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.
Recommended Citation
T. Ding et al., "Negative Reactance Impacts on the Eigenvalues of the Jacobian Matrix in Power Flow and Type-1 Low-Voltage Power-Flow Solutions," IEEE Transactions on Power Systems, vol. 32, no. 5, pp. 3471 - 3481, Institute of Electrical and Electronics Engineers (IEEE), Sep 2017.
The definitive version is available at https://doi.org/10.1109/TPWRS.2016.2645608
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
