Transient Load Model of an Induction Motor

TLDR: In this article, the power invariant, nonlinear differential equations that describe the behavior of a two-phase equivalent of a balanced three-phase induction motor, are linearized about an arbitrary nominal point.

Abstract: The power invariant, nonlinear differential equations, that describe the behavior of a two-phase equivalent of a balanced 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 tb the motor during transient conditions. These newly developed 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 represeptation 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. Eigenvalues of the linearized system of equations for a group of typical induction motors are given. For a small low voltage motor, a sensitivity study of the dominant eigenvalue to changes in nominal point quantities and parameters is made. Values of active and reactive power calculated by a numericzal solution of the motor nonlinear differential equations are compared with those values of power predicted by the model for certain specific rates of change of voltage and frequency.