Enhancement of Power System Stability with FACTS Using Adaptive Fuzzy Controller

Tomonobu Senjyu*, S hotaro Yamanet, Katsumi Uezato' *Department of Electrical and Electronics Engineering

University of the Ryukyus 1 Senbaru Nishihara-cho Nakagami Okinawa 903-0213 Japan

E-mail: b985542f3tec.u-ryukyu.ac.jp

ABSTRACT

This paper presents the adaptive fuzzy controller for the flexible AC transmission system(FACTS) equipment in or- der t o improve the stability of powcr system. The adaptive fuzzy controller is systematically constructed on the basis of control law with the system stability obtained from sliding- mode control. Moreover, the proposed fuzzy controller pos- sesses the on-line adjustment system which adaptively ad- justs the coefficients for thc operation part of the fuzzy rules so as to damp a oscillation of generators. The simulation results show that the proposcd controller can robust control to the variations of the system parameters, system operat- ing conditions, and fault points.

1. INTRODUCTION

In recent years, power systcms have been a tendency to have their power source facilities a t a longer distance from the demand side and to greatly increase capacity. The flex- ible AC transmission system(FACTS)[l] t o overcome this problem have been proposed. The purpose of this system is to improve power system stability and transmission capac- ity of power flow using FACTS equipment applying power electronics.

Many kinds of control techniques using FACTS equipment in order t o improve power systcm stability have been pro- posed [2-51. It is a desirable that the control technique in power system possesses robustness for various fault con- ditions and disturbances. Thcn the researchcs applying fuzzy controller with FACTS are actively reported. The fuzzy control expresses control algorithm which is obtained from knowledge and experience of person by a rule of if- then- form and calculates by fuzzy theory. Therefore the fuzzy control can perform as a non-linear controller with- out a complicated mathematical model of system. However fuzzy control methods which have ever becn reported are many problems for power system control since structure of fuzzy rule, membership function and parameters in design of fuzzy controller are determined by trial and error depend- ing on computer simulations and skilled person's intuition.

In this paper, in order t o solve such a problem, adaptive fuzzy control based on the idea of sliding-mode control which can consider a system stability is proposed and is applied with VSrC (Variable Series Capacitor) which is a kind of FACTS equipments. Proposed controller can syste-

Bus 6

Fig. 1. System configuration.

0.0 (P.U.) / Adjustment mechanism

Fig. 2. Block diagram of VSrC. matically be composed on the basis of control principle con- sidered a system stability. Moreover, the proposed control scheme introduces the on-line adjustment system in this fuzzy controller. This on-line adjustment system adaptively adjusts the coefficients for the operation part of the fuzzy rules so as to damp a oscillation of generators. We verify that the proposed method has good control performance demonstrated by the simulation results on a multi-machine power system.

2. DESIGN OF FUZZY CONTROLLER APPLYING SLIDING-MODE CONTROL

We consider a multi-machine power system. The schematic diagram of the power system is shown in Fig. 1. Generated power is sent in the parallel transmis- sion lines. The synchronous generators are equipped with an AVR and GOV. The block diagram of VSrC is shown in Fig. 2. The control signal for VSrC, U,,,,, is determined by the adaptive fuzzy controller.

0-7803-5731-0/99!#10.00 01999 IEEE VI-533

http://b985542f3tec.u-ryukyu.ac.jp

U ~0.05, 6,=0.05, 6270.15

Fig. 3. Membership functions.

Table 1. Fuzzy rules.

R1 R2 R3 R4 R5 R6 R7 RE R9 R'O R" RI2 RI3 R14 R15

- Rule,

R2 R3 R4 R5 R6 R7 R8 R9 R'O R" R'2 R13 R14 RI5

R'

- N :

PS P T NS NM NB PM PT Z

NT NM PB PM PS NT NS

2 2

N N N N N Z Z Z Z Z P P P P P

gative T S

Z : Zero P : Positive

"41' P, - P,*

NB NS Z

PS PB NB NS Z

PS PB NB NS Z

PS PB

B : E M : h

- f' - PS PT NS NM NB PM PT Z

NT NM PB PM PS NT NS

dium

-

S : Small T : Tiny

We design the fuzzy controller applying sliding mode control. Sliding mode control that is a kind of nonlinear control sets up switching hyperplane on state space and switch the control structures. Therefore sliding mode control switches the system's trajectory on hyperplane. Sliding mode control can realize a robust control system against parameter error, nonlinearity, and noise. The control rule to stabilize system is finally expressed as follows[2]:

where P,* is the criterion of electrical output power P, for stabilizing system. Pm is the mechanical in- put, M is the inertia constant of generator (Mmin < M < M,,,), D is the damping constant of generator

Table 2. Coefficient of operation part.

vz - - PS PT NS NM NB PM PT Z

NT NM PB PM PS NT NS -

- f' - PS PT NS NM NB PM PT Z

NT NM PB PM PS NT NS -

Z L Fig. 4. Decision of coefficient size

on the operation part of the fuzzy rules.

