Fault location for underground distribution feeders: An extendedimpedance-based formulation with capacitive current compensationAndr D. Filomenaa,*, Mariana Resenerb, Rodrigo H. Salimc, Arturo S. BretasbaCompanhia Estadual de Gerao e Transmisso de Energia Eltrica (CEEE-GT), Av. Joaquim Porto Villanova 201, Prdio F, Sala 214, Porto Alegre, BrazilbElectrical Engineering Department, Federal University of Rio Grande do Sul (UFRGS), Av. Osvaldo Aranha 103, Porto Alegre, BrazilcElectrical Engineering Department, University of So Paulo (USP), So Carlos, Brazilarti cle i nfoArticle history:Received 30 September 2008Received in revised form 26 March 2009Accepted 29 March 2009Keywords:Fault locationPower distribution protectionUnderground distribution systemsabstractUnderground distribution systems are normally exposed to permanent faults, due to specic constructioncharacteristics. In these systems, visual inspection cannot be performed. In order to enhance service res-toration, accurate fault location techniques must be applied. This paper describes an extended imped-ance-based fault location algorithm for underground distribution systems. The formulation isdeveloped on phase frame and calculates the apparent impedance using only local voltage and currentdata. The technique also provides an iterative algorithm to compensate the typical capacitive componentcurrent of underground cables. Test results are obtained from numerical simulations using a real under-ground distribution feeder data from the Electrical Energy Distribution State Company of Rio Grande doSul (CEEE-D), southernBrazil. Comparativeresultsshowthetechniquesaccuracyandrobustnessinrespect to fault type, distance and resistance. 2009 Elsevier Ltd. All rights reserved.1. IntroductionElectricalpowersystems(EPS)canbecomposedbyoverheadand underground lines. Overhead lines are commonly exposed totransient faults. Lightning, insulation breakdown, wind, and treesacrosslinesarethemostcommonfaultcausesonthesefeeders.In these systems, fault identication and location can be easily as-sisted by visual inspection. Considering the occurrence of perma-nent faults, the existence of fault distance estimates may restrictthe search areas, allowing a faster system restoration. These esti-matesmaybeprovidedbyembeddedfault locationtechniquesfrom fault locator equipments and also by digital protection relaysand fault recorders. In order to supply these needs, several imped-ance-basedfaultlocationformulationshavebeenproposed, con-sidering overhead transmission [1,2] and distribution lines [35].Undergrounddistributionsystems(UDS)arecharacterizedbyhighreliabilityandareusuallyappliedinbigurbanareas. How-ever, undergroundpowercablesaretypicallyexposedtoperma-nent faults. Cable isolation deterioration and water-treeingphenomena are the most common fault causes onthese systems[6]. Hence, maintenancecrewinterventionisrequiredtolocateand substitute, or repair, the faulty feeder. Therefore, system resto-ration becomes maintenance crew dependant. Due to the topolog-ical characteristics of UDS, visual inspection cannot be performedas overhead power systems. Inordertoenhance system restora-tion, online fault location equipment should be used. These devicesprovideafaultdistanceestimateafterthefaultclearance. Ifthefault location estimate is unavailable, system restoration becomesvery time consuming, delaying service restoration.Traditional UDSfault locationprocedureisbasedontwoormoremethodsandisdevelopedthroughtwostages: pre-locateandpinpoint. Thepre-locatestepisbasedonterminalmethods,which measure electrical quantities at one or both line-ends. Tra-cer methods are used to pinpoint the fault location, and usually re-quest walking the cable route. Both are considered ofine and onsitetechniques, beingexecutedwiththesystemout-of-serviceandalsocharacterizedbylowperformanceefciency[7,8]. Re-cently, faultlocationtechniquesforundergroundsystemsbasedon transient voltages and currents traveling waves have also beenproposed[9]. However, this approachrequires expensive dataacquisition systems, with high bandwidth frequency capacity[10]. Theapplicationof articial intelligenceapproachonfaultlocation schemes, as Wavelets and neuro-fuzzy systems, has alsobeen