An Effective and Computationally Efficient Similarity-Based Method for Fault Region Identification in Electrical Distribution Systems

As power distribution systems continue to grow in size and complexity, distribution line outages increasingly affect customers, requiring more time and resources to locate and repair potential faults. As a result, it is important for utilities to identify fault locations as quickly as possible to improve system availability and minimize economic losses.

The effectiveness of fault location algorithms depends on the operating conditions and the availability of information related to the power grid. With advances in computational power, Artificial Intelligence (AI)-based methods have emerged as an attractive alternative to perform this function, primarily because they do not require detailed distribution system parameters. In this context, Refs. [1,2,3,4,5] developed methodologies based on Artificial Neural Networks (ANNs), however, always requiring a previous training step with a large amount of data.

Another important aspect to consider in distribution systems is the growing penetration of distributed generation (DG). By considering this issue, Refs. [6,7,8,9,10] employed different techniques such as ANNs, Support Vector Machine (SVM), and Wavelet Transform (WT) for locating faults in distribution networks. It is important to note that the accuracy of such methods is directly influenced by three main factors: unbalanced conditions, fault resistance (FR), and the existence of multiple generation sources on the grid. Depending on the levels of these three factors, the methods discussed may be inefficient.

The problem of fault detection and location can also be addressed using concepts of similarity between electrical signals. In [11,12], the authors proposed a fault location method based on similarity analysis. The Fréchet distance is applied to estimate the fault direction by comparing current waveforms, thereby identifying the most probable location of the faulty section. In [13,14], the authors employed the Euclidean distance as a similarity measure to perform the FD function, demonstrating that this approach is a simple and robust alternative that does not require complex formulations or significant computational effort.

More elaborate metrics for assessing similarity, such as the Hausdorff distance (HD), may have greater potential for applications in electrical distribution systems [15]. In [16] was demonstrated that, by analyzing the similarity of transient zero-sequence current waveforms, the fault point can be determined by comparing the modified HD of the transient zero-sequence current in each section of the faulted feeder. In [17] was proposed a new section location method for multistage feeders in distribution grids, based on the use of Spearman’s correlation coefficient. In this study, by analyzing the characteristics of the zero-sequence component of the fault current at buses upstream and downstream of the fault point, and employing the HD, the faulted section can be effectively located. With respect to distribution system applications, Ref. [18] employed the HD to develop a novel load prediction method. The method was tested in a real system, yielding promising results and demonstrating the potential of HD-based methods for applications in real-world problems related to electrical systems. Although the methods discussed demonstrate potential applications, some of them assume the availability of a Wide Area Monitoring System (WAMS), which requires Phasor Measurement Units (PMUs) and data concentrators. This fact is not yet a reality in many power grids, making fault location methods more complex and expensive.

It is worth noting that, as highlighted in the literature, the HD is particularly suitable for fault waveform comparison because it evaluates waveform similarity without requiring time synchronization or point-to-point data correspondence. Furthermore, it can be implemented to be inherently robust to noise, data outliers, and phase shifts, which are common disturbances that affect fault transient [19]. Therefore, Ref. [20] proposed a faulty feeder selection method based on HD to address the low accuracy of faulty feeder selection caused by the complex structure of AC distribution systems. Similarly, Ref. [21] presented an adaptive current differential protection method based on HD, employing waveform similarity comparison to improve the accuracy of protection systems applied to power grids with distributed generation. In [22] was developed a robust faulted line-section location method based on HD algorithm for detecting single-phase-to-ground faults in distribution networks.

Considering the changes experienced by modern distribution power grids, the promising results obtained with similarity-based methods in power system applications, and the need for new solutions to improve utility indices and power system availability, this work proposes a new faulted region identification method based on HD.

The proposed method is simple, fast, and robust, relying only on basic concepts, local current signals, and available resources, which makes it readily applicable to practical situations. The main advantages and contributions of the proposed method are as follows:

This paper is organized as follows. Section 2 presents the key concepts related to the adopted technique and the proposed similarity-based method. Section 3 discusses the steps involved in developing and testing the faulted region identification method using a simple distribution system with distributed generation. In Section 4, the proposed HD-based method is validated using the IEEE 34-bus test system. Finally, the conclusions are presented in Section 5.

