We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Electricity tracing in systems with and without circulating flows : physical insights and mathematical proofs.

Achayuthakan, C. and Dent, C. J. and Bialek, J. W. and Ongsakul, W. (2010) 'Electricity tracing in systems with and without circulating flows : physical insights and mathematical proofs.', IEEE transactions on power systems., 25 (2). pp. 1078-1087.


This paper provides new insights into the electricity tracing methodology, by representing the inverted tracing upstream and downstream distribution matrices in the form of matrix power series and by applying linear algebra analysis. The n th matrix power represents the contribution of each node to power flows in the other nodes through paths of length exactly n in the digraph of flows. Such a representation proves the link between graph-based and linear equation-based approaches for electricity tracing. It also makes it possible to explain an earlier observation that circulating flows, which result in a cyclic directed graph of flows, can be detected by appearance of elements greater than one on the leading diagonal of the inverted tracing distribution matrices. Most importantly, for the first time a rigorous mathematical proof of the invertibility of the tracing distribution matrices is given, along with a proof of convergence for the matrix power series used in the paper; these proofs also allow an analysis of the conditioning of the tracing distribution matrices. Theoretical results are illustrated throughout using simple network examples.

Item Type:Article
Keywords:Power system economics, Power transmission economics.
Full text:(VoR) Version of Record
Download PDF
Publisher Web site:
Publisher statement:©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Record Created:26 Jul 2010 16:50
Last Modified:13 Sep 2010 14:44

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Look up in GoogleScholar | Find in a UK Library