Oscillation transient energy function applied to the design of a TCSC fuzzy logic damping controller to suppress power system interarea mode oscillations

D.Z. Fang, Y. Xiaodong, S. Wennan and H.F. Wang

Abstract: An oscillation transient energy function (OTEF) is proposed for the analysis and damping of power system area-mode oscillations. The OTEF interprets an area-mode oscillation as the conversion between oscillation kinetic energy and potential energy. Based on this interpretation, an OTEF descent method has been developed to design a supplementary fuzzy-logic thyristor controlled series compensator (TCSC) controller to damp the area-mode oscillation. Since the proposed method guarantees the continuous descent of oscillation energy, the fuzzy-logic TCSC damping controller designed is robust to the variations of power system operating conditions. A 4-generator 2-area interconnected power system is presented to demonstrate the effectiveness and robustness of the TCSC fuzzy logic damping controller installed in the power system.

List of symbols

Ai fuzzy set corresponding to linguistic

B, fuzzy set corresponding to linguistic variable of CA,

Dr output of the reset filter from the input, - P A

variable of p,,,

gain factor determined by fuzzy-logc unit 2 (FLU2)

[ r ip integral of D p KDP scaling factor for D p K G scaling factor for CA, Kr scaling factor for P,,, P A

P?,,

W;

- .YRE.c reference of -XTcsc

active power flowing along the part of tine line which is near to area A magnitude of D p at each zero crossing of

weight corresponding to B, for defuzzifi- cation

equivalent reactance produced by TCSC grade of membership of G,,, in the fuzzy set E, membersbip function of 0 representing A X is negative membership function of H representing A X is Dositive

ID,

- xrcsc PBi

PA.)

P A . )

,Q IEE. 2003 IEE Procwdiqp online no. 20030098 doi: 10.1@4Y/ip-gtd.ZM300)IH Online publishing datc: 20 January 2003. Paper first rmivrd 8th Februaly 2002 and in rrvised form 3rd &rober 2002 D.Z. Fang. Y. Xiarxlong and S. Wrnnan are with the School of Elect"m1 Aulumalion and Energy Engineering. Tianjin University, Tianpn 300072. China H.F. W m g is with the Deparlment of Elcc tkd Engjneering, Bach Univcrsily, Bath. UK

ILz'Proi.-Genrr Tr<zn.si Drnrib.. VoL 150, Nil. 2, Murdi 2023

1 Introduction

Power system area-mode oscillation has been of interest to power system researchers and engineers for many years. The addition of a supplementary damping control signal on the normal operation functions of flexible AC transmission systems (FACTS) devices, such as a thyristor controlled series compensator (TCSC), provides a new option to suppress power system area-mode oscillation [1-3]. Various eigensolution techniques based 011 a linearised model of power systems have been developed and tested for the design of the FACTS damping controllers [4]. However, as far as the area-mode oscillation damping of a large interconnected power system is concerned, it is neither simple to established a detailed lincarised system model for the design of a FACTS damping controller, nor is necessary as has been demonstrated by applications of fuzzy-logic control strategy in power systems to enhance system stability [W]. On the other hand, as power system oscillations are essentially caused by excessive energy, an energy function approach has k e n proposed in emergency control schemes such as generation and load shedding [8]. A damping control strategy for FACTS devices using the transient energy function of a structure-preserving model of power systems has been reported [9]. The control of series capacitors to alleviate transient stability 'crises' has been proposed and tested [IO]. All these have facilitated the work presented in this paper.

A new energy function, the oscillation transient energy function (OTEF), for appreciation of the mechanism of area-mode oscillations of power systems is proposed. An OTEF descent strategy has been developed to design a TCSC supplementary modulation controller to damp area- mode oscillations. This strategy is implemented by two fuzzy-lop units which achieve oscillation suppression by continuously reducing the OTEF. One of the fmy-logic units smooths the TCSC modulation and the other adjusts the controller's gain value adaptively. To demonstrate the effectiveness of the TCSC fuzzy-logic damping controller, 4 generator '-area power system is presented [ I I]. Simulation

233

results show that the TCSC damping controller designed by the OTEF descent method can not only effectively suppress system area-mode oscillation but also is robust to variations of system operating conditions.

2 control

2.1 OTEF in area-mode oscillations A two-area power system with a TCSC installed on the tie line is shown in Fig. I . The relative dynamic rnotioii between the centres of inertia (Cols) of areas A and B can he described by the following equations:

Damping control strategy for TCSC damping

w a a L = (PA" PA) - L ( P E 0 + PE) ( '1 MA M E

where SAn and oAB denote the difference in swing angles and speeds between the two Cols, respectively; Pao and Pm represent the differences between the total power generation and consumption in the two areas; Pa and PB is the transmission power as shown in Fig. I ; M A and Ma ,denote the inertial constants of the two COIs [12].

