CorrespondenceDESIGN OF DECENTRALISED STABILISERSIN MULTIMACHINE POWER SYSTEMS

Indexing terms: Power systems and plant, Stabilisers

Abstract: First-order subsystem characteristicequations are derived by means of a new par-titioning method of the system operational-transfer matrix during the model-reductionprocess. The existence of multiple solutions forpower system stabiliser (PSS) parameters toexactly assign specified electromechanical modesis indicated by a numerical example.

Introduction

Recently, a new method was proposed by Lim andElangovan [1] for designing decentralised stabilisers inmultimachine power systems. As shown by the numericalexample in the paper, the method is useful in that someor all of the system's electromechanical-mode eigenvaluescan be exactly assigned to prescribed locations in thecomplex plane. Thus the dynamic stability of the powersystem studied is greatly enhanced after the installationof the designed stabilisers. This achievement is praise-worthy and has demonstrated some advantages over pre-vious works. It is noted that the reduction procedurewhich partitions the system's operational-transfer func-tion matrix and retains the rotor-angle and speed devi-ations of each subsystem can be used to determine thesecond-order characteristic equation of that subsystem.However, much more simplified first-order characteristicequations for the closed-loop system can be derived by aslight modification of the reduction process in Reference1.

In this correspondence, such a modified reductionmethod is put forward and a numerical example is givento demonstrate the effectiveness of the improved method.In the following sections, all notations adopted areinherited from the discussed paper.

Derivation procedure

It is well known that electromechanical modes are themodes associated with rotor oscillations which aredescribed by the state variables A<5 or Aw. To fully char-acterise these rotor oscillations, it is sufficient to retainthe speed deviation Aco in the model-reduction process[2] since the deviations in rotor angle and angular speedare closely related to each other by the following equa-tion:

Aco = — A<5dt (1)

Thus, the second-order characteristic equation derived inthe Appendix of Reference 1 can be reduced to first order.The key steps are to reorder the state variables such thatAtOj is the first and then partition the system operational-transfer matrix Mj{s) as

M'{S)

The order of M^s) is now chosen to be 1 x 1. After com-pleting the same procedure in the original reductionprocess, the final equation derived is given as

f3jsbjFJ{s) = s-MrJ(s)

where Mr^s) = M^s) + M

(3)

- M2j(sJ]M4/s).

This reduction process is repeated for) = 1, . . . , k, wherek is the number of PSSs to be installed, to determine thefirst-order characteristic equations of the k subsystems.

Let Sj,j = 1 , . . . , k, be the prespecified locations for theclosed-loop electromechanical-mode eigenvalues, a set ofk simultaneous equations can then be derived by substi-tuting these eigenvalues into eqn. 3:

f ^ bj FJ(SJ) = Sj - Mr}{Sj) j = l , 2 , . . . , k (4)

Then the fixed-point method [1] is used to solve eqn. 4.

Numerical example

Consider the three-machine infinite-busbar system whoseconfiguration and system data are given in Reference 1.And for comparative study, the same transfer function fora PSS as adopted by Lim and Elangovan will be used,that is

Fj{s) = kj j = 1, 2, 3

The damping ratios for the desired electromechanical-mode eigenvalues and T2j are chosen to be 0.3 snd 0.055,respectively. Sample results are shown in Table 1.

Table 1 : PSS parameters and closed-loop eigenvalues

K,7"nK2

* 3

7-13

closed-loopsystemeigenvalues

1

19.60.223

17.60.335

20.250.169

-8.1 +y13.54-8.3+y 10.6-1O.5+/7.28-2.37+/7.56*-2.18+/6.92*-1.17+/3.72*-34.4-31.6-29.0-5.52-3.17-1.49

II

25.060.2249.4270.419

19.670.169

-8.2+y12.98-8.1 +/10.98-10.8+y7.17-2.37+y7.53*-2.18+y6.92*-1.17+y3.72*-33.3-32.7-28.7-5.54-3.18-1.50

III

31.30.1715.8660.903

34.360.113

- 5.97+y19.7-7.76+/8.56-12.4+/4.36-2.37+y7.53*-2.18+y6.92*-1.17+y3.72*-40.4-30.6-26.7-4.96-2.50-1.51

(2)

* denotes exact assignment of electromechanical modes

It is noted that multiple solutions for PSS parametersexist and exact assignment of electromechanical modescan be achieved by either set of parameter values. A goodchoice of the parameters can be made based on otherpractical considerations such as voltage profile, transient-stability limit etc.

Conclusions

A more efficient method for the design of multimachinepower-system stabilisers has been presented. This isachieved by deriving first-order, rather than second-

IEE PROCEEDINGS, Vol. 134, Pt. C, No. 4, JULY 1987 289

order, characteristic equations through the introduction Referencesof a novel method for partitioning the systemoperational-transfer matrix in the reduction process. The ' %£^£existence of multiple solutions for PSS parameters is also 132, (3), pp. 146-153indicated, which is a serious deficiency in the previous 2 CHEN, C.L., and HSU, Y.Y.: 'Coordinated synthesis of multi-paper fl]. machine power system stabilizer using an efficient decentralized

modal control (DMC) algorithm'. Presented at the IEEE/PES 1986C.L. CHEN 28th August 1986 Summer meeting, Mexico City, Mexico, July 1986, Paper 86 SMY.Y. HSU 3 2 M

Department of Electrical EngineeringNational Taiwan UniversityTaipeiTaiwanRepublic of China

290 IEE PROCEEDINGS, Vol. 134, Pt. C, No. 4, JULY 1987