Fault Line Selection in Distribution Networks Based on Dual-Channel Time-Frequency Fusion Network

Abstract

In distribution networks, single-phase ground faults often lead to abnormal changes in voltage and current signals. Traditional single-modal fault diagnosis methods usually struggle to accurately identify the fault line under such conditions. To address this issue, this paper proposes a fault line identification method based on a multimodal feature fusion model. The approach combines time-frequency images—generated using a Short-Time Fourier Transform (STFT) and Wigner–Ville Distribution (WVD) fusion algorithm with one-dimensional time-series signals for classification. The time-frequency images visualize both temporal and spectral features of the signal and are processed using the RepLKNet model for deep feature extraction. Meanwhile, the raw one-dimensional time-series signals preserve the original temporal dependencies and are analyzed using a BiGRU network enhanced with a global attention mechanism to improve feature representation. Finally, features from both modalities are extracted in parallel and fused to achieve accurate fault line identification. Experimental results demonstrate that the proposed method effectively leverages the complementary nature of multimodal data and shows strong robustness in the presence of noise interference.

1. Introduction

China’s distribution networks predominantly operate either in a neutral non-grounding mode or through arc suppression coil grounding [1], among which approximately 80% of faults are classified as single-phase-to-ground faults (SPGFs) [2]. If not addressed in a timely and effective manner, such faults may compromise the stability of the entire power system and pose significant safety hazards to personnel [3]. However, existing fault line selection methods are often inadequate for practical deployment [4]. Therefore, the development of accurate and reliable fault line selection methods for distribution networks has become a critical research focus.

According to the nature of the characteristic quantities employed, fault line selection methods can be categorized into three main types [5]: (i) transient characteristic methods, (ii) steady-state characteristic methods, and (iii) injection-based methods. Steady-state characteristic methods typically identify fault lines by analyzing variations in steady-state zero-sequence voltage and admittance characteristics. However, the integration of distributed energy resources and changes in network topology have diminished the distinguishability of steady-state features. Additionally, the presence of arc suppression coils can significantly influence diagnostic results [6]. Transient characteristic methods utilize abrupt changes in transient signals, such as zero-sequence current and residual voltage, that occur at the instant of fault inception [7]. While these methods can be effective, their performance degrades in high-resistance grounding scenarios. Injection-based methods, which require additional equipment, also struggle under high-resistance conditions and hence have limited practical applicability [8]. Reference [9] proposes a fault line selection method based on one-dimensional convolutional neural networks (1DCNN) and bidirectional long short-term memory networks (BiLSTM). This approach constructs a sequence fusion feature vector from transient zero-sequence currents across multiple lines, normalizes the data, and extracts local features using 1DCNN. BiLSTM is then employed to learn contextual dependencies, with a final SoftMax layer used for classification. Despite its advantages, this method incurs high computational complexity when processing long time-series data. Reference [10] introduces a CNN-based model enhanced by an attention mechanism. Initially, the S-transform is used to convert time-series zero-sequence currents into two-dimensional matrices compatible with CNN input. Attention layers are integrated to improve the accuracy and robustness of classification. However, the method exhibits limited generalization performance on small datasets. Reference [11] proposes a traveling wave-based fault identification approach that acquires the zero-mode current traveling waves from all feeders in the distribution system. By determining reference lines and applying cross-wavelet transform, the method constructs several time–frequency sets to isolate the fault-related information. However, its applicability is constrained in complex network topologies. With the rapid advancement of artificial intelligence, deep learning-based methods have become a promising direction for fault diagnosis in distribution systems. Reference [12] employs a time–frequency matrix as input to a ResNet model for fault line identification. Reference [13] presents a fault line selection method using the Hausdorff distance of transient currents. It extracts the 5th and 7th order components from zero-sequence currents to distinguish faulty and healthy lines, enabling accurate identification. This method, however, is highly sensitive to noise. References [14,15] directly input characteristic diagrams of zero-sequence current signals into deep learning models but neglect the global temporal characteristics of the signals, limiting their performance in complex scenarios. With the success of Transformer architectures in time-series modeling, advanced structures such as Informer and Temporal Fusion Transformer (TFT) have demonstrated superior long-range dependency modeling capabilities in power system data analysis [16]. Simultaneously, Vision Transformer (ViT) and its variants have been employed in time–frequency image modeling, significantly improving global feature extraction from images. Furthermore, cross-modal attention mechanisms have shown promising robustness and generalization performance in multimodal data fusion tasks [17].

To overcome the aforementioned limitations, this paper introduces a fault line selection method based on a multimodal feature fusion strategy. First, a hybrid time–frequency analysis is performed by combining the Short-Time Fourier Transform (STFT) and Wigner–Ville Distribution (WVD) to generate comprehensive time–frequency representations. A dual-branch architecture is then devised to concurrently extract temporal features from zero-sequence current signals and spatial features from the derived time–frequency images. The image branch adopts RepLKNet to capture cross-regional structural features, while the time-series branch employs a BiGRU network enhanced with Global Attention to model temporal dependencies. Finally, a multimodal feature fusion network integrates both modalities to perform fault identification. Simulation results demonstrate that the proposed method outperforms traditional single-modal models in terms of accuracy, robustness, and generalization.