Multiplying both sides of ( I ) by uAR and from wAB= dfiaB/df, we obtain

That is

Suppose that wAm and SAM) are, respectively, the values of aiAB and SAB at the system equilibrium point and wABO = 0, integrating both sides of the above equation, we obtain

That is

= constant (3) In (3) we can consider the first and second terms to he the oscillation kinetic energy (OKE) and the oscillation potential energy (OPE) of the system area-mode oscillation. respectively. The sum of OKE and OPE is the total OTEF as far as the system area-mode oscillations are concerned. Equation (3) indicates that during system area-inode oscillations, the OTEF remains constant for a zero-damped

234

area-mode oscillation. Hence the OTEF can be used as a measurement of area-mode oscillation and an OTEF descent method can be proposed to design a TCSC damping controller to suppress the area-mode oscillation.

2.2 OTEF descent method During one cycle of the area-mode oscillation, OKE and OPE are converted into each other. The cycle can be divided into the following four phases. Pliuse I: huckivurd uccderutiun phuse (0 > wAa> W ~ H ~ , ~ ~ , ,

(was: O+W,.,~,~,;,,)). In this phase [ i A s < O and OPE is converted to OKE. When wAn= w,,~,,,;,,. OKE arrives at its maximum value where OKE,,, = 1 / 2 ~ ; ~ , , ~ . Phuse 11: huckivurd deceliwtion pliuse ( w ~ ~ , , ~ ; ~ c w A D i 0 (aAn: wAn,,,,,,+O)). This phase is characterised by hAE>0 and OKE is converted to OPE. At the end of this phase, OKE reaches its minimum value where OKE,,,,,=O with

Phu.ye Ill: forward occeleruution plime (0 < uaR> (wAs: O+wAs~,z~,J) and phase 1V:~ori~~urd~li~ceIeruti~ii phase ( o j A n , , , , . ~ > f ~ j a B > O ( ~ ~ j A n : wAn,,.rr-O)) are similar to phases I and I I with the same process of energy conversion. Therefore, the area-mode oscillation is a process of periodical conversion between OKE and OPE. If we introduce the time interval of [to, tb], [ lb: &I, [/<.- /$ and [t<,> t J for those four phases of area-mode oscillation and from the definition of OPE, we have

Sin(r"j

dAH = o A B ? i a i ~

(4) s OPE(/,) =OPE(/,) +

6r*If,J

If we assume the area-mode oscillation has zero damping with the OTEF being constant and OK&?(/,,) = OKE(t,) = 0. we have

OPE(t,) = OPE(&) ( 5 )

From (4) and ( 5 ) we have

Let d P ( t ) z O denote a positive COntrO~ldbk power incre- ment. If a tie-line power modulation control can be applied in the cycle such that in phases I and I I , Pa and Pn increase by d P ( f ) , and in phase 111 and IV, Pa and Pa decrease by LIP(/). From (4), the OPE at t,, becomes

Considering (6), we have

where

If the AP(t)>O can he properly controlled to make OPE(f,)-AOPE(f,)>O, the OTEF is reduced by dOPE(f,,) in the oscillation cycle because OPE(t,) and OPE(/,) represent the total OTEF of the system at 1, and f , , respectively. Furthermore, with this modulation control being continuously applied in every oscillation cycle, the total OTEF will descend continuously and hence the power swing will he effectively suppressed by this modulation control. This is the principle of the OTEF descent method, which will be tested for the design of the TCSC damping controller to suppress area-mode oscillation as follows.

2.3 Application of the OTEF descent method for TCSC damping control By ignoring the loss of the tie-link transmission line and from Fig. 1 , it is easy to show that Pa = P,-P with

where XI, X , and -Xrcsc denotes the reactance of two sections of the tie line and the equivalent reactance of the TCSC, respectively. To show the OTEF descent method implemented by the TCSC in Fig. I: X,,, can be represented as Xrc,yc= XREF+AX. where XREF and AX, respectively, denote the refercncc and increment reactance of the TCSC. From (IO) it can be seen that when dX>O. P increases and when dX<O, P is reduced. Therefore, to implement the modulation control strategy, the TCSC should be controlled in such a way that dX>O when wAR<O and AX<O when w A B > O . This result is similar to that derived from the damping torque analysis in [13].

