A Comparison of Impedance-Based Fault Location Methods for Power Underground Distribution Systems

energies Article A Comparison of Impedance-Based Fault Location Methods for Power Underground Distribution Systems Enrique Personal *, Antonio García, Antonio Parejo, Diego Francisco Larios, Félix Biscarri and Carlos León Department of Electronic Technology, University of Seville, 41011 Seville, Spain; [email protected] (A.G.); [email protected] (A.P.); [email protected] (D.F.L.); [email protected] (F.B.); [email protected] (C.L.) *Correspondence: [email protected]; Tel.: +34-954-559-500 Academic Editor: Gianfranco Chicco Received: 14 October 2016; Accepted: 25 November 2016; Published: 7 December 2016 Abstract: In the last few decades, the Smart Grid paradigm presence has increased within power systems. These new kinds of networks demand new Operations and Planning approaches, following improvements in the quality of service. In this sense, the role of the Distribution Management System, through its Outage Management System, is essential to guarantee the network reliability. This system is responsible for minimizing the consequences arising from a fault event (or network failure). Obviously, knowing where the fault appears is critical for a good reaction of this system. Therefore, several fault location techniques have been proposed. However, most of them provide individual results, associated with specific testbeds, which make the comparison between them difficult. Due to this, a review of fault location methods has been done in this paper, analyzing them for their use on underground distribution lines. Specifically, this study is focused on an impedance-based method because their requirements are in line with the typical instrumentation deployed in distribution networks. This work is completed with an exhaustive analysis of these methods over a PSCADTM X4 implementation of the standard IEEE Node Test Feeder, which truly allows us to consistently compare the results of these location methods and to determine the advantages and drawbacks of each of them. Keywords: power distribution network; power delivery; underground distribution system; fault location 1. Introduction The energy needs and quality requirements of our society have been increasing in the last few decades. These improvements follow the lead of the new Smart Grid (SG) tendencies [1–4]. Moreover, the improvement of the quality of service is one of their main priorities [5,6]. Thus, an essential characteristic of a SG network is its strong Distributed Generation (DG) [7] and Distributed Energy Storage (DES) [8] presence, which together with Demand-Side Management (DSM) [9,10] systems make up microgrids [11] and provide improvements in the network reliability [12]. However, this presence shifts the traditional philosophy of Transmission and Distribution (T&D) systems, adding bidirectional energy flows along them. Unfortunately, as will be seen below, these changes in the flow directions are a significant constraint on network fault analysis, requiring complex systems to guarantee a proper operation in these environments. In this sense, this SG network seeks the Self-Healing [13] concept where Fault Detection, Isolation and Restoration (FDIR) [14] philosophy is applied by the Outage Management System (OMS) to improve the network operation, automatically solving or mitigating the fault consequences. Specifically, a self-healing grid is a system which detects and isolates faults and reconfigures the Energies 2016,9, 1022; doi:10.3390/en9121022 www.mdpi.com/journal/energies Energies 2016,9, 1022 2 of 30 distribution network, reducing the impact of an electrical fault and improving the resiliency of the network. Self-healing is not a new concept. For decades, electric utilities have been implementing automatic reclosers to restore the power supply without human intervention. However, current electric distribution utilities are big and complex systems and commonly operate in a high load factor. In this scenario, self-healing systems need to be more intelligent, acting in real-time to locate the fault and to efficiently reconfigure the topology on SG networks. Thus, as can be seen in Figure 1, when a fault happens in a self-healing power network, it is easy to distinguish two main stages. PM PM PM PM PF PF Alternative Lines Isolated Area PM PM PM PM PF PF Alternative lines Fault detection (disconect line under fault) Fault classif. Fault location Analisys of safe reconf. topologies Network reconfig. (based on distributed automation) Restoration of main service (where possible) customers customers customers customers customers Substation Substation Analysis stage Reaction stage Self-Healing Figure 1. Brief description of the self-healing process. Firstly, the analysis stage is executed. In this stage, the OMS protects the feeder and characterizes the fault (type, position, etc.). Immediately after, in the reaction stage, the OMS reconfigures the affected network, according to the results obtained from the analysis stage, and restores the supply to as many customers as possible. On the one hand, time spent on this second stage (associated with isolation and restoration procedures) directly depends on the automation level of each network. An example of this fact is presented in [15], where the need of a holistic Distribution Automation (DA) integration is discussed. Additionally, a novel approach that integrates protection, control, and monitoring based on DA is also proposed. On the other hand, the analysis stage requires different studies, and it is typically divided into four steps: detection, classification, and location analyses. Obviously, the first step (fault detection) should be fast. It is typically associated with Digital Protective Relays (DPRs), which measure voltage and current and quickly disconnect the line under fault conditions. They are typically based on sequential components [16] and impedance [17] analysis. Additionally, other methods use spectral analyses such as Fast Fourier Transform (FFT) [18] or Discrete Wavelet Transform (DWT) [19]. The purpose of the second step is to extract features and to classify faults using the information captured by DPRs or Digital Fault Recorders (DFRs). Traditionally, these techniques apply direct analysis over symmetrical