2. Time–Frequency Fusion Analysis Based on STFT-WVD

2.1. Phase-Mode Transformation

The parameters of the $\mathit{ABC}$ three-phase currents in power distribution networks exhibit intricate electromagnetic coupling characteristics [18], which render their analytical processing particularly complex. To address this issue, phase-shifting transformation serves as an effective tool by transforming the problem from the complex domain to a more tractable real-valued framework, thereby significantly reducing computational complexity. This transformation technique is particularly advantageous when dealing with discretely sampled electrical signals, enabling the decoupling of phase quantities. In the time domain, the relationship between the phase mode conversion and the inverse conversion is expressed by Equation (1).

$$\left\{\begin{array}{cc}\hfill {\left(\begin{array}{ccc}{i}_{\mathrm{m}}^{\left(0\right)}& i_{\mathrm{m}}^{\left(1\right)}& i_{\mathrm{m}}^{\left(2\right)}\end{array}\right)}^{\mathrm{T}}& =S^{-1}{\left(\begin{array}{ccc}{i}_{\mathrm{a}}& i_{\mathrm{b}}& i_{\mathrm{c}}\end{array}\right)}^{\mathrm{T}}\hfill \\ \hfill {\left(\begin{array}{ccc}{i}_{\mathrm{a}}& i_{\mathrm{b}}& i_{\mathrm{c}}\end{array}\right)}^{\mathrm{T}}& =S{\left(\begin{array}{ccc}{i}_{\mathrm{m}}^{\left(0\right)}& i_{\mathrm{m}}^{\left(1\right)}& i_{\mathrm{m}}^{\left(2\right)}\end{array}\right)}^{\mathrm{T}}\hfill \end{array}\right.$$

(1)

where $i_{\mathrm{m}}^{\left(0\right)}$, $i_{\mathrm{m}}^{\left(1\right)}$, and $i_{\mathrm{m}}^{\left(3\right)}$ represent the current modulus components of 0, 1, and 2.

Upon undergoing phase-mode transformation, the original ABC three-phase parameters are decomposed into three modal components: mode 0, mode 1, and mode 2. Among them, the mode 0 component is grounded and thus significantly influenced by various ground-related factors such as soil resistivity and grounding impedance. Due to these complexities, most fault analysis studies preferentially utilize mode 1 or mode 2 components for accurate diagnosis. This approach not only inherits the time-domain benefits of traditional matrices but also enables a single-modulus representation for all types of faults, thereby enhancing diagnostic reliability. The transformation matrix S and its inverse $S^{-1}$ are defined in (2).

$$S={\displaystyle \frac{1}{15}}\left(\begin{array}{ccc}5& 5& 5\\ 5& -1& -4\\ 5& -4& -1\end{array}\right); S^{-1}=\left(\begin{array}{ccc}1& 1& 1\\ 1& 2& -3\\ 1& -3& 2\end{array}\right)$$

(2)

The phase-mode transformation matrix $S^{-1}$ converts the current vector into its modal form as given in (3).

$$\left(\begin{array}{c}{i}_{\mathrm{m}}^{\left(0\right)}\\ i_{\mathrm{m}}^{\left(1\right)}\\ i_{\mathrm{m}}^{\left(0\right)}\end{array}\right)=\left(\begin{array}{ccc}1& 1& 1\\ 1& 2& -3\\ 1& -3& 2\end{array}\right)\left(\begin{array}{c}{i}_{\mathrm{a}}\\ i_{\mathrm{b}}\\ i_{\mathrm{c}}\end{array}\right)$$

(3)

Table 1. Fault types and corresponding boundary conditions and modal responses.

Fault Type	Boundary Condition	Modulus 1 / Modulus 2
AG 1	$i_{\mathrm{fb}}=i_{\mathrm{fc}}=0$	$i_{\mathrm{fa}}$/$i_{\mathrm{fa}}$
BG 2	$i_{\mathrm{fa}}=i_{\mathrm{fc}}=0$	$2i_{\mathrm{fb}}$/$-3i_{\mathrm{fb}}$
CG 3	$i_{\mathrm{fa}}=i_{\mathrm{fb}}=0$	$-3i_{\mathrm{fc}}$/$2i_{\mathrm{fc}}$
AB 4	$i_{\mathrm{fc}}=0;i_{\mathrm{fa}}=-i_{\mathrm{fb}}$	$i_{\mathrm{fb}}$/$-4i_{\mathrm{fb}}$
BC 5	$i_{\mathrm{fa}}=0;i_{\mathrm{fb}}=-i_{\mathrm{fc}}$	$5i_{\mathrm{fb}}$/$-5i_{\mathrm{fb}}$
CA 6	$i_{\mathrm{fb}}=0;i_{\mathrm{fa}}=-i_{\mathrm{fc}}$	$4i_{\mathrm{fa}}$/$-i_{\mathrm{fa}}$
ABG 7	$i_{\mathrm{fc}}=0$	$i_{\mathrm{fa}}+2i_{\mathrm{fb}}$/$i_{\mathrm{fa}}-3i_{\mathrm{fb}}$
BCG 8	$i_{\mathrm{fa}}=0$	$2i_{\mathrm{fb}}-3i_{\mathrm{fc}}$/$2i_{\mathrm{fc}}-3i_{\mathrm{fb}}$
CAG 9	$i_{\mathrm{fb}}=0$	$i_{\mathrm{fa}}-3i_{\mathrm{fc}}$/$i_{\mathrm{fa}}+2i_{\mathrm{fc}}$
ABC 10	$i_{\mathrm{fa}}+i_{\mathrm{fb}}+i_{\mathrm{fc}}=0$	$i_{\mathrm{fa}}+2i_{\mathrm{fb}}-3i_{\mathrm{fc}}$/$i_{\mathrm{fa}}-3i_{\mathrm{fb}}+2i_{\mathrm{fc}}$