Establishing a certain level of similarity is fundamental to the high performance of various automated systems, whether comparing characters, linguistic expressions, or images. The task of measuring the degree of proximity between two sets remains a persistent challenge for developers, particularly when considering factors such as efficiency and computational cost. The fault region identification problem can also be framed in this context, where decisions can be made based on the degree of similarity between sets of samples from a faulty electrical system, such as voltage or current measurements. As will be shown, by comparing current waveforms acquired from the field with those previously stored in a database, HD enables the implementation of a waveform pattern-matching mechanism, allowing the identification of faulted regions in distribution systems.

The Hausdorff distance (HD) owes its definition to the efforts of Felix Hausdorff and is widely used in computer vision [15]. Originally, HD is defined as shown in Equations (1) to (3):

where $$A=\left\{{a}_{1}, {a}_{2}, \cdots , {a}_{m}\right\}$$ and $$B=\left\{{b}_{1}, {b}_{2}, \cdots , {b}_{n}\right\}$$ are two finite sets, and ∥⋅∥ is a measure of distance between two points, such as the Euclidean distance or the Manhattan distance.

The function $$h\left(A,B\right)$$ is called the Hausdorff directed distance from $$A$$ to $$B$$ for identifying the farthest point $${a}_{i}\in A$$ from its nearest neighbors in $$B$$. The expression $$h\left(B,A\right)$$ is defined similarly, but considers the distance from $$B$$ to $$A$$ instead. In general, $$h\left(A,B\right)\ne h\left(B,A\right)$$. Finally, the Hausdorff Distance $$H\left(A,B\right)$$ will be given by the maximum value between $$h\left(A,B\right)$$ and $$h\left(B,A\right)$$, representing the degree of compatibility between the two sets. A graphical representation of the HD for two-dimensional sets is shown in Figure 1.

The HD can be used to establish the similarity between any two discrete signals or sets of samples. In this case, a measured waveform is represented by a set of samples, and each sample from that waveform is compared to another set of samples relative to a reference waveform. This process is illustrated in Figure 2.

In the case illustrated in Figure 2, after sampling a measured waveform, the comparison between these samples and the previously stored samples that represent the reference waveform must be performed. Thus, the HD is calculated as follows:

This paper proposes a method that identifies the faulted region in primary distribution feeders, based on the comparison between fault signals measured in the field and reference signals stored in a database. In this context, the proposed HD-based method will be applied to assess the similarity between fault current signals measured at the substation and stored signals obtained from simulations or historical events. It is assumed that the fault has already been detected and that the fault current waveform is recorded and available in the digital relay responsible for the feeder. Thus, the oscillography can be recovered (automatically or on demand) and processed at a local or regional operational center.

To exemplify how the method works, it is assumed that for a given fault event, the current $${I}_{a}^{F}$$ was measured (and stored) in the substation digital relay using a sampling rate $${t}_{A}$$. Additionally, it is assumed that a set with $${n}_{f}$$ reference current signals ($${I}_{a}^{{R}_{1}}, {I}_{a}^{{R}_{2}}, \dots , {I}_{a}^{{R}_{{n}_{f}}}$$), representative of different fault events, are available in the database located at the operational center. For each event included in the database, there is a unique fault location associated with it. At this point, it is important to mention that phase a was used to develop this explanation, but a similar procedure can be extended to phases b and c. Once again, it is emphasized that the fault has already been detected, as this method is intended to support operators in the decision-making process, operating in offline mode. Regarding this proposal, the fault location problem in distribution feeders can be formulated as follows:

where $$HD\left({I}_{a}^{F},{I}_{a}^{{R}_{i}}\right)$$ is the Hausdorff distance between the measured fault current $${I}_{a}^{F}$$ and the one recorded in the database $${I}_{a}^{{R}_{i}}$$. In this way, the most likely fault location should correspond to the lowest HD.