recently considered [11]. The usage of neural networks, how-ever, needsaspeciclearningprocesstoeachanalyzedfeeder.Consequently, this approach does not allow its application on gen-eric feeders. Distribution parameter approach considering under-groundpowercableshasbeenalsoproposed[12]. Althoughthisapproach allows an accurately analysis of the underground powercables, the usage of symmetrical components restricts its applica-tion to ideally balanced and transposed feeders.0142-0615/$ - see front matter 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijepes.2009.03.026*Corresponding author. Tel.: +55 51 33825220; fax: +55 51 33824349.E-mail addresses: alomena@ece.ufrgs.br (A.D. Filomena), mariana@ece.ufrgs.br(M. Resener), salim@sel.eesc.usp.br (R.H. Salim), abretas@ece.ufrgs.br (A.S. Bretas).Electrical Power and Energy Systems 31 (2009) 489496ContentslistsavailableatScienceDirectElectrical Power and Energy Systemsj our nal homepage: www. el sevi er . com/ l ocat e/ i j epesPowerdistributionsystems(PDS) aretypicallycomposedbyunbalanced radial feeders with intermediate loads taps and lateralsbranches. These systems have important characteristics which mayinterfere, if not considered, in the accuracy level of fault locationtechniques[8,10]. Someofthesecharacteristicsaregiveninthefollowing:(a) Heterogeneityoffeedersgivenbydifferentsizeandcablelength.(b) Unbalances duetotheuntransposedfeeders andbythepresence of single, double and three-phase loads.(c) Presence of laterals branches along the main feeder.(d) Presence of load taps along the main feeder and laterals.Also, PDS are more commonly exposed to higher fault resistancevalues, which can affect fault location and also protection systems[8].Undergroundsystemsarealsocharacterizedbyasignicantdistributedshuntcapacitivecomponent,muchhigherthanover-headlines, duetothecablecharacteristics[13]. Inthiscase, thecapacitive effect can be considered as an infeed source. These spe-cics system characteristics still represent challenges for standardfault location techniques [8].Inorder toovercome theperformancelimitations ofstandardfault location methods for UDS, an extended impedance-based for-mulation is described in this paper. The technique is based on theapparent impedance approach, usingone-terminal data andisdeveloped on phase frame. The formulation can be applied on gen-ericbalancedandunbalancedgroundeddistributionfeeders. Aniterative algorithm is developed to estimate the fault current andalso to compensate the typical cables distributed capacitive com-ponent. TheproposedschemewasimplementedinMatlab[14]and tested with numerical simulation data of a real undergrounddistributionfeederfromCompanhiaEstadual deDistribuiodeEnergiaEltrica(CEEE-D), aBrazilianpowerdistributionutility,simulated with ATP/EMTP [15].This paper is organized as follows. Section 2 describes the pro-posedfault locationformulationconsideringthree-phase(3PH)and single line-to-ground (SLG) faults. The case study is presentedin Section 3. Test results and conclusions are discussed in Sections4 and 5, respectively.2. Fault location formulationThe proposed fault location formulation is based on the appar-ent impedance calculation. The method uses the sending-end volt-ages and currents as input data, as well as system parameters, suchas loads, cables series impedances, and shunt admittance matrices.Inordertoconsiderthemutuallinecomponents, themathe-matical development is done using the phase frame representation.Theformulationisdevelopedforthree-phaseandsingleline-to-ground faults considering the underground distribution feeder rep-resented as an ideal p-line model, as illustrated by Figs. 1 and 2.Still, the formulation considers a negligible shunt conductance va-lue. Also, supposing a grounded neutral, the electric eld createdby the phase conductor is conned to the cables insulation. Thus,only self capacitances are considered by the formulation, withoutanymutual shuntcomponentandtheshuntadmittancematrix,therefore, is composed only by non-zero elements in its main diag-onal [16].2.1. Three-phase faultsReferring to the three-phase fault illustrated in Fig. 1, the send-ing-end voltages during the disturbance are given by (1), which de-scribes the steady-state fault