[Paper Review] Multivariate Physics-Informed Convolutional Autoencoder for Anomaly Detection in Power Distribution Systems with High Penetration of DERs

Mehdi Jabbari Zideh, Sarika Khushalani Solanki|arXiv (Cornell University)|Jun 5, 2024

Machine Fault Diagnosis Techniques4 citations

TL;DR

This paper proposes a multivariate physics-informed convolutional autoencoder (PIConvAE) that integrates Kirchhoff’s circuit laws into the loss function of a convolutional autoencoder to enhance anomaly detection in unbalanced, high-DER penetration power distribution systems. The method achieves state-of-the-art performance, with F-1 scores of 95.12% and 97.09% on the IEEE 123-bus and RCA real-world feeder, respectively, significantly outperforming data-driven baselines under data scarcity.

ABSTRACT

Despite the relentless progress of deep learning models in analyzing the system conditions under cyber-physical events, their abilities are limited in the power system domain due to data availability issues, cost of data acquisition, and lack of interpretation and extrapolation for the data beyond the training windows. In addition, the integration of distributed energy resources (DERs) such as wind and solar generations increases the complexities and nonlinear nature of power systems. Therefore, an interpretable and reliable methodology is of utmost need to increase the confidence of power system operators and their situational awareness for making reliable decisions. This has led to the development of physics-informed neural network (PINN) models as more interpretable, trustworthy, and robust models where the underlying principled laws are integrated into the training process of neural network models to achieve improved performance. This paper proposes a multivariate physics-informed convolutional autoencoder (PIConvAE) model to detect cyber anomalies in power distribution systems with unbalanced configurations and high penetration of DERs. The physical laws are integrated through a customized loss function that embeds the underlying Kirchhoff's circuit laws into the training process of the autoencoder. The performance of the multivariate PIConvAE model is evaluated on two unbalanced power distribution grids, IEEE 123-bus system and a real-world feeder in Riverside, CA. The results show the exceptional performance of the proposed method in detecting various cyber anomalies in both systems. In addition, the model's effectiveness is evaluated in data scarcity scenarios with different training data ratios. Finally, the model's performance is compared with existing machine learning models where the PIConvAE model surpasses other models with considerably higher detection metrics.

Motivation & Objective

• Address the challenge of limited and noisy data in power distribution systems with high penetration of distributed energy resources (DERs).
• Improve the reliability and interpretability of anomaly detection models by embedding physical laws into deep learning architectures.
• Develop a robust, generalizable method that maintains performance under data scarcity, a common issue in real-world power system operations.
• Enhance operator situational awareness by ensuring model predictions remain physically consistent across system transitions.
• Outperform existing data-driven models in detecting cyber anomalies in unbalanced, nonlinear power distribution systems.

Proposed method

• Integrate Kirchhoff’s voltage and current laws into the loss function of a multivariate convolutional autoencoder (ConvAE) to constrain reconstructed outputs to physical consistency.
• Use a rolling window strategy to sub-sample time-series data, preserving temporal patterns for training and testing.
• Formulate a customized physics-informed loss function that penalizes deviations from Kirchhoff’s laws during autoencoder training.
• Train the model in an unsupervised manner on normal operational data to learn a compact latent representation.
• Reconstruct input measurements and compute reconstruction error as the anomaly score, with high error indicating anomalies.
• Apply the model to both simulated (IEEE 123-bus) and real-world (Riverside, CA) unbalanced distribution feeders to validate generalization.

Experimental results

Research questions

• RQ1 Can integrating Kirchhoff’s circuit laws into a convolutional autoencoder improve anomaly detection performance in unbalanced, high-DER distribution systems?
• RQ2 How does the proposed physics-informed model perform under data scarcity, particularly at 10%, 30%, and 50% training data ratios?
• RQ3 Does the inclusion of physical constraints enhance generalization and robustness compared to purely data-driven autoencoders?
• RQ4 How does the PIConvAE model compare to established machine learning models like Random Forest, K-Means, and OCSVM in terms of F-1 score and recall?
• RQ5 Can the model maintain high accuracy and physical consistency when detecting cyber anomalies in real-world distribution feeders?

Key findings

• The PIConvAE model achieved an F-1 score of 95.12% on the IEEE 123-bus system, a significant improvement from the baseline ConvAE’s 84.37%.
• On the real-world RCA feeder, the PIConvAE achieved a 97.09% F-1 score, outperforming Random Forest (92.23%) and K-Means (93.91%).
• The model recorded 99.14% recall on the RCA feeder, the highest among all models tested, indicating strong detection of true anomalies.
• Even at 10% training data ratio, the PIConvAE maintained high performance, demonstrating strong generalization and extrapolation under data scarcity.
• The integration of physics-informed loss increased the F-1 score of the base ConvAE from 37.66% to 94% on the IEEE 123-bus system, proving the effectiveness of physical constraints.
• Confusion matrix analysis confirmed the PIConvAE had the highest true positive count (917) and lowest false negative count (11) on the IEEE 123-bus system.