a novel approach to conventional power system stabilizer design using tabu search

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  • A novel approach to conventional power system stabilizer design usingtabu searchM.A. Abido1,*

    Electrical Engineering Department, King Fahd University of Petroleum and Minerals, KFUPM Box 183, Dhahran 31261, Saudi ArabiaReceived 18 June 1998; received in revised form 29 October 1998; accepted 17 December 1998

    Abstract

    A tabu search (TS) based power system stabilizer (PSS) is presented in this article. The proposed approach uses the TS algorithm to searchfor the optimal settings of conventional lead-lag power system stabilizer (CPSS) parameters. Incorporation of the TS algorithm in the PSSdesign significantly reduces the time consumed in the design process. One of the main advantages of the proposed approach is the fact that theTS algorithm leads to the optimal solution regardless of the initial guess. The performance of the proposed PSS under different disturbancesand loading conditions is investigated for single machine infinite bus and multimachine power systems. The eigenvalue analysis andsimulation results show the effectiveness of the proposed PSSs to damp out the local and the interarea modes of oscillations and workeffectively over a wide range of loading conditions and system parameter variations. q 1999 Elsevier Science Ltd. All rights reserved.

    Keywords: Conventional PSS; Tabu search; Dynamic stability; Low frequency oscillations

    1. Introduction

    Power systems are experiencing low frequency oscilla-tions due to disturbances. The oscillations may sustain andgrow to cause system separation if no adequate damping isavailable. To enhance system damping, the generators areequipped with power system stabilizers (PSSs) that providesupplementary feedback stabilizing signals in the excitationsystems. These stabilizers extend the power system stabilitylimit by enhancing the system damping of low frequencyoscillations associated with the electromechanical modes[1,2].

    DeMello and Concordia in 1969 [3] presented theconcepts of synchronous machine stability as affected byexcitation control. They established an understanding ofthe stabilizing requirements for static excitation systems.In recent years, several approaches based on the moderncontrol theory have been applied to PSS design problem.These include optimal control, adaptive control, variablestructure control, and intelligent control [47].

    Despite the potential of modern control techniques withdifferent structures, power system utilities still prefer aconventional lead-lag power system stabilizer (CPSS) struc-ture [8,9]. The reasons behind that might be the ease of on-

    line tuning and the lack of assurance of the stability relatedto some adaptive or variable structure techniques. Kundur etal. [10] have presented a comprehensive analysis of theeffects of the different CPSS parameters on the overalldynamic performance of the power system. It is shownthat the appropriate selection of CPSS parameters resultsin satisfactory performance during system upsets.

    Many different techniques has been reported in the litera-ture pertaining to optimum location and coordinated designproblems of CPSSs. Generally, most of these techniques arebased on phase compensation and eigenvalue assignment[818]. Different techniques of sequential design of PSSsare presented [1113] to damp out one of the electromecha-nical modes at a time. Generally, the dynamic interactioneffects among various modes of the machines are found tohave significant influence on the stabilizer settings. There-fore, considering the application of stabilizer to onemachine at a time may not finally lead to an overall optimalchoice of PSS parameters. Moreover, the stabilizersdesigned to damp one mode can produce adverse effectsin other modes. In addition, the optimal sequence of designis a very involved question. The sequential design of PSSs isavoided in [1418] where various methods for simultaneoustuning of PSSs in multimachine power systems areproposed. Unfortunately, the proposed techniques are itera-tive and require heavy computation burden due to systemreduction procedure. This gives rise to time consumingcomputer codes. In addition, the initialization step of these

    Electrical Power and Energy Systems 21 (1999) 443454

    0142-0615/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved.PII: S0142-0615(99)00004-6

    * Tel.: 1966-3-8604379; fax: 1966-3-8603535E-mail address: mabido@dpc.kfupm.edu.sa (M.A. Abido)

    1 On Leave from EE Department, Menoufia University, Egypt.

    www.elsevier.com/locate/ijepes

  • algorithms is crucial and affects the final dynamic responseof the controlled system. Hence, different designs assigningthe same set of eigenvalues were simply obtained by usingdifferent initializations. Therefore, a final selection criterionis required to avoid long runs of validation tests on thenonlinear model.