¹ Phase A single phase to ground; ² Phase B single phase to ground; ³ Phase C single phase to ground; ⁴ Phase A is connected to phase B; ⁵ Phase B is connected to phase C; ⁶ Phase C is connected to phase A; ⁷ Phase A and phase B are simultaneously grounded; ⁸ Phase B and phase C are simultaneously grounded; ⁹ Phase C and phase A are simultaneously grounded; ¹⁰ Phase A, phase B, and phase C are interconnected with each other.

illustrates the modal components derived from the proposed phase-mode transformation matrix under different fault conditions. As observed, each fault type exhibits non-zero responses in the corresponding modal components, especially in modes 1 and 2. This indicates that these two modal components independently possess the capacity to capture the characteristics of all types of fault. Such findings confirm the effectiveness of the proposed transformation matrix in providing a comprehensive and fault-sensitive modal decomposition.

2.2. STFT-WVD

To enhance the accuracy of the time–frequency analysis, this study uses a short-time Fourier transform (STFT) and the Wigner–Ville distribution (WVD) fusion method to eliminate WVD cross-term interference and improve STFT resolution. The fused time–frequency spectrogram provides fine details at frequency mutation points while maintaining a clear spectrum in stable signal regions, thereby optimizing the analysis of zero-sequence current data [19]. The STFT segments the fault signal into short time windows and applies the Fourier transform to each segment to obtain the instantaneous frequency. The short-time Fourier transform is expressed by the formula in (4).

$$\mathit{X}\left(t,f\right)=\int x\left(\tau \right)\omega \left(\tau -t\right)e^{-j2\pi f\tau }d\tau$$

(4)

where:

$X\left(t,f\right)$ represents the time–frequency representation obtained by the STFT;

$x\left(\tau \right)$ denotes the input signal;

$w\left(\tau -t\right)$ is the short-time window function for localizing the signal;

f is the frequency variable;

j is the imaginary unit.

The Wigner–Ville distribution (WVD), used to compute the time–frequency distribution of the signal, is mathematically defined as shown in Formula (5).

$${\mathit{W}}_{\mathit{x}}\left(t,f\right)=\int x\left(t+\tau /2\right)x^{*}\left(t-\tau /2\right)e^{-j2\pi f\tau }d\tau$$

(5)

where:

$W_x\left(t,f\right)$ represents the time–frequency distribution obtained by WVD;

$x^{*}\left(t-\tau /2\right)$ denotes the complex conjugate of the signal.

Finally, the fused time–frequency representation is given by Formula (6).

$$\mathit{TF}\left(t,f\right)=\alpha ·\left|\mathit{X}\left(\mathit{t},\mathit{f}\right)\right|+\beta \left|\mathit{Wx}\left(\mathit{t},\mathit{f}\right)\right|$$

(6)

where:

$TF\left(t,f\right)$ is the combined time–frequency representation;

$\alpha$ and $\beta$ are weighting coefficients that adjust the contributions of STFT and WVD, respectively.

By integrating STFT and WVD, the proposed method leverages the clear spectral representation of STFT in stable signal regions and the high resolution of WVD at frequency mutation points, enabling accurate time–frequency analysis for single-phase grounding fault signals.

3. Line Selection Method Based on a Dual-Channel Time–Frequency Fusion Network

3.1. RepLKNet Is Used for Feature Extraction from Time–Frequency Images

In the process of extracting features from time–frequency images, this study incorporates the Parameterized Large Kernel Network (RepLKNet) [20], a convolutional neural network architecture that employs large convolutional kernels. Figure 1 shows the schematic diagram of the RepLKNet structure. The use of large kernels facilitates the capture of contextual information in a wide area, which is particularly effective in modeling the long-term frequency variation patterns characteristic of fault signals. Moreover, the integration of re-parameterization techniques ensures training efficiency while simultaneously enhancing the generalization ability of the network. These properties collectively contribute to improved accuracy in fault classification. A detailed description of the network architecture is provided in

Table 2. RepLKNet-based Upgraded Image Branch Architecture.

