Volume 17, Issue 18 p. 4215-4233
Open Access

A novel superimposed voltage energy-based approach for single phase to ground fault detection and location in distribution networks

Sajjad Miralizadeh Jalalt

Sajjad Miralizadeh Jalalt

Faculty of Electrical and Computer Engineering, Urmia University, Urmia, Iran

Contribution: Conceptualization, Data curation, Formal analysis, Methodology, Software, Writing - original draft

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Sepideh Miralizadeh

Sepideh Miralizadeh

School of Industrial engineering, Tehran University, Tehran, Iran

Contribution: Conceptualization, Data curation, Formal analysis, Software

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Vahid Talavat

Vahid Talavat

Faculty of Electrical and Computer Engineering, Urmia University, Urmia, Iran

Contribution: Conceptualization, ​Investigation, Project administration, Supervision

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Tohid Ghanizadeh Boalndi

Corresponding Author

Tohid Ghanizadeh Boalndi

Faculty of Electrical and Computer Engineering, Urmia University, Urmia, Iran


Tohid Ghanizadeh Boalndi, Faculty of Electrical and Computer Engineering, Urmia University, Urmia, Iran.

Email: [email protected]

Contribution: Conceptualization, Formal analysis, ​Investigation, Project administration, Supervision, Validation, Writing - review & editing

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First published: 12 September 2023


The structure complexity and the extended geographical area are among the factors that create challenges in accurate fault location and detection in distribution networks. The single-phase to ground (SPG) faults are considered as most frequent reasons for distribution network interruption, which can threaten the network's reliability. Signal processing methods are usually used as common approaches to distinguish and locate faults in distribution networks. This paper proposes a novel scenario to select optimal wavelet packet transform (WPT) coefficients for SPG fault location and a method based on superimposed voltage energy to distinguish the faulty phase according to these coefficients. Furthermore, employing the energies of the superimposed voltages helps to minimize the effects of high resistance faults (HRFs) and load encroachment on the efficiency of the faulty phase detection part. Comparing the obtained results with other scenarios demonstrates the considerable efficiency of the proposed scenario. Finally, with the help of general regression neural networks (GRNN) as machine-learning tools, a new algorithm is derived for detecting and locating the SPG fault and capacitor bank switching overvoltage (COV). Simulation results are implemented on the IEEE 34-bus standard distribution network, demonstrating the efficiency and superiority of the suggested method.


Improving the reliability of electricity distribution networks is of great importance due to the direct connection to the end-users. To achieve this aim, accurate fault detection and location can lead to reducing the duration of interruption and improving network reliability indices. However, due to the vastness and complexity of distribution networks, implementing an accurate and cost-effective method for fault location and detection has always been challenging. In this regard, signal processing-based methods can play a significant role. One of the most important applications of signal processing in distribution networks is its ability to detect and locate faults [1]. The measured voltage and current signals usually contain information about the behaviour and characteristics of phenomena occurring in the distribution networks. Their correct processing can provide helpful information to analyze the contingencies [2]. SPG faults are the most prevalent faults in distribution networks, which have the potential to cause disturbances and power outages in the system. Since the accurate detection and fast isolation of SPG faults is essential for improving the reliability of distribution networks, implementing a reliable protection scheme based on signal processing would be of interest and still need further development.

According to IEEE 60071-1 standard, overvoltage occurs when voltage amplitude becomes greater than the system's basic insulation level. Overvoltage created by SPG faults is placed in the category of temporary overvoltage. Recently, the identification and location of faults leading to overvoltage in distribution network is one of the most significant challenges in network protection, which has been considered in the literatures. Because of the direct connection of electric distribution networks to customers, structural complexity and low insulation level, the damage caused by overvoltage in these networks is more than other parts of the power system. In addition, with the increase of underground distribution networks in large cities, the detection and location of damaged cable in these networks is more complicated than aerial lines [3]. The switching overvoltage frequency range is about [250–2500 μs]. Phase-to-ground faults or phase-to-phase faults usually cause temporary overvoltages in distribution networks. Temporary overvoltage waves are relatively long-term signals that oscillate undamped or gradually decay [4]. Phase-to-ground faults or phase-to-phase faults usually cause temporary overvoltages in distribution networks. Many researchers have studied the characteristics, mechanism of occurrence and effect of overvoltages on power system [5]. Series capacitors, shunt reactors, and surge arresters are employed to restrict the amplitude of temporary and transient overvoltages in power system. However, due to the static nature of these devices, they cannot identify and locate overvoltages created in distribution networks.

Numerous methods for locating and diagnosing faults in distribution networks have been proposed in recent years. One of them is the impedance-based method. However, the accuracy of this method can be affected by fault resistance and the line parameters [6, 7]. The traveling wave-based method is another approach that estimates the fault location using Fourier and wavelet transforms [8]. Although the proposed method is not affected by fault resistance and line parameter, its implementation requires a fast communication network. A combination of artificial neural networks and wavelet transform has been used for fault location in a distribution network using a four-layer MLP method with two hidden layers in [9]. In addition, discrete wavelet transform and neural networks are also used to design an intelligent protection system [10], detect high impedance faults in distribution network [11, 12], improve power quality [13], and detect the fault type in AC and DC smart grids [14, 15]. In [16], based on conventional neural network (CNN) and Hilbert Huang transform (HHT), a fault pattern recognition algorithm is proposed to identify the SPG fault. A SPG fault location method is proposed in [17] based on a wavelet fuzzy neural network (WFNN) in distribution network according to post-fault and steady-state signals. Although the proposed method has acceptable accuracy, the possibility of its implementing in large networks has not been evaluated. A convolutional neural network (CNN) method based on Choi–Williams time-frequency distribution is proposed in [18] for fault detection and location. However, its implementation in ring distribution networks is challenging. An algorithm for SPG fault location using a one-dimensional convolutional neural network (1D CNN) and waveform concatenation is proposed in [19] for resonant grounding distribution networks. High accuracy, suitable computational speed, low cost and simplicity are the advantages of this algorithm. However, this method requires a large amount of training data, which leads to an increase in complexity. The main drawback of the neural networks (NNs) methods is their need for training. If there is a change in the distribution network, either in the length of the line or in the number of loads, the NNs have to be trained again based on those changes, which is time-consuming.

Recently, various methods have been developed to monitor the occurrence of different types of overvoltage in distribution networks. An online monitoring system and an advanced programmable logic device (CPLD) are employed to detect internal and external overvoltages [20]. In [3], the S-transform is used to extract the frequency features of the overvoltages, and then a support vector machine (SVM) is used to classify them. A combination of discrete wavelet transforms and neural networks is used in [21] to locate the overvoltages created by capacitor banks switching. Some recently published papers that use signal processing and artificial intelligence methods (AI) to detect and locate faults in power systems are compared in Table 1.