conditions:VSfaVSfbVSfc264375 x zaazabzaczbazbbzbczcazcbzcc264375 IXaIXbIXc264375 VFaVFbVFc264375 1where VSfm is the phase m sending-end voltage; x, the fault distance[m]; zmm, the phase m self impedance [X/m] and zmn is the mutualimpedance between phases m and n [X/m]. Also,IXm ISfm ICapm2where ISfm is the phase m sending-end current; ICapm, the phase mcapacitivecurrent;VFm, thephasemfaultpointvoltageandm, nare the phases a, b, or cVFm ZFm IFm3ZFm is the phase m fault impedance; IFmis the phase m fault current.Considering the fault impedances strictly resistive, constant andunknown, the voltage equations given by (1) can be expanded intoits real and imaginary parts:VSfar x M1a RFa IFar4VSfai x M2a RFa IFai5VSfbr x M1b RFb IFbr6VSfbi x M2b RFb IFbi7VSfcr x M1c RFc IFcr8VSfci x M2c RFc IFci9wherethesubscriptsrandi represent, respectively, therealandimaginarypartsandRFmarethefaultresistances. Also, M1mandM2m are dened by:S[Y ]RabcFig. 1. Three-phase fault.VSfcVSfbVSfaISfaVFcVFbVFaZL abcxLRSILcISfbISfaISfcZFaIFaILbILa(L-x)(z)cc(L-x)(z)bb(L-x)(z)aa[I ]Capabc[Y ]Sabc[Y ]RabcFig. 2. Single line-to-ground fault.490 A.D. Filomena et al. / Electrical Power and Energy Systems 31 (2009) 489496M1m Xkfa;b;cgzmkr IXkr zmki IXki 10M2m Xkfa;b;cgzmkr IXki zmki IXkr 11From (4)(9), there is a set of six independent expressions andfour unknown variables. Nevertheless, only four independentexpressions are necessary to calculate the fault distance and resis-tances. Isolating the unknown variables from (4)(6) and (9) yieldsthefaultdistanceandresistanceexpressions, whichcanbede-scribed in matrix form according to (12)xRFaRFbRFc2666437775 M1aIFar0 0M2aIFai0 0M1b0 IFbr0M1c0 0 IFcr26664377751VSfarVSfaiVSfbrVSfcr266643777512Themathematical solutionof (12) is dependant of twoun-known variables: the fault current and the sending-end capacitivecurrent. In order to calculate such estimates, an iterative algorithmis proposed, which will be described in Section 2.3.2.2. Single line-to-ground faultsReferring to the single line-to-ground (A-g) fault, as illustratedin Fig. 2, the sending-end voltage during the disturbance is givenby (13):VSfa VFa x zaa IXa zab IXb zac IXc 13Supposing again the fault impedance strictly resistive and con-stant, (13) may be expanded into its real and imaginary parts:VSfarVSfai" # M1aIFarM2aIFai" #xRFa 14From (14), the fault distance may be calculated as a function ofthe sending-end voltages and currents, as well as the lineparameters:xRF 1M1aIFai M2aIFarIFaiIFarM2aM1a VSfarVSfai" #15From (15), the fault distance independent mathematical expres-sion can be obtained (16):x VSfar IFai VSfai IFarM1a IFai M2a IFar16Once again, fault distance expression (16) is dependant to faultcurrent and sending-end capacitive current, both unknown. Theseestimates are provided through an iterative algorithm described inSection 2.3.2.3. Capacitive and fault currents estimatesFault distance estimates for three-phase andsingle line-to-ground faults provided by expressions (12) and (16) are dependantof two unknown variables: fault current and sending-end capaci-tivecurrent. Inordertoestimatesuchvalues, aniterativealgo-rithmisproposed. Thealgorithmconsiderssystemstopologicalcharacteristics and the voltages and currents measured at the sub-station terminal. Initially, this section aims to provide the theoret-ical fundamentals to calculate these unknown currents estimates,which are applied during the fault distance iterative algorithm lat-ter described in this section.2.3.1. Sending-end capacitive currentLine shunt capacitance is a typical and non-negligible parame-terofundergroundcables, whichisideallydistributedalongthefeeder length [13]. However, the fault location formulation devel-oped previously is based on an ideal p-line model, supposing linecapacitance lumped at sending and receiving ends. In order to con-sider the capacitive effect by the fault location process, the capac-itanceideal distributednatureisapproximated. Intheproposedformulation, thelinecapacitanceis not equallydistributedbe-tweenbothends, but dependant tothefaultdistanceestimate.Therefore, the sending-end shunt capacitance is supposed propor-tional to the fault distance, as described by (17)ySm xL yLm17where ySm is the