Fast Fault Line Selection Technology of Distribution Network Based on MCECA-CloFormer

Abstract

When a single-phase grounding fault occurs in resonant ground distribution network, the fault characteristics are weak and it is difficult to detect the fault line. Therefore, a fast fault line selection method based on MCECA-CloFormer is proposed in this paper. Firstly, zero-sequence current signals were converted into images using the moving average filter method and motif difference field to construct fault data set. Then, the ECA module was modified to MCECA (MultiCNN-ECA) so that it can accept data input from multiple measurement points. Secondly, the lightweight model CloFormer was used in the back end of MCECA module to further perceive the feature map and complete the establishment of the line selection model. Finally, the line selection model was trained, and the information such as model weight was saved. The simulation results demonstrated that the pre-trained MCECA-CloFormer achieved a line selection accuracy of over 98% under 10 dB noise, with a remarkably low single fault processing time of approximately 0.04 s. Moreover, it exhibited suitability for arc high-resistance grounding faults, data-missing cases, neutral-point ungrounded systems, and active distribution networks. In addition, the method was still valid when tested with actual field recording data.

1. Introduction

The distribution network, serving as the vital link between the transmission system and users, plays a crucial role in ensuring power supply reliability. According to statistics, approximately 80% of all faults are attributed to single-phase grounding issues [1]. In small-current grounding systems, these faults exhibit weak characteristics and susceptibility to noise interference, which hampers fault line identification. Failure to promptly address such faults may lead to inter-phase faults and pose potential risks to personnel safety. Therefore, conducting research on rapid and accurate fault line selection holds significant practical significance.

In small-current grounding systems, the amplitude of the fault transient component is several times larger than that of the steady-state component, and the method based on the transient electrical signal is not easily affected by the grounding mode, so many scholars choose the transient electrical signal for in-depth research [2,3,4,5,6]. Gong proposed to use db6 wavelet to carry out three-scale wavelet packet decomposition for zero-sequence current of each line, extract the wavelet coefficients of the characteristic frequency band for comparison, and select the fault line with the largest amplitude and different phase from other lines [7]. However, the selection of wavelet basis function requires certain professional knowledge and experience, and improper selection would cause misjudgment. Hou et al. used modified complementary ensemble empirical mode decomposition (MCEEMD) to divide the zero-sequence current into a series of intrinsic mode functions (IMF), then selected the optimal IMF for signal reconstruction, and input the reconstructed signal into the Duffing system for fault line selection [8]. But during signal reconstruction, there may be signal reconstruction errors, resulting in distortion of the original signal, which would further affect the subsequent fault line selection process. Li et al. employed fast Fourier transform (FFT) to analyze the transient zero-sequence current to determine the decomposition scale of variational modal decomposition (VMD), then performed VMD and combined it with the energy method to quantitatively describe the decomposition results to achieve fault line selection [9]. Notwithstanding, the FFT method has the problem of spectrum leakage. Some scholars have combined machine learning to achieve fault line selection [10,11]. Li et al. extracted pure transient electrical quantities based on the improved Hilbert–Huang transform (IHHT), constructed feature vectors by combining standard deviation, energy entropy and amplitude distortion, and established the fault line selection model through a random forest classifier, transforming the fault line selection problem into a binary classification problem and realizing automatic identification of fault lines [10]. Liu et al. used ensemble empirical mode decomposition to decompose zero-sequence currents before and after faults into five kinds of IMFs with different components, and obtained the energy entropy of transient zero-sequence currents via Hilbert transformation. Then, the feature vectors were input to STOA-SVM for training to achieve fault line selection [11]. However, this method is affected by the parameter selection of the sooty tern optimization algorithm. In general, the above methods all require feature extraction of signals, and the result of this feature extraction directly affects the accuracy of line selection, so the robustness of these methods is poor.

