Abstract
Accurate and timely fault diagnosis is of great significance for the safe operation and power supply reliability of distribution systems. However, traditional intelligent methods limit the use of the physical structures and data information of power networks. To this end, this study proposes a fault diagnostic model for distribution systems based on deep graph learning. This model considers the physical structure of the power network as a significant constraint during model training, which endows the model with stronger information perception to resist abnormal data input and unknown application conditions. In addition, a special spatiotemporal convolutional block is utilized to enhance the waveform feature extraction ability. This enables the proposed fault diagnostic model to be more effective in dealing with both fault waveform changes and the spatial effects of faults. In addition, a multi-task learning framework is constructed for fault location and fault type analysis, which improves the performance and generalization ability of the model. The IEEE 33-bus and IEEE 37-bus test systems are modeled to verify the effectiveness of the proposed fault diagnostic model. Finally, different fault conditions, topological changes, and interference factors are considered to evaluate the anti-interference and generalization performance of the proposed model. Experimental results demonstrate that the proposed model outperforms other state-of-the-art methods.
WITH the expansion of modern distribution systems and the increase in load access, distribution systems are more likely to suffer from faults due to the occurrence of stochastic events such as lightning strikes, insulation breakdowns, and improper operations [
With the development of distribution automation (DA), more operational data are obtained from intelligent electronic devices [
With the continuous development of AI technology, deep learning methods are widely utilized in the field of fault diagnosis [
Graph neural network (GNN) is a type of novel neural network model based on spatial structural information. The physical structural relationship acts as a significant constraint during the model learning process. It makes the GNN have stronger feature extraction ability and faster training speed. The latest studies have implemented GNN for fault diagnosis [
1) A novel fault diagnostic model based on spatiotemporal graph learning is proposed to complete fault location and fault classification in the distribution system. The measurement information processing derives from the physical structure of distribution network. Compared with traditional data-driven methods, the graph-based method can embed topological information into the model learning process, which makes the proposed model learn the deeper structure information of data and be more resistant to abnormal data and condition changes.
2) To improve the information processing capabilities of the model, a special spatiotemporal convolutional block is designed to extract fault features. This structure employs an efficient process for dealing with waveform and spatial information, which can combine the feature extraction of data numerical features and data structural information. Compared with the common GCNs, the proposed method has stronger feature extraction and anti-interference abilities. The results show that the proposed blocks improve the diagnostic results and narrow the input data windows, which ensures the speed and sensitivity of relay protection devices.
3) With the effective utilization of the structural information and the enhancement of feature extraction ability, the proposed model can deal with unknown system conditions. Experiments show that the proposed model offers a better generalization performance. It can maintain the performance of fault diagnosis under different topologies, fault resistances, and noise interference conditions. The effectiveness of the proposed model is verified using the IEEE 33-bus and IEEE 37-bus test systems. In addition, other state-of-the-art intelligent methods are utilized for comparative experiments.
The remainder of this paper is organized as follows. Section II describes the significance of fault type analysis and fault location in distribution network. Section III introduces the proposed fault diagnostic framework in terms of theoretical basis and technical details of the implementation. Section IV verifies the effectiveness of the proposed model through case studies. Section V concludes the study.
Different handling techniques can be used for different fault scenarios in distribution networks. For example, when the neutral point is not effectively grounded, the single-phase-to-ground fault is not necessary to be removed [
Fig. 1 Operating principle for sectionalizers and fault location.
In this case, accurate fault location and fault type analysis reflect the higher automation level of the distribution system. Fault type analysis and fault location can be combined to determine the specific area affected by the fault and the accurate fault diagnosis will make the loss caused by fault as small as possible. In addition, narrowing the data window can improve the performance of protection devices. A smaller time window can make the protection device obtain a faster response speed, which also means that the protection device needs to have a stronger information extraction ability. To realize an intelligent fault diagnostic model using global information for global judgment, a novel fault diagnostic model based on deep graph learning is proposed in this study. In addition, this study verifies the adaptability of the proposed model under different conditions.
In this section, the principles and structures of GNN and spatiotemporal graph convolutional network (STGCN) are introduced. The proposed fault diagnostic framework based on the STGCN and multi-task learning is then illustrated in detail.