sending-end phase m shunt admittance; yLm, totallinesectionphasemshunt admittanceandListhelinesectionlength.However, from the supposed p-line model, in this formulationthe maximum value of the equivalent lumped capacitance at eachline-end is restricted to 50% of the line section capacitance. There-fore, even for faults located close to the remote bus, the sending-end lumped shunt capacitance will not be close to the total sectionlinecapacitance. Inthisfaultcondition, thecapacitancewill beconsideredequallydistributedthroughthesendingandremoteends.Based on the estimated shunt admittance values to each phase,the sending-end capacitive currents are calculated using the send-ing-end voltages, as given by (18)ICap YS VSf 18whereYS ySa0 00 ySb00 0 ySc264375 192.3.2. Fault currentSince the fault currents (IFm) are also unknown in (12) and (16),these estimates may be calculated through electric circuit analysis.Referring to the faulty systems illustrated by Figs. 1 and 2, the faultcurrent can be calculated as function of: load current, sending-endcapacitive current and the sending-end currentIF ISf ICap IL 20Duetosystemdynamics, theloadcurrentduringthedistur-bancemaybedifferentfromthepre-faultperiod[3]. Therefore,the usage of the pre-fault load current as estimate during the faultmay provide inaccurate load currents estimates.In order to overcome this limitation, the proposed formulationdevelops an iterative algorithm, as described in the following.2.3.3. Iterative algorithmIn order to consider the dependency of the fault distanceexpressions(12)and(16)tothesending-endcapacitivecurrentandtheloadcurrent duringthefault, aniterativealgorithmisdeveloped. The iterative procedure, which is summarized onFig. 3, is fault type independent and is executed until the estimatedfault distance value converges. The algorithm is composed by thefollowing steps:(I) Line section shunt admittances are initially consideredequally distributed between sending and receiving line-ends(21)ySm yRm yLm221where yRm is the receiving-end phase m shunt admittance.A.D. Filomena et al. / Electrical Power and Energy Systems 31 (2009) 489496 491(II) Load currents during the disturbance are initially consideredequal to the pre-fault period valuesIL

abc IS

abc22whereISis thethree-phasepre-fault sending-endcurrentvector.(III) Sending-endcapacitivecurrent vector is calculatedusing(18).(IV) Fault currents are calculated by (20).(V) Fault distance is estimated using (12) or (16), according tothe analyzed fault type.(VI) A newsending-end shunt admittance is calculated by(17).(VII) Thealgorithmveriesiftheestimatedsending-endshuntadmittance violates the capacitive restriction, due to the p-line model, dened by (23)ySmPyLm223(a) IfthecalculatedshuntadmittanceySmisgreaterthanthe set value, 50% threshold is applied to the total linesectionadmittance. Thus, shuntadmittanceisequallydistributed by the two section terminals (ySm = yRm), asdescribedby(21), duetotheconsidered p-linemodeltopology.(b) Otherwise, consider the estimated value from (17).(VIII) A newsending-end capacitive current is calculated by(18).(IX) Fault location voltages are estimated through (24):VFaVFbVFc264375 VSfaVSfbVSfc264375 x zaazabzaczbazbbzbczcazcbzcc264375 IXaIXbIXc264375 24(X) Areceiving-endcapacitive reactance matrix is denedby (25)XC L x YL

125where YL is the shunt admittance matrix of the line section.(XI) Anequivalent line-endadmittancematrixbetweenload,receiving-endcapacitivereactance, andalsoseriesimped-ance betweenthe fault locationandthe sending-endisestablished by (26)Yleq fL x Z ZL==j XCg126where Z is the impedance matrix per unit length and ZL is theload impedance matrix.(XII) Theloadcurrent duringthefault is calculatedusingtheequivalent admittance matrix dened by (26) and the faultvoltages calculated by (24), according to (27):IL

abc Yleq VF

