Sliding Mode Control Of A Doubly Fed Ig Supplying An Isolated Rl Load

CIIEP

(-

r*

WR

il

2006

Puebla, MEXICO 16-18 October

Sliding Mode Control of a Doubly Fed Induction Generator Supplying an Isolated RL Load

R. Galindo-del-Valle

Centro Nacional de Investigacion y Desarrollo Tecnolgico Int. Intemado Palmira s/n, Col. Palmira. Cuemavaca, Morelos, 62490, Mexico. e-mail: robertogalindogcenidet.edu.mx

M. Cotorogea-Pfeifer

Centro Nacional de Investigacion y Desarrollo Tecnologico Int. Intemado Palmira s/n, Col. Palmira. Cuemavaca, Morelos, 62490, Mexico. e-mail: [email protected]

Abstract- In this paper the authors present preliminary results concerning the Sliding Mode Control (SMC) of a Doubly Fed Induction Generator (DFIG) supplying an isolated RL load in a Variable Speed-Constant Frequency (VSCF) generation system. This kind of system has already been considered in the past by other researchers, mainly by using PI-type regulators. However, it must be reminded that in electrical machines the existence of parameter changes (caused by several reasons like winding temperature variation, hysteresis and saturation, amongst others) is well recognized, but rarely accounted for. For this reason, a non-linear control strategy, namely SMC, has been considered. SMC has various attractive features like order reduction, robustness, disturbance rejection, and, sometimes, simple implementation. In this paper, some ideas of SMC applied by Utkin et. al. for controlling the speed or torque of a squirrel-cage induction motor are used to design a controller for regulating amplitude and frequency of the voltage generated by a DFIG, which is a wound-rotor induction generator. First simulation results are presented as well. Finally, the conclusions of the work are given and future activities are described.

I. INTRODUCTION

Since the second half of the 1980's, a higher research effort has been devoted to Wind Energy Conversion Systems (WECSs), because of the increasingly world interest for achieving a sustainable development by using renewable energies. To face the changing nature of wind, in order to generate constant frequency voltages, constant-speed-WECS were firstly proposed. However, variable speed WECS operation can be considered advantageous, because additional energy can be collected when wind speed increases. Variable speed WECS must use an electronic power converter, so they can be classified in full power handling WECS (also called direct-in-line) and partial power handling WECS, considering both the converter placement and ratings. In full power handling WECS, the power converter is in series with the induction or synchronous generator, in order to transform the variable amplitude/frequency produced voltages into constant amplitude/frequency voltages, and it must be able to process all the generated power. In partial power handling WECS, the converter to control the electric machine is in a secondary generator circuit, and it only processes a portion of the total

1-4244-0545-9/06/$20.00 ©2006 IEEE

D. Biel-Sole

Dpt. d'enginyeria Electr6nica. E.U.P.V.G., Universidad Politecnica de Catalunfa (UPC), c/ Victor Balaguer s/n 08800- Vilanova i la Geltrui (Barcelona), Espafta. e-mail: [email protected]

generated power (e.g. slip power), which constitutes an advantage in terms of reduced cost of the converter and increased efficiency of the system [1]. This paper is focused on a partial power handling stand-alone WECS based on a doubly-fed induction generator (DFIG). Variable speed WECSs supplying an isolated load have already been considered by other researchers. In [2], a stator voltage direct control is proposed using PI regulators. It offers a good dynamic performance, but is load dependent, which causes some practical difficulties. In [3], a system, where the rotor is fed from a battery through a PWM current source inverter, is presented. Additionally, regulation of the rms generated voltages is proposed, which results in considerable voltage errors and load dependency. In [4]-[6], several PI-based indirect stator voltage vector control approaches are presented, for a WECS in which a back-to-back (B2B) converter is used to manage the power interchange between the stator and rotor circuits. The proposed control strategies produce good dynamical performance without any load dependency. However, DFIG parameter changes might degrade the control performance. In order to take advantage of the robustness and disturbance rejection features of the SMC, in this paper a stator voltage sliding-mode controller is proposed. To present the work, this paper is organized as follows. In Section II, the considered system and its model are described. In Section III, the stator voltage controller design is explained. In Section IV, preliminary simulation results are presented. Finally, in Section V, the conclusions are given and some future activities are listed. II. SYSTEM DESCRIPTION