The space-based GCN primarily originates from the convolutional operation of traditional CNNs [
(1) |
where the time-domain signal is converted into the frequency-domain signal by the basis function , which is the characteristic function of the Laplacian operator and satisfies . When the Laplacian operator is extended to the graph structure with nodes, the function is an -dimensional vector denoted as , where is the function value of at node . The gain between nodes i and j in the weighted graph is , and the operation of the Laplacian operator at node is given as:
(2) |
This holds for any , and we have:
(3) |
According to (2) and (3), the graph Fourier transform is constructed as:
(4) |
where and are obtained from Laplacian analysis . Here, is the
(5) |
Therefore, the matrix form of the graph Fourier transform can be expressed as , and its inverse transform is . Based on graph convolutional theory, many studies have conducted extensive research on reducing the computational burden and improving the performance [
(6) |
where is the signal matrix after convolution; is the input signal, and is the feature dimension; and is the parameter matrix of filter. The feature dimension is changed to by convolution. In this case, the graph convolution is transformed into a learning neural network .
STGCNs have already been used in human dynamic action recognition [
The structure and feature-update mode of GCN [
Fig. 2 Structure and feature-update mode of GCN.
The node connection relationship is considered to be a constraint to update the node features in the graph. Each node in the graph updates its information at each feature update by gathering information from its neighbors, where the closer neighbors have a greater effect on node features. This forms the basic rule for node feature updates. The node feature update policy of GCN is given by:
(7) |
where is the feature information at layer ; is the neural network weight at layer ; is the activation function of layer ; and is the calculation rule derived from the original adjacency matrix . The transformation process of is given as:
(8) |
where , and is the identity matrix; and . Adding a self-loop can integrate the information of node. Introducing the degree matrix can more effectively deal with multiple connection relationships. Normalization can transform the node feature values into a reasonable region. The processed adjacency matrix reflects the rules of information flow and has a constant value during the calculation operation at any layer. Here, the feature mapping ability of the network derives from the learnable matrix of each layer. However, when the number of GCN layers increases, the features of nodes will show an average trend called over-smoothing [
To improve its feature perception ability, the STGCN contains a special spatiotemporal convolutional block. The temporal convolution module extracts the node features along the time axis before and after the spatial information aggregation based on GCN rules, as illustrated in
Fig. 3 Calculation of spatiotemporal convolutional block.
In the spatiotemporal convolutional block, convolutional kernels similar to one-dimensional convolution are utilized to extract waveform features. The kernels can scan all waveform features along the time axis and map them into new features with stronger expression. Different from the traditional GCN, the feature processing of STGCN is composed of a type of temporal-spatiotemporal structure, and the first temporal convolutional layer is expressed as:
(9) |
(10) |
(11) |
(12) |
where is the output feature of the first temporal convolutional layer; is the feature of layer l in the GNN, and when , indicates the input fault features of the model; , , and are three convolutional kernels with the same shape; represents the batch normalization operation; and and are the activation functions. After the first temporal convolutional layer, the spatial convolutional layer is expressed as:
(13) |
(14) |
(15) |
(16) |
(17) |
(18) |
where is the output feature of the spatial convolutional layer; - and - represent the learnable parameters; and the sign denotes the feature splicing operation. After the spatial convolutional layer, the temporal convolutional layer with the same structure as the first temporal convolutional layer further extracts data features. The feature operation process is expressed as:
(19) |
(20) |
(21) |
(22) |
where is the output feature from the last temporal convolutional layer, which is also a feature of the layer in the GNN; and , , and are three convolutional kernels with the same shape.
Converting the power network into a graph structure is essential to the application of the GNN. A power network consists of transmission lines, power equipment, and buses. The graph is composed of edges and nodes. During the operation of GNN, the node message flows through the connection relationships of the edges. In the power network, the effects of state changes on the buses are also carried over to other buses and electrical equipment along the lines. In this case, the relationship between the power line and bus can be transformed into the relationship between the edge and node. The bus voltages, branch currents, and line impedances are the basic features of power network. With buses as nodes and lines as edges, distribution networks can be converted into graph structures. Voltage can be considered as the node feature, and the current and line impedances are edge features. However, it is not easy to obtain accurate line impedance on a large scale. In addition, various distribution networks exhibit different impedance characteristics. The fixed impedance feature will reduce the generalization performance of the model. Therefore, the line impedance feature is not utilized in the proposed model. In addition, the current value that flows into the node is considered as the node feature. In this case, the information of each node includes the voltage and current features converging to the bus. The features at node are denoted by , where 1, 2, and 3 represent the three phases; and represents observable nodes. All features are root mean square (RMS) values and no features exist at the edges. The input feature of the GNN model is the input node feature . The objective of the fault diagnostic model is to obtain the fault type and location information through the observed node information . In addition, the topology structure of distribution network is also the input of the fault diagnostic model for embedding physical information. The function of the fault diagnostic model is expressed as:
(23) |
where represents the fault diagnostic model. Note that is the connection relationship of the nodes, which is derived from the structure of the distribution network, and specifies the feature update rules for the graph convolutional layer. The model maps the fault features to the fault type and fault location information. The algorithm in this study is constructed using a deep graph library and Pytorch deep learning framework.
