Information-Theoretic Grid Topology Reconstruction using Low-Precision Smart Meter Data

Accurate knowledge of power grid topology is a prerequisite for effective state estimation and grid stability. While data-driven methods for topology reconstruction exist, the minimum requirements for measurement quality, specifically regarding quantization, precision, and sampling frequency, remain under-explored. This study investigates the data fidelity required to reconstruct distribution grid topologies using voltage magnitude measurements. Adopting an information-theoretic approach, we utilize the Chow-Liu algorithm to generate maximum spanning trees based on mutual information. Rather than proposing a new reconstruction algorithm, our primary contribution is a comprehensive sensitivity analysis of the measurement data itself. We systematically evaluate the impact of data bit-depth, significant digit truncation, time-window length, and different mutual information estimators on reconstruction accuracy. We validate this approach using IEEE test cases (via MATPOWER) and time-series data from GridLAB-D. Our results demonstrate that grid topology can be successfully recovered even with highly quantized 8-bit data or millivolt-level precision. However, performance degrades significantly when downsampling intervals exceed 20 minutes or when data availability is limited to short durations. These findings establish an optimistic theoretical lower bound, suggesting that costly high-precision instrumentation may not be strictly necessary for structural inference under ideal conditions. This rigorous baseline provides a foundation for future evaluations of noisy real world smart meter data and hybrid approaches that incorporate existing engineering priors.