abc27(XIII) Check if the fault distance has converged, using (28)jxn xn 1j < d 28where n is the iteration number and d is the error tolerance,whichispreviouslydenedaccordingtotheaccuracyand2mm mLR Syy yIntial shuntadmitance estimateCapacite current estimatein terminal STerminal S shuntadmitance estimatem mL SyLxyFault distanceestimateYesNoFaultDistanceInitial load currentestimateConvergence AnalysisConverged?Fault locationvoltage calculationReceiving-end capacitivereactance matrixcalculationTerminal R admitanceequivalent estimateLoad currentestimateFault currentcalculationS LI ISTARTL x 5 . 0Yes2mm mLR Syy yNo?Fig. 3. Iterative fault location algorithm overview.492 A.D. Filomena et al. / Electrical Power and Energy Systems 31 (2009) 489496computational time desired. In this work a tolerance equal to0.1% of each analyzed section line length has been used.(XIV) If the fault distance has converged, stop the iterative algo-rithm. Otherwise, return to Step V with the updated send-ing-endcapacitiveandloadcurrents until theestimatedfault distance value converges.2.4. Intermediate loadsThe previous described algorithm is developed for radial feederswith a single load. In order to consider radial distribution systemswithintermediateloads, thefault locationprocess is extendedthroughaniterativesearchprocess. Theprocedurestartsusingvoltages and currents measured atthe substation terminal. Withthe presented fault location formulation, fault distance is initiallyestimated. If thefaultdistanceestimateobtainedisbeyondtheanalyzed section length (L), the fault is considered external. In thiscase, the algorithm is applied again using the voltages and currentsupdated to the downstream bus. Since the measured voltages andcurrentsareavailableonlyfromoneterminal (substation), thevoltages and currents at the downstreambus are estimatedthrough electric circuit analysis, described by (29)Vt1 Vt Zt It 29where[Vt] bus t three-phase voltages vector.[Zt] impedance matrix of the line section between buses t andt + 1.[It] bus t three-phase currents vector.Considering a constant impedance load model, the downstreamload current is given by (30)ILt1 YLt1 Vt1 30where [ILt+1] is the bus t + 1 three-phase load current and [YLt+1] isitsadmittancematrix. Thus, thedownstreamlinecurrentcanbecalculated by (31):It1 It ILt1 31Basedonthevoltages andcurrents estimates at thedown-stream bus, the fault location algorithm is once again executed tothe respective line section. The process is repeated until the faultlocation estimate converges to a distance internal to the analyzedsection.2.5. System lateralsPowerdistributionsystemsare typically composedby amainfeederandlateralsbranches. Lateralsaremainfeederbranchesnotalwayscomposedbythree-phaseconnections. Theproposedformulation was developed considering radial feeders without lat-erals. InordertoextendthedescribedformulationforPDSwithlaterals, it is proposed the application of equivalent radial systems.Inthiscase, theproposedformulationcalculatesequivalentsys-tems to each possible power ow path (PPFP), resulting on n equiv-alent radial systems, where n is the number of laterals.The equivalent systems are dened through the transformationof the lines and loads outside the path being analyzed, into equiv-alent constant impedances along the system. Since the fault loca-tionscheme analyzes the systeminthe rst fault cycle, thisassumption can be considered as a reasonable approximation [17].Theconsiderationofequivalentimpedanceshasalreadybeenproposedinpreviouslypublishedpapers[4]. Thisconsiderationwas basedina systematic computationof parallel andseriesimpedances, representing lines and loads. Such approach, however,is not well suited for large distribution systems, especially on sys-temswithahighdegreeofcouplingbetweenphases. Instead, apowerowalgorithmcouldbeused. Theadvantageofsuchap-proach is that these algorithms are well known, have great preci-sion and are easy to be applied in general distribution systems.The proposed fault location scheme applies a ladder technique-based three-phase power ow [16], which is an iterative processdeveloped for radial distribution systems applications. Theimplemented power owconsiders the distribution systemsnon-linearitiesandasymmetrical phasecoupling. Thus, thepro-posed fault location formulation can be applied to each equivalentsystem. Thefollowingprocedureisproposedtodevelopafaultlocation diagnosis to general feeders with laterals.(I) Runathree-phasepowerowalgorithm[16], consideringthe pre-fault conditions.