In recent years, deep learning methods have been extensively studied due to their ability to significantly reduce the accumulation of errors inherent in manual feature extraction processes, coupled with their end-to-end advantages and strong generalization capabilities [12]. Guo et al. concatenated the transient zero-sequence currents, measured at both ends of the line section after a single-line-to-ground fault occurrence by the digital fault indicator, to construct characteristic waveforms. Thereafter, they employed a one-dimensional convolutional neural network (1-D CNN) to adaptively extract features from these waveforms, facilitating the localization of the faulty section [13]. Wang proposed a fault line selection method grounded in a modified artificial bee colony optimization deep neural network (ACB-DNN), which could reduce training time [14]. Cheng et al. improved the complete ensemble empirical mode decomposition adaptive noise algorithm (CEEMDAN) to decompose the zero-sequence current of each line into a series of intrinsic mode functions, converted it into image form, and then processed it through wavelet transform and used a convolutional neural network to output the fault probability, so as to locate the fault line [15]. Nonetheless, data-driven deep learning methodologies are inherently susceptible to the constraints imposed by the quantity and caliber of their training samples. Insufficient sample numbers or failure to meet requisite quality standards can impinge upon the ultimate accuracy of the models’ predictions. In order to solve the problem of deep learning requiring a large amount of training data, transfer learning has gradually attracted the attention of scholars [16,17,18]. A. Anbarasi et al. used the pre-trained VGG-16 as the backbone model, and then fine-tuned the model using less than 900 public chest CT images to achieve the identification of COVID-19 patients [16]. Through a large number of experiments, Karim A.A. Mahmoud et al. found that fine-tuned pre-trained convolutional neural network models can effectively classify thermal images captured by switchgear units and achieve higher accuracy [17]. Jintao Hu et al. proposed a continuous domain distribution adversarial network (CDDAN) based on deep domain adversarial network, which can realize transfer learning to a continuous and multi-dimensional target domain, and verified the feasibility and superiority of the method on datasets generated based on twin-spool turbofan engines [18]. Liu et al. used domain adaptive transfer learning to complete variable condition migration to achieve fault line selection in the target domain, but a large number of target domain samples were still needed in the migration process [19]. Su et al. extracted similar fault features from other substation instances and migrated these features to target substation instances with limited samples [20]. This method achieved higher fault line selection accuracy than other methods in cases with small sample sizes, but this method was affected by the similarity between substation instances.

To address the above problems, a fault line selection method without samples from the target distribution network is proposed, which centers on training the model based on domain knowledge. Specifically, the main contributions of this paper can be summarized as follows:

• A method based on moving average filter (MAF) and motif difference field (MDF) for converting time series into images is proposed. The method starts with a moving average denoising of the one-dimensional zero-sequence current signal and then encodes it into a two-dimensional image using the motif difference field. The color distributions in MDF images are more intuitive and contain richer information than time-series data, and the image data can also be used directly as input for deep learning-based visual models.
• A faulty line selection model based on MCECA-CloFormer is proposed. The line selection model utilizes the MCECA module to fuse fault images from multiple measurement points and the CloFormer module with a two-branch structure to sense the difference between fault and non-fault feature maps. It has been demonstrated that the model can achieve fast and accurate fault line selection in target distribution networks under different operating conditions and line parameters.

The rest of this paper is organized as follows: Section 2 briefly analyzes the single-phase ground fault characteristics; Section 3 presents the MAF-MDF based imaging method; Section 4 introduces the MCECA-CloFormer based line selection model; the validity of the proposed method is verified and discussed in Section 5; and finally, Section 6 presents conclusions and future directions.

2. Characteristics Analysis of Single-Phase Grounding Fault

The simplified equivalent network of a resonant grounding system during a single-phase grounding fault occurrence is illustrated in Figure 1, for a distribution network comprising n feeders, with the fault taking place on the ith feeder. Here, u₀ represents the zero-sequence voltage of the bus bar, u_0i denotes the zero-sequence voltage of the power supply, and i_L signifies the equivalent zero-sequence current of the arc suppression coil. The variables i₀₁, …, i_0n denote the zero-sequence currents of respective feeders, while C₀₁, …, C_0n represent the zero-sequence capacitances of these feeders. The directions of zero-sequence currents in faulted and healthy lines, as illustrated in the figure, indicate their respective flow patterns.

From the diagram, expressions for the zero-sequence currents in both the faulty and healthy feeders can be derived, as represented by the following equations:

$$i_{0m}=C_{0m}{\displaystyle \frac{\mathrm{d}{u}_0}{\mathrm{d}t}}$$

(1)

$$i_{0i}=-(i_L+{\displaystyle \sum _{m=1,m\ne i}^n{i}_{0m}})=-(i_L+{\displaystyle \sum _{m=1,m\ne i}^n{C}_{0m}\frac{\mathrm{d}{u}_0}{\mathrm{d}t}})$$

(2)

As Equation (1) illustrates, the healthy feeders, being under the same zero-sequence voltage condition, exhibit identical expressions for their zero-sequence currents and display a high degree of waveform similarity. Equation (2), on the other hand, reveals that the magnitude of the zero-sequence current in the faulty feeder equals the sum of the zero-sequence currents from all healthy feeders combined with the current from the arc suppression coil. Comparing this with Equation (1), it becomes evident that there exists a disparity in the waveforms of the zero-sequence currents between the healthy and faulty feeders. The subsequent work in this paper will focus on exploring these waveform discrepancies.

