A generative graph model for electrical infrastructure networks
Abstract
We propose a generative graph model for electrical infrastructure networks that accounts for heterogeneity in both node and edge type. To inform the design of this model, we analyze the properties of power grid graphs derived from the U.S. Eastern Interconnection, Texas Interconnection, and Poland transmission system power grids. Across these datasets, we find subgraphs induced by nodes of the same voltage level exhibit shared structural properties atypical to smallworld networks, including low local clustering, large diameter and large average distance. On the other hand, we find subgraphs induced by transformer edges linking nodes of different voltage types contain a more limited structure, consisting mainly of small, disjoint star graphs. The goal of our proposed model is to match both these inter and intranetwork properties by proceeding in two phases: we first generate subgraphs for each voltage level and then generate transformer edges that connect these subgraphs. The first phase of the model adapts the ChungLu random graph model, taking desired vertex degrees and desired diameter as inputs, while the second phase of the model is based on a simpler random star graph generation process. We test the performance of our model by comparing its output across many runs tomore »
 Authors:

 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Oregon State Univ., Corvallis, OR (United States)
 Publication Date:
 Research Org.:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1508032
 Report Number(s):
 PNNLSA130657
Journal ID: ISSN 20511310
 Grant/Contract Number:
 AC0576RL01830
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Complex Networks
 Additional Journal Information:
 Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 20511310
 Publisher:
 Oxford University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 24 POWER TRANSMISSION AND DISTRIBUTION; power grid graph model; ChungLu model; networkofnetworks
Citation Formats
Aksoy, Sinan G., Purvine, Emilie AH, Cotilla Sanchez, Eduardo, and Halappanavar, Mahantesh. A generative graph model for electrical infrastructure networks. United States: N. p., 2018.
Web. doi:10.1093/comnet/cny016.
Aksoy, Sinan G., Purvine, Emilie AH, Cotilla Sanchez, Eduardo, & Halappanavar, Mahantesh. A generative graph model for electrical infrastructure networks. United States. doi:10.1093/comnet/cny016.
Aksoy, Sinan G., Purvine, Emilie AH, Cotilla Sanchez, Eduardo, and Halappanavar, Mahantesh. Mon .
"A generative graph model for electrical infrastructure networks". United States. doi:10.1093/comnet/cny016. https://www.osti.gov/servlets/purl/1508032.
@article{osti_1508032,
title = {A generative graph model for electrical infrastructure networks},
author = {Aksoy, Sinan G. and Purvine, Emilie AH and Cotilla Sanchez, Eduardo and Halappanavar, Mahantesh},
abstractNote = {We propose a generative graph model for electrical infrastructure networks that accounts for heterogeneity in both node and edge type. To inform the design of this model, we analyze the properties of power grid graphs derived from the U.S. Eastern Interconnection, Texas Interconnection, and Poland transmission system power grids. Across these datasets, we find subgraphs induced by nodes of the same voltage level exhibit shared structural properties atypical to smallworld networks, including low local clustering, large diameter and large average distance. On the other hand, we find subgraphs induced by transformer edges linking nodes of different voltage types contain a more limited structure, consisting mainly of small, disjoint star graphs. The goal of our proposed model is to match both these inter and intranetwork properties by proceeding in two phases: we first generate subgraphs for each voltage level and then generate transformer edges that connect these subgraphs. The first phase of the model adapts the ChungLu random graph model, taking desired vertex degrees and desired diameter as inputs, while the second phase of the model is based on a simpler random star graph generation process. We test the performance of our model by comparing its output across many runs to the aforementioned real data. In nearly all categories tested, we find our model is more accurate in reproducing the unusual mixture of properties apparent in the data than the ChungLu model. We also include graph visualization comparisons, as well as a brief analysis of edgedeletion resiliency. Ultimately, our model may be used to generate synthetic graph data, test hypotheses and algorithms at different scales, and serve as a baseline model on top of which further electrical network properties, device models, and interdependencies to other networks, may be appended.},
doi = {10.1093/comnet/cny016},
journal = {Journal of Complex Networks},
issn = {20511310},
number = 1,
volume = 7,
place = {United States},
year = {2018},
month = {8}
}
Works referenced in this record:
The Power Grid as a complex network: A survey
journal, June 2013
 Pagani, Giuliano Andrea; Aiello, Marco
 Physica A: Statistical Mechanics and its Applications, Vol. 392, Issue 11
Graphtheoretic algorithms for PMU placement in power systems under measurement observability constraints
conference, November 2012
 Anderson, Joel E.; Chakrabortty, Aranya
 2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm)
Assortative Mixing in Networks
journal, October 2002
 Newman, M. E. J.