This process is illustrated in Figure 3, where the initial and final instants define the data window length. In this context, $${\delta }_{f}$$ denotes the fault inception angle (FIA). After assessing the similarity between the measured fault current $${I}_{a}^{F}$$ and all historical records of fault events, the lowest HD value will indicate the most likely fault location.

As can be seen, the idea behind this proposal is simple, as the measured current waveform from the field is compared one-to-one with all other waveforms stored in a database. With respect to the example shown in Figure 3, where the database has only two historical events (red and blue fault current waveforms), the blue waveform is the found solution, as it has the shortest HD to the test current waveform. Therefore, the location associated with the blue waveform will be presented as the possible fault location, providing support to the system operator during the decision-making process, when specifying the right place to send the maintenance team. In real-world scenarios, the database may include thousands of historical events obtained from simulations and/or oscillography records from IEDs stored over time.

The HD-based method presented was developed and validated by considering two different distribution systems, i.e., the IEEE 5-bus test system and the IEEE 34-bus test system. The first one is a distribution network with three generation sources and loads distributed throughout the system. This one, smaller than the second one, was adopted for developing and testing the proposed solution, while the second one, larger and more complex, was used to validate the proposed method, showing its comprehensiveness and accuracy.

The first test system is shown in Figure 4. The diagram represents a 9 MW wind farm equipped with asynchronous generators that export power to a 120 kV grid via a 25 kV distribution feeder. The 120 kV main power supply is modeled as a voltage source with a short-circuit capacity of 1200 MVA. A smart meter (IED) is assumed to be installed upstream of bus B120, where the fault signals are measured and subsequently compared with the corresponding signals stored in the database (DB).

To build the database of fault current waveforms, single-phase faults were simulated at six locations, as shown in Figure 4. These locations were labeled as follows: TR1p (primary side of transformer TR1), TR2p (primary side of transformer TR2), Bus (beginning of the feeder), Feeder (along the feeder), End (end of the feeder), and TR3s (secondary side of transformer TR3). Several fault events were generated assuming different fault resistances, fault locations, and fault inception angles. This work focuses exclusively on single-phase faults, as they constitute the vast majority of faults in distribution systems, accounting for approximately 85% of all fault events. Therefore, they represent the main concern for electric utilities [22].

As demonstrated in Figure 5, each fault location presents a distinct fault current signal, which can be considered a fault signature.

The DB was generated considering the following parameters:

Considering all possible combinations of the mentioned parameters, a DB containing 100 cases was generated. Firstly, when developing the method, a sensitivity analysis was performed with different values of sampling rate ($${t}_{A}$$) and number of windows ($${n}_{j}$$). Subsequently, when testing the method, scenarios with variation of fault resistances and fault inception angles were considered.

The first test aims to analyze the sensitivity of the proposed method, considering different sampling rates ($${t}_{A}$$) and number of windows ($${n}_{j}$$). It is worth noting that all these tests considered only single-phase faults, which are more frequent in distribution systems. The main goal of this section is to define the values of $${t}_{A}$$ and $${n}_{j}$$ that make the method more accurate and feasible for practical applications. The following values for $${t}_{A}$$ (in samples by cycle) and $${n}_{j} \left(\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e}\right)$$ were considered, totaling nine combinations:

The results are presented in Table 1 and Table 2. For each fault case tested, the HD was calculated, and the response associated with the nearest stored event was given. A green symbol “✓” is used in cases where the event with the lowest HD matched the exact fault location. Cases that did not match are indicated by the red symbol “✓”. Initially, only test faults pre-existing in the DB were considered (Table 1), i.e., those with both fault resistance and fault inception angle equal to zero. Subsequently, new cases were tested under conditions not previously included in the DB (Table 2).

As can be seen from Table 1 and Table 2, when the method is tested by using pre-existing events, the results are always correct, regardless t_A and n_j. On the other hand, when using new events, the sampling rate of 64 samples per cycle must be disregarded, regardless of the number of windows employed. For the other cases, a hit rate of 90% was achieved, regardless of t_A and n_j. As will be discussed, this performance can be further improved by including additional cases in the DB.