components [20] or use spectral analysis (such as FFT [18] or DWT [21]) to extract the fault features. These studies are commonly supported by computational intelligence, such as Artificial Neural Networks (ANNs) [22], Fuzzy Logic (FL) [23], Decision Trees (DTs) [24] or Support Vector Machines (SVMs) [25]. Finally, the fault location (third step) is responsible for finding the position where the fault occurs. Obviously, a good estimation of this position is essential for the next stages (e.g., isolate the fault). As a proof of its importance, we found the recently reedited IEEE C37.114 standard [26], where the most relevant techniques are summarized. However, as will be seen below, these techniques are quite conditioned by the network topology [27,28] and especially by the presence of DG. Thus, as was described above, fault location is an essential issue in SG systems. However, this concept has been widely used in transmission networks. Conversely, in distribution networks, they are less common because typically, this network level has complex topologies and limitations in Energies 2016,9, 1022 3 of 30 its instrumentation. Fortunately, in the last few years, this tendency is changing. Following the SG philosophy and supported by Information and Communication Technologies (ICT), the fault location analysis is being extended to distribution networks [29]. Besides, the use of underground lines is more common everyday in urban areas, which poses new challenges to apply some location methods. In this sense, a review of several location methods for distribution networks has been done in this paper. As can be seen below, this work is focused on impedance-based methods because they are more applicable on distribution networks (due to it having less instrumentation requirements). This study compares several location methods highlighting their problems and dependencies, mainly associated with underground scenarios (increasingly common in modern networks, especially in urban environments). Moreover, the main advantage provided in this paper is the use of a standard network as a testbed (unusual in individual studies), allowing us to truly compare coherently amongst these analyzed methods, and providing the ability to compare with other proposals in future work. Therefore, this paper is divided as follows; Section 2shows a brief overview of traditional fault location methods. Following this review, Section 3is focused on the impedance-based fault location methods, analyzing their two main approaches, and describing some relevant examples of them. Section 4describes the testbed characteristics and poses the simulation set for it. A comparative analysis of the studied methods and its dependency on the parameter variations in the simulated cases is shown in Section 5. Finally, conclusions are shown in Section 6. 2. Fault Location Family Methods Overview As discussed above, a fast fault location technique is key to improving the OMS. However, theses techniques directly depend on the measurement characteristics. In this sense, they are divided into three families: based on traveling waves; based on high-frequency measurements; and based on phasor measurements. •Traveling Waves (TW) methods are based on the analysis of propagation time associated with fault effects [30]. This time is measured at one-end (taking advantage of the wave reflections [31]) or multi-end (analyzing the time differences or the delay between them [32]). Unfortunately, this family poses complications under complex topologies (with many reflections). Due to this, it requires the combined use of advanced feature extraction techniques (e.g., DWT combined with Multi-Resolution Analysis, MRA [33]) and classification techniques, the last of them being based on computational intelligence such as Artificial Neural Networks (ANN) [34,35] or Support Vector Machines (SVM) [36] to solve this problem. •High frequency based methods determine the fault position using high frequency information contained within voltage and current measurements. In this sense, it is possible to distinguish two approaches: time domain methods [37–39], or frequency domain methods where MRA [40] is one of their most common tools. Thus, this approach traditionally is also supported by any of the classification techniques, such as ANN [41], FL [42], a combination of both, Adaptive-Network-based Fuzzy Inference System (ANFIS) [43], etc. •Phasor based methods determine the fault position based on the relationship between main harmonic (or phasor) of voltages and currents. It is the most commonly used family in distribution networks because it has the least requirements for their measurements. The most traditional implementations are based on one-end measurements [44–51] and are commonly known as apparent impedance methods. These methods only need a voltage and current measurement (typically registered at line header). Conversely, two-end (or multi-end) methods [52–58] use measurements at several nodes, analyzing the differences or imbalances between them, and using this information in order to locate the fault. Searching in the literature, it is easy to find several comparatives of different fault location techniques. As an example, [59] shows a general overview of the three fault location families cited Energies 2016,9, 1022 4 of 30 above. Other works, such as [60], make comparisons using two representative fault localization methods of different families. Work [61], very cited in the literature, presents a general comparison of classical fault location techniques, classifying them in function of the requirement of each technique. Another classical comparison is [62], that makes an exhaustive comparison of ten fault location methods under different fault parameters. This study focuses only on one-end impedance-based, not being therefore compatible with DG scenarios. Conversely, this DG scenario is considered in [63], comparing methods of different families that combine measurements at different points, highlighting the necessity of synchronization between them to operate consistently. This method has good accuracy. However, it uses techniques that require complex and expensive devices, which may compromise the deployment viability. As can be seen, most of the previous comparisons or explored techniques are not compatible