Variable Structure-Based Synchronous Generator Excitation Controller for an Infinite Bus Power System

VARIABLE STRUCTURE-BASED SYNCHRONOUS GENERATOR EXC. ..

14th World Congress ofTFAC

0-7c-09-S

Copyright '[) 1999 IF AC 14th Triennial World Congress, BeUing. P.R. China

VARIABLE STRUCTURE-BASED SYNCHRONOUS GENERATOR EXCIT A TION CONTROLLER FOR AN INFINITE BUS POWER SYSTEM

Wei Liu·, Yixin Yu·

i,

and Shubao Tian I

i

§ Department a/Automaton Engineering, Hebei Institute a/Technology, Tangshan City, Hebei 063009, PR. China., E-mail: [email protected]

§ § Department a/Electrical Power Systems and Automation Engineering, Tianjin University, Tiarijin 300072, PR. China

Abstract: In this paper, an excitation controller is designed by the variable structure control theory to improve the transient stability of a single machine infinite bus system. The pole assignment techniques are employed for determining the switching hyperplane. The computer simulation and experiment in a scaled power system show that the designed controller can provide effective damping torque and improve the dynamic performance for the power system. Copyright © 1999 lFAC Keywords: Variable structure control, Power system control, Generator, Excitation control, Disturbance parameters, Dynamic stability

I. INTRODUCTION

The excitation control of synchronous generator is very important to improve the transient stability of power system. It has attracted researchers' attention for several decades. The literature on excitation control is extensive and various approaches have been proposed. Since the sixties the power system stabilizer (PSS) was already being investigated (deMello and Concordia, 1969; Moussa and Yu, 1975) and many papers had been published on this subject. Later, deMello (1980) presented the coordinated application of stabilizers in multimachine power systems. Fleming et al. (1981) addressed a method for selecting parameters of stabilizers in multimachine power system. Since the early seventies, the optimal control theory has been widely applied for the design of excitation control of synchronous generator, for example, (Yu and Siggers, 1970; Vu, 1983). In recent years, along with the development of power electronics and non[inear control theory, many researchers are exploring nonIinear excitation control, especially from differential geometric control

approaches to enhance steady states performance as well as transient stability (Lu and Sun, 1993). However, the complex of the computation has limited its further application to power system. Since the 1970's, variable structure control (VSC) has become a useful branch of control theory. During the recent decade(Utikin, 1992; Wang, et al. 1992; Wang , et al., 1994 ), VSC received much attention due to its robust response characteristics, for example: Q.

VSC potentially can maintain a desire response characteristic almost independent of the system structure;

b. VSC is one of the most developed branches of nonlinear control theory and theoretically be used for any nonlinear system. But other nonlinear control theories generally have their own restrictions, such as "globallinearization methods" and "decoupling linearization methods;"

7475

Copyright 1999 IF AC

ISBN: 008 0432484

VARlABLE STRUCTURE-BASED SYNCHRONOUS GENERATOR EXC. ..

c. Relative to most nonlinear controls, VSC is easy to realize; d. The greatest advantage of VSC is its adaptiveness

to external disturbances and to internal model perturbations.

To a large extent, the above features correspond to the transient stability control problem in power systems. The contribution of this paper is the design and application of a variable structure control law to synchronous generator excitation controller connected to an infinite bus power system. The paper is organized as follows. The principle of VSC is briefly introduced in section 2. The design procedures of the controller is described in section 3. The simulation performance results of the controller are demonstrated and the variability of such a control strategy is established and further research is suggested in section 4 and section 5.

14th World Congress ofIFAC

X will reach at the plane S=O in a finite time t under the control action, a two phase variable case is shown in Fig. l. The state X passes through switching plane and enters the domain of SO once more, which forms a sliding mode control. It is obvious that the state X can be restricted on the switching plane ~ by the discontinuous control u . Therefore, the condition to fonn a sliding mode is

lim S <0 { S-)OO+ limS>O

2. SYNTHESIS OF THE VARIABLE STRUCTURE CONTROLLER

x = A(X) + B(X)u

(1)

T. xn ) IS a state vector,

x2

A(X) and B(X) are the appreciate non linear vector

functions, and u is a scalar control variable. Assuming discontinuous control:

where u+ eT

= (c 1

;#.

u-, S is a linear switching hyperplane, C2

.~-+o -

that is SS < 0, which forces the system motion toward the hyperplane s=o. The following approaching law is chosen in the design.

