Structure- and Physics-Preserving Reductions of Power Grid Models
Abstract
The large size of multiscale, distribution and transmission, power grids hinders fast systemwide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable for fast simulations and follow-up applications. While the classical Kron reduction has been successful in reduced order modeling of power grids with traditional, hierarchical design, the selection of reference nodes for the reduced model in a multiscale, distribution and transmission, network becomes ambiguous. In this work we extend the use of the iterative Kron reduction by utilizing the electric grid's graph topology for the selection of reference nodes, consistent with the design features of multiscale networks. Additionally, we propose further reductions by aggregation of coherent subnetworks of triangular meshes, based on the graph topology and network characteristics, in order to preserve currents and build another power-flow equivalent network. Our reductions are achieved through the use of iterative aggregation of subgraphs that include general tree structures, lines, and triangles. Important features of our reduction algorithms include that (i) the reductions are either equivalent to the Kron reduction or otherwise produce a power-flow equivalent network; (ii) due to the mentioned power-flow equivalence, the reduced network can model the dynamicmore »
- Authors:
-
- Nansen Environmental and Remote Sensing Center, Bergen (Norway)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Nansen Environmental and Remote Sensing Center, Bergen (Norway)
- Sponsoring Org.:
- USDOE Office of Electricity (OE); Norwegian Research Council
- OSTI Identifier:
- 1514951
- Report Number(s):
- LA-UR-17-25447
Journal ID: ISSN 1540-3459
- Grant/Contract Number:
- 89233218CNA000001; 250711
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Multiscale Modeling & Simulation
- Additional Journal Information:
- Journal Volume: 16; Journal Issue: 4; Journal ID: ISSN 1540-3459
- Publisher:
- SIAM
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; power grids; networks; graph reduction; visualization
Citation Formats
Grudzien, Colin, Deka, Deepjyoti, Chertkov, Michael, and Backhaus, Scott N. Structure- and Physics-Preserving Reductions of Power Grid Models. United States: N. p., 2018.
Web. doi:10.1137/17M1138054.
Grudzien, Colin, Deka, Deepjyoti, Chertkov, Michael, & Backhaus, Scott N. Structure- and Physics-Preserving Reductions of Power Grid Models. United States. https://doi.org/10.1137/17M1138054
Grudzien, Colin, Deka, Deepjyoti, Chertkov, Michael, and Backhaus, Scott N. Thu .
"Structure- and Physics-Preserving Reductions of Power Grid Models". United States. https://doi.org/10.1137/17M1138054. https://www.osti.gov/servlets/purl/1514951.
@article{osti_1514951,
title = {Structure- and Physics-Preserving Reductions of Power Grid Models},
author = {Grudzien, Colin and Deka, Deepjyoti and Chertkov, Michael and Backhaus, Scott N.},
abstractNote = {The large size of multiscale, distribution and transmission, power grids hinders fast systemwide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable for fast simulations and follow-up applications. While the classical Kron reduction has been successful in reduced order modeling of power grids with traditional, hierarchical design, the selection of reference nodes for the reduced model in a multiscale, distribution and transmission, network becomes ambiguous. In this work we extend the use of the iterative Kron reduction by utilizing the electric grid's graph topology for the selection of reference nodes, consistent with the design features of multiscale networks. Additionally, we propose further reductions by aggregation of coherent subnetworks of triangular meshes, based on the graph topology and network characteristics, in order to preserve currents and build another power-flow equivalent network. Our reductions are achieved through the use of iterative aggregation of subgraphs that include general tree structures, lines, and triangles. Important features of our reduction algorithms include that (i) the reductions are either equivalent to the Kron reduction or otherwise produce a power-flow equivalent network; (ii) due to the mentioned power-flow equivalence, the reduced network can model the dynamic of the swing equations for a lossless, inductive, steady state network; (iii) the algorithms efficiently utilize hash tables to store the sequential reduction steps. The third feature allows for easy reintroduction of detailed models into the reduced, conceptual network and makes the final reduced order model backward compatible with a sequence of intermediate, partially reduced networks with varying resolution---the ordered sequence of iterative reductions corresponds to a sequence of reduced order models. The performance of our graph reduction algorithms and features of the reduced grids are discussed on a real-word transmission and distribution grid. We produce visualizations of the reduced models through open source libraries and release our reduction algorithms with example code and toy data.},
doi = {10.1137/17M1138054},
journal = {Multiscale Modeling & Simulation},
number = 4,
volume = 16,
place = {United States},
year = {Thu Nov 29 00:00:00 EST 2018},
month = {Thu Nov 29 00:00:00 EST 2018}
}
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Figures / Tables:
Fig. 1: The Kron reduction of nodes {b1, b2, b3} on the left-hand side produces the complete graph on the right-hand side.
Figures / Tables found in this record: