f logic baseed contingency analysis

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Fuzzy Logic Based Contingency AnalysisK. L LO A. K. I. ABDELAALPower System Research GroupUniversity of Strathclyde

Abstract: This paper deals with the contingency selection problemin power system. T he main o bjective is to explore the application offuzzy logic on contingency selection for voltage ranking. It showsho w fuzzy logic could be used to tune both the weighting factorsand the exponent index and hence reduce the masking effect.Firstly, the post-contingent voltages are expressed in fuzzy logic.Secondly, fuzzy logic rules are applied to rank the contingencies.There are two types of fuzzy control rules: Mamdani- and Sougeno-rules. The first part of this paper investigates the use of theMamdani method for voltage ranking. The second part examines theapplication of Sougeno method to voltage ranking. Numericalresults for th e IEEE-30 bus test system are given. At the end o f thispaper there is a comparison study between these methods. It isfound that the Soug eno method is much m ore flexible, suitable, andgives better results than the M amdani method.Keywords: Contingency analysis, voltage ranking, fuzzy logic,masking effect, weighting factors, exponent index, Sougenomethod, and Mamd ani method.

I. INTRODUCTIONS e c u r i t y assessment of a power system ha s two functions.The first is to detect any violation in the actual systemoperating state. The second function is contingency analysis

Contingency analysis behaves like a fictitiou s test performedon a list of postulated contingency cases (single or multipleequipment outages). Tho se cases that would create line flow;voltage and reactiv e power violation should be identified andranked in order of their sev erity for more detailed study.

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Usually contingency analysis is divided into three parts,contingency definition, selection, and evaluation [25]. Formore than two decades contingency selection has receivedconsiderable attention whose aim is to reduce the originallong list of contingencies by selecting only those cases thatwould result in limit violations. There are two approaches forperforming contingency selection; ranking methods andscreening methods. In screening methods 11-61 the mostsevere cases are identified and they are given top priority inthe conting ency list for more detailed ac analysis, at the same

time the non-critical cases are removed fiom the list. Thesemethods depend basically on the local solution methods [7]and bounding methods [1-61 which use the local nature of anoutage and the network is divided into two or three sub-networks. The first sub-network contains the buses near theoutage. In many cases it can be extended to three o r four tiersor can be determined by the return path of the active power[3], then a complete ac load flow will be run for the sub-network. The second sub network contains the boundarybuses between the first and the third sub-network, which isthe rest of the system. Since the cornerstone of these methodsdepends basically on the determination of the first sub-network, any error in ide ntification of this sub-netw ork willlead to incorrect results. The main difficulty of this method isthe determination of the first network.Ranking methods [S-151 use a performance index as scalarfunction to describe the effects of an outage on the wholenetwork. Ranking methods can be divided into two sub-groups depending on the way in which the performanceindex is formulated, direct methods [S-101 and indirectmethods 111-141. For line flows or MW ranking directmethods are used and they give good results. Those methodsare many times faster than the indirect schemes. However;the application of direct scheme for voltage ranking givesunreliable results. There have been considerable efforts touse the direct method for voltage ranking [S-lo], but theresults obtained are not as accurate as the indirect scheme.On the other hand the indirect scheme is slower than thedirect scheme. The indirect methods use a variety ofapproaches starting fi-om using only the first iteration of theac load flow, one iteration of the fast-decoupled load flow,and distribution factors methods [l l-141. The main drawbackof these methods is the mas king effect. A few attempts havebeen made to remedy the masking effect [15-171 but untilnow there is no an effective method to completely eliminatethe masking effect. By masking effect it means that a non-critical contingency case can take the position of a criticalone. In [17] it was stated that the second order term is themain cause for the masking effect and it recommen ded that ahigher exponent index should be used. The use of highexponent index for all values of the bus voltage magnitudewill increase computational time. This paper attempts topresent a new method for voltage ranking taking in to accounthow to reduce the masking effect by tuning both theexponent index and weighting factors by using fuzzy logicapproach [18-231. A new adaptive technique is used to tunethe exponent index, and it depends on the actual voltagedeviation. Also this paper presents an altemative method to

Paper accep ted for presentation at the InternationalConference on Electric Utility Deregulation andRestructuring and Power T echnologies2000,City University, London, 4-7 April 2000.

