Graphical Models in Meshed Distribution Grids: Topology Estimation, Change Detection & Limitations

Graphical models is a succinct way to represent the structure of a probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of graphical models, algorithms exactly determining topology and...

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Bibliographic Details
Published in:IEEE transactions on smart grid 2020-09, Vol.11 (5), p.4299-4310
Main Authors: Deka, Deepjyoti, Talukdar, Saurav, Chertkov, Michael, Salapaka, Murti V.
Format: Article
Language:English
Subjects:
Algorithms
Change detection
Change detection algorithms
Concentration matrix
conditional independence
distribution grids
Electric power distribution
Estimation
graphical lasso
Graphical models
line outage
Mathematical model
measurement noise
Noise measurement
Power flow
power flows
Topology
Voltage measurement
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Summary:Graphical models is a succinct way to represent the structure of a probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of graphical models, algorithms exactly determining topology and detecting line changes for distribution grids are presented along with their theoretical limitations. We show that if distribution grids have cycles/loops of size greater than three, then nodal voltages are sufficient for efficient topology estimation without additional assumptions on system parameters. In contrast, line failure or change detection using nodal voltages does not require any structural assumption. Under noisy measurements, we provide the first non-trivial bounds on the maximum noise that the system can tolerate for asymptotically correct topology recovery. The performance of the designed algorithms is validated with non-linear AC power flow samples generated by Matpower on test grids, including scenarios with injection correlations and system noise.
ISSN:1949-3053
1949-3061
DOI:10.1109/TSG.2020.2978541