This section presents the results considering fault cases with different resistances, locations, and inception angles. The tested faults were located at 5, 10, 15, and 20 km, with fault resistances and inception angles as listed in Table 3. These test cases do not correspond to any fault configurations stored in the historical database. The test faults were evaluated using the two best sampling rates identified in the previous section (t_A = 128 and 256), with n_j = 1.

The performance in locating faults is evaluated considering the error of the estimated distance in relation to the actual distance of the fault, according to Equation (5):

where $${distance}_{real}$$ is the real fault distance from the substation and $${distance}_{HD}$$ the distance computed by using HD, while $${L}_{s}$$ is the section length under analysis.

It is worth noting that Equation (5) represents the standard approach for measuring the error in fault distance estimation for distribution feeders and transmission lines. The factor (L) expresses the estimation error as a percentage, making it possible to compare fault location methods across different power systems [23].

Table 3 presents the fault distance estimation errors, expressed as a percentage of the distance to the fault location. Larger errors were observed for faults located at the remote end of the feeder. However, new cases can be added to the DB to improve the method’s performance under these conditions, emphasizing that updating the DB is a quick and straightforward process.

Table 4 shows the percentage errors when the HD is computed with $${t}_{A}=256$$ and $${n}_{j}=1$$. As can be seen, there was a slight improvement in the performance of the proposed method. However, this improvement was achieved by increasing the computational cost. This trade-off between performance and computational burden depends on the requirements of each application and should be carefully evaluated, taking into account the expected accuracy, the number of cases available for inclusion in the DB, and the hardware infrastructure (e.g., memory size and processing power).

Figure 6a,b compare the test fault current (dashed line) with other fault current waveforms stored in the database for faults located at 25 km (end of the feeder) and 22.5 km, respectively. This suggests that each fault signal exhibits distinct characteristics and that, even with a small number of cases, identifying the closest signals would be nearly impossible without an appropriate similarity measure, such as the Hausdorff distance (HD). For illustration purposes, Figure 6 was elaborated using only the current signal from phase A.

The findings presented in this section indicate that the proposed methodology is able to effectively identify the faulted region at different locations along the distribution feeder, thereby fulfilling the primary objective of this study.

It was observed that the method accurately identifies the faulted region when using sampling rates of 128 and 256 samples per cycle, but demonstrates poor performance at 64 samples per cycle. Regarding the data window length, no significant difference was observed between using one or two cycles of fault current (either for the test fault and the recorded samples). Therefore, to ensure the simplest and most efficient implementation, the proposed method is applied and tested throughout this work using 128 samples per cycle and a data window of one cycle. As will be shown, this configuration effectively achieves the goal of identifying faults along the feeder, regardless of fault characteristics or grid operating conditions. It is also worth noting that the method’s performance improves as the size of the database increases, which can be dynamically expanded over time.

It should be emphasized that, in the proposed methodology, the HD is not intended to establish a direct relationship with individual fault parameters, such as fault resistance, fault inception angle, or feeder location. Instead, HD is employed exclusively as a waveform similarity metric to compare a fault current measured in the field with a database of previously simulated or registered fault currents. Therefore, the effectiveness of the proposed method relies on the ability of the database to adequately represent the range of expected fault scenarios, rather than on a deterministic mapping between HD values and specific fault electrical parameters.

The main objective of this section was to highlight the potential of the proposed method despite the simplicity of its underlying concept. For validation purposes, the next section evaluates the proposed method on a second, more complex electrical system widely recognized by the technical community.

The proposed method is tested against the IEEE 34-bus system, whose single-line diagram is illustrated in Figure 7. The network operates with a nominal frequency of 60 Hz and a distribution voltage of 24.9 kV, with multiphase loads, either balanced and unbalanced. The main features of this network are:

For analysis purposes, the system is divided into two parts, according to Figure 7. The first (in red) corresponds to the main three-phase section, while the second (in green) includes the single-phase and two-phase lateral sections.

To construct the database, a large number of fault scenarios were simulated under various operating conditions and fault characteristics, by varying the fault location, fault parameters (resistance and inception angle), and loading levels. For each scenario, a data window of one cycle and 128 samples per cycle is considered, and the resulting fault current waveform is stored in the database and associated with a specific location along the feeder.

