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Power control of grid connected

Doubly Fed Induction Generator using

Adaptive BackStepping approach

Abstract This paper presents the findings of investigation of

decoupled power control of grid-connected doubly fed induction

generator (DFIG) based on Adaptive Back Stepping Control

(ABSC) technique. The Adaptive Back Stepping control

technique offers a systematic stabilizing procedure wherein

unwanted cancellation of favourable nonlinearities can be

avoided. Incorporation of the proposed controller improves bothtransient and steady state performances due to the excellent

tracking response for the given power references. Numerical

simulations are carried out in MATLAB programming

environment for the laboratory DFIG test set up.

Keywords- Doubly fed induction generator, power control,

Adaptive backstepping control, unity power factor

I. INTRODUCTION (HEADING 1)In recent years Doubly Fed Induction Generators (DFIG)

are becoming increasingly acceptable due to their suitability inthe context of variable speed wind power generating systems.The power converters in the rotor circuit handling the slip

power can be of a lower rating thereby offering a cost effectivealternative [1]-[2]. Conventionally the power control of a DFIGis based on field oriented vector control using rotationaltransformations, and linear PI controllers [1]-[5]. However,with the classical control schemes the system response deviatesif the operating point varies which further leads to a non-optimal behaviour of the overall control scheme over a wideoperation range. The Adaptive Back Stepping controltechnique offers a systematic stabilizing procedure whereinunwanted cancellation of favorable nonlinearities can beavoided [6], [7]. In contrast with the conventional approach

based on the certainty equivalence schemes, control andparameter update laws are obtained using a single Lyapunov

function, there by resulting in desired closed loopperformance.The focus of this paper is to mathematicallyformulate and implement the Adaptive Back Stepping control(ABSC) for the DFIG power control problem.

II. ADAPTIVE BACK STEPPINGFig. 1 show the schematic of the wind turbine driven, grid

connected DFIG with back to back connected power

converters in the rotor circuit. The dc link voltage (Vdc), the

front end converter and rotor side converter currents (ifeq, ifed,

irq, ird) are considered as the state variables of the DFIG

system which are given by

[ ] [ ]TTrdrqfedfeqdc xxxxxiiiiVX 54321==

A. Front End Converter control approachThe mathematical equations representing the front end

converter (grid side) are as follows.

[ ]rdrdrqrqsqsqdc

dc iViViVCVdt

dV=

2

3. (1)

( )feqsqf

fedefeqf

ffeqVV

Lii

L

R

dt

di+=

1 (2)

( )fedsdf

feqefedf

ffedVV

Lii

L

R

dt

di++=

1 (3)

From (1) to (3) the input matrix is given by

[ ]( ) ( ) T

f

fedsd

f

feqsqTfedfeqfec

L

VV

L

VVuuU

==

A set of new variablesz1, z2, z3 is defined as

Figure. 1.Schematic of the doubly-fed induction generator configuration.

A.Karthikeyan, Sujan Kumar Kummara, C.Nagamani, G.Saravana IlangoEEE, National Institute of Technolgy

Tiruchirappalli, India

jakarthik@yahoo.com, cnmani@nitt.edu,

978-1-4244-8782-0/11/$26.00 2011 IEEE

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==

==

==

333

2112

111

xxiiz

xiz

xxVVz

reffedfedref

feq

refdcdcref

(4)

where 1 is the virtual control law to stabilize the DC link

voltage (Vdc).

Taking a=3Vsq/2C, b=-3Vrq/2C, c=-3Vrd/2C, d=Rf/Lf

Using (1) to (4) the time derivatives ofz1, z2, z3 can be writtenas

1

5

1

4

1

211

x

cx

x

bx

x

axxz ref = (5)

13212 qfeqe uxdxz ++= (6)

12333 dfederef uxdxxz += (7)

where q1 and d1 are uncertainties.For the dc link voltage control, the energy fluctuation in the dclink capacitor (C) is taken as a positive definite Lyapunovfunction.

210

2

1CzVn =

From (5) the time derivative ofVn0 is given by

( )

=

1

5

1

421

1110

x

cx

x

bxz

x

axCzV refn

(8)

To ensure the first derivative of positive definite Lyapunov

function to be negative (8) can be written as

1

212110

x

zaCzCzkV nn +=

(9)

for

+= 11

1

5

1

41

11 zk

x

cx

x

bxx

a

xnref ; kn1>0

For the front end converter control, the energy fluctuations inthe dc link capacitor and the ac side front end convertercoupling reactances (Lf , Rf) are taken as the positive definite

Lyapunov function with the uncertainties augmented as givenbelow.