0-7803-5902-X/00/$10.002000 IEEE.499


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tune the weighting factors. There was a previous attempt touse fuzzy logic in contingency analysis [24], but that attemptwas based on Mamdani control rules, and it gave manymisra nkin gs. In this paper two approaches are considered, thefirst meth od is based on Mamd ani control rules, which can beused to tune the weighting factor. The other method is basedon Sougeno control rules, which can be used to tune theexponent index.

11. FUZZY LOGICFuzzy logic is a superset of conventional (Boolean) logic.The fuzzy set can handle the concept of partial truth-valuesbetween "completely true" and "completely alse" .Fuzzy logic co ntrol is very powerful in many control systemapplications due to the following advantages [20]: it allowsthe use of linguistic expressions to describe the behaviour ofthe system. Using this property, it is possible to imitate theaction of the operator. The second advantage is that fuzzylogic con trol is inheren tly non-linear and is thus able toperform control actions, which are not possible with linearcontro .Steps in using fuzzy logic control to voltage rankingIn applying fuzzy logic control to contingency analysis, oneshould identify the input and output to the fuzzy logiccontroller (FLC). In our case the input will be thenormalized voltage dev iations and the output will be thevalue of the severity index. The main parts of the fuzzy logiccontroller are [20,22, and 231:

1) Fuzzification of the input2) Knowledge base3) Fuzzy in ferenc e using approximate reasoning4) Defuzzification process

1) Fuzzification of the inputIn this stage the non-fuzzy input is coded into fuzzy logic.The ch oice of the m embership function is an important taskin designing FLC. The number and shapes of thememb ership functions and how they are related to each other,as well as their overlaps, determine the resulting controlleroutputs which are expressed as functions of the inputs[20,2212) Knowledge base and fuzzy nferenceThe know ledge base is the cornerstone of any FLC and hastwo components: namely database and fuzzy rule base[20,23]:Database

1 . Discretization of the universe of discourse.In this stage the universe o f discourse is divide d into a certainnumber of segments. Each segment is given a certain labeland is assigned grade of memb ership values.2. Choosing the mem bership functions for the labels.Rule baseFuzzy control rules are used to represent the knowledgeimplemented in the controller. There are two types of fuzzycont rol rules: Mamd ani- and Sougeno-rules. Mam danicontrol rules have the following form:IF x is S , THEN y is Y,The conclusion, yz in this case, is a fuzzy variable. While inthe case of Sougeno control rule , he conclusion is a functionand has the followin g form:I F x i s S, THEN y = f ( x )The output y in this case is not necessary to be a fuzzyvalue.It will be shown that in ranking process, the Sougeno schemeis deterministic and is more flexible than the Mamd ani one4) Defuzzification processThe output of th e fuzzy reasoning should be defuzzified. Inthis paper the center of gravity [23] method is used fordefuzzification.

III. APPLICATION TO VOLTAGE RANKINGA. Identification of control variables for input and outputWhen a contingency occurs in a power system, somevariables may exceed their limits. The most importantvariables in a power system are the line flows, the busvoltage magnitudes and the generated reactive power. Incontingency analysis for voltage ranking the variables are thebus voltage magnitudes and the g enerated reactive power. Inthis paper only the bus voltage magnitudes are considered.So the input to the FLC will be the normalized voltagedeviations given by the equation

The construction of any database contains the following twoaspects [203:where

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Vi is the post contingency voltage at bus iy"" and cminre the maximum and minimum voltagerespectively at bus i.

OutputLinguisticTermSeverityIndex

The output variable will be the sev erity index showing thedegree of severity of the contingency.