3. Imaging Method Based on MAF-MDF

3.1. Moving Average Filter

Data collected by actual measuring devices for fault events often contain noise and may occasionally suffer from missing data issues [21], which can degrade the accuracy of fault line selection algorithms. Consequently, preprocessing is essential before mapping the zero-sequence currents into a two-dimensional representation. The moving average filter (MAF) possesses a certain degree of noise reduction capability and, in cases of data absence, can endeavor to fill gaps using neighboring data points. Compared to methods such as modal decomposition and wavelet transformation, its implementation is simpler and does not rely on subjective, experience-based parameter tuning. Since there are not enough sampling points to complete the average calculation of a complete window when processing the data at the beginning and end of the sequence by the method of moving mean filtering, a formula suitable for the complete sequence is given in this paper, as shown in Equation (3).

$$y(n)=\left\{\begin{array}{l}{\displaystyle \frac{1}{2m+1}}{\displaystyle \sum _{k=n-m}^{n+m}x(k), \frac{N+1}{2}\le n\le T-\frac{N-1}{2}}\\ {\displaystyle \frac{1}{2n-1}}{\displaystyle \sum _{k=1}^{2n-1}x(k), n<\frac{N+1}{2}}\\ {\displaystyle \frac{1}{2(T-n)+1}}{\displaystyle \sum _{k=2n-T}^{T}x(k), n>T-\frac{N-1}{2}}\end{array}\right.$$

(3)

where y(n) denotes the filtered signal value; n represents the index of the signal sequence; 2m + 1 signifies the width of the sliding filter window, with the window width set as an odd number; x(k) is the value of the original signal; and T represents the length of the time series.

3.2. Motif Difference Field

The motif difference field (MDF) is a methodology that encodes one-dimensional time series into two-dimensional images, effectively conveying structural information inherent in the time series. Compared to the Gramian angular field (GAF), MDF boasts a simpler implementation and is more straightforward to construct [22].

Suppose a discrete-time signal X = (x_t, t = 1,2,3,…, T) of total duration T is given. The image set of signal X in the time domain can be defined as follows:

$${\mathrm{M}}_d^n=\{M_{d,s}^n,s=1,2,\dots ,T-(n-1)\cdot d\}$$

(4)

where $M_{d,s}^n$= (x_t, t = s, s + d, s + 2d, …, s + (n − 1)d); n represents the length of the subsequence sampled from X using a sliding window, satisfying 1 < n ≤ T; s denotes the initial time index corresponding to the subsequence within X; and d is the sampling interval size between two data points from X, an integer that fulfills 1 ≤ d ≤ [(T − 1)/(n − 1)].

${\mathrm{M}}_d^n$ measures the complexity of a time series only by comparing the values of adjacent points in the time series. However, the relative amplitude in the time series contains more structural information in the series, so the sequence of motif differences is further defined.

$${\mathrm{dM}}_d^n=\{d{M}_{d,s}^n,s=1,2,\dots ,T-(n-1)\cdot d\}$$

(5)

$$d{M}_{d,s}^n=\left\{x_{s+d}-x_s,x_{s+2d}-x_{s+d},\dots ,x_{s+(n-1)d}-x_{s+(n-2)d}\right\}$$

(6)

Due to the variation in the length of ${\mathrm{dM}}_d^n$ with respect to d, zero padding is necessary to ensure uniform sequence lengths. Consequently, a new sequence ${\mathrm{I}}_d^n$ is defined as:

$${\mathrm{I}}_d^n=\{I_{d,s}^n,s=1,2,\dots ,T-(n-1)\}$$

(7)

$$I_{d,s}^n=\left\{\begin{array}{l}d{M}_{d,s}^n, 1\le s\le T-(n-1)\cdot d\\ 0, T-(n-1)\cdot d<s\le T-(n-1)\end{array}\right.$$

(8)

Then, the motif difference field (MDF) is defined as the stack of ${\mathrm{I}}_d^n$ with all possible delay values d from 1 to dmax.

$${\mathrm{MDF}}^n=\{{\mathrm{I}}_1^n,{\mathrm{I}}_2^n,\dots ,{\mathrm{I}}_{d_{\max }}^n\}$$

(9)

