Real-time Faulted Line Localization and PMU Placement in Power Systems through Convolutional Neural Networks

Wenting Li; Deepjyoti Deka; Michael Chertkov; Meng Wang

Source-linked AI summary

Real-time Faulted Line Localization and PMU Placement in Power Systems through Convolutional Neural Networks

Wenting Li, Deepjyoti Deka, Michael Chertkov, Meng Wang

arXiv:1810.05247v2Oct 11, 2018eess.SYcs.LGstat.ML

TL;DR

Real-time fault localization is challenged by diverse transients, restrictive assumptions, and limited measurement availability. The paper uses physically interpretable voltage-based features with a CNN classifier and joint PMU placement, achieving strong localization performance under partial observability and varied measurement conditions.

Problem
Real-time faulted-line localization remains challenging because existing methods may assume static loads, require high sampling rates, or depend on extensive measurements.
Method
The paper extracts physically interpretable features, classifies faulted lines with a CNN, and optimizes PMU placement using the localization loss.
Results
The CNN localizes most faults with more than 90% accuracy under partial observability, exceeds 95% accuracy with 30% measured buses, and the placement method improves average performance by about 10% over Random.
Takeaways & Limitations
The method retains useful fault-location information under low observability, including high probability for the correct line or nearby lines when exact prediction is difficult.

Abstract

from arXiv · show

Diverse fault types, fast re-closures, and complicated transient states after a fault event make real-time fault location in power grids challenging. Existing localization techniques in this area rely on simplistic assumptions, such as static loads, or require much higher sampling rates or total measurement availability. This paper proposes a faulted line localization method based on a Convolutional Neural Network (CNN) classifier using bus voltages. Unlike prior data-driven methods, the proposed classifier is based on features with physical interpretations that improve the robustness of the location performance. The accuracy of our CNN based localization tool is demonstrably superior to other machine learning classifiers in the literature. To further improve the location performance, a joint phasor measurement units (PMU) placement strategy is proposed and validated against other methods. A significant aspect of our methodology is that under very low observability (7% of buses), the algorithm is still able to localize the faulted line to a small neighborhood with high probability. The performance of our scheme is validated through simulations of faults of various types in the IEEE 39-bus and 68-bus power systems under varying uncertain conditions, system observability, and measurement quality.

I. INTRODUCTION

Real-time faulted-line localization is difficult because conventional methods rely on restrictive assumptions, high-resolution measurements, or broad observability. The paper proposes physically interpretable features, CNN classification, and joint PMU placement for localization under limited measurements.

Conventional impedance-based methods assume static loads and are sensitive to line-parameter values.
Wide-area fault localization is challenging because many candidate lines must be distinguished from limited measurements.
High-resolution approaches require more than 2000 Hz or 1 MHz sampling and have limited analysis of load fluctuations and inaccurate voltage measurements.
The proposed method defines physically interpretable features, uses a four-layer CNN classifier, and targets faulted-line or faulted-area localization under limited measurement availability.
A joint PMU placement algorithm is proposed to improve localization performance after CNN-based classification.

A. Substitution Theory and Features for Full Observability

The method derives a physically informed feature vector from pre-fault and during-fault network quantities using substitution theory. Its dominant sparse component identifies the terminal buses of the faulted line, while imaginary feature components are used for classification.

The analysis models a single fault in an n-bus system using positive-sequence data when three-phase measurements are unavailable.
For a fault between buses i and j, the during-fault admittance matrix augments the network with fault point F.
Un-transposed lines with different mutual impedances between buses are beyond the analysis.
The unbalanced current ∆Iu is 2-sparse, with nonzero entries corresponding exactly to the terminal buses of the faulted line.
The feature vector ψ is defined from bus-voltage variations and the pre-fault admittance matrix.
The imaginary part of ψ is selected as classifier input because experiments found it more effective than the real part.

B. Physical Interpretation of the Features

The feature vector combines a sparse fault-terminal signal with neighborhood information from voltage and current variations. This structure gives its entries a direct physical interpretation related to fault location and nearby buses.

The dominant component ∆Iu has nonzero values at the two terminal buses of the faulted line.
The feature vector ψ is sparse, and its entry distribution indicates the location of the faulted line.
For a faulted line between buses i and j, entries at other buses reflect current variations in their neighborhoods.
The minor components in ∆I therefore provide indicators of the neighborhood around the faulted line.