 Physical Review Letters, Vol. 89, Issue 20
The Structure and Function of Complex Networks
journal, January 2003
 Newman, M. E. J.
 SIAM Review, Vol. 45, Issue 2
Grid Structural Characteristics as Validation Criteria for Synthetic Networks
journal, July 2017
 Birchfield, Adam B.; Xu, Ti; Gegner, Kathleen M.
 IEEE Transactions on Power Systems, Vol. 32, Issue 4
PowerLaw Distributions in Empirical Data
journal, November 2009
 Clauset, Aaron; Shalizi, Cosma Rohilla; Newman, M. E. J.
 SIAM Review, Vol. 51, Issue 4
Local clustering in scalefree networks with hidden variables
journal, February 2017
 van der Hofstad, Remco; Janssen, A. J. E. M.; van Leeuwaarden, Johan S. H.
 Physical Review E, Vol. 95, Issue 2
Catching the Head, Tail, and Everything in Between: A Streaming Algorithm for the Degree Distribution
conference, November 2015
 Simpson, Olivia; Seshadhri, C.; McGregor, Andrew
 2015 IEEE International Conference on Data Mining (ICDM)
ScaleFree Networks
journal, May 2003
 Barabási, AlbertLászló; Bonabeau, Eric
 Scientific American, Vol. 288, Issue 5
Collective dynamics of ‘smallworld’ networks
journal, June 1998
 Watts, Duncan J.; Strogatz, Steven H.
 Nature, Vol. 393, Issue 6684
Diameters in Preferential Attachment Models
journal, January 2010
 Dommers, Sander; van der Hofstad, Remco; Hooghiemstra, Gerard
 Journal of Statistical Physics, Vol. 139, Issue 1
Structural vulnerability of the North American power grid
journal, February 2004
 Albert, Réka; Albert, István; Nakarado, Gary L.
 Physical Review E, Vol. 69, Issue 2
Controlled islanding using transmission switching and load shedding for enhancing power grid resilience
journal, October 2017
 Amraee, Turaj; Saberi, Hossein
 International Journal of Electrical Power & Energy Systems, Vol. 91
Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid
journal, January 2010
 Pinar, Ali; Meza, Juan; Donde, Vaibhav
 SIAM Journal on Optimization, Vol. 20, Issue 4
A MetricBased Validation Process to Assess the Realism of Synthetic Power Grids
journal, August 2017
 Birchfield, Adam; Schweitzer, Eran; Athari, Mir
 Energies, Vol. 10, Issue 8
A complex network approach for identifying vulnerabilities of the medium and low voltage grid
journal, January 2015
 Pagani, Giuliano Andrea; Aiello, Marco
 International Journal of Critical Infrastructures, Vol. 11, Issue 1
Spectral analysis of a real power network
journal, January 2012
 Fioriti, Vincenzo; Sforna, Marino; D', Gregorio
 International Journal of Critical Infrastructures, Vol. 8, Issue 4
Note on the heights of random recursive trees and random mary search trees
journal, April 1994
 Pittel, Boris
 Random Structures & Algorithms, Vol. 5, Issue 2
A Scalable Generative Graph Model with Community Structure
journal, January 2014
 Kolda, Tamara G.; Pinar, Ali; Plantenga, Todd
 SIAM Journal on Scientific Computing, Vol. 36, Issue 5
Stochastic kronecker graphs
journal, July 2010
 Mahdian, Mohammad; Xu, Ying
 Random Structures & Algorithms, Vol. 38, Issue 4
Do topological models provide good information about electricity infrastructure vulnerability?
journal, September 2010
 Hines, Paul; CotillaSanchez, Eduardo; Blumsack, Seth
 Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 20, Issue 3
Admissible Locational Marginal Prices via Laplacian Structure in Network Constraints
journal, February 2009
 CheverezGonzalez, D.; DeMarco, C. L.
 IEEE Transactions on Power Systems, Vol. 24, Issue 1
Measuring and modeling bipartite graphs with community structure
journal, March 2017
 Aksoy, Sinan G.; Kolda, Tamara G.; Pinar, Ali
 Journal of Complex Networks, Vol. 5, Issue 4
Bipartite graphs as models of complex networks
journal, November 2006
 Guillaume, JeanLoup; Latapy, Matthieu
 Physica A: Statistical Mechanics and its Applications, Vol. 371, Issue 2
Islanding the power grid on the transmission level: less connections for more security
journal, October 2016
 Mureddu, Mario; Caldarelli, Guido; Damiano, Alfonso
 Scientific Reports, Vol. 6, Issue 1
The average distances in random graphs with given expected degrees
journal, December 2002
 Chung, F.; Lu, L.
 Proceedings of the National Academy of Sciences, Vol. 99, Issue 25