${\mathrm{I}}_d^n$ denotes the set of n − 1 collections corresponding to when the spacing is d, thereby generating n − 1 channel images. For the i^th channel, an image array is defined as follows:

$${\mathrm{G}}_i^n={[{\overrightarrow{I}}_1^n(i),{\overrightarrow{I}}_2^n(i),\dots ,{\overrightarrow{I}}_d^n(i),\dots ,{\overrightarrow{I}}_{d_{\max }}^n(i)]}^T$$

(10)

$${\overrightarrow{I}}_d^n(i)={[I_{d,1}^n(i),I_{d,2}^n(i),\dots ,I_{d,T-n+1}^n(i)]}^T$$

(11)

where the superscript ‘T’ denotes transpose; 1 ≤ i ≤ n − 1.

To address the multitude of zero elements in ${\mathrm{G}}_i^n$, each channel of the MDF image is defined as follows:

$${\mathrm{IMG}}_i^n={\mathrm{G}}_i^n+{\mathrm{K}}^n\odot {G^{\prime }}_i^n$$

(12)

where ⊙ is the Hadamard product, and ${\mathrm{G}\prime }_i^n$ is the 180-degree rotation of ${\mathrm{G}}_i^n$. In order to prevent the overlap of two arrays, ${\mathrm{K}}^n$ is defined as:

$$K_{d,s}^n=\left\{\begin{array}{l}0, 1\le s\le T-(n-1)\cdot d\\ 1, T-(n-1)\cdot d<s\le T-(n-1) \end{array}\right.$$

(13)

In this paper, n in Equation (13) is set to three to produce two fault differential images, which are then stacked vertically to form a composite fault image. Figure 2 illustrates the process of generating an MDF image from the zero-sequence current signal.

3.3. MAF-MDF

In practical distribution networks, noise present in the waveforms recorded by phasor measurement units (PMUs) can interfere with fault line selection. To tackle this issue, the zero-sequence current signals collected at each measurement point from 10 milliseconds before to 20 milliseconds after the fault event are first subjected to a moving average denoising process. These signals are then subjected to normalization, ensuring noise reduction while preserving the inherent pattern of signal variation. Subsequently, the normalized current sequences are transformed into two-dimensional images via the motif difference field (MDF) methodology.

Figure 3 illustrates the zero-sequence current waveforms at the primary endpoints of each feeder in a four-terminal distribution network during a single-phase grounding fault on Feeder 1, along with the imaging results. On the left side of the figure are the original signals, the center portion displays waveforms after undergoing moving average denoising and normalization, and the rightmost section presents the MDF images.

Observably from the figure, following denoising and MDF transformation of the zero-sequence current sequences captured at various points, the MDF fault images of non-faulty feeders exhibit nearly uniform color distributions, whereas there is a conspicuous distinction in color distribution between the faulty and healthy feeders. By mapping one-dimensional zero-sequence current data into a two-dimensional space, waveform disparities are visually translated into discernible color variations.

4. Fault Line Selection Model Based on MCECA-CloFormer

It can be seen from the analysis in Section 3.3 that the MDF images of faulty feeders and non-faulty feeders have obvious color differences. Accordingly, this paper proposes the MCECA-CloFormer fault line selection model, which improves the ECA model to MCECA (MultiCNN-ECA) so that it can accept and integrate multiple measuring point information. Then, the two-branch structure of the lightweight model CloFormer is used to perceive color distribution differences to achieve fault line selection.

4.1. Efficient Channel Attention

Attention mechanisms can significantly enhance model performance, yet most of them increase model complexity and computational cost alongside optimization. The efficient channel attention (ECA), however, employs a lightweight architecture that requires no dimensionality reduction, enabling effective cross-channel interactions locally with minimal parameters [23].

The structure of the ECA module is depicted in Figure 4, where W, H, and C denote the width, height, and channel dimensions of the input feature map X, respectively. Initially, global average pooling (GAP) is applied to the input features, yielding a feature vector of shape 1 × 1 × C. Subsequently, a one-dimensional convolution with kernel size K is employed to efficiently facilitate local cross-channel interactions, where K is adaptively determined by Equation (14) based on the total channel count C. The convolution outcome is normalized via the sigmoid function to obtain weights for each channel. Finally, these weights are element-wise multiplied with the original input feature X to yield the weighted feature X′. The computation formula for the kernel size K is as follows:

$$K=\psi (C)={\left|{\displaystyle \frac{{\log }_2(C)}{\gamma }}+{\displaystyle \frac{b}{\gamma }}\right|}_{odd}$$

(14)

where |t|_odd denotes the nearest odd integer to t; γ is the scaling coefficient for the global average pooling output; and b represents the bias value when adaptively determining the convolution kernel size.

