Fault Location in Power Distribution Systems via Deep Graph Convolutional Networks

Kunjin Chen; Jun Hu; Yu Zhang; Zhanqing Yu; Jinliang He

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Fault Location in Power Distribution Systems via Deep Graph Convolutional Networks

Kunjin Chen, Jun Hu, Yu Zhang, Zhanqing Yu, Jinliang He

arXiv:1812.09464v2Dec 22, 2018cs.LGstat.APstat.ML

TL;DR

Fault location in distribution systems must integrate measurements across buses despite irregular topology and measurement errors. This paper addresses the problem with a topology-aware GCN and data augmentation. Simulations report strong fault-location effectiveness, robustness to noise and data loss, and adaptation to topology changes and limited measurements.

Problem
Fault location must process spatially distributed measurements across buses while accounting for topology, noise, and data loss.
Method
The paper proposes a graph convolutional network that preserves bus spatial correlations, integrates multiple measurements, and uses data augmentation for robustness.
Results
Simulations show the GCN is effective on IEEE 123-bus and 37-bus systems and more robust to measurement errors than SVM, RF, and FCNN.
Takeaways & Limitations
The model adapts to topology changes and performs well with a limited number of measured buses.

Abstract

from arXiv · show

This paper develops a novel graph convolutional network (GCN) framework for fault location in power distribution networks. The proposed approach integrates multiple measurements at different buses while taking system topology into account. The effectiveness of the GCN model is corroborated by the IEEE 123 bus benchmark system. Simulation results show that the GCN model significantly outperforms other widely-used machine learning schemes with very high fault location accuracy. In addition, the proposed approach is robust to measurement noise and data loss errors. Data visualization results of two competing neural networks are presented to explore the mechanism of GCN's superior performance. A data augmentation procedure is proposed to increase the robustness of the model under various levels of noise and data loss errors. Further experiments show that the model can adapt to topology changes of distribution networks and perform well with a limited number of measured buses.

I. INTRODUCTION

Fault location is essential for rapid outage restoration, but increasing measurements expose limitations in traditional methods. The paper proposes a topology-aware GCN that integrates measurements across buses and improves robustness to noise and data loss.

Accurate, rapid fault localization supports timely outage clearing and restoration in distribution systems.
Traditional approaches include impedance-based, voltage sag-based, outage mapping, traveling-wave, and machine-learning methods.
Traveling-wave methods generally require high sampling rates, communication overhead, and GPS-based synchronization.
Additional measurement devices improve situational awareness but create challenges for flexibly integrating multiple-bus measurements and handling data loss.
The proposed GCN preserves spatial bus correlations, integrates multiple measurement units, and extracts features layer by layer for faulty-bus classification.
A data augmentation procedure is designed to improve robustness under varying noise and measurement-error levels.

II. FAULT LOCATION BASED ON GRAPH CONVOLUTIONAL NETWORKS

The method represents distribution-system measurements as graph signals and constructs localized spectral convolutions using graph structure. Chebyshev polynomial filters provide an efficient, K-hop-localized implementation.

A. Formulation of the Fault Location Task: The fault-location task uses voltage and current phasor measurements at observed buses and formulates faulty-bus identification as classification.
A. Formulation of the Fault Location Task: Traditional CNNs target Euclidean inputs, whereas distribution-system measurements are spatially distributed over network graphs.
B. Spectral Convolution on Graphs: Spectral graph convolution applies Fourier-like transformations defined by the graph Laplacian’s eigenvectors and eigenvalues.
B. Spectral Convolution on Graphs: Smooth spectral filters address the lack of guaranteed spatial localization in the basic spectral formulation.
B. Spectral Convolution on Graphs: Truncated Chebyshev expansions stabilize polynomial filtering and express the operation recursively through graph-Laplacian powers.
B. Spectral Convolution on Graphs: The resulting graph filter has computational complexity O(K|E|) and is localized within K hops.

C. GCN Approach for Fault Location

The fault-location GCN processes bus-indexed measurements through graph convolutional and fully connected layers, using topology-derived adjacency weights to produce a faulty-bus prediction.

