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Although knowing the feeder topology and line impedances is a prerequisite for solving any grid optimization task, utilities oftentimes have limited or outdated information on their electric network assets. Given the rampant integration of smart inverters, we have previously advocated perturbing their power injections to unveil the underlying grid topology using the induced voltage responses. Under an approximate grid model, the perturbed power injections and the collected voltage deviations obey a linear regression setup, where the unknown is the vector of line resistances. Building on this model, topology processing can be performed in two steps. Given a candidate radial topology, the line resistances can be estimated via a least-squares (LS) fit on the probing data. The topology attaining the best fit can be then selected. To avoid evaluating the exponentially many candidate topologies, this two-step approach is uniquely formulated as a mixed-integer linear program (MILP) using the McCormick relaxation. If the recovered topology is not radial, a second, computationally more demanding MILP confines the search only within radial topologies. Numerical tests explain how topology recovery depends on the noise level and probing duration, and demonstrate that the first simpler MILP yields a tree topology in 90% of the cases tested.
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A complete metric topology on relative low energy spaces
In this paper, we show that the low energy spaces in the prescribed singularity case Eψ (X, θ, φ) have a natural topology which is completely metrizable. This topology is stronger than convergence in capacity.
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- Award ID(s):
- 1846942
- PAR ID:
- 10523912
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Mathematische Zeitschrift
- Volume:
- 303
- Issue:
- 3
- ISSN:
- 0025-5874
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00209-023-03218-5
