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A modeling framework based on normal form theory and singular perturbation techniques is proposed for analyzing the nonlinear behavior of power system models described by nonlinear differential-algebraic equations (DAEs). The method exploits the time scale separation of power system dynamic processes, to avoid reduction of the original DAE model and may therefore be used to assess control effects and network characteristics on system behavior. This approach allows the full potential of the normal form formulation to be reached, and is applicable to a wide variety of nonlinear phenomena described by DAEs. Using a control theory framework, a constructive approach is outlined for transforming a system of DAEs to a state space approximation that is suitable for normal form analysis. By casting the problem in the context of singular perturbation theory, a structure-preserving nonlinear mathematical model of the power system is then established for the study of nonlinear behavior. Criteria for this representation are derived and implementation issues are discussed. The developed procedures are tested on a four-machine, two-area test system. The accuracy of the model is quantified by comparing normal form simulations with those from a commercial stability software.