(Dmin < D < D m a z ) , C is the slope of switching line, 9 is the offset to decrease chattering, 2 2 is the speed deviation of generator, and p is a sigmoid function.

If the control is performed such as electrical output power P, agree with criterion P,*, then sliding-mode is formed and the oscillation of generator is damped. However, it is difficult to set directly the value of a VSrC so that it usually satisfies the above control rules due to parameter fluctuation in the power system and modeling ambiguity. We will employ fuzzy control in which it is possible to deal with these kinds of ambigu- ity and construct a fuzzy controller in order to deter- mine the amount of control for the VSrC.

The membership functions and the fuzzy rules for fuzzy control are shown in Fig. 3 and Table 1, respectively. The fuzzy rules are constructed in the form "if - then - " (if - :precondition ; then - : operation part) so

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as to satisfy Eqn. (2).

The operation part of the fuzzy rules is given by

f ' =uI (zz (+w'(Pe-P,s I : i = l , . . . , 1 5 (3)

where U , , ut are the coefficients in the operation part. The control signal I.TvSrc of VSrC is determined as fol- lows

where w, represents the product of fit value for the membership functions. Stabilization in the power sys- tem can be realized by using the control signal of Eqn.(4) for VSrC. Coefficients u i and o; in Eqn. (3) are deter- mined by on-line adjustment system illustrated follow- ing chapter.

3. ON-LINE ADJUSTMENT SYSTEM

We must spend a lot of effort since the operation part f' of the fuzzy rules in Eqn. (3) is generally determined by trial and error. On-line adjustment system which adjusts the operation part of the fuzzy rules such as damping the oscillation of generator without trial and error is introduced on the above fuzzy controller. This system is composed that the coefficients U , and U , in Eqn. (3) are automatically adjusted so as to satisfy the control law with sliding-mode control. The adjustment law of U , and v, is expressed with speed deviation 2 2 and electrical power deviation P, - P,* as follows,

U , ( k + l j = o l U ~ ( k ) $- Elr22(L jWAi (k ) ( 5 )

o i ( k + l ) = a 2 2 ) z ( k ) -k & Z z ( P e ( k j - P z ( h ) ) W B r ( k ) ( 6 )

where I; is time, cy1 and cy2 are the forgetting factors

fitness of the precondition part of each fuzzy rule. The adjustment parameters & I r , E Z , are determined on the basis of the fuzzy rule shown in Table 1. & I r , 2, express learning speed of the adjustment law.

We illustrate about the method in order to determine the adjustment parameters &Ir and 2' in Eqns. (5) and ( 6 ) . A sign of the operation part f ' shown in Eqn. (3) depends on a sign of U' and v,. The size and sign of elr and eZ, so as to obtain f' designated in Table 1 should be determined. It is easy that a sign of the control signal is agreed with a sign o f f ' of fuzzy rule since variables 5 2 and Pe - P,* in Eqn. (3) are expressed at a absolute value respectively. A size of U , and o, is determined by 61' and ~ 2 ' in Eqns. (5) and (6) so as to satisfy a size o f f ' designated in Table 1. A size of and ~ 2 , is relatively given according to the fuzzy rule, then the control signal such as satisfying the fuzzy rule is finally obtained by on-line adjustment system. The initial values ug(o) and "'(0) of U , and U, start from zero,

(0 5 a1 5 170 5 a2 5 I), W A t ( k ) and u B r ( k ) are the

I . - 8 , : with &sc control :: J - - - - - - - - : without Uvsc control -0.7

-0.6' L 1

0.0 2.0 4.0 6.0 8.0 10.0 t (SI

0.5 1

___ : with Uvsc control - - - - - - - - : without Uvsc control

-0.5' 2.5 1

-2.51 1 0.0 2.0 4.0 6.0 8.0 10.0

t 6) Fig. 5. Time responses of phase-angle

and speed deviation.

and the coefficients is adjusted so as to satisfy the fuzzy rule designated in Table 1.

