DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 small-world 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 intra-network 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 Chung-Lu 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 » 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 Chung-Lu model. We also include graph visualization comparisons, as well as a brief analysis of edge-deletion 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.« less

Authors:
 [1]; ORCiD logo [1];  [2]; ORCiD logo [1]
  1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
  2. Oregon State Univ., Corvallis, OR (United States)
Publication Date:
Research Org.:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1508032
Report Number(s):
PNNL-SA-130657
Journal ID: ISSN 2051-1310
Grant/Contract Number:  
AC05-76RL01830
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Complex Networks
Additional Journal Information:
Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 2051-1310
Publisher:
Oxford University Press
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; power grid graph model; Chung-Lu model; network-of-networks

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. https://doi.org/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. https://doi.org/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 small-world 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 intra-network 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 Chung-Lu 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 Chung-Lu model. We also include graph visualization comparisons, as well as a brief analysis of edge-deletion 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},
number = 1,
volume = 7,
place = {United States},
year = {Mon Aug 13 00:00:00 EDT 2018},
month = {Mon Aug 13 00:00:00 EDT 2018}
}

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
  • DOI: 10.1016/j.physa.2013.01.023

Graph-theoretic algorithms for PMU placement in power systems under measurement observability constraints
conference, November 2012


Assortative Mixing in Networks
journal, October 2002


The Structure and Function of Complex Networks
journal, January 2003


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
  • DOI: 10.1109/TPWRS.2016.2616385

Power-Law Distributions in Empirical Data
journal, November 2009

  • Clauset, Aaron; Shalizi, Cosma Rohilla; Newman, M. E. J.
  • SIAM Review, Vol. 51, Issue 4
  • DOI: 10.1137/070710111

Local clustering in scale-free 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
  • DOI: 10.1103/PhysRevE.95.022307

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)
  • DOI: 10.1109/ICDM.2015.47

Scale-Free Networks
journal, May 2003


Collective dynamics of ‘small-world’ networks
journal, June 1998

  • Watts, Duncan J.; Strogatz, Steven H.
  • Nature, Vol. 393, Issue 6684
  • DOI: 10.1038/30918

Diameters in Preferential Attachment Models
journal, January 2010

  • Dommers, Sander; van der Hofstad, Remco; Hooghiemstra, Gerard
  • Journal of Statistical Physics, Vol. 139, Issue 1
  • DOI: 10.1007/s10955-010-9921-z

Structural vulnerability of the North American power grid
journal, February 2004


Controlled islanding using transmission switching and load shedding for enhancing power grid resilience
journal, October 2017


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
  • DOI: 10.1137/070708275

A Metric-Based Validation Process to Assess the Realism of Synthetic Power Grids
journal, August 2017

  • Birchfield, Adam; Schweitzer, Eran; Athari, Mir
  • Energies, Vol. 10, Issue 8
  • DOI: 10.3390/en10081233

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
  • DOI: 10.1504/IJCIS.2015.067394

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
  • DOI: 10.1504/IJCIS.2012.050109

Note on the heights of random recursive trees and random m-ary search trees
journal, April 1994


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
  • DOI: 10.1137/130914218

Stochastic kronecker graphs
journal, July 2010

  • Mahdian, Mohammad; Xu, Ying
  • Random Structures & Algorithms, Vol. 38, Issue 4
  • DOI: 10.1002/rsa.20335

Do topological models provide good information about electricity infrastructure vulnerability?
journal, September 2010

  • Hines, Paul; Cotilla-Sanchez, Eduardo; Blumsack, Seth
  • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 20, Issue 3
  • DOI: 10.1063/1.3489887

Admissible Locational Marginal Prices via Laplacian Structure in Network Constraints
journal, February 2009


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
  • DOI: 10.1093/comnet/cnx001

Bipartite graphs as models of complex networks
journal, November 2006

  • Guillaume, Jean-Loup; Latapy, Matthieu
  • Physica A: Statistical Mechanics and its Applications, Vol. 371, Issue 2
  • DOI: 10.1016/j.physa.2006.04.047

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
  • DOI: 10.1038/srep34797

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
  • DOI: 10.1073/pnas.252631999

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
  • DOI: 10.1016/j.physa.2013.01.023

HyperHeadTail: a Streaming Algorithm for Estimating the Degree Distribution of Dynamic Multigraphs
conference, January 2017

  • Stolman, Andrew; Matulef, Kevin
  • Proceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2017 - ASONAM '17
  • DOI: 10.1145/3110025.3119395

Algebraic connectivity of graphs [Algebraic connectivity of graphs]
journal, January 1973