power system excitation control using master-slave fuzzy power system stabilisers

ELSEVIER Fuzzy Sets and Systems 102 (1999) 85-94

FUZZY sets and systems

Power system excitation control using master-slave fuzzy power system stabilisers C.S. Chang*, H.B. Quek, J.B.X. Devotta

Department of Electrical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. Singapore

Received June 1998

Abstract

This paper proposes a multilevel fuzzy power system stabiliser (FPSS) for damping power system low-frequency oscillations. It investigates the design and implementation of a master-slave fuzzy power system stabiliser (MSFPSS) designed to provide optimal performance at all operating conditions. The paper also proposes a simple off-line training algorithm known as the table lookup scheme [9] for the proposed power system stabiliser. The training set is created using a set of the conventional power system stabiliser's (PSS) dynamic response. The parameters for the conventional PSS were tuned using a well-established pole-placement algorithm [1] for a defined operating condition.

The proposed FPSS and a scheme of universal FPSS are then trained against the conventional PSS on a single-machine infinite-bus power system model. A Simulink/MATLAB model [6] was developed for conducting simulation studies on the proposed scheme. From the simulation results, the MSFPSS conclusively demonstrates itself to be far more superior and robust compared to the other schemes of power system stabilisation in its use as a form of supplementary excitation control in suppressing low-frequency electromechanical oscillations. ~) 1999 Elsevier Science B.V. All rights reserved.

Keywords: Single-machine infinite-bus model; Conventional power system stabiliser; Universal fuzzy power system stabiliser; Master-slave fuzzy power system stabiliser; Master fuzzy classifier; Pole-placement algorithm; Table lookup scheme; Membership function (MF); Fuzzy associative memory (FAM) matrix; Integral of time-multiplied square-error (ITSE) criterion; Integral of error-multiplied change-in-error (IECE) criterion

1. Introduction

Stabilization o f electromechanical oscillations has been an important aspect in the reliable operation o f modem power systems. The techniques for the design of conventional power system stabilisers (PSS) and their parameters have traditionally been based on the linear systems theory [2]. Hence, the desired effective- ness o f the conventional PSS is limited to a bounded

* Corresponding author. E-mail: [email protected].

region around the system operating point. More re- cently, fuzzy logic control (FLC) has been effectively employed [3] to deal with many power systems stability problems due to its robustness and ability to handle imprecision. An ideal scheme of fuzzy power system stabiliser (FPSS) should, in contrast to conventional PSS, be able to extend its region of control operation across a wide range of varying operating conditions.

This paper thus proposes a multilevel FPSS com- prising a master fuzzy controller and a set o f slave FPSSs capable o f automatically adjusting its control

0165-0114/99/$ - see front matter (~ 1999 Elsevier Science B.V. All rights reserved. PII: S0165-0114(98)00205-X

86 C.S. Chan9 et al./Fuzzy Sets and Systems 102 (1999) 85-94

parameters against the connected power system's operating condition. Each slave FPSS is designed for a specific control subproblem or for a region of operation. The master controller is actually a fuzzy classifier which does the job of switching in and out the various slave FPSSs and deciding upon the degree of activation of each to achieve coordinated control of the prescribed control task.

The proposed master-slave controller configuration inherits all the advantages of fuzzy control [5]. In addition, due to its modular design, more slave FPSSs may be added for expansions in interconnected networks to cater to more widely varying operating conditions. In operation, the main advantage of the master-slave FPSS lies in the fact that its control parameters can be changed very quickly in response to changes in system operating conditions. Besides being an effective method of control to compensate for system nonlin- earities and other unpredictable system dynamics, it is also simpler to design and implement than other schemes of adaptation [5].

To correctly tune the fuzzy logic controller is important in ensuring accurate control and robustness of the FPSS. So far, fuzzy rulebase tuning has often been based on heuristics and trial and error [7]. This method, however, lacks objectivity. This paper proposes a simple off-line training algorithm known as the Table Lookup Scheme [9] for tuning each slave FPSS locally. The training set is created using a set of conventional PSS dynamic response. The parameters for the conventional PSS were tuned using a well- established pole-placement algorithm [ 1 ] for a defined operating condition.

