“…Assumption 2.1 is a typical one in DAE problems, which can realize the transformation of the DAE problem to a differential equation. In the stability analysis of power systems, except for the singularity bifurcation study, this assumption is a common one and the system satisfies it for the most cases [1,8]. Under above assumption, from G(x(t), y(t),z) = 0 and the implicit function theorem, it exists an unique C 1 mapping q for each t ∈ [0, T ]…”