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

This paper presents an application of singular perturbation theory to model ing induction motors in system simuladons. The focus is on model approximat ions 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 ro tor dynamics are eliminated from a full motor model using singular perturba tions with a first order correction factor added. This leads to a reduced o rder motor model referred to as the singularly perturbed model. The startin g performance of this model is compared to that of a full model, and to tha t 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 pertu rbed model is much closer to that of the full model than is that of the mod el 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 moto r can yield a more accurate speed response than a conventional uncorrected first-order slip model during frequency and voltage changes, The response o f models are also compared to disturbances applied to a two-area, four-mach ine power system and again the singularly perturbed model performance is cl oser to that of the full model than is the model with the rates of change o f 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.