To test the method under more comprehensive and practical conditions, the loads had their active and reactive power reduced by 50% and 70%. The objective of this variation was to verify the impact of the loading system on the performance of the proposed method and to identify possible limits of its operation. Three cases were considered: (1) nominal loading; (2) 50% of the nominal load; (3) 70% of the nominal load.

Single-phase faults were simulated at multiple locations along the distribution feeder, considering variations in both fault impedance and fault inception angle. As before, once a fault occurs, the fault current waveform at bus 800 is stored and then compared with a historical database using the HD method. Since approximately 85% of faults in distribution systems are single-phase, they are the main concern for electric utilities and therefore the primary focus of this study [22].

Unlike the previous tests, which used only the phase-A current waveform to calculate the HD, this section analyzes combinations of voltage and current waveforms from all phases, as illustrated in Figure 8. The input signals are labeled according to the waveform(s) used to compute the HD, as follows: HD Ia (phase-a current waveform), HD Va (phase-a voltage waveform), HD Iabc (three-phase current waveforms), and HD IabcVabc (combination of three-phase voltage and current waveforms).

By considering different load conditions and fault locations, both in the main feeder and in the lateral branches, the accuracy and robustness of the proposed method were verified using the IEEE 34-bus system. It is worth noting that the test fault cases were simulated using fault parameters that are not represented in the constructed database, as indicated in Table 5.

Table 6 presents the results of the proposed method for each input signal configuration, considering different sampling rates and data window sizes. This analysis supports selecting an appropriate configuration to implement an accurate fault-region identification scheme in distribution systems. As observed from the results, the best trade-off between performance and simplicity is achieved with a configuration of 128 samples per cycle and a data window size of one cycle. To illustrate how this configuration performs with different input signals, Figure 9 presents the method’s results, represented as heatmaps derived from Equation (5), for a large number of fault cases. The database comprises 360 cases (5 fault resistances × 4 fault inception angles × 18 fault locations), while 162 additional cases (3 fault resistances × 3 fault inception angles × 18 fault locations) are used for testing.

As shown in Figure 9, when the input signals Ia and Iabc are used, the proposed method exhibits better performance compared with the cases employing Va and IabcVabc. It is also important to note that, in general, between Ia and Iabc, the latter provides slightly superior performance, as illustrated in the figure.

To evaluate the method’s performance under different operating conditions, the tests were repeated with 70% and 50% of the nominal load, considering the two best-performing input signals identified in the previous analysis, namely the current waveforms Ia (Figure 10a,c) and Iabc (Figure 10b,d). The results suggest a weak correlation between fault location estimation errors and load levels. The observed variations are mainly attributed to the different input signal waveforms used. The number of test fault cases correctly identified for each operating condition is presented in Table 7.

Another important aspect of the evaluation concerns the impact of the database size on the method’s performance. To this end, the database was expanded using the parameters listed in Table 8, considering only single-phase faults, given their prevalence in distribution systems. As shown in Table 8, combining the new values assigned to each variable yields dataset DB-1, comprising 1584 fault cases, and dataset DB-2, comprising 6336 fault cases, thereby enabling a more comprehensive analysis. Using the values presented in the last column of Table 8, new test cases were generated to evaluate the performance of the proposed method.

After completing all simulations and tests, the results were compiled and summarized in Table 9, which, as in the previous analyses, presents the fault location estimation error for fault cases occurring along the main feeder from bus 802 to bus 840. To comprehensively assess the impact of the database size on the method’s performance, a total of 324 test fault cases were evaluated (18 buses × 3 fault resistances × 3 fault inception angles × 2 databases). It is important to emphasize that the primary purpose of this table (and its correspondent heatmaps) is to illustrate the influence of the database size on the accuracy of the proposed solution by comparing the color patterns across the heatmaps, while the variable axes are maintained the same for all analyzed cases. The results show that the database size has a significant impact on the method’s performance. The performance obtained using datasets DB-1 and DB-2 was generally improved compared with that achieved using the previous database containing 360 fault cases (see Table 5, Figure 9 and Figure 10). Moreover, in general, DB-2 yielded more accurate results than DB-1, indicating that larger databases lead to higher fault-location accuracy. Also, it can be observed that DB-2 renders the method independent of the load condition.

Another important conclusion drawn from the observed results concerns the selection of the input signal. As can be observed, in most cases, the use of Iabc resulted in higher accuracy than Ia. Therefore, the configuration using Iabc as the input signal is adopted for the subsequent evaluations, considering the lateral branches, consistently maintaining 128 samples per cycle and a one-cycle data window, as previously discussed.

In this section, the proposed similarity-based method is evaluated for faults occurring along the lateral branches of the IEEE 34-bus system. Initially, a new database (DB-3) was constructed using the input signal Iabc, selected based on its previously demonstrated superior performance. An important aspect is that DB-3 contains fault signals only from the main feeder and does not include fault signals from the lateral branches. Consequently, the method is expected to identify the fault location in DB-3 that is closest to the fault point in the lateral branch. For this simulation, the FR and FIA parameters are those listed in Table 10, with test fault cases applied at buses 816, 818, 819p, 820, 821p, 822, 863p, and 864.

Figure 11 illustrates the poor performance of the method in this test scenario. In fact, regardless of the loading condition, the absence of fault cases in the lateral branches significantly reduces the accuracy of the proposed solution, since a sufficient level of similarity is not achieved between the faulted signal (from the field) and those stored in DB-3. As can be observed, since the method always provides discrete responses through a waveform pattern-matching approach, and the approximation error depends on the database size, all cases were similarly affected regardless of their operating conditions.

To address the previously identified issue of low accuracy for faults occurring in the lateral branches, the original DB-3 dataset was updated to include fault signals from the lateral branches. The final dataset includes fault records from both the main feeder and the lateral branches, expanding from 6336 to 9152 fault cases through the inclusion of different fault locations, FR, and FIA values, as previously defined in Table 10.

The simulation results are presented in Figure 12. As expected, once DB-3 is updated with the fault records from the newly introduced buses, a higher level of accuracy is reached, regardless of the operating condition. The results also confirm that using 128 samples per cycle and a one-cycle data window for computing the HD yields robust performance across the scenarios considered, as all evaluations consistently produced similar heatmaps.

Once again, it becomes evident that the method’s performance depends on the size of the database, which can be updated as needed to meet specific requirements and desired levels of accuracy. It should be noted that the proposed similarity-based method, which employs the HD, is simple and relies only on readily available resources (from simulations or historical field data). Moreover, it can serve as an important tool to help utility maintenance teams accurately identify faulted regions, thereby speeding system restoration and enhancing distribution system availability.

It should be noted that the results presented in this section are intended to illustrate the influence of database density on the performance of the proposed methodology rather than to establish a universal minimum database size. The optimal database configuration should be selected according to the requirements of each specific application, considering factors such as network characteristics, desired identification resolution, and computational constraints. Furthermore, the performance of the proposed approach is always evaluated in terms of correct identification of the faulted region rather than the absolute fault-distance error.

Compared with the alternative approaches summarized in Table 11, the primary advantage of the proposed method is its computational simplicity. The method quantifies the similarity between electrical signals using HD to identify the faulted region and relies solely on simple mathematical operations applied directly to the sampled current, without requiring any complex preprocessing stage. Moreover, the method performs well at low sampling frequencies, reducing the requirements imposed on existing hardware and making it readily applicable in real-world scenarios.

As shown in Table 11, approaches with different complexity levels offer distinct capabilities and can address different fault scenarios depending on the required accuracy. The solution proposed in this work provides an acceptable trade-off between simplicity and performance, supporting operators in routine tasks while enabling rapid identification of fault regions and timely restoration of the distribution system.

In general terms, the main advantage of the proposed method is its ability to support utility maintenance teams without requiring additional investment, as it relies solely on available resources and appropriate processing of fault current waveforms. As shown in Table 11, other methods that achieve higher robustness generally require higher sampling frequencies, communication links, and more complex signal processing schemes, which may limit their practical applicability.