The considered WECS is depicted in Figure 1. In this system, energy is collected by a wind turbine (WT) and transferred to a DFIG by a rotational movement through a drive train (DT). The DT increases the rotational speed using a gear box (GB). The DFIG transforms the received mechanical energy into electrical one in order to supply an isolated load (both main and auxiliary). The system operation is controlled

by a B2B converter. At this first stage, only a main RL load has been considered and the WT has been substituted by a speed-controlled dc motor. Afterwards, the auxiliary load and the WT will be considered. In the WECS, the front end converter (FEC) manages the power flow between rotor and stator circuits by a cascaded control system, in which the inner loop controls the converter currents and the outer one regulates the dc-link voltage, similar to the approach in [4]-[5]. This paper presents the design of a SMC controller that uses the machine side converter (MSC) for regulating the stator voltage generated by the DFIG. Figure 2 shows the electrical subsystem of the considered WECS. The converters forming the B2B are taken as threephase voltage sources. Applying Kirchhoff voltage and current laws to the circuit shown in Figure 2 and considering the three-phase DFIG model derived in [7], matrix equation (1) results. The model of the B2B is based on [8] and [9]. In this model, the output voltage of each converter depends on the gate signals or pulses (g) and on the dc-link voltage (VO). This way, relations (2) are valid. To determine the dc-link voltage, Kirchhoff current law is applied to the upper bus node and yields expression (3).

(Lsr )

Lsr (Lr+ LI3 )

-LLI3

03

L

-(L2 ±LL)13]dt

)'

-rL

Vg

iL VL

)dt

rsi+ d (b

VS

L [Ll+L L/S inLs Ls =

2 L 1

Lms L

1 1

Rotor

WT...

GB= Gear Box. DFIG = Doubly Fed Induction Generator. v

I'

(Ilb)

Lr =

I c)

-2L+] ms1

Ll

-2 Lms|

n

Ms

Lr

Lls + L

-2 Lmr

-2 Lmr

2

Lmr

Llr +mr

2

Lmr

-2 Lmr

-2 Lmr| Ll

mr

COS(Or +7) COS(Or 7)1

COsOr

COSr COS(Or+7) y 27 Lsr Lsr, CoS(0r -) LCOS(Or+7v) COS(Or Y) COSr I i* =[i ib ic]]T * s, r,gandL. rs and rr

are

*

r andg.

stator

and

rotor

winding

resistances

Lms

and Lmr

are

mutual inductances between two stator

or

Lsr cos a, with: a = OrO + 7 or 0 -7, are mutual inductances between a stator winding and a rotor winding (H), 0 P2 0 is the angular position of the axes associated with rotor electro2

r

magnetic fields (rad), 0 is the mechanical angular position of the rotor shaft (rad) and P is the DFIG pole number.

Legend

wr = Wind Turbine.

M.;Ci(-= IVU LU. OIA U,,Unnvprtpr IVvv1- Mqr.hinp IVcU III IU .Ciii FEC= Front End Converter. VCM= Voltage and Current Measurement.

-

rotor windings (H),

DRG

WT

rL) 131

L-21+Lms

Lr

Fr

winding (H),

Stator

Side

GB

-(r2

(Q), LIS and LIr are leakage inductances corresponding to a stator or rotor

High Speed

Low Speed Side

(l

03

03

3

Igg

ISs

where: Auikliary Load

i]

d (Lsr )/dt I g rlI ... =::: v, - d (L sr /dt ( rr + rl )1I3

vs [Va. Vb. Vc MiLod Main Load

(1 a)

-L2I

l

I

- -- -

Controllerl2

Fig. 1 Wind Energy Conversion System (WECS) to supply an isolated load.

I

ias

v abc

T 1i pii A

Jf|bs

L

L

DFIG

Aabc

13

1

=- -1 3

LI

vil

(2g.

where: 0

=

FEC

Fig.2 Electrical subsystem of the considered WECS.