( ) ( ) ( )2113

2

112

22

2101

2

12

1

2

1ddqqfnn

mmzzLVV ++++= (10)

where 1q , 1d

are the estimates of the uncertainties and

m2,m3 are the adaptive gains.

According to Lyapunov theorem to achieve a stable condition(10) can be written as

( )

( ) ( )

++

++

+++

+++++

=

33

1112

2

111

1233333

1321221

12

233

222

2111

zLm

zLm

uxdxzkxzL

uxdxzkxL

aCzzL

zLkzLkCzkV

fd

ddfq

qq

dfedenreff

qfeqenf

f

fnfnnn

forkn2, kn3 >0 (11)

For the stable operation of front end converter, the 1nV must

be negative which can be achieved by the following conditions.

2213211

1 zkxdxxL

aCzu nqe

ffeq ++++=

(12)

331233 zkxdxxu ndereffed ++= (13)

+= 11

1

5

1

41

11 zk

x

cx

x

bxx

a

xnref

221 zLm fq =

, 331 zLm fd =

where (12) and (13) are the modulating signals for the front

end converteras shown in Fig. 2.

B. Rotor Side Converter control approachThe mathematical equations governing the rotor side converter

are given as

( )

=

dt

diLiLiLiRV

Ldt

di sqmsdmrdrslrqrrq

r

rq

1(14)

( )

+=

dt

di

LiLiLiRVLdt

di sdmsqmrqrslrdrrd

r

rd

1

(15)

where sl is slip speed,Rr andLrare rotor resistance and self

inductance respectively andLm is mutual inductance.

From (14) and (15) the input matrix is given by

[ ] TrdrqT

r

rd

r

rqrsc uu

L

V

L

VU =

=

A set of new variablesz4, z5 are defined as

Figure. 2. Front end converter controller based on Adaptive backstepping

Approach

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Figure. 3. Transient response of step changes in stator active and reactive

powers

==

==

555

444

xxiiz

xxiiz

refrdrdref

refrqrqref(16)

Takingp=Rr/Lr, q=-Lm/Lr,

Using (14) to (16) the time derivatives ofz4, z5can be writtenas

( ) 25444 qrqsdsdslref udt

diqqixpxxz ++= (17)

( ) 24554 drdsq

sqslref udt

diqqixpxxz += (18)

where q2 andd2 are uncertainties.

To achieve the rotor side control, the energy fluctuation in therotor windings is taken as positive Lyapunov function with theuncertainties augmented as given below

( ) ( ) ( )2225

2

224

25

240

2

12

1

2

1ddqqrm

mmzzLV ++++=

(19)

where 2q

, 2d

are estimates of the uncertainties and m4, m5

are the adaptive gains

According to Lyapunov theorem to achieve the stable condition(19) can be written as

( )

( )

( ) ( )

++

++

+++

++++

=

55

2224

4

2

22

2455555

2544444

255

2440

zLm

zLm

udt

diqqixpxxzkzL

udt

diqqixpxxzkzL

zkzkV

rd

ddr

q

qq

drdsd

sqslrefnr

qrq

sq

sdslrefnr

nnm

for kn4,kn5>0 (20)

For the stable operation of rotor side converter, the 0mV must

be negative, which can be achieved by the following

conditions.

( ) 254444 qsq

sdslrefnrqdt

diqqixpxxzku +++= (21)

( ) 245555 dsdsqslrefnrddt

diqqixpxxzku ++= (22)

442 zLm rq = , 552

zLm rd =

where (21) and (22) are the modulating signals for the rotor

side converter.

III. RESULTS AND DISCUSSIONSThe transient response of the 3 hp laboratory DFIG system

(parameters are given in appendix) based on ABSC strategy isshown in Fig. 3. MATLAB/Simulink package is used for the

computer simulations. During the start-up the machine runs at1430 rpm (Fig. 3e) as motor where stator active power

Ps=1310 W and stator reactive powerQs=1100var. At t=3s therotor side controller is switched on when the initial stator

power references are set such that the reactive power drawnfrom the grid is zero while the real power drawn from the gridremains same as before (Figs. 3(a) and (b)). At t=5s, the statorreal power is also made zero so that the machine is in floating

condition (both active and reactive power are zero, i.e., zeroinjection/ absorption with respect to the grid). Then at t=7s, thestator real power is increased to -1250 W while the reactive

power is maintained zero for the unity power factor operationduring generating condition.