It should be noted that the methods summarized in Table 11 were developed for different distribution systems, datasets, fault scenarios, and evaluation criteria. Therefore, a direct quantitative comparison of performance metrics is not possible. The purpose of this comparison is to highlight the methodological differences and practical contributions of the proposed approach with respect to related studies, rather than to establish a benchmark under identical experimental conditions.

After an extensive evaluation, the final configuration of the proposed method (three-phase currents (Iabc), sampling rate of 128 samples per cycle, and one-cycle data window) was found to be insensitive to load variations but sensitive to the sampling rate, data window size, and database construction. In addition, the method demonstrated robustness to variations in fault resistance and fault inception angle. When the objective is limited to identifying faulted regions in the main feeder, either the phase-A current (Ia) or the three-phase currents (Iabc) can be used interchangeably, although Ia results in a lower computational burden. However, when faulted region identification in the lateral branches is also required, the three-phase currents (Iabc) constitute the more suitable input, providing higher accuracy at the expense of increased computational cost.

As demonstrated, the accuracy of faulted region identification mainly depends on the comprehensiveness of the database. Therefore, it is possible to create a general database representing the original power system configuration, as well as secondary databases representing the distribution system under different network configurations resulting from topology changes, for example, after switching operations.

The proposed methodology is intended for offline post-fault analysis, where oscillographic records obtained after fault occurrence are compared with a database of previously simulated or recorded fault waveforms. Therefore, it can be periodically expanded and refined offline as new fault records become available, allowing utilities to tailor its size and coverage according to network characteristics, operational requirements, and maintenance policies.

Considering all the evaluations performed in this study, the favorable trade-off between performance and implementation cost makes the proposed method an attractive and readily applicable solution for supporting engineers responsible for power system operation.

This paper presents a method for identifying the faulted region in distribution systems. The method was initially developed and evaluated using a small system with distributed generation and was subsequently applied to a larger distribution network to validate its effectiveness and demonstrate its applicability.

Several input signals, sampling rates, and data window lengths were evaluated to determine the most suitable configuration for the proposed method. The selected configuration was capable of identifying the faulted region under varying load conditions, fault inception angles, and fault resistances. In addition, the proposed method was found to be insensitive to load variations but strongly dependent on the size and completeness of the database, which can be readily updated to meet the specific requirements of a given distribution system.

A key characteristic of the proposed HD-based fault region identification method is its simplicity: it relies solely on basic mathematical operations and incurs low computational cost. The method requires only existing, readily available infrastructure, offering a promising low-cost solution without additional IEDs or communication networks. Consequently, it can assist utility operators by rapidly identifying the faulted region, thereby facilitating fault isolation and service restoration.

As future work, the proposed method could be evaluated in larger and more complex modern distribution systems with a high penetration of converter-interfaced renewable energy sources. In addition, its performance could be investigated under high levels of measurement noise and high-impedance fault conditions, in which the fault and load currents are often very similar.

This study focuses exclusively on single-phase-to-ground faults because they represent the vast majority of fault events in distribution systems and therefore constitute the primary application of interest for the proposed methodology. Extending the database and validation procedure to include two-phase, two-phase-to-ground, and three-phase faults is also left as future work.

The authors would like to thank the Coordination for the Improvement of Higher Level Personnel (CAPES) and the Ministry of Education of Brazil for its financial support, and also the National Institute of Science and Technology of Electric Energy-Brazil (INCT-INERGE).

Conceptualization, R.C.d.S. and J.S.d.L.; Methodology, R.C.d.S. and J.S.d.L.; Software, E.W.S.d.Â. and J.S.d.L.; Validation, E.W.S.d.A. and J.S.d.L.; Formal Analysis, R.C.d.S. and E.A.B.; Investigation, J.S.d.L.; Data Curation, J.S.d.L.; Writing—Original Draft Preparation, R.C.d.S., E.W.S.d.Â. and E.A.B.; Writing—Review & Editing, G.T.d.A., A.M.d.S. and R.C.d.S.; Visualization, J.S.d.L., G.T.d.A. and A.M.d.S.; Supervision, R.C.d.S.

Not applicable.

Not applicable.

The data supporting the findings of this study are not publicly available.

This research was funded by CAPES Brazil, Finance Code 001.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.