Method of estimating transients in induction machines

Abstract

The present paper is concerned with induction motors with wound and squirrel-cage rotors. It is assumed that the magnetic field produced by the stator windings is constant in magnitude and rotates with constant angular velocity. Differential equations that describe relations between the electromagnetic torque and main electric and mechanical quantities of the induction motors under consideration are derived in detail, the geometry of the rotors of motors being fully taken into account. A special nonsingular transformation is applied to the initial systems of equations (with angular coordinates) to split them up and reduce to a lower-order (in fact, third-order) system. A local stability analysis of the resulting equations is carried out. The stable equilibrium states that correspond to the operating modes of induction motors are determined. Methods of speed control of induction motors with wound and squirrel-cage rotors are considered. The limit load problem on motors and the control problem of the speed of motors are discussed; these problems lead to the necessity to estimate the transients in induction motors. The method of estimating transients that occur due to changes of the operating parameters of motors is developed based on a modification of the nonlocal reduction method. Using this method in combination with Barbashin and Tabueva’s methods to apply to the obtained systems made it possible to find analytical estimates of the ultimate permissible loads on induction motors and the control ranges of the parameters of the system that correspond to additional external active and inductive resistances. Moreover, estimates for the region of the attraction of stable equilibrium states of systems that describe the dynamics of induction motors are obtained.