The proposed FPSS was implemented on a single- machine infinite-bus power system (Fig. 2). The design and implementation of the master-slave FPSS on the multi-machine power system model (Fig. 1 ) will be reported at a later stage. A MATLAB/Simulink model [6] has been developed for conducting simulation studies on the proposed scheme. Simulation re- suits show conclusively that the master-slave FPSS is able to demonstrate superiority over all other PSS schemes, including the conventional PSS as well as universal FPSS.

The notation used in this paper is outlined below: Vt terminal voltage of synchronous machine V0 infinite bus voltage M inertia constant of machine in seconds

I~ Q~i=I,..N

CPSS T Olf-Liae CI~S I~peme Tna.,~ rPSS T ~

Fmzy Pa_ra.~teN (Tuned ltul~ues)

/ l "--.. t1~ o'1 ---~ [ " ~ ..........

Ua Ua U~

Om-Lhw

Fig. 1. Flowchart for the off-line training and on-line operation of the master-slave fuzzy power system stabiliser (FPSS).

Oer~rator@ "] Vt ] '[--'~Z=R4jxTransmissi°n Inrpedarce.[l Vo

L°ad Admittance ~OrdY=O÷JB

Fig. 2. Single-machine infinite-bus power system model.

Tm, T~

Ue Kc T~,T2 6

#

(DO

A~o tr

transient open circuit time constant mechanical and electrical torque input to machine supplementary excitation control signal gain constant of conventional PSS time constants of conventional PSS rotor phase angle of synchronous machine degree of membership in a membership function base or synchronous speed rotor angular velocity deviation rotor angular acceleration

2. Power system modelling and PSS design

2.1. Sinole-machine infinite-bus model

Fig. 3 shows the Heffron and Phillips transfer function model [ 10] for a single-machine infinite-bus

CS. Chang et al. / Fuzzy Sets and Systems 102 (1999) 85-94 87

1 J

÷

A8

+ Ue

Fig. 3. Heffron and Phillips Transfer function model for studying low frequency oscillations.

power system. There are two linearised loops in the model, the top mechanical loop and the lower electrical loop. Linearised equations are used in the model because we are dealing with low-frequency oscillations due to small perturbations about the original operating condition.

There are two summing junctions in the model for the perturbed mechanical torque ATm to be injected and for the supplementary excitation Ue control to be injected. The other signal AVt at the bottom right summing junction represents the perturbed generator terminal voltage, which is a combination of the two signals flowing from the two blocks/£5 and K6.

2.2. Conventional PSS design and tuning by pole-placement

The idea of supplementary excitation is to apply a signal through the excitation system to increase the damping torque of the generator in a power system. For the Heffron and Phillips Transfer Function model of Fig. 3, the supplementary control Ue is applied through the TA, T~o, and/£5 blocks to obtain the extra damping ATe.

Because of the phase lags of the (1 + sTA) and (1 + sTdoK3 ) blocks, a phase lead compensation must be included in the supplementary excitation design, so as to have a damping torque ATe in phase with Aa~ at the oscillating frequency. The compensation must also have a gain in order to have an adequate magnitude of damping [10].

Reset Block

I K¢gl +sTDfl +sTl) " (I +sT2)(l +sT2) ~J,

Phase LeA-lag CompensRlor

Fig. 4. Conventional power system stabiliser (PSS) transfer function.

The conventional PSS consists of a reset block and a phase lead-lag compensator as shown in Fig. 4. Es- sentially the objective of the PSS is to generate a positive damping torque when applied to the excitation control loop of the generator. The function of the reset block is to activate the supplementary excitation control only when low-frequency oscillations start to develop. At steady state, the reset block terminates the excitation control.

