PaToPa: A Data-Driven Parameter and Topology Joint Estimation Framework in Distribution Grids

Abstract

Abstract-The increasing integration of distributed energy resources (DERs) calls for new planning and operational tools. However, such tools depend on system topology and line parameters, which may be missing or inaccurate in distribution grids. With abundant data, one idea is to use linear regression to find line parameters, based on which topology can be identified. Unfortunately, the linear regression method is accurate only if there is no noise in both the input measurements (e.g., voltage magnitude and phase angle) and output measurements (e.g., active and reactive power). For topology estimation, even with a small error in measurements, the regression-based method is incapable of finding the topology using non-zero line parameters with a proper metric. To model input and output measurement errors simultaneously, we propose the error-in-variables (EIV) model in a maximum likelihood estimation (MLE) framework for joint line parameter and topology estimation. While directly solving the problem is NP-hard, we successfully adapt the problem into a generalized low-rank approximation problem via variable transformation and noise decorrelation. For accurate topology estimation, we let it interact with parameter estimation in a fashion that is similar to expectation-maximization fashion in machine learning. The proposed PaToPa approach does not require a radial network setting and works for mesh networks. We demonstrate the superior performance in accuracy for our method on IEEE test cases with actual feeder data from South California Edison.

On Identification of Distribution Grids

“…The closest lines of work to ours are [17], [18] which jointly address topology detection and model parameter estimation problems. In [17], these problems are merely studied in a radial network setting and the results are not extended to poly-phase and mesh systems.…”

A Survey on State Estimation Techniques and Challenges in Smart Distribution Systems

“…In [67], graph-theoretic interpretation of principal component analysis and energy conservation are employed in the context of graph theory to obtain radial distribution system topology through smart meter energy usage data. A more general approach (applicable to meshed networks even with missing PMU phase measurements) for estimating both the topology of the network and the line parameters is proposed in [68], where the line parameters and system topology are updated consecutively through an EM-based approach. Starting with an initial topology guess, at each step of the algorithm, the topology is updated by removing edges with small estimated susceptance values to improve the estimation likelihood.…”

Learning Graphs From Linear Measurements: Fundamental Trade-Offs and Applications

“…Graph learning has been widely used electric grids applications, such as state estimation [11,12] and topology identification [38,16]. Most of the literature focuses on topology identification or change detection, but there is not much recent work on joint topology and parameter recovery, with notable exceptions of [28,46,34]. Moreover, there is little exploration on the fundamental performance limits (estimation error and sample complexity) on topology and parameter identification of power networks, with the exception of [48] where a sparsity condition is provided for exact recovery of outage lines.…”