with DG scenarios, or are based on complex devices not so common in underground distribution networks. Moreover, none of these works use a testbed on an underground network. However, as we show below, in the literature, there exist many localization techniques that can be used in underground networks. Therefore, this is the main motivation of the presented work: analyze fault location techniques to evaluate their performance in underground distribution networks, considering both DG and not DG compatible techniques. Additionally, distribution networks are more complex and need more equipment than transmission networks to deploy an infrastructure. This fact hinders the use of expensive instrumentation. Due to this, if we analyze the typical infrastructure of distribution networks, it is easy to note that currently, the typical deployed instrumentation of these facilities can only be used to do low-frequency (or phasor) analysis. Due to this, TW and high-frequency based methods are not considered in this work. In this sense, the third of these studied families (phasor based method) has the lower requirements, being the best solution for this network level. This is why the authors have focused their efforts on this family of methods, as we will see in the next section. Therefore, the present paper proposes a revision of phasor based methods focusing on underground distribution networks. The main advantage of this work is to study the advantage and constrains of different methods under a standard underground testbed, beyond the individual comparisons made by each author based on different specific networks, and which do not allow us to compare their results consistently. 3. Impedance-Based Fault Location Methods As seen earlier, this family of methods is based on equivalent impedance calculation from phasor information (amplitude and angle of the main harmonic) of voltage and current. In this sense, their two variants—one-end and multi-end method—have been analyzed. 3.1. One-End Methods One-end impedance–based measurement techniques consist of estimating the equivalent fault impedance through the voltage and current measurements held just at one point (typically at line header, see Figure 2). d I0,f V0,f IZ d·ZL(1-d)·ZL Rf If Z0,f ZLd Figure 2. Simplified line model for general one-end methods. Energies 2016,9, 1022 5 of 30 Additionally, this impedance is combined with a distribution line model (depending on topology, line impedance, etc.) and loads model, which allows us to estimate how these voltages and currents are propagated along them, and the main objective of these methods being to estimate d in the complex Equation (1). V0,f=d·ZL·I0,f+Rf·If(1) This technique’s main advantage is to simplify the measurement infrastructure. However it poses some drawbacks. The most common of them is the multiple fault location estimation problem, when a solution of dcorresponds with different network points (each one in a different branch). A traditional solution for this problem is to combine these fault location methods with additional instrumentation [64,65], or a complementary analysis of signal information (e.g., voltage sag, currents fluctuation, etc.). This complementary analysis uses common base-knowledge classifiers to distinguish the real affected zone (e.g., Learning Algorithm for Multivariate Data Analysis [66], ANN [67], k-Nearest Neighbors [68], etc.). Another typical problem of these location methods is their high dependency on the fault resistance (Rf), which drastically increases the position error when it is not small. However, the worst problem of this set of methods appears in DG scenarios, where they are not applicable. This is because one measurement point (main characteristic of this group of methods) is not enough to characterize a fault model based on impedance, when in several points, there is energy being injected. In this case, the equivalent impedance estimated at one point is probably incorrect. An example of a basic one-end impedance-based fault location method is [44]. This method proposes a fault location method for simple transmission lines using symmetrical components analysis and dismissing the load. Reference [45] completes this approach adding load effects. Both ideas are extended by [46,47] to more complex topologies. In the same sense, for three-phase component analysis, [48,49] use direct net analysis of each phase in a simple line to fault location. Reference [50] extends this approach to typical distribution feeder topologies and [51] completes its formulation for underground networks. Specifically, for this paper, three traditional one-end methods ([44,50,51]) have been selected as relevant examples of these families. The first of them, [44] has been selected as classic one-end reference, providing an excellent relationship between its complexity and its results (as is commented in [62]). Reference [50] represents a classic general one-end method. Finally, [51] was selected to highlight the benefits of using a method which takes into account the characteristics of underground networks. In general, the chosen methods use a short line model which is accepted for distribution networks (usually with lengths less than 15 km). In this sense, the three chosen methods will be described briefly in the next sections: 3.1.1. Reactive Component Method Reactive component [44] approach is a classical fault localization technique, which is highlighted by its simplicity. It is based on the supposition that fault current is higher than loads currents, and hence neglecting the effect of them (see Equation (2)). This assumption allows this method to rewrite Equation (1), and to estimate the equivalent impedance (Z0,f) as a measured voltage (V0,f) and current (I0,f) ratio (see Equation (3)). If≃I0,f(2) Z0,f≃V0,f I0,f =d·ZL+Rf(3) In this sense, assuming that Rfis purely resistive, it is possible to estimate the normalized fault position (d) through analysis of the imaginary term of the complex equation (see Equation (4)). d≃Im[Z0,f] Im[ZL]=Im[V0,f/I0,f] Im[ZL](4) Energies 2016,9, 1022 6 of 30 This approach greatly simplifies the fault position calculation. Nevertheless, for high values of Rf, it may produce relevant miscalculations. Additionally, this method also keeps other typical one-end problems as the multiple fault