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Article

A Practical Approach for Fault Location in Transmission Lines with Series Compensation Using Artificial Neural Networks: Results with Field Data

by
Simone Aparecida Rocha
1,
Thiago Gomes de Mattos
1 and
Eduardo Gonzaga da Silveira
2,*
1
Postgraduate Program in Mathematical and Computational Modeling, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte 30180-001, Brazil
2
Department of Electrical Engineering, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte 30180-001, Brazil
*
Author to whom correspondence should be addressed.
Energies 2025, 18(1), 145; https://doi.org/10.3390/en18010145
Submission received: 25 October 2024 / Revised: 18 December 2024 / Accepted: 27 December 2024 / Published: 2 January 2025
(This article belongs to the Section F3: Power Electronics)
Browse Figures
Figure 1
<p>Voltage–current characteristic of a MOV.</p> "> Figure 2
<p>Capacitor bank protection using varistors.</p> "> Figure 3
<p>MOV conduction during a short-circuit phase B.</p> "> Figure 4
<p>Flowchart of the fault location process.</p> "> Figure 5
<p>Compensated line transmission indicating Brazil’s electrical system.</p> "> Figure 6
<p>Voltages and currents for an AG fault. (<b>a</b>) Sobradinho Terminal; (<b>b</b>) S. J. Piauí Terminal.</p> "> Figure 7
<p>Currents in the transmission line, capacitor bank, and protective equipment for the AG fault.</p> "> Figure 8
<p>Elimination of source parameters.</p> "> Figure 9
<p>Algorithm proposed for fault location.</p> "> Figure 10
<p>Electrical system with an AG fault for the proposed algorithm.</p> "> Figure 11
<p>The selection of phasors to define the source values when assembling the circuit in the ATP.</p> "> Figure 12
<p>ATP model used for obtaining ANN training files.</p> "> Figure 13
<p>Models to simulated faults: (<b>a</b>) AG, (<b>b</b>) BC, (<b>c</b>) ABC, and (<b>d</b>) ACG (adapted from [<a href="#B1-energies-18-00145" class="html-bibr">1</a>]).</p> "> Figure 14
<p>Selection of input quantities in the ANN according to the type of fault.</p> "> Figure 15
<p>The selection of current phasors inputted into the ANN.</p> "> Figure 16
<p>Modular ANN structure for fault location.</p> "> Figure 17
<p>Voltages and currents for a BCG fault. (<b>a</b>) Sobradinho Terminal; (<b>b</b>) S. J. Piauí Terminal.</p> "> Figure 18
<p>Currents in the transmission line, capacitor bank, and protective equipment (BCG fault) (adapted from [<a href="#B1-energies-18-00145" class="html-bibr">1</a>]).</p> ">
Versions Notes

Abstract

:
This paper presents a new method for fault location in transmission lines with series compensation, using data from voltage and current measurements at both terminals, applied to artificial neural networks. To determine the fault location, we present the proposal of using current phasors, obtained from the oscillography recorded during the short circuit, as the input to the neural network for training. However, the method does not rely on the internal voltage values of the sources or their respective equivalent Thevenin impedances to generate training files for the neural network in a transient simulator. The source data are not known exactly at the time of the short circuit in the transmission line, leading to greater errors when neural networks are applied to real electrical systems of utility companies, which reduces the dependency on electrical network parameters. To present the new method, a conventional fault location algorithm based on neural networks is initially described, highlighting how the dependency on source parameters can hinder the application of the artificial neural network in real cases encountered in utility electrical systems. Subsequently, the new algorithm is described and applied to simulated and real fault cases. Low errors are obtained in both situations, demonstrating its effectiveness and practical applicability. It is noted that the neural networks used for real cases are trained using simulated faults but without any data from the terminal sources. Although we expect the findings of this paper to have relevance in transmission lines with series compensation, the new method can also be applied to conventional transmission lines, i.e., without series compensation, as evidenced by the results presented.

