978-1-4799-6251-8/14/$31.00 2014 IEEE Elimination of multiple estimation for single phase fault location in power distribution systems considering the load current J. Ramrez-Ramrez1, J. Arrieta-Giraldo2, J. Mora-Florez3 Department of Electrical Engineering Universidad Tecnolgica de Pereira Pereira, Colombia daviramirez@utp.edu.co1, jsarrieta@utp.edu.co2, jjmora@utp.edu.co3 AbstractThispaperpresentsamodificationtoincreasethe robustnessofthemethodologyusedtoeliminatethemultiple estimationproblem,offaultlocationmethodsbasedonthe impedanceestimation.Theapproachhereproposedusesthe power system parameters and the availablemeasurements at the mainpowersubstation.Testsarecarriedoutondifferentpower systems,analyzingtheeffectoffaultresistanceandloadcurrent on the fault location. The obtained results show that it is possible toobtainauniquefaultlocation,eliminatingthemultiple estimationproblemseveninthecaseof40impedancefaults. Thismethodalsohelpstoimprovethepowercontinuityindexes in power distribution systems by the determination of the faulted node. Index TermsFault location, multiple estimation, radial power systems, service continuity indexes, load current. NOMENCLATURE IPk: Fault voltage at phase k (a, b, c) in the initial node of the analyzed line section. IPk: Fault current at phase k (a, b, c) between the initial and the faulted node, at the analyzed line section. ILk: Load current in phase k (a, b, c) for the analyzed section. IPn:Current through the fault resistance. Zkk: Self line impedance of the phase k (a, b, c) in ohms. ZkI: Mutuallineimpedancebetweenthephasek(a,b,c)and the phase l (a, b, c) in ohms. m: Distance from the initial node to the faulted node. m]: Additional estimation obtained using voltages and currents at not faulted phases. n: Number of additional estimations. Rf: Fault resistance. I. INTRODUCTION Service continuity in transmission and distribution systems isconsideredasanimportantaspect,especiallywhen electricitymarkets are included in a competitive environment. Themostcommonindexesofservicecontinuityarethe SystemAverageInterruptionFrequencyIndex(SAIFI)and SystemAverageInterruptionDurationIndex(SAIDI)and faultscausesupplyinterruptionsthatareresponsibleforlow rates of these service continuity. Intransmissionsystems,usingequipmentand measurementsatbothlineends,whichallowlocatingthesite ofthefaultwithahighaccuracy,solvesthisproblem.Onthe otherhand,measurementsinpowerdistributionsystemsare normallyonlyavailableatthemainpowersubstation.The presenceoftappedloads,laterals,nothomogeneous conductors,unbalancesandlargeloadfluctuationsmakethis asanunsolvedproblem.Additionally,thepresenceofseveral lateralsatthepowerdistributionsystem,difficultiesthe location of a single faulted node [1]. Currently,manyoftheeffortstosolvethisproblemare focusedondevelopingmethodologieswhichonlyusethe voltageandcurrentmeasurementsatthemainpower substationandthenetworktopology,inordertoexecutea circuitanalysistofindthedistancetothefault;these methodologiesareknownasMBM(ModelBasedMethods). Othermethodologiesarefocusedonfindingthefaultedarea bytraininglearningmachinesusingfaultdatabases,which known as KBM (Knowledge Based Methods). One of the problems of MBM is the multiple estimation of thefaultednode.Analternativetosolvethisproblemis associatedtothedevelopingofhybridapproaches,by strengthening an MBM using a KBM, which is able to identify possiblyfaultedareas.However,onethemajordrawbacksof the KBM are the requirement of a fault database, which is not availableinallofthecases.Additionally,thesemethods usually involve high computational cost [2]. According to the previously exposed, this paper presents a novel proposal that improvesthe MBM, by the eliminationof multipleestimationproblem,throughacollaborativescheme, which considers the variation of the load current. Thispaperispresentedinfivesections.InsectionII,the theoreticalaspectsaregiven.Next,insectionIIIthe methodologicalapproachisdetaileddescribed.InsectionIV thetestsandtheresultanalysisarepresented.Finally,section V is aimed to conclude and summarize the main contributions of this research. II. THEORETICAL ASPECTS Some MBM eliminates the multiple estimation of the fault