location estimation, requiring the techniques discussed above to solve them. 3.1.2. Salim et al. Method Salim et al. [50] method is really an extension of a simple fault method, which is based on an iterative direct network analysis [48]. This extension is focused on three aspects: different fault configurations, radial topologies and variable loads. Specifically for the first of these aspects, it poses four scenarios (see Figure 3). Rf If,a ZLd d ILda,b,c IN,aIM,a IM,b IM,c VM,c M VM,b VM,a N IN,b IN,c VF,a F (a) “l-g” simple fault at phase a ZLd d ILda,b,c IN,aIM,a IM,b IM,c VM,c M VM,b VM,a N IN,b IN,c If,a VF,a F If,b VF,b Rf (b) “l-l” fault between phases aand b ZLd d ILda,b,c IN,aIM,a IM,b IM,c VM,c M VM,b VM,a N IN,b IN,c If,a VF,a F Rfa If,b VF,b R� Rfab (c) “l-l-g” earthed fault at phases aand b ZLd d ILda,b,c IN,aIM,a IM,b IM,c VM,c M VM,b VM,a N IN,b IN,c If,a VF,a F Rfa If,b VF,b R� Zfabc Rfc If,c I3Ф VF,c (d) “l-l-l-g” three-phase fault Figure 3. Simplified model of a faulted section in the Salim et al. method [50]. In this sense, this method proposes using a matrix notation to estimate the fault resistance (Rf x) and fault position din a generic line section (between Mand Nnodes) for a simple fault under phase x(see Equation (5) and an example in Figure 3a). "d Rf x #=1 M1,x·Im[If,x]−M2,x·Re[If,x]·"Im[If,x]−Re[If,x] −M2,xM1,x#·"Re[VM,x] Im[VM,x]#(5) Additionally, VM,xis the measured voltage at Mnode and three-phase line x(line under fault). If,xis the fault current. Constants M1,xand M2,xare defined by Equations (6) and (7) respectively, Energies 2016,9, 1022 7 of 30 where IM,xis the input current of the section M-N(in phase x) and Zx,kis the impedance vector of affected section, between xand kphases. M1,x=∑ k=a,b,cRe[ZL x,k]·Re[IM,k]−Im[ZL x,k]·Im[IM,k](6) M2,x=∑ k=a,b,cRe[ZL x,k]·Im[IM,k] + Im[ZL x,k]·Re[IM,k](7) Based on the simple fault analysis, “l-l” fault between xand yphases (see example in Figure 3b) is resolved through Equation (8), and constants M3and M4(Equations (9) and (10) respectively). "d Rf#="M3Re[If,x] M4Im[If,x]#−1 ·"Re[VM,x]−Re[VM,y] Im[VM,x]−Im[VM,y]#(8) M3=∑ k=a,b,chRe[ZL x,k]−Re[ZL y,k]·Re[IM,k]−Im[ZL x,k]−Im[ZL y,k]·Im[IM,k]i(9) M4=∑ k=a,b,chRe[ZL x,k]−Re[ZL y,k]·Im[IM,k] + Im[ZL x,k]−Im[ZL y,k]·Re[IM,k]i(10) Other cases under “l-l-g” earthed faults between xand yphases (see example in Figure 3c) are solved through Equation (11). Where Rf x and Rf y represent the resistances connected to each affected line, and Rf xy is the ground resistance. Constants M1,x,M2,x,M1,yand M2,yare calculated through Equations (6) and (7).      d Rf x Rf y Rf xy      =     M1,xRe[If,x]0 Re[If,x] + Re[If,y] M2,xIm[If,x]0 Im[If,x] + Im[If,y] M1,y0 Re[If,y]Re[If,x] + Re[If,y] M2,y0 Im[If,y]Im[If,x] + Im[If,y]      −1 ·     Re[VM,x] Im[VM,x] Re[VM,y] Im[VM,y]      (11) Finally, three-phase faults (see example in Figure 3c) are solved through Equation (12). Constants M1,a,M2,a,M1,b,M2,b,M1,nand M2,b, as in the previous case, are also calculated through Equations (6) and (7).          d Rf a Rf b Rf c Rf abc Xf abc          =          M1,aRe[If,a]0 0 Re[I3Φ]−Im[I3Φ] M2,aIm[If,a]0 0 Im[I3Φ]Re[I3Φ] M1,b0 Re[If,b]0 Re[I3Φ]−Im[I3Φ] M2,b0 Im[If,b]0 Im[I3Φ]Re[I3Φ] M1,c0 0 Re[If,c]Re[I3Φ]−Im[I3Φ] M2,c0 0 Im[If,c]Im[I3Φ]Re[I3Φ]          −1 ·          Re[VM,a] Im[VM,a] Re[VM,b] Im[VM,b] Re[VM,c] Im[VM,c]          I3Φ=If,a+If,b+If,cZf abc =Rf abc +j·Xf abc (12) Another extension of this method defines a procedure to apply it over radial topologies. In this way, this method proposes dividing the analysis into equivalent circuits (as many end sections as the line has). This approach names each equivalent circuit as Possible Power Flow Paths (PPFPs). Each PPFP is obtained by grouping in each bifurcation node the load and line section which are not directly related to the PPFP. Once this is done, this location method is applied (section by section) over each PPFP, obtaining each possible location associated with a fault. Beside, this method compensates for load fluctuation through a load correction factor which is estimated by a prefault analysis. Unfortunately, this method does not correct typical errors associated with one-end location methods either. The PPFP approach is only a procedure to estimate all possible fault points. Energies 2016,9, 1022 8 of 30 However, one still needs one of the systems discussed above to determine which of them is affected. Furthermore, the location errors with high values of fault resistance are also present. 3.1.3. Filomena et al. Method Following the same idea of the previous method, Filomena et al. [51] approach extends its philosophy to underground networks, compensating the typical capacitive currents associated with this line type. This study is only focused on two typical fault scenarios (see Figure 4); simple (“l-g”) or three-phase (“l-l-l-g”). This is due to the fact that most underground lines are designed as a group of individual underground cables, each one with a metallic sheath. This sheath of each cable and their earth connection make (in this topology) only both fault cases (l-gor l-l-l-g) possible. ZLd d ILd,aIM,a IM,b IM,c VM,c M VM,b VM,a N VF,a F IM,a IM,b IM,c [YM]abc [YN]abc Rfa If,a ICap ILd,b ILd,c (a) “l-g” simple fault at aphase ZLd d ILd,a IM,a IM,b IM,c VM,c M,b VM,a Ld,b ILd,c If,a VF,a F Rfa If,b VF,b Rfb Rfc If,c VF,c IM,a IM,b IM,c [YM]abc [YN]abc ICap M V N I (b) “l-l-l-g” three-phase fault Figure 4. Simplified model of an underground faulted section in the Filomena et al. method [51]. In order to compensate the capacitive currents, this method uses a π-model where these effects are characterized by a distributed admittance diagonal matrices (YMand YN). YM=YN=YL/2 =d L·   YL,a0 0 0YL,b0 0 0 YL,c   (13) These admittance matrices allow this method to estimate their capacitive current, introducing them in the iterative calculation through the matrix Equations (14)–(16): ICap=[YM]·[IM](14) I0 M=[IM]−ICap(15) hIfi=[IM]−[ILd]−ICap(16) Thus, in each iteration, the fault position (d) is obtained through the Equation (5) for a simple fault (see Figure 4a) or the Equation (17) for a three-phase fault (see Figure 4b).      