1. Introduction

Overhead transmission lines are responsible for transporting energy from generation units to end consumers. Due to the extent and possibility of exposure to undesirable events, such as atmospheric discharges (ADs), storms, fires, and falling trees, components are vulnerable to defects, which can cause their operation to be interrupted. The occurrence of a short circuit in a transmission line represents a random phenomenon with distinct characteristics, such as the point of occurrence, duration, fault resistance (RF), and type of fault (single phase to ground, phase to phase, phase to phase to ground, and three phase) [1]. Determining the location of the fault is critically important as it avoids the need for a complete inspection of the transmission line, enabling a quicker restoration of power supply, increasing reliability, and preventing financial losses for companies, including fines from regulatory bodies overseeing the sector.
Artificial neural networks (ANNs) are structures that enable the use of intelligent processes for pattern recognition, generally involving the identification and classification of information into categories [2]. These structures consist of processing units capable of storing experiential knowledge and making it available for use. They have an input layer, an output layer, and one or more hidden layers. Each layer may have one or more processing units called neurons, which receive a set of weighted inputs that determine their activation and output value. For an ANN to provide satisfactory results, a training process is necessary, during which the numerical values of the weights are gradually adjusted to establish a connection between the input data and the expected output. Iterative adjustment processes occur during learning until a generalized solution to a specific problem is achieved.
The architecture of a neural network, defined by the number of layers used, the number of neurons in each layer, the type of connection established between neurons, and its topology, associated with how the weights are adjusted during the network learning process, characterizes the existing ANN models [2].
When using an ANN for fault location, it is necessary to develop a set of patterns that represent the fault scenarios in the analyzed system, which are used for the training and validation of the network. To this end, variations in parameters such as the distance to the fault, the type of short circuit, and the fault resistance are simulated in electromagnetic transient programs. This results in a set of patterns with voltage and current values of the transmission line terminals that, after being processed, feed the inputs of the neural network, associating them with the indication of the fault location. An important aspect to highlight is the generalization and adaptation capacity of the ANN to the operations of the electrical system. The implemented network must reproduce learning, accumulate knowledge, and provide the desired output not only for data presented in the training but for any input related to the trained patterns, enabling successful performance.
Since the early 2000s, various authors have researched fault location in electric power systems using ANNs, as can be seen in the references presented in Table 1.
No single structure is used in the literature, but certain characteristics are more commonly applied, and the results achieved by various authors highlight the possibilities explored. Multilayer feedforward perceptron networks are predominant, with supervised learning using backpropagation and the Levenberg–Marquardt training algorithm. In most existing studies, with some variations among authors, the training data were obtained by simulating faults along the transmission line, using different values of fault resistance, fault types, and fault incidence angles. The parameters of the sources connected to the transmission line terminals are also used as the input data, necessary for generating the ANN training files in electromagnetic transient simulation programs.
Only the study conducted by Aggarwall [26] presents results for real fault location cases, applied to a transmission line without series compensation in the electrical system of Iran. This fact highlights limitations in the generalization of ANNs, which provide low errors in simulated fault location cases but do not perform well when applied to oscillographs recorded from real-field electrical systems. The main cause of this issue is the difficulty in ensuring that the data used for neural network training effectively represent the electrical systems of utilities in order to achieve good results. As in some other fields involving practical applications, in determining the location of a short circuit in transmission lines, there are not enough measurements to create a comprehensive database (oscillographs from relays or digital disturbance recorders, recorded in COMTRADE format) with the necessary range for training the neural network with variations in fault location, fault resistance, and fault type. In such cases, electromagnetic transient programs, like the Alternative Transients Program (ATP) [32], are used to simulate the scenarios for training. When an artificial neural network is trained using a transient simulator (e.g., the ATP) and the same circuit is subsequently used for validation, no uncertainties related to source parameters—which this proposed method seeks to eliminate—are introduced. This paper aims to present real-world cases based on field oscillography. These cases highlight not only typical uncertainties, such as those associated with potential and current transformers, transmission line parameters, and the mutual inductances of nearby lines, but also additional uncertainties related to source parameters, including internal voltage and impedance.
This paper proposes a new methodology for fault location in transmission lines using artificial neural networks, which can be applied to real short-circuit problems based on data files in COMTRADE format, recorded at electrical substations. The main difference between the proposal presented in this paper and others in the literature is how the data are generated in the electromagnetic transient program to train the ANN. This approach uses fault oscillography data from the transmission line, recorded by equipment at the electrical substation, in COMTRADE format. This methodology is independent of the parameters of the sources connected to the transmission line terminals, enabling reduced errors compatible with this type of application. Source impedances are typically obtained through short-circuit calculation programs, which provide values suitable for power flow studies, equipment sizing, protection relay settings, and other applications. However, this factor can significantly increase errors in fault location, where precision is critical. To illustrate the effectiveness of the proposed methodology, the results of using the ANN for fault location in real short-circuit cases are presented for transmission lines without series compensation and with a series capacitor bank.

