On Bifurcations of Power Systems at Singularities

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 respective differential-algebraic equations (DAEs) model. 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. Several numerical examples are included.