In this study, a fault diagnostic framework based on the STGCN structure is proposed to combine fault type analysis and fault location in the distribution network. During the fault process, the fault impact spreads from the fault point to the entire graph based on the connection between nodes and edges. Different fault types generate different fault waveforms and affect the surrounding nodes. The spatiotemporal convolutional block can effectively perceive differences in node information and generate stronger feature expressions. In this case, the proposed fault diagnostic framework outputs accurate fault diagnostic results. The structure of the proposed fault diagnostic framework using a simple circuit as an example is shown in
Fig. 4 Structure of proposed fault diagnostic framework.
Multi-task learning [
Two independent classifiers are designed for the two tasks because of different feature requirements of fault location and fault type analysis. In the fault location task, the output depends mainly on the spatial information of the nodes.
The positional relationship between the input features and output results is relatively regular. Therefore, the classifier for the fault location task is constructed using fully connected layers. However, faults can occur at any line in the distribution network. Therefore, the classification of fault types requires a classifier to identify valid mapping features among all nodes. CNN can search for effective features regardless of their positions in the input information. Therefore, a CNN is utilized to construct the fault type classifier for the features extracted by STGCN. The fault directly affects the edge and then severely affects the nodes connected to the edge. Therefore, two nodes can be used to indicate that a fault occurs on the edge between them in fault location task. In this case, the two nodes with the largest activation values represent the feature of the two buses are most severely affected by the fault. This indicates that a fault occurs between the two buses. In the fault type analysis, the information extracted from the blocks will be identified by a CNN-based classifier. This can be considered as a common multi-classification task.
In this section, the fault data are obtained by simulated test systems, and the structure of the proposed spatiotemporal convolutional block is introduced in detail, and the diagnostic results of the model are presented and analyzed. In addition, different conditions such as fault resistance changes, topological changes, and data interference are considered to verify the performance of the proposed model.
To obtain labeled transient fault samples, a simulated distribution network model based on the IEEE 33-bus test system [
Fig. 5 Graph structure of IEEE 33-bus test system for fault diagnosis.
Because of the mutual influence between buses, the information transmission on the edge is set as bidirectional. In addition, because the current information in the distribution network is attributed to node information, the edges in the graph only play the role of indicating the direction of information transmission during this task. In this case, the network uses three-phase voltage and current data of all nodes for global fault diagnosis.
The fault location task can be regarded as a 32-class classification task because of the 32 lines in the test system. In addition, each fault point contains 10 types of faults, and therefore the fault type analysis can be regarded as a 10-class classification task. Thus, the total number of output categories of the proposed model is . When the fault occurs, the three-phase voltage and current on the bus are collected. Taking bus 9-bus 10 as an example, the voltage waveforms of different fault types are shown in
Fig. 6 Voltage waveforms of different fault types. (a) Phase-A-to-ground (AN). (b) Phase-A-to-phase-B (AB). (c) Two-phases-to-ground (ABN). (d) Three phases (ABC).
The proposed model can accept a data window with fewer sampling points instead of complete waveforms. In this study, the transient metallic faults are implemented to verify the proposed fault diagnostic model. During the simulation, the total sampling time after the faults is 0.05 s.
The sampling frequency is 1 kHz, and the original fault data contain 50 time points. After downsampling, each fault sample contains 21 time points. The entire fault waveform is resampled repeatedly in steps at each sampling point. The 21 time points indicate that each fault sample for fault diagnosis obtains 0.02 s of fault data. In this case, the proposed model could utilize any 0.02 s of fault data within 0.05 s after the fault to determine the fault type and location. The length of the downsampling window refers to the fault information contained in each sample. With a longer data window, the sample contains more fault information, and the difficulty of fault diagnosis will be reduced. Twenty five sub-samples of each original fault sample are obtained for training and the number of samples for each fault resistance condition is , where 70% of the samples are selected for model training, and the remaining data are used for model testing. The subsampling process of fault data is suitable for real-time fault diagnosis. Therefore, the fault diagnostic model can be applied to real-time fault diagnosis. The parameters of fault states for training are listed in
Fault parameter | Values or types |
---|---|
Fault type | AN(1), BN(2), CN(3), AB(4), AC(5), BC(6), ABN(7), CAN(8), BCN(9), ABC(10) |
Fault position | Midpoint of 32 lines |
Fault resistance (Ω) | 0.01, 0.1, 0.5, 1, 2, 5, 10, 15, 20, 50, 100, 150, 200, 300, 400, 500, 600 |
Operating load | Basic load |
In the proposed fault diagnostic model, the per-unit values of the voltage and current are directly utilized as the input of the model without other data processing. The structure and parameters of the proposed spatiotemporal convolutional block are shown in
Fig. 7 Proposed spatiotemporal convolutional block.