2. Protection of Capacitor Banks with a Metal Oxide Varistor

Capacitor banks (CBs) connected in series are subjected to voltage and current transients associated with short circuits. It is necessary to use a protection system to limit the voltage at the capacitor terminals and prevent equipment damage. In this context, the protection system should be specified to restrict the maximum overvoltage that each capacitor unit must endure. For voltages below the specified limit, the CB should function normally. According to [33], the metal oxide varistor (MOV) is one of the main protection devices, known for its high nonlinearity. Figure 1 illustrates the operating curve of an MOV with a maximum withstand voltage of 283 kV, used to protect a 55.62 μF capacitor bank.
A simplified system is represented in Figure 2. When the overvoltage across the capacitor reaches or exceeds the trigger level, the varistor starts conducting, diverting the current. After the fault is eliminated, the operating conditions are restored. The spark gap starts conducting to protect the varistor when the voltage reaches a predetermined limit, and the circuit breaker is closed if the varistor’s temperature limit is exceeded, preventing equipment damage due to overheating.
Figure 3 shows the conduction moments of the varistor, whose curve is shown in Figure 1, during a fault BCG that occurs in a 211 km and 500 kV series-compensated transmission line. The recording is made with field oscillographs. It can be observed that during the short circuit, the MOV enters conduction for three periods until the spark gap is triggered.

3. Steps of the Process

Before solving the fault location problem using an ANN, preprocessing routines are applied to prepare the data once they are loaded into the implemented computational program. Figure 4 illustrates the basic steps involved in the developed algorithm.
The process starts with the reading of voltage and current data from both terminals of the line, collected from recorders located in substations and formatted in COMTRADE [34]. The next phase involves identifying the fault instant, which enables the division of the data into pre-fault and fault periods. Signal preprocessing begins with low-pass filtering to eliminate higher frequencies, utilizing a second-order Butterworth filter set at 100 Hz. Following the filtering, data interpolation is applied to achieve a sampling frequency of 16 points per cycle at the fundamental frequency [35]. The least squares method described in [36] is then used to estimate the phasors corresponding to the fundamental frequency. The following step is fault classification, during which the voltage and current phasors related to the short circuit are selected for the fault location algorithm. An example of the fault detection and classification processes is provided in [37], although a variety of techniques can be used [38]. The procedures illustrated in Figure 4 are executed using MATLAB, version R2018a software. The specific section for fault location, located at the end of the flowchart in Figure 4, is elaborated on in Section 5.

4. Fault Dynamics in a Compensated Line

To illustrate the dynamics of a short circuit on a compensated transmission line, the single-line diagram of an existing transmission line in the northeast region of Brazil, with a length of 211 km, 500 kV, and 70% compensation (XCN = 47.69 Ω), is shown in Figure 5.
Field data from an actual AG fault that occurred on this line are presented in Figure 6, starting at a time of 0.189 s. The oscillogram is captured using the digital disturbance recorder at the S. J. Piauí substation, where the capacitor bank is located, and at the Sobradinho substation.
Figure 7 provides a detailed view of the currents in the transmission line, spark gap, capacitor bank, and MOV (the voltage–current characteristic is represented in Figure 1) for phase A, corresponding to the AG fault shown in Figure 6. In approximately 0.21 s, the spark gap is triggered.