TABLE 1. The proposed method versus other newly published approaches.
References Neural network Number of NN Fault resistance consideration Utilized signal Feature extraction tool Fault detection /location Fault type detection Size of training data Size of test data Output accuracy High fault resistance Load encroachment application
[22] (2022) RFa Yes Voltage /current DMDb D/L Yes 2730 630 D –100% No No PSCAD
[23] (2022) RNNc/LSTMd Yes Phasor ROCOFe D/L Yes 750 250 D –100% L – 98% No Yes DIgSILENT
[24] (2021) FFNNf 1 Yes Voltage /current WANg D/L Yes 5040 1080 99% No Yes Matlab
[25] (2020) 1D CNNh 1 Yes Current Time domain D No 250 200 100% Yes No Matlab/Simulink
[26] (2021) CNN/SAEi 2 Yes Current S A E $SAE$ D/L Yes 900 760 98% No No PSCAD
[27] (2020) 2-D CNN AlexNet 1 Yes 2D image CWTj D Yes 2400 1036 73% No No Matlab
[28] (2022) R F $RF$ 1 Yes Voltage /current. MMk D/L No 700 300 97% No No PSCAD
[29] (2019) ANN Taguchil 1 No Voltage /current DWTm D Yes 306 102 No Yes OP5600 real-time digital simulator
[30] (2020) C N N $CNN$ 4 No 2D image D Yes 1292 323 94% No No
[31] (2020) Bi–GRUn 1 Yes Current Time domain L Yes 1530 170 99% No No
[32] (2020) ACNNo 1 Yes Voltage /current Time domain D/L No 1800 4200 98% No Yes Matlab
[33] (2022) C N N $CNN$ 1 Yes Voltage CWTp D No 110 100 99.2% No Yes PSCAD/EMTDC
Proposed Algorithm GRNNq 4 Yes Voltage WPTr D/L No 348 1082 D –100% L – 98% Yes Yes ATP/Matlab
  • a) Random forest;
  • b) Dynamic mode decomposition;
  • c) Recurrent neural network;
  • d) Long short-term memory;
  • e) Rate-of-change-of-frequency;
  • f) Feedforward neural network;
  • g) Wavelet-alienation-neural;
  • h) 1D convolutional neural networks;
  • i) Sparse auto encoder;
  • j) Continuous wavelet transform;
  • k) Mathematical morphology;
  • l) Taguchi based artificial neural network;
  • m) Discrete wavelet transform;
  • n) Bidirectional gated recurrent unit;
  • o) Adaptive convolutional neural network;
  • p) Choi–Williams distribution;
  • q) General regression neural network;
  • r) Wavelet packet transform.

As mentioned above, the outcomes of the methods designed based on a combination of signal processing and AI tools depend on the accuracy and reliability of the recorded data, the number of them, the type of signal processing and AI tools and the structure of the proposed algorithms. This paper presents a novel scenario for selecting optimal WPT coefficients for SPG fault location to deal with the challenges mentioned above. In addition, to reduce the number of AI tools, a mathematical approach to detect the faulty phase is proposed, which leads to the reduction of AIs training data and detect the faulty phase without using AIs. Finally, a novel algorithm based on WPT transform and general regression neural network (GRNN) is designed to locate COV and SPG faults in distribution network. The proposed method is inspired by [4], but it has a significant advantage over this reference. In other word, the main goal of this paper is to introduce a method for the accurate detection and location of SPG faults, unlike the approach proposed in [4], which focuses on identifying the faulty area. Instead of using a neural network for each branch of the network to increase the accuracy of the fault location and detect the most probably affected area (MPA), the proposed method is focused on the accurate location estimation of SPG faults with minimum training data with neural networks, which reduces the need to store a large amount of data, reduces the related cost and finally enhances the accuracy of fault location and detection method. Moreover, the impact of the HRF and load encroachment is considered in this study.

The comparison presented in Table 1 confirms the superiority of the proposed method over other newly published approaches. In summary, the main innovation and contributions of the proposed protection scheme are as follows:
  • Detecting faulty phase based on calculating the energy of WPT coefficients without AIs,
  • Not affected by HRF and load encroachment,
  • Determining the best coefficient of WPT transform for SPG fault detection.
  • Exact fault location without the need to specify the faulty zones or the most probably affected area.
  • Dependent on a small number of AIs and thus reducing the amount of the training data.
  • Independence from the location of the monitoring unit.

The remainder of this paper is organized as follows: Section 2 describes some signal processing and AI methods, including frequency feature extraction and machine learning tools. Section 3 presents the proposed algorithm, the WPT coefficients selecting scenario, and finally, the faulty phase detection method. Section 4 evaluates the performance of the proposed method by simulation on the IEEE 34-bus network. Finally, Section 5 presents the conclusions of the paper.


Most of the fault detection and location methods which are based on the signal processing, consist of two stages. First, the main features of the waveform are extracted. Afterward, according to the obtained features, the fault location is identified by exploiting tools such as neural networks, support vector machines (SVM), and advanced fuzzy systems. In this section, the signal feature extraction tools are first introduced, and then the basics of machine learning tools are reviewed.

