TY - JOUR

T1 - Generating statistically correct random topologies for testing smart grid communication and control networks

AU - Wang, Zhifang

AU - Scaglione, Anna

AU - Thomas, Robert J.

N1 - Funding Information:
Manuscript received September 18, 2009; revised February 24, 2010. Date of publication May 10, 2010; date of current version May 21, 2010. This work was supported in part by the UIUC TCIP Project under Grant NSF CNS 05-24695 and in part by the Department of Energy and the Department of Homeland Security. Paper no. TSG-00002-2009.

PY - 2010

Y1 - 2010

N2 - In order to design an efficient communication scheme and examine the efficiency of any networked control architecture in smart grid applications, we need to characterize statistically its information source, namely the power grid itself. Investigating the statistical properties of power grids has the immediate benefit of providing a natural simulation platform, producing a large number of power grid test cases with realistic topologies, with scalable network size, and with realistic electrical parameter settings. The second benefit is that one can start analyzing the performance of decentralized control algorithms over information networks whose topology matches that of the underlying power network and use network scientific approaches to determine analytically if these architectures would scale well. With these motivations, in this paper we study both the topological and electrical characteristics of power grid networks based on a number of synthetic and real-world power systems. The most interesting discoveries include: the power grid is sparsely connected with obvious small-world properties; its nodal degree distribution can be well fitted by a mixture distribution coming from the sum of a truncated geometric random variable and an irregular discrete random variable; the power grid has very distinctive graph spectral density and its algebraic connectivity scales as a power function of the network size; the line impedance has a heavy-tailed distribution, which can be captured quite accurately by a clipped double Pareto lognormal distribution. Based on the discoveries mentioned above, we propose an algorithm that generates random topology power grids featuring the same topology and electrical characteristics found from the real data.

AB - In order to design an efficient communication scheme and examine the efficiency of any networked control architecture in smart grid applications, we need to characterize statistically its information source, namely the power grid itself. Investigating the statistical properties of power grids has the immediate benefit of providing a natural simulation platform, producing a large number of power grid test cases with realistic topologies, with scalable network size, and with realistic electrical parameter settings. The second benefit is that one can start analyzing the performance of decentralized control algorithms over information networks whose topology matches that of the underlying power network and use network scientific approaches to determine analytically if these architectures would scale well. With these motivations, in this paper we study both the topological and electrical characteristics of power grid networks based on a number of synthetic and real-world power systems. The most interesting discoveries include: the power grid is sparsely connected with obvious small-world properties; its nodal degree distribution can be well fitted by a mixture distribution coming from the sum of a truncated geometric random variable and an irregular discrete random variable; the power grid has very distinctive graph spectral density and its algebraic connectivity scales as a power function of the network size; the line impedance has a heavy-tailed distribution, which can be captured quite accurately by a clipped double Pareto lognormal distribution. Based on the discoveries mentioned above, we propose an algorithm that generates random topology power grids featuring the same topology and electrical characteristics found from the real data.

KW - Graph models for networks

KW - Power grid topology

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U2 - 10.1109/TSG.2010.2044814

DO - 10.1109/TSG.2010.2044814

M3 - Article

AN - SCOPUS:77952887424

VL - 1

SP - 28

EP - 39

JO - IEEE Transactions on Smart Grid

JF - IEEE Transactions on Smart Grid

SN - 1949-3053

IS - 1

M1 - 5463043

ER -