To improve the performance of the model, parallel structures and regularization techniques are implemented in both temporal and spatial convolutions. For example, the data shape of the fault samples is (33, 21, 6), where 33 indicates that the number of buses is 33; 21 indicates that the samples contains 21 time points; and 6 indicates the number of features.
In the processing of features forward in a single spatiotemporal convolutional block, the samples first pass through the temporal convolution. The shape of the 2D-convolutional kernel size is (1, 3), and the filter channel is 64. Because the convolutional kernels must scan the waveform information on the time axis, it is necessary to adjust the dimensions of the sample features. Accordingly, two temporal convolutions and one spatial convolution form a spatiotemporal convolutional block. Multi-channel feature extraction can make the network easier to capture key fault features. The two types of convolutional layers are combined to extract the fault features in greater depth. In this case, the feature extraction capability of STGCN is improved by the extended learnable parameters.
The proposed fault diagnostic model has two main functions: fault type analysis and fault location The accuracy of the proposed model for the training process is illustrated in
Fig. 8 Accuracy of proposed model for training process. (a) Fault type analysis. (b) Fault location.
In addition, GCN [
Model | Accuracy | |
---|---|---|
Fault type analysis | Fault location | |
Proposed | 0.999 | 0.992 |
GCN [ | 0.973 | 0.917 |
CNN [ | 0.899 | 0.981 |
PCA-SVM [ | 0.920 | 0.870 |
The results show that the proposed model has a better performance than other models. The improved spatiotemporal convolution block can significantly improve the feature extraction ability of the model.
In addition, the outputs of the penultimate layer from different models are extracted to represent the feature space for the tasks. We utilize t-distributed stochastic neighbor embedding (t-SNE) [
Fig. 9 Visualization of output of each task from GCN and proposed model. (a) Visualization of fault type output from GCN. (b) Visualization of fault type output from proposed model. (c) Visualization of fault location from GCN. (d) Visualization of fault location from proposed model.
As shown in the two-dimensional space, the feature outputs of the proposed model have a more reasonable and accurate distribution, illustrating that the proposed model has higher accuracy and better generalization performance.
In
Fig. 10 Test accuracies of proposed model and CNN for training process. (a) Fault type analysis. (b) Fault location.
In point of fact, the data acquisition devices are influenced by different levels of noise or loss of data due to different working environments. In addition, the changes in load also affect the performance of the fault diagnostic model. Therefore, the generalization ability of the model is a core feature of the fault diagnostic model. In our study, different interference factors are considered to verify the generalization and anti-interference performance of the model.
Electrical measurements are easily influenced by electromagnetic interference and other environmental factors. In this study, Gaussian white noise is used to simulate the interference of environmental factors. The signal noise ratios (SNRs) [
Fig. 11 Effects of different SNRs on waveform of bus 9-bus 10 under AN fault. (a) SNR is 35 dB. (b) SNR is 25 dB. (c) SNR is 15 dB. (d) SNR is 10 dB.
The test accuracies for fault type analysis and fault location of the proposed model, GCN, and PCA-SVM under different SNRs are shown in
Fig. 12 Test accuracies for fault type analysis and fault location of proposed model, GCN, and PCA-SVM under different SNRs. (a) Fault type analysis. (b) Fault location.
Typically, the sampled signal may have outliers due to inaccurate measurements and interference. Thus, eliminating the interference of abnormal values is a major requirement of the fault diagnostic model. Outliers are simulated by multiplying the standard measurements and random numbers between 0.7 and 1.3. The numbers of outliers are set as 1%, 2%, 5%, 10%, and 20% of the total sampled data. The model will be verified under these five outlier conditions. The effect of different outlier rates on waveform of bus 9-bus 10 under AN fault is shown in
Fig. 13 Effect of different outlier rates on waveform of bus 9-bus 10 under AN fault. (a) Outlier rate is 10%. (b) Outlier rate is 20%.