    Recently, H1 based techniques and sequential loopclosure method [19,20] have been applied to PSS designproblem. However, the importance and difficulties in theselection of weighting functions of H1 optimization

    problem have been reported. In addition, the order of theH1 based stabilizer is as high as that of the plant. This givesrise to complex structure of such stabilizers and reducestheir applicability. Although the sequential loop closuremethod is well suited for on-line tuning, there is no analy-tical tool to decide the optimal sequence of the loop closure.

    In most recent articles [21,22], genetic algorithm (GA), asa heuristic search algorithm, has been applied to theproblem of PSS design. Various eigenvalue based objectivefunctions were optimized to select the optimal set of CPSS

    M.A. Abido / Electrical Power and Energy Systems 21 (1999) 443454444

    Fig. 1. The computational flow chart of TS algorithm.

  • parameters. The results are promising and confirming thepotential of GA to search for the optimal settings of CPSSparameters. However, GA is characterized as memorylesssearch algorithm. Generally, using a flexible memory ofsearch history can significantly enhance the search process.

    In the last few years, tabu search (TS) algorithm [2327]appeared as another promising heuristic algorithm for hand-ling the combinatorial optimization problems. TS algorithmuses a flexible memory of search history to prevent cyclingand to avoid entrapment in local optima. It has been shownthat, under certain conditions, the TS algorithm can yieldglobal optimal solution with probability one [26]. In powersystems, TS was applied to a number of power system opti-mization problems with impressive successes [2830].However, to the best of the authors knowledge, the poten-tial of the TS algorithm to the PSS design problem has notyet been exploited.

    In this article, a novel approach to the PSS designproblem is developed using the TS algorithm. The problemof CPSS design is formulated as optimization problem.Then, the TS algorithm is employed to solve this optimiza-tion problem with the aim of getting the optimal or nearoptimal settings of the PSS parameters. The proposed designapproach was applied to both a single machine infinite bussystem and a multimachine power system. The eigenvalueanalysis and simulation results were carried out to assess theeffectiveness of the proposed PSS to damp out the electro-mechanical modes of oscillations and enhance the dynamicstability of power systems.

    2. Problem statement

    2.1. PSS structure

    To enhance the power system dynamic stability andextend the power system stability limit, synchronous

    generators are equipped with PSSs. A widely used CPSSis considered in this study. It can be described as [1]

    Ui Kci sTw1 1 sTw1 1 sT1i1 1 sT2

    1 1 sT3i1 1 sT4 Dvi; 1

    where Tw is the washout time constant, Ui the PSS outputsignal at the ith machine, and Dv t the speed deviation of thismachine. The time constants Tw, T2 and T4 are usuallyprespecified. The stabilizer gain Kci and time constants T1iand T3i remain to be determined.

    2.2. Power system model

    A power system can be modeled by a set of nonlineardifferential equations as:

    X f X;U; 2where X is the vector of the state variables and U is thevector of input variables. In this study, X d;v;E 0q;EfdT and U is the PSS output signals.

    In the design of PSSs, the linearized incremental modelsaround an equilibrium point are usually employed [13].Therefore, the state equation of a power system with nmachines and m stabilizers can be written as:

    D X A DX 1 BU; 3where A is 4n 4n matrix and equals 2f/2X, while B is 4n m matrix and equals 2f/2U. Both A and B are evaluated at theequilibrium point. DX is 4n 1 state vector while U is m 1input vector.

    2.3. Identification of electromechanical modes and psslocations

    The state equation of linearized model (3) of undrivensystem can be rewritten as:

    D X A DX:

    M.A. Abido / Electrical Power and Energy Systems 21 (1999) 443454 445

    Fig. 2. Objective function variations of example 1.

  • Then the 4n eigenvalues of the system matrix A can bedetermined. Out of these eigenvalues, there are n 2 1 modesof oscillations related to machine inertias [31].

    For the stabilizers to be effective, it is extremely impor-tant to identify the eigenvalues associated with electro-mechanical modes and the machines to which theseeigenvalues belong [18]. Participation factors method [32]and sensitivity of PSS effect (SPE) method [33] are used forthis purpose.

    2.4. Objective function and PSS tuningTo increase the system damping to electromechanical

    modes, an objective function J defined below is proposed.J max {Reli; i [ set of electromechanical modes};

    5where l i is the ith eigenvalue associated with electromecha-nical modes. This objective function is proposed to shiftthese eigenvalues to the left of s-plane in order to improve

    the d