=

[V1.

V2*

V33

]T

2 -1 1 2]1

1)

2 '

g.(j+3)

r for the MSC and 0

voltage, with i=a, b, c; MSC

v123*

X

-1 -1

F2

LL

vc I

Vbh

[Va.

iaL

j

(2)

123.

abc

Vabco =

g.j

=

=

1 -g.j , and j= 1,2,3 g for the FEC;

Vi. is an output phase

0, 1 is the gate signal applied

switch and V is the dc-link voltage.

to the j-th

-iol + i02 where:

Io

~g 2'b

+

-Io

=

(3)

°

is the current feeding the dc-link capacitor,

gg3'g is the FEC "output"

current and

io

=

io2

=

ggliag +

grliar + gr2ibr

+

kdqs LS T FT

dV /dt = IO /C

=

(4)

(I2 i )/C

To obtain a dq WECS model, for simplifying the DFIG controller design, it is necessary to apply an abc to dq transformation to the three-phase model (1). This transformation is defined by the expressions given in TABLE I [9]. Applying the arbitrary reference frame transformation, given in TABLE I, to the three-phase model (1), the next dq model is derived.

di/dt =£-L' [Q(w)L + R] * i +L-' idqL

dqL

idqs

dqs

idqg

(5c)

rsidqs ± J2dqs ±(dqs )/dt TABLE I. ARBITRARY REFERENCE FRAME TRANSFORMATION

-2F1

abc

fdq

Aadq

Adq

-,[3T/2] af

L_seno

cos

abc(A .xabc aCP \abc ab

abc

abc fx a/8 x - Aa'8 3~a abcT

a

(Aac\)

Adqa/3= (Aa')dq f1 where:

0= 0

2

a)

2

02

°2

-w)L2J2

J2

-rl2_

2

-co (L2+ LL)j2 _ LS L + M , Lr = L,r + M M 2Lm Lr Lr +LI r =r +rl L= L2 +LL r = r2 +LL Co= do/dt, or =dOr/dt, rel=Ct) r

[2

J2

[°

12

-10

0

K

1

°0

I

02

[ 2] [°

0

III. CONTROLLER DESIGN

In a stand-alone system, it is necessary to regulate both the amplitude (Vs) and the frequency (fe) of the generated stator voltage. This is associated with the following control obj ectives:

iBi + d

S=*

dq

0= 0-0

-r212

L[m(f* .fe)=

(6)

t>or

L SMO £BgBv g dqg +L SMO0 £Brv r dqr

(7)

To satisfy the control objectives (6), the following sliding surfaces have been proposed:

A afdT

for stator variables and

02

°2

rr2

Bi= LSMOL 1[fI(4C)L + R] -(Rsoo + XSMO) i =idqs LSMO =[Ls2 Af2 02] idqr idqgI RSoo VS2 02 02] XSMo [WL5J2 wMJ2 02] B = ['2 02 12] and Br = [02 '2 02]

s1j

Inverse transformation

f

L-cLLJ2

2

-L_2

w)MJ2

Q(w)L =w,rlMJ2 w,rel

V

sen1

F cos

-LI2_

qg

Before starting the controller design, it is necessary to rewrite the stator voltage in a more proper form. Substituting (5d) and (5a) in (5c) results in:

121

1/

3 LOv'2 L0 3/2

A

R

Vdg

Vqr

Vdr s

°2

LsJ2

t>or

Afabc

Vq

-2 2

°2

I

1

L

Lim(V -V) =O and

Direct transformation =

L-4L2

(5a)

v

(5b)

fw

M2

C2r2

Accordingly, the dc-link capacitor voltage will be given

F

Vdqgj

Vdqr

ts2

(5d)

T]

T

Ldg

V

9r3icr is the MSC "input" current. by:

*idqs + M idqr

dqs

for rotor

variables. Furthermore, 0 is the arbitrary reference frame position (rad). NOTE: Superscript + denotes the pseudo-inverse.

where:

Vdqs

dqs

-V(8)

is the desired stator voltage vector, which implicitly contains

the desired amplitude and frequency.