The test accuracies for fault type analysis and fault location of the proposed model, GCN, and PCA-SVM under different outlier rates are shown in
Fig. 14 Test accuracies for fault type analysis and fault location of proposed model, GCN, and PCA-SVM under different outlier rates. (a) Fault type analysis. (b) Fault location.
In practice, smart meters package and upload collected information. In this process, missing data cannot be ignored because of internet and equipment factors. Therefore, it is highly probable that the information of each node will be missing. When the meters fail to upload data, the voltage and current values collected by the meter cannot be obtained by the model. The model must diagnose the fault using the remaining information. During the verification, the possibility of data missing at each node are set to be 0.5%, 1%, 2%, 5%, and 10%. In the worst case with data missing rate of 10%, each data window has only a probability of containing complete original data. The test accuracies for fault type analysis and fault location of the proposed model, GCN, and CNN under different data missing rates are shown in
Fig. 15 Test accuracies for fault type analysis and fault location of proposed model, GCN, and PCA-SVM under different data missing rates. (a) Fault type analysis. (b) Fault location.
It can be observed from
Various load conditions are simulated by multiplying the basic load value by a random number between 0.7 and 1.3. The test accuracy for fault type analysis and fault location of the proposed model under various load conditions is shown in
Fig. 16 Test accuracies for fault type analysis and fault location of proposed model under various load conditions.
In an actual distribution system, the fault resistances are unknown and may differ from the fault conditions during model training. In this case, fault diagnostic models need to have a good adaptability to untrained fault resistance conditions. To further verify the effectiveness of the model under different unknown fault resistance conditions, the model trained with a 0.1 Ω fault resistance is directly applied to other fault resistance conditions. In addition, CNN and GCN are compared to verify the effectiveness of the proposed model. The test results of the proposed model under different fault resistances are presented in
Fault resistance (Ω) | Accuracy of proposed model | Accuracy of CNN | Accuracy of GCN | |||
---|---|---|---|---|---|---|
Fault type analysis | Fault location | Fault type analysis | Fault location | Fault type analysis | Fault location | |
0.01 | 0.998 | 0.989 | 0.894 | 0.982 | 0.975 | 0.924 |
0.1 (train) | 0.999 | 0.992 | 0.899 | 0.981 | 0.973 | 0.917 |
0.5 | 0.999 | 0.992 | 0.894 | 0.981 | 0.973 | 0.915 |
1 | 0.997 | 0.992 | 0.893 | 0.983 | 0.974 | 0.908 |
2 | 0.997 | 0.992 | 0.891 | 0.983 | 0.969 | 0.884 |
5 | 0.993 | 0.993 | 0.883 | 0.981 | 0.970 | 0.831 |
10 | 0.990 | 0.991 | 0.869 | 0.976 | 0.971 | 0.739 |
15 | 0.988 | 0.986 | 0.852 | 0.965 | 0.955 | 0.640 |
20 | 0.981 | 0.975 | 0.835 | 0.955 | 0.932 | 0.584 |
50 | 0.941 | 0.897 | 0.693 | 0.879 | 0.789 | 0.414 |
In an actual distribution system, the performance of the proposed model needs to be generalized to a specific range of fault resistance. To verify the effectiveness of the proposed model under a specific fault resistance range, the proposed model is trained with 0.01 Ω+50 Ω fault resistance and tested in the range from 0.01 Ω to 50 Ω. In addition, CNN and GCN are used in comparative experiments to verify the effectiveness of the proposed model.
Table IV shows that the performances of CNN and GCN decrease significantly when the fault resistance increases. Even if the 50 Ω fault resistance are utilized as the training condition for model learning, CNN and GCN could not adapt to the entire fault resistance range due to the lack of a feature extraction ability. This indicates that the embedding of topological information and the designed processing of waveform features are effective with the fault diagnostic model.