Layer	Filters/Units	Size/Stride	Input	Output
0 Conv2D	64	$3\times 3/1$	$64\times 64\times 3$	$64\times 64\times 64$
1 BN + GELU	-	-	$64\times 64\times 64$	$64\times 64\times 64$
2 MaxPool	-	$2\times 2/2$	$64\times 64\times 64$	$32\times 32\times 64$
3 RepLK Block 1	128	$31\times 31/1$	$32\times 32\times 64$	$32\times 32\times 128$
4 MaxPool	-	$2\times 2/2$	$32\times 32\times 128$	$16\times 16\times 128$
5 RepLK Block 2	256	$31\times 31/1$	$16\times 16\times 128$	$16\times 16\times 256$
6 MaxPool	-	$2\times 2/2$	$16\times 16\times 256$	$8\times 8\times 256$
7 RepLK Block 3	64	$31\times 31/1$	$8\times 8\times 256$	$8\times 8\times 64$
8 MaxPool	-	$2\times 2/2$	$8\times 8\times 64$	$4\times 4\times 64$
9 Conv2D	128	$3\times 3/1$	$4\times 4\times 64$	$4\times 4\times 128$
10 MaxPool	-	$2\times 2/2$	$4\times 4\times 128$	$2\times 2\times 128$
11 Conv2D	256	$3\times 3/1$	$2\times 2\times 128$	$2\times 2\times 256$
12 MaxPool	-	$2\times 2/2$	$2\times 2\times 256$	$1\times 1\times 256$
13 GlobalAvgPool2D	-	-	$1\times 1\times 256$	$1\times 256$
14 Fully Connected	1000	-	$1\times 256$	$1\times 1000$
15 Flatten	-	-	$1\times 1000$	1000

.

To evaluate the adaptability and effectiveness of the selected RepLKNet architecture for time–frequency feature extraction tasks, a comparative experiment was conducted using the widely adopted ResNet50, a classical residual network based on small convolutional kernels, as a reference. The comparison was performed under consistent conditions, including the same dataset, the pretreatment method, and the training strategy. All networks were configured with the same input size of 64 × 64 × 3, and the Adam optimizer was used with an initial learning rate of 0.0001. The training process was carried out over 30 epochs with a batch size of 64. To ensure fairness in the downstream fusion process, the output feature vectors of each network were concatenated with those obtained from the BiGRU-based temporal branch, and the subsequent architecture remained identical across all configurations.

Table 3. Comparison of large kernel convolutional networks.

Model Structure	Accuracy	F1-Score	Recall	Convergence Time (s)
RepLKNet	92.5%	0.92	0.91	16
ResNet50	89.7%	0.89	0.88	25

presents the performance comparison of each model in the test set.

It can be observed that although both RepLKNet and ResNet50 are large convolutional kernel networks, they exhibit significant differences in parameter scale and performance. This indicates that RepLKNet has relatively lower model complexity, making it potentially more suitable for resource-constrained scenarios. Despite having fewer parameters, RepLKNet slightly outperforms ResNet50 in terms of precision (92.5%), F1 score (0.92) and recall (0.91) compared to ResNet50 accuracy (89.7%), F1 score (0.89) and recall (0.88), demonstrating its stronger feature extraction and classification capabilities with the same or fewer parameters. Additionally, RepLKNet’s convergence time (16 s) is shorter than that of ResNet50 (25 s), indicating higher training efficiency, likely due to its superior network architecture or parameter optimization strategies. In general, RepLKNet exceeds ResNet50 in parameter efficiency, performance, and training speed.

3.2. BiGRU Network Optimized by GlobalAttention

For one-dimensional time-series signal processing, this study employs a Bidirectional Gated Recurrent Unit (BiGRU) to extract temporal features and introduces a Global Attention mechanism to enhance the model’s ability to focus on key information [21]. The BiGRU effectively captures both forward and backward dependencies within the sequence through bidirectional information flow modeling, enabling a more comprehensive understanding of temporal correlations. However, conventional BiGRU models may suffer from an uneven distribution of information weights when handling long sequences, which can hinder the accurate identification of salient features. To address this issue, a Global Attention mechanism is integrated to compute the relevance score of each hidden state across all time steps and generate a weighted average, thereby dynamically emphasizing critical time points in the sequence. This mechanism is built upon a soft-attention strategy, which produces a globally weighted context vector. As a result, feature representation capability is significantly enhanced, leading to better classification accuracy, particularly in the extraction and identification of fault-related features [22]. Figure 2 is the schematic diagram of the structure of the bidirectional gated recurrent unit (BiGRU).

BiGRU captures the forward and backward dependencies of the signal through bidirectional propagation, and its mathematical expression is as follows.

$${\overrightarrow{h}}_t=GRU\left(x_t,{\overrightarrow{h}}_{t-1}\right)$$

(7)

$${\overleftarrow{h}}_t=GRU\left(x_t,{\overleftarrow{h}}_{t-1}\right)$$

(8)

$$h=W_{{\overrightarrow{h}}_t}{\overrightarrow{h}}_t+W_{{\overleftarrow{h}}_t}{\overleftarrow{h}}_t+b_t$$

(9)

Here, GRU represents the conventional GRU network computation process. ${\overrightarrow{h}}_t$ and $W_{{\overrightarrow{h}}_t}$ denote the state and weight of the current hidden layer forward, while ${\overleftarrow{h}}_t$ and $W_{{\overleftarrow{h}}_t}$ represent the state and weight of the hidden layer backward at the same time. $b_t$ is the bias of the hidden layer state at time t.

