Author(s)

Wieslaw Marszalek, Zdzislaw Trzaska

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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.

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

W. Marszalek and Z. Trzaska, "Singular Hopf Bifurcations in DAE Models of Power Systems," Energy and Power Engineering, Vol. 3 No. 1, 2011, pp. 1-8. doi: 10.4236/epe.2011.31001.