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Electrical Engineering
Published in: Electrical Engineering 1/2017

09-07-2016 | Original Paper

Mathematical reconsideration of number of variables in power flow computation

Authors: Seong-Deog Yang, Sang-Joong Lee

Published in: Electrical Engineering | Issue 1/2017

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Abstract

It has been conventionally believed that there exist 4n variables P, Q, V, \(\theta \) for an n-bus system in the power flow computation, while we have 2n power flow equations. In this article, the authors argue that the number of variables in an n-bus system is not 4n but \(4n-1\), hence the power flow solution can be obtained without specifying the reference angle of the slack bus. We then deliver a mathematical reasoning why the number of variables in an n-bus system is not 4n but \(4n-1\).
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Literature
1.
Pai MA (1979) Computer techniques in power system analysis. Tata Mcgraw Hill Inc., USA, pp 120–121
2.
Milano F (2009) Continuous Newton’s method for power flow analysis. IEEE Trans Power Syst 24(1):50–57
3.
Song H et al (2000) Determination of interface flow margin for voltage stability analysis using the modified continuation power flow, PES 2000 Summer Meeting. IEEE 1:32–37
4.
Hwang P, Jang G et al (2015) DC microgrid operational method for enhanced service reliability using DC bus signaling. J Electr Eng Technol 10(2):452–464CrossRef
5.
Lee B et al (2002) A study on determination of interface flow limits in the KEPCO system using modified continuation power flow. IEEE Trans Power Syst 17(3):557–564CrossRef
6.
Lee S, Kim K (2002) Re-construction of Jacobian Matrix by Angle Reference Transposition and Application to New Penalty Factor. IEEE Power Eng Rev 22(2):47–50CrossRef
7.
Strang G (1988) Linear algebra and its applications, 3rd edn. Harcourt Brace and Co., San DiegoMATH
Metadata
Title
Mathematical reconsideration of number of variables in power flow computation
Authors
Seong-Deog Yang
Sang-Joong Lee
Publication date
09-07-2016
Publisher
Springer Berlin Heidelberg
Published in
Electrical Engineering / Issue 1/2017
Print ISSN: 0948-7921
Electronic ISSN: 1432-0487
DOI
https://doi.org/10.1007/s00202-016-0383-4

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