Distribution grid impedance & topology estimation with limited or no micro-PMUs

With more distributed energy resources (DERs) connected to distribution grids, better monitoring and control are needed, where accurate system topology and branch impedance are the prerequisites. However, this information is usually unknown or inaccurate due to limited observability in distribution grids. Therefore, the topology and branch impedance estimation methods are necessary for distribution grid operations. Among existed works, the regression-based methods have been frequently discussed, which leverages the estimated impedance matrix and graph theory to recover the radial topology. However, most of them assume that micro Phasor Measurement Units (micro-PMUs) have been placed at all load-nodes, which is unrealistic due to the sensor cost. In this paper, we target real cases where only nodes with high-variability loads have sensors, either micro-PMUs or smart meters. Firstly, we convert the micro-PMU-based or the smart meter-based impedance estimation to an Ordinary Least Square (OLS) estimation, where only measurements of observed nodes can be utilized for the estimation while hidden quantities cause errors. To quantify the error, we propose a Factorized Ordinary Least Squares (FOLS) method to decompose the error of OLS with the whitening matrix. Under Cholesky whitening, we theoretically provide the upper error bound and claim the error is negligible with our metering assumption. Finally, we introduce the Recursive Grouping algorithm to estimate the branch impedance & topology with hidden nodes. The numerical results demonstrate that the proposed algorithm achieves accurate results on real-world load data and IEEE standard test systems.