5. Proposed Algorithm

The proposed algorithm aims to eliminate source parameters in the ANN training process, as these parameters are not known precisely at the time the fault occurs, as illustrated in Figure 8. Small changes in these parameters lead to variations in the short-circuit values, which affects the accuracy and estimation of the results from artificial neural networks.
Thus, the proposed algorithm has the following main characteristics: (a) elimination of the voltage and impedance values of the Thevenin equivalent in the electrical system used in the ATP for generating training files, and (b) individualization of the fault location process, meaning that for each occurrence where the location of a short circuit needs to be determined, network training must be performed. Based on the file containing the voltage and current data from the analyzed fault, simulations are carried out to generate the training scenarios for the ANN. Figure 9 presents a flowchart of the new algorithm related to the fault location task, which occurs after the preprocessing shown in Figure 4.

5.1. Fault Circuit Representation/Generation of Patterns for ANN Training

Figure 10 presents a three-phase model of a transmission line, where L is the length and dF is the distance from the fault point to Terminal S. The sources are adjusted using the phasors (amplitude and phase) EAs, EBs, and ECs, and EAR, EBR, and ECR are estimated from the COMTRADE file of the fault input, recorded at the terminals of the line under short-circuit conditions. As an example, for the AG fault in Figure 10, the value of EAs is the average of the phase A phasors contained in the window where they are most stable, as indicated in Figure 11. The same method is applied to the voltages for the other phases. It is important to note that the pre-fault values of the internal voltages of the sources or their impedances are not required, as these are parameters that the solution aims to eliminate from the problem.
From the voltage phasors of the fault period, the circuit is assembled in the ATP for simulation and generation of files for ANN training, as shown in Figure 12. For an AG fault like the one in Figure 6, only switch S1 is closed.
Training files are generated for each fault occurrence to be located. The training and validation variables (fault distance and fault resistance) for the neural network are described in Table 2 and Table 3. As indicated in [37], the training and validation data, respectively, correspond to 80% and 20% of the dataset. The fault model is represented in Figure 13.

5.2. Neural Network for the Proposed Method

The ANN is implemented using a feedforward structure trained with backpropagation supervised learning, the Levenberg–Marquardt training algorithm, and the hyperbolic tangent activation function, with 12 and 8 neurons in the hidden layers and 1 neuron in the output layer. Several tests are performed to define the inputs as a function of the current phasors, and the phasor module provides the best results. For phase–ground faults, there are two inputs; for phase–phase–ground and phase–phase faults, there are four inputs; and for the three-phase fault, there are six inputs in the ANN, as shown in Figure 14. Figure 15 shows the selection of the current phasors for the AG fault in Figure 6, adopting the average of the fault phasors in the most stable region.

6. Results Obtained

6.1. Real Signals—Lines Without Series Compensation

For the application of the proposed method in real short-circuit cases, oscillography files from nine fault cases in the Brazilian power system on lines without series compensation were used to show that the terminal source impedance has no effect. To evaluate the effectiveness of the proposed method, we compared this approach to the approach presented in Reference [39], where the training of the ANN depends on the values of the terminal source parameters, as is common in the literature. The topology of the neural network used is shown in Figure 16. The equivalent impedances of the sources at the transmission line terminals, provided by the electric utility, are listed in Table 4, except for line 4, where only the oscillography data at the terminals are available. Table 5 presents the errors obtained, calculated according to Equation (1).
e ( % ) = e s t i m a t e d   l o c a t i o n − i n s p e c t i o n   r e s u l t × 100 l i n e   l e n g t h
The average error for the proposed method was 1.14%, with the highest value being 2.96%, which is significantly lower than the values obtained using the method outlined in Ref. [1]. When tested with real signals, the ANN trained with the proposed method provided viable results for practical use, even though it was trained with simulated signals from the ATP.
From the results obtained, it can be observed that the source data had a significant influence on the errors in the method outlined in Ref. [39]. As shown in Table 5, the average error was 12.27%, reaching 31.41% in one case. This occurred because the impedances in Table 4 were not the same at the moment of the short circuit due to the dynamics of the power system. Since these impedances were used to generate data in the ATP for training the ANN in Ref. [39], larger errors were produced. The proposed method removes the source parameters from the problem’s solution, resulting in lower errors, and making it suitable for practical applications.