The objective of the conventional PSS design is to find Kc and Ti for the phase lead compensator. The pole assignment method [ 1 ] is used to determine these two parameters. The steps involved are as follows: T2 is set to 0.07 s and the desired damping factor ~ to be 0.5. The desired closed loop eigenvalues are then given by

2 = -~09, :k jo ) ,x /~ - ~2),

where 09, is the natural frequency of the system mechanical mode.

Kc and/'1 can then be evaluated as

Llm~,z ~ [ Re(~) . . . . ]-1 T, = /r--zzz,~.,mt~) - Re(2) ,

Kc= [ Im(O ]2, [Im(2)T1

where

1 +AT2

{c(z/-

0 ~Oo 0

KI /('2 0

M M

A = KA 0

rJo KAK5

0 rA

0

0

1 1

rdo

KAK6 1 1/, TA

88 C.S. Chang et aL /Fuzzy Sets and Systems 102 (1999) 85-94

0 0

B = L '

C = [ 0 1 0 0],

1 0 0 0

0 1 0 0 I =

0 0 1 0

0 0 0 1

3. Fuzzy PSS training

3.1. The table lookup training algorithm

This algorithm consists of the following four steps [9]:

Step 1: Divide the input and output spaces into fuzzy regions.

Assume that the domain intervals of Aog, a, and U~ are [A~o(min), Ao)(max)], [a(min), a(max)], and [Ue(min), U~(max)] respectively. Divide each domain intervals into 2N + 1 membership functions (MFs), say LN, MN, SN, ZE, SP, MP, and LP. Fig. 5 shows an example where the domain interval is divided into 7 regions (N = 3), each characterized by a membership function. The shape of each membership function is triangular. This is done for all the input and output domains Aog, a, and U~.

Step 2: Generate fuzzy rules from the given data pairs.

First, determine the degrees of membership of the given Ao9(i), a(i), and Ue(i) input--output data in the different membership functions. For example, A~o(1 ) in Fig. 5 has degree 0.8 in MP and 0.2 in LP and zero degrees in all other membership functions. Similarly, Ue(1 ) has degree 1.0 in membership function ZE and zero degrees in all other regions.

Next, assign a given Aog(i), a(i), or Ue(i) to the membership function with the maximum degree. For example, A~o(1) in Fig. 5 is considered to be MP and a(1 ) is considered to be MN, and Ue(l ) assigned to ZE.

MN SN ZE SP MP LP

0!8 . . . . . . . . .

MN SN ZE SP MP LP 1 ' - -

0.3 2- o(1) ~"

~u,)

u,(1} u~

Fig. 5. Fuzzification of the input and output spaces.

Finally, obtain one rule from one pair of desired input-output data. For example, with input-output data pair 1:

[Aoj(1) =0.8 in MP; a(1) =0.7 in MN;

Ue(1) = 1.0 in ZE]

gives

Rule 1: IF Aco is MP and a is MN THEN U~ is ZE.

The rules generated this way are "and" rules, that is, rules in which the conditions of the IF part (an- tecedent) must be both satisfied in order for the result of the THEN part (consequent) to occur.

Step 3: Assign a degree to each rule. Since there are usually many data pairs and each

data pair generates one rule, it is highly possible and almost unavoidable that there will be some conflict- ing rules, that is, rules having the same IF part (an- tecedent) but a different THEN part (consequent). One way to resolve this conflict is to assign a degree to each rule generated from the data pairs and accept the rule from a conflict group that has the maximum degree. In this way not only is the conflict problem resolved, but also the number of rules is greatly reduced.

We use the following product strategy to assign a degree to each rule: for the rule "IF Aco is A and a is B THEN Ue is C", the degree of this rule, denoted by

c.s. Chang et aL /Fuzzy Sets and Systems 102 (1999) 85-94 89

DEG(Rule) is given by

DEG(Rule) = /.tA(AOg)- ~13(ff)' #c(Ue).