location,usingonlynetworkparametersandvoltageand currentmeasurementsatthedistributionsubstation[2].The methodhereproposedforeliminatingthemultipleestimation problemisbasedontheclassicalreactanceapproach,but consideringtheloadcurrentatthefaultedphases,which increases its robustness. Theapproachproposedin[2]toeliminatethemultiple estimationassumesthatthefaulthaszeroimpedanceand thereforenocurrentflowsdownstreamthefaultednode.The estimationoftheloadcurrentinthehereproposed methodology is performed by an iterative process, by using an additional fault location method. A. Estimation of multiple faulted node Themultipleestimationproblemofthefaultednodeis explainedbyconsideringthepowerdistributionsystemof Fig.1,wherefourdifferentplaceswiththesamevalueof electricalreactancetolocatethefaultF1areobtained (Xd1=Xd2=Xd3=Xd4).Byidentifyingonlyonefaultednode,theapproach providesaccurateinformationtothemaintenanceteam,in ordertofindandrestorethefaultassoonaspossible [2].Considering that it is not common to find identical laterals in power distribution systems, the here proposed methodology isbasedonthedeterminationofdifferencesbetweenthe laterals,suchasthetopology,tappedloadsandimpedance lines,tolocatethefaultdistance,eliminatingtheproblemof multiple estimation, using a MBM as the method based on the estimation of reactance [5] [6]. B. Estimation of the load current Theloadcurrentandthecurrentthroughthefaultare included in this proposal, as a contribution to the methodology initiallyproposedat[2].Thecurrentthroughthefaultis estimatedbyaniterativeprocess,whichconsidersthree variables,thevoltageatthefaultednode,thefaultresistance andthefaultdistancefromtheinitialnodeoftheanalyzed section.Initially,itisassumedthattheloadcurrentandthepre-faultcurrentarethesame.Then,thecurrentflowingthrough thefaultiscalculated.Withthisapproximatevalueof IFn,the circuitparametersandtheavailablemeasurements,the distancetothefaultisestimatedaspresentedin[4]. Subsequently, using the estimated fault distance and the Fig. 2, theloadcurrentisrecalculated.Aniterativeprocessis performedtoimprovetheestimationoftheIFn,untiltheerror in thefault distancefrom one iteration respect to the previous one, become lower than a defined tolerance [4]. III. PROPOSED METHODOLOGY FOR ELIMINATION OF MULTIPLE ESTIMATION Apossiblesolutiontothemultipleestimationofthe faultednodeispresentedin[3],wherestraightforwardfault locationmethodisusedtoshowinasimpleway,the application of the proposed concept [5] [6]. Best results could Fig. 1. Problem of multiple estimation of MBM fault location methods. beobtainedwithmoreelaboratedmethodologies,asthese presented from [7] to [12]. Oneofthemaindisadvantagesforthecurrent implementationofafaultlocatorthateliminatesthemultiple estimationproblem,isthatitisnotpossibletoobtain equationstoincludethelinemutualimpedanceofthepower distribution system [3]. Thispaperpresentsamethodologytoeliminatemultiple estimationofthefaultednode,alsoconsideringthemutual effectatthelineimpedance.Additionally,amorerobust approachisalsoproposed,byconsideringtheeffectofthe load current [3]. Usingtheproposedapproach,itispossibletoestimatean error for each lateral. Having estimated multiple distances, the lateralwiththelowesterrorcorrespondstofaultedlateral, becausethebehaviorofthethree-phasemeasurementsis uniqueforeachlateral.Thisispossibleduetodifferencesin line impedance, parameters and loads on each lateral. A. General approach of the method Theimplementedalgorithmconsidersaniterative procedure,whichisperformedsectionbysection,oneach lateralofthepowerdistributionsystemunderanalysis.In general, this allows the estimation of a set of distances,where the error is obtained as is presented in(1). Error= 1n |m - m]|n]=1m (1) Theproposedmethodconsidersthatatthelateralwhich has the lowest error (weighted differences of the distances), is where the fault is found. Thus, the faulted lateral is selected. Aspowerdistributionsystemsareunbalanced,the proposalpresentedin[2]considerstheanalysisofphase components. The line impedance from node N to N+1, and the loadimpedanceaccumulatedfromtheendoftheline,are given by (2) and (3) respectively. ZInc= _ZuuZubZucZbuZbbZbcZcuZcbZcc_ (2) ZLoud= _ZLuZLubZLucZLbuZLbZLbcZLcuZLcbZLc_(3) ZLoud