The network architecture of the sequence branching is shown in

Table 4. Model layer details of the BiGRU-GA-based sequence branch.

Layer	Filters/Units	Size/Stride	Input	Output
0 Conv1D	64	$5/1$	$801\times 1$	$801\times 64$
1 ReLU + LayerNorm	-	-	$801\times 64$	$801\times 64$
2 BiGRU	$256\times 2$	-	$801\times 64$	$801\times 512$
3 Attention Layer	-	-	$801\times 512$	$1\times 512$
4 Dropout	-	$p=0.5$	$1\times 512$	$1\times 512$
5 Fully Connected	1000	-	$1\times 512$	$1\times 1000$
6 Flatten	-	-	$1\times 1000$	1000
7 Fully Connected	128	-	$1\times 2000$	$1\times 128$
8 Fully Connected (Output)	2	-	$1\times 128$	2

.

Unlike conventional CNNs or RNNs, the Transformer leverages a self-attention mechanism to model global dependencies within sequences, offering superior feature extraction capabilities and inherent advantages in parallel computation [23]. To enhance the comparative depth of this study, we introduce a dual-branch fusion architecture combining RepLKNet and Transformer, wherein the original BiGRU-GA temporal branch is replaced by a Transformer-based sequence modeling branch, while the image branch remains unchanged. This modified architecture serves as a baseline for comparison, further validating the superiority of the proposed multimodal fusion network. To ensure a fair and rigorous comparison, both the proposed RepLKNet-BiGRU-GA fusion network and the comparative RepLKNet-Transformer model adopt identical settings in terms of image input processing, data sampling, time–frequency representation (STFT-WVD), fusion strategies (feature concatenation), optimization configurations (Adam optimizer with a learning rate of 0.0001) and loss function (MSE). The parameters of the Transformer branch structure are shown in

Table 5. Model layer details of the Transformer-based sequence branch.

Layer	Filters/Units	Size/Stride	Input	Output
0 Conv1D	64	$5/1$	$801\times 1$	$801\times 64$
1 Positional Encoding	F/L	-	$801\times 64$	$801\times 64$
2 Transformer Encoder × 2	H4-D512	-	$801\times 64$	$801\times 512$
3 Dropout	-	$p=0.5$	$801\times 512$	$801\times 512$
4 GlobalAvgPool1D	-	-	$801\times 512$	$1\times 512$
5 Fully Connected	1000	-	$1\times 512$	$1\times 1000$
6 Flatten	-	-	$1\times 1000$	1000

.

The training comparison of the two methods is shown in

Table 6. Performance comparison between the proposed method and Transformer.

Model Structure	Accuracy (%)	F1-Score	Training Time (min)	Learning Rate	Batch Size
RepLKNet + BiGRU-GA	94.87	0.945	16	0.001	32
RepLKNet + Transformer	92.65	0.930	24	0.0005	64

.

Experimental results indicate that although the Transformer exhibits strong capabilities in sequence modeling, its feature extraction accuracy is slightly inferior to that of the RepLKNet + BiGRU-GA combination when dealing with small sample and unstructured signal inputs. Furthermore, the Transformer incurs a higher computational cost under the same conditions. These findings validate the comprehensive advantages of the proposed fusion architecture in terms of both accuracy and efficiency for the current task scenario.

4. Experimental Validation

4.1. Establish Fault Sample Database

Given the high cost and significant risks associated with ground fault experiments in real-world distribution networks, this study constructs a hybrid sample library based on a self-built radial distribution network model and the standardized IEEE-13 node model [24]. This hybrid dataset is generated based on simulation models constructed in Simulink, where various fault scenarios are implemented using dedicated fault modules. It offers several advantages. It allows precise control over line parameters (e.g., impedance, length, and structure), facilitates flexible configuration of fault resistance and fault phases, and supports the introduction of complex conditions such as hybrid lines (combinations of overhead lines and cables), adjustable node numbers, noise disturbances, and load variations. These features enhance the realism and applicability of the simulated scenarios to actual engineering conditions. The IEEE-13 node model, as a widely recognized benchmark for distribution network studies, features a well-established structure and parameter configuration, making it suitable for standardized comparison and performance evaluation in fault diagnosis tasks. Therefore, incorporating the IEEE-13 node model into the study improves the comparability and generalizability of the proposed method, while also verifying its adaptability and robustness across different distribution network topologies.

The sample library constructed using the radial distribution network and the IEEE-13 node model is illustrated in Figure 3 and Figure 4.