The model passes input X through Lc graph convolution layers, Lf fully connected layers, and a softmax activation.
Each graph-convolution feature map combines previous-layer feature maps using trainable polynomial-filter coefficients.
The final graph-convolution output is flattened, processed by fully connected layers, and classified by the largest final activation.
The weighted adjacency matrix is constructed from shortest-path distances between buses.

D. The IEEE 123 Bus Distribution System Test Case

The IEEE 123-bus test case supplies a topology-based benchmark with simulated faults and phasor measurements. The implementation expands inputs to all buses, representing unmeasured values as zeros.

The benchmark contains 128 buses, including 85 load-connected buses, with topology used to represent bus connections rather than geometrical locations.
Simulations include single-phase-to-ground, two-phase-to-ground, and two-phase short-circuit faults with resistances from 0.05 Ω to 20 Ω.
The model structure consists of several graph convolution layers followed by two fully connected layers.
The study generates 20 samples for each fault type at each bus, producing 13,520 samples and 119 faulty-bus classes.
The GCN input is expanded to 128 × 12, with 380 measured entries and zeros assigned to nonmeasured buses.

III. RESULTS AND DISCUSSION

The study evaluates a GCN fault-location model against baseline approaches, using topology-aware graph filtering and noisy or incomplete measurements. Its implementation includes localized spectral filters, PCA-based baselines, and explicit perturbations for robustness testing.

The GCN uses three graph convolution layers followed by two fully connected layers, with Kn = 20 and graph orders K of 3, 4, and 5.
With Kn = 20, increasing filter order expands the graph region explored, while properly chosen filters retain locality.
The evaluation compares the GCN with SVM, random forest, and fully connected neural network baselines.
The model processes noisy and incomplete measurements through Gaussian noise, bus-level data loss, and random loss of individual measurements.

B. Fault Location Performance of the Models

The GCN achieves the strongest reported fault-location performance among the evaluated models and remains robust when measurements are corrupted or lost. Visualization results examine whether learned representations cluster samples by faulty bus.

The GCN has the highest classification accuracy among the compared approaches, while SVM and random forest also perform well on one-hop accuracy.
Measurement-loss errors greatly reduce classification accuracy, but the GCN remains robust and significantly outperforms the other schemes under varied modifications.
When data-loss errors are present, FCNN exceeds SVM and random forest accuracy despite being roughly 10% lower in unmodified classification accuracy.
Training with Gaussian noise produces mild GCN improvements, and GCN retains superior performance even though data-loss modifications are excluded from training.
The visualizations reduce test data with PCA to 200 dimensions, apply t-SNE, and compare whether samples from the same faulty bus cluster together.

C. Visualization of Data After Transformations

t-SNE visualizations show that GCN transforms noisy and error-modified measurements into more class-separable features than FCNN, supporting its higher fault-location accuracy.

GCN features form tighter same-class clusters than FCNN features when both models are trained and tested with Gaussian noise.Only a small fraction of GCN samples are separated from their main clusters, whereas FCNN samples generally do not cluster by class.
More than 10% higher classification accuracy accompanies GCN’s improved feature extraction under Gaussian-noise conditions.
With Gaussian noise and two data-loss modifications, FCNN produces many scattered clusters while GCN largely preserves the data structure.
GCN’s structure-preserving features yield more than 30% performance gain over competing models under combined measurement modifications.

D. Increasing Model’s Robustness by Data Augmentation

Data augmentation exposes the GCN to varied noise and data-loss conditions during training, substantially improving fault-location robustness across severity levels.

Data augmentation adds variable Gaussian noise and data-loss errors to each mini-batch, generating modified training samples across multiple conditions.The procedure samples noise and loss parameters with equal probability, except when all sampled modifications are zero.
One-hop accuracies exceed 95% for cases 1, 2, and 3 after data augmentation.
84% one-hop accuracy is exceeded in case 5 despite SNR 25, five lost buses, and 0.05 probability of individual measurement loss.
The augmented model still makes some assignments to buses more than two hops from the correct faulty bus.The paper lists specific erroneous bus pairs and notes that random noise and data losses make results vary by trial.
Setting K to hurts performance by limiting the measurement-information range available to each graph-convolution node.

E. Performance Under Distribution Network Reconfiguration

The GCN is evaluated on two unseen switch-based network reconfigurations and maintains high fault-location performance without retraining for those scenarios.