2) Feature Extraction under Partial Observability:

Under partial observability, the method constructs features from measured-bus voltage variations and applies a CNN to classify fault locations. The resulting feature values retain fault-terminal and neighboring-bus information despite incomplete measurements.

When only a subset S of buses is measured, the partial-observability feature vector is constructed from their pre-fault and during-fault voltage variations.
Each partial-observability feature entry aggregates admittance-weighted voltage variations or equivalent line-current variations involving measured neighboring buses.
3) Numerical Example:: In a simulated IEEE 68-bus fault on line 5-6, the feature values ψ5 and ψ6 are relatively large, while other buses can also become nonzero as their voltages change.
2) Feature Extraction under Partial Observability:: The partial feature vector is used instead of partial unbalanced-current measurements because the latter would require measurements from all buses.
A. Architecture Design: The classifier uses imaginary feature components as input and processes them through convolution, ReLU, pooling, and fully connected operations.
A. Architecture Design: The CNN outputs probabilities for the possible lines, with the highest-probability line determining the predicted fault location.

B. Training Process

The CNN is trained by minimizing a regularized cross-entropy loss that estimates fault-location probabilities from measured-bus features. Stochastic optimization and overfitting controls support classifier training.

Training objective: The CNN minimizes cross-entropy loss with an L2 regularization term to estimate the probability that each candidate line is faulted.The measured-bus set is fixed after PMU placement, and the regularization coefficient controls the penalty.
Training objective: The loss labels each training sample by its faulted-line class, while the CNN output gives the corresponding probability for every possible fault location.The target indicator is one for the sample’s class and zero otherwise.
Optimization: Stochastic gradient descent, Adam, and RMSprop are identified as optimization methods capable of achieving high classification accuracy.The paper notes that rigorous convergence proofs for these gradient-based methods are lacking.
Optimization: Early stopping limits overfitting, while batch normalization addresses covariance shift during training.These techniques are presented as ways to reduce initialization effects and improve classification accuracy.

C. Motivations of Applying CNN Classifier

CNN is selected because its sparse connectivity and local-feature extraction suit the sparse, neighborhood-structured feature vector. PMU placement is jointly optimized to reduce CNN localization loss under a fixed measurement budget.

Motivations of Applying CNN Classifier: CNN sparse connectivity is better suited than fully connected operations to the sparse feature vector used for fault localization.The paper also motivates CNN through its ability to reveal local rather than global features.
Motivations of Applying CNN Classifier: The CNN’s small kernels learn local features that match the neighborhood property of the feature vector.This provides the stated architectural motivation for using convolutional layers.
PMU placement: With limited PMUs, placement is optimized for fault-localization quality rather than guaranteed full-system observability.The proposed objective reduces the CNN loss under the constraint |S| = K.
PMU placement: The placement method is data-driven and jointly aware of fault localization and CNN learning through optimization of the CNN loss.The regularization term also constrains the learned parameter norm.
PMU placement: The placement problem is NP-complete, motivating the proposed greedy approximation instead of exhaustive optimization.The algorithm increases the measured-bus set one bus at a time from an initial set S0.
PMU placement: The placement algorithm greedily adds buses until K measured buses are selected, balancing CNN loss with bus degree through β/d_i.At each step, candidate placements are evaluated using the minimized loss for the enlarged measured-bus set.

V. NUMERICAL RESULTS

Numerical evaluation uses multiple fault types and uncertain load conditions in IEEE 39-bus and 68-bus systems, with CNN performance examined under partial measurements. The 39-bus classifier uses a four-convolutional-layer architecture and evaluates location accuracy across fault categories.

Test conditions: Four fault types—three-phase short circuit, line-to-ground, double-line-to-ground, and line-to-line—are simulated under uncertain load conditions.Loads are drawn from a Gaussian distribution, and fault impedance varies from 0.0001 to 0.1.
Test systems: The proposed approach is validated on IEEE 39-bus and IEEE 68-bus power systems using CNN classifiers for each system.The evaluation examines partial measurements between 15% and 30% of buses, with measured buses selected by the proposed PMU placement algorithm.
39-bus classifier: The 39-bus CNN contains four convolutional layers, one fully connected layer, and one output layer.The architecture uses convolutional kernels and stride size 1, as summarized in Table I.
39-bus classifier: The 39-bus classifier has 47 output classes: 46 faulted-line locations and one null-outage line.This class structure defines the location categories evaluated by the classifier.
Training setup: Training uses regularization coefficient λ = 0.001, learning rate 0.001, early stopping, and RMSprop with decay coefficient α = 0.9.The reported early-stopping settings are p = 1000 and p* = 4.
Accuracy evaluation: Table II reports the CNN location accuracy rate η (%) for four fault types in the 39-bus system under partial measurements.The table is the designated accuracy evaluation for the four fault categories.

