Singular Hopf Bifurcations in DAE Models of Power Systems

Wieslaw Marszalek, Zdzislaw Trzaska

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DOI: 10.4236/epe.2011.31001                

Abstract

We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the corresponding different- tial-algebraic equations (DAEs). In a generic case, the SIB phenomenon in a system of DAEs signals Hopf bifurcation in the singularly perturbed systems of ODEs. The analysis is based on the linear matrix pencil theory and polynomials with parameter dependent coefficients. A few numerical examples are included.

Keywords

Power Systems, Singularly Perturbed Systems, DAEs, Bifurcations, Matrix Pencils

Conflicts of Interest

The authors declare no conflicts of interest.

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