6.2. Simulated Signals—Series-Compensated Lines

A 256 km, 345 kV transmission line was simulated in the ATP using the frequency-variable parameter model proposed by Martí. The data from Table 3 and Table 4 were used to generate the training and validation scenarios for the ANN. Compensation levels of 35% and 70% were applied for faults involving one, two, and three phases. Table 6 presents the errors obtained for some simulated cases, demonstrating the performance of the proposed algorithm.

6.3. Real Signals—Series-Compensated Lines

The proposed method was applied to locate faults caused by atmospheric discharge on the 211 km transmission line with 70% compensation, i.e., the Sobradinho-S. J. Piauí line, using oscillograms provided by a Brazilian power utility, as highlighted in Figure 5. Two cases were analyzed: an AG fault, the oscillogram of which is presented in Figure 6, and a BCG fault, the oscillograms of which are shown in Figure 17 and Figure 18. It is important to emphasize that the authors had access to the oscillographic records of voltages and currents. However, the data related to the sources, such as the value of the equivalent impedance, as shown for transmission lines 1, 2, and 3 without series compensation in Table 4 and Table 5, were not provided. The results are displayed in Table 7.
It is observed that the errors obtained for compensated lines make the methodology viable for practical purposes in electric power utilities. Despite the nonlinearity introduced by the MOV due to its actuation curve, it is possible to achieve good results with reduced errors when using ANNs in real cases through the proposed methodology.

7. Conclusions

The method presented in this paper aims to locate faults in transmission lines with series compensation in power systems operated by utility companies, applying artificial neural networks (ANNs) and using field oscillography data, the MOV operating curve, and transmission line parameters. This approach eliminates the need to know any parameters related to terminal sources or the power system connected to the transmission line.
The nonlinearity of the capacitor protection element, the metal oxide varistor (MOV), has a significant influence on the process by altering the transmission line impedance and complicating the application of traditional analytical methods. However, this difficulty is overcome through ANNs, particularly because the proposed method does not rely on source parameters to generate scenarios for neural network training in the ATP, as these parameters are often not precisely known at the time of the short circuit.
Fault location is determined based on the current recorded at the transmission line terminals and captured in oscillography during the short circuit. This value is inputted into the trained ANN to determine the fault location. Small variations caused by uncertainties in source voltage values and the Thevenin equivalent impedance at the terminals could alter the short-circuit current used for ANN training, negatively affecting the results. By eliminating these uncertainties, the proposed method significantly improves the reliability of the results, making it more suitable for practical applications in power utility operations, as demonstrated by the low error rates observed in the real cases that we analyzed.
The processing time for fault location, using a computer with a 2.78 GHz processor and 8 GB of RAM, is approximately 5 min, with the algorithm implemented in MATLAB. Studies are underway to evaluate the application of the method in lines equipped with thyristor-controlled series capacitors (TCSCs), aiming to validate its effectiveness in systems with this topology.
The code to train and evaluate the ANN is available at the following link: https://github.com/Eduardo-Gonzaga-CEFET/Fault_Locator/tree/main (accessed on 18 December 2024).

Author Contributions

Conceptualization, S.A.R. and E.G.d.S.; methodology, S.A.R., E.G.d.S. and T.G.d.M.; software, T.G.d.M. and S.A.R.; validation, S.A.R. and E.G.d.S.; supervision, T.G.d.M.; writing, S.A.R., E.G.d.S. and T.G.d.M. All authors have read and agreed to the published version of the manuscript.