The controller design has been performed by following the same procedure used by Utkin and collaborators to design a controller for the squirrel-cage induction motor (SCIM) in [9]-[10]. The main differences are: (i) The SCIM is fed and controlled from the stator, while the DFIG is fed both from stator and rotor, and it is controlled from the last one, and (ii) Utkin et. al. consider a stationary reference frame in their design, while in this work an arbitrary reference frame is assumed. Moreover, this implies that actually a controller family is obtained, where each member is associated to a particular reference frame. The simplest choices are a stationary reference frame and a synchronous reference frame oriented by the stator voltage vector. A synchronous reference frame oriented by stator field vector could be another option. The controller design is described in the following paragraphs. In order to satisfy the defined control objectives, the system must move on manifolds sT= [s, S2] = [O 0], which is known as the sliding regime. To verify that the sliding regime can be established, it is necessary to project the system motion on the subspace s. By using (8), (7), (2) and the expressions from TABLE I, it is possible to obtain:

(9a)

=FI,2 + D,*V23r Fl2 Vd

2

Ldqs(Q(w)L + R) - LsmoL- d (Q(ot)L)

~ ~ ~dWt

LsMOL-'iJ+ BjiL BgVdqg D= A 1,2 * Aadq * A abc. /3 A123 abc = A 1,2 . AaX dq Aabc

A12 BL a, a2

=

B

J

da)r

(9b) (9c) (9d)

+

r*LL

+r

Vector F1,2= [Fl F2] in (9b) is a function of Vdqg, dew.11rivatives of v and °r as well as machine parameters and stattes. It can be thought of as depending on possible disturbances. Furthermore, matrix D is rectangular, and its pseudo inve]rse is

given by:

J1

(D) = D[TEDDD T Q~~~~~~~~~~~~~

Q= A1

A

T

3

TQ

(IlOa) (1 Ob)

In accordance with [9], for determining the discoritinuous control vector capable of the sliding mode enforceiment, next Lyapunov candidate function is defined: (11 a) v =Xs..Q.s > O

(1 lb)

In the next step, following transformation and control vector are proposed: s =D S

S*

)=[sign(s*)

sign(s

(12a)

S*T

S*

2±Vsign(s

v123r V,

=

(12b)

)

sign(s2) sign (s3 )]T

0 is the dc-link voltage.

>

By using (9d), (10) and (12), expression ( lib) can be written as:

2d.2d .

2

3

a

a

2

s O + T+Ss2 cos(O O(TY [sCoso y)±|+| + 2

.±s3COO(TO+±y) ()2( (IV)(2s1 1

a d4

2

daQ

±s* ±s)

where: I

(13)

c)

and

OF = arctg (F2/IF,)

m . n with 1, m, n E {1, 2,3}.

From (13), it can be deduced that there is a dc-link voltage Vo high enough such that v < 0 for all possible combina.0 and (a2 + a) .0 tions of 1, m and n, provided that and regardless the possible variations of disturbances contained in vector F. This implies that sliding regime can be reached in finite time by directly switching the controls vI, v2r and v3r given in (12b). The controller implementation must consider next steps: (i) determining sliding surfaces (8) from measurements; (ii) to carry out sliding surfaces transformation by using (12a); (iii) determining control vector with (12b); and (iv) determining gate pulses with proper expression associated with (2). Some facts must be highlighted: (A) expression (12a) implicitly considers reference frame transformation. So, its final form depends on the chosen orientation; (B) matrix A1,2 can be expressed as a multiple of eA(-J2Oa), where 0a= tg-'(a2la,). Because of this, transformation (12a) can be considered equivalent to a dq-to-abc transformation of a vector s scaled and rotated in accordance with system parameters; (C) last tefm of (13) shows that DFIG speed behavior affects the conditions for sliding regime enforcement. This way, an increasing speed will help the dc-link voltage to enforce the sliding mode. However, a decreasing speed will act in the opposite

||sll

L2LL (rLL* L2LL) -(r +A)] ML2LLdW, d =cL+L2LLL, c = (LL*_M2)

M

SQS

-

al

_a

Q*(F+D*V123r ) +

v=S

OT = 0 Or +Oa +OF , 0, = arctg (a2/a,)

dt]

