Multiresolution Graph Fusion Based Time Series Clustering for Phase Identification in Electric Distribution Systems

Graph-based methodologies have emerged as a powerful paradigm for analyzing time-series data and revealing the latent structure of complex networks. In electric distribution systems, phase identification - determining the electrical phase to which each consumer is connected - remains a critical operational task, where graph-based clustering of smart meter voltage measurements offers a practical, scalable, and non-intrusive alternative to conventional field-based approaches. Existing techniques for constructing graphs from time-series data predominantly rely on temporal variation while placing comparatively limited emphasis on signal volatility. However, time-series measurements obtained from smart meters in power distribution networks are often highly volatile, with sudden transients and small temporal misalignments that can adversely affect clustering performance. To address this challenge, this paper proposes a multiresolution time-series graph construction and fusion framework based on Discrete Wavelet Transform (DWT) decomposition, enabling the modeling of both slow-varying trends and high-frequency fluctuations. Graphs inferred at multiple frequency bands are fused through a consensus mechanism based on total variation normalization, with individual bands adaptively weighted using graph partitioning quality metrics such as modularity. Experimental results indicate that the proposed multiresolution timeseries graph fusion approach provides a meaningful contribution toward improving phase identification in electric distribution networks.