(II) Calculatetheequivalentimpedancesineachnode, Zeqkp,using (32)Zeqkpm Vkm I1kpm32where VKmis the phase m pre-fault voltage at bus k [V]; Ikpm, thepre-fault phase m current owing from bus k to bus p [A]; k, the lat-eral upstream bus to be modeled as equivalent constant impedanceandpisthelateraldownstream bustobemodeled asequivalentconstant impedance.(III) Determine the possible number of PPFP.(IV) Select one PPFP and determine the nodes with laterals.(V) Foreachnodewithlateral, determineanequivalentload,considering only the previously calculated equivalentimpedances, Zeq, outside the path being analyzed.(VI) For each node with lateral and also loads, calculate the par-allel between loads and the equivalent load determined onStepV. Thisisthenal equivalent loadfor thenodesinthe path being analyzed.(VII) GobacktoStepIVuntil all thenequivalentsystemsaredetermined.(VIII) Execute the fault location algorithm for each equivalent sys-tem. A total of n fault locations will be determined.(IX) Determine the correct fault location and path, using a faultsection determination algorithm, as proposed by the authorsin [18]. In this paper, the fault section determination is con-sidered previously known.3. Case studyIn order to analyze the proposed fault location technique per-formance, themodel of areal 13.8 kVundergrounddistributionfeeder from Companhia Estadual de Distribuio de Energia Eltri-ca (CEEE-D), Brazil, was simulated with ATP/EMTP [15]. The volt-agessourcewasdescribedasType14ACsource, simulatedat60 Hz with a sample rate of 192 samples per cycle. A modied Fou-rier lter [19] was implemented to remove the DC component andestimate the voltages and currents fundamental components.The analyzed underground feeder, denominated PL1 (East Pri-vate 1) and illustrated by Fig. 4, is composed by 9 load buses andfour independent three-phase branches. The main feeder is com-posedby750MCMandthelateralsbranchesby4/0AWG, bothAluminum tape shieldedcables. PL1 system isalsocomposed bythree-phaseloads,which were modeled as Y-connected constantimpedances with neutral grounding and given by Table 1.Inorder torepresent thedistributednatureof lines shuntcapacitance, each line section was modeled in ATP/EMTP cascadingseveral p-circuits, calculated from Carsons equations [16,20]. ThisA.D. Filomena et al. / Electrical Power and Energy Systems 31 (2009) 489496 493procedureapproximatesthefrequencydependencyeffectofthehyperbolic correction factors [21].Single line-to-ground (A-g) and three-phase faults were simu-lated considering the following scenarios: Seventy-seven different fault locations (covering all system lat-erals and sections). Five different fault resistances: 0, 10, 20, 50, and 100 X. Total: 770 faults.Fault distance estimate error was calculated according to (33)e% jx distjLT100 33where x is the fault distance estimate, dist is the real fault distance,andLTisthetotal linelength, equal to3363metersforthePL1feeder.4. ResultsThe obtained test results are analyzed in this section consider-ingthefollowing aspects:faultresistance,faultdistanceand theshuntadmittancecomponent effect. Also, acomparisonbetweenthe proposed technique and a recently published impedance-basedfault locationformulationfor power distributionsystems[4] isperformed. Theresultspresentedinthispaperrepresentexclu-sivelytheproposedformulationperformance, withoutanyaddi-tional errors, as the ones introduced by measurement devices.4.1. Fault resistance effectIn order to analyze the effect of different fault resistance valueson the fault location formulation performance, simulations consid-ering vedifferent faultresistances havebeen used. Thetestre-sults obtainedfor singleline-to-groundandthree-phasefaultsare presented on Table 2.Analyzing the results, it can be observed an error increase forhigherfaultresistances. However, thefaultdistanceestimateisnot signicantly affected by the fault resistance value. Consideringthe average errors over the 77 simulated fault locations, the differ-ence between the results associated to 0.001 X and 100 X is smal-ler than 0.8% for SLG and 3PH faults.Thus, thehighesterrorswereobtainedwiththehighestfaultresistancetestset, equalto100 X. However, theobtainederrorsshow theefciency androbustness ofthemethodology. Inthesefaultconditions, thefaultlocationschemeyieldedmaximumer-rors smallerthan 2%and 3%for