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The stability of differential-algebraic equations (DAEs) was analyzed using singularity induced bifurcation (SIB) with one parameter. This kind of bifurcation arises in pararreter-dependent DAEs having the form x = f, 0 = g. Extended DAE system reduction is introduced as a convenient method to compute the SIB points. Non-degeneracy conditions on the function g are needed. Aften verifying these conditions, the extended DAE system can be solved as an ODE by applying the implicit function theorem near the equilibrium point of the extended DAE system. These equilibrium points in turn include the SIB points of the original DAEs. The study of SIB points enables analysis of power system stability problems.