d Rf a Rf b Rf c      =     M1,aRe[If,a]0 0 M2,aIm[If,a]0 0 M1,b0 Re[If,b]0 M1,c0 0 Re[If,c]      −1 ·     Re[VM,a] Im[VM,a] Re[VM,b] Re[VM,c]      (17) However, in both cases, the constants M1,xans Ms,xare modified following the next expressions: M1,x=∑ k=a,b,cRe[ZL x,k]·Re[I0 M,k]−Im[ZL x,k]·Im[I0 M,k](18) Energies 2016,9, 1022 9 of 30 M2,x=∑ k=a,b,cRe[ZL x,k]·Im[I0 M,k] + Im[ZL x,k]·Re[I0 M,k](19) 3.2. Multi-End Methods The two-end (or multi-end) impedance–based measurement techniques also use voltage and current measurements at two (or more) points (see Figure 5). d Rf VXVY IXIY If (1-d)·ZLd·ZL Vf Figure 5. Simplified line model for general multi-end methods. These methods use the fault voltage (Vf) as common elements between two circuits (see Equation (20)). Due to this, it is possible to simplify this term (or what is the same, Rfvalue influence), resulting Equation (21). VX=d·ZL·IX+Vf;VY= (1−d)·ZL·IY+Vf(20) VX−d·ZL·IX=VY−(1−d)·ZL·IY(21) Therefore, the value of Rfis not critical as in one-end methods. In the same way, multi-end method philosophy, which measures at several points, makes these methods compatible with DG scenarios and bidirectional flows. This compatibility is due to the fact that these methods model the impedance of line segments, obviating the possible power sources outside of it. Obviously, at the minimum, a measurement point is necessary at each generation or consumption spot. This philosophy also prevents the multiple position estimation, knowing the input and output points affected. All these characteristics make multi-end methods a better option than one-end. However, they have the disadvantage of requiring higher deployment. Additionally, this deployment consists of different voltage and current sensors which require a strict time synchronization to operate consistently with their measurements. Specifically, a lack or attack on this synchronization could seriously compromise its operation [69]. This approach follows the Wide-Area Monitoring, Protection, and Control (WAMPAC) [70] philosophy which poses the deployment of Phasor Measurement Units (PMUs) [71] to know the network status at any time, including the position of a fault when it occurs. However, this constraint significantly increases the price, conditioning the economic viability for their deployment. A good example of multi-end impedance-based fault location methods is [52], which poses the basic idea of these methods over a simple line. Reference [53] extends this approach to a simple line with several sections, and [54,55] extend it to multi-section non-homogeneous lines. Additionally, an alternative approach is proposed by Jiang [56], which studies all nodes comparing them with a normal situation, identifying the affected section with this difference. Focused on underground networks, [57] proposes taking advantage of cable characteristics. It estimates the fault position analogizing the sheath circuits and using only current measurements. Specifically, in this paper, as was done for one-end methods, three multi-end methods ([52,56,57]) have been selected as relevant examples of this family. The first of them has been chosen due to it being a classic reference. The second option, [56] is a multi-end general method based on the new WAMPAC philosophy. And finally, [57] taking advantage of underground topologies to improve its location results. In this sense, the three chosen methods will be described briefly in the next sections. Energies 2016,9, 1022 16 of 30 rejects incoherent results when they are outside of the section (d<0 or d>1). This analysis is shown in Figure 11a. application rate (%) 0 20 40 60 80 100 30.31% 24.36% 24.88% 99.13% 92.99% 99.85% Reactive Comp. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] (a) Application rate location error (%) 0 20 40 60 80 Reactive Comp. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] (b) Location error Figure 11. Global analysis results. In Figure 11a, it is easy to note that one-end methods (the blue ones) have a significantly lower application rate than multi-end methods (the green ones). This fact is mainly caused because these methods fail when the fault appears in segments away from the network header (measurement point). Thus, this problem slightly decreases in the Reactive Component method. This is due to the fact that this method compensates its inability in three-phase faults with its greater applicability under low value load cases. As opposed, multi-end methods provide excellent application rates. However, this comparison must take into account that one-end methods require less information (only measurements at the network header), so that they are at a disadvantage to get a result. Thus, the Personal et al. method highlights with its highest applicability index, only with a 0.15% of inability cases. This small percentage is associated with three-phase faults and lowers sheath-to-ground resistance values under which the sheath currents are insufficient to apply this method. In the second stage, the methods’ errors in the estimated position (d) are compared amongst them (see Figure 11b). These errors are represented by box-and-whisker diagrams, it is possible to note how the error dispersion of Jiang et al. and Personal et al. methods are significantly lower than others. Besides, Filomena et al. is the best option of studied one-end methods. This fact is logical because this method is aimed at underground networks. However, many outliers can be observed in this figure. These values mainly correspond to sets of cases where each analyzed method has trouble. Specifically, this fact will be easily noted in the dependency study (Sections 5.1–5.7), where parameters such as line-to-sheath resistance, which has a high error when it increases, concentrates many cases on outlier area, especially for one-end methods. As a summary, Table 3shows all of this information, reflecting both studies numerically. In this table, average, maximum and standard deviation of error values can be compared amongst all studied methods. Thus, after analyzing the results of the complete data set, the following sections will focus on the dependence analysis with the different parameters covered by the simulated cases. Table 3. Global result summary. Method Application Outliers Error (%) Rate (%) Rate (%) Maximum Average σ Reactive comp. [44] 30.3112 6.22043 89.9846 18.2264 1.8242 Salim et al. [50] 24.3634 12.4811 89.9477 10.0512 1.5182 Filomena et al. [51] 24.8753 11.9599 89.8714 9.67601 1.41644 Girgis et al. [52] 99.1276 14.778 89.3025 7.40104 1.52542 Jiang et al. [56] 92.9949 12.7302 25.6445 0.275457 0.106662 Personal et al. [57] 99.8481 13.2406 5.10298 0.00536093 0.00526791 Energies 2016,9, 1022 17 of 30 5.1. Fault Type Analysis In this section, a fault type analysis has been selected as the first study. Following the philosophy of the global analysis, it has also been divided into two stages: an applicability study (see Figure 12a) and an error study (see Figure 12b). Additionally, numerical results of both stages are summarized in Table A1 (in the Appendix section). application rate (%) 0 20 40 60 80 100 Reactive Com p. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] a-g b-g c-g a-b-c-g (a) Application rate location error (%) 0 5 10 15 20 25 a-b-c-g c-g b-g a-g React. Comp. Salim Filomena Girgis Jiang Personal (b) Location average error Figure 12. Fault type analysis. From this study, it is easy to note the lack of information for three-phase fault in the Reactive Component method. It is due to its inability to estimate a position under this situation. Thus, a reduction in the effectiveness in some of these methods (on the application rate in Jiang et al., and on the location error in Salim et al. and Filomena et al.) for single fault in line ccases is detected. However, this error is not an effect of the fault type. It is due to the fact that this line is unbalanced and has a higher load than others. In summary, based on the obtained data, it could be argued that the studied methods do not have a strong dependency on the type of fault. 5.2. Insertion Angle Analysis This analysis evaluates the dependency on the instant when the fault occurs, sweeping values of 0◦, 90◦, 180◦and 270◦. In this sense, Figure 13a shows an applicability study and Figure 13b shows an error study for each method. Additionally, numerical results are summarized in Table A2 (in the Appendix section). application rate (%) 0 20 40 60 80 100 Reactive Com p. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] 0o 90o 180o 270o (a) Application rate location error (%) 0 5 10 15 20 25 270o 180o 90o 0o React. Comp. Salim Filomena Girgis Jiang Personal (b) Location average error Figure 13. Insertion angle analysis. From this study, it is possible to determine that the insertion angle is not a critical parameter for the estimation of fault position in analyzed methods. Energies 2016,9, 1022 18 of 30 5.3. Normalized Position Analysis The next analyzed parameter is the normalized position (d) within the line section. In this case, the studied cases sweep the values 0.1, 0.3, 0.5, 0.7 and 0.9. From this analysis, Figure 14 is generated, showing the application rates and location errors for each method. Additionally, Table A3 (in the Appendix section) summarizes their numerical results. application rate (%) 0 20 40 60 80 100 Reactive Com p. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] 0.1 0.3 0.5 0.7 0.9 (a) Application rate location error (%) 0 5 10 15 20 25 0.9 0.7 0.5 0.3 0.1 React. Comp. Salim Filomena Girgis Jiang Personal (b) Location average error Figure 14. Normalized position analysis. From this study, it is possible to note that the Reactive Component method performs better in the central portion of the line sections. Salim et al., Filomena et al. and Girgis et al. behavior methods worsen by the increase of d. The Jiang et al. method keeps the error retaining its approximately constant value, but worsens its application rate (about 10%) by moving away from the center of the line sections. Conversely, the Personal et al. method shows a similar behavior for the entire analysis. 5.4. Affected Fault Section Analysis In the same direction as the previous section, this study analyzes the behavior of each method result related to the fault position. However, in this case, it is associated with different line sections (see network topology, Figure 10). Specifically, this parameter has been swept for sections 1, 5, 23, 28, 34, 12, 19, 21 and 14 (in order of distance), their results being shown in Figure 15. Thus, numerical results are summarized in Table A4 (in the Appendix section). application rate (%) 0 20 40 60 80 100 Reactive Com p. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] Sec. 01 Sec. 05 Sec. 12 Sec. 14 Sec. 19 Sec. 21 Sec. 23 Sec. 28 Sec. 34 (a) Application rate location error (%) 0 20 40 60 80 100 Sec. 34 Sec. 28 Sec. 23 Sec. 21 Sec. 19 Sec. 14 Sec. 12 Sec. 05 Sec. 01 React. Comp. Salim Filomena Girgis Jiang Personal (b) Location average error Figure 15. Affected fault section analysis. In this Figure, it is easy to note that the methods of Salim et al. and Filomena et al. exhibit a bad performance, if we turn away from the measuring point (obtaining acceptable results only for the three closest segments). The Reactive Component method is also affected by this parameter, but to a lesser degree. Conversely, as was expected, multi-end methods are not affected by this parameter, because their estimation is directly based on the measurements at both sides of each segment. Energies 2016,9, 1022 19 of 30 5.5. Line-To-Sheath Resistance Analysis A typical trouble in fault location methods is their dependency on the fault resistance value. In this work, in order to achieve better characterization of the underground network behavior, this resistance is divided into two parts. Specifically, dependency related to the resistance between the conductor and cable sheath in a fault situation will be analyzed in this section. This line-to-sheath resistance (RLS,x) has been swept for 0.01, 0.1, 0.5, 1, 5, 10 and 100 Ωvalues; their results being shown in Figure 16 and their numerical results in Table A5 (in the Appendix section). application rate (%) 0 20 40 60 80 100 Reactive Com p. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] 0.01Ω 0.1Ω 0.5Ω 1Ω 5Ω 10Ω 100Ω (a) Application rate location error (%) 0 10 20 30 40 50 60 100Ω 10Ω 5Ω 1Ω 0.5Ω 0.1Ω 0.01Ω React. Comp. Salim Filomena Girgis Jiang Personal (b) Location average error Figure 16. Line-to-sheath resistance analysis. In this sense, it is easy to note in Figure 16 that the applicability of one-end methods decreases dramatically for high values of this resistance. Additionally, the location error of these methods also gets worse, as was commented in Section 3.1. Conversely, multi-end methods keep their behavior approximately constant, with only Girgis et al. showing an increase in the error for very high values of this parameter. 