singleline-to-groundandthree-phase faults, respectively. Considering the simulated cases withoutany fault resistance, the proposed formulation obtained negligibleerrors on both analyzed fault types.The fault resistance effect may be explained by the erroneousestimation of the fault current during high resistance faults[22],and is also associated to the so-called reactance error [8]. This ef-fectiseasilyobservedconsideringthetestconditionswithnon-negligible fault resistances values. During solid faults, the currentdivider circuit of the faultedsystemis composedbytheloadSubstationPAL 41 2 3 546789111694 m 763 m95 m295 m360 m245 m200 m114 m 100 m 152 m13.8 kV10750 MCM4/0 AWGFig. 4. PL1 distribution feeder.Table 1Three-phase loads in 1PL feeder.Bus Load [kVA] Bus Load [kVA] Bus Load [kVA]2 500 5 600 9 5003 2500 6 600 10 6004 500 8 500 11 500Table 2Proposed fault location formulation performance.RF [X] Single line-to-ground faults Three-phase faultsAverage error [%] Maximum error [%] Minimum error [%] Average error [%] Maximum error [%] Minimum error [%]0.001 0.019 0.060 0.001 0.096 0.245 0.00210 0.038 0.173 0.005 0.052 0.144 0.00320 0.079 0.303 0.003 0.111 0.32 0.00250 0.282 0.586 0.053 0.379 1.252 0.001100 0.799 1.845 0.010 0.74 2.763 0494 A.D. Filomena et al. / Electrical Power and Energy Systems 31 (2009) 489496impedance and the negligible fault resistance. Therefore, thesourcecurrententirelyfeedsthefaultandthefaultcurrentwillbe close to the rst. Consequently, the associated error to the faultdistanceisnegligible. However, withnon-negligiblefault resis-tance values, this condition cannot be considered. In this condition,the faulted equivalents circuit is also composed by the fault resis-tance. Consequently, inaccuraciesassociatedtotheloadcurrentestimatesprocess become asource oferror tothefault distanceestimate, introduced by the fault current value.4.2. Fault distance effectIn order to characterize the fault distance effect in the proposedfaultlocationformulation, theobtainedtestresultsoverthe77simulated fault points are illustrated by Fig. 5ac considering sin-gle line-to-ground faults.Based on the obtained results, it can be observed that the for-mulation efciency is independent of the fault location. From thesimulatedtest caseswith100-Xfault resistance, illustratedbyFig. 5c, thefaultlocationschemeperformanceshowsthatthereis no signicant variation of the fault distance estimate as the sim-ulated fault distance is modied.However, Fig. 5calsoclearlyillustratestheexistenceof twoareas of the PL1 feeder where the proposed method provides high-er errors. These areas are located close to 2500 and 3000 m fromthe substation terminal and represent the internal faults in lateralbranches between buses 3-4 and 5-6, respectively. The above citedhigher errors are associated to faults located inside these branchesandmaybeexplainedbytheinaccuraciesassociatedtosystemequivalents determination process. The equivalent constantimpedances, whicharecalculatedwiththepre-faultdata, intro-duce inaccuracies regarding to the load current estimate iterativeprocess. Consequently, although the method performance is not di-rectlyaffectedbythefaultdistance, thesystemtopologyaffectsthe fault location schemes performance. According to tests, this ef-fect may be explained by the presence of lateral equivalents alongthe feeder length.4.3. Capacitive effectTheproposedfaultlocationschemeisbasedonthedevelop-ment of a capacitive current compensation procedure. The benetsof thiscompensationareanalyzedthroughthecomparisonbe-tween the proposed techniques results with a recently publishedimpedance-based fault location formulation for power distributionsystems [4]. This technique does not consider the shunt capacitivecomponent in its formulation.Table 3 presents the obtained results from [4] considering PL1simulations. One of the rst aspects related to the comparison be-tween [4] and the proposed formulation isthe effect of the faultresistance value. The 0-X test set demonstrated that the effect ofthecapacitivecurrent compensationis minimizedduringsolidfaults. In this test scenario, both techniques presented similar per-formances for SLG and 3PH faults. This is explained by the smallamplitudeofthecapacitivecurrentwhencomparedtothefaultcurrent.However, for