2) Performance of the CNN under Partial Observability:

Under partial observability, the CNN maintains high location accuracy in the 39-bus system while identifying likely neighboring lines in misclassified cases.

15%–30% of buses are covered by PMUs in the partial-observability scenarios.
The 39-bus CNN’s location accuracy rates are mostly above 90% and below 100%, with fault-type variations under 5% as measured-bus coverage changes.
Misclassified faults: At 15% measured-bus coverage, 89.5% of highest-probability lines are exactly faulted lines and 100% lie within one hop of them.
68-bus configuration: The 68-bus CNN uses four convolutional layers, one fully connected layer, and one output layer, with 87 line classes.
68-bus configuration: For the 68-bus system, training uses 1642 datasets and testing uses about 1210 datasets generated under varied initial conditions.

2) Performance of the CNN under Partial Observability:

Across the 68-bus partial-observability tests, CNN localization remains accurate and outperforms MSVM and fully connected neural networks, especially with 15%–30% bus measurements.

Most 68-bus faults are localized with more than 90% accuracy, while measured-bus ratios change location accuracy rates by less than 10%.
Classifier comparison: Figure 4 compares location accuracy rates for neural networks with different layer depths across measured-bus percentages.
Classifier comparison: Figure 5 compares CNN, MSVM, and NN location accuracy rates across four fault types and measured-bus percentages.
Classifier comparison: Neural networks with equal or greater hidden-unit counts achieve similar average performance, but remain below CNN performance.
Classifier comparison: At 30% measured-bus coverage, CNN reaches more than 95% fault-localization accuracy for all four fault types.
Classifier comparison: With 15%–30% of buses observed, CNN fault localization is much better than MSVM and two-layer NN across the four fault types.

D. The ARC of CNN under ≤15% of nodal observability

When observability falls to 7%–15%, CNN still ranks the correct faulted line among a few high-probability candidates and often places it in a small neighborhood.

The ARC measures how many high-probability lines must be considered on average to identify the correct faulted line, with exact localization equal to 1.
The average rank of the correct line is less than 3 for all four fault types with only 7%–15% of buses measured.
Neighborhood property: Under low PMU coverage, the highest-probability lines can localize the fault to a small graphical neighborhood of its true location.
Neighborhood property: In the illustrated three-phase fault, the top-five CNN probability lines are marked red and lie in the neighborhood of the faulted line.
Practical implication: Low ARC and neighborhood localization are identified as useful for initial recovery or maintenance crew dispatch.

F. Comparison with other PMU placement algorithms

The proposed PMU placement algorithm outperforms Random and 2-hop Vertex Cover placement in average fault-location accuracy, while the CNN remains robust across load uncertainty and measurement noise.

About 10% average improvement over other methods is achieved by the proposed PMU placement algorithm across fault types.The comparison uses 12 measured buses in the 68-bus system.
8% average improvement over Random placement is achieved by the 2-hop Vertex Cover method, but it still trails the proposed algorithm.
LARs remain above 90% when the uncertainty index ζ is less than 0.4.The testing uncertainty index ranges from 0.13 to 0.51, and performance declines as ζ increases.
When SNR exceeds 60 dB, all fault types achieve LARs of 90% or higher.Increasing the measured-bus fraction from 20% to 30% further strengthens robustness to noise.

I. The Impacts of Voltage Quality

The method is evaluated under synchronization delays, varying fault-clearing times, and phase-angle jumps. It remains robust under the tested transmission-system conditions, while broader distribution-system and real-data validation remains future work.

1) The Impacts of inaccuracy of synchronization: When delay is around 20 ms, location performance is almost unaffected, with νd below 1%.For mean delays of 30–40 ms, νd remains within 5% under 30% bus measurement.
2) The Impacts of fault clearing time: Fault-clearing-time variation from 0.05 s to 0.2 s produces νf below 2% across fault types.Training uses a fault-clearing time of 0.2 seconds and testing varies this value.
Voltage-quality effects: The method is robust to phase-angle jumps around 10°–20° in the tested transmission system.Application to distribution systems with jumps up to 60° is identified as future research.
Conclusion: The paper reports robust fault-line localization using physically interpretable feature vectors and CNN classification under varied conditions.The authors identify extension to distribution systems and validation on real data as future work.