

m p m P AC V K ρ λ β ω = = (3)

where, ρ is the air density (kg.m-3) and A is therotor rotational area, i.e., π R2.

The corresponding torque produced by the windturbine is given by (4) which simplifies to (5)

m

m

m

P T

ω

= (4)

( )2

1m mT K ω = (5)

where, ( )3

1 30.5 ,

p

OPT

R K AC ρ λ β

λ =

This maximum power value at various windspeed may be derived by using (1) and (4) to

yield (6) and the referenced wind turbine with avariation in wind speed is presented in Fig 2.

3 3

max p opt m P k V k ω = = (6)

In order to obtain the maximum power, the pitchangle (β) is usually held to an optimum value(typically less then 100 [4]) for BRWS and arate limiter is often used to limit the rate of

change of the pitch angle. Present concern ofthis paper assumes the pitch

Fig. 3 Wind turbine output power as a functionof rotational speed of the turbine

4. DYNAMIC MODEL OF DFIG

In order to investigate the actual behavior of theDFIG, dynamic equation needs to be consideredfor more realistic observation. From the point of

view of the control of the machine, the dq representation of an induction machine leads tocontrol flexibility. The dynamic behavior of theDFIG in synchronous reference frame can be

represented by the Park equations provided allthe rotor quantities are referred to the statorside. The stator and rotor voltages are expressedas follows:

( )

( )

ds

ds s ds s qs

qs

qs s qs s ds

dr

dr r dr s r qr

qr

qr r qr s r dr

d V R i

dt

d V R i

dt d

V R idt

d V R i

dt

ϕ ω ϕ

ϕ ω ϕ

ϕ ω ω ϕ

ϕ ω ω ϕ

⎧ ⎫= + −⎪ ⎪

⎪ ⎪⎪ ⎪

= + +⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪= + − −⎪ ⎪⎪ ⎪⎪ ⎪= + + −⎪ ⎪⎩ ⎭

(7)

The flux linkage equations of the stator androtor can be related to their currents and areexpressed as follows:





ds ss ds m dr

qs ss qs m qr

dr rr dr m ds

qr rr qr m qs

L i L i

L i L i

L i L i

L i L i

ϕ

ϕ

ϕ

ϕ

= +⎧ ⎫⎪ ⎪= +⎪ ⎪⎨ ⎬

= +⎪ ⎪⎪ ⎪= +⎩ ⎭

(8)

where, ss s m

L L L= + andrr r m

L L L= +

The electromagnetic torque developed by theDFIG is related to the torque supplied by the

turbine and can be expressed as

( )1.5 2 m

e ds qs qs ds m m

d T p i i H B T

dt

ω ϕ ϕ ω = − = + +

(9)

where,mT is positive for motoring operation

and negative for generator operation. Equations

(7) to (9) are the set of differential equationswhich represent a fourth order model fordescribing the dynamic behavior of DFIG.

5. VECTOR CONTROL

STRATEGY

In order to achieve a decouple control of active

and reactive power, stator flux oriented vectorcontrol scheme is adopted. Based on the previous research the following assumptions areconsidered:

• Stator voltage drop across resistancehas been neglected as the effect of

stator resistance is quite lowcompared to the grid voltage [5].

• The DFIG is connected to a stiffgrid, i.e., the frequency and

amplitude of the stator or gridvoltage is assumed constant [7].

• Magnetizing current of the stator isassumed to be determined by thegrid [7].

• The q-axis is 900 ahead of the d-axis

and rotating at synchronous speed inthe direction of rotation [8].

• The stator flux vector is aligned withthe d-axis of the stator [8].