4.2. CloFormer

CloFormer is a lightweight vision transformer designed with a dual-branch architecture, incorporating both local and global pathways. In the global branch, standard attention mechanisms are employed to capture the global low-frequency information of the input, whereas the local branch combines context-aware weights with shared weights to extract high-frequency local information from the input. This dual-branch configuration facilitates the model’s enhanced perception of both high and low-frequency components in the input feature maps. Experimental evidence demonstrates its superior performance across a range of visual tasks, including image classification, object detection, and semantic segmentation [24], as illustrated in Figure 5. The overarching architecture consists of four main components: the Conv stem, Clo blocks, ConvFFN, and the Output module.

• Conv stem. This component primarily comprises five convolutional layers, with the detailed structure illustrated in Figure 5a.
• Clo block. This part is constituted by a local branch and a global branch. As shown in Figure 5b, within the global branch, K and V are initially downsampled, followed by the execution of a standard attention process on Q, K, and V to extract global low-frequency information, as outlined in Equation (15).

$$X_{global}=\mathrm{Attntion}(Q_g,\mathrm{Pool}(K_g),\mathrm{Pool}(V_g))$$

(15)

In the local branch, linear transformations are first applied to obtain Q, K, and V. Subsequently, depthwise convolution (DWConv) with shared weights is employed on V for local feature extraction, as illustrated in Equations (16) and (17).

$$Q,K,V=\mathrm{FC}(X_{in})$$

(16)

$$V_s=\mathrm{DWconv}(V)$$

(17)

where FC denotes a fully connected layer.

Meanwhile, local information aggregation for Q and K is performed using deep convolutions, following which the Hadamard product of the aggregated Q_l and K_l is computed. This product undergoes a series of non-linear transformations to yield context-aware weights within the range of −1 to 1. These generated context weights are then employed to enhance the local features V_s. The entire process is outlined in Equation (18).

$$\left\{\begin{array}{l}{Q}_l=\mathrm{DWconv}(Q)\hfill \\ K_l=\mathrm{DWconv}(K)\hfill \\ Att{n}_t=\mathrm{FC}(\mathrm{Swish}(\mathrm{FC}(Q_l\odot K_l)))\hfill \\ Attn=\mathrm{Tanh}({\displaystyle \frac{Att{n}_t}{\sqrt{d}}})\hfill \\ X_{local}=Attn\odot V_s\hfill \end{array}\right.$$

(18)

where d is the number of token’s channels, ⊙ is the Hadamard product.

Finally, the outputs from the global and local branches are concatenated along the channel dimension, followed by passing through a fully connected layer to yield the final output of the Clo block, as illustrated in Equation (19).

$$\left\{\begin{array}{l}{X}_t=\mathrm{Concat}(X_{local},X_{global})\\ X_{out}=\mathrm{FC}(X_t)\end{array}\right.$$

(19)

where Concat(·,·) denotes the concatenation of two tensors along the channel dimension.

• ConvFFN. This component primarily bolsters its local information aggregation capacity by introducing depthwise convolution following the GELU activation function. Two modes are adopted: one without downsampling (depicted on the left in Figure 5c), which is utilized in all layers except the last, and another incorporating a downsampling module (shown on the right in Figure 5c), which is employed in the final layer of the CloFormer architecture.
• Output module. The output module consists of a global average pooling layer and a linear classifier. The overall structure of CloFormer is depicted in Figure 5d, wherein a CloLayer is composed of a combination of two Clo blocks and a ConvFFN, with downsampling incorporated in the ConvFFN of the final layer.

4.3. MCECA-CloFormer

To fully leverage the distinctions between faulted and healthy power line MDF images, as well as the high similarity among healthy line images, this paper constructs MCECA (MultiCNN-ECA), a module designed to accept multiple image inputs. Specifically, it begins by employing a convolutional layer with a kernel size of 1 × 1 to map the two-dimensional images generated by measurement points deployed at the head ends of each feeder into feature maps, which are then concatenated along the channel dimension. Subsequently, the ECA (efficient channel attention) mechanism is utilized to capture cross-channel interaction information from the concatenated tensor, assigning different weights for attention-guided feature fusion. Finally, the features are fed into the CloFormer model, which employs a dual-branch structure to perceive the color distribution of signals, thereby facilitating fault line identification. The detailed architecture is illustrated in Figure 6.

