Design And Analysis Of An Adaptive Fuzzy Power System Stabilizer

455IEEE Transactions on Energy Conversion, Vol. 11, No. 2, June 1996DESIGNAND ANALYSISPOWEROF AN ADAPTIVESYSTEMFUZZYSTABILIZERK. TomsovicP. HoangSchool of Electrical Engineering and ComputerWashington State University99164-2752Pullman. WAsystem stabilizerAbstractScience(PSS) providesa positivedampingtorque[1,2] in phase with the speed signal to cancel the effect ofPower system stabilizers(PSS) must be capable of providinga broadappropriatestabilizationsignals overoperating conditions and disturbances. TraditionalrangeofPSS relyon robust linear design methods. In an attempt to cover awider range of operating conditions,expert or rule-basedcontrollers have also been proposed. Recently, fuzzy logic asa novel robust control design method has shown izzycontroldesignin system parameterscentersand operatingconditions. Such an emphasis is of particular relevance asthe difficultyof accuratelymodellingthe connectedgenerationis expectedto increaseunderpowercontrollersare based on empiricalrules. In this paper, a systematic approachcontrol design is proposed.Implementationreqtures awhichof performancetranslatesintocan be calculatedcontrolto fuzzy logicfor a specificcriteria.threeoff-lineThiscontrolleror computedinin response to system changes. The robustness ofthe controlleris emphasized.Small signalanalysis methods are discussed. This workdevelopingrobustappropriatewhen fuzzy logic is applied.stabilizerdesignand transientis directed atand analysismethodsPower system stabilizersoperatingstabilizationconditions039-8 ECControlimplementedhas shown promising(PSS) must be capable of providingsignalsoverand disturbances.results [6,7].algorithmsbased on fuzzy logic have beenin many processes [8,9]. The application ofsuch control techniqueshas been motivatedthat obtained(2) simplifiedby the desire for(1) improvedrobustness overusing conventionallinear control algorithms.control design for difficult to model systems.e.g., the truck backer-upper problem [10], and (3) simplifiedimplementation.In power systems, several controllers havebeen developed for PSS. One such controllerhdyro unithas been undergoingfield[8] for a smalltest in Japan. Othersystems have been developed for voltage regulatorsthe controlof FACTSdeviceshave been tuned to a specificnumericalsolutionsgenerally[12]. Most[11] andof these designssystem. Unfortunately,requiresucha large computationalgeneraldesign and analysisThe proposed method alsoptirsues small signal stability analysis which provides theopportunityto design a system with adjustable controllera broadrangeA traditionalofpowerpaperrecommendedandapprovedby the IEEE EnergyDevelopment and Power Generation Committee of the IEEE Power96 Wrule-based controllerseffort.In this paper, amethodologyis proposed.1. Introductionappropriatecondition,they may not be valid for a wide range ofoperating conditions. Considerable efforts have been directedtowards developing adaptive PSS. e.g. [3,4]. In an attempt tocover a wide range of operatingconditions,expert orrule-based controllershave been proposed for PSS [5].Recently,the introductionof fuzzylogicintotheseone or more of the following:deregulation.Fuzzy logicmachineindustrythe system negative damping torque. Because the gains ofthis controllerare determinedfor a particularoperatingAparameters to obtain suitable root locationAlthough[13].fuzzy logic methods have both a well-foundedtheoretical basis and numerous successful implementations,controversy has surrounded the developed systems. This isdue in part to the lack of satisfying performance measures.Recently, there have been efforts directed at appropriateEngineeringSociety for presentation at the 1996 IEEE/PES Winter Meeting,January 21-25,1996, Baltimore, MD. Manuscript submitted July 27, 1995;stability measures for fuzzy logic controllers [10, 13]. In thepower system, performance concerns are particularlyacutemade availablewith the high reliabilityfor printingJanuary 4, 1996.of instabilities.modelsmayrequirementsand the costly effectsYet, analysis using precise mathematicalbe infeasibledue to the arities,uncertainties in load fluctuations, disturbances and generatordynamics, and so on). The viewpointoffered here is that0885-8969/96/ 05.00 @ 1996 IEEE