::]

d

whose time derivative, by using (9), is:

way. Undoubtedly, all this will increase the dc-link voltage necessary to face a changing speed behavior. In order to cope this, it is believed that an alternative transformation can be proposed. In fact, if transformation (12a) takes the form: s*=D'Ts, then the Lyapunov candidate function (1 la) can be defined as v=0.5 sT.s>O, and its derivative will not depend on behavior of elements of Q. Currently, this idea is being investigated more deeply; (D) in synchronous reference frames the desired stator voltage amplitude is explicitly considered, while its desired frequency is taken into account through the transformation formulas, in a similar way to that used in [4][5]. However, in a stationary reference frame both the amplitude and the frequency of the stator voltage are explicitly considered, which could mean that better frequency control can be achieved; and, finally (E) an interesting advantage of the proposed SM controller, with regard to the PI controllers used in a cascaded configuration in classical vector control, is that only stator voltage and mechanical position/speed measurements are needed if stationary reference frame is used. In other reference frames it is also necessary to measure/observe the variables associated with reference frame orientation.

Sliding surfaces

o

0.5

X1lo-3

1

1.5

Transformed

2

t (s)

sliding surfaces

f

*.5

o.,I

-0.5 -1

o

0. 5

1

1.5

2

t (s)

Fig.3 Original and transformed sliding surfaces.

IV. SIMULATION RESULTS

The controller designed in the previous section has been simulated in Simulink/MATLABR in a stationary reference frame and in a stator-voltage-oriented one. In the last one, the dc-link voltage must be too high in order to enforce the sliding regime. This makes that approach to be practically unfeasible. Better results have been obtained in a stationary reference frame, since (13) imposes less severe restrictions on the dc-link voltage. Figs. 3-6 show some corresponding simulation results. In simulations it has been considered a 50 hp DFIG, a 200 hp dc motor and a three-phase RL load, whose parameters are: (i) r,=0.087 Q, LI,= Lir'=0.8e-3 H, rr'=0.228 Q, Lm=34.7e-3 H, P=2, (ii) r1l2 Q, L79 H, ra=0.012 Q, La=35 e-5 H, La 0.18 H, Jm=30 Kg.m2, and (iii) rL=10 Q y LL=0.015 H, respectively. In addition, it has been supposed an initial dc motor speed of 391.5 rpm (41 rad/s) and a desired one of 400 rpm (41.9 rad/s). In addition, simulations suppose the dc motor is mechanically coupled to the DFIG through a rigid shaft without any friction and an ideal gearbox of ratio 4. Consequently, the generator has an initial speed of 1566.1 rpm (164 rad/s) and a desired one of 1600 rpm (167.5 rad/s). Moreover, the dc-link voltage is considered to be initially equal to its desired value (V0 = 600V). This voltage is regulated by PI-controllers through the FEC. Finally, a filtered stator voltage, using a second order band-pass filter, will be presented. Fig. 3 shows the original and transformed sliding surface behavior. In Fig. 4, it can be noted that sliding regime establishes in a time period of a quarter of the reference signal cy-

Vt

t (s) Ps

vs. V Ps

t (s)

Fig.4 Stator voltage

a,/

components.

cle with a relatively small tracking error. Fig. 5 presents a detail of the generated stator voltage (phase a) and its associated current. Note that the generated stator voltage satisfies the desired amplitude and frequency. At the end, Fig. 6 shows the behavior of the dc-link capacitor voltage/current and the DFIG speed. In the upper image it can be observed that the PI-controlled dc-link voltage suffers a disturbance (associated with the start of the DFIG generation) that is coped with in a time less than Is. Furthermore, the lower image shows that the DFIG speed reaches its desired value in a similar interval. This settling time is imposed by the PI controller of the dc motor that drives the DFIG. V. CONCLUSIONS

This paper presents a SMC controller design for the voltage generated by a DFIG that supplies a RL load in a stand-

tween the SM current controller and the stator field estimation algorithm has produced wrong results. It is expected to solve this problem soon. In addition, two SMC controllers have been designed for the FEC. First of them considers direct control of the dc-link voltage and has not been able to perform its function. Reasons of this are unknown at this moment. The second one is a SM current controller that operates in the inner loop of a cascaded system and has provided good performance in first simulations. In the future, it is expected to design a SMC observer for the DFIG speed, in order to obtain a sensorless controller. Finally, the experimental assessment is being prepared in order to carry it out before the end of this year. Associated results, including harmonic pollution, will be presented later.