88.37% fault-location accuracy and 98.28% one-hop accuracy are obtained for the first unseen reconfiguration scenario.The scenario opens the switch between nodes 18 and 135 and closes the switch between nodes 151 and 300.
91.89% fault-location accuracy and 98.61% one-hop accuracy are obtained for the second unseen reconfiguration scenario.The scenario opens the switch between nodes 97 and 197 and closes the switch between nodes 151 and 300.
Because the reconfiguration scenarios were excluded from training, the results indicate stability against unseen network reconfigurations.

F. Performance Under Multiple Connection Scenarios of Branches

The paper tests phase changes in selected branches and high-impedance faults, finding robust phase-change performance when training covers added scenarios and decreasing exact-location accuracy as fault resistance increases.

Multiple Connection Scenarios of Branches: The phase-change experiments alter one selected branch’s connected phase and add generated samples to the training and test datasets.The examined branches connect buses 36–38–39, 67–71, and 108–114.
Multiple Connection Scenarios of Branches: GCN achieves the highest accuracies across phase-change scenarios, with one-hop accuracies above 99%.Accuracies for modified buses are lower than those for all buses across the evaluated schemes.
Multiple Connection Scenarios of Branches: Additional phase-change data has almost no impact on GCN, while accuracies for other models decrease by 1–5%.The paper concludes that GCN is robust to single-branch phase changes when the training data covers the additional connection scenarios.
High Impedance Faults: High-impedance fault tests add single-phase-to-ground faults with resistance sampled from 100 Ω to 5000 Ω across five test ranges.The study reports zero-hop through three-hop accuracies for these resistance ranges.
High Impedance Faults: Exact fault-location accuracy drops as fault resistance increases, while two-hop and three-hop accuracies rise rapidly with hop count.The higher resistance makes exact fault localization more difficult in the evaluated ranges.

H. Discussion on the Types of Measurements Used for the Model

The study examines which measurements and architectural choices most support GCN fault-location performance, including voltage and current phasors, phase angles, graph-convolution depth, and measured-bus coverage. On the IEEE 37-bus system, voltage phasors are especially important, additional layers improve accuracy with diminishing gains, and sparse measurements preserve vicinity detection better than exact localization.

Measurement scenarios: The model mainly relies on voltage phasors, while current phasors perform much worse and phase angles are important under data-loss errors.The study also suggests that branch-current measurements could improve accuracy.
Hyper-parameters: The GCN model performs stably across different values of Kn and K on the IEEE 37-bus system.
Hyper-parameters: Increasing graph-convolution layers improves fault-location accuracy, but the gain decreases when the third layer is added.
Measured-bus coverage: Reducing measured buses lowers fault-location accuracy, although two-hop accuracy remains relatively insensitive until the final reduction.The original scenario monitors 25 buses, while the final reduction leaves only 4 measured buses.
Measured-bus coverage: 94.12% two-hop accuracy is achieved using measurements from only 9 buses at branch ends.The results indicate that exact fault localization requires more measured buses than locating the faulty bus's vicinity.
Training data: Reducing training data degrades performance, with two-hop accuracy only a little above 50% when each fault type at each bus has one training sample.The authors suggest combining field and synthetic data with transfer learning, but that formulation is beyond the paper's scope.

IV. CONCLUSION AND FUTURE WORK

The paper develops a GCN model for fault location in distribution systems and evaluates it on IEEE 123-bus and 37-bus systems. The model is robust to measurement errors, adapts to topology changes, and performs well with limited measured buses, while realistic field-data use and transfer across topologies remain open directions.

The proposed GCN model targets fault location in distribution systems and processes fault-related data across IEEE 123-bus and 37-bus systems.
The model is more robust to measurement errors than SVM, RF, and FCNN, with activations indicating robustness to missing measurement entries.
Further experiments show that the model can adapt to topology changes and perform well with a limited number of measured buses.
Future work: More realistic settings require further investigation, including fine-tuning synthetic-data-trained models with field data or using both data sources through transfer learning.
Future work: Transferring a learned model to distribution systems with different topologies and handling distributed-generation uncertainties are identified as future challenges.