Modeling effects of system frequency variations in induction motor dynamics using singular perturbations

This paper presents an application of singular perturbation theory to modeling induction motors in system simulations. The focus is on model approximations and their impact on a motor's response to changes in system frequency as well as voltage. The fast states associated with the motor stator and rotor dynamics are eliminated from a full motor model using singular perturbations with a first order correction factor added. This leads to a reduced order motor model referred to as the singularly perturbed model. The starting performance of this model is compared to that of a full model, and to that of a simple model in which the fast states are modeled by neglecting the rates of change of the fast variables. The response of the singularly perturbed model is much closer to that of the full model than is that of the model which neglects the rates of change of the fast variables completely. It is also noted that a corrected first-order slip model of the induction motor can yield a more accurate speed response than a conventional uncorrected first-order slip model during frequency and voltage changes. The response of models are also compared to disturbances applied to a two-area, four-machine power system and again the singularly perturbed model performance is closer to that of the full model than is the model with the rates of change of the fast states neglected completely. While the simulation time using the singularly perturbed model is longer than that using the simple model, it is considerably less than that of the full model.