4.4. Implementation Flow of Line Selection Method

The specific route selection process designed in this paper is as follows: when the zero sequence voltage of the bus is monitored to be greater than 0.15 times the phase voltage, the zero-sequence current signals recorded by the PMU device deployed at the head-end of each feeder from 10 ms before the fault to 20 ms after the fault are first extracted. The signals are then converted into images using the MAF-MDF method and finally inputted into the pretrained MCECA-CloFormer model for fault line selection.

In this study, the specific parameters of MAF-MDF and MCECA-Cloformer are shown in

Table 1. Parameters for each algorithm component.

Algorithm	Parameters
MAF	Window width = 19
MDF	n = 3
ECA	γ = 2; b =1
CloFormer	Channels: [32, 64, 128, 256]; Heads: [4, 4, 8, 16]; Kernel Size: [3, 5, 7, 9]

.

5. Simulation Results and Discussion

5.1. Dataset

The proposed method in this paper primarily learns color differences in images to discern faulty lines, with the intention of being unaffected by line parameters or line length. Consequently, two distinct 10 kV distribution network models with small current grounding were constructed using PSCAD/EMTDC. These models are depicted in Figure 7, while their line parameters are detailed in

Table 2. Line parameters for Model 1.

Type	Sequence	Resistance/(Ω/km)	Inductance/(mH/km)	Capacitance/(μF/km)
Line	positive	0.1273	0.9337	0.0127
	zero	0.3864	4.1264	0.0078
Cable	positive	0.2650	0.2550	0.1700
	zero	2.5400	1.1019	0.1530

and

Table 3. Line parameters for Model 2.

Type	Sequence	Resistance/(Ω/km)	Inductance/(mH/km)	Capacitance/(μF/km)
Line	positive	0.1700	1.0170	0.1150
	zero	0.3200	3.5600	0.0060
Cable	positive	0.2700	0.2550	0.3760
	zero	2.7000	1.1090	0.2760

respectively. Each feeder’s head in both distribution network models was equipped with a PMU device to collect zero-sequence current data. The transformers had a capacity of 50 MVA and a voltage ratio of 110 kV/10.5 kV. In Figure 7, Model 1 is depicted as a resonant grounding system, utilized for creating the training dataset. In Figure 7, Model 2 is utilized for generating the test set. Within Model 2, when the switch at the busbar was open, it represented a neutral ungrounded system (NUS), whereas when the switch was closed, it signified a neutral resonant grounding system (NES). In the resonant grounding systems, an overcompensation strategy was uniformly employed, with the compensation degree set to 10%.

A dataset was constructed by simulating various fault scenarios across each line in the distribution grid models, encompassing different fault locations, initial fault angles, and fault grounding resistances. The specific scenarios are detailed in

Table 4. Scenario settings for simulation training set.

Type	Parameter
faulty line	L1, L2, L3, L4
fault location	10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%
fault ground resistance	0.1 Ω, 1 Ω, 10 Ω, 100 Ω, 1000 Ω, 3000 Ω, 5000 Ω, Emanuel
initial fault phase angle	0°, 30°, 60°, 90°, 120°, 150°, 180°

.

In Table 4, ’Emanuel’ refers to an arc high resistance model [25], illustrated in Figure 8, which comprises two diodes, two voltage sources, and two resistors connected in inverse parallel. This model was designed to mimic the random fluctuations in arc voltage and arc resistance observed in real-world situations, where U_p, U_n, R_p, and R_n fluctuate randomly over time within a range of ±10% of their set central values. By adjusting these parameters, simulations of diverse grounding medium conditions could be achieved. The specific parameters for this model are listed in

Table 5. Parameters for Emanuel model.

Model	Up/kV	Un/kV	Rp/Ω	Rn/Ω
HIF 1	2	3	350	350
HIF 2	1.3	1.6	450	450
HIF 3	2.4	3.4	650	650

.

Based on the scenarios outlined in Table 4 and Table 5, training, validation, and test datasets—namely, NES training set, NES test set, and NUS test set—were generated. Each of these datasets comprised 2520 fault sample groups, with each group containing data from four measurement points. Ultimately, the time-domain datasets were transformed into image datasets using the methodology outlined in Section 3.2.

