307546_fuzzy logic and its application to power systems este

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Fuzzy logic and its application to power systemsR W Dunn'. K W Bellt and A R Daniels*t Department of Electrical Engineering and Electronics,UMIST$ Department of Electronic and Electrical Engineering, University of Bath

IntroductionElectrical power systems are large, complex extended electro-mechanical dynamic systems. There aremany potential operating points to match generation to demand, many causes of disturbance withm thesystem, many control inputs, many security factors and econom ic considerations to be taken into accountwhen operating such a diverse system.Uncertainty exists within the operation due to a large number of causes. Just a few exam ples of the m ainuncertainties are:

Imprecisely known system variable measurements, involving collected over theSCADA system.Inaccuracy in the values of system parameters used in the modelling of the systemplant.Approximations and simplifying assumptions made withm the model structures usedfor system planning and operation.Inaccuracies in load forecasting.Unpredictable events, such as equipment failure and adverse weather condt ion s.Incomplete information about the state of the power system.Variability in the application of control to the system by hu man op erators.

Privatisation of electricity supply industries around the world, leading to the break-up of monolithccompanies has added further complexity. It is now necessary for the power producers, transmissionnetwork controllers and distribution companies to co-operate w i h competitive framework to acluevethe task of supplying power cheaply, securely and within the correct statutory standards. The motivationsof the separate companies adds an extra dimension of uncertainty to the whole power system operationand planning problem.Algorithm that are developed to provide solutions to specific power system operational and planningissues. However, currently the majority of these are based on highly optimised numerical algorithm thatare dependent on the validity of the data that is fed to them. The reality of the situation is that the errors int h s data can have a severe effect on the results of such numerically based algorithms.A better approach is to employ algorithms that are not as sensitive to indvidual data items. That is,alg or ithm that can survive imprecision in the data and ambiguity in the meaning of rules that are used tocarry out power system operation. Fuzzy logic provides one such approach [1,2,3].

Fuzzy LogicTraditional logic uses variables that have precise values, called 'crisp' values. Fuzzy logic, on the otherhand, attempts to model the impreciseness of human reasoning by representing uncertainty for thevariables that are used by assignment of a 'set' of values to the variable. Each value has a 'degree ofmembership' of the set wluch represents the probability of the variable having that value [l]. A'membership function' identifies the degree of mem bership over the range of possible values, known as

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the 'universe of discourse'. This function can be defmed to represent an adjective, known as a 'linguisticvalue' or 'fuzzy set', w h c h describes the set of values. It is th~s bility to handed common linguisticterminology that allows fuzzy logic to model qualitative reasoning and to be used in knowledgerepresentation.The idea of fuzzy sets is an extension of conventional set theory formalised by L.A. Zadeh in 1965 [3] inorder to deal with uncertainty concerning a statement's exact meaning. While a 'crisp' variable either is, oris not, a member of a particular set, a 'fuzzy' variable has a 'degree of membership' or 'degree of truth'which for the range of the variable is described by a 'membership function'. A membership function isgenerally denoted by p(x) where x is the variable whose degree of membership is being described. Afuzzy variable's value may be described not by a number but by an adjective. In this way, a fuzzy variableis also known as a 'linguistic variable' and its value as a 'hguistic value' [11. It is h s roperty that givesfuzzy logic its power to m odel human qualitative reasoning. A cr isp variable can also have a m em ber shpfunction. In this case, there would only be one value for which the degree of mem ber shp of the set, or thedegree of truth, would be non-zero. Fuzzy systems can include crisp functions.

Fuzzy ControlFuzzy c ontrol is an area for which there is a wealth of published work and real applications. It is based onusing fuzzy sets to mo del control decisions which are sem antically uncertain. In a manner similar to thatof conventional rule-based expert systems, the fuzzy sets are combined in sets of rules to represent theknow ledge applicable in a decision malung process. Such sets of rules are known as fuzzy expert systems.According to Kickert and Mamdani [4], "the basic idea...was to incorporate the 'experience' of a humanprocess operator in the design of a controller. From a set of linguistic rules whch describe the operator'scontrol strategy, a control algorithm is constructed where the words a re defmed as fuzzy sets. The mainadvantages of this approach seem to be the possibility of implementing 'rule of thumb' experience,intuition and heuristics, and the fact that it does not need an [exact] model of the process."Fuzzy expert systems' advantages over conventional production-rule based expert systems have beencharacterised as including [5,6]:1.2.3.4.

Fuzzy sets neatly sym bolise natural language terms used by experts.Since knowledge captured in 'IF..THFN statements is often not naturally true or false, fuzzysets affor d representation of the knowledge in a smaller number of rules.Fuzzy rules can be tuned on- or off-h e .A smooth mapping can be obtained between input and output data.

A fuzzy expert system executes a series of rules or conditional statements similarin form to:IF x is low AN D y is high THEN z is medium

Since the inputs to fuzzy control systems are crisp and crisp control signals are required, fuzzy expertsystems used in co ntrol work in four steps as shown in the above figure:1.2.3.4.

Fuzzifcation. From knowledge of the crisp value of the variable being fuzzified and themem bership function of the linguistic value, the degree of truth of the proposition is found.Inference. The truth value for each rule's premise is computed and related to the conclusion partof the rule.Composition. All the fuzzy subsets (membership functions) assigned to each output variable arecombined to form a single subset or membership function for each output variable.Defuzzifcation. This converts a fuzzy set to a crisp value.

