| Abstract: | The power invariant, nonlinear differential equations, that describe the behavior of a two-phase equivalent of a three-phase induction motor, are linearized about an arbitrary nominal point. Under the assumption that terminal voltage and system frequency can be approximated by a straight line segment over any interval of time, solutions of these small perturbation equations are used to give expressions for active and reactive power delivered to the motor during transient conditions. These expressions for power, which turn out to be implicit functions of voltage and frequency, and explicit functions of time and the rates of change of voltage and frequency, are proposed as a load model representation of an induction motor for use in transient stability studies. An intuitively appealing, corrective technique, which reduces the error introduced by the use of a linearized model, is presented. Also, methods of implementing the proposed model in a conventional transient stability program are discussed. One eigenvalue of the system is observed to play a dominant role in the response for small, low voltage motors. A study is made of the sensitivity of this dominant eigenvalue to the motor parameters and nominal point quantities for a particular motor. Experimental work was conducted to verify the model in a laboratory environment. Active and reactive power delivered to an induction motor, along with the rates of change of voltage and frequency, during transient conditions were measured. These measured values of power were compared to those values of power predicted both by the model and by a numerical solution of the differential equations that describe the motor behavior. The model was found to agree reasonably well with the solutions of the differential equations and the laboratory measured values. |
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