Fault resistance (Ω) | Accuracy of proposed model | Accuracy of CNN | Accuracy of GCN | |||
---|---|---|---|---|---|---|
Fault type analysis | Fault location | Fault type analysis | Fault location | Fault type analysis | Fault location | |
0.01 (train) | 0.998 | 0.991 | 0.893 | 0.981 | 0.972 | 0.910 |
0.1 | 0.997 | 0.991 | 0.894 | 0.981 | 0.974 | 0.901 |
0.5 | 0.999 | 0.992 | 0.894 | 0.979 | 0.973 | 0.901 |
1 | 0.999 | 0.993 | 0.896 | 0.979 | 0.974 | 0.900 |
2 | 0.999 | 0.992 | 0.896 | 0.978 | 0.973 | 0.871 |
5 | 0.998 | 0.995 | 0.896 | 0.977 | 0.975 | 0.844 |
10 | 0.998 | 0.996 | 0.895 | 0.979 | 0.973 | 0.799 |
15 | 0.998 | 0.996 | 0.893 | 0.979 | 0.971 | 0.765 |
20 | 0.999 | 0.996 | 0.893 | 0.981 | 0.969 | 0.763 |
50 (train) | 0.996 | 0.994 | 0.890 | 0.945 | 0.968 | 0.802 |
The higher fault impedances indicate weaker fault features, which affect the performance and generalization ability of the fault diagnostic model. To verify the performance and generalization ability of the proposed model under a high-impedance fault, fault data with a 300 Ω fault resistance are selected for model training, and 100-600 Ω fault resistances are selected for model testing. The comparative results of the proposed model, CNN, and GCN experiments are presented in
Fault resistance (Ω) | Accuracy of proposed model | Accuracy of CNN | Accuracy of GCN | |||
---|---|---|---|---|---|---|
Fault type analysis | Fault location | Fault type analysis | Fault location | Fault type analysis | Fault location | |
100 | 0.973 | 0.960 | 0.867 | 0.676 | 0.881 | 0.429 |
150 | 0.989 | 0.991 | 0.912 | 0.817 | 0.932 | 0.551 |
200 | 0.994 | 0.999 | 0.934 | 0.905 | 0.967 | 0.677 |
300 (train) | 0.999 | 0.999 | 0.960 | 0.956 | 0.978 | 0.739 |
400 | 0.999 | 0.999 | 0.947 | 0.931 | 0.969 | 0.650 |
500 | 0.996 | 0.998 | 0.905 | 0.883 | 0.960 | 0.496 |
600 | 0.993 | 0.993 | 0.853 | 0.832 | 0.934 | 0.385 |
It can be observed from
It may be owing to that representation ability of GCN is insufficient, which make it not extract key features under different fault resistances. The proposed model has a better fault diagnostic and generalization performances under a high-resistance fault because of its stronger feature extraction ability and physical information embedding.
In an actual distribution system, the topology of the distribution network can be changed because of different operating states. To test the performance of the proposed diagnostic model for topological changes, three types of mesh distribution networks and different fault resistance conditions are modeled. Three mesh topological structures are obtained from the original IEEE 33-bus topology by connecting different branches. It should be noted that to verify the effectiveness of the model on a weak mesh distribution network, the line impedance parameters in the experiments are five times that of the original system. The topology numbers and connection methods of three mesh topological structures are listed in
Topology number | Connection method |
---|---|
G1 | Connect bus 8-bus 21, bus 9-bus 15, bus 12-bus 22, bus 18-bus 33, and bus 25-bus 29 |
G2 | Connect bus 9-bus 15, bus 12-bus 22, bus 18-bus 33, and bus 25-bus 29 |
G3 | Connect bus 8-bus 21, bus 12-bus 22, bus 18-bus 33, and bus 25-bus 29 |
To verify the generalization performance of the proposed model for mesh topologies and topological changes, the data under the G1 topology are utilized as the training dataset, and the data under the G2 and G3 topologies are utilized as the verification dataset. The fault state parameters utilized for the collected data are listed in
Fault parameter | Values or types |
---|---|
Fault type | AN(1), BN(2), CN(3), AB(4), AC(5), BC(6), ABN(7), CAN(8), BCN(9), ABC(10) |
Fault position | The midpoint of length at bus 1-bus 2, bus 2-bus 3, bus 3-bus 23, bus 6-bus 7, bus 8-bus 9, bus 11-bus 12, bus 14-bus 15, bus 17-bus 18, bus 21-bus 22, bus 26-bus 27, bus 29-bus 30, and bus 32-bus 33 |
Fault resistance (Ω) | 0.01, 0.1, 1, 10, 20, 50, 100, 200, 300, 500 |
For the G1, G2, and G3 topologies, 10 types of fault resistance conditions are set. The fault resistances of 1 Ω+200 Ω in the G1 topology will be utilized as the training environment of the model. Other fault resistance conditions in the G2 and G3 topologies will be utilized as the test environment. The graph structure of G1 topology is shown in
Fig. 17 Graph structure of G1 topology.