The above adjustment law of U ; and oi is the conven- tional method[2]. However the adjustment law of Eqns. (5) and (6) adjusts only coefficients of the operation part for rule which has excitation after fault, but an- other coefficient remains to be not adjusted after fault. Therefore in this paper adjustment scheme such as the coefficients of the operation part for all rule are ad- justed is proposed and is illustrated as follows.

The rule z which has the biggest product WA, x WB, of the fitnesses W A ~ and W B ~ of the precondition part is searched from rule 1 to 15 at all instants. The coef-

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0.81

. , * '. LQ -0.4

-0.8 : with Uvsc control

- - - - - - - : without Uvsrc control

-0.7' -0.5' 0:O 210 4:O 6:O 8.0 10.0

t 6) 0:O 210 410 610 8.0 10.0

t (s) 0.4 1

-0.30' : with Uvsc control . - - - - - - - : without Uvsc control 3.01

-3.OI tf= 1.00 S , t,= 1.15 S , ti= 1.25 S

: with fisc control -0.4' - - - - - - - - : without l l vsc control

-3.OI tf = 1.00 S , t , = 1 .I5 S , ti = 1.25 S

-3.0: I 0.0 2.0 4.0 6.0 8.0 10.0

t (s) Fig. 6. Time responses of phase angle

and speed deviation.

-3.0' I

0.0 ' 2.0 4.0 6.0 8.0 10.0 t 6)

Fig. 7. Time responses of phase angle and speed deviation.

ficients ui and U; of the operation part for the rule i are adjusted by using the adjustment law of Eqns. ( 5 ) and (6). The relative size and sign of the coefficients of the operation part for another rule are determined by using the rule and size shown in Table 2 and Fig. 4 on the basis of Ju;J and Jv iJ for rule i.

4. SIMULATION RESULTS

The effectiveness of the proposed control is demon- strated by computer simulations on the dynamic re- sponses of a multi-machine power system. A three line- to-ground fault is considered for simulations. The line condition is assumed as follows: (1) 0.0 5 t < tf : par- allel transmission, (2) t f < t < t , : three phase ground

fault continued in one side of parallel transmission, (3) t , < t < t: : fault transmission line opened and the other transmission line sending, (4) t', 5 t : paral- lel transmission (re-closing). Table 3 shows the system constants and operating conditions considered in sim- ulations. The initial values of (ui ,vi) start from zero in all simulations.

Fig. 5 shows the responses of phase angle S and speed deviation Au for each generator. In case of applying the proposed controller, the oscillation of generator is damped at a short time compared with that without control. It is seen that a better performance can be achieved from these results. The performance of the proposed controller for a change in the fault point is shown in Fig. 6. The three-to-ground fault is occurred

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0.6 -

U211

u26,uZI2

U21 P U213 0.3 -

2 0.0- U28 U29rU214

U23 ,U215

U24 tu210

U25

-0.3

- 0.6 - 0.0 3.0 6.0 9.0 12.0 15.0

: Proposed method 1 ' - -. - - - - - : Conventional method -0.25

-0.3: 0.0 3.0 6.0 9.0 12.0 15.0

t (SI Fig. 8. Time responses of phase angle.

-0.8 I 1.21

- 1 2 1 - .- 0.0 3.0 6.0 9.0 12.0 15.0

Fig. 9. Time responses of speed deviation.

0.24

0.12

.U

>m 0.00

-0.12

v 2 2 ,v27

-0.24 0.0 3.0 6.0 9.0 12.0 15.0

f(S)

Fig. 10. Coefficients ui and U; for the operation part of the fuzzy rules (proposed method).

Table 3. System constants.