The radial distribution network consists of four feeder lines. Lines 1 and 2 are hybrid lines composed of both overhead conductors and underground cables; Line 3 is a dedicated overhead line; and Line 4 is an underground cable line. The zero-sequence and positive-sequence parameters of the overhead line are given in Equation (10).

$$\left\{\begin{array}{cc}{R}_0=0.251\Omega /\mathrm{km},\hfill & L_0=4.560\times {10}^{-3}\mathrm{H}/\mathrm{km}\hfill \\ C_0=0.0056\times {10}^{-6}\mathrm{F}/\mathrm{km},\hfill & R_1=0.178\Omega /\mathrm{km}\hfill \\ L_1=1.250\times {10}^{-6}\mathrm{H}/\mathrm{km},\hfill & C_1=0.0098\times {10}^{-6}\mathrm{F}/\mathrm{km}\hfill \end{array}\right.$$

(10)

The zero-sequence and positive-sequence parameters of the cable are shown in Equation (11).

$$\left\{\begin{array}{cc}{R}_0=2.850\Omega /\mathrm{km}\hfill & L_0=1.218\times {10}^{-3}\mathrm{H}/\mathrm{km}\hfill \\ C_0=0.490\times {10}^{-6}\mathrm{F}/\mathrm{km},\hfill & R_1=0.288\Omega /\mathrm{km}\hfill \\ L_1=0.266\times {10}^{-6}\mathrm{H}/\mathrm{km}\hfill & C_1=0.538\times {10}^{-6}\mathrm{F}/\mathrm{km}\hfill \end{array}\right.$$

(11)

For the IEEE-13 node model, the system operates at a voltage level of 4.16 kV. To assess the impact of distributed generation on fault line selection, a solar power station and a wind power station are integrated at nodes 634 and 692, respectively. After excluding non-three-phase lines, the network is divided into three feeder sections. Fault points are configured in both the radial distribution network and the IEEE-13 node model. The detailed distribution of the samples is summarized in

Table 7. Fault line selection sample data distribution.

Fault Parameter	Parameter Value Range
Fault Location	One fault point is set every 0.1 km along the line
Fault Type	Single-phase-to-ground faults: AG, BG, CG
Fault Resistance ($\Omega$)	1 to 1500
Fault Angle (°)	$0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, ${270}^{\circ }$
Number of Training Samples	6200
Number of Testing Samples	2400

.

This paper proposes a fault line selection method based on a dual-channel time–frequency fusion network, which integrates one-dimensional zero-sequence current signals with their corresponding time–frequency images to exploit the complementary characteristics of multimodal data. The signal is analyzed using the Short-Time Fourier Transform (STFT) and Wigner–Ville Distribution (WVD) to extract its time–frequency features. These features are then weighted and fused in a ratio of 0.5:0.5. The fused result is normalized and scaled to a size of 64 × 64 pixels, converted into an RGB three-channel image, and used as input for a convolutional neural network. The sampling frequency is set to 12,800 Hz and the signal is truncated to capture one cycle preceding and one cycle following the fault occurrence. The STFT window length is 256 samples with an overlap of 200 samples to ensure a good balance between time and frequency resolution. Finally, the image contrast is enhanced using a logarithmic scale, visualized with the jet colormap, and saved as a PNG image. This provides standardized input image data for subsequent fault identification models. The image features are extracted using RepLKNet, while the temporal features are captured by a BiGRU enhanced with a Global Attention mechanism. These features are fused into a concatenate module and passed through fully connected layers followed by a sigmoid function to output fault probabilities. The model architecture is illustrated in Figure 5.

The prepared dataset was imported into the training model with a learning rate set to 0.0001. The loss function used was the root mean square error (RMSE), and the Adam optimizer was adopted to optimize the gradient descent process. A total of 30 training epochs were conducted. The training process is illustrated in Figure 6. During the initial training iterations, the network shows a rapid decline in loss and a significant rise in training accuracy. As the number of epochs increases, the training curves gradually stabilize, indicating that the model converges effectively and achieves fast convergence and high accuracy in fault line selection.

4.2. Sample Analysis and Comparison

Figure 7 illustrate the STFT-WVD time–frequency representations of current signals from four distribution lines when a high-resistance single-phase-to-ground fault occurs on line 4. [25]. In Figure 7a, Line 1 exhibits a predominantly dark blue distribution, indicating stable frequency-energy characteristics without significant disturbances, reflecting normal operating conditions. In Figure 7b, Line 2 shows localized light blue to green regions within specific frequency bands, suggesting minor electromagnetic interference with limited amplitude, insufficient to indicate a fault condition. Line 3, as shown in Figure 7c, shows a higher concentration of yellow and orange regions, which may visually imply higher energy levels. However, this phenomenon is mainly attributed to its stronger coupling with the faulted Line 4, making it more susceptible to indirect fault-induced disturbances and resulting in localized energy enhancement in certain frequency bands. In contrast, line 4 (Figure 7d), which is the actual faulted line, presents a more structured and continuous energy concentration in the high-frequency region. Although its overall color intensity may appear slightly less prominent than that of Line 3, it exhibits distinctive features, such as dense red-orange clusters during the initial fault stage, characteristic of transient shocks, and spectral broadening. These attributes serve as key indicators for fault identification. The pronounced high-frequency disturbances and coherent energy structures observed in Line 4 provide strong evidence for its fault status, demonstrating the effectiveness of time–frequency features in supporting accurate fault diagnosis.