Funding

The APC was funded by the Federal Center for the Technological Education of Minas Gerais.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Acknowledgments

The authors would like to acknowledge the Companhia Energética de Minas Gerais (CEMIG) and Companhia Hidro Elétrica do São Francisco (CHESF) Eletrobras for providing the data for the real cases, which significantly contributed to the research and validation of the applied methods.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Voltage–current characteristic of a MOV.
Figure 1. Voltage–current characteristic of a MOV.
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Figure 2. Capacitor bank protection using varistors.
Figure 2. Capacitor bank protection using varistors.
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Figure 3. MOV conduction during a short-circuit phase B.
Figure 3. MOV conduction during a short-circuit phase B.
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Figure 4. Flowchart of the fault location process.
Figure 4. Flowchart of the fault location process.
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Figure 5. Compensated line transmission indicating Brazil’s electrical system.
Figure 5. Compensated line transmission indicating Brazil’s electrical system.
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Figure 6. Voltages and currents for an AG fault. (a) Sobradinho Terminal; (b) S. J. Piauí Terminal.
Figure 6. Voltages and currents for an AG fault. (a) Sobradinho Terminal; (b) S. J. Piauí Terminal.
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Figure 7. Currents in the transmission line, capacitor bank, and protective equipment for the AG fault.
Figure 7. Currents in the transmission line, capacitor bank, and protective equipment for the AG fault.
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Figure 8. Elimination of source parameters.
Figure 8. Elimination of source parameters.
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Figure 9. Algorithm proposed for fault location.
Figure 9. Algorithm proposed for fault location.
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Figure 10. Electrical system with an AG fault for the proposed algorithm.
Figure 10. Electrical system with an AG fault for the proposed algorithm.
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Figure 11. The selection of phasors to define the source values when assembling the circuit in the ATP.
Figure 11. The selection of phasors to define the source values when assembling the circuit in the ATP.
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Figure 12. ATP model used for obtaining ANN training files.
Figure 12. ATP model used for obtaining ANN training files.
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Figure 13. Models to simulated faults: (a) AG, (b) BC, (c) ABC, and (d) ACG (adapted from [1]).
Figure 13. Models to simulated faults: (a) AG, (b) BC, (c) ABC, and (d) ACG (adapted from [1]).
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Figure 14. Selection of input quantities in the ANN according to the type of fault.
Figure 14. Selection of input quantities in the ANN according to the type of fault.
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Figure 15. The selection of current phasors inputted into the ANN.
Figure 15. The selection of current phasors inputted into the ANN.
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Figure 16. Modular ANN structure for fault location.
Figure 16. Modular ANN structure for fault location.
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Figure 17. Voltages and currents for a BCG fault. (a) Sobradinho Terminal; (b) S. J. Piauí Terminal.
Figure 17. Voltages and currents for a BCG fault. (a) Sobradinho Terminal; (b) S. J. Piauí Terminal.
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Figure 18. Currents in the transmission line, capacitor bank, and protective equipment (BCG fault) (adapted from [1]).
Figure 18. Currents in the transmission line, capacitor bank, and protective equipment (BCG fault) (adapted from [1]).
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Table 1. Characterization of ANNs in fault location studies in transmission lines.
Table 1. Characterization of ANNs in fault location studies in transmission lines.