5.6. Sheath-To-Ground Resistance Analysis This section analyzes the second part of the fault resistance model. It characterizes the resistance which appears between the cable sheath and earth potential in a fault event. As in the previous section, this sheath-to-ground resistance (RF,x) has been swept for 0.01, 0.1, 0.5, 1, 5, 10 and 100 Ω values; their results being shown in Figure 17 and their numerical results in Table A6 (in the Appendix section). application rate (%) 0 20 40 60 80 100 Reactive Com p. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] 0.01Ω 0.1Ω 0.5Ω 1Ω 5Ω 10Ω 100Ω (a) Application rate location error (%) 0 5 10 15 20 25 100Ω 10Ω 5Ω 1Ω 0.5Ω 0.1Ω 0.01Ω React. Comp. Salim Filomena Girgis Jiang Personal (b) Location average error Figure 17. Sheath-to-ground resistance analysis. As can be seen in both Figures, it is not only the behavior of the six studied methods that is affected by this parameter. This fact can be explained because the sheath acts as a better way (with less resistance) for the fault current than ground potential, only appreciating small variations for very small values of this parameter. Energies 2016,9, 1022 20 of 30 5.7. Applied Load Percentages Analysis The last study is related to the network load level. For this study, several percentages of a load factor have been applied over the network. Specifically, this parameter has been swept for 0%, 25%, 50%, 75% and 100% of the load associated with this network. Following the philosophy of previous sections, it has also been divided into two stages: an applicability study (see Figure 18a) and an error study (see Figure 18b). Additionally, numerical results of both stages are summarized in Table A7 (in the Appendix section). application rate (%) 0 20 40 60 80 100 Reactive Com p. [43] Salim [49] Filomena [50] Girgis [51] Jiang [55] Personal [56] 0% 25% 50% 75% 100% (a) Application rate location error (%) 0 5 10 15 20 25 30 100% 75% 50% 25% 0% React. Comp. Salim Filomena Girgis Jiang Personal (b) Location average error Figure 18. Applied load percentage analysis. In this sense, on the one hand, the Reactive Component method is highlighted by its strong dependency on this parameter. This fact occurs because, as already discussed above, this method assumes that overall registered current is completely due to the fault event (dismissing the load effects). Obviously, it operates significantly worse when this load current is not negligible. Thus, the behavior of the other one-end methods remains approximately stable under changes in this parameter. In the other one-end methods, their behavior remains approximately stable with this parameter. On the other hand, regarding the multi-end methods, Jiang et al. and Personal et al. show a fairly stable behavior. This fact is logical, due to their multi-end philosophy (with measurements at both ends of the line section). However, the Girgis et al. method does not have this characteristic, increasing its error with this parameter. 6. Conclusions Throughout this paper, the needs for better strategies on operation and planning tasks are highlighted as a key factor in SG networks. In this sense, fault location is a cornerstone of the OMS, allowing this system to identify the fault position and mitigate its consequences. In this paper, a comparative review of different fault location techniques has been done. Specifically, this study is focused on impedance-based methods because they are more in line with typical instrumentation deployed in the distribution systems, distinguishing two sets of methods. On the one had, one-end methods have been analyzed, the main advantage being less deployment needs (only one measuring point). However, they have higher errors than the second set of methods, and have the significant drawback of not being compatible with DG scenarios. Reactive Component, Salim et al. and Filomena et al. methods have been chosen as relevant examples for their evaluation. On the other hand, multi-end methods have also been studied. This set provides better results than one-end methods. However, this fact mainly occurs because they are supported by a greater measurement infrastructure, which is significantly more expensive than one-end method deployments. Additionally, multi-end methods are compatible with DG scenarios, thus being a perfect solution for SG networks. For this second set, the methods of Girgis et al., Jiang et al. and Personal et al. have been the chosen methods as relevant examples for their evaluation. In this sense, these six chosen methods have been widely tested, studying their dependencies under different conditions. All of these studies have been based on an implementation over Energies 2016,9, 1022 21 of 30 PSCADTM of a standard test network (the IEEE 37 Node Test Feeder). The use of a common testbed has allowed this study to coherently compare the different method results, beyond typical individual analyses in these methods. Thus, for these studies, the multi-end methods of Personal et al. and Jiang et al. are the best options due to their excellent results. However, Filomena et al. is the best option of the analyzed one-end method, being a good option for underground networks where a multi-end deployment is not possible. Acknowledgments: The authors would like to thank “Ministerio de Educación, Cultura y Deporte” of Spain for its funding through FPU2010 scholarship program. Also, authors would like to thank “Ministerio de Economía y Competitividad” of Spain for funding this work through the research projects reference TEC2013-40767-R. Author Contributions: The authors contributed equally to the work. Conflicts of Interest: The authors declare no conflict of interest. Appendix A. Summary Tables of Dependency Analysis Table A1. Fault type analysis. Method Parameter Application Error (%) Fault Type Rate (%) Maximum Average σ a-g 41.03 89.96 17.53 1.85 Reactive b-g 38.91 89.98 18.33 1.82 component [44] c-g 41.30 89.84 18.82 1.80 a-b-c-g 0.00 - - - Salim et al. [50] a-g 24.61 89.07 9.59 1.46 b-g 24.54 89.95 10.81 1.59 c-g 23.17 88.34 12.65 1.62 a-b-c-g 25.13 84.51 7.37 1.34 Filomena et al. [51] a-g 24.97 89.46 