2.1 Frequency features extraction tools

Time domain data analysis requires large storage memory; furthermore, it needs a lot of information and details, which makes processing and characterization difficult. Accordingly, modern signal processing methods are used to convert signals from time domain to frequency, phasor, or other to reduce the data size using various mathematical transforms. Fourier transform, short-time Fourier transform (STFT), and wavelet transform, are the most common signal processing tools. some advantages and disadvantages of these signal processing tools are presented in Table 2. Wavelet transform has other models, namely discrete wavelet transform (DWT), continuous wavelet transform (CWT), and packet wavelet transforms (PWT) [34]. The DWT presented in Equation (1) is frequently used in fault detection due to its high computational speed compared to the CWT [35]. Figure 1 illustrates different signal processing tools that convert a signal from time domain to frequency or scale domains. If some of the remaining information in the details coefficient cannot be extracted by DWT, then WPT can be used to extract the detail coefficient by approximation, and the obtained detail coefficients can be used in the next level of WPT. Therefore, the approximate coefficients extracted from the current or voltage waveforms can be seen more clearly using this type of transform [9], [21]. Figure 2 illustrates the wavelet transforms in the normal and the packet decomposition method. CWT can be obtained as follows:
C W T f , a , b = 1 a f t ψ t a b d t $$\begin{equation}CWT\ \left( {f,a,b} \right) = \frac{1}{{\sqrt a }}\ \mathop \smallint \limits_{ - \infty }^\infty f\left( t \right){{\psi}}\left( {\frac{{t - a}}{b}} \right){\mathrm{d}}t\end{equation}$$ (1)
where a and b are the scaling (dilation) and translation (time shift) constants, respectively, and ψ is the wavelet function. The selection of the wavelet function (mother wavelet) is flexible, provided that it satisfies the so-called admissibility conditions. The f is the sampled waveforms of the initial signal.
TABLE 2. Advantages and disadvantages of the signal processing tools.
Advantages Disadvantages
Fourier transform
  • Powerful tool for analyzing signals in the frequency domain
  • Simplicity and ability to be implemented in both linear and nonlinear systems
  • Ability to identify and isolate specific frequencies or frequency bands in a signal
  • Widely used in signal and image processing and communication
  • Limitation in analyzing the continuous signals in time and cannot to be used for discrete signals
  • Sensitivity to noise
  • High computational burden for the signals with long length
  • Lack of ability to analyze the non-periodic signals
  • Lack of ability to detect the moment of variation and turbulences
  • Time–frequency analysis
  • Localization of frequency components
  • High resolution
  • Signal transients and time localization
  • Real-time analysis
  • Time–frequency tradeoff
  • Fixed window size
  • Spectral leakage
  • Boundary effects
  • Sensitivity to noise
  • Time–frequency localization
  • Multiresolution analysis
  • Adaptability to signal characteristics
  • Edge and singularity detection
  • Time variant analysis
  • Complexity of wavelet selection
  • Difficulty in interpretation and visualization of the results
  • Boundary effects
  • Sensitivity to noise
  • Computational complexity
Details are in the caption following the image
A comparison between different signals transform tools.
Details are in the caption following the image
(a) Wavelet Packet Transform (WPT). (b) Discrete wavelet transform.
For discrete signals, DWT can be implemented as follows:
D W T f , m , n = 1 a 0 m k f k ψ n k a 0 m a 0 m $$\begin{equation}DWT\ \left( {f,m,n} \right) = \frac{1}{{\sqrt {a_0^m} }}\ \mathop \sum \limits_{\mathrm{k}} f\left( k \right){{\psi}}\left( {\frac{{n - ka_0^m}}{{a_0^m}}} \right)\end{equation}$$ (2)
where f [ k ] $f[ k ]$ is the sample k of waveform f. ( a 0 m = a ) $( {\ a_0^m = \ a} )$ and ( k a 0 m = b ) $( {\ ka_0^m = \ b} )$ are the discretised parameters of scaling and translation, respectively. Furthermore, signals are decomposed into two parts of detail ( d j ( k ) $({d}_j( k )\ $ and approximation ( a j ( k ) ) $( {{a}_j( k )} )\ $ by using WPT, based on (2) as follows [35]:
f t = k a j k φ 2 j t b + j k d j k ψ 2 j t b $$\begin{equation}f\ \left( t \right) = \mathop \sum \limits_k {a}_j\left( k \right)\varphi \left( {{2}^jt - b} \right)\ + \mathop \sum \limits_j \mathop \sum \limits_k {d}_j\left( k \right)\psi \left( {{2}^jt - b} \right)\end{equation}$$ (3)
where φ ( ω ) $\varphi ( \omega )$ , and ψ ( ω ) $\psi ( \omega )$ are the scaling and wavelet functions in different types and shapes. The approximations and details of the signal can be obtained as follows:
a j k = 2 j f t φ 2 j t k d t $$\begin{equation}{a}_j\ \left( k \right) = {2}^j\ \smallint f\left( t \right)\varphi \left( {{2}^jt - k} \right){\mathrm{d}}t\end{equation}$$ (4)
d j k = 2 j f t ψ 2 j t k d t $$\begin{equation}{d}_j\ \left( k \right) = {2}^j\ \smallint f\left( t \right)\psi \left( {{2}^jt - k} \right){\mathrm{d}}t\end{equation}$$ (5)
where j and k are the levels and the coefficients of the WPT. In this study, the packet wavelet transform with Daubechies 4 wavelet function (db4) from the Shannon family is used.

2.2 Machine learning tools

Computational intelligence is a branch of artificial intelligence that can be used to extract knowledge, algorithms, or map various numerical data online. One of the main advantages of using computational intelligence is the reduction of computational time for complex equations, low computational errors, and high flexibility. Artificial Neural Networks are another powerful tool of artificial intelligence using modern computational methods for machine learning, data presentation, and applying the obtained knowledge to predict the output of complex systems. Neural networks are composed of various components, the most important of which are neurons, transfer functions, and layers. A neuron is the smallest unit of an artificial neural network that forms the function of neural networks. Figure 3a illustrates a neuron model with only one input (p). The relationship between the neuron and weight (w) parameter is defined based on the transfer function (f), which has various types. In Figure 3b, a biased neuron is created by adding a numerical value to the structure of a neuron. Transfer functions are used to characterize neurons to solve different problems and have different types with various applications. Depending on the application, architecture, and reversibility, neural networks can be classified into various types. The most important neural networks are feed networks, perceptron, post-diffusion, base radius, self-organized, and vector and reversal. General regression neural networks (GRNNs) are often used for function approximation. These networks have a base radius layer and a particular linear layer [36].

Details are in the caption following the image
Architecture of a single neuron in a neural network. (a) Without bias, (b) with bias.
GRNN is a single-pass associative memory feed-forward Artificial Neural Network (ANN) and uses normalized Gaussian kernels in the hidden layer as activation functions. As shown in Figure 4, GRNN is composed of input, hidden, summation, and output layers. When GRNN is trained; it memorizes every unique pattern. This is why it is a single-pass network and does not require any back-propagation algorithm. After GRNN is trained with good training patterns, it can generalize to new inputs. The output of GRNN can be calculated using (6) and (7).
D i = X X i T X X i $$\begin{equation}\ {D}_i = \ {\left( {X - {X}_i} \right)}^T\left( {X - {X}_i} \right)\end{equation}$$ (6)
Y ̂ = i = 1 N Y e D i / 2 σ 2 i = 1 N e D i / 2 σ 2 $$\begin{equation}\ \hat{Y}=\frac{\mathop{\sum }_{i = 1}^{N}Y{{e}^{\left( -{{D}_{i}}/2{{\sigma }^{2}} \right)}}}{\mathop{\sum }_{i = 1}^{N}{{e}^{\left( -{{D}_{i}}/2{{\sigma }^{2}} \right)}}}\end{equation}$$ (7)
where D i ${D}_i$ is the Euclidean distance between the input X i ${X}_i$ and the training sample input; X, Y is the training sample output; Y ̂ $\hat{Y}$ is the output of GRNN, and σ is the smoothing parameter of GRNN.
Details are in the caption following the image
General regression neural network (GRNN) architecture.