As an example, Rule 1 has degree

DEG(Rulel) = ~Mp(A(D)" ]AMN(6 ) " ]AzE(Ue)

= 0.8 x 0.7 × 1.0 = 0.56.

Step 4: Create a combined fuzzy rule base. We fill the boxes of the fuzzy rulebase or look-up

table according to the following strategy: A combined fuzzy rulebase is assigned rules according to step 2; If there is more than one rule in one box or cell of the fuzzy rulebase (i.e. fuzzy associative memory or FAM matrix), use the rule with the highest degree. In this way, a combined rulebase can be drawn up i.e. all the cells of the FAM matrix which have corresponding input-output data pairs will be filled.

3.2. Implementation of the training algorithm

The table lookup scheme as implemented in the fuzzy PSS rulebase tuning algorithm works like this [6]:

Step 1: First, the input variables A~o and a are fed into the conventional PSS in order to obtain a set of desired excitation output Ue corresponding to this set of input data. Together, the set of input-output pair forms the training data for the training step.

Step 2: Next, the desired input-output (training) data is inputted into fuzzy tuning algorithm (table lookup scheme) to obtain a tuned FAM matrix (fuzzy rulebase) for the fuzzy PSS. The table lookup scheme actually performs backward training by using desir- able training results to obtain the desired PSS parameters that will yield these results.

Step 3: Finally, upon successful training (FAM matrix or fuzzy rulebase successfully tuned), the trained fuzzy PSS can then be installed in the power system for on-line operation. The fuzzy PSS so trained is able to generate the appropriate excitation output Ue corresponding to any real-time A~o and a inputs fed into the PSS in order to suppress the rotor oscillations effectively.

4. Universal FPSS design and tuning

The universal fuzzy PSS [6] is a one-level fuzzy logic controller with a single rulebase applied to con-

trol the entire power system for all operating conditions. The fuzzy rules, or rather the FAM matrix or fuzzy rulebase is tabulated or tuned using the fuzzy training algorithm (table look-up scheme). The universal fuzzy PSS is trained for seven different operating conditions in total: 1. Normal operating condition, 2. Light loading condition, 3. Heavy loading condition, 4. Leading power factor condition, 5. Lagging power factor condition, 6. Low transmission reactance condition, 7. High transmission reactance condition.

To obtain a combined rulebase from all the seven trainings at the seven different operating conditions (since each training will yield its own specific rulebase), steps 1-4 are followed:

Step 1: Train the fuzzy PSS for the first operating condition and obtain the first rulebase.

Step 2: Train the fuzzy PSS for the second operating condition and obtain the second rulebase.

Step 3: Merge the 2 rulebases into a combined rulebase by following the code below:

Ifcell( i , j ) of the 1st rulebase and the same cell(i,j) of the 2nd rulebase contains the same consequent, say LN and LN, then the entry for cell(/,j) of the combined rulebase is LN. If the consequents of the same cell of the 2 rulebases do differ, we do this: If consequent is SP and consequent 2 is SN, then the resulting consequent is ZE. If consequent is SP and consequent 2 is LP, then the resulting consequent is MP. If consequent is ZE and consequent 2 is SN, then the resulting consequent is SN. If consequent is ZE and consequent 2 is SP, then the resulting consequent is SP. If consequent is SN and consequent 2 is LN, then the resulting consequent is MN. If consequent is SN and consequent 2 is MP, then the resulting consequent is SP... and so on ...

The rationale for the above code is this: We assign a numerical value to each of the consequents, in this case

L N = - 3 ; M N = - 2 ; S N = - I ; Z E = 0

S P = I ; M P = 2 ; L P = 3 ;

90 CS. Chang et al./Fuzzy Sets and Systems 102 (1999) 85-94

To obtain the resulting consequents from two consequents, we simply take the average of the two values representing the 2 consequents. If the result is an integer, we simply convert the numerical result into its corresponding linguistic variable (consequent). For example, for code 2, SP + LP = MP, i.e. [1 + 3]/2 = 2 or MP.