higher fault resistance values, the capacitive cur-rent effect increases. According to Table 3, during these test condi-tions, fault distance estimates obtained by [4] are strongly affectedby the capacitive current. Nevertheless, the proposed formulationis not affected by the capacitive current effect.The analysisof the20-Xthree-phase faults case-test shows amaximumerror obtainedby[4] closeto9%of thelinelength,whichrepresentsapproximately300 m. Inthesamefaultcondi-tion, the proposed extended formulation presented a better perfor-mance, obtaining a maximumerror equal to 0.206%, whichrepresents less than 7 meters of inaccuracy.Considering the 100-X scenario, the average and maximum er-rors obtained from [4] on both analyzed fault types are higher than70% and 79%, respectively. In this case, the capacitive current intro-0.000.020.040.060.08169 1525 2228 2528 2723 2872 2992 3072 3137 3241169 1525 2228 2528 2723 2872 2992 3072 3137 3241169 1525 2228 2528 2723 2872 2992 3072 3137 3241Fault Distance [m]Error [%]0.000.100.200.300.400.50Fault Distance [m]Error [%]0.000.501.001.502.00Fault Distance [m]Error [%]abcFig. 5. Singleline-to-ground(A-g)faultlocationresultsindifferentfaultpointsfrom proposed formulation. (a) RF = 0 X, (b) RF = 20 X, (c) RF = 100 X.Table 3Lee et al. fault location formulation performance.Fault type RF [X] Lee et. al.Average error [%] Maximum error [%]SLG 0.001 0.023 0.06410 2.293 2.52520 7.804 8.82050 30.512 36.645100 70.948 79.4263PH 0.001 0.024 0.04610 2.294 2.23420 7.811 8.80150 30.534 36.492100 71.017 79.565A.D. Filomena et al. / Electrical Power and Energy Systems 31 (2009) 489496 495ducesanaverageerrorhigherthan2354 m, notsuitabletoanyfault location process.Considering the same fault conditions,the proposed extendedformulationobtainederrorscloseto1%and2%foraverageandmaximumerrorsforSLGand3PHfaults. Intheseextremefaultconditions, theaverageinaccuracyintroducedbytheproposedtechnique represents approximately 33 m.5. ConclusionsThis paper proposes anddiscusses anextendedimpedance-based fault location formulation for underground distribution sys-tems. The formulation uses as input data, local voltages and cur-rents, measured at one terminal (substation) and is developed forsingle line-to-ground and three-phase faults. A capacitive currentcompensationprocedure is proposed to consider undergroundcables typical characteristic. Furthermore, the fault locationschemeissuitableforgroundedgenericbalancedorunbalanceddistribution systems with laterals branches and intermediateloads.Test results demonstrate an accurate and robust fault locationtechnique. Themethodperformanceisindependentof thefaultresistanceanddistancevalues. Systemtopology, regardingtheexistence of lateral branches, may affect the fault distance estimateaccuracy level. However, even in the worst simulated test condi-tions, the formulation obtained encouraging results.The comparison with a recently published [4] impedance-basedfault location technique demonstrates the accuracy improvementsobtained by the proposed extension. Since recently proposedimpedance-based[35] fault locationformulations for PDS donot consider lines capacitance, its applicationonundergroundfeedersproducesveryinaccurateresults. Accordingtoobtainedtest results, this inaccuracy is dependant and proportional to thefault resistance value.The proposed formulation based on underground feederscapacitivecurrent compensationovercomesthislimitation. Theformulation provides accurate fault distance estimates, and is suit-able even in higher fault resistance values conditions. Finally, theapplication of the proposed fault locationformulation in realunderground distribution feeders can be easily implemented andmayreducethemaintenancecrewinterventiontime, enhancingsystems restoration.References[1] Takagi T, Yamakoshi Y, Yamaura M, Kondow R, Matsushima T. Development ofa new type fault locator using the one-terminal voltage and current data. IEEETrans Power Apparatus Syst 1982;PAS-101(8):28928.[2] Lina X, Wengb H, Wanga Bin. A generalized method to improve the locationaccuracyof thesingle-endedsampleddataandlumpedparameter modelbased fault locators. 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