The first conventional step of signal processing-based methods is to receive signals from the power system and then analyze them with different mathematical transforms to extract the required feature of different phenomena. However, selecting a suitable signal that can provide more features of a phenomenon and is less affected by other distribution network changes, such as HRF, load variations, noise etc., is necessary to reduce calculation time and increase accuracy. In this regards, superimposed voltage signals as an effective method are employed and their extracted features are used to train, validate, and test the NN. In a digital environment, the superimposed component of a sampled signal can be extracted by subtracting the current sample from its corresponding sample in the previous cycles. To mitigate the adverse impact of load dynamic changes and noise on the extracted superimposed component, an additional term is introduced within parentheses as follows [37]:
Superimposed voltage = Δ V k = V k V k 2 N V k 2 N V k 4 N $$\begin{eqnarray} {\mathrm{Superimposed\ voltage}}\ &=& \ \Delta V\ \left[ k \right] = \ V\left[ k \right] - V\left[ {k - 2N} \right]\nonumber\\ &&- \left( {V\left[ {k - 2N} \right] - V\left[ {k - 4N} \right]} \right)\end{eqnarray}$$ (8)
where Δ V [ k ] $\Delta V[ k ]\ $ and V [ k ] $V[ k ]\ $ are the superimposed sample and the current sample of the digital voltage signal, respectively. N is the total number of signal samples taken per power-frequency cycle and k is the sample number. Therefore, using the superimposed component can avoid the impact of the noisy input signal on the performance of wavelet decomposition approach.
As mentioned before, one of the practical signal processing tools is WPT, which has a high ability to analyze the high frequency signals. Since each level of WPT includes all signal frequencies, the selection of an appropriate level and suitable approximation coefficients of the wavelet transform is usually performed according to the fault frequency range, researchers' point of view etc. Selecting the coefficients of a specific level of the WT is a prevalent method. Here, different scenarios for selecting the optimal coefficients of the WPT for SPG fault are considered. In this regard, different SPG faults at different locations of each line with various fault resistances are simulated in a case study network depicted in Figure 5. In the following, the frequency features of the signals are extracted, and the energy of the selected frequency bands is calculated, whose equations are presented for continuous and discrete signals x ( t ) $x( t )$ and x ( n ) $x( n )\ $ in (9) and (10), respectively.
E s = x t , x t = x t 2 d t $$\begin{equation}{E}_s = \ \left\langle {x\left( t \right),x\left( t \right)} \right\rangle = \ \mathop \smallint \limits_{ - \infty }^\infty {\left| {x\left( t \right)} \right|}^2dt\end{equation}$$ (9)
E s = x n , x n = x n 2 $$\begin{equation}{E}_s = \ \left\langle {x\left( n \right),x\left( n \right)} \right\rangle = \ \mathop \sum \limits_{ - \infty }^\infty {\left| {x\left( n \right)} \right|}^2\end{equation}$$ (10)
Details are in the caption following the image
The case study network.

Three main reasons for focusing on SPG fault location compared to COV are as follows: Firstly, due to the predetermined number and placement of capacitor banks in the network, GRNN can accurately predict their locations using extensive training data. Secondly, COV occurs due to improper operation of capacitor bank switching. Third, SPG faults are common in distribution networks and have a high potential to cause disruptions in power system.