If however, the average fails to give an integer, then we either ceil (for positive non-integer result) or floor (for negative non-integer result) the result to obtain an integer. This integer is then converted into its linguistic counterpart. For example, for code 4, ZE + SP = SP, i.e. [0 + 1]/2 = 0.5. Upon ceiling the result of 0.5, we obtain the resulting consequent as 1 or SP.

Step 4: Train the fuzzy PSS for the third operating condition and obtain the third rulebase; then repeat step 3. Train the fuzzy PSS for the remain- ing operating conditions making sure to obtain the intermediate combined rulebase at the end of each training. After the end of the seven trainings, a final combined rulebase for the universal fuzzy PSS is obtained.

5. Master-slave FPSS design and tuning

The master-slave fuzzy PSS configuration is the answer to a totally robust power system controller that is able to provide optimal performance at all operating conditions. In the master-slave fuzzy PSS, the master controller is a fuzzy classifier which does the job of switching in and out the various slave controllers.

The slave controllers are miniature versions of the universal fuzzy PSSs each trained for optimal performance at a specific operating condition. The master fuzzy classifier decides on which slave PSS controllers to activate and the degree of activation or contribution of each in a coordinated effort to suppress the system oscillations of the power system.

at its own training condition using the fuzzy training algorithm (table lookup scheme).

The 7 slave PSSs are trained using the conventional PSS (as described in Section 3 using the table lookup scheme) for the conditions below: Slave controller 0: Normal operating condition, Slave controller 1: Light loading condition, Slave controller 2: Heavy loading condition, Slave controller 3: Leading power factor condition, Slave controller 4: Lagging power factor condition, Slave controller 5: Low transmission reactance

condition, Slave controller 6: High transmission reactance

condition.

5.2. Master fuzzy control." the input variables

The master fuzzy classifier works in a fuzzy manner in deciding on which slave fuzzy PSSs to activate and the individual degree of activation of all 7 fuzzy slave controllers. The inputs to the master fuzzy classifier include:

real power (P), reactive power (Q), transmission reactance (X). These three parameters are the key variables in-

volved in the operating (domain) space of a single- machine to infinite-bus power system. The real power P determines the loading condition of the power system; the reactive power Q controls whether the generating unit is operating in the leading or lagging power factor mode; and the transmission reactance X decides on the external impedance connecting the single- machine and the infinite-bus.

Based on the values of P, Q, and X, the master fuzzy classifier controls the actions of the slave PSSs in a coordinated way according to the prevailing operating condition. The mode of action of the master fuzzy classifier is explained and illustrated in the next section.

5.1. Tunin9 the slave fuzzy PSS

In our MATLAB/Simulink model for conducting simulation studies on the master-slave FPSS, there are a total of seven individual slave fuzzy PSSs. Each of slave fuzzy PSSs are trained for optimal performance

5.3. The master fuzzy classifier

The fuzzy classifier works on the following basis: It controls the seven slave PSSs each trained op-

timally for a specific operating condition, i.e. light and heavy loading, leading and lagging PF, low and

C.S. Chang et aL /Fuzzy Sets and Systems 102 (1999) 85-94 91

~(P) FUZZY CLASSIFIER RULES

N . IF P is NE THEN eetivate St - ,IF P is PS THEN aetiwtte 52

',IF Q is ~ THEN ~t iwte SO _ _ _ _ ~ . . . . ~IF Q is NE THEN eeti, atte $3

,IF Q is PS THEN ~tiv~te $4 13.5 ~ 1.0 1.25 ',IF X is 27E. THE.N netiwte SO

P-0.9 ',IF X is NE THEN" ~'livate $5 ',IF X is PS THEN netivnte $6

v(Q)

Q=o.2

v(x)

N E ~ PS

4 ~ X &

0.5 0 75[ 1,0 /

X=0.825

, o.s(so) + o.2(52)

,0.6(50) + 0.4(54)

• 03(50) + 0 3(56)

£O- .glava 0 ouelaut ,5~=,ffave2 output £4:$Iav¢4 ontput S'6- ,ffav# 6 output

~U~0.81'$0~+0 .~fS~'lrt-0.6C'Sltle~,-0 tgg#~4-O 'h~0~'0.3¢$6'1 0.8+0.'2+0.6+0.4+0.7+0.3

Fig. 6. Fuzzy inferencing: the master fuzzy classifier.

high transmission reactance, and normal operating condition.

