Power system dynamics are typically described by differential algebraic equations (DAE) equations. Singular perturbation technique can be used to approximate DAE systems by ODE systems. Note that for singular perturbation techniques to preserve bifurcation properties of the original DAE system, the fast dynamics is required to converge to the algebraic constraints. This requirement, so far, has not been seriously considered. With this requirement in mind, a new remodeling technique named PTE is proposed in this paper. This new approach has the advantage that direct integration can be applied to analyze the system dynamics while maintaining the essential bifurcation properties of original systems. Also, a simple and feasible criterion was proposed here to gauge the accuracy of remodeled ODE system, which can help us select proper perturbation parameters for numerical simulation. Our numerical tests demonstrate the feasibility of our new approach.