Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
Volume 63, Issue 1, Pages 114-121Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2015.2497559
Keywords
Constant power loads; dc LTI circuits; equilibria; stability
Categories
Funding
- Government of Russian Federation [074-U01, GOSZADANIE 2014/190, 2118]
- Ministry of Education and Science of Russian Federation [14.Z50.31.0031]
- Government of Spain through Ministerio de Economia y Competitividad [DPI2013-41224-P]
- Generalitat de Catalunya [2014SGR 267]
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The problem of existence and stability of equilibria of linear systems with constant power loads is addressed in this paper. First, we correct an unfortunate mistake in our recent paper [10] pertaining to the sufficiency of the condition for existence of equilibria in multiport systems given there. Second, we give two necessary conditions for existence of equilibria. The first one is a simple linear matrix inequality hence it can be easily verified with existing software. Third, we prove that the latter condition is also sufficient if a set defined by the problem data is convex, which is the case for single and two-port systems. Finally, sufficient conditions for stability and instability for a given equilibrium point are given. The results are illustrated with two benchmark examples.
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