As an illustration, if the operating condition is such that P = 0.9, Q = 0.2 and X = 0.825, then the fuzzy classifier acts thus: it first fuzzifies the inputs P, Q and X into membership values in the fuzzy domain. After fuzzification, the fuzzy classifier decides on which slave controllers to activate based on a set of rules, and the degrees of activation of the selected controllers based on their membership values in the respective membership functions. Finally, the outputs of the various slave controllers are combined or de- fuzzified controllers to obtain a single crisp control output. The entire fuzzy process is illustrated in detail in Fig. 6.

6. Performance assessment

We shall discuss two error criteria in which the performance indexes are integrals of some function or weighted function of the deviation of the system output. The optimal control system is the one which yields the smallest value of the integral.

Integral of time-multiplied square-error (ITSE) criterion. The performance index based on the ITSE criterion is given by [4]

ITSE = te2(t) dt.

The optimal control system is the one that minimises this integral.

This criterion has a characteristic in that a large initial error is weighted lightly, while errors oc- curring late in the transient response are penalised heavily. This criterion has a better selectivity than the integral of square error (ISE) criterion which is given by

ISE= e2(t)dt.

Integral of error-multiplied change-in-error (IECE) criterion. The performance index defined by the IECE criterion is given by

/0 IECE = e(t)O(t) dt.

An optimal control system based on this criterion is one that has reasonable damping and a satisfactory transient-response characteristic. The rationale in using the integral of error-multiplied change-in-error as a performance criterion is that for optimal response to a disturbance, the value of error multiplied by the change-in-error should always be minimised at all times.

7. Simulation and case studies

Simulink is an extension of MATLAB that is used to simulate dynamic systems. Simulink differs from Matlab in that it has a window-based graphical inter- face. With the use of block diagrams, Simulink offers a highly versatile simulation tool especially when used with Matlab's extensive numerical resources.

In the simulation, the universal and master-slave fuzzy PSSs were both trained using the table lookup using the conventional PSS as the trainer. Upon completion of their training, i.e. their rulebases fully tuned, the performances of the three types of power system stabilisers are compared when all three were subjected to a sudden but brief disturbance, that is, a

92 C.S. Chang et al./Fuzzy Sets and Systems 102 (1999) 85-94

Table 1 ITSE results for the different PSSs at the seven training conditions

Operating Real Reactive Trans Conventional Universal Master-slave condition power (P) power (Q) react (X) PSS fuzzy PSS PSS

Normal 0.952 0.015 0.4 3.88 4.455 3.612 Light load 0.45 0.015 0.4 0.864 1.501 0.9379 Heavy load 1.25 0.015 0.4 6.816 10.2 8.671 Leading PF 0.952 -0 .5 0.4 3.781 3.603 3.006 Lagging PF 0.952 0.5 0.4 3.907 5.332 4.168 Low X value 0.952 0.015 0.2 3.769 5.699 3.681 High X value 0.952 0.015 0.6 3.909 4.612 3.662

Table 2 IECE results for the different PSSs at the seven training conditions

Operating Real power Reactive Trans Conventional Universal Master-slave condition (P) power (Q) react (X) PSS fuzzy PSS fuzzy PSS

Normal 0.952 0.015 0.4 4.55 5.119 4.708 Light load O. 45 0.015 0.4 1.116 1.6 1.274 Heavy load 1.25 0.015 0.4 8.871 11.26 10.75 Leading PF 0.952 -0 .5 0.4 4.412 4.764 4.385 Lagging PF 0.952 0.5 0.4 4.641 5.506 4.801 Low X value 0.952 0.015 0.2 5.068 8.112 6.001 High X value 0.952 0.015 0.6 4.266 4.396 3.885

same 100 ms three phase fault. The tests are repeated for the single machine power system at different operating conditions. The criterion for judging the relative performance o f the 3 different types o f PSSs is by the use o f the two performance indices described in the previous section, namely the ITSE and IECE indices.