iscalculatedastheratiobetweenthepre-fault voltage and pre-fault current in the main power substation,F1 Substation Xd1 Xd2 Xd3 Xd4 Fig. 2. Three phase equivalent for a single-phase fault in the phase a. assumingtheoff-diagonalvaluesofthematrixequalszero, i.e., the load is supposed to be Y-connected. ForthelinesectionbetweenthenodesNandN+1,as showninthetestsystemproposedinFig.2,itispossibleto obtainanequationofthevoltagedropcausedbythefault,as is shown in (4) [2]. _IPuIPbIPc_ = _mZuumZubmZucmZbuZbb + ZLbZbc + ZLbcmZcuZcb + ZLcbZcc + ZLc_ _IPuIPbIPc_ +_R]u uu u uu u u_ _IPncIPnbIPnc_ (4) ThecurrentIPniscalculatedbyaniterativestrategyas describedin[3].Similarly,themethodthereproposed, determines if the fault is located in the analyzed section or in a sectiondownstream.In(4),theloadcurrentisconsideredat thefaultedphasestoimprovetheclassicalreactancemethod. Fromthefirstrowof(4),thefaultdistancemisobtained,as shown in (5). m =imog _vFcIFnc]imog _zcc+zcbIb+zccIcIFnc](5) m1 =imog _vFc-vFb+vFc+BIFb+CIFcIFnc]imog _zccIFcIFnc- Zbu + Zuc +AIFnc](6) m2 =imog _vFc+vFb-vFc-BIFb-CIFcIFnc]imog _zccIFcIFnc+ Zbu - Zuc +AIFnc](7) Where A, B, and C are given by 8. A = ZubIPb +ZucIPc B = Zbb + ZLb - Zcb -Zcb(8) C = Zbc + ZLbc -Zcc - ZLc Furthermore,itispossibletoobtaintwootherlinearly independentequationsofthecomplexequationpresentedin (4).Thetwopossibleadditionalsolutions,consideronlythe imaginarycomponentofthefaultreactance,becausethisis relatively constantunder variations of Rf. These equationsare presented in 6 and 7 respectively. Accordingtotheinformationpresentedabove,themost appropriate equation to estimate the fault distance is presented in(5).Equations6and7areadditionalestimationsofthe distance obtained in (5), taking into account all the parameters of the analyzed lateral. Usingtheproposedequations,thefaultedlateralcanbe determined,sincethebehaviorofthree-phasemeasurements foreachlateralisonlyduetodifferencesatlineimpedance parametersorloadoneachlateral.Therefore,itispossibleto obtainafaultdistanceusingthephasemeasurementsduring fault steady state, as presented in (5). Further, by using the two additional distances, the error presented in 1 can be estimated. Variablenrepresentsthenumberofpossibleadditional distances (in case of single-phase fault, this number is 2)[2]. Using(1)theerrorisestimatedtodeterminethefaulted node using information of the faulted phase. The fault is in the lateralwiththelowesterror,calculatedusingtheestimations of (5), (6) and (7). Themultipleestimationerrorontheunfaultedlateralsis greaterthantheerrorcalculatedonthefaultedlateral.Thisis duetoelectromagneticcouplingoccurringonthefaulted lateral, at the time of occurrence of the fault. Finally,thesweeptothedistributionsystemtakesinto accountallthepowersystemparameters,includingtheshunt admittance of the line and load couplings. IV. TESTING AND ANALYSIS Alloftheproposedpowersystemsusedintestswere modeledandsimulatedinATP.Twoadditionaltoolsas Atpxchange and SimulacionRF were also used [16], [17]. The proposed method was implemented in Matlab. A. Test power systems The first system selected for the validation of the proposal is presented in Fig.3, and was implemented using section lines and loads from the IEEE 34 nodes, 24.9 kV system [13]. This isusedtoconsidertheeliminationofthemultipleestimation problem in a power system with similar laterals. ThepowerdistributionsystemofFig.3hasthesameline parametersinthelaterals1and3,andthesameimpedance load in the lateral 2 and 3.Sections of line of the laterals 1 and 3correspondtotheconfiguration300oftheIEEE34nodes system.Additionally,theloadinthelateral1isthesameas thenode860.Theimpedanceofeachsectionofthelateral2 corresponds to the configuration 301 and the lateral load at the end of 2 is the same as the load on the node 830 [2]. ThesecondproposedtestsystemisshowninFig.4,and correspondstoarealpowerdistributionsystemlocatedat Cundinamarca, Colombia. It has unbalanced loads, laterals and differentlineconfigurations,consideringundergroundand overhead lines. IFc IFb IFa IFna Ila Rf m N+1N ZLabc VFabc Fig. 3. Power system with similar laterals. Fig. 4. Real power distribution system B. Test proposed