Y1 Y2 Y3 Y4 YS Y6 Y7

0.0 0.8 3.0 8.0 30 70 150- + + -+ -+ -+ -+ -+1.0 5.0 10.0 SO 100 200 1000

B. Fuzzification process1 ) The universe of discourse for the input and the output

variablesBefore choosing the membership function one should firstdefine the universe of discourse. In practical power systemthe values of the bus voltage is restricted to certain limits (forexample 0.95 I vi51.05). In the event of contingency thevalue of the bus voltage may exceed this limit, but if it isbelow c ertain value (say 0.80 for example) this may lead tovoltage collapse. So in such cases the program should give analarm. The universe of discourse in our case will be in therange of ( ) and outside these limits theprogram w ill generate an alarm show ing that the contingencyis critical. Within these ranges the normalized voltagedeviation w ill be [0-41. The alarm signal could trigger the useof a high exponent index to reflect the severity of thecontingency.

0.90 5 vi5 .1

3) The shape of the membership fimction: Input and Ou tputThe selection of the shape and the number of the membershipinput functions will affect the ranking process. Fo r exam plethe membership function of the isosceles triangle given infigure 1which is used in [24] is not s uitable for contingencyanalysis. This can be explained by the following example: ifthe value of the normalized voltage deviation is [0.2 and 0.81both of them will give the same membership value [0.3].This means that the isosceles triangle function is not suitablefor contingency analysis. Instead the saw tooth function asgiven in figure 2 is chosen. Figure 3 shows the completemembership fimctions for the input. The membershipfunction of the output is shown in figure 4C. Fuzzy control ruleIn this part of the paper Mamdani control rule will beconsidered which h as the following general form

2) Choosing the set of linguistic termsAs previously mentioned the number of linguistic terms willaffect the final results. The larger the number of linguisticterms the more accurate should be the results [l]. In ourinvestigation the number of linguistic terms is 8. The nameand range of each linguistic term is given in table 1.

InputLinguisticTermNormalized 0.6 1.0 1.6 2.0 2.4 2.8 3.2Voltage -+ -+ -+ -+ + -+ -+ -+Deviation. 0.8 1.2 1.8 2.2 2.6 3.0 3.4 4.0

Table 1 Range of the linguistic terms for the inputThe output variable is the severity index, which shows thedegree of severity of the contingency. The linguistic termsand the range o f each linguistic term for the output are givenin table 2.

Figure 1 Isosceles membership function

Figure 2 awtooth membership function

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MembershipFunctionL0.4 I / I / I / I / I / I / It 1 2 1 6 2 0 2 4 2 8 3 2 3 6 4 0Normalued vonage DenabonFigure 3 membership functions for the input

MembershipFWlCtiCil

Figure 4 The membership function of the output

If (a set of conditions are satisfied) THEN (a set ofconsequences can be inferred)A fuzzy control rule is a fuzzyconditional statement in whichthe antecedent is a condition and the consequent is a controlaction [23]. The following fuzzy rules will be applied in ourcase:

0 IF x is SI THEN y is zeroIF x is S2 THEN y is Y1

0 IF x is S3 THEN y is Y 20 IF x is S4 THEN y is Y30 IF x is S5 THEN y is Y4IF x is S6 THEN y is Y50 IF x is S7 TKEN y is Y6

IF x , i s S8 THEN y is Y7The value and the range of each linguistic variable arealready given in tables 1and 2D. Sougeno inference

The general form of Soug eno fuzzy inference rule is:

y=a,x+a$+a,x +..In the performance index ranking method, the rankingaccuracy will depend on the weighting factors [26] and thevalue of the exponent index [I7 and 271. In the Mamdanimethod, the fuzzy logic controller is geared towards theadjustment of the weighting factors. It has been shown inprevious investigation that the value of the exponent indexhas a significant effect on the ranking accuracy [17].Sougeno method reflects better on the adjustment of theexponent index. In this case the rules used as follow s:

IF x is SI THEN y is zeroIF x is S2 THEN y= x 2

0 IF x is S3 THEN y = x 40 IF x is S4 T H E N y = x 60 IF x is S5 T H E N y = x 8

IF x is S 6 THEN y=x'OThe ranges of the linguistic variables are given in table 6 .

