Unsupervised Impedance and Topology Estimation of Distribution Networks-Limitations and Tools

Distribution network models are often inaccurate or nonexistent. This work considers the problem of estimating the impedance and topology of distribution networks from noisy synchronized phasor measurements of nodal voltages and current injections, without any prior network information. We prove fundamental limits for unsupervised estimation of electrical networks, establishing effective impedance between active nodes as the core, generally-attainable network information. We propose a noise-robust technique for estimating effective impedances via the reduced Laplacian form of the Kron reduced admittance matrix, termed the "subKron" form. We present the Complex Recursive Grouping algorithm to reconstruct radial networks from effective impedances. Simulation results on noisy data demonstrate the efficacy of the proposed methods for small networks, and the challenges of applying them to large networks. Evaluations of estimation and reconstruction accuracy with decreasing signal to noise ratio highlight fundamental tradeoffs in unsupervised network estimation performance from noisy measurements.