Consider the following system

where: X = ( XI

S=

-ssgn(S) - KS

(4)

where sgn(S) is the sign function of S and the term Esgn(s) generates the desired variable control structure for the different sides of the switch hyperpiane in the state space and item KS makes the trajectories coverage exponentially in the ideal case. The control u can be gotten by the following procedures.

from (5) the control u is obtained

Br [eT

en ) is a constant vector. If

u = [- e T

assume S >0, when t=0 , then, the system state vector

AX -

s]

(6)

Substitution of (4) into (5) yields:

Xl

a: Switching state

S=crX l+X2=O

(3)

U=_[C TBr [eTAX +esgn(S) +KS]

b: Sliding model Xl

(7)

where E and K are given positive constants which are not sensitive to system operator point.

a

3. POWER SYSTEMS WITH VARIABLE STRUCTURE CONTROLLER 3.1 The model ofthe power system

Fig. 1. The state trace

In this paper, we consider the power system is a

7476

Copyright 1999 IF AC

ISBN: 0 08 043248 4

VARIABLE STRUCTURE-BASED SYNCHRONOUS GENERATOR EXC. ..

14th World Congress ofTFAC

Therefore the system (8) is transformed as X, "" (AI, - A J2 C;'C,)X2 + A I2C;'S

S=

[(ClAn +C2 A 1 ,)-(C\AI2 +C2A2Z)C;ICI]XI

+ (ClAn + C2~2)C2IS + C 2 B2 u In the subspace So = ker C , there are: Fig. 2 A single generation infinite system

S = C 1X 1 + C 2 X

single generating unit connected to an infinite bus which is shown in Fig.2. On the system operating point 0=70°, the model of the system can be written as

X=AX+Bu

i.e. .

A=

-I

Xl = (All - A, zC 2 Cl )Xz

u eq = (C 2 B 2 )-/[(Cj A lI +C2 A 21 )

(8)

- (C\A12

SF-"

T;S,.

TlS

D

_ iD.

H SE

-R"SE

()

H

-s,.

SE' -Sr-

TlRFS,.

R,

B=l R~

-~

°

T,[o

T;S,

R'E TdQRV

I

°

:5=Cr X j +C2 X 2 =0

where

SI:. -SI

2 :==

+ C 2 A n )C;'C, ]X\

Let K = C;lC) and det(A\I - A12K) = P(S) where

1 ~O2"

0.691

= -39.5

-0.625

r=

L- 0. 134

-0.0015

[0.081

0

~":"j -0.078

O_051

f

and the Pi are the assigned poles.

C = (Cl' C 2] = [C 2K, C 2] = C 2 [K,1 m ] if Jet C 2 = Im ,then the C = [K,Im] can only be

As

For

determined.

the

case

power

system

X = [LV:tl(1)~U,Y u = ~Er

The data are obtained from (Lu, et aI., 1983).

- 0.215 A == [ - 39.5

3.2 Determination of the sWitchtngplane Once the system has been established, the next step is to construct the sliding surface so that restricted to this surface the system has a desired response. In this paper, the selection of the switching vector is done using a pole assignment technique as outlined as below.

-0.134 B XI

= ~co,

==

[0.081

0

-°0.1251 -0.078

0.051Y

Al I = -0.625, A]2 = -0.625 ,

X2

Suppose the state equation of the system(8) can be

0.691 - 0.625 -0.0015

= [Me

~V;r,

expressed as

0.691 ]

t

+ A 12 X

2

= Az,X,

+ A 2Z X

Z

Xl

=

Xl

A l1 X

A21

+ Bzu

= [ -O.OOlS '

(9)

= [- 0.215 - 0.125J - 0.134

B = [0.081J

- 0.078 '

0.051'

the switching plane is

do linear transform (10) i. e.

