Negative Reactance Impacts on the Eigenvalues of the Jacobian Matrix in Power Flow and Type-1 Low-Voltage Power-Flow Solutions

Abstract

It was usually considered in power systems that power flow equations had multiple solutions and all the eigenvalues of Jacobian matrix at the high-voltage operable solution should have negative real parts. Accordingly, type-1 low-voltage power flow solutions are defined in the case that the Jacobian matrix has only one positive real-part eigenvalue. However, an important issue that has not been well addressed yet is that the 'negative reactance' may appear in the practical power system models. Thus, the negative real-part eigenvalues of the Jacobian matrix at the high-voltage operable solution may be positive and also the type-1 low-voltage solutions could have more than one positive real-part eigenvalues, being a major challenge. Therefore, in this paper, the recognition of the type-1 low-voltage power flow solutions is re-examined with the presence of negative reactance. Selected IEEE standard power system models and the real-world Polish power systems are then tested to verify the analysis. The results reveal that the negative reactance in the practical power systems has a significant impact on the negative real-part eigenvalues of the Jacobian matrix at the high-voltage operable solution as well as the number of positive real-part eigenvalues at the type-1 low-voltage power flow solutions.

Department(s)

Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center

Keywords and Phrases

Eigenvalues and Eigenfunctions; Jacobian Matrices; Continuation Power Flow; Eigenvalues; Negative Reactance; Power Flows; Power-Flow Solution; Electric Load Flow; Power Flow; Type-1 Power Flow Solution

International Standard Serial Number (ISSN)

0885-8950

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Sep 2017

Link to Full Text

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