9.13 1.36 b-g 24.88 89.13 9.95 1.41 c-g 23.64 89.87 12.11 1.53 a-b-c-g 26.01 89.31 7.73 1.33 Girgis et al. [52] a-g 98.88 88.33 7.94 1.57 b-g 98.99 89.30 8.13 1.60 c-g 98.64 88.56 7.92 1.56 a-b-c-g 100.00 86.21 5.64 1.35 Jiang et al. [56] a-g 96.93 20.04 0.25 7.82 ×10−2 b-g 94.62 23.43 0.28 7.67 ×10−2 c-g 80.43 25.64 0.53 0.19 a-b-c-g 100.00 6.67 9.27 ×10−23.50 ×10−2 Personal et al. [57] a-g 100.00 0.34 3.20 ×10−31.20 ×10−3 b-g 100.00 0.51 3.31 ×10−31.56 ×10−3 c-g 100.00 0.98 8.19 ×10−33.32 ×10−3 a-b-c-g 99.39 5.10 6.76 ×10−39.81 ×10−3 Energies 2016,9, 1022 22 of 30 Table A2. Insertion angle analysis. Method Parameter Application Error (%) Insertion Angle Rate (%) Maximum Average σ 0◦29.18 89.98 18.95 1.92 Reactive 90◦31.98 89.49 16.96 1.67 component [44] 180◦28.61 89.97 19.46 1.93 270◦31.48 89.96 17.72 1.77 Salim et al. [50] 0◦24.10 88.71 10.75 1.59 90◦24.40 89.07 10.13 1.45 180◦24.20 88.34 10.05 1.54 270◦24.75 89.95 9.30 1.49 Filomena et al. [51] 0◦24.63 89.87 10.26 1.47 90◦24.94 83.50 9.75 1.34 180◦24.71 84.30 9.70 1.44 270◦25.23 89.46 9.01 1.41 Girgis et al. [52] 0◦99.12 89.30 7.41 1.53 90◦99.18 89.30 7.39 1.53 180◦99.03 89.29 7.41 1.52 270◦99.18 89.30 7.40 1.53 Jiang et al. [56] 0◦90.78 24.86 0.30 0.12 90◦96.50 23.43 0.24 8.05 ×10−2 180◦90.96 25.64 0.30 0.13 270◦93.75 20.92 0.27 9.15 ×10−2 Personal et al. [57] 0◦99.85 5.10 6.05 ×10−36.44 ×10−3 90◦99.84 0.98 3.97 ×10−32.06 ×10−3 180◦99.85 5.05 5.99 ×10−36.38 ×10−3 270◦99.85 3.84 5.44 ×10−34.96 ×10−3 Table A3. Normalized position analysis. Method Parameter Application Error (%) d Rate (%) Maximum Average σ 0.1 29.30 89.98 20.22 2.25 Reactive 0.3 32.55 69.99 17.39 1.65 component [44]0.5 33.19 49.98 16.84 1.37 0.7 31.76 69.87 16.90 1.53 0.9 24.76 89.72 20.53 2.27 Salim et al. [50] 0.1 18.36 88.25 4.32 1.14 0.3 22.89 67.41 6.47 0.87 0.5 26.00 50.00 10.67 1.37 0.7 27.00 69.52 12.61 1.66 0.9 27.56 89.95 13.76 1.92 Energies 2016,9, 1022 23 of 30 Table A3. Cont. Method Parameter Application Error (%) d Rate (%) Maximum Average σ Filomena et al. [51] 0.1 19.01 84.82 3.87 0.89 0.3 23.57 69.96 6.76 0.91 0.5 26.76 49.99 10.78 1.35 0.7 27.32 69.93 11.92 1.55 0.9 27.72 89.87 12.86 1.78 Girgis et al. [52] 0.1 100.00 17.47 1.51 0.25 0.3 100.00 29.65 4.47 0.76 0.5 100.00 49.55 7.45 1.27 0.7 100.00 69.43 10.44 1.78 0.9 95.64 89.30 13.40 2.34 Jiang et al. [56] 0.1 88.62 23.43 0.15 7.10 ×10−2 0.3 94.99 18.85 0.22 8.60 ×10−2 0.5 97.05 25.64 0.31 0.12 0.7 95.37 23.94 0.37 0.14 0.9 88.95 19.77 0.32 0.1 Personal et al. [57] 0.1 99.89 5.10 8.81 ×10−39.61 ×10−3 0.3 99.84 1.90 5.75 ×10−34.29 ×10−3 0.5 99.79 0.58 2.53 ×10−31.31 ×10−3 0.7 99.84 1.31 3.88 ×10−32.40 ×10−3 0.9 99.89 2.41 5.83 ×10−34.49 ×10−3 Table A4. Affected fault section analysis. Method Parameter Application Error (%) Section Rate (%) Maximum Average σ Section 01 36.71 87.97 12.19 1.54 Section 05 40.01 72.82 11.60 1.44 Section 12 31.20 89.96 20.16 1.92 Reactive Section 14 18.46 89.91 25.41 1.71 component [44]Section 19 22.86 89.97 24.01 2.05 Section 21 26.40 89.98 25.58 2.17 Section 23 39.44 89.69 13.69 1.56 Section 28 28.12 89.33 21.77 1.80 Section 34 29.60 89.84 19.83 1.69 Salim et al. [50] Section 01 75.03 64.08 8.90 1.36 Section 05 74.43 83.02 9.91 1.49 Section 12 0.00 - - - Section 14 0.00 - - - Section 19 0.00 - - - Section 21 0.00 - - - Section 23 68.91 89.95 10.62 1.53 Section 28 0.50 88.25 77.99 1.12 Section 34 0.39 78.73 69.18 0.59 Energies 2016,9, 1022 24 of 30 Table A4. Cont. Method Parameter Application Error (%) Section Rate (%) Maximum Average σ Filomena et al. [51] Section 01 76.40 57.99 8.59 1.28 Section 05 75.91 76.11 9.29 1.34 Section 12 0.31 75.05 59.66 1.32 Section 14 0.00 - - - Section 19 0.00 - - - Section 21 0.00 - - - Section 23 69.97 89.87 10.62 1.52 Section 28 7.14 ×10−284.19 80.97 0.31 Section 34 1.21 89.31 30.66 2.37 Girgis et al. [52] Section 01 99.93 88.87 19.80 2.25 Section 05 99.85 89.30 11.55 1.91 Section 12 100.00 55.25 2.52 0.73 Section 14 100.00 81.66 5.67 1.35 Section 19 100.00 74.39 3.97 1.07 Section 21 99.86 48.31 2.22 0.60 Section 23 97.40 84.16 7.86 1.50 Section 28 95.11 87.09 9.92 1.68 Section 34 100.00 63.83 3.23 0.85 Jiang et al. [56] Section 01 97.73 24.72 1.05 0.21 Section 05 94.61 25.64 0.42 0.15 Section 12 92.57 5.17 0.12 2.98 ×10−2 Section 14 92.90 6.71 0.12 4.03 ×10−2 Section 19 91.68 3.26 6.06 ×10−21.63 ×10−2 Section 21 91.94 18.54 0.13 6.95 ×10−2 Section 23 91.85 23.43 0.17 7.02 ×10−2 Section 28 92.53 20.04 0.19 8.76 ×10−2 Section 34 91.14 17.96 0.17 7.25 ×10−2 Personal et al. [57] Section 01 99.20 2.37 1.59 ×10−26.68 ×10−3 Section 05 99.81 5.10 1.53 ×10−21.35 ×10−2 Section 12 99.94 9.30 ×10−26.88 ×10−42.57 ×10−4 Section 14 99.98 0.30 1.72 ×10−37.11 ×10−4 Section 19 99.96 1.31 3.99 ×10−32.28 ×10−3 Section 21 99.98 0.45 1.94 ×10−39.38 ×10−4 Section 23 99.88 0.77 4.58 ×10−32.49 ×10−3 Section 28 99.94 1.36 3.19 ×10−32.37 ×10−3 Section 34 99.94 0.57 9.68 ×10−47.46 ×10−4 Energies 2016,9, 1022 25 of 30 Table A5. Line-to-sheath resistance analysis. Method Parameter Application Error (%) RLS,xrate (%) Maximum Average σ 0.01 Ω53.73 89.91 15.15 1.69 0.1 Ω53.30 89.69 15.88 1.73 Reactive 0.5 Ω50.98 89.97 17.83 1.66 component [44]1Ω38.47 89.98 23.98 2.14 5Ω11.70 81.02 15.91 1.20 10 Ω4.00 88.99 47.20 1.10 100 Ω0.00 - - - Salim et al. [50] 0.01 Ω32.77 48.31 3.89 0.63 0.1 Ω31.55 70.57 5.85 0.99 0.5 Ω31.14 72.54 5.00 0.91 1Ω32.42 84.78 2.96 0.52 5Ω27.88 72.21 15.68 0.90 10 Ω14.79 89.95 48.25 1.31 100 Ω0.00 - - - Filomena et al. [51] 0.01 Ω32.77 48.29 3.91 0.63 0.1 Ω31.55 70.54 5.89 0.99 0.5 Ω31.14 72.51 5.04 0.90 1Ω32.42 84.82 3.02 0.51 5Ω29.45 84.30 13.98 0.94 10 Ω16.81 89.87 41.93 1.31 100 Ω0.00 - - - Girgis et al. [52] 0.01 Ω98.32 52.10 2.33 0.57 0.1 Ω98.15 52.56 2.38 0.57 0.5 Ω98.23 56.61 2.70 0.64 1Ω99.30 60.79 3.07 0.72 5Ω100.00 76.13 5.85 1.17 10 Ω100.00 81.96 8.94 1.51 100 Ω99.89 89.30 26.25 2.54 Jiang et al. [56] 0.01 Ω88.85 17.96 0.38 0.13 0.1 Ω87.07 25.64 0.43 0.17 0.5 Ω90.11 23.94 0.38 0.12 1Ω93.06 9.64 0.17 5.29 ×10−2 5Ω98.92 13.01 8.51 ×10−22.53 ×10−2 10 Ω97.44 5.13 0.10 2.74 ×10−2 100 Ω95.51 20.92 0.42 0.13 Personal et al. [57] 0.01 Ω99.98 0.12 1.72 ×10−34.43 ×10−4 0.1 Ω100.00 6.32 ×10−21.65 ×10−34.10 ×10−4 0.5 Ω100.00 6.66 ×10−21.64 ×10−34.15 ×10−4 1Ω100.00 0.21 1.67 ×10−34.69 ×10−4 5Ω100.00 2.37 2.29 ×10−32.75 ×10−3 10 Ω99.96 1.65 2.94 ×10−33.26 ×10−3 100 Ω99.00 5.10 2.58 ×10−21.31 ×10−2