The above assumptions lead to the following

0 and

0

ds ds s

qs s qs

V

V V

ϕ ϕ

ϕ

= =⎧ ⎫ ⎧ ⎫⎪ ⎪ ⎪ ⎪⎨ ⎬ ⎨ ⎬

= =⎪ ⎪ ⎪ ⎪⎩ ⎭ ⎩ ⎭ (10)

Neglecting the stator resistance, i.e., 0 s

R = (7)

becomes

0

( )

( )

ds

ds s qs

qs

qs s ds s s ds

dr

dr r dr s r qr

qr

qr r qr s r dr

d

V dt

d V V

dt

d V R i

dt

d V R i

dt

ϕ

ω ϕ

ϕ ω ϕ ω ϕ

ϕ ω ω ϕ

ϕ ω ω ϕ

⎧ ⎫

= = −⎪ ⎪⎪ ⎪⎪ ⎪

= = = +⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪= + − −⎪ ⎪⎪ ⎪⎪ ⎪= + + −⎪ ⎪⎩ ⎭

(11)

And (8) becomes

0

s ss ds m dr

ss qs m qr

dr rr dr m ds

qr rr qr m qs

L i L i

L i L i

L i L i

L i L i

ϕ

ϕ

ϕ

= +⎧ ⎫

⎪ ⎪= +⎪ ⎪⎨ ⎬

= +⎪ ⎪⎪ ⎪= +⎩ ⎭

(12)





Fig. 4 Block diagram of the control system

Fig. 5 Simulink model of the DFIG based wind turbine

The rotor voltages are then obtained as





0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

Time (sec)

R o t a t i o n a l s p e e d ( p u )

( )

( )

2

2

2

2

m dr

dr r dr rr

ss

m

s r rr qr

ss

qr m

qr r qr rr

ss

m m s

s r rr dr

ss s ss

L diV R i L

L dt

L L i

L

di LV R i L L dt

L L V L i

L L

ω ω

ω ω ω

⎧ ⎫⎛ ⎞= + −⎪ ⎪⎜ ⎟

⎝ ⎠⎪ ⎪⎪ ⎪⎡ ⎤⎛ ⎞⎪ ⎪− − −⎢ ⎥⎜ ⎟⎪ ⎪⎢ ⎥⎝ ⎠⎪ ⎣ ⎦ ⎪⎨ ⎬

⎛ ⎞⎪ ⎪= + −⎜ ⎟⎪ ⎪⎝ ⎠⎪ ⎪

⎪ ⎪⎡ ⎤⎛ ⎞⎪ ⎪+ − − +⎢ ⎥⎜ ⎟⎪ ⎪⎢ ⎥⎝ ⎠⎣ ⎦⎩ ⎭

(13)

The active and reactive power produced in thestator, the rotor fluxes and voltages can bewritten in terms of the rotor current as [9]

2

*

*

m

s s qr ss

s s m

s dr

s ss ss

L P V i

L

V V LQ i

L Lω

−⎧ ⎫=

⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪= −⎪ ⎪⎩ ⎭

(14)

Thus from (14), the q-axis current vectorcomponent, iqr can be used to regulate the active power generated by the stator of DFIG while, idr can be used to control the reactive power produced by the stator. Essentially, control of

the active and reactive power is decoupled and adecoupler is not necessary. A block diagram ofthe control system is presented in Fig. 4.

5. SIMULATION RESULTS

The system described above is simulated usingMatlab-Simulink TM blocks and the simulinkmodel is presented in Fig 5. The stator of theDFIG is connected to a 690 V rms, 60 Hznetwork. The DFIG is rated at 2MW and the

Fig. 6 Variation of rotational speed with time





0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

4

Time (sec)

C u r r e n t ( p u )

q-axis rotor current component

d-axis rotor current component

0 0.5 1 1.5 2 2.5 3 3.5 4-8

-6

-4

-2

0

2

4

6

Time (sec)

P o w e r ( p u )

Stator active power

Stator reactive power

Fig. 7 q- and d- axis rotor current component

Fig. 8 Stator generated active and reactive power





rotor is fed to the grid via an ac-dc (RSC) anddc-ac (GSC) converters. Built-in converters ofSimulink for the RSC and GSC are consideredfor the simulation. The nominal DC link voltageis set to 1200V and the DC capacitance is 16mF.