scenariosTablesIandIIshowthecomparativebehaviorofthe proposedapproachforsinglephasefaults,considering differentfaultresistancesandforrandomloadvariations[14], [15]. Single-phase faults on a fault resistance range from 0 to 40weresimulatedinallnodesforbothpowerdistribution systems[16].Consideringthesizeofthepowersystem,the analyzedfaults(a-g,b-gandc-g),thefaultresistances(0,20 and 40 ohms) and the load scenarios (rated load, 1.5 rated load and0.6ratedload),thenumberofanalyzedfaultsare864in thecaseofthepowersysteminfigure3,while1188inthe case of the power system in figure 4. Efficiencyiscalculatedastheratioofthefaultsadequate locatedandthetotalfaultnumberofconsideredfaults,under the same condition, as is given by (9).It should be noted that it isconsideredasacorrectlylocalizedfault,theonelocatedat the corresponding lateral an also near to the faulted node (In a range of two nodes from the faulted one). Eicicncy = 1uu numbcr o oults oJccuotc locotcJtotol numbcr o oults(9) 1)Result analysis at the power system with similar laterals In the case of the results reported in table I, in case of a 0 faultresistance,typeoffaulta-t,andthesystemoperatingat nominalload,theobtainedefficiencywithandwithout considertheapproachhereproposed,isthesame.Itindicates that27faults(85.1852%)areidentifiedatthecorresponding lateralandattherightdistance.Theaveragereportedinthe lastrowofeachtablecorrespondtotheefficienciesthe performanceofthemethodologywithandwithoutthe proposal, for each load variation stage. The efficiency in localization of the methodology with and withouttheproposedforsingle-phasefaults,unsurprisingly, presentsaverysimilarbehaviortosolidfaults,regardlessof variationintheload.Whenthefaultimpedanceincreases,is wheretheproposedapproachmakesitscontribution,because as it considers the effect of the load current. Despite the similarity in the laterals at the power system, it isnoticedthatinmostcasestheproposalimprovesthe efficiency of the method. 2)Result analysis at the real power system ForthepowersystemonFig.4,43faultsweresimulated, using three different fault resistances and also considering load variationsrespecttothenominalvalue.Theresultsare presented in table II. Althoughthisisarealpowersystem,whichisheavily loadedandisnotbalanced,itshowsthattheproposed approach helps to obtain good results. Itcanbeclearlyseenthatinmostofthecases,the efficiencyoftheproposedmethodologyissimilartothe obtainedintheoriginalmethodology.Anacceptableoverall efficiencyofthestrategyhereproposedisobserved,thenthe approachimprovesthelocationandeliminationofmultiple estimation when the fault resistance is different of zero. TABLE I. TESTS PERFORMED IN THE CIRCUIT OF FIG. 3 Efficiency with original methodEfficiency with the proposed method RfFault typeZloadZload 150%Zload 60%ZloadZload 150%Zload 60% 0 a_t85.18555.55640.74185.18555.55640.741 b_t81.48259.25937.03781.48259.25937.037 c_t62.96366.66737.03762.96366.66737.037 20 a_t59.25955.55640.74170.37055.55640.741 b_t59.25959.25937.03759.25959.25940.741 c_t55.55633.33333.33359.25933.33337.037 40 a_t3.7040.00037.03755.5563.70440.741 b_t0.0000.00033.33355.5563.70440.741 c_t0.0000.0007.40744.4443.70437.037 Average45.26836.62633.74563.78637.86039.095 TABLE II. TESTS PERFORMED IN THE CIRCUIT OF FIG.4 Efficiency with original methodEfficiency with the proposed method RfFault typeZloadZload 150%Zload 60%ZloadZload 150%Zload 60% 0 a_t74.41988.37290.69874.41990.69890.698 b_t88.37290.69886.04788.37290.69886.047 c_t86.04793.02383.72186.04793.02383.721 20 a_t65.11662.79179.07065.11662.79179.070 b_t74.41962.79169.76774.41962.79169.767 c_t76.74462.79181.39576.74462.79181.395 40 a_t23.25620.93034.88430.23320.93034.884 b_t20.93011.62830.23334.88411.62830.233 c_t18.60511.62830.23330.23311.62830.2326 Average58.65656.07265.11662.27456.33165.116 V. CONCLUSIONS AND FUTURE WORKS The methodology was successfully implemented including theloadcurrent,improvingtheefficiencyinthecaseofhigh fault resistance values, as it was demonstrated by the obtained results. This method helps to determine the faulted lateral, even in caseofsimilarlineandloadcharacteristicsatthepower distribution system. 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