In General, the maximum energy of the three-phase voltages recorded by the monitor is usually in the frequency range [0–10] kHz for an SPG fault [4, 36]. In this study, three different scenarios are presented to select the most appropriate WPT coefficients. The first scenario is adopted according to the selected coefficients presented in [4], which are ten different scales of various levels of WPT, whose frequency is in the range of [0–10 kHz]. Their calculated energies are also used as training data for the neural networks. The coefficients of scenario-1 are represented as E d i j , $Edi - j,$ where i and j are the selected levels and scales of the calculated energies defined as follows:
E s c e n a r i o 1 = [ E d 11 1 , E d 9 1 , E d 9 2 , E d 9 3 , E d 9 4 , E d 9 5 , E 9 6 , E 9 7 , E 9 8 , E d 9 9 , , E ( d 8 _ 5 , d 7 _ 3 , d 5 _ 1 , d 4 _ 1 , d 3 _ 1 , d 2 _ 1 , d 1 _ 1 ) ] $$\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {{E}_{scenario1} = \ [Ed{{11}}_1,\ Ed{9}_1,Ed{9}_2,\ Ed{9}_3,Ed{9}_4,Ed{9}_5,E{9}_6,E{9}_7,}\\[6pt] {E{9}_8,Ed{9}_9, \ldots ,\sum E(d8\_5,d7\_3,d5\_1,d4\_1,d3\_1,d2\_1,d1\_1)]} \end{array} \end{equation}$$ (11)
The second scenario is to select the first ten approximate coefficients of a specific level of WPT. In this case, level 11 is chosen and presented in (12). Finally, the third and proposed scenario is to detect and employ the coefficients with the most significant changes during the occurrence of SPG fault to show the energy difference among the network lines. For this purpose, a SPG fault is simulated at a specific distance from each line in the case study network. After that, for 11 levels of WPT, all energy approximation coefficients are calculated for the same fault in each line. A part of the calculated energies of approximate coefficients of WPT (4070 items) for a SPG fault in phase A is presented in Table 3. After that, the standard deviation (SD) of each row is calculated and normalized by dividing the sum of SDs of each row by the mean of that row. The normalized standard deviation (NDS) is obtained by (13). Finally, the calculated values are sorted from the highest to the lowest and are presented in Table 4. These steps are repeated for fault resistance of 1 and 5 Ohms and different faulty phases. It is evident that for all states, the first 50 values of Table 4 are similar, and all are from levels 11, 10, 9, 8, and 7 of the WPT transform. Therefore, the first ten values are selected as the third scenario to train the neural networks as the input matrix. The results presented in Table 4 demonstrate that the proposed method for selecting the optimal coefficients of the WPT, compared to the method proposed in [4] achieves superior outcomes. The coefficients of the third scenario are presented in (14).
E s c e n a r i o 2 = [ E d 11 _ 1 , E d 11 _ 2 , E d 11 _ 3 , E d 11 _ 4 , E d 11 _ 5 , E d 11 _ 6 , E d 11 _ 7 , E d 11 _ 8 , E d 11 _ 9 , E d 11 _ 10 ] $$\begin{equation} \def\eqcellsep{&}\begin{array}{l} {E}_{scenario2} = \ [Ed11\_1,Ed11\_2,Ed11\_3,Ed11\_4,\\[6pt] Ed11\_5,Ed11\_6,Ed11\_7,Ed11\_8,Ed11\_9,Ed11\_10] \end{array} \end{equation}$$ (12)
Normalized S D = σ j μ j = ( x i μ j 2 N μ j $$\begin{equation}{\mathrm{Normalized}}\ SD\ = \ \frac{{\sigma \left( j \right)}}{{\mu \left( j \right)}} = \ \frac{{\sqrt {\frac{{\sum ({x}_i - \mu {{\left( j \right)}}^2}}{N}} }}{{\mu \left( j \right)}}\end{equation}$$ (13)
where N is the size of the population (here is 10), x i ${x}_i$ is each value from the population, μ represents the population mean and j is the number of the row.
E _ s c e n a r i o 3 = [ E d 10 _ 1 , E d 11 _ 3 , E d 11 _ 1 , E d 8 _ 1 , E d 9 _ 3 , E d 8 _ 3 , E d 10 _ 6 , E d 11 _ 13 , E d 9 _ 6 , E d 9 _ 1 ] $$\begin{equation} \def\eqcellsep{&}\begin{array}{l} E\_scenario3 = \ [Ed10\_1,Ed11\_3,Ed11\_1,Ed8\_1,\\[6pt] Ed9\_3,Ed8\_3,Ed10\_6,Ed11\_13,Ed9\_6,Ed9\_1] \end{array} \end{equation}$$ (14)
TABLE 3. Total calculated energy of 11 levels of the wavelet packet decomposition (WPD) on different branches of the case study network with fault resistance equal to 10 Ohm for single phase to ground (SPG) fault on phase A.
coefficient line 1 line 2 line 3 line 4 line 5 line 6 line 7 line 8 line 9 line 10
Level 1 d1_1 273,558 214,791.1 354,012.9 290,021.6 1,751,254 2,500,414 4,190,961 1,251,757 1,271,711 839,766.6
Level 2 d2_1 2,990,382 5,668,387 11,290,690 2,552,131 10,080,579 6,540,625 10,194,991 13,964,704 5,075,970 3,067,692
d2_2 23,442.66 29,145.99 32,928.39 39,965.52 56,872.57 226,773.7 2,505,186 444,717.3 68,165.44 126,713.9
d2_3 250,115.4 185,645.3 321,084.5 250,056.1 1,694,381 2,273,641 1,685,774 807,039.5 1,203,546 713,052.7
Level 3 d3_1 25,723,762 24,623,213 46,035,718 31,809,386 36,493,670 53,909,009 42,971,574 35,712,086 20,805,146 23,083,635
d3_2 470,142.9 1,100,065 1,072,022 264,060.4 696,459.8 978,325.5 6,501,154 4,915,183 895,204.2 760,484.9
d3_3 2,520,266 4,568,349 10,218,682 2,288,084 9,384,129 5,562,309 3,693,845 9,049,530 4,180,776 2,307,219
d3_4 1362.728 930.6001 2314.199 2583.395 2501.854 18,205.73 1,232,752 280,922 26,095.6 20,026.8
d3_5 22,079.97 28,215.43 30,614.21 37,382.14 54,370.73 208,567.9 1,272,434 163,795.3 42,069.85 106,687.1
d3_6 143,298.7 66,268.79 196,545.4 142,335.5 946,071.5 1,465,275 397,075.8 515,381.3 831,644.4 552,823
d3_7 106,816.9 119,376.6 124,539.1 107,720.7 748,309.9 808,365.3 1,288,698 291,658.3 371,901.5 160,229.8
Level 11 d11_1 5.79E+09 1.05E+10 8.91E+09 7.89E+09 6.89E+09 6.98E+09 6.9E+09 5.13E+09 4.99E+09 3.16E+09
d11_2047 304.1145 280.2049 189.6327 688.215 1955.08 202.8752 2269.93 5369.267 3333.437 422.736
TABLE 4. The highest ten computed (standard deviations/mean) wavelet packet decomposition (WPD) approximated coefficients.
Faulty phase—A Faulty phase—B Faulty phase—C
R = 1 Ω R = 5 Ω R = 10 Ω R = 10 Ω R = 10 Ω
Coefficient NSD Coefficient NSD Coefficient NSD Coefficient NSD Coefficient NSD
1 d10_1 2.53E+09 d10_1 2.63E+09 d10_1 2.36E+09 d11_3 1.22E+09 d10_1 1.63E+10
2 d11_3 2.47E+09 d11_3 2.59E+09 d11_3 2.33E+09 d10_1 1.22E+09 d11_3 1.6E+10
3 d11_1 2.4E+09 d11_1 1.84E+09 d11_1 1.05E+09 d11_1 1.2E+09 d11_1 8.59E+09
4 d8_1 4.15E+08 d8_1 3.78E+08 d8_1 3.37E+08 d8_1 3.32E+08 d8_1 3.03E+09
5 d9_3 3.03E+08 d9_3 2.75E+08 d9_3 2.44E+08 d8_3 2.44E+08 d9_3 2.21E+09
6 d8_3 2.59E+08 d8_3 2.34E+08 d8_3 2.08E+08 d9_3 2.36E+08 d8_3 1.85E+09
7 d10_6 2.52E+08 d10_6 2.26E+08 d10_6 1.96E+08 d10_6 2.05E+08 d10_6 1.8E+09
8 d11_13 2.4E+08 d11_13 2.15E+08 d11_13 1.87E+08 d9_6 1.91E+08 d11_13 1.71E+09
9 d9_6 2.29E+08 d9_6 2.07E+08 d9_6 1.83E+08 d11_13 1.84E+08 d9_6 1.62E+09
10 d9_1 2.27E+08 d9_1 2.05E+08 d9_1 1.77E+08 d9_1 1.39E+08 d9_1 1.45E+09
After calculating the energies of the specified frequency bands, an intelligent tool is needed to analyze the data, identify the differences between them, and then detect the type of faults. In this study, neural networks are used for this aim due to their high processing speed and acceptable efficiency. In order to test the accuracy of each scenario, various neural networks are trained with different numbers of data. These trained neural networks are tested with the same number of test data in the following. Table 5 presents the results. Phase A is the faulty phase and others are the sound phases. General Regression Neural Network (GRNN), Feedforward Neural Network (FFNN), Radial Basis Function neural network (RBF), and Pattern Recognition neural network (PRNN) are all utilized for analyzing the accuracy of the fault type detection and SPG fault location. The following conclusions can be obtained from Table 5:
  • As the number of NN training data increases, the accuracy of the outputs increases.
  • The results obtained by Scenario 3 are more accurate than other scenarios,
  • The results obtained by GRNN are better and more reliable than others,
  • Using one GRNN (GRNN_ABC) instead of three different GRNNs for each phase has better results in a few training samples; However, increasing the number of training samples leads to better outcomes for separated GRNNs.
TABLE 5. Outputs of different neural networks based on same training and test data obtained for three scenarios in the case of faulty phase A.
Train sample Scenarios The number of correct answers out of 100 test samples (each phase)
12 sample Ref. [4] 23/100 28/100 26/100
level 11 12/100 19/100 17/100
Proposed method 34/100 29/100 31/100
18 sample Ref. [4] 28/100 37/100 33/100
level 11 29/100 42/100 23/100
Proposed method 39/100 46/100 35/100
24 sample Ref. [4] 31/100 43/100 48/100 7/100 13/100 7/100 8/100 8/100 8/100 7/100 5/100 5/100
level 11 39/100 38/100 36/100 8/100 20/100 11/100 8/100 8/100 8/100 5/100 9/100 3/100
Proposed method 48/100 52/100 49/100 15/100 7/100 8/100 8/100 8/100 8/100 8/100 3/100 10/100
3*12 sample Ref. [4] 26/100 33/100 29/100
level 11 13/100 16/100 18/100
Proposed method 39/100 35/100 32/100
3*18 sample Ref. [4] 32/100 47/100 34/100
level 11 32/100 46/100 27/100
Proposed method 41/100 48/100 46/100
3*24 sample Ref. [4] 35/100 41/100 49/100 11/100 4/100 13/100 10/100 10/100 10/100 4/100 7/100 7/100
level 11 38/100 38/100 34/100 9/100 9/100 5/100 10/100 10/100 10/100 5/100 8/100 8/100
Proposed method 39/100 47/100 49/100 12/100 11/100 6/100 10/100 10/100 10/100 4/100 9/100 7/100