A step increase in wind speed from 8.4 m/s to12.0 m/s is applied after a stable condition (2seconds). Although such a step change is notvery realistic, the change can be considered asthe most drastic change from the point of the

control of the system. The simulation is startedfrom 2 seconds and within 3 seconds all thequantities reach to their steady state values. Thespeed of the wind turbine increases (from .82 puto 1.2 pu) due to the change in wind speed (Fig.6) which ensures the maximum power production as found in the reference windturbine modeling curve corresponding to this

two wind speeds(Fig. 3). The corresponding power increase from 0.21 pu to 0.7 pu (Fig. 8)

while reactive power remains the same. The power curve for both active and reactive powercontains ripple and is mainly due to thecontroller parameters. An average value isconsidered to describe the power quantity.

As a result of the change in active power production by the DFIG, the q-axis componentof the rotor current increases to 0.5 pu andremains at that value afterwards while d-axiscomponent of the rotor current remain

unchanged (Fig. 7) thus show the effectiveness

of the proposed control strategy.

Various challenges to system simulation wereexperienced during the simulation. Limiters andmemory elements have been placed in severalnodes to eliminate convergence problems.However, this limits the range of effective

parameter variations. In particular, the controller parameters tuning need more attention. Infurther work, methods of removing suchlimitations will be reported.

7. CONCLUSIONS

Discussion of the dynamic modeling andassociated control strategy of a DFIG based

wind turbine has been presented. The statorflux oriented vector control scheme isincorporated with the DFIG control to realizethe fast and accurate control. Active power production by the DFIG is controlled throughthe q-axis rotor current while reactive power

through d-axis rotor current. Furtherdevelopment of the system including grid sideconverter control will be presented in a future paper.

ACKNOWLEDGEMENTS

The authors would like to thank the NationalScience and Engineering Research Council(NSERC) Canada for providing financialsupport of this research

Appendix

TABLE A.1 PARAMETERS OF THE SIMULATED

DFIG

Rated power 2MW

Stator voltage 690V

s R 0.0108pu

r R 0.0121pu

m L 3.362pu

ls L 0.102pu

lr L 0.11pu

Lumped Inertiaconstant

3

REFERENCES

[1] Zhao, Y., Zou, X.D., Xu, Y.N., Kang, Y.,Chen, J. “Maximal Power Point Trackingunder Speed-Mode Control for Wind

Energy Generation System with DoublyFed Introduction Generator,” Proceedingsof the IEEE International Power Electronics and Motion Control Conference2006 , Shanghai; China, Vol: 1, pp.1 – 5,2006

[2] Cardenas, Roberto., Pena, Ruben.,

“Sensorless Vector Control of InductionMachines for Variable-Speed Wind Energy

Applications,” IEEE Transaction on EnergyConversion, Vol: 19, No: 1, pp. 196 – 205,2004.

[3] Li, H., Chen, Z., Pedersen J.K., “OptimalPower Control Strategy of Maximizing

Wind Energy Tracking and Conversion forVSCF Doubly Fed Induction GeneratorSystem,” Proceedings of the IEEE International Power Electronics and





Motion Control Conference 2006, Shanghai; China, Vol: 3, pp.1 – 6.2006

[4] Senjyu, T., Sakamoto, R., Urasaki, N.,Funabashi, T., Fujita, H., Sekine, H.,“Output power leveling of wind turbine

Generator for all operating regions by pitchangle control,” IEEE Transaction on Energy Conversion, Vol: 21, No: 2, pp. 467 – 475, 2006.