3 Design of the fuzzy-logic TCSC damping controller

3.7 Control signal As mentioned above, a significant contribution to system area-mode oscillation damping can be achieved when the TCSC damping control is properly modulated according to

,! the variations of wAB. If wAB is used directly as the control signal, sophisticated techniques and expensive measure instruments [ I l l are required. Hence in this paper, the locally available tie-line power PA is used as the control signal [6]. Fig. 2 shows the proposed configuration of a fuzzy-logic TCSC damping controller using Pa as the feedback control signal, where D p is the output signal of the reset filter from -Pa and IDp is the integral of Dp. It have been shown [6] that Dp and IDp can be used as the control signals to identify the oscillation phases.

3.2 Control scheme With the control signals D d k ) and Iodk), the discrete value of D p and lop, oscillation phases can be identified according

IEE Proc.-Gnm Tronr,!. Uhnili.. Vol. ISU. M2. 2, Munli 2m.g

to the following equation:

where K,,>O is a scaling factor to co-ordinate the magnitude of D p (k) and I,,, (k). To implement the OTEF descent method, two fuzzy rules for TCSC damping control modulation are employed

Rule 1: IF O(k)t(O,n) THEN AXiO Rule 2 IF 0 ( k ) ~ ( - x [ _ O ) THEN AX>O

If A X takes a tixed value, the above control rules result in a bang-bang control scheme. However, a sudden change of the TCSC damping control may not be beneficial to power system operation. Hence, a fuzzy-logic unit 1 (FLUI) using the two membership functions shown in Fig. 3 is adopted to modulate the reactance of TCSC smoothly. The output of FLU1 is calculated by

d X ( k ) = G d x ( ~ p ( O ( k ) ) - h ( ' K k ) ) ) (12)

where GdX is a gain factor adaptively tumed, p>dO) and pP(0) are the membership functions representing A X i O and AX>O. respectively.

3.3 Fuzzy-logic tuning of the gain factor To achieve a quick damping of area-mode oscillation, the gain factor GAXcan he modulated by the fuz.zy-lo&k unit 2 (FLUZ) at the points when ID&) reaches its zero crossing. Let the magnitudes of Ddk) and GdXat each zero crossing of I,,&) be ... P,., P,,,i+l ..., and ... C A ~ , ; , Gz,x.i+l ..., respectively. As shown in Fig. 2_ the input P ,,,_,, E',,,.,+ I and GdX.i (i= I , Z...) are first normahed by the scaling Ikctors, K p and Kc;, and then a new gain GdX.;+ is generated by FLU2.

3.3. 7 Rule base of FLU2 A set of control rules for FLU2, called the rule base (Table I), is constructed based

235

Table 1: Fuzzy control rules

P , ( is L Pm,< is M Pm,i is S

Pm.i, L M S Pm.i, M S P,*l S GdXi GaVi GAXi

L L L s L L s L s M L M z M L s M z S M s Z S M z S z Z s z z Z s z Z z*

L=Large. M=medium. S=small Z=zero

on the following reasoning:

(a) If the previous control action damps the oscillation effectively but it remains large, then retain the previous GM; otherwise decrease GdX appropriately. (b) If the effect of the previous control is not obvious and the prcsent amplitude of oscillation remains large, GdX should be increased. On the other hand, if the present oscillation is weak GAXshould either be retained or reduced.

The general application of the rules is in the form of ‘IF premise THEN consequence’. For example, the conse- quence marked by ‘*’ is obtained by the reasoning: IF is s) and (Pm,z+~ is SI and (CAy,; is Z)) THEN (GAx,~+ I is 3.

3.3.2 Process of fuzzy-logic tuning: The !procedure to calculate the output of FLU2 is [14]. Step I Fumjcation: Three fuzzy partitions are considered for P,, and a linguistic variable is associated with each set: { A , : large (L), Az: medium (M), A?: small (s)} as shown by Fig. 4.

S M L

0 0.25 0.50 0.75 1 .o

Fig. 4 Membership Junction for P,,,

with the parameters (U;, ai): L(0.33, 0.9), M(0.33, O S ) , S(0.25, 0.25), Z(0.33, 0.05). Step 2 In/krence: The rules in Table I are divided into four groups according to their consequences. For each rule. the lowest one of the three antecedent membership grades is defined as the rule’s ‘degree of firing (DOF)’. The maximum DOF in each group is chosen as pB; (i= IM), which is the composite membership degree of the output fuzzy set B,- S/ep 3 Dcfiizzijcotion: The defuzifier output U is

= &p8,/kP8i i= I ,=I (14)

where W; is a weight which initially equals to the corresponding xi in (13) and will be tuned during the control process.