Case study - Modelling of heuristics in dispatch for security enhancementControl of voltage is one of the primary requirements of the management of a large electrical powerutility. Thls is generally viewed as the need to maintain the voltage magnitudes at all the nodes in thesystem within pre-determined limits, although voltage stability is now receiving more attention. Inaddition, limitations on the amount of pow er that can be transmitted by a line or transfonner are set su ch

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that the temperatures of plant components do not increase above acceptable levels. The controls that areused to keep the required voltage levels include generator and Static VAr Compensator (SVC) voltagereference points, Mechanically Switched Capacitors (MSC) and transformer tap ratios. Those used tocontrol powe r flows are MW generation and quadrature booster settings.The work described as part of this colloquium presentation combines the balancing of different criterialnherent in operators' judgments with the more traditional numerical algorithms. Use is made of fuzzyexpert systems to mode l qualitative judgm ents normally made by the operators in the light of informationsupplied by num erical computer based tools. The main numerical tool is sensitivity analysis used to derivethe necessary movem ents in controller settings. When combined with fuzzy expert systems, this creates afast and flexible fuzzy logic controller.A fuzzy expert system for dispatchThe expert system used for reactive and active dispatch consists of two subsystems, one for each of thereactive and active parts of the problem. These subsystems are applied alternately to the power systemscenario that is under consideration, as shown in figure 1.

(=Ivoltage limits MW limits stop

Do reactivedispatch

for actions

/

Do load flowfor actionsAdispatch

tge limits\ . W limits \ "figure I

As well as using approximate reasoning to reach a good compromise decision, the fuzzy expert systemallows easier adjustment of p riorities than the equivalent numerical optimistation routines. The rule basesfor each sybsystem are:Reactive dispatch1 IF voltage is low AND sensitivity IS positive AND con trol margin IS enough to raise AND costIS low THEN setting ISA V a x .2 IF voltage is high AND sensitivity IS positive AND control margin IS enough to lower ANDcost IS low THEN setting ISAU"".3 IF voltage is low AND sensitivity IS negative AND control margin IS enough to lower ANDcost IS low THEN setting IS AU"".

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4 IF voltage is high AND sensitivity IS negative AND control margin IS enough to raise AND costIS low THEN setting IS AU"".Active dispatch1 IF loading IS very hlgh AND sensitivity IS positive AND control margin IS enough to lower

AND cost IS low THEN setting is AU"'".2 IF loading IS very high AND sensitivity IS negative AND control margin IS enough to raiseAND cost IS low T HEN setting is AU""".These rules are used as part of an overall scheme that also limits the number of controller actions whenmeeting any given reactive and active dispatch requirement. This represents a new approach to thescheduling of controls for the enhancem ent of power system security using fuzzy logic to model operators'decisions. Previous work by the authors [7,8] has show n that the new approach outperforms a traditionallinear programming method in terms of execution speed, improvement in security, convergence,maintenance of control margin, number o f controls used and cost.ConclusionsThe brief description of the work in this paper and the co lloquium presentation have provided a n insightto the application of fuzzy logic, in the form of a fuzzy controller, to a real power system operationsproblem. It has been seen how fuzzy logic can deal with the complex problems posed by the. reactive andactive dispatch problem taking into account security and cost.Future work can exploit the opportunity that the outlined method provides to base dispatch on anycriterion for which some measure can be made. An example of this would be an index of proximity ofvoltage collapse. This could be used in the rules, or in the place of the sensitivity index that is currentlyused when malung the judgement as to whether a new dispatch is an improvement. This could then beused as a voltage instability prevention system.AcknowledgementsThe author gratefully acknowledge the contributions of the National Grid Company plc and theEngineering and Physical Sciences Research Council, UK, to this work.References1234567

ZADEH, L.A.: 'Outline of a new approach to the analysis of complex systems and decisionprocesses', IEEE Systems, Man and C ybemetics, Vol. SMC -3, No. 1, pp. 2840,1973.FU,L.: 'Neural networks in computer intelligence', McGraw-Hill, 1994.ZADEH, L.A.: 'Fuzzy sets', Information and C ontrol, Vol. 8,pp. 338-353, 1965.KICKE RT, W.J.M., and MAM DANI, E.H.: 'Analysis of a fuzzy logic controller', Fuzzy Sets andSystems, Vol. 1 , No. 1, pp. 29-44, 1978.BERE NJI, H.R.: 'The unique strength of fuzzy logic control', IEEE Exp ert, pp. 9, August 1994.VADIEE, N., and JAMSHIDI, M.: 'The promising future of fuzzy logic', lEEE Expert, pp, 36-38, August 1994.BELL, K.R.W., DANIELS, A.R., and DUNN, R.W.: 'A fuzzy expert system for low-costsecurity-constrained reactive Qspatch', Proceedmgs of Stockholm Power Tech., Stockholm, JuneBELL, K.R.W., DANIELS, A.R., and DUNN, R.W.: 'A fuzzy expert system for overloadalleviation', Proceedings of Power Systems Computational Conference, Dresden, pp. 1177-1 183,August 1996.

18-22, 1995.8

0 1997The Institution of Electrical Engineers.Printed and published by the IE E, Savoy Place, LondonWC2R OBL, UK.

307546_fuzzy logic and its application to power systems este

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