[5] Mohamed, M.B., Jemli, M., Gossa, M.,Jemli, K., “Doubly fed induction generator(DFIG) in wind turbine modeling and power flow control,” Proceedings of the IEEE International Conference on Industrial Technology 2004, AL; USA,Vol: 2, pp. 580-584, 2004

[6] Siegfried, Heier. “Grid Integration of WindEnergy Conversion Systems,” John Wiley

& Sons Ltd, 1998, ISBN 0-471-97143-X

[7] He, Yikang., Hu, Jiabing, Zhao, Rende.“Modeling and control of wind-turbine usedDFIG under network fault conditions,” Proceedings of the International

Conference on Electrical Machines andSystems 2005, China, Vol: 2, pp. 986-991,2005

[8] Holdsworth, L., Wu, X.G., Ekanayake, J.B.,Jenkins, N., “Comparison of fixed speedand doubly-fed induction wind turbinesduring power system disturbances,” Proceedings of the IEE Generation,

Transmission and Distribution, Vol:150, Issue 3, pp.343 – 352, 2003

[9] Toufik, B., Machmoum, M., Poitiers, F.,“Doubly fed induction generator with activefiltering function for wind energy

conversion system,” Proceedings of the European Conference on Power Electronics and Applications 2005,

Dresden; Germany, pp. 1-9, 2005

Md. ARIFUJJAMAN received his M.Eng. degree in Electrical and Computer

Engineering from Memorial University of Newfoundland (MUN), Canada onSeptember 2006. Prior to that, he fulfilled his B.Sc. degree in Electrical and Electronic

Engineering from the Khulna University of Engineering and Technology (KUET),Bangladesh. Afterwards he joined as a lecturer at the same university and

consequently held the position of a Consultant and Research Testing Officer for about2 years before starting his M. Eng. at MUN. He is currently working on his Ph.D. in

the wind energy at the High Voltage Engineering Laboratory of MUN. His research

involves simulation, control and innovative design level approach of renewable energysystems with an intense to small wind energy conversion systems.

M. T. IQBAL received the B.Sc.(EE) degree from the University of Engineering and

Technology, Lahore in 1986, the M. Sc. Nuclear Engineering degree from the Quaid-e-Azam University, Islamabad in 1988 and the Ph.D. degree in Electrical Engineeringfrom the Imperial College London in 1994. From 1988 to 1991 and from 1995 to 1999

he worked at the Pakistan Institute of Engineering and Applied Science(www.pieas.edu.pk ), Islamabad, Pakistan as an Assistant Engineer and later as a

Senior Engineer. From 1999 to 2000 he worked as an Associate Professor at, RiphahInternational University (www.riphah.edu.pk ). Since 2001 he is working at Faculty ofEngineering and Applied Science, Memorial University of Newfoundland. His

teaching activities cover a range of electrical engineering topics including controlsystems, power electronics and renewable energy systems. His research focuses on

modeling and control of renewable energy systems.





John E. QUAICOE received the B.Sc. degree from the University of Science and

Technology, Kumasi, Ghana in 1973, and the M.A.Sc. and Ph.D. degrees from theUniversity of Toronto, Canada in 1977 and 1982 respectively. In 1982 he joined the

Faculty of Engineering and Applied Science at Memorial University of Newfoundland, where he is presently a Professor and Associate Dean (UndergraduateStudies) with teaching and research activities in power electronics and related areas.

His undergraduate and graduate teaching activities are in the areas of electric circuit

analysis, electronic circuit analysis and design, energy systems, power electronics and power electronics systems, including modeling, analysis, control and design of power

converters for various applications. Dr. Quaicoe was the recipient of the President’sAward for Distinguished Teaching at Memorial University of Newfoundland for 2001and the IEEE Canada Outstanding Educator Medal for 2002. His research activities

include inverter modulation and control techniques, utility interface systems and power quality, and uninterruptible power supplies. His recent research activities focus

on the development of power electronic systems and control strategies for fuel cells and wind generation systems.He is a member of the Association of Professional Engineers and Geoscientists of Newfoundland and Labrador.

vector control of a dfig based wind turbine

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