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The dynamic of a large class of power systems can be represented by parameter dependent differential-algebraic models of the form x˙ = f (x, y, p) and 0 = g(x, y, p). When the parameter p of the system (such as load of the system) changes, the stable equilibrium points may lose their dynamic stability at local bifurcation points. The systems will lose its stability at the feasibility boundary, which is caused by one of three different local bifurcations: the singularity induced bifurcation, saddle-node and Hopf bifurcation. In this paper, the dynamic voltage stability of a power system is introduced and analyzed. Both the reduced and unreduced Jacobian matrix of the system are studied and compared. It is shown that the unreduced Jacobian matrix, whose eigenstructure matches well with the reduced one; and thus can be used for bifurcation analysis. In addition, the analysis avoids the singularity induced infinity problem, which may happen at reduced Jacobian matrix analysis, and is more computationally attractive.