Figure 8 illustrates the STFT-WVD time–frequency representations of current signals in the IEEE-13 node test system when a pure metallic C-phase grounding fault occurs on Line 3. In Figure 8a, line 1 shows a dense and uniform distribution dominated by red and yellow tones, indicating a high background energy level but without localized anomalies, suggesting stable and non-faulted behavior. Similarly, Figure 8b (line 2) and Figure 8d (line 4) present comparable visual patterns: high overall energy levels with consistent horizontal striping and only minor color variations, both consistent with normal or weakly affected lines. In contrast, Figure 8c, corresponding to Line 3, shows a clearly distinct spectral pattern. The color palette shifts toward cyan and light green with scattered patches of blue, indicating a significant reduction in energy density across multiple frequencies. This deviation from the surrounding lines is not only visual but also structurally different, reflecting transient energy dispersal and local damping characteristics caused by the metallic fault in the C-phase. The unique pattern of attenuation of energy and color variation in Line 3 serve as reliable indicators of the occurrence of the fault. This highlights the effectiveness of STFT-WVD representations in identifying faults even under complex background interference conditions, such as those in multi-node systems like the IEEE-13 benchmark.

4.3. Fault Diagnosis Performance Analysis

To further validate the superiority of the proposed STFT-WVD time–frequency fusion method in multimodal feature extraction, this study conducts a comparative analysis with two representative time–frequency analysis techniques: the traditional Short-Time Fourier Transform (STFT) and Ensemble Empirical Mode Decomposition (EEMD) [26]. Using the STFT-WVD parameters as a baseline, the STFT method employs the same sampling frequency (12.8 kHz), window length (256), and overlap (200), with its spectrogram computed via the ‘spectrogram’ function and normalized; the EEMD method adds noise with an amplitude of 0.2 and performs 100 ensemble decompositions, after which the first three significant IMF components undergo Hilbert transforms and are interpolated to the same dimensions as the STFT output and normalized. All resulting time–frequency representations are then resized to 64 × 64 RGB images to ensure consistent feature expression when fed into the deep network. The mean squared error (MSE) is used as the loss function, and the Adam optimizer is applied with the learning rate set to 0.0001. The performance metrics of the three methods under a standard signal-to-noise ratio (SNR = 30 dB) are presented in the following

Table 8. Comparison of the results of different time–frequency feature maps using the proposed method model.

Line	EEMD			STFT			STFT-WVD
	Accuracy (%)	Recall	F1	Accuracy (%)	Recall	F1	Accuracy (%)	Recall	F1
Line 1	86.5	0.854	0.859	89.8	0.889	0.893	98.2	0.975	0.978
Line 2	88.1	0.871	0.875	91.2	0.903	0.907	98.7	0.982	0.985
Line 3	89.4	0.884	0.889	92.5	0.917	0.921	99.1	0.987	0.990
Line 4	87.2	0.861	0.866	90.4	0.894	0.898	98.5	0.978	0.981

.

The data in Table 8 demonstrate that the proposed STFT-WVD method consistently achieves superior performance compared to EEMD and STFT in all fault lines. It shows higher values in terms of accuracy, recall and F1 score, indicating improved fault line identification capacity and robustness under varying conditions. These results validate the effectiveness of the proposed multimodal feature fusion approach in accurately selecting fault lines in distribution networks.

4.4. Fault Diagnosis Effect Analysis in Dual-Channel Model

To verify that the proposed dual-branch multimodal fusion network outperforms the single-branch model architecture (RepLKNet with fully connected layers) in fault signal modeling and recognition, a comparative analysis was conducted under identical training conditions. Specifically, based on STFT-WVD time–frequency images, we evaluated and compared the classification performance of the single-branch model and the proposed dual-branch multimodal fusion network in the fault line identification task. Training was carried out using a batch size of 32, a learning rate of 0.001, and the Adam optimizer for 100 epochs. All input images were resized to 64 × 64 × 3, and the same training and test sets were used for both models.

Table 9. Comparison of fault line identification methods under different fault lines.

Fault Line	Single Model (RepLKNet + FC Layer)			Proposed Fusion Network
	Accuracy (%)	Recall	F1-Score	Accuracy (%)	Recall	F1-Score
Line 1	89.1	0.880	0.884	98.4	0.976	0.979
Line 2	87.8	0.868	0.872	98.9	0.982	0.984
Line 3	88.5	0.874	0.879	99.1	0.986	0.988
Line 4	86.9	0.859	0.863	98.6	0.978	0.981

presents the performance comparison between the two methods.

Through the analysis of experimental data, Table 9 clearly illustrates the significant performance advantages of the dual channel multimodal fusion network proposed in this paper over the single model (RepLKNet + Fully Connected Layer) in the fault line identification task of three types of faults. Specifically, the dual-channel multimodal fusion network demonstrates marked improvements in accuracy, recall, and F1 score. By integrating multimodal information, this network captures fault characteristics more fully, thereby reducing false detections and missed detections. The results validate its effectiveness and superiority in recognizing complex fault features, offering a superior solution for fault line identification.

To evaluate the independent contributions of each module in the model for fault identification, ablation experiments were designed to sequentially remove or replace key modules in the model. By analyzing performance changes, the role of each module can be assessed, providing theoretical support for the design of the model.

Table 10. Performance comparison of ablation experiments.