TermNormalizedVoltage 0.0 0.6 0.8 1.6 2. 6 3.4

0.6 0.8 1. 6 2 .6 3. 4 4.0Deviation. - + + -9 + - +Table 3 Range of the linguistic variables fo r the input

IV. NUMERICAL RESULTSIn this section the results of the IEEE-30 bus system will besummarized. The results obtained fiom the performanceindex method (PI) and the proposed fuzzy ogic methods willbe compared. The performance index is defined by thefollowhg equation [7]

whereAV : s the voltage deviation at bus iA.V;.""' s the maximum allowable voltage deviation at bus iB: is the set of load busesW, weighting factors, which will be set to unity.Table 4 shows the ranking process for IEEE-30 bus systemobtained fiom the performance index method. Column 1shows the contingency number, columns 2 and 3 showsending and receiving end of the line. Columns 5 shows theresults for the performance index method in case theexponent index is 2 (2n=2).To show the effect of raising the

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exponent index on the ranking process column 4 shows theresults for 2n = 22. By comparing both columns, it can beseen that the exponent index has a profound effect in theranking process. For example contingency number 2 wasranked as 2"dwhen the exponent index was 22, whereas itwas ranked in the 5" place when the exponent index was 2.Also contingency number 5 was ranked as 51h when theexponent index was 22, but it was ranked in the 26" placewhen the exponent index was 2. Column 6 shows the resultsfor the same system by using fuzzy logic controller(Mamdani method). It can be seen from the results obtainedthat this method can reach good accuracy when comparedwith the performance index method. T his method can capturethe most critical cases (from contingency 1 to contingency24) with very little misranking cases at the end of the list.

35363738

A006 A008 35 37 30 35A006 A007 36 36 33 36A006 A009 37 35 32 3';A004 A012 38 38 37 38

This method is much better than the conventional methodwhen the exponent index is 2.0ne should tune the numberand the shape of the membership function in order toenhance the results. These problems are under investigationat the present time and will form the content of anotherpaper. Column 7 shows the results in the case of Sougenomethod. As can be seen from the table by comparingcolumns 4 and 7 the results are approximately identical andthis method is better than Mamdani method.V. CONCLUSION

This paper presents two methods for voltage ranking. Thefirst one is based on Mamdani method. This method canidentify the most critical cases and is better than theconventional method when the exponent index is low (2n=2).This method tries to tune the weighting factors. The secondmethod is based on Sougeno rules, which can approach thesame results as the conventional method with high exponentindex. Sougeno method gives more flexibility and accurateresults than Mamdani method.VI. REFERENCES

Galiana F.D., " Bound Estimates of the Severity of Line Outage inPower System Contin gency Analysis and Ranking", I EEE trans. onpower Apparatus and systems, VoLPas-103, No. 9, Sept. 1984Brandwajn V. '' Efficient bounding method for linear contingencyanalysis." IEEE transactions on power systems, Vol.PwRs-3, No. 1,Feb. 1988Brandwajn V. and Lauby M.G., '' Complete bounding method for ACcontingency screening", IEEE transactions on power systems, PWRS-4, No. 2, May 1989N.Hadjasaid, M.Benahmed, J.Fandino, J.C.Sabonnadiere and G.Nerin," Fast Contingency screening for voltage-reactive consideration insecurity analysis "IEEE transactions on pow er systems, Vo1.8, No. 1,Feb. 1993N.Hadjasaid, J.Fandino, Q.T.Tran J.C.Sabonnadiere and G.Nerin, " Anadaptive correction forvoltage security analysis using a local approachmethod "IEEE transactions on power systems, Vo1.9,No. 2, May 1994G.C.Ejebe, R.F.Paliza, and W.F. Tinney " An adaptive localizationmethod for real-time security analysis IEEE transactions on powersys tems, Vo1.7, No. 2, May 1992John Zaborszky, Keh-Wen Whang and Krishna, 'I Fast ContingencyEvalution using concentric relaxation" IEEE transactions on P.A.S.,Vol.PAS-99, No. 1, JanJFeb 1980Iraj Dabbaghchi and G. Irisani" AEP Automatic contingency selector:Branch Outage Impacts on Load Bu s Voltage Profile" IEEETransaction on power systems, Vol. 1,No. 2, October 1986Yilang Chen and Anjan Bose ''Direct ranking for voltage contingencyselection" IEEE Transaction on power systems, Vol. 4, No. 4, October1989.