5.2. Training and Testing of the Model

The color image dataset generated by Model 1 was divided into a new training set and a validation set at a ratio of 4:1. There were 2016 sets of images in the training set and 504 sets of images in the validation set. Subsequently, the MCECA-CloFormer model was constructed, with training samples from the training set being fed into the model for training. The training process was deemed complete when the accuracy rate stabilized. At this point, the optimal hyperparameters and weights of the model were saved. Employing the pretrained model, tests were conducted on the test set. Experimental validation confirmed that the line selection neural network based on MCECA-CloFormer achieved an accuracy rate of 100% in both the resonant grounding distribution networks and the ungrounded neutral point distribution networks of Model 2. This led to the conclusion that the method proposed in this paper was insensitive to variations in operating conditions.

The testing results on the NES and NUS datasets were visualized using t-SNE, with the outcomes presented in Figure 9.

In Figure 9, four distinct colors correspond to the four feeders, demonstrating that the MCECA-CloFormer model possesses remarkable clustering capability.

In order to verify the influence of inverter interfaced distributed generation (IIDG) on the algorithm proposed in this paper, the IIDG model was added to the distribution network model, which adopts PQ control during normal operation and employs a low voltage crossing and negative sequence suppression strategy during fault operation [26]. Because IIDG grid-connected transformer adopts star triangle connection, that is, IIDG is not in zero-sequence network, it has little influence on the method presented in this paper. In Figure 7, 50% of lines L₁ and L₂ of the resonant grounding system are connected to the IIDG with a capacity of 2 MW. The fault points were set at 25% and 75% of each line, respectively. After testing, the accuracy rate was 100%.

In order to verify the influence of fault phase angle, fault resistance, and fault location on the algorithm, the test scenario shown in

Table 6. Test scenario settings.

Type	Faulty Line	Fault Location	Fault Ground Resistance	Initial Fault Phase Angle	Test Content
parameter	L1, L2, L3, L4	15%, 35%, 75%	10 Ω	0°	Effect of fault location
		50%	2 Ω, 200 Ω, 4000 Ω	0°	Effect of fault ground resistance
		50%	10 Ω	20°, 45°, 160°	Effect of Initial fault phase angle

was set up. After testing, the accuracy rate was 100%.

5.3. Noise Resistance Test and Algorithm Comparison Analysis

In this paper, MCloFormer-ECA, MCECA-MobileNetV2, MCNN-CloFormer, and MCECA-ECANET are used to compare with the proposed algorithm. MCEA-CloFormer adopts the early fusion strategy, MCloFormer-ECA adopts the late fusion strategy, and the model structure is shown in Figure 10a. MCNN-CloFormer is a model that does not use ECA’s attention mechanism, and the model structure is shown in Figure 10b.

In order to test the anti-noise ability of the algorithm, 300 groups of samples were randomly selected from the NES test set for testing, including 100 groups of arc high-resistance grounding samples. Different degrees of Gaussian white noise were added to test the noise resistance of the algorithm. The test results are shown in

Table 7. Results of line selection accuracy under different noise intensities.

Model	SNR = 40 dB	SNR = 30 dB	SNR = 20 dB	SNR = 10 dB
MCECA-CloFormer	100%	100%	100%	99.33%
MCloFormer-ECA	100%	100%	99.67%	98.33%
MCNN-CloFormer	99.00%	99.00%	99.00%	98.33%
MCECA-MobileNetV2	98.00%	97.67%	98.00%	96.33%
MCECA-ECANet	100%	100%	100%	99.01%

.

As can be seen from Table 7, the accuracy rate of all algorithms decreased at a noise intensity of 10 dB, with the accuracy rate of MCECA-MobileNetV2 decreasing to 96.33%. However, based on the performance of the algorithms at various noise intensities, MCECA-CloFormer, MCloFormer-ECA, and MCECA-ECANet demonstrated better anti-noise capability than other algorithms.

Rapid and accurate fault line selection can significantly reduce maintenance time and ensure power supply reliability. Therefore, the fault line selection time of the above algorithms were compared.

Table 8. Comparison of single fault line selection time of different models.

Model	Time
MCECA-CloFormer	0.0420 s
MCloFormer-ECA	0.1290 s
MCNN-CloFormer	0.0350 s
MCECA-MobileNetV2	0.0220 s
MCECA-ECANet	0.1800 s

shows the time required by the different models to process a single fault.

It can be seen that the time required for line selection of lightweight models MCECA-CloFormer, MCNN-CloFormer, and MCECA_MobileNetV2 was much shorter than other algorithms.

By integrating the data from Table 7 and Table 8, it is evident that while MCECA-MobileNetV2 and MCNN-CloFormer demanded shorter durations for fault line identification, they exhibited weaker noise tolerance capabilities. Conversely, MCECA-ECANet and MCloFormer-ECA, while demonstrating superior resilience against noise interference, necessitated longer periods for line selection. Consequently, upon consolidating these dual metrics, the proposed algorithm, MCECA-CloFormer, manifests a prominent advantage, excelling in both efficiency and noise robustness.