Generator 1 M = 100, D = 2.6, x: = 0.324, xq = 1.569, xd = 1.548, Tio = 5.14

Generator 2 M = 9.0, D = 2.0, X: = 0.55, x q = 1.651, sd = 1.590, TAo = 5.9

Generator 3 M = 6.0, D = 2.0, X: = 0.40, xq = 1.22, Xd = 1.16, T;,, = 8.97 -"

AVR, GOV TA = 0.3, K A = 50.0, TG = 2.0, KG ~ 2 0 . 0

VSrC Tvsrc = 0.1, K"src = 1.0

Transmission lines 2114 = 0.050 + j0.50, Z115 = 0.030 + j0.30 2124 = 0.040 + j0.40, Zlz6 = 0.035 + j0.35

L A = 0.30 + j0.12, LB = 0.24 + j0.08, 2135 = 0.020 +j0.20, Z136 = 0.045 + j0.45

L c = 0.27 + jO.10 Proposed controller

C = 0.015(VSrC1), C = 0.2(VSrC2, VSrC3) M,,,, = 1.2M, D,,, = 1.20 Mmin = 0.8M,.Dmi, = 0.8D

a1 = 0.99, Q2 = 0.99

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O I ventional adaptation mechanism.

Figs. 10 and 11 show the adaptation mechanism behav- ior with the fuzzy controller for VSrC equipped with generator2 corresponding to the simulation in Figs. 8 and 9. Fig. 10 shows the proposed adaptation mech- anism behavior and Fig. 11 shows the conventional adaptation mechanism behavior. It can be seen that the proposed adaptation mechanism adjusts all coeffi- cients of the operation part so as to damp the oscilla- tion of generator.

0.3 4

2 4 a

- O . j l -0.6

0.0 3.0 6.0 9.0 12.0 15.0

0.07

0.00

-0.07

I v 2 S

-0.14 0.0 3.0 6.0 9.0 12.0 15.0

f ( S )

Fig. 11. Coefficients U; and U; for the operation part of the fuzzy rules (conventional met hod).

between Bus 3 and Bus 6. From these results in the pro- posed method, it is seen that a better performance can be achieved since the oscillation of generator is damped at a short time regardless of the fault point.

The performance of the proposed controller for a change in input power and parameters of generator is shown in Fig. 7. The input power increases by +20% and the parameters M and D of generator decreases by -20%. From Figs. 7 it can be seen that the damping effect of the proposed controller is quite well for a change in input power and parameters of generator.

The fuzzy controller with the proposed adaptation mech- anism is compared with the fuzzy controller with the conventional adaptation mechanism (Reference [2]). In order to show the validity of the adaptation law, we have considered the occurrence of a fault at t = Is, and then at t = 6s again. The line opened time and re-closing time in the first fault are 1.10s and 1.20s, re- spectively. The line opened time and re-closing time in the second fault are 6.15s and 6.25s respectively. Figs. 8 and 9 show the responses of phase angle 6 and speed deviation Aw respectively. From Figs. 8 and 9, it can be seen that the damping effect of the proposed adap- tation mechanism well compared with that of the con-

5. CONCLUSIONS

This paper proposes an adaptive fuzzy controller as a control technique of VSrC which is a kind of FACTS equipments. The proposed method can realize a ro- bust control for the variations of the system param- eters, system operating conditions, and fault points since the fuzzy controller is constructed on basis of idea of sliding-mode control. Moreover, the proposed con- trol scheme introduces the on-line adjustment system in this fuzzy controller. This on-line adjustment sys- tem adaptively adjusts the coefficients for the opera- tion part of the fuzzy rules . Simulation results show that the proposed method is efficient for improving the power system stability.

6. REFERENCES

[l] N. G. Hingorani, Flexible AC Transmission Sys- tems (FACTS), IEEE Spectrum, April, pp. 40- 45, 1993.

[2] T . Senjyu, M. Molinas, T. Shiroma, and K. Uezato, Power System Stabilizing Control For FACTS Devices Using An Adaptive Fuzzy Con- troller, Proc. of International Power Engineer- ing Conference 97 (IPEC 97), pp. 178-183, 1997.

[3] Einar V. Larsen et al., Concept for Design of FACTS Controllers to Damp Power Swings, IEEE Transactions on Power Systems, Vol. 10, NO. 2, pp. 948-956, 1995.

[4] G. N. Taranto and J. H. Chow, A Robust Fre- quency Domain Optimization Technique for Tun- ing Series Compensation Damping Controllers, IEEE Transactions o n Power Systems, Vol. 10, No. 3, pp. 1219-1225, 1995.

[5] L. Rouco and F.L. Pagola, An Eigenvalue Sen- sitivity Approach to Location and Controller De- sign of Controllable Series Capacitors for Damp- ing Power System Oscillations, IEEE Trunsac- tions on Power Systems, Vol. 12, No. 4, pp. 1660-1666, 1997.

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