From Table 5, It can be seen that detecting the faulty phase before sending its energy matrix to the neural network can improve the accuracy of the fault location process in the distribution network using GRNNs, which are trained with SPG faults data for that specific phase. In this regard, the sum of each column of energy matrix elements is calculated, and the obtained results confirm that the faulty phase always has the highest value among the three phases. Table 6 and Figure 6 demonstrate this fact. Disconnecting a part of the network at the fault point and the limited time of the recorded signal (2.5 cycles) causes the low value of the Thevenin-equivalent impedance measured in the monitoring unit. Consequently, because of the low fault resistance in the faulty phase in comparison with other phases, the calculated energy of the faulty phase is higher than the other ones before tripping.

TABLE 6. total sum of energy of the selected coefficients of wavelet packet decomposition ( W P D $WPD$ ) in the test network.
Faulty phase B B B C C
Line 1 5 7 4 10
Phase A B C A B C A B C A B C A B C
E1 12.62 78.35 8.16 12.38 93.98 9.36 12.04 92.46 9.18 6.28 6.79 18.06 5.1 5.82 18
E2 4.92 9.14 4.85 29.97 41.83 29.92 39.65 48.19 39.61 2.64 2.66 5.7 13.68 13.7 14.01
E3 1.54 1.87 1.54 0.21 3.18 0.21 0.73 5.27 0.73 0.29 0.29 0.5 0.06 0.06 1.93
E4 6.51 9.28 6.5 2.27 21.02 2.26 3.64 32.79 3.64 3.95 3.95 6.34 1.55 1.55 11.03
E5 0.84 2.05 0.84 0.01 0.07 0.01 0.01 0.03 0.01 0.53 0.53 1.29 0.01 0.01 0.04
E6 0.3 0.88 0.3 0.14 0.42 0.14 0.2 0.69 0.2 0.2 0.2 0.41 0.07 0.07 0.19
E7 2.49 3.42 2.49 0.33 0.52 0.33 0.25 0.88 0.25 1.75 1.75 0.95 0.12 0.12 0.2
E8 1.91 2.07 1.91 0.27 0.97 0.27 0.21 0.41 0.21 1.49 1.49 2.74 0.21 0.21 0.29
E9 0.31 1.71 0.31 0.09 0.37 0.09 0.44 1.94 0.44 0.2 0.2 1.00 0.04 0.04 0.14
E10 0.06 0.35 0.06 0.06 0.24 0.06 0.09 0.39 0.09 0.03 0.03 0.16 0.03 0.03 0.07
1 10 E i $\mathop \sum \limits_1^{10} {{\bf{E}}}_{\bf{i}}$ 31.5 109.13 27 47.53 162.6 42.35 57.26 182.9 54.36 17.3 17.8 37.15 20.8 21.6 45.9
Details are in the caption following the image
Calculated energy of the total selected wavelet packet decomposition (WPD) coefficient for faults on each phase in different lines.
The outcomes of the signal processing procedure of the waveforms received from the monitor located in the test distribution network can be represented as follows:
E T = E V E C 1 E V E C 2 E V E C 3 $$\begin{equation}\ {E}_T = \left[ { \def\eqcellsep{&}\begin{array}{*{20}{c}} {{E}_{VEC1}}&{{E}_{VEC2}}&{{E}_{VEC3}} \end{array} } \right]\end{equation}$$ (15)
where E V E C 1 $\ {E}_{VEC1}$ , E V E C 2 ${E}_{VEC2}$ ,and E V E C 3 ${E}_{VEC3}$ are 10×3 matrices of the calculated energies related to three-phase voltages obtained from the monitor, that will be sent to the data processing unit.

In this regard, a new algorithm is proposed to increase the speed of signal processing process, improve the accuracy of overvoltage location and reduce the number of neural networks [4]. This method leads to the reduction of memory storage used by neural networks. Therefore, it can be seen that the proposed algorithm has high accuracy in fault detection and location. The executing process of the proposed algorithm is depicted in Figure 7.

Details are in the caption following the image
Proposed algorithm for single phase to ground (SPG) fault detection and location.

After calculating the energy matrix E, this matrix is sent to the processing unit, which consists of a GRNN neural network for fault detection and overvoltage fault type identification. Additionally, processing unit 1 includes a section that detects the faulty phases in the event of SPG fault. Faulty phase detection can be achieved after distinguishing the SPG fault; after that, the input matrix is sent to one of the three neural networks trained by SPG faults on the detected phase in processing unit 2. As a result, the computational speed and the accuracy of fault location are increased. The flowcharts of the employed method are presented in Figures 8 and 9.

Details are in the caption following the image
Flowchart of the single pahse to ground (SPG) fault and capacitor bank switching overvoltage COV location scheme.
Details are in the caption following the image
SPG fault and COV location algorithm.

In [4], different topologies which are depicted in Figure 10, are used to detect and locate the transient overvoltages. However, the fault location accuracy of the topologies presented in (a) and (b) is not sufficient; Furthermore, in the proposed topology in (c), one neural network is used for each line in the network, and another neural network is used to detect the fault type. Despite the excellent accuracy of this topology, due to the use of a large number of neural networks, the calculation speed decreases, and the memory storage required to implement the proposed method increases. Therefore, it is challenging to implement it in distribution networks, which have many lines. In addition, the fault location method presented in [4] is defined based on the determination of the most probably affected area (MPA), so this area differs depending on the selected. In the proposed topology in this paper, the exact location of the fault can be obtained with few neural networks, which increases the speed and accuracy of the proposed algorithm.

Details are in the caption following the image
Different employed topologies in [4]; (a) a unique general regression neural network (GRNN), (b) two GRNN working in parallel, (c) Nb + 1 GRNNs working in parallel.