ANNsReferences
ModelMultilayer perceptron[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]
Others[7,8,25,26]
FeedingFeedforward[3,4,5,8,9,12,13,14,15,16,17,18,19,20,21,23,24,25,27,28,29,30]
LearningBackpropagation[4,5,6,8,9,11,24,25,28,30,31]
TrainingLevenberg–Marquardt[3,4,5,8,9,10,12,13,14,15,16,17,18,19,20,21,24,25,28,30]
Others[8,11]
Activation FunctionNon-linear[4]
Sigmoid[5,10,14,18]
Hyperbolic tangent[3,8]
Logarithmic[10,12,14]
Gaussian[26]
Table 2. Set of variables to generate the training patterns based on fault type.
Table 2. Set of variables to generate the training patterns based on fault type.
VariablesTraining DataTotal
Fault locations (%)Simulated faults every 2.5% of the transmission line39
Phase–ground and phase–phase–ground
RF (Ω)		0–3–6–9–12–15–18–21–24–27–30–33–36–39–4215
Phase–phase and three-phase
RF (Ω)		0–1–2–3–4–5–67
Number of scenarios for each fault typePhase–ground and phase–phase–ground: 1 × 15 × 39 = 585585
Phase–phase and three-phase:
1 × 7 × 39		273
Table 3. Set of variables to generate the validation patterns based on fault type.
Table 3. Set of variables to generate the validation patterns based on fault type.
VariablesValidation DataTotal
Fault locations (%)Simulated faults every 7% of the transmission line14
Phase–ground and phase–phase–ground
RF (Ω)		2–10–14–19–22–28–35–408
Phase–phase and three-phase
RF (Ω)		2.5–3–4.5–5.54
Number of scenarios for each fault typePhase–ground and phase–phase–ground: 1 × 8 × 14112
Phase–phase and three-phase:
1 × 4 × 14		56
Table 4. Source parameters provided by the power company.
Table 4. Source parameters provided by the power company.
LineVoltage (kV)Extension
(km)		Sending End (ZS)Receiving End (ZR)
Positive Sequence (ohms)Zero Sequence (ohms)Positive Sequence (ohms)Zero Sequence (ohms)
R1X1R0X0R1X1R0X0
134574.404.0007734.110304.0692033.603206.3318353.845002.7306939.36370
2500105.580.9297920.057502.3047025.389701.2857026.191702.2083440.56020
3500342.710.9297920.057502.3047025.389700.5730318.032800.5385114.04110
423036.41----------------
Table 5. Errors for real short-circuit cases (lines without series compensation).
Table 5. Errors for real short-circuit cases (lines without series compensation).
LTExtension (km)FaultInspection Results (km)CauseRef. [39]Proposed Method
Error (%)Error (%)
174.40AG60.0AD12.410.38
BG54.031.402.29
2105.58AG30.0Fire12.702.96
3342.71AG55.0Fire4.900.19
CG76.08.900.06
CG317.0AD3.300.10
434.61ABG16.0AD--1.44
Average error (%)12.271.14
Table 6. Errors for simulated short-circuit cases (lines with series compensation).
Table 6. Errors for simulated short-circuit cases (lines with series compensation).
Compensated LevelLocation
(km)		Type of FaultRF
(Ω)		Error (%)
35%51.2CG250.63
AB2.50.05
ABC1.50.01
166.4CG250.32
AB2.50.10
ABC1.50.23
Table 7. Errors for real short-circuit cases (lines with series compensation).
Table 7. Errors for real short-circuit cases (lines with series compensation).
Voltage (kV)Extension (km)TypeLocation (km)Inspection Results (km)Error (%)
500211AG5.77.00.62
BCG129.38132.321.39
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Rocha, S.A.; de Mattos, T.G.; da Silveira, E.G. A Practical Approach for Fault Location in Transmission Lines with Series Compensation Using Artificial Neural Networks: Results with Field Data. Energies 2025, 18, 145. https://doi.org/10.3390/en18010145

AMA Style

Rocha SA, de Mattos TG, da Silveira EG. A Practical Approach for Fault Location in Transmission Lines with Series Compensation Using Artificial Neural Networks: Results with Field Data. Energies. 2025; 18(1):145. https://doi.org/10.3390/en18010145

Chicago/Turabian Style

Rocha, Simone Aparecida, Thiago Gomes de Mattos, and Eduardo Gonzaga da Silveira. 2025. "A Practical Approach for Fault Location in Transmission Lines with Series Compensation Using Artificial Neural Networks: Results with Field Data" Energies 18, no. 1: 145. https://doi.org/10.3390/en18010145

APA Style

Rocha, S. A., de Mattos, T. G., & da Silveira, E. G. (2025). A Practical Approach for Fault Location in Transmission Lines with Series Compensation Using Artificial Neural Networks: Results with Field Data. Energies, 18(1), 145. https://doi.org/10.3390/en18010145

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