X

2

= C 2-'S - C;lC t X

° '~ 1 ° 1

Xl =X 1 t

then

7477

Copyright 1999 IF AC

ISBN: 008 0432484

VARIABLE STRUCTURE-BASED SYNCHRONOUS GENERATOR EXC ...

x = AX + Bu ::::::> X' = A'X' + B'u

3.3 Synthesis of the contro/law

where: A'=TAT · 1

=

=

["

2IS "orO. -

0

0 0

I 0

0.691 -0.625 - 0.0015

39.3 - 0.134

I

rO.OOI94

0.693 - 0.625 -0.0015

- 39.3

- 0.134

-0.:°0

r

_0;2SP

0

t2

1

- 0.078

0

0 1

0

14th World Congress oflFAC

98]

- 0.078

According to the VSC theory, the control is to force system motion toward the hyerplane S=O. In this paper, a control u(t)(l2) is synthesized, which has two possible structures.

u = {u+ whenS = C T X> 0 u-whenS =C T X <0

(12)

Depending on the location of the system 's state point X with respect to the switch hyperplane S(X)=O, the u + andu - as follow:

o 1

o

u+ =20t:..Pe

+9~aJ+15~~

u- = -ISMe t

0.081 =-1.59 0.051 '

=2

Let K = C;IC I equation is

= [k1

I:..w"

I

det[SI - (All - A 12 K)]

K=[k\

kz1=[8547.9

from (10). As S =

C' =CT =

=C 2 [C;ICI = C 2 [8547.9

= C 2 [8547.9

C2

V

IJr=C 2 [K 375.69 375.69

S] ,2

= 4 ± j3,

the

375 .69]can be solved

e1x; + e2x~

[Cl

4. SIMULATION RESULTS

(10)

PI )(s - P 2) = 0

if the poles are assigned at

=

ex' = e'X

where

IV

lE

9~aJ -13,1J~

X' =[M:]

k 2 ] ,then the characteristic

= peS) = (s -

(13) -

0

1

In the simulation study, we consider that the power system shown in Fig.2 with a large sudden fault at 1DOms and the fault was removed at 250ms. The response of power angle 8(t) and generator terminal voltage V, are shown in Fig. 3 and Fig. 4 , which are controlled by the variable structure excitation controller (solid line) and general PID controller (dash line).

From the simulation results given above, we see that using the variable structure controller proposed in this paper can maintain transient stability and achieve voltage regulation and has better dynamic perfonnance then using the general PID excitation controller.

cS

~ lt9]

140 120 100

80 60

0

-13590.16]

rr··· if, ..

o let C 2 = 8547.9 , then C = [1 0.044 -1.59]. Therefore the switching hyperplane S is below.

S = Mo + 0 .0441:..w -1.59I:..V,

_.

:

J

,.

.......

iD. (

l

L

v

,';.,

\,::(

: 2

4

/

h '

...

, ~ : ':L 6

.•..•......... .

i

,

8

10

.'.'"

..

12

14

Time (Seconds) Fig.3 The Rotor angle response curves

(11)

7478

Copyright 1999 IFAC

ISBN: 0 08 043 248 4

VARIABLE STRUCTURE-BASED SYNCHRONOUS GENERATOR EXC. ..

V,

~--~---'---o----r---;----r--~

1.20 1.00 0.80 0.60 . 0.40 .

o

2

4

6

8

10

12

14

Time (Seconds) Fig.4 The voltage response curves

5. CONCLUSION In this paper transient stabilization and voltage regulation of power system with a variable structure excitation control law have been discussed. The variable structure control scheme has been given. The variable structure excitation control proposed in this paper can transiently stabilize a class of po.wer systems with a large sudden fault and can achIeve voltage regulation. Simulation results show that the variable structure excitation controller possess a good dynamic performance.