In this section, the usefulness and the capability of the proposed algorithm for COV and SPG fault location are investigated on IEEE 34-bus standard distribution system depicted in Figure 11. In this regard, three monitoring units are placed at buses 8, 18, and 29 to record three-phase voltage signals and compare them with results obtained by the proposed method. These monitors sample three-phase instantaneous voltage values, and the recorded signals are used to extract the frequency features and calculate the energy of specific frequency bands utilizing WPD. After that, the E matrix is sent to the processing unit of the proposed algorithm to determine the type and location of SPG fault in the event of an overvoltage. The simulations are programmed with ATP and MATLAB software and executed on a PC with Intel Core i7 CPU @4 GHz and 16 GB RAM. Using this system, each Wavelet Packet Transform (WPT) calculation requires approximately 0.9 s to calculate all Wavelet Packet Decomposition (WPD) coefficients at level 11, and 1.1 s to calculate all the selected coefficients.

Details are in the caption following the image
Locations of the monitors on the IEEE 33-bus standard network.

To evaluate the effectiveness of the proposed scenario for the optimal selection of the WPD coefficient and the faulty phase detection method in case of SPG fault, the calculation process is implemented in this section, and the results are reported in Tables 7, 8 and Figure 12.

TABLE 7. Total calculated energy of 11 levels of the WPD transform on different branches of the network.
coefficient line 1 line 2 line 3 line 4 line 5 line 6 line 7 line 8 line 9 line 10 Line 33
level 1 d1_1 287,321.476 226,347.375 379,642.4 297,504.3 1,834,841 2,619,411 4,387,955 1,342,385 1,332,357.05 880,150.2 1405.4
level 2 d2_1 3,233,965.14 5,991,837.14 122,31013 2,652,486 10,626,382 6,927,643 10,672,163 15,075,071 5,336,604.88 3,303,228 70,985.2
d2_2 25,675.9882 30,917.3303 36,191.12 41,181.03 60,113.52 238,051 2,622,999 476,907.3 71,524.9367 133,131.6 450.2
d2_3 261,645.548 195,430.091 343,451.3 256,323.3 1,774,727 2,381,360 1,764,956 865,477.4 1,260,832.14 747,018.6 955.20
level 3 d3_1 27,479,533.6 26,436,137.1 5,155,0731 334,53262 39,583,816 59,537,106 44,970,484 4,055,3477 23,338,688.4 255,49881 568,060.3
d3_2 493,476.743 1,163,778.72 1,167,771 280,531.5 738,583.2 1,054,914 6,806,479 5,287,629 955,666.314 812,166.2 6686.36
d3_3 2,740,504.79 4,828,070.97 1,106,3250 2,371,963 9,887,806 5,872,736 3,865,691 9,787,450 4,380,946.43 249,1072 64,312.49
d3_4 1442.84223 1006.94156 2576.475 2688.556 2696.685 19,224.06 1,290,739 300,936.7 27,407.0572 21,041.16 25.577
d3_5 24,233.1678 29910.4057 33,614.65 38,492.49 57,416.84 218,827 1,332,260 175,970.6 44,117.8904 112,090.5 424.7107
d3_6 148,717.043 69979.012 209,529.8 145,725.8 990,545 1,534,496 415,651.8 552,061 870,387.028 578,976.7 259.181
d3_7 112,928.598 125451.146 133,921.5 110,597.6 784,182.5 846,864.5 1,349,304 313,416.5 390,445.149 168,041.9 696.09
Level 11 d11_1 2.462E+10 2.3963E+10 7.93E+09 7.25E+09 6.33E+09 6.58E+09 6.55E+09 4.88E+09 4732341041 3.04E+09 .. 2.6E+09
d11_2047 306.755587 286.696746 207.0546 707.3245 2031.619 205.6244 2364.751 5708.894 3561.78582 428.9645 .. 1.1810
TABLE 8. The first 10 numbers of the sorted values of all rows of Table 7.
Faulty phase—A Sound phase—B Sound phase—C
R = 5 Ω R = 5 Ω R = 5 Ω
Coefficient NSD Coefficient NSD Coefficient NSD
1 d11_1 7648692362 d11_1 4.97E+08 d11_1 9.59E+08
2 d11_3 1400960927 d11_3 4.52E+08 d11_3 5.15E+08
3 d10_1 1330219441 d10_1 4.51E+08 d10_1 4.98E+08
4 d8_1 880955811 d8_1 93098744 d8_1 93462101
5 d8_3 677711796 d8_3 69151143 d8_3 69279101
6 d9_3 566732788 d9_3 65875488 d9_3 66167765
7 d10_6 491718487 d10_6 56879864 d10_6 57313606
8 d9_6 477483109 d9_6 55039039 d9_6 55096564
9 d11_13 356868209 d11_13 51331346 d11_13 51560969
10 d9_1 294871610 d9_1 43805961 d9_1 51557895
Details are in the caption following the image
Calculated energy of the total selected wavelet packet decomposition (WPD) coefficient for each phase in different lines.

After selecting the optimal coefficients of the WPT for a SFG fault, the performance of the proposed method in the case of HRFs, different faulty phases, and load encroachment are investigated in Tables 9–11. It is evident that in 100% of the faults, the faulty phase can be detected easily from other phases, which means that the extracted data can be sent to the GRNN which is trained for this fault.

TABLE 9. The results of proposed method for detecting faulty phase with different resistances and high resistance faults (HRFs).
Monitor 1 Monitor 2 Monitor 3
R (Ω) Faulty phase A B C A B C A B C
2 A 1E+09 53,427,838 53,428,228 1.72E+09 55,935,497 55,935,607 1.04E+10 8.18E+08 8.18E+08
5 A 8.91E+08 36,036,808 36,037,163 1.53E+09 38,189,880 38,189,973 9.16E+09 7.33E+08 7.33E+08
10 B 1.19E+08 3.78E+09 1.19E+08 1.23E+08 6.43E+09 1.23E+08 2.64E+09 3.38E+10 2.64E+09
2 C 2.85E+08 2.85E+08 4.78E+09 1.31E+08 1.31E+08 7.81E+09 1.88E+09 1.88E+09 1.76E+10
50 A 1.43E+08 3,412,481 3,412,649 2.43E+08 3,243,172 3,243,191 2.26E+09 2.4E+08 2.4E+08
100 B 4,351,811 1.74E+08 4,351,622 3,492,963 2.91E+08 3,492,935 4.02E+08 3.54E+09 4.02E+08
1000 C 55,190 55,220 2,408,536 44,623 44,626 3,791,687 5,313,276 5,313,270 52,426,159
TABLE 10. The results of the proposed method for faulty phase detection at different moments and phases.
Monitor 1 Monitor 2 Monitor 3
T (s) Faulty phase A B C A B C A B C
0.021 C, R = 2 2E+08 2E+08 3E+09 2.2E+08 2.2E+08 5.5E+09 2.8E+09 2.8E+09 3.6E+10
0.315 B, R = 100 5,867,701 72,150,461 5,867,444 4,825,943 1.2E+8 4,825,924 3.3E+09 2.8E+10 3.3E+09
0.044 A, R = 25 1.7E+08 5.1E+06 5.1E+06 3E+08 1E+06 1E+06 822,338,000 73,122,858 73,122,819
1.115 C, R = 75 13,300,619 13,300,613 365,940,138 8,155,705 8,155,723 608,862,193 3.4E+09 3.4E+09 3.3E+10
TABLE 11. The results of the proposed method for faulty phase detection during load encroachment.
Monitor 1 Monitor 2 Monitor 3
Load location Load changes Faulty phase A B C A B C A B C
Bus 3 +200 A 2.0E+09 4.0E+07 5.3E+07 1.8E+9 6.8E+7 6.8E+7 10E+9 8.1E+08 8.2E+08
Bus 3 −50 A 2.3E+09 1.5E+07 1.5E+07 2E+09 4.9E+7 4.9E+7 1.1E+10 8.5E+08 8.5E+08
Bus 10 +300 B 1.6E+08 5.8E+09 1.6E+08 1.6E+08 9.3E+09 1.6E+08 3.1E+09 4.2E+10 3.1E+09
Bus 10 +100 C 9.5E+07 9.5E+07 1.8E+9 7E+07 7E+07 2.9E+9 7.4E+08 7.4E+08 9.9E+09
Bus 8 −100 A 1.2E+09 3.1E+7 3.1E+7 2.1E+09 4.9E+7 4.9E+7 1.1E+09 8.4E+7 8.4E+7
Bus 8 −100 No fault 0 0 0 0 0 0 0 0 0