7.1. S i m u l a t i o n resu l t s

Short-circuit simulations are carried out at a total o f fourteen operating conditions for all the three types o f PSSs. The results o f the simulations are tabulated in the Tables 1-4 below for easy comparison.

Simulations carried out at the seven training conditions yielded the results given in Tables 1 and 2. Sim- ulations carried out at 7 other arbitrarily set operating conditions yielded the results given in Tables 3 and 4.

7.2. C o m m e n t s on resu l t s

Tables 1-4 show the ITSE and IECE performance indexes for the three different PSSs for 14 different

operating conditions. The relative performances o f the three different PSSs are gauged from their corresponding ITSE and IECE performance indexes. Tables 1 and 3 refer to the ITSE index while Tables 2 and 4 contain the IECE index.

From the results, we can clearly see that the mas te r - slave fuzzy PSS outperforms the universal fuzzy PSS at all operating conditions (i.e. the performance indexes are smaller). This explicit ly indicates that the master-s lave fuzzy PSS configuration is the more robust type o f fuzzy control for use in power system stability applications.

From Tables 1-4, we can see that in many instances, the master-s lave fuzzy PSS actually outperforms the conventional PSS (its trainer). It should be noted that for each o f the fourteen simulations conducted in Tables 1-4, the conventional PSS was re-tuned for optimal performance at that operating condition using the pole-placement procedure as described in Section 2. The fact that the master-s lave fuzzy PSS actually can outperform the conventional PSS (its trainer) goes further to demonstrate that the master-s lave PSS

CS. Chan# et al./Fuzzy Sets and Systems 102 (1999) 85-94

Table 3 ITSE results for the different PSSs at seven arbitrary test conditions

93

Real power React power Trans react Conventional Universal Master-slave (P) (Q) (X) PSS fuzzy PSS fuzzy PSS

1.25 0.45 0,6 6.737 12.9 10.04 0.45 -- 0.45 0,2 0.8215 1.311 0.7963 0.62 0.19 0.31 1.682 2.655 1.784 1.10 --0.16 0.27 5.18 6.561 5.112 0.54 0.28 0.47 1.295 2.141 1.411 0.86 0.32 0.51 3.212 4.041 3.176 0.92 0.40 0.23 3.652 5.558 3.81

Table 4 IECE results for the different PSSs at seven arbitrary test conditions

Real power React power Trans react Conventional Universal Master-slave (P) (Q) (X) PSS fuzzy PSS fuzzy PSS

1.25 0.45 0.6 6.865 7.915 6.878 0.45 --0.45 0.2 1.177 1.828 1.369 0.62 0.19 0.31 2.131 3.054 2.448 1.10 - 0.16 0.27 6.877 9.079 7.715 0.54 0,28 0.47 1.598 2.263 1.781 0.86 0.32 0.51 3.527 3.902 3.559 0.92 0,40 0.23 4.923 7.152 5.669

is a far more superior and robust PSS for use in power system stability applications.

8. Conclusions

This paper investigates the design and implementation of a master-slave FPSS for damping power system low-frequency oscillations. This proposed FPSS and a scheme of universal FPSS have been trained against a conventional PSS on a single-machine infinite-bus model. Our design is by large self-tuning or self-learning. The individual slave PSSs are tuned according to the proven-working conventional PSS, not heuristically tuned or using trial and error means. The only thing maybe that the master-classifier has heuristically defined rules of action, which certainly leaves still more to be desired. And we have compared the performance of our master-slave design with that of the "self-tuning" universal fuzzy PSS, and proven the superiority of our design. From the simulation results, the master-slave FPSS has demonstrated to be superior to other schemes of PSSs.