CNN and GCN are utilized in comparative experiments to show the effectiveness of the proposed model. The performances of different models for G1 topology in the training case of 1 Ω+200 Ω fault resistances are presented in
Model | Accuracy | |
---|---|---|
Fault type analysis | Fault location | |
Proposed | 0.998 | 0.999 |
GCN [ | 0.973 | 0.899 |
CNN [ | 0.799 | 0.984 |
Fault resistance(Ω) | Accuracy of proposed model (G2) | Accuracy of CNN (G2) | Accuracy of GCN (G2) | Accuracy of proposed model (G3) | Accuracy of CNN (G3) | Accuracy of GCN (G3) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Fault type | Fault location | Fault type | Fault location | Fault type | Fault location | Fault type | Fault location | Fault type | Fault location | Fault type | Fault location | |
0.01 | 0.998 | 0.989 | 0.789 | 0.801 | 0.970 | 0.912 | 0.999 | 0.993 | 0.794 | 0.913 | 0.970 | 0.907 |
0.1 | 0.999 | 0.990 | 0.795 | 0.804 | 0.971 | 0.911 | 0.997 | 0.990 | 0.794 | 0.912 | 0.971 | 0.916 |
1 (train) | 0.997 | 0.991 | 0.796 | 0.802 | 0.977 | 0.917 | 0.998 | 0.993 | 0.795 | 0.913 | 0.975 | 0.912 |
10 | 0.999 | 0.988 | 0.797 | 0.795 | 0.964 | 0.914 | 0.999 | 0.988 | 0.792 | 0.913 | 0.968 | 0.879 |
20 | 0.999 | 0.988 | 0.797 | 0.791 | 0.968 | 0.809 | 0.999 | 0.985 | 0.791 | 0.907 | 0.967 | 0.803 |
50 | 0.999 | 0.985 | 0.785 | 0.792 | 0.968 | 0.761 | 0.999 | 0.977 | 0.776 | 0.898 | 0.969 | 0.776 |
100 | 0.998 | 0.986 | 0.764 | 0.775 | 0.963 | 0.766 | 0.998 | 0.972 | 0.768 | 0.862 | 0.964 | 0.788 |
200 (train) | 0.992 | 0.981 | 0.726 | 0.724 | 0.936 | 0.790 | 0.993 | 0.976 | 0.744 | 0.791 | 0.930 | 0.816 |
300 | 0.968 | 0.984 | 0.697 | 0.679 | 0.913 | 0.775 | 0.979 | 0.982 | 0.729 | 0.740 | 0.867 | 0.801 |
500 | 0.898 | 0.971 | 0.656 | 0.642 | 0.823 | 0.724 | 0.912 | 0.965 | 0.709 | 0.685 | 0.787 | 0.721 |
It can be observed that the proposed model performs better when directly generalized to similar topologies because of its stronger feature extraction ability. In addition, CNN is most affected by topological changes. It may be due to that the fault diagnostic models based on CNN cannot embed physical topological information so that CNN extracts more numerical features of data but could not learn the deeper structure information. When dealing with changes in data, the reliability of CNN is significantly reduced. The graph-based models could learn the structural information of the data, which makes the models have reliable performance under different topology change conditions. With improved spatiotemporal convolutional operations, the proposed model shows more effective generalization performance during topological change conditions, which means the model could be implemented in existing distribution systems.
In an actual distribution system with lower voltage levels, the values of the line parameters may be larger. In addition, the three-phase load may be unbalanced due to different operating conditions and load levels. The structure of IEEE 37-bus test system for fault diagnosis is shown in
Fig. 18 Structure of IEEE 37-bus test system for fault diagnosis.
