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Underdetermined Library-aided Impedance Estimation with Terminal Smart Meter Data

Federico Rosato, Lorenzo Nespoli, Vasco Medici

Abstract

Smart meters provide relevant information for impedance identification, but they lack global phase alignment and internal network nodes are often unobserved. A few methods for this setting were developed, but they have requirements on data correlation and/or network topology. In this paper, we offer a unifying view of data- and structure-driven identifiability issues, and use this groundwork to propose a method for underdetermined impedance identification. The method can handle intrinsically ambiguous topologies and data; its output is not forcedly a single estimate, but instead a collection of data-compatible impedance assignments. It uses a library of plausible commercial cable types as a prior to refine the solutions, and we show how it can support topology identification workflows built around known georeferenced joints without degree guarantees. The method depends on a small number of non-sensitive parameters and achieves high identification performance on a sizeable benchmark case even with low-size injection/voltage datasets. We identify key steps that can be accelerated via GPU-based parallelization. Finally, we assess the tolerance of the identification to noisy input.

Underdetermined Library-aided Impedance Estimation with Terminal Smart Meter Data

Abstract

Smart meters provide relevant information for impedance identification, but they lack global phase alignment and internal network nodes are often unobserved. A few methods for this setting were developed, but they have requirements on data correlation and/or network topology. In this paper, we offer a unifying view of data- and structure-driven identifiability issues, and use this groundwork to propose a method for underdetermined impedance identification. The method can handle intrinsically ambiguous topologies and data; its output is not forcedly a single estimate, but instead a collection of data-compatible impedance assignments. It uses a library of plausible commercial cable types as a prior to refine the solutions, and we show how it can support topology identification workflows built around known georeferenced joints without degree guarantees. The method depends on a small number of non-sensitive parameters and achieves high identification performance on a sizeable benchmark case even with low-size injection/voltage datasets. We identify key steps that can be accelerated via GPU-based parallelization. Finally, we assess the tolerance of the identification to noisy input.
Paper Structure (20 sections, 21 equations, 9 figures, 4 tables)

This paper contains 20 sections, 21 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Structure of the paper
  3. Problem setup
  4. Wire library
  5. Derivation of feasible impedance polyhedron
  6. The geometry of as identifiability
  7. Rank deficiency due to data
  8. Rank deficiency due to topology
  9. Noise
  10. Directional sampling
  11. Bounded polytope
  12. Sampling
  13. Refinement
  14. Optional thinning
  15. GPU parallelization
  16. ...and 5 more sections

Figures (9)

  • Figure 1: Block scheme overview of the method.
  • Figure 2: Libraries derived from the Pandapower standard line types. The graph is in log scale on both axes.
  • Figure 3: Library of the IEEE LV test network, with bounds from (\ref{['eq:msharp']}). See Table \ref{['tab:workingparams']}. The graph is in log scale on both axes.
  • Figure 4: Identification results
  • Figure 5: Violin plot of the MAPE values mapped to the degree-simplified network setup.
  • ...and 4 more figures