The trends in stator and rotor currents are shown in Figs.3(c) and 3(d). Perfectly decoupled control of the stator activeand reactive power is observed even during step changes ineither of the power reference commands.

Implementation of the ABS controller renders the DFIGsystem immune to parameter variations. Fig. 4(b) shows thestep change in stator resistance [increased to 200% of theactual value] from t=9s to t=10s. The stator active and reactive

power are perfectly stable at the set reference values evenwhile the stator resistance is varying. The transients in statorand rotor currents shown in Figs. 4(b) and (c) reflect this.

W

var

A

A

rpm

(a)

(b)

(c)

(d)

(e)

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Figure. 4. System transient response for stator resistance

variation

The dynamic response of front end converterd-axis currentand dc link voltage are shown in Figs 4 (d) and 4 (e). The d-axis current (ifed) reference of the front end converter is fixed atzero, so as to maintain unity power factor at the grid. Similarly

the dc link voltage (Fig. 4(e)) is maintained constant for bettercontrol. It can be observed that the two control loops viz., dclink voltage and front end converterd-axis current are totallydecoupled and the response of each one is unaffected by thechange in the other.

IV. CONCLUSIONSPower control of grid connected DFIG using Adaptive

Back Stepping Control is presented. It is observed that thecontroller can perfectly track the power references withexcellent decoupling in both steady state and transientconditions. Further with the proposed scheme, the systemtracking performance is immune to changes in stator resistance.Simulation results demonstrate the merits of the control

scheme.

REFERENCES

[1] S. Muller, M. Deicke, and R. W. De Doncker, Doublyfed induction generator systems for wind turbines, IEEEInd. Appl. Mag., vol. 8, no.3, pp. 2633, May/Jun. 2002.

[2] R. Pena, J. C. Clare, and G. M. Asher, A doubly fedinduction generator using back-to-back PWM converters

and its application to variable-speed wind-energy

generation, Proc. Inst. Electr. Eng. B, Electr. Power

Appl., vol. 143, no. 5, pp. 231241, May 1996.

[3] R. Datta and V. T. Ranganathan, Decoupled control ofactive and reactive power for a grid-connected doubly-fed

wound rotor induction machine without position sensors,

in Proc. Conf. Rec. 1999 IEEE/IAS Anu. Meeting, pp.

2623-2630, 1999.

[4] Jun Yao, Hui Li, Yong Liao, and Zhe Chen, AnImproved Control Strategy of Limiting theDC-Link Voltage Fluctuation for a Doubly Fed Induction

Wind Generator, IEEE Trans. on Power

Electronics, vol. 23, no. 3, pp.1205-1213, May 2008.

[5] Shiyi Shao, Ehsan Abdi, Farhad Barati, and RichardMcMahon, Stator-Flux-Oriented Vector Control forBrushless Doubly Fed Induction Generator, IEEE Trans.

on Industrial Electronics, vol. 56, no. 10, pp. 4220-

4228, October 2009.[6] Si-Ye Ruan, Guo-Jie Li, Xiao-Hong Jiao, Yuan-Zhang

Sun, T.T. Lie, Adaptive control design for VSC-HVDCsystem based on Back-stepping method. ElectricalPower Systems Research, vol 77, no.5-6, pp. 559-565.

April 2007.[7] M.Y. Hammoudi, A.Allag, S.M. Mimoune,. M.Y. Ayad,

M. Becherif, A.Miraoui, Tracking control via adaptivebackstepping approach for a three phase PWM AC-DCconverter, IEEE International Conference on IndustrialTechnology, 2006, pp. 1676 - 1681.

APPENDIX

Induction machine specifications.

3 Hp, 415V, 50Hz, 3 phase; Stator: 415V, Y connected, 4.7A;Rotor: 185V, Y connected, 7.5A

TABLE I: Machine parameters

Parameter Symbol Actual value in SIunits

Stator resistance Rs 3.678

Rotor Resistance Rr 5.26

Stator Inductance Ls 306.82 mH

Rotor Inductance Lr 306.82 mH

Stator Leakage Inductance Lls 24.87 mH

Rotor Leakage Inductance Llr 24.87 mH

Magnetizing Inductance Lo 281.95 mH

W&var

&

A

A

A

V

(a)

(b)

(c)

(d)

(e)