Fault parameter | Values or types |
---|---|
Fault type | AN(1), BN(2), CN(3), AB(4), AC(5), BC(6), ABN(7), CAN(8), BCN(9), ABC(10) |
Fault position | The midpoint of fault lines |
Fault resistance (Ω) | 0.01, 0.1, 1, 10, 20, 30, 40, 50, 100 |
The fault resistance of 0.1 Ω is utilized as the training environment, and other fault resistance conditions are utilized as the test conditions. The results are listed in
Fault resistance (Ω) | Accuracy of proposed model | Accuracy of CNN | Accuracy of GCN | |||
---|---|---|---|---|---|---|
Fault type analysis | Fault location | Fault type analysis | Fault location | Fault type analysis | Fault location | |
0.01 | 0.998 | 0.998 | 0.878 | 0.971 | 0.980 | 0.923 |
0.1 (train) | 0.999 | 0.999 | 0.881 | 0.970 | 0.977 | 0.923 |
1 | 0.998 | 0.999 | 0.881 | 0.971 | 0.978 | 0.919 |
10 | 0.979 | 0.994 | 0.877 | 0.933 | 0.957 | 0.797 |
20 | 0.959 | 0.959 | 0.854 | 0.853 | 0.905 | 0.602 |
30 | 0.925 | 0.924 | 0.812 | 0.778 | 0.845 | 0.603 |
40 | 0.895 | 0.871 | 0.785 | 0.709 | 0.774 | 0.548 |
50 | 0.887 | 0.822 | 0.706 | 0.617 | 0.738 | 0.501 |
In an actual distribution network, the system scale is relatively large, and measuring devices may be scarce for all buses. The topology of the distribution network can be simplified to a smaller topology by the key buses. In this manner, the proposed model can realize fault analysis of the entire distribution network through limited measurement data. The fault diagnostic model can locate a fault in a specific subregion through the key nodes. In this study, the experimental results verify the fault type analysis and fault location performances of the proposed model for subregions. Eleven key nodes are selected from the IEEE 33-bus test system, and 10 subregions are divided to verify the effectiveness of the proposed model. This verifies the capability of the proposed fault diagnostic framework under less measurement data and topological simplification.
The structure of simplified topology of IEEE 33-bus test system is presented in
Fig. 19 Structure of simplified topology of IEEE 33-bus test system.
The fault diagnostic model utilizes the information of these key nodes. The data sources of the nodes and the definitions of edges are presented in
Node No. | Data source | Edge | Location label (IEEE 33-bus test system) |
---|---|---|---|
0 | 1 | 0-1 | Bus 1-bus 2 |
1 | 2 | 1-2 | Bus 2-bus 3 |
2 | 3 | 2-3 | Bus 3-bus 6 |
3 | 6 | 3-4 | Bus 6-bus 11 |
4 | 11 | 4-5 | Bus 11-bus 14 |
5 | 14 | 5-6 | Bus 14-bus 18 |
6 | 18 | 1-7 | Bus 2-bus 19, bus 19-bus 22 |
7 | 22 | 2-8 | Bus 3-bus 23, bus 23-bus 25 |
8 | 25 | 3-9 | Bus 6-bus 26, bus 26-bus 29 |
9 | 29 | 9-10 | Bus 29-bus 33 |
10 | 33 |
For the simplified system, the required measurement information is the data from the key nodes. The proposed fault diagnostic model can determine the fault type and locate the fault in the subregion between these key nodes. For example, if the model output edge is 9-10, the sub-region between buses 29 and 33 in the original IEEE 33-bus system has experienced a fault. CNN and GCN are utilized for comparative experiments, as shown in
Fault resistance (Ω) | Accuracy of proposed model | Accuracy of CNN | Accuracy of GCN | |||
---|---|---|---|---|---|---|
Fault type analysis | Fault location | Fault type analysis | Fault location | Fault type analysis | Fault location | |
0.01 | 0.999 | 0.990 | 0.973 | 0.926 | 0.910 | 0.976 |
2 | 0.999 | 0.980 | 0.966 | 0.922 | 0.888 | 0.952 |
50 | 0.954 | 0.923 | 0.751 | 0.760 | 0.770 | 0.855 |
The measurement information of the bus is represented by the RMS values of the voltage and current. PMUs can be implemented as measuring devices for bus data. The sampling frequency of a PMU can reach 10 kHz, and its real-time data transmission is within 20 ms. Accordingly, PMUs can be applied to the actual measurements of the proposed fault diagnostic framework. In addition, the proposed fault diagnostic framework is based on AI technology. The input sample length, sampling frequency, and fault detection interval can be determined based on actual situations.
In this study, a combined fault type analysis and fault location model based on spatiotemporal graph learning is proposed to perform fault diagnostic tasks for distribution systems. Based on the excellent feature processing ability of the spatiotemporal convolutional block, fault type analysis, and fault location can be performed accurately in multi-task learning models. The topological information of the distribution network could be embedded to act as a significant constraint during model training, enabling the model to learn the deeper structural information of the fault data and giving it stronger resistance to abnormal data. Meanwhile, the waveform features and structural information are effectively combined by the spatiotemporal convolutional block, significantly improving the performance of the fault diagnostic model. Thus, the proposed fault diagnostic model has higher accuracy and stronger generalization ability under topological changes, unknown fault resistance conditions, and different types of signal interference. The effectiveness of the proposed framework is verified under different test system and fault conditions. The results show that the proposed framework has better performance and generalization ability than GCN and other intelligent models.
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