3.3.3 Self-tuning of the parameters: Self-tuning of control parameters is especially useful when the set of fuzzy rules is inadequate. I t is noted that when P,, and CA, become relatively small in comparison with the scaling factors, the fuzzy set classification becomes inaccurate. In such a case, the scaling factors Kc, K p and the weights W, should be regulated according to the current magnitudes of P,, and GAx It is known that if P,,8,i and P,w,i+ I are close to Sand GAx; is close to Z, the rule marked by ‘*’ in Table I will produce a very high DOE Therefore the DOF of this rule can act as a criterion of the diminution of P,, and GAX. When this DOF becomes higher than others, supposing it is in the ith operation of FLU2, the scaling factors KG, KF and the weights W;(i= 14) are to be tuned by (15H17) and the regulated values will take effect from the next (i.e. (i+ 1)th) operation of FLUZ.

In the same way, four linguistic values are encoded into the fuzzy sets of G A ~ {B,. large(l), B2: mediuni(i\.i), B3: small (8. B4: zero(Z)} as shown by Fig. 5 , where

L -

\ I

1 .o

Fig. 5

236

Membership function fur CA,

It can be seen that the tuning of CA, always uses its previous value as an input. Hence a small initial gain, GAx.I, is required to start the control action. For a severe oscillation, GAX,] may be less effective at the initial stage. However, the small intial value can avoid an overdone control action.

4 Cases studies

Numerical simulations were performed in an example 4- generator ?-area power system [I41 as shown by Fig. 6 (SHASE = 900 WVA). A TCSC with a supplementary

itx PFOC.-G‘WC~. T W ~ ~ U ~ i s i ~ i b . , vu/. isn. NO. 2. lwarcil 2w3

aieaA tie-line , area B ! !

Fig. 6 Four-generutor mu-ureu i c w power s,we,n

fuzzy-logic damping controller (-A',,= 0.267 p.u. and G,lx,l = 0.015) is installed in the power system to enhance the cdpahility of power transmission and the additionally to suppress area-mode oscillations. In the simulation, two-axis model with third-order exciter controller of generators is adopted and the system load is represented by constant impedance.

Cuse I : A 3-phase short occurs at bus 7 ckared in 0.1 s at the operating condition, Pa = 0.535 p.u. Case 2 A 3-phase short occurs at bus 7 cleared in 0.1 s at the operating condition of Pa = 0.345 p.u.

Cuse 3: The mechanical input power of G4 suddenly curtails 10% and recovers in 0.10s at the operating condition, P,, = 0.445 p.u. Case 4: The active power of the load on bus-7 suddenly increased from 0.967 p.u. to 1.080 p.u. at the operating condition. P4 = 0.445 p.u.

Simulation results for the four study cases are shown in Figs. 7-10, Results in Figs. 7 and 8 show that initially, the damping control is not so effective due to the small initkal GZqx. However, the controller is able to increase CA, adaptively and then GAS is gradually reduced with the attenuation of the oscillation. Results in Figs. 9-10 demonstrate that the initial value of GAx., is suitable and by assessing the effect of controller, CA, decreases gradually. These results verify that the damping control is effective and robust to the variations in the operating conditions.

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

=

n!

'I 0.1 0 2 4 6 8 10

time. s

Sinrulu/ion re.su/r.s f i r case I Fig. 7

Tests also show that the fuzzy-logic controller can enhance the transient stability of system operation. For instance, with the controller installed, the critical clearing time is extended from 0.314.32s to 0.34-0.35s for the 3-

ILZ' Pm.-Gener. Tmnvnz. Dirtrib.. VoL 180, No. 2, Mor& 2GO3

0 2 4 6 8 10 lime. s

Fig. 8 Simulation rrsultsfur case 2

0.50 r Pa With 1 0.39 0.48

0.46

2 0.44 4

0.42

=

0.40 1- ' 1 0.27

0.38 'I 0.24 0 2 4 6 8 10

time, 5

Siniulutiofi resultsfor case 3 Fig. 9

0.43 n 1 0.35 0.42

= a 0.41

3

0.40

0.39 0 2 4 6 8 10

time. s

Fig. 10 Siniulution vrsults fa. cue 4

phase short circuit occurred at bus 7 cleared in 0.1 s by tripping one of lines 7-9 on the 4-generator test system.

5 Conclusions

This paper proposes the concept of the OTEF to describe power system area-mode oscillations and suggests an OTEF descent method for the design of a TCSC damping controller to suppress system area-mode oscillations. Furry-logic control and adaptive techniques are employed to implement the TCSC damping controller. Case studies show the effectiveness and the robustness of a TCSC damping controller installed in an example power system.

237

6 Acknowledgments

The authors acknowledge the support of the Natural Science Foundation of China (grant 59977015) for their studies of the new oscillation transient energy function and for developing the techniques of fuzzy-logic control for the stability enhancement of power systems.

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