5.4. The Impact of Missing Data on Algorithm Performance

As described in Section 3.3, data from 10 ms before the fault to 20 ms after the fault is used for fault line selection. Considering that the zero-sequence current before the fault is approximately zero, in order to test the influence of data loss on the line selection accuracy, the zero-sequence current after the fault is introduced into the random data loss. Specifically, 300 samples were randomly selected from the NES test set. For each corresponding fault event, two lines were randomly selected, and the missing data event was imposed on the zero-sequence current data sampled from these two lines. The experimental outcomes are presented in

Table 9. Data missing test results.

Data Missing Rate	Accuracy
5%	99.67%
10%	100%
20%	99.00%
30%	94.68%

.

In Table 9, the data missing rate is calculated as the number of missing sample points after the fault occurrence divided by the total number of sample points after the fault occurrence. From the table above, it can be concluded that the algorithm proposed in this paper exhibits a certain tolerance to situations involving missing data.

5.5. Analysis and Testing of Actual Waveform Recordings

To further illustrate the feasibility of the method proposed in this paper, actual waveform data collected on-site were used to test the algorithm. Figure 11 shows a simplified topology diagram of the actual 10 kV distribution network test site, where the fault occurred in line L1. Figure 12 displays the zero-sequence current waveform exported from the waveform viewing software (CAAP2008X) and the fault image generated using the MAF-MDF method.

From Figure 12, it is evident that the zero-sequence current signals acquired from actual measurement points contained noise, with varying levels of intensity across different lines. In particular, the signals collected by the measuring device from line L3 exhibited notably prominent noise. However, after the application of moving average denoising to both healthy and faulty feeder signals, the resulting MDF images still displayed significant differences. There was a high degree of similarity observed between MDF images of healthy feeders. Testing shows that the pre-trained MCECA-CloFormer model can accurately select fault lines.

5.6. Discussion

The discussion on the methodology of this paper could be divided into two main parts: data preprocessing and model applicability.

In terms of data preprocessing, the imaging method based on MAF-MDF avoids the process of subjective parameter selection, such as the wavelet packet function in wavelet transform [2] and the number of decomposition layers of VMD [5]. It only requires setting the filter window size of MAF according to the sampling frequency, offering certain end-to-end advantages.

In terms of model applicability, the training data and test data used in this paper were collected from distribution networks with different working conditions and different line parameters, which better simulate data distribution changes in actual distribution networks. Compared to methods where both the training set and the test set are taken from the same distribution network simulation model [1,15], the proposed method demonstrates more generalization ability. Meanwhile, compared to the transfer learning method [19], the proposed method does not require target distribution network samples, which has been verified by NES test set, NUS test set, and actual wave recording data.

6. Conclusions and Future Work

The proposed methods, including the MAF-MDF-based image generation approach and the MCECA-CloFormer model capable of processing information from multiple measurement points, address the challenge of identifying difficult fault lines in low-current grounding systems due to the subtle characteristics of single-phase ground faults. After denoising the zero-sequence current data through moving average filtering and subsequently transforming it into images using MDF, noticeable color differences between the faulted and healthy feeder fault images were observed. Furthermore, high similarity among images of healthy feeders was also revealed. The fault line selection model was adapted to receive and process fault data collected from measurement devices on each feeder of the distribution network through the enhancement of the ECA module to the MCECA module.

To address the challenge of deep learning methods requiring a large volume of samples, a strategy was proposed that entailed obtaining data from simulation models to train the line selection model and employing pre-trained models for actual line selection tasks. The testing results on both simulated and actual recorded data demonstrated that the pre-trained MCECA-CloFormer model was insensitive to fault resistance, fault location, initial fault angle, missing data, line parameters, and length variations, rendering it applicable across NES, NUS, and ADN.

In comparison to various deep learning models, MCECA-CloFormer demonstrates a high level of noise immunity and accomplishes fault line selection in a shorter time frame, indicating substantial practical significance for its application.

Future work could involve studying how to localize single-phase ground faults based on line selection. Specifically, it is necessary to first collect a large amount of literature on distribution network localization to study the distribution pattern of zero-sequence current, then construct a localization dataset combined with actual distribution network scenarios, propose a localization method that does not require or only requires a small number of target distribution network samples, and finally conduct a large number of tests and comparative experiments on the proposed localization method.