A Topological Investigation of Power Flow

This paper combines the fundamentals of an electrical grid, such as flow allocation according to Kirchhoff's laws and the effect of transmission line reactances with spectral graph theory, and expresses the linearized power flow behaviour in slack-bus independent weighted graph matrices to asse...

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Bibliographic Details
Published inIEEE systems journal Vol. 12; no. 3; pp. 2524 - 2532
Main Authors Cetinay, Hale, Kuipers, Fernando A., Van Mieghem, Piet
Format Journal Article
LanguageEnglish
Published New York IEEE 01.09.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Complex networks
Critical components
Graph theory
Line spectra
load flow
Mathematical model
Network topologies
Network topology
Power flow
Power grids
Resistance
Sensitivity analysis
Symmetric matrices
Topology
Transmission line matrix methods
Transmission lines
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Summary:This paper combines the fundamentals of an electrical grid, such as flow allocation according to Kirchhoff's laws and the effect of transmission line reactances with spectral graph theory, and expresses the linearized power flow behaviour in slack-bus independent weighted graph matrices to assess the relation between the topological structure and the physical behaviour of a power grid. Based on the pseudoinverse of the weighted network Laplacian, the paper further analytically calculates the effective resistance (Thevenin) matrix and the sensitivities of active power flows to the changes in network topology by means of transmission line removal and addition. Numerical results for the IEEE 118-bus power system are demonstrated to identify the critical components to cascading failures, node isolation, and Braess' paradox in a power grid.
ISSN:1932-8184
1937-9234
DOI:10.1109/JSYST.2016.2573851