It is natural for any form of real-life controller to have a tradeoff in terms of complexity and performance. The crux of the matter seems to be: Is the design so complex that any sort of improvement in performance will be far outweighed by the overheads involved in its implementation? The answer seems clear that though the design is admittedly complicated by nature of the master and slave concept, one should realise an intricate design does not obviously imply that the implementation will be just as tedious, since in practice these days, a fuzzy controller is no more than a fuzzy IC chip that can be customized to suit different user needs or perhaps a dedicated RISC (reduced instruction-set computing) microprocessor with the relevant A/D and D/A conveners (as in digital control).

The argument that a (rule-based) gain-scheduling + conventional PSS being much simpler seems viable. Still, the problem of switch transit time delays with gain scheduling will be more prominent with conventional PSS which are essentially phase lead-lag com- pensators effected in practice by hardware which does

94 CS. Chano et al./ Fuzzy Sets and Systems 102 (1999) 85-94

not respond instantaneously. In the fuzzy PSS, with increased sampling rates, the switch transit time delay can effectively be annihilated by super-fast fuzzy chips or dedicated processors that switches in split nanosec- onds (imagine current instruction processing speeds at hundreds o f millions o f instructions per second i.e. MIPs).

Our experience has confirmed the potential for training FPSSs to stabilise the increasingly complex and geographically widely distributed power systems of today. Tremendous computational savings can be re- alised by breaking up the global operating space into a number o f regions each controlled by a local controller. This effectively decentralises the control effort but a global controller plays the role o f coordinating the local controllers.

The master-slave FPSS scheme does this by frag- menting the enormous job o f controlling the power system into a number o f smaller and more manageable tasks each controlled by an independent controller but all under direct supervisory control o f the central controller. In addition, due to its modular design, more slave FPSSs may be added within the framework o f the master-slave scheme, without affecting its overall structure, as the connected power system expands: a key overriding advantage in modem PSS design and implementation which will result in huge cost savings in the long term.

In final terms, the coordination o f PSSs on different machines in a m u l t i - m a c h i n e system is an area o f further research definitely worth looking into in our insatiable quest for newer, more robust ways to control the modem power system.

References

[1] S. Elangovan, C.M. Lim, An efficient pole-assignment method for designing stabilisers in multi-machine power systems, IEE Proc. Part C 134 (6) (1986) 383-384.

[2] R.J. Fleming, M.M. Gupta, J. Sun, Improved power system stabilisers, IEEE Trans. on Energy Conversion 5 (I) (1990) 23-27.

[3] E. Handchin, W. Hoffmann, F. Reyer, T. Stephanblome, A new method of excitation control based on fuzzy set theory, IEEE PICA Conf., Publication 0-7803-1301-1/93503.00, 1993.

[4] K. Ogata, Modem Control Engineering, 2nd ed., Prentice- Hall, Englewood Cliffs, NJ, 1990.

[5] W. Pedrycz, Fuzzy Sets Engineering, CRC Press, Boca Raton, 1995.

[6] H.B. Quek, Power system stability control using fuzzy gain scheduling of power system stabilisers, B. Eng. Final Year Thesis, National University of Singapore, May 1996.

[7] H.A. Toliyat, J. Sadeh, R. Ghazi, Design of augmented fuzzy logic power system stabilisers to enhance power systems stability, IEEE PES Summer Meeting, Publication 95 SM- 446-5 EC, 1995.

[8] L.X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice-Hall, Englewood Cliffs, N J, 1994.

[9] L.X. Wang, J.M. Mendel, Generating fuzzy rules by learning from example, IEEE Trans. Systems Man Cybemet. 22 (6) (1992) 1414-1427.

[10] Y.N. Yu, Electric power system dynamics, Academic Press, New York, 1983.

power system excitation control using master-slave fuzzy power system stabilisers

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