[IO] Yilang Chen and Anjan Bose " Direct ranking for voltage contingencyselection including injection outages" conf. Paper 1990

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[l I] Marija Ilk-Spong and Arun Phadke redistribution of reactive powerflow in contingency studies IEEE Transaction on power systems, Vol.Taylor and L. J. Maahs a reactive contingency analysisalgorithm using mw and mvar distribution factoirs IEEE Transactionon power systems, Vol. PWRS-6, No. 1, February 1991.[13] Ching-Yin Lee and Nanming Chen Distribution factors of reactivepower flow in transmission line and transformers outage studies IEEETransaction on pow er systems, Vol. PWRS-7, No. 1 February 1992.[14] S.N. Singh and Srivastava Improved voltage and reactive powerdistribution factors for outage studies IEEE Transaction on powersystems, Vol. PWRS -12, No. 3 February 1997.

[I51 T.F.Halpin, R.Fisch1, and R.Fink, analysis of autom atic contingencyselection algorithms , EEE trans. on power Apparatus and systems,[16] R.Fisch1, T.F.Halpin, J.J.Helferty, V.Gershm an and F.Mercede, Analgorithm for automaticlly tunning the w eights ofperfformance indecesfor monitoring power system loading or security, IEEE trans. onPower Systems, Vol.PWRS-I, No. 3, AUGUST 1986[17] K.F.Schafer and J.F.Verstege Adaptive procedure for masking effectcompensation in contingency selection algorithms IEEE trans. onPower Systems, vol.-5, No. 2, AUGUST 1990.[18] George J. Klir & B o Yuan Fuzzy sets, fuzzy ogic, and fuzzy systemsSelected papers by Iotfi A. Zadeh World Scientific Publishing Co.1996.[I91 H. J. Zimmermann I Fuzzy set theory and it s applications - Secondedition Kluwer Academic Publishers 1991[20] Spyros G. Tzaafestas and A.N. Venetsanopoulos Fuzzy reasoning inInformation Decisionand control systems Kluwer AcademicPublishers 1994.[21] Ronald Yager and Lotfi A.Zadeh An introduction to fuzzy logicapplications in intelligent systems Kluwer Academ ic Publishers 1992[22] C.C. LEE Fuzzy logic in control systems: Fuzzy logic controller PartI IEEE Trans. on Systems, Man, and Cybernetics V01.20, No.2,March/ April 1990.

PWRS-1 ,NO .3, August 1986.[I21 D. G.

V01.Pas-103, NO.5, MAY 1984

[23] Ba rt Kos ko Fuzzy thinking Harper Collins Publishers 1993[24] Yuan-Yih Hsu and Han-Ching Ku o Fuzzy set based contingencyranking IEEE trans. on Pow er Systems, Vol.-7, No. 3, AUGUST1992.[25] Brian Sto tt Ongun Alsac and Alcir J. Monticelli Security Analysisand optimization Proceeding of the IEEE VOL.75 No.12, Dec. 1987[26] K. L. Lo and M. Arshad Bismil A coparison of voltage rankingmethods International Joumal of Electric Power System Research,Vol. 16 ,N o. 2, pp. 127-140, 1989

VII. BIOGRAPHIESKwok L.Lo received his MSc and PhD from UMIST. He is a Professor atStrathclyde University. His research interests includes Power systemsanalysis, planning, operation, monitoring and control including theapplication of expert systems and artificial neural networks, transmissionand distribution management systems and privatization issues. He is a fellowof the IEE and a fellow o f the Royal Society of Edinburgh.A K. I. Abdelaal was born in Suez, Egypt, on January 9, 1966. Hegraduated fiom Cairo University with honor degree in July 1989. Heobtained his Msc From Cairo University in speed control of inductionmotors in 1995. From 1991 to 1997, he worked at the High Institute ofEfficient Productivity, Zagazig University, Egypt. Cu rrently he is doing hisPhD. His areas o f interest are in voltage and reactive pow er control, optimalpower flow, and application of expert systems to power systems

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f logic baseed contingency analysis

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