Voltage and current of phase "a" of stator

200

=

f

100 0

27

=~~~~~~~~~Dsrdsao

276

28

286

29

t (s)

otg

mltd

296

3

VI. ACKNOWLEDGEMENT

Fig.5 Stator voltage and current corresponding to phase a. Voltage and current in 111

800

First author thanks the financial support from the Mexican National Council for Science and Technology (Consejo Nacional de Ciencia y Tecnologia: CONACyT), received through the scholarship with registration number 130885.

C0

666 400

200

VO

-------

_

-

6 0

05

1

168

165 t (s) DFIG speed

2

lo

25

VII. REFERENCES 3

[2]

166-

[3]

DmDFIG speed

164 162

[1]

l w*m 0

05

1

1.5

t (s)

2

[4]

desired DFIG speed 25

3

Fig.6 dc-link capacitor voltage and current (upper image) and DFIG speed (lower image).

alone WECS. The design has been performed following the same procedure used by Utkin et. al in speed/torque squirrelcage induction motor control. Preliminary simulation results have been presented, which show good behavior. However, some items are currently being verified, like the assessment of controller performance to variations in system parameters and its disturbance rejection feature. At present, it has been proposed another control approach, which consists in a cascaded configuration with a SM current (vector) controller in the inner loop and other kind of controllers (initially PIs) in the outer one for the generated voltage, similar to the approach presented in [5]. This option has been simulated in a stator field oriented reference frame, in order to verify its performance. Nevertheless, the interaction be-

[5]

[6]

[7]

[8]

[9] [10]

S. Mtller, M. Deicke, and R.W. De Doncker, "Doubly fed induction generator systems," IEEE Industry Applications Magazine, May-June, 2002, pp. 26-33. S. Tnani, S. Diop, S.R. Jones, and A. Berthon, "Novel Control Strategy of Double-fed Induction Machines," in Proceedings of the EPE'95, 1995, Sevilla, 6 pp. A. Mebarki, and R.T. Lipczynski, "A Novel Variable Speed Constant Frequency Generation System with Voltage Regulation," in Proceedings of the EPE'95, 1995, Sevilla, 7 pp. R.S. Pefna, G.M. Asher, J.C. Clare, and R. Cardenas, "A constant frequency constant voltage variable speed stand alone wound rotor induction generator," Opportunities and Advances in International Power Generation, March 1996, Conference Publication No. 419, pp. 111-1 14. R. Pefia, J.C. Clare, and G.M. Asher, "A doubly fed induction generator using back-to-back PWM converters supplying an isolated load from a variable speed wind turbine," IEE Proc.-Electr. Power Appl., Vol. 143, No. 5, September 1996, pp. 380-387. R.S. Pefia, R.J. Cardenas, G.M. Asher, and J.C. Clare, "Vector controlled induction machines for stand-alone wind energy applications," Record of the 2000 IEEE Industry Applications Conference, 8-12 Oct. 2000, Vol. 3 , pp. 1409 -1415. Paul C. Krause, Analysis of Electric Machinery, Mc Graw Hill Company, Singapore, 1987. V.F. Pires, and J.F. Silva, "Teaching Nonlinear Modeling, Simulation, and Control of Electronic Power Converters Using MATLAB/SIMULINK," IEEE Transactions on Education, Vol. 45, No. 3, August 2002, pp. 253-261. V.I. Utkin, J. Gtldner, and J. Shi: Sliding Mode Control in Electromechanical Systems, CRC Press, UK, 1999. V.I. Utkin, "Sliding mode control design principles and applications to electric drives," IEEE Transactions on Industrial Electronics, Vol. 40, No. 1, Feb. 1993, pp. 23 -36.