Model ID	Accuracy (%)	Precision	Recall	F1-Score
RepLKNet + BiGRU + GA + STFT-WVD	99.32	0.996	0.992	0.985
Replace STFT-WVD with STFT	98.10	0.982	0.979	0.980
ResNet replaces RepLKNet	97.42	0.974	0.970	0.972
Remove Global Attention mechanism	96.23	0.963	0.960	0.961
Remove BiGRU	94.35	0.944	0.938	0.941

summarizes the contribution of each submodule to the overall model performance.

As seen in the table above, the removal of any module leads to a decline in performance. Among them, the time–frequency fusion module (STFT-WVD) and RepLKNet contribute most significantly to improving image feature extraction. The BiGRU and Attention mechanism work together to strengthen the temporal branch’s ability to capture time-dependent features. The complete dual-channel structure maximizes the advantages of multimodal fusion.

4.5. Noise Robustness Analysis

To comprehensively assess the noise robustness of the proposed multimodal fault line selection model, this study extends the signal-to-noise ratio (SNR) range from 10–40 dB to more challenging conditions of 0 dB and −10 dB, simulating signal inputs in extreme electromagnetic environments [27]. At each SNR setting, interference is simulated by injecting Gaussian white noise of the corresponding intensity. During training, the model structure remains unchanged, and different noise intensities are applied only during the testing phase to evaluate the robustness of the trained model. For comparative analysis with existing methods, the previously used RepLKNet + Transformer approach is again used to evaluate the robustness of the noise. As shown in

Table 11. Performance comparison under different SNRs.

SNR (dB)	RepLKNet + Transformer			RepLKNet + BiGRU + GA
	Accuracy (%)	Recall	F1-Score	Accuracy (%)	Recall	F1-Score
−10	63.06	0.588	0.621	82.20	0.816	0.823
0	70.03	0.661	0.674	87.48	0.838	0.845
10	85.18	0.807	0.822	93.28	0.923	0.927
20	91.81	0.893	0.903	96.98	0.961	0.964
30	95.25	0.923	0.931	99.00	0.983	0.986
40	96.38	0.939	0.946	99.13	0.997	0.996

, the proposed RepLKNet + BiGRU + GA method significantly outperforms this comparative model in fault identification tasks under all SNR conditions. Specifically, under high-SNR conditions (30 dB and 40 dB), the method achieves an accuracy close to or exceeding 99%; even in low-SNR scenarios (0 dB and −10 dB), its performance remains stable, with an accuracy maintained between approximately 82% and 88%, markedly surpassing the Transformer-based approach. Furthermore, the proposed method demonstrates balanced distributions of recall and F1 scores across different SNR conditions, indicating good generalizability and high reliability. In general, the multimodal fusion network maintains excellent anti-interference ability and stable classification performance even in strong noise environments.

To evaluate the practical applicability of the proposed method, the trained model was deployed and tested on an embedded device. The raw fault current data obtained from a simulation platform was imported into a Raspberry Pi, where the signals were transformed into STFT-WVD time–frequency feature images. The proposed model was then used to identify the fault lines. The fault diagnosis results of the Raspberry Pi device are shown in

Table 12. Result of fault diagnosis for Raspberry Pi device.

Fault Line	Accuracy (%)	Recall	F1-Score
Line 1	97.8	0.975	0.978
Line 2	96.5	0.962	0.964
Line 3	96.9	0.968	0.967
Line 4	97.3	0.970	0.972

. The results demonstrated high classification accuracy across various fault angles and single-phase-to-ground fault types, confirming the method’s effectiveness and potential for real-world applications. The physical simulation of the faulty line selection is shown in Figure 9.

5. Conclusions

This paper proposes a fault line identification method based on the fusion of STFT-WVD and a dual-channel deep network, which innovatively combines the RepLKNet image feature extraction network with the BiGRU-GlobalAttention temporal modeling network. This method achieves high-precision identification and classification of single-phase grounding faults in power distribution networks.

Several sets of experimental results demonstrate the following.

(1). The STFT-WVD fusion algorithm offers high-resolution and interference suppression capabilities in the time–frequency representation of fault signals. Compared to STFT and EEMD methods, the proposed STFT-WVD time–frequency map construction strategy shows a superior overall performance in terms of classification accuracy, recall rate, and computational efficiency. This method not only accurately captures key feature information, but also offers good deployability, making it suitable for real-time fault detection systems in smart grids.

(2). A dual-channel time–frequency fusion network model for fault line selection is established. RepLKNet effectively captures cross-regional structural features in the time–frequency maps, while BiGRU-GlobalAttention enhances the modeling of temporal dependencies. By performing a multimodal fusion of time–frequency images and one-dimensional time series signals, the complementary nature of these two types of data is fully utilized to thoroughly excavate the fault characteristics of the system. As a result, fault diagnosis performance exceeds that of single-model fault diagnosis approaches.

(3). By extending the test to extremely low-SNR scenarios such as 0 dB and −10 dB, it is validated that the proposed STFT-WVD dual-channel fusion model can still maintain high identification accuracy under strong noise conditions, demonstrating excellent anti-interference capability. This further enhances the model’s credibility and practicality in real-world distribution system fault line identification tasks.

This study confirms the effectiveness of the multimodal fusion structure in the identification of faults in the power distribution network and provides new information on complex modeling and diagnostics of power signals.