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This work presents a novel approach for multitime-scale power system dynamic simulation based on differential and algebraic equations (DAEs). By properly selecting the continuation (local) parameter, the approach can avoid the numerical divergence encountered by a conventional approach, due to the singularity of the algebraic part of the equations. Meanwhile, by setting step size in a local parameterization, the approach varies its time step size according to the first- or second-order sensitivity of the solution to the variation of local parameter. It employs larger time step sizes for slow dynamics and smaller ones for fast dynamics. The approach presents an advanced tool to study voltage dynamics in multiple time scales and is easily adaptable for quasisteady-state analysis (QSS). The applicability of the approach to multiple time scales and QSS is demonstrated through a 39-bus New England system.