Unbalanced Multi-Phase Distribution Grid Topology Estimation and Bus Phase Identification

Abstract: There is an increasing need for monitoring and controlling uncertainties brought by distributed energy resources in distribution grids. For such goal, accurate multi-phase topology is the basis for correlating measurements in unbalanced distribution networks. Unfortunately, such topology knowledge is often unavailable due to limited investment, especially for \revv{low-voltage} distribution grids. Also, the bus phase labeling information is inaccurate due to human errors or outdated records. For this challenge, this paper utilizes smart meter data for an information-theoretic approach to learn the topology of distribution grids. Specifically, multi-phase unbalanced systems are converted into symmetrical components, namely positive, negative, and zero sequences. Then, this paper proves that the Chow-Liu algorithm finds the topology by utilizing power flow equations and the conditional independence relationships implied by the radial multi-phase structure of distribution grids with the presence of incorrect bus phase labels. At last, by utilizing Carson's equation, this paper proves that the bus phase connection can be correctly identified using voltage measurements. For validation, IEEE systems are simulated using three real data sets. The simulation results demonstrate that the algorithm is highly accurate for finding multi-phase topology even with strong load unbalancing condition and DERs. This ensures close monitoring and controlling DERs in distribution grids.

• The paper proposes an information-theoretic method leveraging mutual information and the Chow-Liu algorithm for optimal topology estimation and phase identification in unbalanced grids.
• It converts multi-phase voltages into symmetrical components to correct erroneous bus phase labels and manage load unbalance.
• Simulation on IEEE test cases shows high accuracy and robustness without relying on specialized PMUs, supporting practical grid management and renewable integration.

Unbalanced Multi-Phase Distribution Grid Topology Estimation and Bus Phase Identification

Overview

The paper presents a method for accurately estimating the topology of unbalanced multi-phase distribution grids and identifying bus phase connections using smart meter data. This addresses challenges posed by the lack of prior topology knowledge in low-voltage grids and incorrect bus phase labels. The authors propose an information-theoretic approach utilizing the Chow-Liu algorithm and Carson's equation for phase identification.

Modeling and Problem Formulation

Distribution grids are modeled as trees, with nodes representing buses and edges denoting connectivity. The multi-phase voltages at each bus are decomposed into symmetrical components to address load unbalance. The key challenge is accurately estimating topology using voltage measurements without Phase Measurement Units (PMUs) and correcting erroneous phase labels.

Algorithm for Topology Estimation

The algorithm involves computing mutual information between buses and leveraging the radial structure of distribution grids. It uses a Maximum Weight Spanning Tree approach to identify topology and corrects bus phases based on voltage correlations. The Chow-Liu algorithm is employed for robust topology estimation by finding conditional independence relationships in the transformed grid structure.

Unbalanced Grid Handling

For unbalanced grids, the authors convert multi-phase elements into balanced symmetrical components. This enables the use of mutual information-based topology estimation, allowing the algorithm to tolerate incorrect phase labeling by leveraging the label-invariant properties of mutual information calculations.

Numerical Validation

Simulations were conducted using IEEE test cases and various data sets to validate the algorithm's performance. Results indicated high accuracy in topology estimation under varying degrees of load unbalance and incorrect phase labels. The method consistently outperformed existing single-phase and balanced system approaches.

Sensitivity Analysis

The algorithm's sensitivity to data length, noise levels, load patterns, and resolution was analyzed, confirming its robustness and efficiency in real-world applications with available smart meter data. Even with low-phase correlation due to inconsistent phase labels, the method accurately reconstructs network topology.

Conclusion

This paper introduces a reliable method for distribution grid topology estimation and phase identification, utilizing smart meter data without requiring specialized equipment like PMUs. Its robustness against unbalanced loads and incorrect phase labels makes it applicable to practical grid management and renewable integration scenarios.

Key insights include the use of sequence components for made a balanced system analysis possible and the innovative mutual information-based approach, confirming its utility in modern energy networks with high DER penetration.