TITLE:
Singular Hopf Bifurcations in DAE Models of Power Systems
AUTHORS:
Wieslaw Marszalek, Zdzislaw Trzaska
KEYWORDS:
Power Systems, Singularly Perturbed Systems, DAEs, Bifurcations, Matrix Pencils
JOURNAL NAME:
Energy and Power Engineering,
Vol.3 No.1,
February
25,
2011
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.