456fuzzy Ioglc has been introducedbecause of the aboveditllcultiesand thus, the approach should be better ,systematicanalysis.to address these performancea firstFor simulationstepistakentowardsstudies. the non-linearpower system and controller are linearized and small signalstability analysis is performed,It is proposed to rethink thetraditionalmethodsgreater generatorandsystemmodelspresented (details can be found in the Appendix).diagramtermsFig. 2. Excitation2. SYSTEMInassessmentof the generatorplantmodelareThe blockis shown in Fig.1.Specifically,the plant is modeled based on a generatormodel incorporatingsingle-axis field flux variation and thesimple excitation system shown in Fig. 2. The PSS used forcomparisonstudies is a lead compensatorThe followingH .(s)models the excitationcontinuoustransfer functionsystem and regulator:occur in an overload or islandingcondition.The secondterm of (2) is a lead compensator to account for the phaselag through the electrical system [14].In many practicalcases. the phase lead requiredfroma singleThe developmentof the fuzzy logic approach here islimited to the controller structure and design. More detailedwitha fuzzysignal is introducedin conjunctionIn this study, both a traditionallogic based stabilizerPSS is modeled by the followingwith theexciterrespectively.stabilizing()usingthe filteredof the machine.That is.for the controller.The controloutput,u. is thesignal Vs. Each control rule R, is of the form:The traditionaltransfer function:IFeis A,AND e is B,THEN.rule-basePSS and a fuzzy(FPSS) are analyzed.I sTl—1 sT2logicand accelerationthe deviation from synchronous speed and acceleration of themachine are the error, e, and error change. &, signals,reference voltage to obtain feedback for the regulator-. Tcase. cascaded leaddiscussions on tizzy logic controllers are widely available,e.g., [9, 12]. For the proposed FPSS. the second term of (2)2.1 Power system stabilization (s)In this2.2 Fuzzy stabilizerspeed deviationsystem.is greater than that obtainablelead network.stages are used where k is the number of lead stages.is replacedThe stabilizingSystemu is C,k(2)where.-t,. B ImembershipandC,functionsarefuzzysetswithas shown normalizedtriangularbetween-1 andThe first term in (2) is a reset term that 1s used to “wash1 in Fig. 3. These same fuzzy sets are used for each variableout” the compensation effect after a time lag T. The use ofreset control will assure no permanent offset in the terminalof interest: only the constant of proportionalityis changed.These constants are h-,, K, and k- for the error. errorvoltagechange and control output, respectively. The error and errorchange are classified according to these fuzzy membershipdue to a prolongederror in frequency,whichmayfunctionsmodtiledby an appropriatesignal may have non-zeroSimilarly.a specificcontributionmembershipcontrolof more thanconstant.A specificin more than one set.signalone rule.mayrepresenttheRuleconditionsarejoined by using the minimumintersection operatorthe resulting membership fimction for a rule is:UR,\—-[FfiterFig. 1 Generator Plant Model(e,e) min(h(e) !-h,(e))so that(3)The suggested control output from rule I is the center ofthe membership function C,. Rules are then combined usingthe centerof gravitycontrol output Umethodto determmea normalized

457@MNLNSNSPZEMPLPI-1-.65-.30Fig. 3. Membership(LP lqgeposltwe:positwe;negatwe;MP ZE zero:SN 1LPLPLPAfPIMPSPI ZEMNLPMPA@IUPSPZESlvSNLPMPSPSPZENVAL%i ZEMPIUPSPZESN‘AINlMATSF’MPSPIZESNSNMNLNIscaled from -1 to 1mediumSN snlallsmall.65.3functionsLNSP smallposltwe:negatwe;MN medlumenegative)I(4)I2.3 ProposedLPFPSS design stepsThe fhzzy logic controllerdevelopmentso far is general.particular control design requires specification of all controlThe control rules arerules and membershipfunctions.designed from an understandingcontroller,K,to be symmetriccontrolandmanymanualfunctionsneeded.rules is shown in Table 1. Eachundertheassumptiontuningto establishofcontrolthathaveproposedmethods for tuning the controller).rulesartificialande.g. [15],neuralnetSuch manual tuningmaybe very time consuming and perhaps more importantlyshedssome doubt on the claims for robustness of the fuzzy logicapproach. In this work. a systematic tuning methodology isproposed.It is assumed that the fimdamentalcontrol lawschange quantitativelynot qualitativelywith the operatingIn this vein. control rules and membershipcondition.functionsfunctionsare designed once as above.are modified by scaling througherroris described below:controloutput for Kbased onThe membershipthe constants K,.a significantdisturbancee and served values forduringthesimulationpenocl.If damping appears inadequate then:5. Linearizeifthe desired performancesystem. (There are some exceptions,authorsare italicued)either begin to settle or thestability limit.4. Set A-. and h-,to the maximumpoint will beis no longernecessary any asymmetries could be best handled throughscaling. In addition, adjacent regions in the rule table allowonly nearest neighbor changes in the control ouput (LN toMN. MN to SN and so on).This ensuresthat smallchanges in e and e result in small changes in u.Many of the fuzzy logic controllersproposed in themembership1Isystem and range of operating1. Select the maximumof the 49 controlrules represents a desired controllerresponse to a particularsituation.The control rules werefor a specificoutputs Lhr./Xof the desired effect of thethat the desired operatingset of controlonMNThe methodolo 3. SimulateThis rule anticipatesrelyMNIIthe physical limitations of the controller.2. Replace the FPSS with a constant gain K.reached soon and stabilizationliteratureI SIVand A“ for a particularconditions.IF e is SNAND e is SPTHEN /.{ k ZEdesignedI(ControlFor example, consider the rule:The completeIIL.V,Table. 1. Rules tableZEAIIthe system and FPSS around the nominaloperating6. UsingK.point (see section 4).traditionaleigen valueand K. together (i.e. maintainingmagnitude)As an objectiveadjustto obtain desired damping.of the fuzzy controllerrange of operatinganalysis,the same relativeconditionsis to manage a wideand modellinguncertainties,the simulationin step 3 for method 1 may need to berepeated under a set of parameter variations.The controlleris adaptive in the sense of the varying of these gains but notin terms of varying the control rules. Further discussion onthese design steps can be found in [16].3. NUMERICALIn this section, simulationstoseveraldisturbances.exercise the controllerSIMULATIONillustrateThethe controllerscenariosareresponseintendedtorather than to represent any specificsystem scenario. Two simple systems are presented buthigher order systems have been simulatedwith similarresults. The FPSS constants are found by simulations of a