REFERENCES DeMello, P. F. et at., Coordinated Application of Stabilizers in Multimachine Power Systems, IEEE Trans. on Power Apparatus and Systems, P AS99, No.3, 1980. DeMello, P. F. and C. Concordia, Concepts of Synchronous Machine Stability as Affected by Excitation System Control, IEEE Trans. on Power Apparatus and Systems, PAS-88, No.2, 1969. Fleming, J. R. et al., Selection of Parameters of Stabilizers in Multimachine Power System, Presented at the J 98 J Winter Power System Meeting, Atlanta, Georgia, Feb. 1-6, Power No. 81 WM077-7. Moussa, H. A. and Vu, Y. N., Dynamic Interaction of Multimachine Power System and Excitation Control, IEEE Trans. on Power Apparatus and Systems, PAS-94, No.4, 1975. Lu, Q. et af., Optimal Control of Power Systems, Chinese Academic Press, 1982.

14th World Congress ofTFAC

Lu, Q. and Y. Sun, Nonlinear Control of Power Systems, Chinese Academic Press, 1993. Utikin, 1. V., Sliding Modes in Control and Optimization, Springer-Verlag Berlin, Heideberg, 1992. Wang, Y. et aI., Variable structure FACTS Controllers for power system Transient Stability, IEEE Tram. on Power Systems, 7, No. I, 1992. Wang, Y. et at., Transient Stabilization of Power SYstems with an Adapti.ve Control Law, A~tomatica, 30, No. 9, 1994. Wang, Y. et al., Variable Structure Braking Resistor Control in A Multimachlne Power System, IEEE Tram. on Power Systems, 9, No.3, 1994. Vu, Y. N. and Siggers, c., Stabilization and Optimal Control Signals for a Power System, IEEE Trans. on Power Apparatus and Systems, PAS-90, No.4, 1971. Vu, Y. N., Electric Power System Dynamics, Academic Press, 1983. Liu, W., Y. x. Vu, and S. B. Tian (1998). Study on the Variable structure Model Reference Adaptive Synthetic Controller for Turbo-Generator (1) A~tomation of Electric Power Systems, 22(4), 510, (in Chinese). Liu, W., Y. X. Vu, and S. B. Tian (1998). Study on the Variable structure Model Reference Adaptive Synthetic Controller for Turbo-Generator (II) Automation of Electric Power Systems, 22(6), 1215, (in Chinese). Liu, W., Y. X. Vu, H. Yuan, and S. B. Tian (1997). A Variable structure Model Reference Adaptive Fast Valving Controller. Automation ofElectric Power Systems, 21(8), 34-37, (in Chinese). Liu, w., Y. X. Yu, and S. B. Tian.(1997). A Variable Structure Model Reference Adaptive Controller for Generator Excitation System. Power Systems Technology, 21(5),8-11, (in Chinese). Uu, W., Y. X. Vu, and S. B. Tian(l997). A Generator Excitation Controller Based on the Hybrid Control Scheme with Feedback Linearization and Variable Structure, Journal of Tianjin University, accepted in Feb. 1997, (in Chinese). Liu, W., S. B. Tian, and Y. X. Vu. (1996). Variable Structure Control with Application to Power System. Proceedings of 1996 Chinese Control Conference, I, 1137-1141, (in Chinese). Liu, W. and Q. L. Zhang.(1995). Variable Structure Control with Application to AC Regulator. Proceedings of 1995 Chinese Control Cmiference, 2,1604-1607, (in Chinese).

7479

Copyright 1999 IF AC

ISBN: 008 0432484

VARIABLE STRUCTURE-BASED SYNCHRONOUS GENERATOR EXC. ..

14th World Congress ofTFAC

X2

a: Switching state b: Sliding model

a

Fig. 1. The state trace

Fig.2

A single generation infmite system

5°r-__

~

__

~

____

~

__

~

__

~

____

~

__-'

140 120

lOO 80 60

~If'~~,~-+~~--~+-~~---+-=~

o

2

4

8

6

12

10

14

Time (Seconds)

Fig.3 The Rotor angle response curves

V,

j

1.20 1.00 Ii~\

0.80

\/\. ,. . >'"

f··

/-=: too. l

..

0.60 0.40

-r··'

-...........

k········

6

..

. ......

J

j i 024

~-

8

10

12

14

Time (Seconds)

Fig.4 The voltage response curves

7480

Copyright 1999 IF AC

ISBN: 008 0432484