According to the results obtained for faulty phase detection in SPG faults, it can be seen that after analyzing 346×3 single-phase to ground fault (Number 3 indicates that three monitors are placed in the network), at different times, branches, and phases, almost in 100% of the results, the total summation energy (TSE) of the faulty phase is higher than the other two sound phases. Testing data specifications are presented in Table 12.

TABLE 12. Neural network testing data specification.
The Number of sample of faults on phase A (SPG) 124
The Number of sample of faults on phase B (SPG) 132
The Number of sample of faults on phase C (SPG) 91
The Number of sample of No-faults 2
The Number of sample of COV 24
Total sample 372

Correct detection of the faulty phase during a SPG fault leads that the energy matrix E to be sent to the neural network, which is trained to identify the fault location on that specific phase. So, this strategy increases the accuracy and speed of the fault location and detection in the distribution network. Several test samples (372*3 fault samples include COV faults) and their results are presented in Table 13 for each monitor individually. From these results, it is can be seen that the accuracy of the proposed method is not affected by the monitor's location. The results obtained from the processing of three signals measured by each monitor are completely similar to each other. So, the analysis of the results of the experimental samples shows that the accuracy of the proposed method is 92%, 99%, and 85% in identifying the fault type, the faulty phase, and the fault location, respectively. Some parts of the obtained results are presented in Table 14. For more clarification, the fault type detection and location obtained from monitor #1 are illustrated in Figures 13 and 14. It is worth to notice that the locations of the monitoring devices are randomly selected. So, their locations do not significantly affect the accuracy of the detection and location of SPG faults. The presented results in Table 13 indicate that the accuracy rates for monitors 1, 2, and 3 are 86%, 85.45%, and 84.6% respectively, thereby confirming that the results of the proposed method remain unaffected by the location of the monitors. However, the optimal placement of the monitoring devices will be investigated as an independent issue in future studies.

TABLE 13. The separate results of the proposed algorithm for each monitor.
Fault type detection (COV or SPG) Faulty phase detection (SPG) Fault location SUM
Monitor 1 342/372 (91.9%) 344/346 (99.5%) 107/124 (86.7%) 113/131 (86.5%) 74/91 (81.3%) 320/372 (86%)
Monitor 2 335/372 (90%) 343/346 (99.1%) 115/124 (92.7%) 105/131 (80.1%) 72/91 (80%) 318/372 (85.45)
Monitor 3 348/372 (93.5%) 345/346 (99.7%) 116/124 (93.5%) 108/131 (82.4%) 67/91 (73.6%) 315/372 (84.6%)
TABLE 14. Comparison between the testing data and outputs of neural networks.
Testing data samples Results
Fault type Faulty phase Location Detected fault type Detected faulty phase Location Fault detection validation
SPG B L30 SPG B 30
COV B33 COV 33
SPG C L17 SPG C 21 ×
SPG B L14 SPG B 14
No—Fault No—Fault
COV B27 COV 27
COV B21 COV 21
SPG C L15 SPG C 15
SPG A L26 SPG A 26
COV B24 COV 24
SPG B L30 SPG B 30
SPG C L34 SPG C 34
SPG A L18 SPG A 18
SPG A L16 SPG A 16
SPG C (t1) L9 SPG C (t1) 9
SPG C (t2) L9 SPG C (t2) 9
COV B25 COV 25
COV B31 COV 31
SPG B L10 SPG B 13 ×
SPG A L20 SPG A 20
SPG C L22 SPG C 22
COV B26 COV 26
SPG A L10 SPG A 11 ×
SPG B L13 SPG B 13
SPG C L25 SPG C 25
SPG B L17 SPG B 17
No—fault No—fault
Details are in the caption following the image
Fault type detection results based on the extracted data from monitor 1.
Details are in the caption following the image
Fault location results based on the extracted data from monitor 1.


Here, first, different scenarios are investigated to select the optimal wavelet coefficients. Then a novel scenario is proposed based on the selection of the coefficient with the most variation during a SPG fault. The obtained results confirm that the proposed scenario is more accurate than other scenarios. Since the neural network training data is usually the basic information in a real situation and not in the simulation software, a new energy-based method is also proposed to detect the faulty phase. In this regard, a new fault detection and location scheme is presented. The practicability and effectiveness of the proposed algorithm are demonstrated on the IEEE 34 bus network, with three separate monitoring units and six capacitor banks. The use of three monitoring units confirms that the accuracy of the proposed does not depend on the location of the monitors. In addition, it was shown that the correct detection of the faulty phase helps to send the data to the neural network trained by the faulty phase. This procedure leads to increasing the efficiency of fault location, reducing the data required for training neural networks, and as a result, less storage memory, which is cost-effective. In power systems, two or more faults may simultaneously occur in different locations. Therefore, new algorithms can be designed to identify this type of fault in future works.


Sajjad Miralizadeh Jalalt: Conceptualization, Methodology, Investigation, Software, Writing—original draft. Sepideh Miralizadeh: Investigation, Formal analysis, Writing—review and editing. Vahid Talavat: Data curation, Visualization, Validation. Tohid Ghanizadeh Boalndi: review and editing, Conceptualization, Supervision.


The authors declare no conflicts of interest.


The authors received no specific funding for this work.


Data available on request from the authors: The data that support the findings of this study are available from the corresponding author upon reasonable request.